With the discovery of special relativity by Henri Poincaré and Albert Einstein, energy was proposed to be one component of an energy-momentum 4-vector. Each of the four components (one of energy and three of momentum) of this vector is separately conserved across time, in any closed system, as seen from any given inertial reference frame.

I mentioned how historians think that the first four kings of Rome were mythological, and how the order of the Kings fits the quadrant pattern.



Unstable isotopes decay to their daughter products (which may sometimes be even more unstable) at a given rate; eventually, often after a series of decays, a stable isotope is reached: there are about 200 stable isotopes in the universe. Stable isotopes have ratios of neutrons to protons in their nucleus which are typical about 1 for light elements (e.g. 1 in helium-4) and gradually increase to around 1.5 for the heaviest elements such as lead (there is no complete stability for anything heavier than lead-208). The elements heavier than that have to shed weight to achieve stability, most usually as alpha decay. The other common decay method for isotopes with a high neutron to proton ratio (n/p) is beta decay, in which the nuclide changes elemental identity while keeping the same weight and lowering its n/p ratio. For some isotopes with a relatively low n/p ratio, there is an inverse beta decay, by which a proton is transformed into a neutron, thus moving towards a stable isotope; however, since fission almost always produces products which are neutron heavy, positron emission is relatively rare compared to electron emission. There are many relatively short beta decay chains, at least two (a heavy, beta decay and a light, positron decay) for every discrete weight up to around 207 and some beyond, but for the higher weight elements (isotopes heavier than lead) there are only four pathways which encompass all decay chains. This is because there are just two main decay methods: alpha radiation, which reduces the weight by 4 atomic mass units (AMUs), and beta, which does not change the atomic weight at all (just the atomic number and the p/n ratio). The four paths are termed 4n, 4n + 1, 4n + 2, and 4n + 3; the remainder from dividing the atomic weight by four gives the chain the isotope will use to decay. There are other decay modes, but they invariably occur at a lower probability than alpha or beta decay. (It should not be supposed that these chains have no branches: the diagram below shows a few branches of chains, and in reality there are many more, because there are many more isotopes possible than are shown in the diagram.)


Three of those chains have a long-lived isotope (or nuclide) near the top; this long-lived isotope is a bottleneck in the process through which the chain flows very slowly, and keeps the chain below them "alive" with flow. The three long-lived nuclides are uranium-238 (half-life=4.5 billion years), uranium-235 (half-life=700 million years) and thorium-232 (half-life=14 billion years). The fourth chain has no such long lasting bottleneck isotope, so almost all of the isotopes in that chain have long since decayed down to very near the stability at the bottom. Near the end of that chain is bismuth-209, which was long thought to be stable. Recently, however, bismuth-209 was found to be unstable with a half-life of 19 billion billion years; it is the last step before stable thallium-205. In the distant past, around the time that the solar system formed, there were more kinds of unstable high-weight isotopes available, and the four chains were longer with isotopes that have since decayed away. Today we have manufactured extinct isotopes, which again take their former places: plutonium-239, the nuclear bomb fuel, as the major example has a half-life of "only" 24,500 years, and decays by alpha emission into uranium-235. In particular, we have through the large-scale production of neptunium-237 successfully resurrected the hitherto extinct fourth chain.[2]



On August 24, 2011, a Type Ia supernova, SN 2011fe, initially designated PTF 11kly, was discovered in M101. The supernova was visual magnitude 17.2 at discovery and reached magnitude 9.9 at its peak.[23][24][25] This was the fourth supernova recorded in M101. The first, SN 1909A, was discovered by Max Wolf in January 1909 and reached magnitude 12.1. SN 1951H reached magnitude 17.5 in September 1951 and SN 1970G reached magnitude 11.5 in January 1970.[26] On February 10, 2015, a luminous red nova was observed in the Pinwheel Galaxy by Dumitru Ciprian Vîntdevară from Planetarium and Astronomical Observatory of the Museum Vasile Parvan in Bârlad, Romania.[27]



The Scutum–Centaurus Arm, also known as Scutum-Crux arm, is a long, diffuse curving streamer of stars, gas and dust that spirals outward from the proximate end of the Milky Way's central bar. The Milky Way has been assumed since the 1950s to have four spiral arms although the evidence for this has never been strong.[1] In 2008, observations using the Spitzer Space Telescope failed to show the expected density of red clump giants in the direction of the Sagittarius and Norma arms.[2] In January 2014, a 12-year study into the distribution and lifespan of massive stars[3] and a study of the distribution of masers and open clusters [4] both found evidence for four spiral arms.

SDSS III: 2008–2014[edit]

In mid-2008, SDSS-III was started. It comprises four separate surveys, each conducted on the same 2.5m telescope:[15]






The diagram shows a typical optical experiment of the two-channel kind for which Alain Aspect set a precedent in 1982.[5] Coincidences (simultaneous detections) are recorded, the results being categorised as '++', '+−', '−+' or '−−' and corresponding counts accumulated.


Four separate subexperiments are conducted, corresponding to the four terms E(a, b) in the test statistic S (equation (2) shown below). The settings a, a′, b and b′ are generally in practice chosen to be 0, 45°, 22.5° and 67.5° respectively — the "Bell test angles" — these being the ones for which the quantum mechanical formula gives the greatest violation of the inequality.


For each selected value of a and b, the numbers of coincidences in each category (N++, N−−, N+− and N−+) are recorded. The experimental estimate for E(a, b) is then calculated as:


(1) E = (N++ + N−− − N+− − N−+)/(N++ + N−− + N+− + N−+).


Once all four E’s have been estimated, an experimental estimate of the test statistic


(2) S = E(a, b) − E(a, b′) + E(a′, b) + E(a′, b′)


can be found. If S is numerically greater than 2 it has infringed the CHSH inequality. The experiment is declared to have supported the QM prediction and ruled out all local hidden variable theories.


A strong assumption has had to be made, however, to justify use of expression (2). It has been assumed that the sample of detected pairs is representative of the pairs emitted by the source. That this assumption may not be true comprises the fair sampling loophole.


Prior to 1982 all actual Bell tests used "single-channel" polarisers and variations on an inequality designed for this setup. The latter is described in Clauser, Horne, Shimony and Holt's much-cited 1969 article as being the one suitable for practical use.[3] As with the CHSH test, there are four subexperiments in which each polariser takes one of two possible settings, but in addition there are other subexperiments in which one or other polariser or both are absent. Counts are taken as before and used to estimate the test statistic.


The Christensen et al. (2013)[23] experiment is similar to that of Giustina et al.[21] Giustina et al. did just four long runs with constant measurement settings (one for each of the four pairs of settings). The experiment was not pulsed so that formation of "pairs" from the two records of measurement results (Alice and Bob) had to be done after the experiment which in fact exposes the experiment to the coincidence loophole. This led to a reanalysis of the experimental data in a way which removed the coincidence loophole, and fortunately the new analysis still showed a violation of the appropriate CHSH or CH inequality.[22] On the other hand, the Christensen et al. experiment was pulsed and measurement settings were frequently reset in a random way, though only once every 1000 particle pairs, not every time.[23]



a and a′ are detector settings on side A, b and b′ on side B, the four combinations being tested in separate subexperiments. The terms E(a, b) etc. are the quantum correlations of the particle pairs, where the quantum correlation is defined to be the expectation value of the product of the "outcomes" of the experiment, i.e. the statistical average of A(a)·B(b), where A and B are the separate outcomes, using the coding +1 for the '+' channel and −1 for the '−' channel. Clauser et al.'s 1969[1] derivation was oriented towards the use of "two-channel" detectors, and indeed it is for these that it is generally used, but under their method the only possible outcomes were +1 and −1. In order to adapt to real situations, which at the time meant the use of polarised light and single-channel polarisers, they had to interpret '−' as meaning "non-detection in the '+' channel", i.e. either '−' or nothing. They did not in the original article discuss how the two-channel inequality could be applied in real experiments with real imperfect detectors, though it was later proved (Bell, 1971)[3] that the inequality itself was equally valid. The occurrence of zero outcomes, though, means it is no longer so obvious how the values of E are to be estimated from the experimental data.


E(a, b) in the test statistic S (2). The settings a, a′, b and b′ are generally in practice chosen to be 0, 45°, 22.5° and 67.5° respectively — the "Bell test angles" — these being the ones for which the QM formula gives the greatest violation of the inequality.


In their 1974 paper,[8] Clauser and Horne show that the CHSH inequality can be derived from the CH74 one. As they tell us, in a two-channel experiment the CH74 single-channel test is still applicable and provides four sets of inequalities governing the probabilities p of coincidences.



Examples of other experiments not based on the Michelson–Morley principle, i.e. non-optical isotropy tests achieving an even higher level of precision, are Clock comparison or Hughes–Drever experiments. In Drever's 1961 experiment, 7Li nuclei in the ground state, which has total angular momentum J=3/2, were split into four equally spaced levels by a magnetic field. Each transition between a pair of adjacent levels should emit a photon of equal frequency, resulting in a single, sharp spectral line. However, since the nuclear wave functions for different MJ have different orientations in space relative to the magnetic field, any orientation dependence, whether from an aether wind or from a dependence on the large-scale distribution of mass in space (see Mach's principle), would perturb the energy spacings between the four levels, resulting in an anomalous broadening or splitting of the line. No such broadening was observed. Modern repeats of this kind of experiment have provided some of the most accurate confirmations of the principle of Lorentz invariance.[A 36]



Bell–CHSH inequality tests require four different experiments with different choices of the settings of the observation stations. Specifically, the setting of observation station

can take two values which we denote by

. The choice of setting


may be made at random [2,9,13]. In real experiments, it takes a certain time to switch from one setting to another but this time is less than the average time between two emission events [2]. In the computer experiment, being an idealized perfect experiment, the algorithm is such that this cannot be an issue.



The layout of a CFD-compliant computer model of the EPRB experiment is depicted in Fig. 3. It uses the same units as the non-CFD-compliant model shown in Fig. 2, the only difference being that the input

is now fed into an observation station with setting

and another one with setting

. As each of the four units operates according to the rules given by Eq. (1) and (2), we have


. As the arguments of the functions


are independent and may take any value out of their respective domain, the whole system represented by Fig. 3 satisfies, by construction, the criterion of a CFD theory.


Next, we examine what happens if the time-tag variables

are included. In real EPRB experiments with photons, it is essential to use time-coincidence to identify pairs [2,9,13]. The standard procedure adopted in these experiments is to introduce a time window

and reject pairs that do not satisfy the condition

(and similar for other relevant combinations of

’s) [2]. The computational model defined by Eqs. (1) and (2) together with the time-coincidence criterion yields, in the limit that the time-window

vanishes, the correlation of the singlet state [10,11] if we repeat the experiment pair-wise, i.e. with four pairs of settings (see Fig. 2), in which case the CFD criterion is clearly not satisfied. We emphasize that unlike in the laboratory experiment, in the computer experiment all pairs are created “on demand”, each pair is detected, and the time window only serves as a vehicle to post select pairs, not to identify them. Post-selection only serves to “probe” the complicated, time-dependent many-body physics that is involved when the photon passes through the optical system and triggers the detector. In this sense, the computer experiment suffers from none of the loopholes that may occur in experiments.


We formalize the effect of the time-coincidence window by introducing the binary variables






is the unit step function. In essence, we extend the computational device by taking the output of the two units described earlier and feeding the time-tag output in a “correlator” that computes, for each event

, the four binary variables defined by Eq. (7). Adding the correlator does not change the fact that the computer model is CFD-compliant. Indeed, a given input

together with the settings

completely determines the values of all (two-valued) output variables







, and

. Note that e.g.

means that the particular pair has been discarded by the time-coincidence criterion for the pair of settings

but that this does not imply that e.g.

. In other words, the values of the

’s are used to post-select pairs.


We present the results of four different modes of simulating the EPRB experiments



Artist’s conception of the 30 Arietis star system now known to be composed of four stars. The distant companion 30 Ari A is actually a pair of stars in a close orbit. The research team discovered the fourth star in the system (the left-most star in the image). That star is a small red dwarf. A massive planet orbits the star named 30 Ari B in a nearly year-long orbit. Image credit: Karen Teramura, UH IfA

Growing up as a planet with more than one parent star has its challenges. Though the planets in our Solar System circle just one star — our Sun — other more distant planets, called exoplanets, can be reared in families with two or more stars. Researchers wanting to know more about the complex influences of multiple stars on planets have come up with two new case studies: a planet found to have three parents, and another with four.

The discoveries were made using instruments fitted to telescopes at the Palomar Observatory in San Diego: the Robo-AO adaptive optics system, developed by the Inter-University Center for Astronomy and Astrophysics in India and the California Institute of Technology in Pasadena, and the PALM-3000 adaptive optics system, developed by NASA’s Jet Propulsion Laboratory in Pasadena, California, and Caltech.


This is only the second time a planet has been identified in a quadruple star system. While the planet was known before, it was thought to have only three stars, not four. The first four-star planet, KIC 4862625, was discovered in 2013 by citizen scientists using public data from NASA’s Kepler mission.


The latest discovery suggests that planets in quadruple star systems might be less rare than once thought. In fact, recent research has shown that this type of star system, which usually consists of two pairs of twin stars slowly circling each other at great distances, is itself more common than previously believed.


“About four percent of solar-type stars are in quadruple systems, which is up from previous estimates because observational techniques are steadily improving,” said co-author Andrei Tokovinin of the Cerro Tololo Inter-American Observatory in Chile.


The four stars and one planet of the 30 Arietis system are illustrated in this diagram. This quadruple star system consists of two pairs of stars: 30 Ari B and 30 Ari A. Image credit: NASA/JPL-Caltech

The four stars and one planet of the 30 Arietis system are illustrated in this diagram. This quadruple star system consists of two pairs of stars: 30 Ari B and 30 Ari A. Image credit: NASA/JPL-Caltech

The newfound four-star planetary system, called 30 Ari, is located 136 light-years away in the constellation Aries. The system’s gaseous planet is enormous, with 10 times the mass of Jupiter, and it orbits its primary star every 335 days. The primary star has a relatively close partner star, which the planet does not orbit. This pair, in turn, is locked in a long-distance orbit with another pair of stars about 1,670 astronomical units away (an astronomical unit is the distance between Earth and the Sun — 92,956,000 miles or 149,598,000 kilometres). Astronomers think it’s highly unlikely that this planet, or any moons that might circle it, could sustain life.

Were it possible to see the skies from this world, the four parent stars would look like one small sun and two very bright stars that would be visible in daylight. One of those stars, if viewed with a large enough telescope, would be revealed to be a binary system, or two stars orbiting each other.


In recent years, dozens of planets with two or three parent stars have been found, including those with “Tatooine” sunsets reminiscent of the Star Wars movies. Finding planets with multiple parents isn’t too much of a surprise, considering that binary stars are more common in our galaxy than single stars.


“Star systems come in myriad forms. There can be single stars, binary stars, triple stars, even quintuple star systems,” said Lewis Roberts of JPL, lead author of the new findings appearing in the journal Astronomical Journal. “It’s amazing the way nature puts these things together.”


Roberts and his colleagues want to understand the effects that multiple parent stars can have on their developing youthful planets. Evidence suggests that stellar companions can influence the fate of planets by changing the planets’ orbits and even triggering some to grow more massive. For example, the “hot Jupiters” — planets around the mass of Jupiter that whip closely around their stars in just days — might be gently nudged closer to their primary parent star by the gravitational hand of a stellar companion.


In the new study, the researchers describe using the automated Robo-AO system on Palomar Observatory to scan the night skies, searching hundreds of stars each night for signs of stellar companions. They found two candidates hosting exoplanets: the four-star system 30 Ari, and a triple-star planetary system called HD 2638. The findings were confirmed using the higher-resolution PALM-3000 instrument, also at Palomar Observatory.


The new planet with a trio of stars is a hot Jupiter that circles its primary star tightly, completing one lap every three days. Scientists already knew this primary star was locked in a gravitational tango with another star, about 0.7 light-years away, or 44,000 astronomical units. That’s relatively far apart for a pair of stellar companions. The latest discovery is of a third star in the system, which orbits the primary star from a distance of 28 astronomical units — close enough to have influenced the hot Jupiter’s development and final orbit.


“This result strengthens the connection between multiple star systems and massive planets,” said Roberts.


In the case of 30 Ari, the discovery brought the number of known stars in the system from three to four. The fourth star lies at a distance of 23 astronomical units from the planet. While this stellar companion and its planet are closer to each other than those in the HD 2638 system, the newfound star does not appear to have impacted the orbit of the planet. The exact reason for this is uncertain, so the team is planning further observations to better understand the orbit of the star and its complicated family dynamics.



X-Trans filter array

Typical Bayer sensor arrays have RGB photosites in a repeated 2 by 2 pattern. When it overlaps with a regular pattern that is being captured, a new interference pattern can occur that does not exist in real life. In contrast, X-Trans sensors have a more randomised pattern of RGB photosites than conventional Bayer array sensors,[2] reducing the likelihood of interference and removing a need for a low-pass filter that lowers image resolution.

For example, on a chunky display, each byte represents one pixel. Three pixels in a row would be stored as follows, where up to 256 different colours are available:


Byte index 0 1 2

Value (binary) 00000000 00000001 00000010

Value (decimal) 0 1 2

Resulting pixel Black Blue Green

Whereas a planar data store could use 2 bitplanes, providing for a 4 colour display:


Byte index 0

Bit index 0 1 2 3 4 5 6 7

Plane 0 1 0 0 0 0 0 1 0

Plane 1 0 0 0 1 0 0 1 0

Resulting pixel 1 0 0 2 0 0 3 0

Byte value 146

Adding a third plane would make 23=8 colours available. Where fewer than 256 colours are needed, planar graphics are more economical in RAM compared with 8-bit chunky graphics, as there are no unused bits in a given byte.


A disadvantage of planar graphics is that more RAM address cycles are needed for scrolling and animations, although these operations can be made faster by dedicated hardware such as the blitter chips used in Amiga and some later Atari ST computers.[citation needed]




Depending on whether we consider nodes touching at the corners connected or not, we have two variations: eight-way and four-way respectively.


Stack-based recursive implementation (four-way)[edit]

One implicitly stack-based (recursive) flood-fill implementation (for a two-dimensional array) goes as follows:




The passage that serves as keystone for this entire study is a fragment of the works of Aëtius, a physician of the late 6th century A.D. Herman Diels 1964, 31, 21 A92 cites Aetius, I, 15, 3 (D. 313:)

Ἐ. χρῶμα εἶναι ἀπεφαίνετο τὸ τοῖς πόροις τῆς ὄψεως ἐναρμόττον. τέτταρα δὲ τοῖς στοιχεῖοις ἰσάριθμα, λευκὸν μέλαν ἐρυθρὸν ὠχρόν.

to Plato, Meno, 76D: “SOC. Well, do you speak of certain effluences from things, in agreement with Empedocles?—MENO. Certainly.—SOC. And pores into which and through which the effluences travel?—MENO. Yes, indeed.—SOC. And some of the effluences fit certain of the pores, others are too small or too large?—MENO. Yes.—SOC. And do you say that there is such a thing as sight?—MENO. Yes, I do.—SOC. Well, “take my meaning” from this, to quote Pindar. Colour is an effluence from shapes which is commensurate with sight and perceptible.” (Plato, Meno Edited with Translation and Notes by R.W. Sharples, Chicago 1985.) To this Aëtius commented: “(Empedokles) declared that color fits the pores of vision. And the four colors: white, black, red, yellow are equal in number to the four elements.”



