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# Further fun: Friday is pi day

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World’s best known and best loved irrational number

Here’s a brief publicity bio:

pi is known to be irrational (Lambert 1761; Legendre 1794; Hermite 1873; Nagell 1951; Niven 1956; Struik 1969; Königsberger 1990; Schröder 1993; Stevens 1999; Borwein and Bailey 2003, pp. 139-140). In 1794, Legendre also proved that pi^2 is irrational (Wells 1986, p. 76). pi is also transcendental (Lindemann 1882). An immediate consequence of Lindemann’s proof of the transcendence of pi also proved that the geometric problem of antiquity known as circle squaring is impossible. A simplified, but still difficult, version of Lindemann’s proof is given by Klein (1955).

and a million digits of pi

The only checkout counter mag scandal associated with pi’s career  was the huge scene in a restaurant last year, with the square root of minus one – overheard by at least dozen witnesses:

Square Root: Get rational!

Pi: Get real!

It was then the pi got thrown.

Pi also  starred in the Carl Sagan novel Contact, which was made into the film:

There, see, we got a film in too, nitey nite.

OT: Dr. Stephen Meyer Presents Evidence for Design in the Cosmos, pt. 1 - video http://www.youtube.com/watch?v=tQMs2-GqUkA bornagain77
As to the relationship of the circle to the human body:
Da Vinci Vitruve Luc Viatour – interactive image http://upload.wikimedia.org/wikipedia/commons/2/22/Da_Vinci_Vitruve_Luc_Viatour.jpg "Speaking as one who has examined the original Vitruvian Man drawing, I can say that Leonardo was looking for a numerical design scheme that informs the proportions of the human body. The drawing began as an illustration from Vitruvius’ book, De Architectura where Vitruvius justifies the use of the square and circle as design elements because those shapes are integral to the human body: a man’s height is equal to his width (with arms outstretched) as a square, and a circle drawn with the navel as center and feet as radius is coincident with the hands’ reach. Leonardo also notes the other proportional relationships from Vitruvius such as the head height measures to the whole as well as the arms and hand sections. Leonardo then continued measuring (from the evidence of pin point indentations made by walking dividers, especially along the left vertical edge) to find more proportional relationships. He would take a measure of a part of the figure with the dividers and walk that measure along the height to see if the measure would fit an even number of times. From this drawing and others where Leonardo was working on the same type of problem it is evident that Leonardo believed there was a something like a unified field theory of design where everything in nature was related by numerical and geometrical design systems. He was one of the original ID thinkers." - Dr. Ford Of note: The Vitruvian Man is a world-renowned drawing created by Leonardo da Vinci c. 1487. It is the one commonly associated with the science of physiology Ring Acrobat - video http://www.youtube.com/watch?v=IbEVXNfGS2k
bornagain77
Moreover, epigenetic information has now directly falsified the central dogma of neo-Darwinism as true:
Does the central dogma still stand? – Koonin EV. – 23 August 2012 Excerpt: Thus, there is non-negligible flow of information from proteins to the genome in modern cells, in a direct violation of the Central Dogma of molecular biology. The prion-mediated heredity that violates the Central Dogma appears to be a specific, most radical manifestation of the widespread assimilation of protein (epigenetic) variation into genetic variation. The epigenetic variation precedes and facilitates genetic adaptation through a general ‘look-ahead effect’ of phenotypic mutations.,,, Conclusions: The Central Dogma of molecular biology is refuted by genetic assimilation of prion-dependent phenotypic heredity. This phenomenon is likely to be the tip of the proverbial iceberg,,, Even more generally, the entire spectrum of epigenetic variation, in particular various modifications of DNA, chromatin proteins and RNA, potentially can be similarly assimilated by evolving genomes.,,, http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3472225/ also see J.Shapiro, "Revisiting the Central Dogma", and D.Nobel, "Physiology is rocking the foundations of evolutionary biology".
Amazingly many Darwinists act as if none of this evidence has come forth and falsified their position, and they still dogmatically argue that 'randomly' accumulating mutations can account for all the complexity we see in life. But alas, they are not even on the right playing field to play the game in the first place with their now falsified reductive materialism model of neo-Darwinism. The following article comments on a paper that demonstrated the irreducible nature of structural information and digital information:
Refereed scientific article on DNA argues for irreducible complexity - October 2, 2013 Excerpt: This paper published online this summer is a true mind-blower showing the irreducible organizational complexity (author’s description) of DNA analog and digital information, that genes are not arbitrarily positioned on the chromosome etc.,, ,,,First, the digital information of individual genes (semantics) is dependent on the the intergenic regions (as we know) which is like analog information (syntax). Both types of information are co-dependent and self-referential but you can’t get syntax from semantics. As the authors state, “thus the holistic approach assumes self-referentiality (completeness of the contained information and full consistency of the different codes) as an irreducible organizational complexity of the genetic regulation system of any cell”. In short, the linear DNA sequence contains both types of information. Second, the paper links local DNA structure, to domains, to the overall chromosome configuration as a dynamic system keying off the metabolic signals of the cell. This implies that the position and organization of genes on the chromosome is not arbitrary,,, http://www.christianscientific.org/refereed-scientific-article-on-dna-argues-for-irreducibly-complexity/
Not that I am qualified to say, but I would think the Intelligent Design position, besides syntax and semantics being irreducibly complex, as the preceding article indicated, would hold that syntax (i.e. structural dynamics and configuration) is primary over the semantics (i.e. the digital information of the linear genetic code). This is beautifully illustrated in Wiker and Witt's book 'A Meaningful World':
A Meaningful World: How the Arts and Sciences Reveal the Genius of Nature – Wiker and Witt Excerpt: They focus instead on what “Methinks it is like a weasel” really means. In isolation, in fact, it means almost nothing. Who said it? Why? What does the “it” refer to? What does it reveal about the characters? How does it advance the plot? In the context of the entire play, and of Elizabethan culture, this brief line takes on significance of surprising depth. The whole is required to give meaning to the part. (and yet the part is required to convey that meaning) http://www.thinkingchristian.net/C228303755/E20060821202417/
i.e. It is impossible for a part to stand in isolation to a prior and meaningful whole existing beforehand. Pastor Joe Boot puts the insurmountable syntax/semantics problem for reductive materialism this way:
“If you have no God, then you have no design plan for the universe. You have no prexisting structure to the universe.,, As the ancient Greeks held, like Democritus and others, the universe is flux. It’s just matter in motion. Now on that basis all you are confronted with is innumerable brute facts that are unrelated pieces of data. They have no meaningful connection to each other because there is no overall structure. There’s no design plan. It’s like my kids do ‘join the dots’ puzzles. It’s just dots, but when you join the dots there is a structure, and a picture emerges. Well, the atheists is without that (final picture). There is no preestablished pattern (to connect the facts given atheism).” Pastor Joe Boot – Defending the Christian Faith – 13:20 minute mark of video http://www.youtube.com/watch?v=wqE5_ZOAnKo
CS Lewis, in his unusually crisp way of putting things, puts the syntax/semantics problem for materialistic atheists like this:
“Consequently atheism turns out to be too simple. If the whole universe has no meaning, we should never have found out that it has no meaning: just as, if there were no light in the universe and therefore no creatures with eyes, we should never know it was dark. Dark would be a word without meaning.” CS Lewis – Mere Christianity
i.e. it is impossible for 'semantic' parts to give rise to a meaningful 'syntax' whole without a that prior meaningful whole (an architectural plan) giving definition and direction to the parts in the first place! supplemental quote: “If information underlies the universe, then meaning underlies the universe. Pass it on.” Ms. O’Leary (of UD News) Music and Verse:
Steven Curtis Chapman - More to this Life http://www.youtube.com/watch?v=Ndbma-BQJK8 Psalm 16:2 I say to the LORD, "You are my Lord; apart from you I have no good thing."
bornagain77
To try to relate the insurmountable problem faced by materialists in trying to explain the roundness and flatness of the universe without reference to God, it is interesting to note that materialists/Darwinists have very much the same problem in trying to explain the origin of body plans. Dr. Stephen Meyer puts the insurmountable problem for Darwinists like this:
‘Now one more problem as far as the generation of information. It turns out that you don’t only need information to build genes and proteins, it turns out to build Body-Plans you need higher levels of information; Higher order assembly instructions. DNA codes for the building of proteins, but proteins must be arranged into distinctive circuitry to form distinctive cell types. Cell types have to be arranged into tissues. Tissues have to be arranged into organs. Organs and tissues must be specifically arranged to generate whole new Body-Plans, distinctive arrangements of those body parts. We now know that DNA alone is not responsible for those higher orders of organization. DNA codes for proteins, but by itself it does not insure that proteins, cell types, tissues, organs, will all be arranged in the body. And what that means is that the Body-Plan morphogenesis, as it is called, depends upon information that is not encoded on DNA. Which means you can mutate DNA indefinitely. 80 million years, 100 million years, til the cows come home. It doesn’t matter, because in the best case you are just going to find a new protein some place out there in that vast combinatorial sequence space. You are not, by mutating DNA alone, going to generate higher order structures that are necessary to building a body plan. So what we can conclude from that is that the neo-Darwinian mechanism is grossly inadequate to explain the origin of information necessary to build new genes and proteins, and it is also grossly inadequate to explain the origination of novel biological form.’ - Stephen Meyer - Functional Proteins And Information For Body Plans - video http://www.metacafe.com/watch/4050681 Darwin's Doubt narrated by Paul Giem - The Origin of Body Plans - video http://www.youtube.com/watch?list=PLHDSWJBW3DNUaMy2xdaup5ROw3u0_mK8t&v=rLl6wrqd1e0&feature=player_detailpage#t=290
Just how acute this problem is for Darwinists was perhaps best laid out by Stephen L. Talbott in this following article:
i.e. just what is directing all these countless trillions of molecules to cohere into the functional whole of my body? This is not a minor question in the least but it is a question that I have yet to see a Darwinist address in any meaningful way besides the usual hand-waving and ad hominem attack. Moreover, there are now multiple lines of evidence showing that the 3-D structure of a body plan (form) is irreducible to the linear sequences on information in DNA (as is assumed in neo-Darwinism), but is an independent source of 'epigenetic' information in its own right:
“Live memory” of the cell, the other hereditary memory of living systems - 2005 Excerpt: To understand this notion of “live memory”, its role and interactions with DNA must be resituated; indeed, operational information belongs as much to the cell body and to its cytoplasmic regulatory protein components and other endogenous or exogenous ligands as it does to the DNA database. We will see in Section 2, using examples from recent experiments in biology, the principal roles of “live memory” in relation to the four aspects of cellular identity, memory of form, hereditary transmission and also working memory. http://www.ncbi.nlm.nih.gov/pubmed/15888340 The Types: A Persistent Structuralist Challenge to Darwinian Pan-Selectionism - Michael J. Denton - 2013 Excerpt: Cell form ,,,Karsenti comments that despite the attraction of the (genetic) blueprint model there are no “simple linear chains of causal events that link genes to phenotypes” [77: p. 255]. And wherever there is no simple linear causal chain linking genes with phenotypes,,,—at any level in the organic hierarchy, from cells to body plans—the resulting form is bound to be to a degree epigenetic and emergent, and cannot be inferred from even the most exhaustive analysis of the genes.,,, To this author’s knowledge, to date the form of no individual cell has been shown to be specified in detail in a genomic blueprint. As mentioned above, between genes and mature cell form there is a complex hierarchy of self-organization and emergent phenomena, rendering cell form profoundly epigenetic. http://bio-complexity.org/ojs/index.php/main/article/view/BIO-C.2013.3/BIO-C.2013.3 Not Junk After All—Conclusion - August 29, 2013 Excerpt: Many scientists have pointed out that the relationship between the genome and the organism — the genotype-phenotype mapping — cannot be reduced to a genetic program encoded in DNA sequences. Atlan and Koppel wrote in 1990 that advances in artificial intelligence showed that cellular operations are not controlled by a linear sequence of instructions in DNA but by a “distributed multilayer network” [150]. According to Denton and his co-workers, protein folding appears to involve formal causes that transcend material mechanisms [151], and according to Sternberg this is even more evident at higher levels of the genotype-phenotype mapping [152]. https://uncommondescent.com/junk-dna/open-mike-cornell-obi-conference-chapter-11-not-junk-after-all-conclusion/
etc.. etc.. The following experiment gets this 'irreducible' point of structural information to digital information across fairly clearly:
The World’s Toughest Bacterium - 2002 Excerpt: “When subjected to high levels of radiation, the Deinococcus genome is reduced to fragments,” (…) “RecA proteins may play role in finding overlapping fragments and splicing them together.” http://www.genomenewsnetwork.org/articles/07_02/deinococcus.shtml Extreme Genome Repair - 2009 Excerpt: If its naming had followed, rather than preceded, molecular analyses of its DNA, the extremophile bacterium Deinococcus radiodurans might have been called Lazarus. After shattering of its 3.2 Mb genome into 20–30 kb pieces by desiccation or a high dose of ionizing radiation, D. radiodurans miraculously reassembles its genome such that only 3 hr later fully reconstituted nonrearranged chromosomes are present, and the cells carry on, alive as normal.,,, http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3319128/