Democritus, on the other hand, wrote some sixty-odd works, the titles of which provide valuable evidence of the scope of his interests. The main works were cataloged by Thrasylus into thirteen tetralogies. Two tetralogies are devoted to ethics and four to physics (including Little World-System, On the Planets, On Nature, On the Nature of Man, On the Senses, and On Colors ). These were followed by nine works not arranged in tetralogies—for example, Causes of Celestial Phenomena, Causes concerning Seeds, Plants and Fruits, and three books of Causes concerning Animals. Three tetralogies are classified as mathematics, two deal with music and literature, and two consist of technical works, including treatises on medicine, agriculture, painting, and warfare. Nine other miscellaneous works, mostly concerning travel, are also mentioned by Diogenes Laërtius but are less certainly authentic as they were not included in Thrasylus's catalog.



Empedokles relates this to perception of white and black by the eyes for the purpose of explaining blindness by day and by night. Stulz found no other discussion of color perception by him and denies that a famous passage in which the philosopher mentions color practice of artists (see Chapter II, The Ancient Sources, Empedokles, E) proves that he entertained a theory that four colors were a basis for creating further colors by mixture. Yet it must be granted that he had developed a theory of perception which—combined with his principle of “like gravitates to like”—would indeed offer the framework for a four color theory.



Adding up the available evidence, we are in little doubt that Empedokles was acquainted with a four color physiological system, though the evidence is more indirect than direct. Despite a persistent tendency for water to be associated with dark effects, it does not seem necessary to suppose that he disagreed with the rational equation of black with matter (earth). See especially (G) above. Theophrastus’ report on the color of fire and water in (H) may also be meant physiologically. In any case, it is tantalizing because the passage continues: “the other (thinkers with the exception of Empedokles) claim that white and black are the original colors and that the other colors arise from mixtures of these, and also Anaxagoras spoke only of these two.” Also, Aristotle still represented this view (see Chapter II, The Ancient Sources, Aristotle, paragraph 2) and it is not clear actually how Empedokles differed from it (for he too in the available passages speaks of only these). Krantz makes an inference from (E) that Empedokles derived warm and cool colors alike from mixing the four colors (see note 2). This seems to me (as also to Stulz, see above Chapter I, Prologue, In Particular, paragraph 3) to be an absurdity which one cannot foist on the words of Empedokles. I prefer to remain with the fact that Empedokles nowhere discussed the four colors in a philosophical way either in the macrocosmic or the microcosmic sense.

FOUR MOONS- FOURTH DIFFERENT- fifth not discovered until century later




Both Ariel and the slightly larger Uranian satellite Umbriel were discovered by William Lassell on 24 October 1851.[10][11] Although William Herschel, who discovered Uranus's two largest moons Titania and Oberon in 1787, claimed to have observed four additional moons,[12] this was never confirmed and those four objects are now thought to be spurious.[13][14][15]


All of Uranus's moons are named after characters from the works of William Shakespeare or Alexander Pope's The Rape of the Lock. The names of all four satellites of Uranus then known were suggested by John Herschel in 1852 at the request of Lassell.[16] Ariel is named after the leading sylph in The Rape of the Lock.[17] It is also the name of the spirit who serves Prospero in Shakespeare's The Tempest.[18] The moon is also designated Uranus I.[11]


Herschel named the four known satellites of Uranus in Astronomische Nachrichten, Vol. 34, No. 812, pp. 325/326, 21 June 1852 (communication dated 26 May 1852.)


Thus, Dactyl, the moon of 243 Ida, was at first designated "S/1993 (243) 1". Once confirmed and named, it became (243) Ida I Dactyl. Similarly, the fourth satellite of Pluto, Kerberos, discovered after Pluto was categorized as a dwarf planet and assigned a minor planet number, was designated S/2011 (134340) 1 rather than S/2011 P 1,[23] though the New Horizon team, who disagreed with the dwarf planet classification, used the latter.


All of Uranus's moons are named after characters created by William Shakespeare or Alexander Pope. The name Titania was taken from the Queen of the Fairies in A Midsummer Night's Dream.[13] The names of all four satellites of Uranus then known were suggested by Herschel's son John in 1852, at the request of William Lassell,[14] who had discovered the other two moons, Ariel and Umbriel, the year before.[15]


Titania was initially referred to as "the first satellite of Uranus", and in 1848 was given the designation Uranus I by William Lassell,[16] although he sometimes used William Herschel's numbering (where Titania and Oberon are II and IV).[17] In 1851 Lassell eventually numbered all four known satellites in order of their distance from the planet by Roman numerals, and since then Titania has been designated Uranus III.[18]



Oberon was discovered by William Herschel on January 11, 1787; on the same day he discovered Uranus's largest moon, Titania.[1][10] He later reported the discoveries of four more satellites,[11] although they were subsequently revealed as spurious.[12] For nearly fifty years following their discovery, Titania and Oberon would not be observed by any instrument other than William Herschel's,[13] although the moon can be seen from Earth with a present-day high-end amateur telescope.[9]


All of the moons of Uranus are named after characters created by William Shakespeare or Alexander Pope. The name Oberon was derived from Oberon, the King of the Fairies in A Midsummer Night's Dream.[14] The names of all four satellites of Uranus then known were suggested by Herschel's son John in 1852, at the request of William Lassell,[15] who had discovered the other two moons, Ariel and Umbriel, the year before.[16] The adjectival form of the name is Oberonian, /ˌɒbəˈroʊniən/.[2]


Oberon was initially referred to as "the second satellite of Uranus", and in 1848 was given the designation Uranus II by William Lassell,[17] although he sometimes used William Herschel's numbering (where Titania and Oberon are II and IV).[18] In 1851 Lassell eventually numbered all four known satellites in order of their distance from the planet by Roman numerals, and since then Oberon has been designated Uranus IV.[19]


This evocative movie of four planets more massive than Jupiter orbiting the young star HR 8799 is a composite of sorts, including images taken over seven years at the W.M. Keck observatory in Hawaii.

The movie clearly doesn’t show full orbits, which will take many more years to collect. The closest-in planet circles the star in around 40 years; the furthest takes more than 400 years.

But as described by Jason Wang,  an astronomy graduate student at the University of California, Berkeley, researchers think that the four planets may well be in resonance with each other.



Cosmologist Max Tegmark has provided a taxonomy of universes beyond the familiar observable universe. The four levels of Tegmark's classification are arranged such that subsequent levels can be understood to encompass and expand upon previous levels. They are briefly described below.[54][55]

Level I: An extension of our Universe[edit]

A prediction of chaotic inflation is the existence of an infinite ergodic universe, which, being infinite, must contain Hubble volumes realizing all initial conditions.

Accordingly, an infinite universe will contain an infinite number of Hubble volumes, all having the same physical laws and physical constants. In regard to configurations such as the distribution of matter, almost all will differ from our Hubble volume. However, because there are infinitely many, far beyond the cosmological horizon, there will eventually be Hubble volumes with similar, and even identical, configurations. Tegmark estimates that an identical volume to ours should be about 1010115 meters away from us.[25]

Given infinite space, there would, in fact, be an infinite number of Hubble volumes identical to ours in the universe.[56] This follows directly from the cosmological principle, wherein it is assumed that our Hubble volume is not special or unique.

Level II: Universes with different physical constants[edit]


Bubble universes – every disk represents a bubble universe. Our universe is represented by one of the disks.
Universe 1 to Universe 6 represent bubble universes. Five of them have different physical constants than our universe has.

In the chaotic inflation theory, a variant of the cosmic inflation theory, the multiverse or space as a whole is stretching and will continue doing so forever,[57] but some regions of space stop stretching and form distinct bubbles (like gas pockets in a loaf of rising bread). Such bubbles are embryonic level I multiverses.

Different bubbles may experience different spontaneous symmetry breaking, which results in different properties, such as different physical constants.[56]

Level II also includes John Archibald Wheeler's oscillatory universe theory and Lee Smolin's fecund universes theory.

Level III: Many-worlds interpretation of quantum mechanics[edit]

Hugh Everett III's many-worlds interpretation (MWI) is one of several mainstream interpretations of quantum mechanics.

In brief, one aspect of quantum mechanics is that certain observations cannot be predicted absolutely. Instead, there is a range of possible observations, each with a different probability. According to the MWI, each of these possible observations corresponds to a different universe. Suppose a six-sided die is thrown and that the result of the throw corresponds to a quantum mechanics observable. All six possible ways the die can fall correspond to six different universes.

Tegmark argues that a Level III multiverse does not contain more possibilities in the Hubble volume than a Level I or Level II multiverse. In effect, all the different "worlds" created by "splits" in a Level III multiverse with the same physical constants can be found in some Hubble volume in a Level I multiverse. Tegmark writes that, "The only difference between Level I and Level III is where your doppelgängersreside. In Level I they live elsewhere in good old three-dimensional space. In Level III they live on another quantum branch in infinite-dimensional Hilbert space."

Similarly, all Level II bubble universes with different physical constants can, in effect, be found as "worlds" created by "splits" at the moment of spontaneous symmetry breaking in a Level III multiverse.[56] According to Yasunori Nomura,[32] Raphael Bousso, and Leonard Susskind,[30] this is because global spacetime appearing in the (eternally) inflating multiverse is a redundant concept. This implies that the multiverses of Levels I, II, and III are, in fact, the same thing. This hypothesis is referred to as "Multiverse = Quantum Many Worlds".

Related to the many-worlds idea are Richard Feynman's multiple histories interpretation and H. Dieter Zeh's many-minds interpretation.

Level IV: Ultimate ensemble[edit]

The ultimate mathematical universe hypothesis is Tegmark's own hypothesis.[58]

This level considers all universes to be equally real which can be described by different mathematical structures.

Tegmark writes that:

Abstract mathematics is so general that any Theory Of Everything (TOE) which is definable in purely formal terms (independent of vague human terminology) is also a mathematical structure. For instance, a TOE involving a set of different types of entities (denoted by words, say) and relations between them (denoted by additional words) is nothing but what mathematicians call a set-theoretical model, and one can generally find a formal system that it is a model of.

He argues that this "implies that any conceivable parallel universe theory can be described at Level IV" and "subsumes all other ensembles, therefore brings closure to the hierarchy of multiverses, and there cannot be, say, a Level V."[25]

Jürgen Schmidhuber, however, says that the set of mathematical structures is not even well-defined and that it admits only universe representations describable by constructive mathematics—that is, computer programs.

Schmidhuber explicitly includes universe representations describable by non-halting programs whose output bits converge after finite time, although the convergence time itself may not be predictable by a halting program, due to the undecidability of the halting problem.[59][60][61] He also explicitly discusses the more restricted ensemble of quickly computable universes.[62]



Molecular gas (notably CO) detected in the host galaxy associated with the quasar is the oldest molecular material known and provides evidence of large-scale star formation in the early universe. Thanks to the strong magnification provided by the foreground lens, the Cloverleaf is the brightest known source of CO emission at high redshift[1] and was also the first source at a redshift z = 2.56 to be detected with HCN[2] or HCO+ emission.[3] The 4 quasar images were originally discovered in 1984; in 1988, they were determined to be a single quasar split into four images, instead of 4 separate quasars. The X-rays from iron atoms were also enhanced relative to X-rays at lower energies. Since the amount of brightening due to gravitational lensing doesn't vary with the wavelength, this means that an additional object has magnified the X-rays. The increased magnification of the X-ray light can be explained by gravitational microlensing, an effect which has been used to search for compact stars and planets in our galaxy. Microlensing occurs when a star or a multiple star system passes in front of light from a background object. If a single star or a multiple star system in one of the foreground galaxies passed in front of the light path for the brightest image, then that image would be selectively magnified.







Burmester theory is named after Ludwig Burmester (1840–1927). Burmester introduced geometric techniques for synthesis of linkages in the late 19th century.[1] His approach was to compute the geometric constraints of the linkage directly from the inventor's desired movement for a floating link. From this point of view a four-bar linkage is a floating link that has two points constrained to lie on two circles.



A glider or platform rocker is a type of rocking chair that moves as a swing seat, where the entire frame consists of a seat attached to the base by means of a double-rocker four-bar linkage. The non-parallel suspension arms of the linkage cause the chair to simulate a rocking-chair motion as it swings back and forth.


Gliders are used as alternatives to porch swings, and are also popular as nursery furnishing for assisting parents in feeding newborn babies. Because pinch points are moved away from the floor, a glider is marginally safer for pets and toddlers.



Early patents described different mechanisms for glider chairs, such as rails[1] and four-bar linkages supported by springs.[2] Patents using a swinging seat suspended from a four-bar linkage appeared in 1939, and this is now the general configuration used by most glider chairs.[3]


In the southern United States, porch gliders were referred to as divans. Especially popular was the "basket weave" pattern in the hot non- air conditioned South of the 1950s and 1960s.[citation needed]



During the Industrial Revolution, mechanisms for converting rotary into linear motion were widely adopted in industrial and mining machinery, locomotives and metering devices. Such devices had to combine engineering simplicity with a high degree of accuracy, and the ability to operate at speed for lengthy periods. For many purposes approximate linear motion is an acceptable substitute for exact linear motion. Perhaps the best known example is the Watt four bar linkage, invented by the Scottish engineer James Watt in 1784.[4]



Peaucellier–Lipkin linkages (PLLs) may have several inversions. A typical example is shown in the opposite figure, in which a rocker-slider four-bar serves as the input driver. To be precise, the slider acts as the input, which in turn drives the right grounded link of the PLL, thus driving the entire PLL.


Slider-rocker four-bar

acts as the driver of the Peaucellier–Lipkin linkage



Square four engine[edit]

See also: Motorcycle engine


Ariel Square Four

A square four is a type of four-cylinder engine, a U engine with two cylinders on each side. This configuration was used on the Ariel Square Four motorcycle from 1931 to 1959. Although the engine was compact and had as narrow a frontal area as a 500 cc, parallel twin, the rear pair of cylinders on this air-cooled engine were prone to overheating.


This design was revived as a liquid-cooled two-stroke version on some racing Suzukis, and their subsequent road-going version the Suzuki RG500. Although some racing success was achieved, the road bikes did not sell well and the design was phased out in favour of inline four-stroke designs, as engineering and marketing resources were being applied to more common four-stroke designs at the time.[citation needed]


An experimental square four outboard motor was built for evaluation, but the design was not used due to the complexity of the drivetrain.[12]



The Danish word palæ translates to "mansion", and is most often used as an indication of a non-royal, urban mansion. Exceptions are the four palæer (plural) at Amalienborg Palace, the four individual buildings that make up the Amalienborg Palace complex. These were originally non-royal, urban mansions, which were taken over by royalty in the late 18th century.



However, the conditions necessary to resolve the problem of change can be stated simply by inspection of the problem as follows: (1) Aristotle's three laws must specify or apply to only that which is not changing, since change violates or negates all three laws; (2) If change is to logically exist, there must exist at least a fourth law of logic, one which applies to change; (3) This fourth law must contain the negations of each of the first three laws, since change negates them; (4) To be consistent, in any particular logical case, either the three laws explicitly apply or the fourth law explicitly applies (i.e., either change explicitly exists in that particular case or it does not); (5) Since all four laws must apply at all times, then when the three laws apply explicitly, the fourth law must be implicit - and when the fourth law applies explicitly, the three laws must be implicit.



An early example of electromagnetic rotation was the first rotary machine built by Istvan Jedlik with electromagnets and a commutator, in 1826-27.[2] Other pioneers in the field of electricity include Hippolyte Pixii who built an alternating current generator in 1832, and William Ritchie's construction of an electromagnetic generator with four rotor coils, a commutator and brushes, also in 1832. Development quickly included more useful applications such as Moritz Hermann Jacobi's motor that could lift 10 to 12 pounds with a speed of one foot per second, about 15 watts of mechanical power in 1834. In 1835, Francis Watkins describes an electrical "toy" he created; he is generally regarded as one of the first to understand the interchangeability of motor and generator.



There is a broad range of hardware solutions for radio amateurs and home use. There are professional-grade transceiver solutions, e.g. the Zeus ZS-1[17][18] or the Flex Radio,[19] home-brew solutions,e.g. PicAStar transceiver, the SoftRock SDR kit,[20] and starter or professional receiver solutions, e.g. the FiFi SDR[21] for shortwave, or the Quadrus coherent multi-channel SDR receiver[22] for short wave or VHF/UHF in direct digital mode of operation.



It is possible to choose among several error coding schemes and several modulation patterns: 64-QAM, 16-QAM and 4-QAM. OFDM modulation has some parameters that must be adjusted depending on propagation conditions. This is the carrier spacing which will determine the robustness against Doppler effect (which cause frequencies offsets, spread: Doppler spread) and OFDM guard interval which determine robustness against multipath propagation (which cause delay offsets, spread: delay spread). The DRM consortium has determined four different profiles corresponding to typical propagation conditions:


A: Gaussian channel with very little multipath propagation and Doppler effect. This profile is suited for local or regional broadcasting.

B: multipath propagation channel. This mode is suited for medium range transmission. It is nowadays frequently used.

C: similar to mode B, but with better robustness to Doppler (more carrier spacing). This mode is suited for long distance transmission.

D: similar to mode B, but with a resistance to large delay spread and Doppler spread. This case exists with adverse propagation conditions on very long distance transmissions. The useful bit rate for this profile is decreased.



As a digital medium, DRM can transmit other data besides the audio channels (datacasting) — as well as RDS-type metadata or program-associated data as Digital Audio Broadcasting (DAB) does. DRM services can be operated in many different network configurations, from a traditional AM one-service one-transmitter model to a multi-service (up to four) multi-transmitter model, either as a single-frequency network (SFN) or multi-frequency network (MFN). Hybrid operation, where the same transmitter delivers both analogue and DRM services simultaneously is also possible.


The first "production" all-transistor radio was the Regency TR-1, released in October 1954. Produced as a joint venture between the Regency Division of Industrial Development Engineering Associates, I.D.E.A. and Texas Instruments of Dallas Texas, the TR-1 was manufactured in Indianapolis, Indiana. It was a near pocket-sized radio featuring 4 transistors and one germanium diode. The industrial design was outsourced to the Chicago firm of industrial design firm of Painter, Teague and Petertil. It was initially released in one of four different colours: black, bone white, red, and gray. Other colours were to shortly follow. [24][25][26]



The field-effect transistor, sometimes called a unipolar transistor, uses either electrons (in n-channel FET) or holes (in p-channel FET) for conduction. The four terminals of the FET are named source, gate, drain, and body (substrate). On most FETs, the body is connected to the source inside the package, and this will be assumed for the following description.

  • A four terminal device (e.g. Silicon Controlled Switch -SCS). SCS is a type of thyristor having four layers and four terminals called anode, anode gate, cathode gate and cathode. the terminals are connected to the first, second, third and fourth layer respectively.[10]

  • https://en.wikipedia.org/wiki/Power_semiconductor_device



Ezekiel. It would demand a separate book... However, in the following we shortly outline the background control system “interpretation” of the vision, and the 4 + 16 + 256 system representations. In this rare interpretation one counts the four Cherubims standing at the four corners of the Chariot of God. All the Cherubims have 4 × 4 body-parts (4 faces, 4 wings, 4 hands, and 4 legs) according to the four natures (man, lion, bull, and eagle). This system of 4 + 16 + 256 can be related to the 39th dream of Pauli [46]:

“Dreamer is falling into the abyss. At the bottom there is a bear whose eyes gleam alternately in four colours: red yellow green and blue. Actually it has four eyes that change into four lights.”

Inasmuch the bear symbolizes north in mythology, as well as in astronomy and the Chariot of God arrives from north on the sky in the vision. The algebraic variation system of the four lights of the four eyes can be related in a natural way to the 4 + 16 + 256 system interpreted in the previous paragraphs. According to the par- ity conception of Pauli (right-left sides of space), the above structure can be sim- plified into 128 + 8 + 1. That is, the dream of Pauli connects the Merkabah vision with the fine structure constant – without any knowledge of mythology [46].

In the dream of four rectangles (dream No. 51, see Fig. 4) beside the four colors we can identify 32 geometric elements (12 corners, 16 lines and 4 rectangles). It is originally formed from two basic rectangles, so the structure 32 + 4 + 2 is valid.

– 85 –

P. Várlaki et al. Number Archetypes and “Background” Control Theory Concerning the Fine Structure Constant

The exact text of the dream of World Clock is the following:

“There is a vertical and a horizontal circle, having a common centre. This is the world clock. It is supported by the black bird.

The vertical circle is a blue disc with a white border divided into 4 × 8 = 32 parti- tions. A pointer rotates upon it.

The horizontal circle consists of four colours. On it stand four little men with pen- dulums, and round about it is laid the ring that was once dark and is now golden (formerly carried by the children).

The »clock« has three rhythms or pulses:

1) The small pulse: the pointer on the blue vertical disc advances by 1/32.

2) The middle pulse: one complete revolution of the pointer. At the same time the horizontal circle advances by 1/32.

3) The great pulse: 32 middle pulses are equal to one revolution of the golden ring.”

The rotations define three rhythms that are in an order of powers: 1/32, 1, 32, 322. The archetype number of rotation (or the circle) is naturally the π. In the spatial structure – as Jung analyzes the dream – number 4 dominates over number 3 of temporality. The rotation itself symbolizes Time, in this manner the spatial and temporal structure of the Dream of World Clock is symbolically isomorphic with the formula of the fine structure constant α−1 = 4π3 + π2 + π.

Namely, the dream can be considered as a central algebraic (system) archetype, and at the same time, as an automorphic mapping of the cardinal number arche- type in the symbolic system of the dream.

From the Pauli–Jung letters [27] it is clear that the black bird is supported by the female symbolic figure of anima, where anima is suited with number ‘7’. In this way the black bird (1), the rotating discs and ring (3), and the figure of anima (7) altogether associates to number ‘137’.

Furthermore, the temporal structure (rotation scale) itself is double 32, and the spatial structure is also evidently 2 × (32 + 4) (the four little men with pendulums – horizontal disc, and four cardinal positions of pointers – vertical disc), that alto- gether results in 1 + 2 × 32 + 2 × 36 = 137.

The dreams No. 39 and 51 naturally and evidently contained in the structure of World Clock vision (four little men, four colors create an isomorphic map with the four eyes and four colors of the bear). Therefore, the three power-like rhythms with the four space-like quaternio (like a multiplicator) is a natural and evident isomorphic map of the 4π3 + π2 + π = 137,036... Consequently, the structure of the World Clock vision (together with the dreams No. 39 and 51) is a perfect isomor- phic structure of the above formula of fine structure constant and its discussed

– 86 –

Acta Polytechnica Hungarica Vol. 5, No. 2, 2008

isomorphic interpretations (if π ∼ 4 or π ∼ 2). Jung often refers to the old familiar saying: on the Olympus numbers reign. Following this pattern, we regard the su- preme ruler (“controller“) of number archetypes the specific formula introduced for fine-structure constant.

Remark. The interpretation of the four wheels in the Ezekiel vision with the (then usual) 8 spokes can ensure a structure number of ‘32 + 4 + 2’ beside the above ‘256 + 16 + 4’ one. Since the number of the Hebrew word for wheel (which is a fundamental concept in the tradition of Ezekiel vision) 137 (137 = אופן), so the isomorphy with the structure of World Clock vision and the formula 4π3 + π2 + π can be considered as a complete one. The interpretation of three rhythms and space quaternio also can be easily detected from the structure of the Ezekiel vi- sion. (Other similar historical examples were mentioned in our earlier works [44, 45, 46]). From the point of view of the depth psychology the “numbers” 137 and 4π3 + π2 + π are the twin number archetypes of the Self (Selbst).



Thus, I now will identify similar examples as kernels in mathematical physics that Pauli may have encountered between 1913 and 1918, as follows: (1) the complex numbers z = x + i y and z = |z| e i θ; (2) Maxwell’s equations in electrodynamics; and (3) the Lorentz group in special relativity. In later chapters covering later periods in Pauli's life, I propose that Pauli saw kernels in other areas: (1) the mathematical quaternians used by Sommerfeld and Felix Klein to describe the motion of a top; (2) the angular momentum of the electron and its four quantum numbers; (3) the momentum and position variables in quantum systems, that is, the Heisenberg uncertainty relationship; (4) 2 x 2 Pauli spin matrices and perhaps the 4 x 4 Dirac matrix used to model the electron; and (5) the energy-general relativity, and charge-electromagnetism relationships that form a group in the theory of beta decay, that is to say, the conserved quantities that Pauli used to justify his neutrino hypothesis.



Examples of mandalas that Pauli saw in his later years, as they appear in his letters to Jung, may help to elucidate his earlier noticing of kernels. There are several examples of Pauli's use of mandalas, which he alternately refers to as "quaternios." In a letter of 1950, he draws four physical concepts on two axes in a four-part mandala, as shown below. 133 This image has a holistic quality and an internal “symmetry-breaking” feature, as he showed later when he modified it in a letter of 1952, in which the “poles” of “energy” and “space-time” are broken up into three-dimensional momentum plus energy and three-dimensional space plus time.134


In a letter of 1953 to Jung, Pauli discussed his relationship to physics and psychology:

I can attempt to represent my relationship to physics and psychology through the quaternio [below] in which the people stand for mental attitudes and you [Jung], of course, represent your analytic psychology.135


Figure 2. Pauli’s “personality-type” mandala, from Pauli’s letter to Jung of May 27, 1953.

Then, in a letter to Jung of 1956, Pauli discussed a dream in which opposite psychological symbols are arranged in quaternian fashion, with a “path” through the psychological space of the “mandala-of-countries” symbolism.136

Trigonometric functions combine to form an expression for e and the complex number Z = X + iY = | Z| ei θ, where θ is the angle formed between the vector Z and the X axis. The circular visualization of the complex-number plane involves four mathematical symbols, e, i, 1, and π, and may have been the first mathematical “kernel” or mandala that Pauli recognized during his early education. The symbols e, 1, and π are of similar real-number character, but i introduces the need for an almost mystical perspective to appreciate it fully. And how does one comprehend the deep relationship between these seemingly disparate symbols and mathematical traditions? Are they a product of the human mind, or does the mathematical mind uncover an aspect of deep reality? The symbol for the imaginary number i, the square root of the real number -1, is related to e, the base of the natural logarithms, and to π . This striking visual connection between e, i, and trigonometric functions that include π and represent rotations is mysterious. The circle has the image of a mandala, the mathematics is that of a four-part constituency, and

the beauty is expressible by no means other than as a visually complete symbollism, visible only to the “mind’s eye.” Pauli was exposed to this mandala-like image or kernel and to its mathematics early in his education.



In his encyclopedia article of 1921 on the theory of relativity, Pauli illustrated how the Lorentz transformation could be visualized as a rotation in an abstract mathematical space, as shown in the figure below.151 The space-time distance between two four-

Figure 6. Pauli’s illustration of a Lorentz transformation.

dimensional points, x, y, z, ict and x', y', z', ict' is invariant, giving Pauli in his “mind’s eye” another opportunity to visualize a kernel, with the transformation between coordinate systems perceived visually as a rotation. Pauli adapted the above figure from Hermann Minkowski’s famous lecture of September 21, 1908,152 which Pauli would have encountered during his Gymnasium education, since he was completely familiar with relativity theory before he began his studies with Arnold Sommerfeld in Munich in 1918.153 The above image of 1921 reminds one of a kernel, in which the space-time distance has four components and is invariant under a rotational transformation. Some components within the circle change, but not the underlying measure or radius of the circle. The fourth component, moreover, involves the imaginary number i, an extension

151 Wolfgang Pauli, Theory of Relativity (New York: Dover, 1958), p. 72.

152 Ibid., p. 72. See Pauli’s footnote 108. Also, see Pauli’s footnote 54, p. 21.

153 The second article of Pauli's career to be published in a scientific journal was "Über die Energiekomponenten des Gravitationsfeldes," Physikalische Zeitschrift 20 (1919), 25-27. The article had been submitted by the young Pauli in September of 1918 from Vienna, before he entered the Ludwig Maximillian University in Munich. See Ralph de Laer Kronig and Victor Weisskopf, ed., Collected Scientific Papers of Wolfgang Pauli, Vol. 2 (New York: Interscience Publishers, 1964), p. 12.

in mathematical complexity from the other three components. If Pauli had mystical stirrings, they certainly could have occurred here.

PAULI AND THE INTERPLAY BETWEEN THE NUMBER THREE AND THE NUMBER FOUR (the same thing happened to me originally I liked the number three but then I realized four was the transcendent fourth)


Dynamical systems of four parts, such as complex numbers, electromagnetic fields, and Minkowski space- time, would indicate a “quaternian” way of perceiving the world. Mathematical group transformations would be visualized as rotations of a mandala. Even his own personality would be transformed from being outwardly focused to inwardly consumed, from believing that rationality and the senses were supreme to equally valuing feelings and intuitions.

The topics of a philosophical nature that I believe first appeared in Pauli’s adolescence need further identification. I see them surfacing in his teens as he became aware of kernels, quaternities, rotations, and deep reality. The kernels of Pauli’s adolescence later would become the mandalas of Jung. One might think of kernels as being inert physical wholes larger than the sum of their parts, implying a unity of

mathematics and physics, the “all is number” of Pythagoras. Kernels can be inferred most easily through visualization, with their indicator the circle expressing unity. Pauli’s kernels came in four-part divisions. Another indicator of the presence of kernels was visualization of rotation of these four components.

The four mathematical symbols e, i, π, and 1 comprise the components of the kernel that formed the unit circle in the complex-number plane. The electric and magnetic fields of the four Maxwell equations comprised the kernel that could be visualized as a traveling electromagnetic wave. The four space-time dimensions comprised the kernel found in Minkowski’s view of special relativity, and could be visualized in the Lorentz transformations as rotations. Whenever Pauli encountered rings, circles, wholes dissectible into four parts, and spheres, he became intuitively drawn to them.

By the time Pauli met Jung, Pauli was ready for Jung's concept of mandalas. Jung’s mandalas extended the idea of kernels for Pauli by including animate conscious components. Jung uses the Sanskrit word mandala as a symbolic or “magic circle”154 that captures in the "mind's eye" the psychic center of a transformational process. This idea defies precise definition since the person seeing the mandala image in his or her "mind's eye" is supposed to experience a mystic feeling when viewing the symbol, a feeling going beyond a reductionist attempt at verbal definition. Jung’s mandalas also generally have four components. Thus, the mandala is the “One” whole that is larger than the sum of its four parts.


The four components of most kernels that Pauli saw in his physics later developed into his numerological attraction to the number 4. In his youth, however, I think Pauli was struggling with positivist messages that undermined his trust in his intuition. The number 3, likely derived from his Catholic upbringing and attachment to the Trinity, was another numerological sign to which the young Pauli was sensitive. The number 3 represented an opposition to the number 4; either three or four components existed in a physical system, but not both. The three components of Cartesian space were completely rational and perceptible by the senses. The fourth component in Minkowski space-time, ict, involved a nonrational extension that was not perceptible by the senses; it extended the three to form a unity of four components. Thus, to the youthful Pauli, numerology of

154 Mary Ann Mattoon, Jungian Psychology in Perspective (New York: The Free Press, 1981), p. 139.

the number 4 clashed with his positivist upbringing and rationality. Four components were not subject to proof; instead they had to be accepted on the basis of intuition, symmetry, and aesthetics. He was not ready to accept the numerology of the number 4 until after he met Jung.



In 1955 Pauli wrote about the numerological meaning of the number 4, essentially calling for a reconsideration of Platonism:

For [Pythagoras] ... wherever number is, there also is soul, the expression of the unity which is God. Whole-number relationships, as they occur in the proportions of the frequencies of the simple musical intervals, are harmony, that is to say they are what brings unity into contrasts. As part of mathematics number also belongs to an abstract supersensuous eternal world which can be apprehended not by the

171 Enz and von Meyenn, Wolfgang Pauli (ref. 6), p. 64.

senses but only in contemplation by the intellect. Thus for the Pythagoreans mathematics and contemplative meditation (the original meaning of “theoria”) are very closely connected; for them mathematical knowledge and wisdom (sophia) are inseparable. Special significance was attached to the tetraktys, fourfoldedness, and there is a traditional oath of the Pythagoreans: “by him who has committed to our soul the tetraktys, original source and the root of eternal Nature”....172

We have here the fundamental explanation of Pauli’s attraction to the number 4 and the four components of his physical kernels. Pauli was attracted to Kepler in part because he was a bridge in the history of ideas between “Trinitarian” and “quaternian” thinking. Pauli's analysis of the Kepler-Fludd polemic in the 1940s is connected to this issue. For Pauli, the Kepler-Fludd polemic mirrored the debates over the philosophical interpretation of quantum mechanics:

Modern quantum physics has come closer to the quaternary point of view, which was so violently opposed to the natural science that was germinating in the 17th century, to the extent that it takes into greater consideration the role of the observer in physics than is the case in classical physics.173





Klein and Sommerfeld published their seminal work on the theory of the spinning top in four parts between 1897 and 1910,190 employing the mathematics of quaternians, group theory, and matrices. They treated the rotations of a top and other physical bodies using mathematically visualizable hypergeometry. Pauli cut his mathematical teeth by studying Klein and Sommerfeld’s theory, with its abstract kernel visualizations of rotations, and continued to use them in his physics.191 At the same time, Pauli also experienced resistance to these mathematical methods owing to the psychological messages of his father and his godfather Mach, who opposed abstract mathematics and embraced instead measurement and empiricism. Pauli in 1957 reflected on this tension:



In his Theory of Relativity, Pauli especially acknowledged his debt to Klein. 193 We can assume he also appreciated Sommerfeld’s role, as Sommerfeld wrote the Preface to it. Klein and Sommerfeld worked with quaternian algebra, building on the efforts of William Rowan Hamilton (1805-1865) and Bernhard Riemann. They all recognized the power of quaternian algebra for mathematics and physics, and some of them saw further

190 Felix Klein and Arnold Sommerfeld, Über die Theorie des Kreisels (New York: Johnson Reprint Corporation, 1965).

191 Pauli had to have reviewed Klein and Sommerfeld’s work when he conducted his comprehensive summary of relativity theory, if not before.

192 Enz and von Meyenn, Wolfgang Pauli (ref. 6), p. 129. 193 Pauli, Theory of Relativity (ref. 16), p. vi.

connections. Thus, Hamilton saw mystical connections that likely were not lost on either Sommerfeld or the young Pauli's Shadow. Pauli used quaternian algebra when he introduced spin matrices in 1927, but he might have picked up its mystical connections to Plato’s Tetractys much earlier by the way it was visualized. Hamilton defined quaternians as:

The quotient of two vectors, or the operator which changes one vector into another....

The SYMBOL OF OPERATION q( )q -1 , where q may be called (as before) the operator quaternion, while the symbol (suppose r) of the operand quaternian is conceived to occupy the place marked by the parentheses ... can be regarded as a conical rotation of the axis of the operand round the axis of the operator, through double the angle thereof....194

Klein and Sommerfeld extended the quaternian algebra of the real and imaginary numbers into an algebra that included vectors, matrices, and generalized transformations. Here was a mathematics suitable for describing rotations. Historian of mathematics Simon Altman has commented on Hamilton’s achievements:


We must stress that Hamilton's everlasting monument ... is his construction of objects that, except for commutativity, obey the same algebra as that of the real and complex numbers: and Hamilton was aware of this–although he could not foresee that quaternions were to receive in 1878, at the hands of [Georg Ferdinand] Frobenius, the supreme accolade of being proved to be the only possible objects with this property.195

Klein's and Sommerfeld's treatise, Über die Theorie des Kriesels196, is perhaps the most underappreciated source for the mathematical development of matrix mechanics. We find in it the mathematics of quaternians and matrices, symmetry analysis, noncommutative matrix-multiplication methods, spin matrices, and a mathematical alethic reality used to describe bodies in motion, namely, the rotation of a spinning top. Sommerfeld no doubt put his and Klein's work into the hands of Pauli who, for example,

194 Simon Altmann, Rotations, Quaternians and Double Groups (Oxford: Clarendon Press, 1986), p. 16. 195 Ibid., p. 15.

196 Klein and Sommerfeld, Theorie des Kreisels (ref. 31).

treated a spinning hydrogen nucleus long before electron spin was considered.197 He mastered matrices, vectors, tensors, quaternians, and, in general, Hamiltonian dynamics long before Heisenberg’s discovery of matrix mechanics. Klein and Sommerfeld had used matrix mathematics, infinitesimal rotations, imaginary and complex numbers, and mathematical visualizations to express the deeply embedded rationality behind classical mechanics. These visualizations often were in an abstract alethic space, and Pauli had to become comfortable with them, such as the one that Herbert Goldstein noted in 1950, when he discussed the equations of motion for a rotating rigid body: “Hence the jabberwockian sounding statement: the polhode rolls without slipping on the herpolhode lying in the invariable plane.”198 To illustrate the challenge, Goldstein included the diagram below.199 He relied on Klein and Sommerfeld’s earlier work, where similar



Further, he saw the need for only four-dimensionality in Minkowski space-time, a hint at the numerological significance of the number 4. Pauli thus was seeing alethic reality, kernel wholes, quaternity numerology, and Keplerian mathematical aesthetics in his approach to relativity, in contrast to his father’s and Mach’s positivist and operationalist messages. Pauli became acquainted with alethic reality through the mathematical treatment of Lorentz transformations using rotations of vectors in hypergeometric physical space, the four-dimensional space of Minkowski space-time. He also was exposed to the mathematical concepts of matrices, symmetry invariants, and group representations. He might well have begun taking physical entities not at face value as naïvely visualizable, but as kernel wholes that have deeper alethic dimensions and can be visualized abstractly--any mathematical or physical entity can be expressed and analyzed as kernel wholes with internal subdivisions. He begins to place pure mathematics and visual images on an equal footing with empiricism--and only when the visualizations prove superfluous does he give them up.216



Schrödinger’s wave function Ψ was unobservable, but essential to the theory. The spin matrices that Pauli introduced later were unobservable, but they were necessary for the mathematical description of an electron’s internal alethic dynamics. Reality was alethic, as for Schrödinger’s wave function and Pauli's spin matrices, but one could never trust that they were the final solution or the deepest level of mathematical or physical symbolism. As we will see, Dirac’s extension of Pauli’s spin matrices from 2 x 2 to 4 x 4 matrices is a prime example of “going deeper” into alethic reality.




Later, Pauli intuitively felt a sense of balance when he visualized mandalas marked by a four-part division. When he later emphasized “one” in his writings, he was referring to mandala wholes. To Pauli, the number 3 represented pure reason, empiricism, and logic, something akin to Kepler’s way of doing physics where numerology was a tool but removal of nonrationality was a goal; the number 4 represented Fludd’s addition of a spiritual, nonrational element into the otherwise purely physical 3 to make a quaternity whole, the “one” mandala. In physics, for example, the three spatial dimensions had to be supplemented by a time dimension involving the imaginary number i to complete the wholeness of Minkowski’s space-time. Prior to the discovery of his Pauli Verbot, he had not entertained these feelings in his physics, and thus their spiritual implications had not been pressing. After his discovery, Zweideutigkeit held far more meaning for him than as

During the route to his discovery of the Pauli Verbot, elements of his philosophy of physics surfaced, which I call Pauli’s Platonism. These elements are:
275 Ibid., p. 181.
276 Pais, Inward Bound (ref. 14), p. 314.

belief in doubling of states; attraction to quaternian symmetry in kernels; attraction to visualizable rotations of kernels in his “mind’s eye”; numerological attraction to the numbers 1, 2, 4, and 137; belief in synchronicity; and belief in an alethic, Platonic reality



I believe that in spin matrices we can see the roots of Pauli’s philosophy and style of theoretical physics. He was the first physicist to introduce them into quantum mechanics. Spin matrices are visualizable in an abstract mathematical space involving the complex number i. Pauli showed that the electron can be represented mathematically by spinors, two-valued wave functions, that use spin matrices in their formulations. The "Pauli spin matrices" are 2 x 2 matrices that together form a kernel whole with four components. The three Pauli spin matrices together with the unit matrix form a set of four independent matrices. Herbert Goldstein has pointed out that, “Each of the Pauli spin matrices is therefore associated with rotation about one particular axis and may be thought of as the unit rotator for that axis.” 290 He notes further that:

Characterisitic of the Cayley-Klein parameters, and of the matrices containing them, is the ubiquitous presence of half angles, and this feature leads to some peculiar properties for the uv space [the two-dimensional complex number space

289 Wolfgang Pauli, "Zur Quantenmechanik des magnetischen Elektrons," Zeitschrift für Physik 43 (1927), 601-623, reprinted in Ralph de Laer Kronig and Victor Weisskopf, ed., Collected Scientific Papers by Wolfgang Pauli, Vol. 2 (New York: Interscience Publishers, 1964), pp. 306-328.

290 Herbert Goldstein, Classical Mechanics (Reading, Massachusetts: Addison-Wesley, 1965), pp. 116-118.

in which a transformation from one to another involves the Cayley-Klein parameters and spin matrices]. For example, a rotation in ordinary space about the z axis through the angle 2π merely reproduces the original coordinate system. Thus, if in the D matrix ..., φ is set equal to 2π, then cos φ = 1, sin φ = 0, and D properly reduces to the unit matrix 1 corresponding to the identity transformation. On the other hand if the same substitution is made in Qφ ... we obtain [the 2 x 2 matrices]

Q2π= eiπ 0 = -1 0

0 e-iπ 0-1 ,

which is -1 and not 1. At the same time the 2 x 2 1 matrix must also correspond to the three-dimensional identity transformation. Hence there are two Q-matrices, 1 and -1, corresponding to the 3 x 3 unit matrix. In general, if a matrix Q corresponds to some real orthogonal matrix then –Q also corrresponds to the same matrix. The isomorphism between the two sets thus involves, in this case, a one- to-one correspondence between the single 3 x 3 matrix and the pair of matrices (Q, -Q), and not between the individual matrices. In this sense one may say that the Q matrix is a double-valued function of the corresponding three-dimensional orthogonal matrix.291



Nonetheless, as in any creative leap, confusion and lack of clarity prevail, so a full explanation of Heisenberg’s magic remains elusive. We might look, however, at Heisenberg’s uncertainty principle,

p . q - q . p = h/2πi1 ,

where p , q and 1 now are matrices, to attempt to gain further insight into Pauli's contributions to it. Pauli in his “mind’s eye” might have viewed it as expressing the noncommutivity of matrix rotations. The dynamical variables are in an abstract mathematical space, but the imagery of a rotation remains. Anschaulichkeit appears in the alethic reality of momentum and position variables. The order of the rotation switches from first p then q, to first q then p, and Planck’s constant h is a measure of the minimum element of noncommutivity in this ordered process. Pauli, in addition to visualizing a kernel under rotation, also might have associated the above equation with the Pythagorean tetractys, where p, q, h, and i are the four elements, and the kernel is some visualizable whole uniting all four. Thus, Pauli would not have been surprised by uncertainty; it was a consequence of a rotation-like alethic transformation. Further, Beller has pointed out that it was Pauli who provided Heisenberg with the example of the time-energy uncertainty relation.310



Jammer includes the following footnote:

Quaternions had been applied to physics as early as 1867 by P.G. Tait in his An Elementary Treatise on Quaternions.... Their use in modern physics was revived by [Felix] Klein, who showed in 1910, in a lecture before the Göttingen Mathematical Society, that Lorentz transformations, conceived as four- dimensional rotations in Minkowski space[-time], can be conveniently expressed in terms of quaternions.... Their systematic, though never popular, use in quantum mechanics began when it was recognized that the Pauli spin matrices were essentially quaternion basis elements.313

Pauli was familiar with Lorentz transformations in Minkowski space-time and also with quaternians from Klein and Sommefeld’s treatment of a spinning top. If he was thinking about spin matrices in early 1925, he might well have discussed rotations as Lorentz transformations with Heisenberg, then quaternians and matrices. I thus strongly suspect that Pauli provided Heisenberg with the mathematical tools necessary for the creation of matrix mechanics. Pauli himself always credited Heisenberg for creating matrix mechanics, but I believe that Pauli set the stage for Heisenberg’s work and indicated a route to follow. Pauli dared not publish his intuitions owing to their lack of operationalist support, but the uninhibited Heisenberg felt no such qualms.



Examples of kernels that appeared in his physics between 1925 and 1927 are spin matrices and spinors, or physically the electron; and, with some unknown visualizable form, Heisenberg’s uncertainty relations, or physically Planck’s constant h multiplied by 1/2πi. Examples of quaternians are the four-component mathematical structure of spin matrices; and the four-component “primary entities” of p, q, h, and i in Heisenberg’s uncertainty relations. Examples of rotations that Pauli visualized or perceived as mathmatical operations are the spin of the electron; the mathematical operations generated by spin matrices and spinors, with their double- valuedness; and the mathematical equivalence of matrix and wave mechanics.



It is for this reason, he says, that he no longer referred to them as "neutrons"; indeed, that he made use of no special name for them. However, there is evidence ... that Pauli's recollections are incorrect; that at Pasadena the particles were called neutrons and were regarded as constituents of the nucleus.

...a short note in Time, 29 June 1931, headed "Neutrons?", says that Pauli wants to add a fourth to the "three unresolvable basic units of the universe" (proton, electron and photon); adding, "He calls it the neutron."351



Picture 5. The four eggs change into the following mathematical expressions cos δ/2 sin δ/2

cos δ/2 sin δ/2

Picture 6. This gives the formula cos δ/2 + i sin δ/2

cos δ/2 - i sin δ/2

Picture 7. I say, "The whole thing gives eiδ, and that is the circle."352

Note the quaternities, the imaginary number i, and the factor of 1⁄2. Pauli goes on in this lengthy letter to discuss his hypothesis of the connection between physics and psyche, and does not mention the neutrino. I maintain, however, that his cognitive pattern is the key and not the attached meaning of splitting eggs or mathematical formulas. This is how Pauli thought. Heisenberg recalled Pauli's repeated admonition: “Verdoppelung und Symmetrieverminderung. ‘Das ist des Pudels Kern’.” That is, “The fundamental principle from which all nature is produced is doubling of states and then, later on, reduction of symmetries.”353 In his development of the neutrino hypothesis, the splitting and doubling process within beta decay produced a holistic quaternity of four particles-- the proton, the electron, the photon, and now the neutrino.


Another example of Pauli's recurrent cognitive patterns appeared in a letter of February 27, 1952, to Jung. Pauli refers to the diagram as a "quaternio" involving synchronicity, causality, energy, and time. His quaternio is similar to what I have termed a kernel. Note especially in his diagram, below, that the endpoints of the energy-time axis split into three additional components. Here is an additional example, I maintain, of Pauli's conception of Zweideutigkeit splitting.



Figure 12. Pauli's quaternio of 1952 splitting into many components.354

The above examples of Pauli's recurrent cognitive patterns do not prove he

thought similarly in his path to the neutrino, but do raise interesting speculations that seem relevant to my exploration of his reasoning. Four-part symmetry and Zweideutigkeit splitting were part of his recurrent cognitive patterns, and therefore may have occurred to him along his path to the neutrino. Thus, the neutrino was essential to the nuclear kernel's wholeness and the total symmetry of the nucleus; in his mind the neutrino existed both inside the nucleus at some alethic level and was produced and made a separate entity at the moment of beta decay.



I have suggested that Pauli saw the following Jungian elements in his physics prior to his treatment in the Jung Clinic in 1932: He believed that physics operated in an alethic reality; kernels existed in the alethic reality of physics; kernels often possessed quaternian structure, and hence the number 4 was especially significant numerologically; rotations in his “mind’s eye” corresponded to mathematical transformations between coordinate systems within kernels; within kernels, Zweideutigkeit, doubling of physical parameters, was common and represented some aspect of the Devil’s handiwork; synchronistic events were an aspect of alethic reality; and numerology was an important methodology



After his death two years later, quantum physics continued to unfold along quaternian lines with the identification of the four fundamental forces of nature, the gravitational, electromagnetic, weak, and strong forces, and the continuing attempts to unify them. Pauli would have been pleased to see the appearance of Stephen Adler’s book, Quaternionic Quantum Mechanics and Quantum Fields.381 In 1955 Pauli displayed the extent to which his reflections on the nature of reality had taken him, calling for unification of rationalism and mysticism, physics and psychology:



structure of benzene,376 Pauli’s dream may have been of Bohr’s Aufbauprinzip. Pauli’s dream has a Jungian interpretation of many layers: the clock ticks off the ordered structure of the periodic table of the elements as protons are added to the nucleus and electrons to the atomic shells; the four colors symbolize the four quantum numbers of the electron; the four “sages” symbolize Sommerfeld, Bohr, Mach, and Pauli’s father, all in heated debate over the methods of science; the three rings symbolize the Trinity; and Pauli’s sense of danger ignites over the quaternian kernel intuitive visualization that came to him without rational cause. If Pauli simultaneously experienced a religious conversion with this dream, no wonder he entered into “a brief period of spiritual and human confusion, caused by a provisional restriction to Anschaulichkeit.”377



Both Pauli and Jung were aware of William James’s book, The Varieties of Religious Experience,373 where James delineated four characteristics of a mystical or religious conversion experience: ineffability--the experience defies verbal expression; noetic quality--the experience seems to be another state of knowing, of deep insight; transiency--the experience cannot be sustained nor remembered except imperfectly; and passivity--the person feels his or her own will is in abeyance, as if held by a superior power.374



SPINNING BACKGROUND: Red and green crosses flashing in alternation look bent out of shape, with the right angles no longer looking like right angles. This is because the vertical arms of the crosses lie on the edge of a pie-shaped sector of the moving background, while the horizontal arms lie on the middle of a sector. The edge of a sector has more pulling power than the middle of a sector.



On February 4, 2007, during Super Bowl XLI, Snickers commercials aired which resulted in complaints by gay and lesbian groups against the maker of the candy bar, Masterfoods USA of Hackettstown, New Jersey, a division of Mars, Incorporated. The commercial showed a pair of auto mechanics accidentally touching lips while sharing a Snickers bar. After quickly pulling away, one mechanic says, "I think we just accidentally kissed.", and another mechanic exclaims, "Quick! Do something manly!" and in three of the four versions, they do so mostly in the form of injury, including tearing out chest hair, striking each other with a very large pipe wrench, and drinking motor oil and windshield washer fluid. In the fourth version, however, a third mechanic shows up and asks "Is there room for three in this Love Boat?"




These were eventually replaced by the 'Duo', a double bar pack. Though this change to Duos reduced the weight from 3.5 to 3.29 ounces (99 to 93 g), the price remained the same. The packaging has step-by-step picture instructions of how to open a Duo into two bars, in four simple actions.[9] As Mars stated fulfillment of their promise, the Duo format was met with criticism by the National Obesity Forum and National Consumer Council.[10]


The USDA lists the caloric value of a 2-ounce (57 gram) Snickers bar as 280 kilocalories (1,200 kJ).[12] As of 2016, the United Kingdom bar has a weight of 48g, with 245 kcal,[13] and the Canadian bar 52g with 250 kcal.[citation needed] The four-pack bar in the United Kingdom has a weight of 41.7g, with 213kcal.[citation needed]


Four stars—Rigel, Betelgeuse, Bellatrix and Saiph—form a large roughly rectangular shape, in the centre of which lie the three stars of Orion's Belt—Alnitak, Alnilam and Mintaka. Coincidentally, these seven stars are among the most distant that can easily be seen with the naked eye.


Hanging from Orion's belt is his sword, consisting of the multiple stars θ1 and θ2 Orionis, called the Trapezium and the Orion Nebula (M42). This is a spectacular object that can be clearly identified with the naked eye as something other than a star. Using binoculars, its clouds of nascent stars, luminous gas, and dust can be observed. The Trapezium cluster has many newborn stars, including several brown dwarfs, all of which are at an approximate distance of 1,500 light-years. Named for the four bright stars that form a trapezoid, it is largely illuminated by the brightest stars, which are only a few hundred thousand years old. Observations by the Chandra X-ray Observatory show both the extreme temperatures of the main stars—up to 60,000 kelvins—and the star forming regions still extant in the surrounding nebula.[41]



The Byakkotai was part of Aizu's four-unit military, set up in the domain's drive to finalize its military modernization, in the wake of the Battle of Toba-Fushimi.[2] The other three units were Genbutai,[3] Seiryūtai,[4] and Suzakutai.[5][6] Each of the four was named after the protecting gods of compass directions. Byakkotai was meant to be a reserve unit, as it was composed of the young, 16- to 17-year-old sons of Aizu samurai.[7] It was subdivided further, along the lines of rank within the domain's samurai population: two squads were from the upper (shichū) rank, two from the middle rank (yoriai), and two from the lowest (ashigaru).[8] Twenty of the members of the 2nd shichū squad, cut off from the rest of their unit in the wake of the Battle of Tonoguchihara,[9] retreated to Iimori Hill, which overlooked the castle town. From there, they saw what they thought was the castle on fire, and committed seppuku (with one failed attempt) in desperation, believing their lord and families dead.[10] However these 20 Byakkotai members were mistaken in their assessment of defeat, as the castle defenses had not actually been breached; the castle town surrounding the inner citadel was aflame. As the majority of the town was between Iimori Hill and the castle, the boys saw the rising smoke and assumed that the castle itself had fallen.[10]





The operation of the game starts with an initial configuration on a two dimensional grid. This infinite square grid consists of cells with two possible states, alive or dead. Each cell has eight neighbors, namely the eight cells that touch it. The game operates in iterations, called ticks. Each tick applies the four rules of the game to every cell on the board simultaneously.

Theoretically the many different possibilities of these four simple rules allow the development of any kind of computing. A Turing machine has been implemented in Conway's Game of Life. There are hundreds of other amazing patterns.



The book, 4 Rules of Simple Design, helps us discover these possibilities by creating Conway’s Game of Life while following the following four rules of simple design:

Tests Pass

Expresses Intent

No Duplication — not just code, also knowledge duplication




Patterns relating to fractals and fractal systems may also be observed in certain Life-like variations. For example, the automaton B1/S12 generates four very close approximations to the Sierpiński triangle when applied to a single live cell. The Sierpiński triangle can also be observed in Conway's Game of Life by examining the long-term growth of a long single-cell-thick line of live cells,[40] as well as in Highlife, Seeds (B2/S), and Wolfram's Rule 90.[41]


Immigration is a variation that is very similar to Conway's Game of Life, except that there are two ON states (often expressed as two different colours). Whenever a new cell is born, it takes on the ON state that is the majority in the three cells that gave it birth. This feature can be used to examine interactions between spaceships and other "objects" within the game.[42] Another similar variation, called QuadLife, involves four different ON states. When a new cell is born from three different ON neighbours, it takes on the fourth value, and otherwise, like Immigration, it takes the majority value.[43] Except for the variation among ON cells, both of these variations act identically to Life.



14. Go anytime Monday through Thursday to get their Four-Course Feast for $15.99 (instead of the regular $21.99) — and like them on Facebook to find out about other deals like this.



Carl's Jr. and Hardee's join in the recent spate of $4 value deals among some of the major fast food burger chains with the introduction of the $4 Real Deal.


Similar to Wendy's 4 for $4 deal and Burger King's 5 for $4 deal, the Carl's Jr. and Hardee's special includes four items for $4. Specifically it includes a Double Cheeseburger, Spicy Chicken Sandwich, small fries, and a 16-oz drinks for $4.


Read more at http://www.brandeating.com/2016/01/carls-jr-and-hardees-debuts-4-real-deal.html#M5Qx0sheAGsdG71o.99


News: Del Taco - New $4 Meals


image: http://2.bp.blogspot.com/-n4bJKZTS-UU/UBCLdNPTBEI/AAAAAAAAWYY/KYiHDKig0S4/s1600/del_taco_4_dollar_deals.jpg



For a limited time, Del Taco is offering four new $4 value meals. The four available meals are Del's Deal, the Classic Deal, the Grilled Chicken Deal, and the Variety Deal.


Here's what's comes with each deal:


- Del's Deal includes two half-pound bean and cheese burritos, a regular taco, and a small drink (do keep in mind that a "small" drink is, inexplicably, typically 20 fluid ounces);


- the Classic Deal includes two Classic Tacos, a value bean & cheese burrito, and a small drink;


- the Grilled Chicken Deal includes two grilled chicken tacos, a regular taco, and a small drink;


- and the Variety Deal includes a 2-piece mini cheese quesadilla, a grilled chicken taco, a value bean and cheese burrito, and a small drink.


Read more at http://www.brandeating.com/2012/07/news-del-taco-new-4-meals.html#1qxAssGDRKgpt7CV.99

News: Del Taco - New $4 Meals


image: http://2.bp.blogspot.com/-n4bJKZTS-UU/UBCLdNPTBEI/AAAAAAAAWYY/KYiHDKig0S4/s1600/del_taco_4_dollar_deals.jpg



For a limited time, Del Taco is offering four new $4 value meals. The four available meals are Del's Deal, the Classic Deal, the Grilled Chicken Deal, and the Variety Deal.


Here's what's comes with each deal:


- Del's Deal includes two half-pound bean and cheese burritos, a regular taco, and a small drink (do keep in mind that a "small" drink is, inexplicably, typically 20 fluid ounces);


- the Classic Deal includes two Classic Tacos, a value bean & cheese burrito, and a small drink;


- the Grilled Chicken Deal includes two grilled chicken tacos, a regular taco, and a small drink;


- and the Variety Deal includes a 2-piece mini cheese quesadilla, a grilled chicken taco, a value bean and cheese burrito, and a small drink.


Read more at http://www.brandeating.com/2012/07/news-del-taco-new-4-meals.html#1qxAssGDRKgpt7CV.99




Carl’s Jr. Is Letting You Order 4 Things For 4 BUCKS


Peter Pham

Jan 22, 2016



The year has only just begun and fast food restaurants are already going head-to-head with updated versions of their value menus. Burger King recently added a 5 for $4 special, Pizza Hut threw in their own value menu and McDonald's added a $2 McPick option. Now, Carl's Jr. and Hardee's is unveiling their own variation: the $4 Real Deal.



New meals added! The $4 Menu includes perennial favorites like the Original Double ‘n Cheese, as well as newer offerings like the Cajun and Garlic Double Steakburgers, and the Grilled Cheese Steakburger Melt. All $4 Menu burgers, melts and footlong hot dogs are served with our thin ‘n crispy fries! Upgrade to the Seasoned Fries in four delicious flavors, Cajun, Parmesan Cheese ‘n Herbs, Sea Salt ‘n Cracked Pepper or Salt ‘n Vinegar, for an additional charge.

Church's Brings Back $4 Big Box


image: https://1.bp.blogspot.com/-2z2Pn2snll0/Vx7H-svT4TI/AAAAAAAAuqU/sZ2HnNCWpgsNBzVbjHoy4BIBcvBn7noqQCLcB/s400/churchs-4-dollar-big-box.jpg



The $4 Big Box is back at Church's Chicken for a limited time and, this time around, they've added new Honey-Butter Biscuit Tender Strips as an option.


Read more at http://www.brandeating.com/2016/04/churchs-brings-back-4-dollar-big-box.html#M91JFR8Mm9A2JXGJ.99



Burger King introduces the new $3.99 Whopper Jr. Meal Deal as their latest combo special.


For $3.99, you get a Whopper Jr. Sandwich, 4-piece chicken nuggets, small fry, and small fountain drink. The Whopper Jr. includes a flame-grilled beef patty, tomatoes, onions, lettuce, mayo, ketchup, and pickles on a toasted sesame seed bun.


The promotion looks to be a slightly different take on the 5 for $4 deal that they offered earlier this year and brings it more in line with Wendy's currently-running 4 for $4 deal.


The $3.99 Whopper Jr. Meal Deal can be found at participating Burger King restaurants for a limited time.


Read more at http://www.brandeating.com/2016/12/burger-king-unveils-new-399-whopper-jr-meal-deal.html#ObXF6XZcoPC2isSD.99



Checkers / Rally's Unveils New $4 Meal Deal


image: https://2.bp.blogspot.com/-J2rIvlJCV_k/V1lFVBd6f9I/AAAAAAAAvpg/WkW0f6U3ymkpH7LcP1Cnknp5FMF6eTM0QCLcB/s400/rallys-checkers-4-dollar-meal-deal.jpg



Checkers / Rally's joins in on the flood of recent four-for-$4 (or $5) combo deals with their own new, limited-time $4 Meal Deal.


Read more at http://www.brandeating.com/2016/06/checkers-rallys-unveils-new-4-meal-deal.html#8QS2hrdICIlIxJ0X.99



Promoted as offering More Bang for Your Buck (compared to the competition), the Jack in the Box 4 for $4 combo features two tacos, a Jumbo Jack Jr. Jumbo Jack, a small fries and a drink.


The addition of the Jumbo Jack to the combo comes on the heels of Wendy’s announcing the addition of the Double Stack to their 4 For $4 Meal deal. Perhaps just a coincidence, but the battle in the no-holds-barred value meal space is fierce.


The Jumbo Jack features a 100 percent beef patty topped with hand leafed lettuce, tomato, pickles, chopped onions, and real mayonnaise on a buttery bakery bun.


Jack in the Box Tacos feature beef, American cheese, shredded lettuce, and taco sauce.


The 4 For $4 combo is available for a limited time at participating Jack in the Box locations nationwide. Prices and availability may vary by location.

McDonald's Trying New $4 Meals


Perhaps looking for another value angle, McDonald's is testing/trying new $4 Meals in the Baltimore metro area.


The deal was spotted by one of your fellow readers, Adam.


The $4 Meals feature a choice from a limited selection of entrees plus a medium order of fries and a medium drink.




Dutch scientist and mathematician Christiaan Huygens independently discovered the three stars in 1656 and the fourth member, Theta-1 Orionis B, was discovered by the French astronomer Jean Picard in 1673, completing the Trapezium. Huygens himself observed the fourth component in 1684.


Theta1 Orionis (θ1 Ori) - is the Trapezium and one of the finest multiple stars in the sky. Located at the heart of the Orion Nebula, a small 80mm (3.1-inch) telescope scope easily splits the main components. The brightest four stars are of magnitudes +5.1(C), +6.7(D), +6.7->7.7(A) and +8.0->8.7(B).



The four stars that form the trapezium asterism are designated A, B, C, and D. The brightest and most massive of these, Theta-1 Orionis C, has a visual magnitude of 5.13 and the stellar classification O6pe V. With an absolute magnitude of -3.2, the star is 251,000 times more luminous than the Sun and one of the most luminous stars known. In an infrared survey, the star was revealed to be a close binary system exhibiting optical variability. It is one of the nearest O-type stars to the solar system.






trapezium cluster,orion nebula cluster

Trapezium Cluster stars. Image: NASA, K. Luhmann, J. Barkmann

Components A and B have been identified as Algol-type eclipsing binaries, double stars that orbit and eclipse each other when observed from Earth. Theta-1 Orionis A, also known as V1016 Orionis, varies between magnitudes 6.73 and 7.53 every 65.4325 days, and Theta-1 Orionis B, or BM Orionis, varies between magnitudes 7.95 and 8.52 with a period of 6.4705 days. Component B is the faintest of the four stars that form the Trapezium.



SYRACUSE, N.Y. — Washer-extractors come in four general types with specific sizes within each category. These are the open pocket, the top side loader, the tilting side loader and the end loader.


There are a number of features that are common to all four types. All are typically controlled by some type of microprocessor, with many now using touch screens to enhance the ease of programming. Also, all use either a suspension made up of coil springs and shocks or one that utilizes air bags, and most are inverter-driven.



L'Ocean Caviar Four-Piece Skin Care Set Day & Night Cream Eye & Facial Serum




DI Chamaeleontis, also known as Hen 3-593 or HIP 54365, is a quadruple star system in the constellation Chamaeleon. The system is roughly 700 light years from Earth.



Reveal skin that looks exquisitely luminous and help reduce the appearance of dark spots. This four-piece set helps visibly reduce blue and brown dark under-eye circles over time for a youthful look. Skin feels fully hydrated and is more receptive to additional brightening treatments for dramatic brilliance and luminosity.



After planets, circumstellar disks are one of the most commonly observed properties of planetary systems, particularly of young stars. The Solar System possesses at least four major circumstellar disks (the asteroid belt, Kuiper belt, scattered disc, and Oort cloud)



Around the Solar System[edit]


Artist's impression of a transitional disc around a young star.[3]

Asteroid belt is a reservoir of small bodies in the Solar System located between the orbit of Mars and Jupiter. It is a source of interplanetary dust.

Edgeworth-Kuiper belt, beyond the orbit of Neptune

Scattered disc, beyond the orbit of Neptune

Hills cloud; only the inner Oort cloud has a toroid-like shape. The outer Oort cloud is more spherical in shape, making it a circumstellar envelope.



Epsilon Eridani has been known to astronomers since at least the 2nd century AD, when Claudius Ptolemy (a Greek astronomer from Alexandria, Egypt) included it in his catalogue of more than a thousand stars. The catalogue was published as part of his astronomical treatise the Almagest. The constellation Eridanus was named by Ptolemy (Ancient Greek: Ποταμού, English: River), and Epsilon Eridani was listed as its thirteenth star. Ptolemy called Epsilon Eridani ό τών δ προηγούμενος, Greek for a foregoing of the four (here δ is the number four). This refers to a group of four stars in Eridanus: γ, π, δ and ε (10th–13th in Ptolemy's list). ε is the most western of these, and thus the first of the four in the apparent daily motion of the sky from east to west. Modern scholars of Ptolemy's catalogue designate its entry as "P 784" (in order of appearance) and "Eri 13". Ptolemy described the star's magnitude as 3.[37][38]



Jupiter is known to have 4 sets of rings: the halo ring, the main ring, the Amalthea gossamer ring, and the Thebe gossamer ring.



In 1598 Epsilon Eridani was included in Tycho Brahe's star catalogue, republished in 1627 by Johannes Kepler as part of his Rudolphine Tables. This catalogue was based on Tycho Brahe's observations of 1577–1597, including those on the island of Hven at his observatories of Uraniborg and Stjerneborg. The sequence number of Epsilon Eridani in the constellation Eridanus was 10, and it was designated Quae omnes quatuor antecedit, Latin for which precedes all four; the meaning is the same as Ptolemy's description. Brahe assigned it magnitude 3.[37][40]



Hyperion Cantos by Dan Simmons, a cycle of four books, where the Epsilon Eridani system contains a planet colonized by humans.



Attenuation: Letters from the Man in the Moon (2014) by Keith Basham, where Epsilon Eridani is the target of a half million years of attempts at colonization, while a lone pilot known only as 'Larry' goes about the business of fast-tracking the system's accretion process, rendering habitable worlds and a more Sol-like star from Epsilon Eridani. Larry does his best to keep in touch with his home world, but finds that his very existence has been long forgotten, though the star itself has been rechristened in his name. By the time he is done, There are apparently four Earth-like planets constructed in the habitable zone, with one working colony overseen by Larry himself, whose ship serves as that planet's moon.




"The Boyfriend Complexity" (2010), an episode of The Big Bang Theory, a situation comedy created by Chuck Lorre and Bill Prady, and directed by Mark Cendrowski. The series, embellished by wacky faux-scientific episode titles, concerns the eccentric doings of four hyperintelligent but socially inept scientists and their street-smart neighbor, a blonde waitress and aspiring actress. In this episode (S4:E9), Rajesh Koothrappali is remotely controlling a telescope in Hawaii, watching for varying luminosity as evidence of an extrasolar planet orbiting the star.[25]



Tau Ceti e is an unconfirmed, fourth-known planet orbiting Tau Ceti that was detected by statistical analyses of the data of the star's variations in radial velocity that were obtained using HIRES, AAPS, and HARPS.[6] Few properties of the planet are known other than its orbit and mass. It orbits at a distance of 0.552 AU (between the orbits of Venus and Mercury in the Solar System) with an orbital period of 168 days and has a minimum mass of 4.3 Earth masses. Because the minimum mass of a super-Earth is 5 Earth masses,[54] Tau Ceti e may be Earth sized. If it possesses an Earth-like atmosphere, the surface temperature would be around 68 °C (154 °F).[55]


Quarta Sthrutionum (the fourth of the ostriches


Main propulsion comprises 24 paired bipropellant 10 N thrusters,[52] with four pairs of thrusters being used for delta-v burns. The spacecraft carried 1,719.1 kg (3,790 lb) of propellant at launch: 659.6 kg (1,454 lb) of monomethylhydrazine fuel and 1,059.5 kg (2,336 lb) of dinitrogen tetroxide oxidiser, contained in two 1,108-litre (244 imp gal; 293 US gal) grade 5 titanium alloy tanks and providing delta-v of at least 2,300 metres per second (7,500 ft/s) over the course of the mission. Propellant pressurisation is provided by two 68-litre (15 imp gal; 18 US gal) high-pressure helium tanks.[56]


In addition to its scientific mission, it is the main source of near-real-time solar data for space weather prediction. Along with the GGS Wind, Advanced Composition Explorer (ACE) and DSCOVR, SOHO is one of four spacecraft in the vicinity of the Earth–Sun L1 point, a point of gravitational balance located approximately 0.99 astronomical unit (AU)s from the Sun and 0.01 AU from the Earth. In addition to its scientific contributions, SOHO is distinguished by being the first three-axis-stabilized spacecraft to use its reaction wheels as a kind of virtual gyroscope; the technique was adopted after an on-board emergency in 1998 that nearly resulted in the loss of the spacecraft.



The spacecraft is roughly cylindrical in shape, and has four major components. At the fore of the spacecraft is the Mirror Support Platform, which supports the X-ray telescope assemblies and grating systems, the Optical Monitor, and two star trackers. Surrounding this component is the Service Module, which carries various spacecraft support systems: computer and electric busses, consumables (such as fuel and coolant), solar arrays, the Telescope Sun Shield, and two S-band antennas. Behind these units is the Telescope Tube, a 6.8-metre (22 ft) long, hollow carbon fibre structure which provides exact spacing between the mirrors and their detection equipment. This section also hosts outgassing equipment on its exterior, which helps remove any contaminants from the interior of the satellite. At the aft end of spacecraft is the Focal Plane Assembly, which supports the Focal Plane Platform (carrying the cameras and spectrometers) and the data-handling, power distribution, and radiator assemblies.[32]



The Kepler-223 system contains four planets in an 8:6:4:3 orbital resonance.



November 24 Four-point observations of solar wind discontinuities[96]


November 24 Four-point observations of solar wind discontinuities[96]


Cluster's four-point measurements make it possible to track the motion of the magnetopause as well as elucidate the mechanism for plasma penetration from the solar wind




As part of the European Space Agency's media campaign in support of the Rosetta mission, both the Rosetta and Philae spacecraft were given anthropomorphic personalities in an animated web series titled Once upon a time.... The series depicts various stages in the Rosetta mission, involving the personified Rosetta and Philae on "a classic road trip story into the depths of our universe", complimented with various visual gags presented in an educational context.[172] Produced by animation studio Design & Data GmbH, the series was initially conceived by the ESA as a four-part fantasy-like series with a Sleeping Beauty theme that promoted community involvement in Rosetta's wake up from hibernation in January 2014. After the success of the series, however, the ESA commissioned the studio to continue producing new episodes in the series throughout the course of the mission.[172] A total of twelve videos in the series were produced from 2013 to 2016, with a 25-minute compilation of the series released in December 2016, after the end of the mission.[173] The characters featured in Once upon a time..., designed by ESA employee and cartoonist Carlo Palazzari, became a central part of public image of the Rosetta mission, appearing in promotional material for the mission such as posters and merchandise,[174] and often credited as a major factor in the popularity of the mission among the public.[172][175] ESA employees also role-played as the characters on Twitter throughout the course of the mission.[174][176]


A series of four Go/NoGo checks were performed on 11–12 November 2014. One of the final tests before detachment from Rosetta showed that the lander's cold-gas thruster was not working correctly, but the "Go" was given anyway, as it could not be repaired.[31][32] Philae detached from Rosetta on 12 November 2014 at 08:35 UTC SCET.[33][34]


The Sampling, Drilling and Distribution system obtains soil samples from the comet and transfers them to the Ptolemy, COSAC, and CIVA instruments for in-situ analysis.[103] SD2 contains four primary subsystems: drill, ovens, carousel, and volume checker.[104



The Juno II was a four-stage rocket derived from the Jupiter IRBM. It was used for 10 satellite launches, six of which failed. It launched Pioneer 3, Pioneer 4, Explorer 7, Explorer 8, and Explorer 11.



At 12:10 AM EST on the night of March 2-3, Pioneer 4 lifted from LC-5. This time, the booster performed almost perfectly so that Pioneer 4 achieved its primary objective (an Earth-Moon trajectory), returned radiation data and provided a valuable tracking exercise. A slightly longer than nominal second stage burn however was enough to induce small trajectory and velocity errors, so that the probe passed within 60,000 km of the Moon's surface (7.2° E, 5.7° S) on 4 March 1959 at 22:25 UT (5:25 p.m. EST) at a speed of 7,230 km/h and was not able to impact as planned. The distance was also not close enough to trigger the photoelectric sensor. The probe continued transmitting radiation data for 82.5 hours, to a distance of 409,000 miles (658,000 km),[3] and reached perihelion on 18 March 1959 at 01:00 UT. The cylindrical fourth stage casing (173 cm long, 15 cm diameter, 4.65 kg) went into orbit with the probe. The communication system had worked well, and it was estimated that signals could have been received out to 680,000 miles (1 million kilometers) had there been enough battery power.



The Bell Boeing Quad TiltRotor (QTR) is a proposed four-rotor derivative of the Bell Boeing V-22 Osprey tiltrotor developed jointly by Bell Helicopter and Boeing. The concept is a contender in the U.S. Army's Joint Heavy Lift program. It would have a cargo capacity roughly equivalent to the C-130 Hercules, cruise at 250 knots, and land at unimproved sites vertically like a helicopter.[1]


The primary test objective was to study the aeroelastic effects on the aft wing of the forward wing's rotors and establish a baseline aircraft configuration.[1] Alan Ewing, Bell's QTR program manager, reported that "Testing showed those loads from that vortex on the rear rotor [are the] same as the loads we see on the front [rotors]," and "Aeroelastic stability of the wing looks exactly the same as the conventional tiltrotor". These tests used a model with a three-bladed rotor, future tests will explore the effects of using a four-bladed system.[9]


The conceptual design is for a large tandem wing aircraft with V-22 type engines and 50-foot (15 m) rotors at each of the four wing tips. The C-130-size fuselage would have a 747-inch (19.0 m) cargo bay with a rear loading ramp that could carry 110 paratroopers or 150 standard-seating passengers. In cargo configuration, it would accommodate eight 463L pallets.[9]







Cross Quattro - 4-line kite - The real powerkiting

The Cross Quattro has the same superb price quality ratio as the other kites in the range. The Cross Quattro is a user-friendly and stable kite, ideal for the starting powerkiter who wants to learn kiting with four lines. The kite generates a lot of pull which every powerkiter will enjoy, even after many exciting sessions and plenty of adrenaline rushes. The Cross Quattro is Ready-2-Fly.

Cross Quattro:

• Four-line foil kite

• Includes: lines, handles, kitekillers, manual and bag


• Size 1.5: Blue

• Size 2.5: Red

• Size 3.5: Green

• Size 4.5: Blue


Revolution kite or Rev kites

(four-line revolution stunt kites by Joe Hadzicki)[103][286][287][288][289]


Octagonal kites

Four-stick octagonal kites exist; collapsible eight-stick kites that pop up like a common umbrella have been registered in patents. A fine-art example of an eight-sided regular octagonal kite is illustrated.[262] Stop-sign and octagonal box kites are other examples.[263][264]

Tukkal or Tukal kites

Special four-stick kite[363]



Lawrence Hargrave invented his box kite in 1885, and on 12 November 1894, lifted himself from the beach in Stanwell Park, New South Wales using a four box kite rig, attached to the ground by piano wire. Using this rig he lifted himself 16 feet (4.9 m) above the ground, despite the combined weight of his body and the rig being 208 lb (94.5 kg).



A critical question could be: where is the empirical evidence of an understandable relationship between worldviews and scenarios? In the First Sustainability Outlook (MNP, 2004), a group of experts constructed coherent narratives with images for the four corners in the IPCC-SRES framework. To test the coherence and interpretation of the narratives, people were asked, during a series of interviews and a panel survey, to indicate the probability of certain consequences in the ecological, economic and social-cultural domain and their preferred narrative. The directions of the correlations between what people value (cf. Fig. 2) and their interpretation and preference for a particular world narrative, were as expected, but weak (Aalbers, 2006). For instance, Luxury seekers and Business people are in the A1 corner, whereas the Broad thinkers and Engaged people are nearer to the B1 corner (Fig. 5). Of course, many questions remain for future research.



Ohms Law Formula Wheel

Use the Ohms law formula wheel below for all the mathematical relationships between P, I, V and R.


Ohm's Law and Formulas

Ohm's Law [after physicist Georg Ohm] states that: In an electrical circuit, the current which passes through a conductor between two points is proportional to the potential difference (i.e. voltage drop or voltage) across the two points, and inversely proportional to the resistance between the two point. In mathematical terms, this is expressed as:

I=V/R or V=IR

where I is the current in amperes, V is the potential difference (voltage drop or voltage) in volts, and R is the resistance which is measured in ohms.

The instantaneous electrical power P delivered to a component is the product of voltage and current, which may be expressed in mathematical terms as:


where P is the instantaneous power in watts (joules per second or volt-amperes). The terms I, R and V are as described above.




Electronic amplifiers use current or voltage as input and output, so four types of amplifier are possible (any of two possible inputs with any of two possible outputs). See classification of amplifiers. The objective for the feedback amplifier may be any one of the four types of amplifier and is not necessarily the same type as the open-loop amplifier, which itself may be any one of these types. So, for example, an op amp (voltage amplifier) can be arranged to make a current amplifier instead.


Negative-feedback amplifiers of any type can be implemented using combinations of two-port networks. There are four types of two-port network, and the type of amplifier desired dictates the choice of two-ports and the selection of one of the four different connection topologies shown in the diagram. These connections are usually referred to as series or shunt (parallel) connections.[27][28] In the diagram, the left column shows shunt inputs; the right column shows series inputs. The top row shows series outputs; the bottom row shows shunt outputs. The various combinations of connections and two-ports are listed in the table below.




Crosshair is the G.I. Joe Team's infiltrator and marksmanship instructor. His real name is Don G. Fardie, and he was first released as an action figure in 2003.[39] He can blend into his surroundings so completely that the enemy can't see him. He uses this talent to study his targets and predict where they are going to move.



Crosshairs Truck The Rebirth (Part 1) The Rebirth (Part 3) Neil Ross Alive

Meticulous, cautious, some would say overcautious—won't take a shot unless he's sure he can't miss... won't waste ammo. Pinpointer, his dual rocket-propelled grenade launcher, can lock on target in less than .0003 seconds, but usually trusts Crosshairs to decide when to shoot. In vehicle mode, maximum speed: 160 mph, range: 750 miles; built for traversing rough terrain.



The Nyaya–Vaisesika school developed one of the earliest forms of atomism; scholars date the Nyaya and Vaisesika texts from the 6th to 1st centuries BC. Like the Buddhist atomists, the Vaisesika had a pseudo-Aristotelian theory of atomism. They posited the four elemental atom types, but in Vaisesika physics atoms had 24 different possible qualities, divided between general extensive properties and specific (intensive) properties



The Buddhist atomists had very qualitative, Aristotelian-style atomic theory. According to ancient Buddhist atomism, which probably began developing before the 4th century BC, there are four kinds of atoms, corresponding to the standard elements. Each of these elements has a specific property, such as solidity or motion, and performs a specific function in mixtures, such as providing support or causing growth. Like the Hindu Jains, the Buddhists were able to integrate a theory of atomism with their theological presuppositions. Later Indian Buddhist philosophers, such as Dharmakirti and Dignāga, considered atoms to be point-sized, durationless, and made of energy.



Buddhist atomism is a school of atomistic Buddhist philosophy that flourished on the Indian subcontinent during two major periods[citation needed]. During the first phase, which began to develop prior to the 4th century BCE, Buddhist atomism had a very qualitative, Aristotelian-style atomic theory. This form of atomism identifies four kinds of atoms, corresponding to the standard elements. Each of these elements has a specific property, such as solidity or motion, and performs a specific function in mixtures, such as providing support or causing growth. Like the Hindus and Jains, the Buddhists were able to integrate a theory of atomism with their logical presuppositions.



The Smithsonian Institution has in its collection a clockwork monk, about 15 in (380 mm) high, possibly dating as early as 1560. The monk is driven by a key-wound spring and walks the path of a square, striking his chest with his right arm, while raising and lowering a small wooden cross and rosary in his left hand, turning and nodding his head, rolling his eyes, and mouthing silent obsequies. From time to time, he brings the cross to his lips and kisses it. It is believed that the monk was manufactured by Juanelo Turriano, mechanician to the Holy Roman Emperor Charles V.[29]

The vee or quadrant antenna is a horizontal dipole with its arms at an angle instead of parallel. Quadrant antennas are notable in that they can be used to make horizontally polarized antennas with near-omnidirectional radiation patterns. They are used for transmitting on the HF band.



Power sum near end crosstalk (PSNEXT)

PSNEXT is a NEXT measurement which includes the sum of crosstalk contributions of all adjacent pairs.[1] It is the algebraic sum of near-end crosstalk (NEXT) of three wire pairs as they affect the fourth pair in a four-pair cable (e.g., Category 6 cable). The specification was developed to directly address the effect of transmissions on multiple adjacent pairs on the pair being tested and is relevant to all connecting hardware and associated communications cables.[2]

Cabling bandwidths in excess of 100 MHz (Category 5 cable bandwidth) make consideration of PSNEXT more important. Gigabit Ethernet through Cat-6 uses all four wire pairs simultaneously and bidirectionally. The additional wire pair usage and growing bandwidth increase the need to keep NEXT in check.

PSNEXT is a way of measuring NEXT in the ends of cables due to their close proximity. The (cited) SMP white paper states that the testing process for PSNEXT consists of measuring all pair-to-pair crosstalk combinations and then summing all of the values for each pair.





HAARP, a phased array of 180 crossed dipoles in Alaska which can transmit a 3.6 MW beam of 3 - 10 MHz radio waves into the ionosphere for research purposes



Array of four helical antennas used as a satellite tracking-acquisition antenna, Pleumeur-Bodou, France




A Nakajima J1N1-S night fighter with quadruple Yagi radar transceiver antennas



The Yagi–Uda antenna consists of a number of parallel thin rod elements in a line, usually half-wave long, typically supported on a perpendicular crossbar or "boom" along their centers





The functioning of the radar is completely automatic, controlled by four computers. The software divides the beam time between "surveillance" and "tracking" functions, switching the beam back and forth rapidly between different tasks. In the surveillance mode, which normally consumes about 11% of the duty cycle, the radar repeatedly scans the horizon across its full 240° azimuth in a pattern between 3° and 10° elevation, creating a "surveillance fence" to immediately detect missiles as they rise above the horizon into the radar's field of view. In the tracking mode, which normally consumes the other 7% of the 18% duty cycle, the radar beam follows already-detected objects to determine their trajectory, calculating their launch and target points.


The Stanley R. Mickelsen Safeguard Complex with North Dakota phased arrays (four-face Missile Site Radar and single-face GE Perimeter Acquisition Radar, PAR) became operational in 1975 as part of the Safeguard Program for defending against enemy ballistic missiles.


The "first radio frequency transmission" from the West Coast Site was 23 March 1979[30] (it was completed in October 1979).[9] "ADCOM wanted four [PAVE PAWS] sites, but by the end of 1979 only two had been funded".[5]



A close up of the face of the phased array radar in Cape Cod.

The Cape Cod system reached Initial operating capability (IOC) as the Cape Cod Missile Early Warning Station on 4 April 1981 with initial operational test and evaluation (IOT&E) completed 21 May;[5] Beale AFB reached IOC on 15 August.[1] The two PAVE PAWS, three BMEWS, and the PARCS & FPS-85 radar stations transferred to Strategic Air Command (then Space Command) in 1983.[25] By 1981 Cheyenne Mountain was providing 6,700 messages per hour[47] including those based on input from the PAVE PAWS and the remaining FSS-7 stations.[48] In 1981, as part of the Worldwide Military Command and Control System Information System (WIS), the Pentagon's National Military Command Center was receiving data "directly from the Satellite Early Warning System (SEWS) and directly from the PAVE PAWS sensor systems".[48]


Beam Steering Unit (BSU) and Receiver Beam Former (REX) replacements were made on the four Cape Cod and Beale radars in the 1980s.[49]



The complex was centered on the Missile Site Radar (MSR) site, near to Nekoma, North Dakota, home to the Missile Site Radar itself, as well as the 30 Spartan missiles and 16 of the shorter-range Sprints. All missiles were held in underground launch silos.


The remaining Sprint missiles were distributed at four Remote Sprint Launchers at distances of ten to twenty miles from the Missile Site Radar. These were located at:


RSL 1 48°32′00.24″N 98°34′58.81″W

RSL 2 48°50′58.03″N 98°25′55.84″W

RSL 3 48°45′52.63″N 97°59′9.92″W

RSL 4 48°28′30.91″N 98°15′23.02″W



The de Bothezat helicopter, also known as the Jerome-de Bothezat Flying Octopus,[2] was an experimental quadrotor helicopter built for the United States Army Air Service by George de Bothezat in the early 1920s, and was said at the time to be the first successful helicopter. Although its four massive six-bladed rotors allowed the craft to successfully fly, it suffered from complexity, control difficulties, and high pilot workload, and was reportedly only capable of forward flight in a favorable wind. The Army canceled the program in 1924, and the aircraft was scrapped.



The WGM.21 is an open cockpit quadrotor. Four rotors are mounted at the end of a four tubular supports arranged into a X shape. Cyclic and collective controls are mixed into a single control yoke. Pitch is controlled by foot pedals. A second model, the WGM.22, was developed with side-by-side configuration seating and an enclosed cockpit.[1]



AeroVelo, a team of students and graduates of the University of Toronto, began flight testing its Atlas quad rotor HPH on 28 August 2012.[1] The core team of AeroVelo is the same group that created Snowbird, the first successful human-powered ornithopter.[2] The Atlas is the largest HPH ever flown,[3] and has a tip-to-tip rotor span of 154 ft (47 m), second only to the Russian Mil V-12.[4][5][6][7]



The Scout is a quadcopter in layout, with four rotors mounted on booms and four landing gear legs. Payloads are mounted underneath the fuselage on a gimbal mount.[2]



The Curtiss-Wright VZ-7 (also known as the VZ-7AP[1]) was a VTOL quadrotor helicopter aircraft designed by the Curtiss-Wright company for the US Army. Like the Chrysler VZ-6 and the VZ-8 Airgeep it was to be a "flying jeep" .


The VZ-7 had a fuselage with the pilot's seat, fuel tanks and flight controls. On both sides of the fuselage the propellers were attached, unshrouded (the aircraft did originally have shrouds, but these were later removed). There were four propellers in total. The VZ-7 was controlled by changing the thrust of each propeller. The flying platform was maneuverable and easy to fly.




Phantom 1[edit]

The Phantom 1, originally known as Phantom, was released in January 2013. It was commonly equipped with a GoPro camera for amateur filmmaking or photography. Its battery life was around 15 minutes with a GoPro.



The Phantom 1

Phantom 2[edit]


The Phantom 2


The Phantom 2 Vision

The Phantom 2 was released in December 2013. Upgrades include auto-return, increased flight speed, increased flight time and controllable range, increased battery capacity, smartphones, tablets and even some smart glasses compatibility, Wi-Fi module and is available in different performances. Its configuration allows users to remotely tilt the camera and adjust its orientation on two axes for a better level shot.[9]



Released in April 2014,[10] it features a 4 GB micro SD card, a built-in anti-vibration mount, advanced Wi-Fi module, a GPS-enabled position holding, return-to-home capability, an improved flight control system, self-tightening propellers and flight time. It is compatible with a ground station and iOS or Android devices.




The Phantom 2 Vision+

The Vision+, released in July 2014, added a three-axis stabilizer. It has a new control system and increased range.[11] It received a no-fly zone software-implanted, warning the user of places where not to fly. (ex. airports).




The Phantom FC40

The Phantom FC40, released in January 2014, is an intermediate model between the Phantom 1 and the Phantom 2. Like the Phantom 2 Vision and the Phantom 2 Vision+, it is equipped with an iOS/Android app control, Wi-Fi and GPS modules. Using a 2.4 GHz Wi-Fi connection, it helps its pilot follow in real time via aerial pictures on a mobile device. The camera angle is manually set before the flight and tilted by remote control.


Phantom 3[edit]

The Phantom 3, released in April 2015,[12] adds built-in lightbridge downlink, that gives the controller a maximum range of 2,000 meters (1.25 miles), and the visual positioning system, that allows the Phantom 3 to better maintain its position at lower altitudes and even indoors where GPS is weak or unavailable.


The controller features a plastic front plate and lacks an HDMI out.


There are four models of the Phantom 3:



Records in 4K, and includes a 100 W fast charger.



Records in 2.7K and includes a 57 W charger.



The Standard was released in August 2015. Currently, it is the cheapest and features 2.7K video recording. The standard is the basic model without lightbridge, with a limited range compared to the Advanced and Professional models, and no vision positioning systems. It includes features, as the other models do, such as Point of Interest, Follow Me, GPS Waypoints, Course Lock and Home Lock. It remains the only Phantom 3 manufactured by DJI.[1]



The 4K was released in early 2016. It's almost the same as the Standard but has a 4K camera, vision positioning system, and a more advanced controller.


Phantom 4[edit]

The Phantom 4, released in March 2016,[13] improves usability by adding obstacle avoidance and an ability to track movement, thanks to its many sensors. Some of its features include GPS, GLONASS, sonar, five separate safety sensors, a camera gimbal, gyroscope, and more. It is slightly bigger and heavier than the Phantom 3 due to a larger battery, but it still maintains a longer flight time and greater top speed. It has a top speed of 20 m/s in 'sport mode'.


The controller and camera are very similar to the 3's.


The maximum video transmission range on the Phantom 4 is 5 km.[14]


On April 13, DJI announced the end of the Phantom 4's lifespan span for April 30, 2017.[15]




The Piasecki PA-97 Helistat was an American experimental heavy-lift aircraft, built by Piasecki by fastening four H-34J helicopters to a framework beneath a helium-inflated blimp envelope.[1] It crashed during a test flight, killing one of the four pilots.


The PA-97 was built under a 1980 U.S. Navy contract for the Forest Service to demonstrate a heavy vertical airlifter for harvesting timber from inaccessible terrain. The single demonstrator used a retired Navy ZPG-2W blimp envelope and four H-34J helicopters. The combination of a large blimp with powered lift made the 343 foot (104.57 m) long helistat the largest dynamic lift aircraft in the world.[1]


The helicopters used were aged examples of a long-established design. Their tail rotors were removed, their fuselages shortened and they were attached to a crude tubular aluminum framework beneath the helium-filled envelope. Four freely-castering twin-wheel bogies beneath the framework provided the undercarriage. Criticism has been expressed of the structural qualities and stress analysis of this framework.[2]



According to company spokespeople, the aircraft will combine the best features of a blimp and a helicopter, and will be capable of carrying a 40 ton load up to 200 miles (320 km) without refueling. At 302 feet (92 m) long, it will classify as the largest helicopter in the world, and will be capable of flying up to 800 miles (1,300 km) without a load.[4] The craft will use helium to provide enough lift to carry its own weight, and will use four helicopter rotors to lift the load and to propel the aircraft.[3] By using both helium and helicopter rotors, the aircraft can avoid having to jettison helium after unloading.[1]



Three-blade props offer a nice compromise when it comes acceleration, efficiency, lift and speed. A four-blade propeller, on the other hand, can boost acceleration, efficiency or lift, but at the cost of a lower top speed.


Most outboards — 90 percent by some estimates — are equipped with three-blade propellers, and most offer strong performance. Yet can you expect better performance from a four-blade prop? The answer is yes — and no — according to experts from some of the major outboard brands.


Three-blade propellers are popular because they tend to offer a performance compromise, a pleasing (or at least satisfactory) blend of acceleration, fuel efficiency, lift and speed, says David Meeler, marine product information manager for Yamaha Outboards.

But if you want to improve acceleration, fuel efficiency or lift, a four-blade might help, Meeler says. “Just be aware that performance gains in one area can mean performance losses in another,” he adds. “It’s all about what’s most ­important to you.”


Decide which performance attributes you desire most. The captain of a flats boat, for example, might want to pop up on plane more quickly, and add lift for running in very shallow water. “Often, a four-blade propeller is the ticket,” says Meeler. “The additional blade area grips the water better, allowing for quicker acceleration.”



Three-blade props offer a nice compromise when it comes acceleration, efficiency, lift and speed. A four-blade propeller, on the other hand, can boost acceleration, efficiency or lift, but at the cost of a lower top speed.


Most outboards — 90 percent by some estimates — are equipped with three-blade propellers, and most offer strong performance. Yet can you expect better performance from a four-blade prop? The answer is yes — and no — according to experts from some of the major outboard brands.


Three-blade propellers are popular because they tend to offer a performance compromise, a pleasing (or at least satisfactory) blend of acceleration, fuel efficiency, lift and speed, says David Meeler, marine product information manager for Yamaha Outboards.

But if you want to improve acceleration, fuel efficiency or lift, a four-blade might help, Meeler says. “Just be aware that performance gains in one area can mean performance losses in another,” he adds. “It’s all about what’s most ­important to you.”


Decide which performance attributes you desire most. The captain of a flats boat, for example, might want to pop up on plane more quickly, and add lift for running in very shallow water. “Often, a four-blade propeller is the ticket,” says Meeler. “The additional blade area grips the water better, allowing for quicker acceleration.”


I have heard that propellers with more than four blades are not as efficient as 4 or less blades because of lower thrust which may result from interfering prop-streams. But I see the ATR-42/72 and they have 6 blades. What is the reasoning and the advantages to that prop layout?

FOUR BLADED V THREE (other blades)


In Denmark by 1900, there were about 2500 windmills for mechanical loads such as pumps and mills, producing an estimated combined peak power of about 30 MW. The largest machines were on 24-meter (79 ft) towers with four-bladed 23-meter (75 ft) diameter rotors. By 1908 there were 72 wind-driven electric generators operating in the United States from 5 kW to 25 kW. Around the time of World War I, American windmill makers were producing 100,000 farm windmills each year, mostly for water-pumping.[9]



Rotor efficiency does increase very slightly if four blades are used, rather than three, but the rotor weight would increase and the rotational speed at which peak power would be delivered would drop.







South Africa's Kaapvaal craton and Western Australia's Pilbara craton have similar early Precambrian cover sequences.[13] Kaapvaal's Barberton granite-greenstone terrane and Pilbara's eastern block show evidence of four large meteorite impacts between 3.2 and 3.5 billion years ago.[14] (Similar greenstone belts are now found at the margins of the Superior craton of Canada.)[15]


In 2009 UNESCO's IGCP project 440, named 'Rodinia Assembly and Breakup', concluded that Rodinia broke up in four stages between 825–550 Ma:[19]


The break up was initiated by a superplume around 825–800 Ma whose influence—such as crustal arching, intense bimodal magmatism, and accumulation of thick rift-type sedimentary successions—have been recorded in South Australia, South China, Tarim, Kalahari, India, and the Arabian-Nubian Craton.

Rifting progressed in the same cratons 800–750 Ma and spread into Laurentia and perhaps Siberia. India (including Madagascar) and the Congo-Säo Francisco Craton were either detached from Rodinia during this period or simply never were part of the supercontinent.

As the central part of Rodinia reached the Equator around 750–700 Ma, a new pulse of magmatism and rifting continued the disassembly in western Kalahari, West Australia, South China, Tarim, and most margins of Laurentia.

650–550 Ma several events coincided: the opening of the Iapetus Ocean; the closure of the Braziliano, Adamastor, and Mozambique oceans; and the Pan-African orogeny. The result was the formation of Gondwana.



The solar seasons change at the cross-quarter days, which are about 3–4 weeks earlier than the meteorological seasons and 6–7 weeks earlier than seasons starting at equinoxes and solstices. Thus, the day of greatest insolation is designated "midsummer" as noted in William Shakespeare's play A Midsummer Night's Dream, which is set on the summer solstice. On the Celtic calendar, the traditional first day of winter is 1 November (Samhain, the Celtic origin of Halloween); spring starts 1 February (Imbolc, the Celtic origin of Groundhog Day); summer begins 1 May (Beltane, the Celtic origin of May Day); the first day of autumn is 1 August (Celtic Lughnasadh). The Celtic dates corresponded to four Pagan agricultural festivals.


The traditional calendar in China forms the basis of other such systems in East Asia. Its seasons are traditionally based on 24 periods known as solar terms.[16] The four seasons chūn (春), xià (夏), qiū (秋), and dōng (冬) are universally translated as "spring", "summer", "autumn", and "winter" but actually begin much earlier, with the solstices and equinoxes forming the midpoint of each season rather than their start. Astronomically, the seasons are said to begin on Lichun (立春, lit. "standing spring") on about 4 February, Lixia (立夏) on about 6 May, Liqiu (立秋) on about 8 August, and Lidong (立冬) on about 7 November. These dates were not part of the traditional lunar calendar, however, and moveable holidays such as Chinese New Year and the Mid-Autumn Festival are more closely associated with the seasons.



The Wheel of the Year is an annual cycle of seasonal festivals, observed by many modern Pagans. It consists of either four or eight festivals: either the solstices and equinoxes, known as the "quarter days", or the four midpoints between, known as the "cross quarter days"; syncretic traditions like Wicca often celebrate all eight festivals.


Midsummer is one of the four solar holidays, and is considered the turning point at which summer reaches its height and the sun shines longest. Among the Wiccan sabbats, Midsummer is preceded by Beltane, and followed by Lammas or Lughnasadh.


Samhain (/ˈsɑːwɪn/ SOW-in) is considered by Wiccans to be one of the four Greater Sabbats. Samhain is considered by some as a time to celebrate the lives of those who have passed on, and it often involves paying respect to ancestors, family members, elders of the faith, friends, pets, and other loved ones who have died. In some rituals the spirits of the departed are invited to attend the festivities. It is seen as a festival of darkness, which is balanced at the opposite point of the wheel by the festival of Beltane, which is celebrated as a festival of light and fertility.[24]



One of the major hazards associated with firefighting operations is the toxic environment created by combustible materials, the four major risks are smoke, oxygen deficiency, elevated temperatures, and poisonous atmospheres.[3] Additional hazards include falls and structural collapse that can exacerbate the problems entailed in a toxic environment. To combat some of these risks, firefighters carry self-contained breathing equipment.


One of the major hazards associated with firefighting operations is the toxic environment created by combusting materials. The four major hazards are:[14]


Smoke, which is becoming increasingly dangerous due to the increased variety and amount of synthetic household materials.

Oxygen deficient atmosphere, 21% O2 is normal, 19.5% O2 is considered oxygen deficient.

Elevated temperatures

Toxic atmospheres


There are four elements[19] needed to start and sustain a fire and/or flame. These are a reducing agent (fuel), Heat, an oxidizing agent (oxygen), and a chemical reaction. A fire can be extinguished by taking away any of the four components.[19]


Hamburg after four fire-bombing raids in July 1943, which killed an estimated 50,000 people[22]



The fourfold operator

The fourfold operator applies to analysis, concepts, forms. Consisting of two dichotomies that are mutually orthogonal, or independent, it tells us that in any situation that can be dichotomized, or divided into two opposite aspects, there must exist a second dichotomy which mediates or measures the first.

Consider the old story of Solomon and the two women. Both claimed possession of the baby, so Solomon proposed that the baby be cut in two and each woman given half. One woman agreed. The other said no: she would rather give up possession of the baby and have it live. Solomon recognized the latter as the true mother and gave her the baby.

What happened? Solomon split the dichotomy of possession by introducing an independent dichotomy: the being of the baby as opposed to its nonbeing. Under this scrutiny, like that of a painting under x-ray, the false mother was revealed.


Problem: A married couple quarrels. The wife wants to go into a field, the husband insists that she must not because there is a dangerous bull in the field. The wife says the bull is not dangerous.

If we recognize that the situation contains two issues, safety and obedience, we can combine them differently: We ask the wife if she would obey her husband if the bull were really dangerous. She says no. We ask the husband if he would insist on the wife's obedience even if the bull were not dangerous. He says yes. Obviously, the couple is arguing about obedience, not about the bull.

Generally speaking, we try to discover two independent issues between the two parties. We describe the claims of the two parties in two opposite word pairs.

Once this is done, the rest is easy. We take the two word pairs and cross-product them. Recall the learning cycle in which the infant reaches out and touches things (an example which dealt with kinds of action). In that case, we were able to describe step 1 as unconscious action and step 3 as conscious reaction (both words opposite). The other pair then become (2) unconscious reaction and (4) conscious action.

The same principle can be applied to kinds of relation, or kinds of "things." Take, for example, the contributing factors in a clock (relating them to Aristotle's causes):

Factors                                                                    Aristotle

A clock's function, to keep time                                 Final cause

The material of which it is made, brass                      Material cause

The plan to which the parts conform, the                    Formal cause


The work of putting it together                                  Efficient cause


Now let us fit these causes' into "pairs of opposites":


Obviously, the function is projective. The blueprints are objective. Since the work of assembly is also objective, we are forced to say the material is projective. This may seem untrue until one realizes that the brass could be used for many things besides the clock. This indicates also that the material is general; hence, the work is particular.

We have to choose whether the plan is particular or general. It has to be general because any number of clocks can be made from it. This leaves us with timekeeping, the function, as particular. Here we must recognize that timekeeping, while it seems a general function, actually is not. That is why one can ask "What time is it?" and expect a particular answer. If the watch kept general time, it would not mean anything at all.

The very difficulty of this example tells us what to look for in others. We must overcome the scientific habit of confining attention to what is true generally and objectively, while omitting what is true in the particular situation. Of course, an observed fact is always particular, and it is often very important to give attention to such facts. But this warning has often been stated. What is difficult is the projective particular, the existence in every situation of a "pointingness" that is not general. Like the question "What time is it?" it has one and only one answer, and this answer varies from moment to

Obviously, the function is projective. The blueprints are objective. Since the work of assembly is also objective, we are forced to say the material is projective. This may seem untrue until one realizes that the brass could be used for many things besides the clock. This indicates also that the material is general; hence, the work is particular.

We have to choose whether the plan is particular or general. It has to be general because any number of clocks can be made from it. This leaves us with timekeeping, the function, as particular. Here we must recognize that timekeeping, while it seems a general function, actually is not. That is why one can ask "What time is it?" and expect a particular answer. If the watch kept general time, it would not mean anything at all.

The very difficulty of this example tells us what to look for in others. We must overcome the scientific habit of confining attention to what is true generally and objectively, while omitting what is true in the particular situation. Of course, an observed fact is always particular, and it is often very important to give attention to such facts. But this warning has often been stated. What is difficult is the projective particular, the existence in every situation of a "pointingness" that is not general. Like the question "What time is it?" it has one and only one answer, and this answer varies from moment to moment.

We have already used the map example, but it would pay to note once more the great difference between the kinds of information that fall under each of the map's four aspects. The one we are most accustomed to, because it is intellectual, is the map as a statement of relationship between geographical points. From the map we can see that Albany is between Buffalo and Boston, and so on. We cannot know how long it will take to get from one place to another unless we have additional information, the scale (under which we include the mode of travel, whether we walk, ride, fly, etc.). This information is not on the map. It involves reality. We need to draw on experience. Distances in New York State and distances in the Himalaya Mountains might have the same appearance on a map, but involve altogether different orders of difficulty in their actual traverse.

Here we must not be misled by the fact that scale can be stated as a ratio on the map, because the ratio does not supply the missing ingredient, which must come from experience. On the map it says "10 miles to the inch," but we must know what a mile is. We cannot get this from a map. We might have walked a mile to school when we were young, or run a mile in five minutes on the track team, but our experience of a mile did not come from the study of geography books. It is of a different nature than the conceptual grasp of relationship.

Next, "Where are we on the map?" This is particular and objective: particular because it is a present fact, and objective because it can be communicated to others. This gives no difficulty because, since it is objective, it is given recognition by science, though logic might not accept it because logic gives no formal recognition to facts as such.

Finally, we come to the particular projective. "Which way to Detroit?" (We need know only one orientation. This, together with the map, will provide any other orientation.) But this is particular and projective: particular because it changes as we move about, and projective because it literally projects. It doesn't tell us a present fact, but a future fact. Hence, it is projective.

Note that we are talking in every case about the whole situation. The map is dealing with information about the terrain, to be sure, and may include a great deal of information about the location of towns, roads, etc., and a scale of distances. The significance of the fourfold information is that it goes further: it also includes, or has room for, your participation in the situation, how much effort and time will be required of you, and by its inclusion of the compass, makes it possible to include an ultimate goal, which objective science has to ignore.


The elements designate directions in space, as they do in the signs of the zodiac. These directions in space are also associated with people's poetic understanding of the seasons. Thus, taking the four signs of the zodiac assigned to the equinoctial points (the first day of spring and of fall) and the solstices (the first day of summer and of winter), we have four signs: Aries or spring, Cancer or summer, Libra or fall, and Capricorn or winter.


C. Seven Stages (and Substages) of Process 

Most simply stated, the theory of evolutionary process consists of seven sequential, cumulative stages, each associated with a particular essential property or Power (Figure 1a.). Each of these seven stages of evolution, in turn, contains seven substages with the same sequential powers (developed over the same four levels) as the major stages.

According to Young (1976a; 1980), the seven stages of process, which are found throughout ancient wisdom and esoteric literature, represent the seven topological distinctions possible with the torus, the most complex natural topological entity. The torus (Figure 2) is a self-referential "time-structure" with numerous unique properties (Young, 1976) such as: 

1) composition from two rotating "perpendicular circularities"; 

2) the shape of a vortex, an entity which is consubstantial with its matrix--i.e., the only means by which self-sustained motion can exist in a given medium; 

3) the same volume formula, 2pi²R³, as the Einstein-Eddington universe, the so-called hypersphere. 

4) a universal distribution, occurring with photons and particles through the cellular centriole to the universal hypersphere; 

5) the ability to reconcile the continuum of relativity and the discreteness of quantum theory; 

6) the means to explain the ancient puzzle of "free will in a universe run by God" or how there can be self-determined entities in the continuum; and 

7) seven topological distinctions--(i.e., a map drawn on the surface of a torus requires seven colors in order for all bordering countries to be distinguished by differences in color).

Figure 2a

Toroidal process may be schematically represented by a reflexive 7-staged arc manifesting on the previously described four levels. Through understanding and application of the arc of freedom and constraint, such universal myths as the "fall" of man from the "paradise" of freedom into deterministic matter and his eventual redemptive "virgin birth" (or self organizational/bootstrap "turn" back towards freedom) can be fully appreciated. The concomitant developments of; 1) the descent (and subsequent ascent) through the levels of freedom and constraint, and; 2) the sequential "forward" progression through the seven substages of anthropotheic (man's) process reinforce the validity of the myth of the "fall" and yet are compatible with the principle of the "pre/trans fallacy" (i.e. continuous evolutionary advancement), as discussed by Wilber (1960a; 1981).





Three versions of the SLS launch vehicle are planned: Block 1, Block 1B, and Block 2. Each will use the same core stage with four main engines, but Block 1B will feature a more powerful second stage called the Exploration Upper Stage (EUS), and Block 2 will combine the EUS with upgraded boosters



Core Stage[edit]

The Space Launch System's Core Stage will be 8.4 meters (28 ft) in diameter and use four RS-25 engines




A poster advertising the 1898 exhibition of the shroud in Turin. Secondo Pia's photograph was taken a few weeks too late to be included in the poster. The image on the poster includes a painted face, not obtained from Pia's photograph.



On 24 December 1979, the first Ariane launch, designated as L-O1, was conducted, which was successful.[11] However, in 1980, the second launch, L-O2 ended in a failure shortly after takeoff, which had been caused by a combustion instability that had occurred in one of the Viking first stage engines.[13] The third launch, L-O3 succeeded, which resulted in the orbiting of three separate satellites; the fourth and last qualification launch, L-04, was also a success. However, during the fifth launch, which was the first commercial mission to be performed by Ariane, designated as L5, the rocket ceased functioning after 7 minutes of flight. This failure was traced back to a single turbopump in the third stage that had stopped functioning, and a significant re-design of elements of the third stage was performed as a result.[14]



The fourth stage has multiple variants, depending on the mission. The simplest, Blok D, was used for interplanetary missions. Blok D had no guidance module, depending on the probe to control flight. Three different Blok DM versions (DM, DM2, and DM-2M) were for high Earth orbits. The Blok D/DM were unusual in that the fuel was stored in a toroidal tank, around the engine and behind the oxidizer tank.


The initial Proton tests in 1965–66 only used the first two stages of the booster, the complete four-stage vehicle being flown for the first time in 1967. When the Soviet space station program began in 1971, Protons began being flown with the Blok D removed for use as a heavy-lift LEO launcher.



The standard version of the PSLV (PSLV-G) has four stages using solid and liquid propulsion systems alternately and six strap-on boosters. It currently has capability to launch 1,678 kg to 622 km into Sun-synchronous orbit.


PSLV-CA (Operational)

The PSLV-CA, CA meaning "Core Alone", model premiered on 23 April 2007. The CA model does not include the six strap-on boosters used by the PSLV standard variant. Two small roll control modules and two first-stage motor control injection tanks were still attached to the side of the first stage.[12] The fourth stage of the CA variant has 400 kg less propellant when compared to its standard version.[12] It currently has capability to launch 1,100 kg to 622 km Sun synchronous orbit.[14]



The Minotaur IV vehicle consists of four stages and is capable of placing 1,735 kilograms (3,825 lb) of payload into a Low Earth orbit (LEO).[5][6] It uses the first three stages of the Peacekeeper missile, combined with a new upper stage. On the baseline version, the fourth stage is an Orion 38. However a higher performance variant, designated Minotaur IV+, uses a Star-48V instead. A three-stage configuration (no Orion-38), designated the Minotaur IV Lite, is available for Suborbital trajectories. The Minotaur IV has also been flown with multiple upper stages. A five-stage derivative, the Minotaur V, made its maiden flight on 7 Sep 2013.



ISRO PAM-G[edit]

Indian Space Research Organisation has built an upper stage called PAM-G (Payload Assist Module for GSLV) capable of pushing payloads directly to MEO or GEO orbits from low Earth orbits.[13][14] PAM-G is powered by hypergolic liquid motor with restart capability, derived from PSLV's fourth stage. As of 2013, ISRO has realized the structure, control systems, and motors of PAM-G and has conducted hot tests.[15][16][17] PAM-G would form the fourth stage of GSLV Mk2C launch vehicle,[18] sitting on top of GSLV's cryogenic third stage.



NASA Report, Technical Study for the Use of the Saturn 5, INT-21 and Other Saturn 5 Derivatives to Determine an Optimum Fourth Stage (space tug). Volume 1: Technical Volume, Book 1.[22]



Blok D was also included as fourth stage of Proton-K and as such flew on unmanned Soviet missions to Moon, Mars (Mars 3)and Venus. It was used in the Proton-K configuration of the rocket and is still in use in the newer Proton-M variant (along with the Briz-M).



The Blok DM-03 (Russian: Блок ДМ-03 meaning Block DM-03), GRAU index 11S861-03, is a Russian upper stage used as an optional fourth stage on the Proton-M carrier rocket. Three have been launched, the first in December 2010;[2] the first two launches failed before fourth stage ignition, the first as a result of a problem with the Blok DM's fuel load.[3]



The Agena D's common configuration included four usable modules containing the major guidance, beacon, power, and telemetry equipment, a standard payload console, and a rear rack above the engine for plug-in installation of optional gear-like solar panels, "piggyback" subsatellites, and an optional Bell Aerosystems engine that could be restarted in space as many as sixteen times.[8]



Attitude control and ullage are provided by means of hydrazine monopropellant thrusters located around the stage. There are two 2-thruster pods and four 4-thruster pods, sixteen in total, fed from a pair of bladder tanks carrying 340 pounds of hydrazine. Tank pressurization, as well as some engine functions, use helium gas.[10] The main propulsion system consists of one or two RL10 engines. These engines can be restarted multiple times, given sufficient power, helium, and ullage propellant, allowing Centaur to perform complex orbital insertions and deorbit burns.



The Interim Cryogenic Propulsion Stage (ICPS), a modified DCSS, will be used as a second stage on the debut flight of NASA's Space Launch System,[3] Exploration Mission 1 (EM-1), scheduled for September 2018.[4]



The Exploration Upper Stage (EUS) is being developed as a large second stage for Block 1B and Block 2 of the Space Launch System (SLS), succeeding Block 1's Interim Cryogenic Propulsion Stage. It will be powered by four RL10 engines burning LOX/LH2 to produce a total of 440 kN (99,000 lbf) thrust. As of February 2015 the SLS Block 1B is baselined at 105 metric tons.[4] The EUS is expected to first fly on the Exploration Mission 2 launch of the SLS scheduled for 2021.



Four modified RL10A-5 engines, all of them with the ability to be throttled, were used in the McDonnell Douglas DC-X.[citation needed]


In April 2016 it was reported NASA has chosen to use a design based on four RL10 engines for the Exploration Upper Stage to be used beginning with the crewed EM-2 mission of the Space Launch System.[18]



Four RL-10A-5 liquid-fueled rocket engines

four gaseous oxygen/gaseous hydrogen thrusters



SpaceX calls "Octaweb".[51] Many cores include four extensible landing legs attached around the base of the Octaweb



Fregat upper stage is designed for injecting large payloads into a low, medium-height or high geosynchronous orbit. Fregat is a versatile upper stage, in addition to orbital insertion, it can be used as an escape stage to send modern space probes into interplanetary trajectories (e.g. Venus Express and Mars Express). Fregat stages are currently used as the fourth stage of some Soyuz launch vehicles. The stage can be restarted up to 25 times,[2]


The failure occurred during the flight of the Fregat fourth stage. It occurred about 35 minutes after liftoff, at the beginning of the ballistic phase preceding the second ignition of this stage.



Originally developed for the Space Shuttle, different versions of the PAM were developed:


PAM-A (Atlas class), development terminated; originally to be used on both the Atlas and Space Shuttle

PAM-D (Delta class), uses a Star-48B rocket motor

PAM-DII (Delta class), uses a Star-63 rocket motor

PAM-S (Special) as a kick motor for the space probe Ulysses



From 1962 to 1963, Atlas boosters launched the first four American astronauts to orbit the Earth


Atlas boosters were also used for the last four manned Project Mercury missions, the first United States manned space program


Initial configurations will use the same Centaur upper stage as the Atlas V, with its RL-10 engines. A later advanced cryogenic upper stage—called the "Advanced Cryogenic Evolved Stage" (ACES)—will be LOX/LH2 powered by one to four rocket engines yet to be announced.



The original Delta rockets used a modified version of the PGM-17 Thor, the first ballistic missile deployed by the United States Air Force, as their first stage. The Thor had been designed in the mid-1950s to reach Moscow from bases in Britain or similar allied nations, and the first wholly successful Thor launch had occurred in September 1957. Subsequent satellite and space probe flights soon followed, using a Thor first stage with several different upper stages. The fourth upper stage used on the Thor was the Thor "Delta," delta being the fourth letter of the Greek alphabet. Eventually the entire Thor-Delta launch vehicle came to be called simply, "Delta."[1]


The Delta name stems from its position as the fourth, or D version, of the Thor based rocket combination. The vehicle has been known both as Thor-Delta and simply Delta.[2]



In 1972, McDonnell Douglas introduced a four-digit numbering system to replace the letter-naming system.

The new system could better accommodate the various changes and improvements to Delta rockets (and avoided the problem of a rapidly depleting alphabet).

It specified (1) the tank and main engine type, (2) number of solid rocket boosters, (3) second stage (letters refer to engine, not earlier letter system), and (4) third stage.[11]



Four Sun sensors detected orientation.


It carried four types of instruments. A solid-state X-ray instrument, which was composed of two silicon detectors to study X-rays from solar flares and Jupiter's aurorae. The GRB experiment consisted of two CsI scintillator crystals with photomultipliers. Two different magnetometers were mounted: a vector helium magnetometer and a fluxgate magnetometer. A two axis magnetic search coil antenna measured AC magnetic fields.



Star 24

2 Star 27

3 Star 37

4 Star 48



The Delta II family uses a four-digit system to generate its technical names:[23]


The first digit is either 6 or 7, denoting the 6000- or 7000-series Deltas.

The second digit indicates the number of boosters.

The third digit is 2, denoting a second stage with an Aerojet AJ10 engine. Only Deltas prior to the 6000-series used a different engine, the TR-201.

The last digit denotes the third stage. 0 denotes no third stage, 5 indicates a Payload Assist Module (PAM) stage with Star 48B solid motor, and 6 indicates a Star 37FM motor.



The Yuanzheng-1 (YZ-1) (Chinese: 远征一号; pinyin: Yuǎn Zhēng Yī Hào; literally: "Expedition One") is a restartable rocket upper stage developed by the China Academy of Launch Vehicle Technology (CALT) used as a fourth stage to enable the Long March 3B and Long March 3C launch vehicles to deploy payloads directly to high energy orbits like medium Earth orbit (MEO) and geostationary orbit (GSO). Since the Long March third stage cannot restart, it cannot circularize a GSO orbit from a geostationary transfer orbit. The YZ-1 was designed for restart capability, and to remain operational for more than 6 hours required to reach the transfer orbit apogee for the circularization burn. The YZ-1 enabled the deployment of satellite pairs for the BeiDou Navigation Satellite System and communications satellites directly to their orbits. This eliminates the need for the spacecraft to include a Liquid Apogee Engine or apogee kick motor.[3]



It made its maiden flight on 25 April 2008, at 15:35 GMT. The payload for the first launch was the Tianlian-1 data relay communications satellite. The second carried the Compass-G2 navigation satellite, and was conducted on 14 April 2009. The third launch was made on 16 January 2010, with the Compass-G1 satellite. The fourth carrying the Compass-G3 navigation satellite was launched on 2 June 2010. On 1 October 2010, it successfully launched China's second lunar probe, Chang'e 2.



A carrack was a three- or four-masted ocean-going sailing ship that was developed in the 14th and 15th centuries in Europe. Developed from the single-masted cog, the carrack was first used for European trade from the Mediterranean to the Baltic and quickly found use with the newly found wealth and status of the trans-Atlantic slave trade. In its most advanced forms, it was used by the Portuguese for trade along the African coast and finally with Asia and America from the 15th century before evolving into the galleon of the 16th and 17th centuries.


Astronomers have detected what may be four roughly Earth-size planets orbiting Tau Ceti, the nearest sun-like star.



Like snowflakes, no two planetary systems are the same. Astronomers have now observed one of the most unique planetary arrangements ever seen: four miniature Neptunes locked in perfect synch with each other—and it’s been like this for billions of years.


Astronomers discovered the Kepler-223 star system several years ago using the Kepler Space Telescope, at which time they catalogued four Neptune-like planets spinning close to their star. And by close they mean it; all four of these gaseous planets are orbiting at a distance closer than Mercury is to our sun. But that’s not even the most interesting part. Researchers from UC Berkeley and the University of Chicago have now learned that this quartet of miniature Neptunes is locked in an orbital dance that’s never been seen before.



This system is fairly odd, however, because the stars in the system are a long distance away from one another. The primary and secondary star are 44,000 astronomical units (AU) away from one another. One AU is the average distance from the Earth to the sun. The third star in the system is closer to the primary, as it is 28 AU away. The fourth star discovered is the most proximal, at 23 AU.


Though it seems counterintuitive, the fourth—and closest—star is not believed to have played a role in 30 Ari’s formation. However, the complex gravitational pull from the other three are believed to have influenced the planet’s size.




HR 8799 is a young (~30 million-year-old) main-sequence star located 129 light years (39 parsecs) away from Earth in the constellation of Pegasus, with roughly 1.5 times the Sun's mass and 4.9 times its luminosity. It is part of a system that also contains a debris disk and at least four massive planets


Further observations in 2009–2010 revealed the fourth giant planet orbiting inside the first three planets at a projected separation just less than 15 AU [6][21] which has now also been confirmed in multiple studies.[22]

Near-infrared observations with the Project 1640 integral field spectrograph on the Palomar Observatory have shown that compositions between the four planets vary significantly. This is a surprise since the planets presumably formed in the same way from the same disk and have similar luminosities.[24]


The first simultaneous spectra of all four known planets in the HR 8799 system were obtained in 2012 using the Project 1640 instrument at Palomar Observatory. The near-infrared spectra from this instrument confirmed the red colors of all four planets and are best matched by models of planetary atmospheres that include clouds. Though these spectra do not directly correspond to any known astrophysical objects, some of the planet spectra demonstrate similarities with L- and T-type brown dwarfs and the night-side spectrum of Saturn. The implications of the simultaneous spectra of all four planets obtained with Project 1640 are summarized as follows: Planet b contains ammonia and/or acetylene as well as carbon dioxide, but has little methane; Planet c contains ammonia, perhaps some acetylene but neither carbon dioxide nor substantial methane; Planet d contains acetylene, methane, and carbon dioxide but ammonia is not definitively detected; Planet e contains methane and acetylene but no ammonia or carbon dioxide. The spectrum of planet e is similar to a reddened spectrum of Saturn.[26]


Marois, C.; Zuckerman, B.; Konopacky, Q. M.; MacIntosh, B.; Barman, T. (2010). "Images of a fourth planet orbiting HR 8799". Nature. 468 (7327): 1080–1083. Bibcode:2010Natur.468.1080M. PMID 21150902. arXiv:1011.4918 Freely accessible. doi:10.1038/nature09684.

Jump up ^



The planets, which had previously had been seen as the Gods -- Saturn, Jupiter, and Mars -- had been identified and tracked as they receded in the sky after 3147 BC and after 685 BC. But Venus was not added to the "four planets of antiquity" until after 600 BC -- primarily because of the strange path taken by Venus in the sky. And, in fact, the clear identification of Isis, Horus, and Thoth with the planets Venus, Mars, and Mercury often remained uncertain during the prior period when the Gods raged across the skies.


I should note that Velikovsky may have "Venus not added" wrong. In an address by Abraham Sachs at Brown University on March 15, 1965, Sachs noted:


"In 'Worlds in Collision', p. 161, Dr. Velikovsky says that Babylonian astronomy at one time had a four-planet system, with Venus missing. For this, he refers to a book written in 1915. Not being a cuneiformist, Dr. Velikovsky cannot inspect the original text referred to in his 1915 source. I have read the text and I can report that it is quite true that Venus is missing in the text-- but so are the other four planets. Dr. Velikovsky's 1915 source mistranslated the names of four fixed stars as planets."

It is the same diffraction of any point-source light of a planet or star when behind the last of the equatorial rings which causes the depiction of planets as four- and eight-pointed figures. The refracted light would be at right angles to the pattern of the equatorial ring. Refracted light would radiate left and right from the primary planet behind the ring. If the ring had a granular structure the refracted light would more likely form a "halo." Photographers use filters with etched lines to achieve similar effects.


Strabo lists Seleucus as one of the four most influential Chaldean/Babylonian astronomers, alongside Kidenas (Kidinnu), Naburianos (Naburimannu), and Sudines



Seleucus is known from the writings of Plutarch, Aetius, and Strabo, all of whom were Greeks, and the Persian Muhammad ibn Zakariya al-Razi. Strabo lists Seleucus as one of the four most influential "Chaldean" astronomers:


In Chapter XVI of his Geographia, Strabo mentions several "Chaldaen" astronomers. At the end he adds: "Seleukios of Seleukia was a Chaldaean too." ... Babylonian astrologers and astronomers were often called "Chaldaeans." Strabo calls them "the so-called Chaldaeans". Their writings were translated into Greek and used by later authors like Geminos. The "Chaldaean" astronomers mentioned by Strabo are Kidenas, Naburianos, Sudines, and Seleukos. The first two are also known from astronomical cuneiform texts under their Akkadian names Nabu-Rimannu and Kidinnu.[10]



In classical Greece, astronomy was a branch of mathematics; astronomers sought to create geometrical models that could imitate the appearances of celestial motions. This tradition began with the Pythagoreans, who placed astronomy among the four mathematical arts (along with arithmetic, geometry, and music). The study of number comprising the four arts was later called the Quadrivium.



Velikovsky noticed that prior to the second millennium B.C. ancient Hindu records spoke of four visible planets, excluding Venus. Babylonians, meticulous in their observations, likewise excluded Venus in their earliest list of the planets.

According to Sagan there are four ways in which the same (Venus) legend would be found among widely separated cultures.


1. Common Observation; all cultures witnessed a common event and interpreted it in a similar way.


2. Diffusion; the legend originated with one culture, but traveled to others with the wanderings of mankind.


3. Brain Wiring; psychologically human beings are so alike that their legends reflect the commonality of human hopes and fears.


4. Coincidence; purely by chance all cultures created the same (Venus) legend or myth.


Sagan chose diffusion and coincidence while Velikovsky, of course, chose common-observation. Sagan states,



Again this is not true of all ancient societies. For example, the ancient Roman calendar (which Sagan discusses in the next sentences) had only four months with names during its very early history. Velikovsky discussed this in Worlds in Collision, “According to many classical authors, in the days of Romulus [8th century B.C.] the year consisted of ten months and in the time of Numa, [7th century B.C.] his successor, two months were added: January and February. Ovid writes (Fasti i 27ff) ‘When the founder of [Rome] was setting the calendar in order, he ordained that there should be twice five months in his year… The month of Mars [March] was the first.’” [67] And “March was considered the first month until the reign of Numa…wrote Procopius of Caesarea.”[68] Some seven centuries later, Julius Caesar gave his name to the fifth month, Quintilis, and Augustus gave his name to the sixth month, Sextilis. Thus, in ancient Roman times, the calendar was March, April, May, June, Quintilis, Sextilis, September, October, November, December. There are ten months in all, but only the first four have god names, not eight or ten as Sagan’s expert tells us. This is hardly evidence to support Sagan’s belief. He has merely tried to make the evidence fit his view by ignoring it altogether. Further, Sagan earlier completely ignored the fact that the Roman calendar was made up of ten months just as Velikovsky claimed.



Sagan goes on, “Velikovsky notes that the idea of four ancient ages terminated by catastrophes is common to Indian as well as to Western sacred writing.”[74] Velikovsky introduced this material about “four ancient ages terminated by catastrophes” with the following statement at the very beginning of this chapter, “The World Ages”,




Sagan states, “Velikovsky’s hypothesis begins with an event that has never been observed by astronomers and that is inconsistent with much that we know about planetary and cometary physics, namely the ejection of an object of planetary dimensions from Jupiter.”[173]


Although modern astronomers have not observed such an event ancient man reports the birth of the planet Venus. Evan Hadingham, in fact, informs us that the ancient Mexicans give the precise number of days in the past when Venus was born.[174] Velikovsky tells us,


“Ancient Mexican records give the order of the occurrences. The Sun was attacked by Quetzal-cohuatl; after the disappearance of this serpent-shaped heavenly body, the sun refused to shine, and during four days the world was deprived of its light… Thereafter the snakelike body transformed itself into a great star. The star retained the name of Quetzal-cohuatl [Quetzal-coatl] [Brasseur in Histoire des nations civilisees de Mexique I, p. 181 informs]. This great and brilliant star appeared for the first time in the east. Quetzal-cohuatl is the well-known name of the planet Venus.”[175]


Velikovsky then goes on to cite other ancient authorities that describe the birth of Venus and its description as a “Blazing Star and a “Comet.” He also cites authorities that claim at an early time, ancient man reported a solar system of only four planets. Velikovsky states, “only four planets could have been seen, and that in astronomical charts of this early period the planet Venus cannot be found.


“In an ancient Hindu table of planets, attributed to the year-3102 Venus among the visible planets is absent. [This according to J.B.J. Delambre, Historie de l’astronomie ancienne, (1817), I, p. 407: “Venus alone is not found there.”] The Brahmans of the early period did not know the five-planet system. [This according to G. Thibaut, “Astronomie, Astrologie und Mathematik” in Grundriss der indoarischen Philol und Altertumskunde, III (1899).


“Babylonian astronomy, too, had a four-planet system. In ancient prayers the planets Saturn, Jupiter, Mars and Mercury are invoked; the planet Venus is missing; and one speaks of ‘the four-planet system of the ancient astronomers of Babylonia.’ [This according to E.F. Weidner, Handbuch der babylonischen Astronomie (1915), p. 61, who writes of the star list found in Boghaz Keui in Asia Minor: ‘That the planet Venus is missing will not startle anybody who knows the eminent importance of the four-planet system in the Babylonian astronomy.’ Weidner supposes that Venus is missing in the list of planets because ‘she belongs to a triad with the Moon and the Sun.’] These four-planet systems and the inability of the ancient Hindus and Babylonians to see Venus in the sky, even though it is more conspicuous than the other planets, are puzzling unless Venus was not among the planets. On a later date the planet Venus receives the appellative: ‘The great star that joins the great stars.’ The great stars are, of course, the four planets Mercury, Mars, Jupiter and Saturn…and Venus joins them as the fifth planet. [according to E.F. Weidner ibid. p. 83]


“Apollonius Rhodius refers to a time ‘when not all the orbs were yet in the heavens.’”[176]


Sagan makes a point of refuting Velikovsky’s claim that Venus was a new born planet by claiming in his book Cosmos that, “The Adda cylinder seal, dating from the middle of the third millennium B.C., prominently displays Inanna, the goddess of Venus.” We have already shown the Babylonians saw Venus as a comet. However, Sagan is somehow unable to explain why ancient man describes Venus’ birth as a new star that was a comet nor why ancient civilizations had a four-planet solar system with Venus missing. I thus cannot find his view that it was “an event that has never been observed” very compelling nor his refusal to deal with ancient solar system descriptions in which Venus is missing as adequate refutation.



Let us examine Lyttleton’s work which is based on “fluid dynamics” that illustrates how planets born from Jupiter is “consistent with much that we know about planetary physics.” Lyttleton states,


“In explaining the origin of the solar system, there is the possibility that only four really large planets, Jupiter, Saturn, Uranus and Neptune need be regarded as primitive. If as condensation slowly formed from interplanetary material to give a large planet at somewhere near Jupiter’s present distance from the Sun, the resulting body would rotate in a few hours because of the indestructible rotational momentum drawn into it. With increasing size, its power to draw in material would increase and its resulting speed of rotation would do so too, and eventually render it unstable as a single mass because of centrifugal force. It can only get out of this embarrassing condition by breaking into two very unequal pieces (mass ratio 10 to 1) with the smaller one thrown completely away from the larger portion, to be identified with the present Jupiter. At the surface of Jupiter the escape speed is now about 40 miles a second (59 km/sec) so the smaller piece would easily be thrown right out of the solar system. The same process of breaking up would produce a string of droplets between the two pieces as they separated, and it is even possible that the whole of the terrestrial group of planets [Mercury, Venus, Earth, Mars, Pluto] and Jupiter’s four great satellites were produced this way as droplets. We have seen that their combined mass is less than one percent of that of Jupiter.”[179] [emphasis added]


Thus, according to Lyttleton, the birth of all planets from Jupiter is “consistent” with “planetary physics.” Apparently, neither McCrea nor Lyttleton understood that Sagan had known that their analysis and calculations are “inconsistent” with the laws of gravity.



The Allen-Bradley Clock Tower in Milwaukee, Wisconsin has the largest four faced (non-chiming) clock[citation needed] in the world, with clock diameter 40 ft 3 1⁄2 in (12.281 m); it is 283 ft (86 m) tall. The Elizabeth Tower has the largest chiming clock in the world;[citation needed] it is 315 feet (96 m) tall.



The Allen-Bradley Clock Tower, owned by Allen-Bradley, a product brand of Rockwell Automation, has long been a landmark in Milwaukee. According to the Guinness Book of World Records: "The largest four-faced clock is that on the research and office addition of the Allen-Bradley Company. Each face has a diameter of 40 feet, 3-1/2 inches. Dedicated on October 31, 1962, it rises 280 feet from the streets of Milwaukee, and requires 34.6 kilowatts of electricity for lighting and power."


The current clock tower stands at 283 ft. (86.26 m).[1] Because the octagonal faces are nearly twice the size of the faces of London’s Big Ben, chimes were never added in an attempt to allow Big Ben to remain the largest four-faced chiming clock in the world. In fact, that title has belonged to the Minneapolis City Hall clock since 1909. Each hour hand of the Allen-Bradley Clock Tower is 15.8 feet (4.8 m) long and weighs 490 pounds (220 kg). Each minute hand is 20 feet (6.1 m) long and weighs 530 pounds (240 kg). The hour markings are 4 feet (1.2 m) high.



Central do Brasil clock in Rio de Janeiro, a 20-metre diameter four-face clock on top of a 135-metre tower in a railway station, built in 1943.



This Hubble Space Telescope image shows Sirius A, the brightest star in our nighttime sky, along with its faint, tiny stellar companion, Sirius B. Astronomers overexposed the image of Sirius A (at centre) so that the dim Sirius B (tiny dot at lower left) could be seen. The cross-shaped diffraction spikes and concentric rings around Sirius A, and the small ring around Sirius B, are artifacts produced within the telescope's imaging system. The two stars revolve around each other every 50 years. Sirius A, only 8.6 light-years from Earth, is the fifth closest star system known.