i.e. How can the RecA proteins possible reconstruct fragmented DNA? How can the cell possibly ‘know’ the correct sequence if the reductive materialistic model of neo-Darwinism were actually true? bornagain77
Here is a piece of trivia of related interest to the 'flatness' of the universe. Although not directly related to the 'flatness' of the universe, since the 'flatness' of the universe pertains to fact that the space-time surface of the universe exhibits zero curvature, the following finding is none-the-less remarkable:
Why is the solar system cosmically aligned? BY Dragan Huterer - 2007 The solar system seems to line up with the largest cosmic features. Is this mere coincidence or a signpost to deeper insights? Caption under figure on page 43: ODD ALIGNMENTS hide within the multipoles of the cosmic microwave background. In this combination of the quadrupole and octopole, a plane bisects the sphere between the largest warm and cool lobes. The ecliptic — the plane of Earth’s orbit projected onto the celestial sphere — is aligned parallel to the plane between the lobes. http://www-personal.umich.edu/~huterer/PRESS/CMB_Huterer.pdf
Of related interest to that, is this:
Is there a violation of the Copernican principle in radio sky? - Ashok K. Singal - May 17, 2013 Abstract excerpt: What is intriguing even further is why such anisotropies should lie about a great circle decided purely by the orientation of earth's rotation axis and/or the axis of its revolution around the sun? It looks as if these axes have a preferential placement in the larger scheme of things, implying an apparent breakdown of the Copernican principle or its more generalization, cosmological principle, upon which all modern cosmological theories are based upon. http://arxiv.org/abs/1305.4134 http://arxiv.org/pdf/1305.4134.pdf
Of note to the Tau lecture referenced by Phinehas (No, really, pi is wrong: The Tau Manifesto by Michael Hartl), natural log e (which is found in Euler's identity and in John 1:1) is also found to be necessary for calculating 'growth' of r in the 'golden spiral' of the Fibonacci number;
The Logarithmic Spiral 1. r increases proportionally and remains in proportion with the golden ratio as theta increases if we define the equation as above, multiplied by e^(a*phi). The reasons for this are more thoroughly discussed by Mukhopadhyay. http://goldenratiomyth.weebly.com/the-logarithmic-spiral.html Nature by Numbers - Fibonacci - video http://vimeo.com/9953368 What Phi (the golden ratio) Sounds Like - music http://www.youtube.com/watch?v=W_Ob-X6DMI4
This may be of interest to the Tau - pi contraversy. Euler's formula (the most famous of all formulas), when plotted in 3D, results in a helix!
The following images show the graph of the complex exponential function, e^{ix}, by plotting the Taylor series of e^{ix} in the 3D complex space (a helix) (a third of the way down on the page) http://www.songho.ca/math/euler/euler.html The Physics of Illusion - video (Euler's Identity is derived as a spiral at the 23:00 minute mark) https://www.youtube.com/watch?v=ht3sAP-GQrk
bornagain77
Phineas, he has a solid point. It is also interesting to note that even though pi has a certain beauty to it when put to music,,,
What pi sounds like - music http://www.youtube.com/watch?v=YOQb_mtkEEE
That Tau (2pi) has a deeper beauty to it when put to music:
What Tau (2pi) Sounds Like - music http://www.youtube.com/watch?v=3174T-3-59Q
bornagain77
The Tau Manifesto Phinehas
OT: Does God Exist? - Debate - Frank Turek vs Dennis Nørmark - video (took place on Thursday in Denmark) http://www.youtube.com/watch?v=spnTH9nk0wI bornagain77
Also of note, Einstein's birthday was on March 14, 1879, pi day (at least in American notation it is 3-14). And pi is required in Einstein's General Relativity equation:
The Five Foundational Equations of the Universe https://docs.google.com/document/d/1UlGuMC76IbUDZEqFjeG3zqGw9KHto-ifhYh6CjGObHk/edit
pi is also found in the Bible in Genesis 1:1
This following website, and video, has the complete working out of the math of Pi and e in the Bible, in the Hebrew and Greek languages respectively, for Genesis 1:1 and John 1:1: http://www.biblemaths.com/pag03_pie/
A materialist objected to pi being found in Genesis 1:1 by say that the number was found by 'calculating backwards into it', i.e. by arranging the equation beforehand in such a way as to arrive at the number you want after you perform the calculation. The trouble with his objection is that, using the same exact method of calculation, John 1:1 gives us the natural logarithm e:
Euler's Identity - God Created Mathematics - video http://www.metacafe.com/watch/4003905
Also of note, both pi and e are found in Euler's Identity:
0 = 1 + e ^(i*pi) — Euler God by the Numbers - Connecting the constants Excerpt: The final number comes from theoretical mathematics. It is Euler's (pronounced "Oiler's") number: e^pi*i. This number is equal to -1, so when the formula is written e^pi*i+1 = 0, it connects the five most important constants in mathematics (e, pi, i, 0, and 1) along with three of the most important mathematical operations (addition, multiplication, and exponentiation). These five constants symbolize the four major branches of classical mathematics: arithmetic, represented by 1 and 0; algebra, by i; geometry, by pi; and analysis, by e, the base of the natural log. e^pi*i+1 = 0 has been called "the most famous of all formulas," because, as one textbook says, "It appeals equally to the mystic, the scientist, the philosopher, and the mathematician.",,, The discovery of this number gave mathematicians the same sense of delight and wonder that would come from the discovery that three broken pieces of pottery, each made in different countries, could be fitted together to make a perfect sphere. It seemed to argue that there was a plan where no plan should be.,,, Today, numbers from astronomy, biology, and theoretical mathematics point to a rational mind behind the universe.,,, The apostle John prepared the way for this conclusion when he used the word for logic, reason, and rationality—logos—to describe Christ at the beginning of his Gospel: "In the beginning was the logos, and the logos was with God, and the logos was God." When we think logically, which is the goal of mathematics, we are led to think of God. http://www.christianitytoday.com/ct/2006/march/26.44.html?start=3 (of note; Euler's Number (equation) is more properly called Euler's Identity in math circles.)
Music and verse:
What pi sounds like - music http://www.youtube.com/watch?v=YOQb_mtkEEE Job 26:10 He has inscribed a circle on the face of the waters at the boundary between light and darkness.
bornagain77
And just as with the spherical nature of the CMBR, the flatness of the universe was predicted in the Bible centuries before it was discovered by modern science:
Job 38:4-5 “Where were you when I laid the earth’s foundation? Tell me, if you understand. Who marked off its dimensions? Surely you know! Who stretched a measuring line across it?
Materialists have tried to 'explain away' the highly isotropic nature of the Cosmic Background Radiation, the 'roundness' of the CMBR, (and the 'flatness' of the universe) by postulating inflation in which a quasi infinite number a parallel universes were born in the split second after the big bang thus, I suppose, 'smoothing out' the universe, (squaring the circle anyone?),,,
The inflationary epoch comprises the first part of the electroweak epoch following the grand unification epoch. It lasted from 10?36 seconds after the Big Bang to sometime between 10?33 and 10?32 seconds. Following the inflationary period, the universe continued to expand, but at a slower rate. The term "inflation" is used to refer to the hypothesis that inflation occurred, to the theory of inflation, or to the inflationary epoch. The inflationary hypothesis was originally proposed in 1980 by American physicist Alan Guth, who named it "inflation".[2] As a direct consequence of this expansion, all of the observable universe originated in a small causally connected region. Inflation answers the classic conundrum of the Big Bang cosmology: why does the universe appear flat, homogeneous, and isotropic in accordance with the cosmological principle when one would expect, on the basis of the physics of the Big Bang, a highly curved, heterogeneous universe?,,, http://en.wikipedia.org/wiki/Inflation_%28cosmology%29
But inflation is found to be a 'degenerate science program'. Dr. Sheldon, others, and even one of the originators of inflation theory itself, have repeatedly pointed out, the observational evidence we have undermines any claim inflation theory had to being true as to ‘explaining away’ the fine tuning of the CMBR;
In fact inflation, instead of solving the problem of the CMBR, and as a chief proponent of multiverses himself admits, leads to the epistemological failure of science;
WHAT SCIENTIFIC IDEA IS READY FOR RETIREMENT? Infinity - Max Tegmark - January 2014 Excerpt: Physics is all about predicting the future from the past, but inflation seems to sabotage this: when we try to predict the probability that something particular will happen, inflation always gives the same useless answer: infinity divided by infinity. The problem is that whatever experiment you make, inflation predicts that there will be infinitely many copies of you far away in our infinite space, obtaining each physically possible outcome, and despite years of tooth-grinding in the cosmology community, no consensus has emerged on how to extract sensible answers from these infinities. So strictly speaking, we physicists are no longer able to predict anything at all! MAX TEGMARK – Physicist http://www.theguardian.com/science/2014/jan/12/what-scientific-idea-is-ready-for-retirement-edge-org
Finding the universe to be structure on the transcendent and infinite number of pi gives yet another piece of evidence that omniscient God, who is infinite in knowledge, created the universe: Here are a couple of other places in the universe where 'unexpected roundness' is found:
Sun's Almost Perfectly Round Shape Baffles Scientists - (Aug. 16, 2012) — Excerpt: The sun is nearly the roundest object ever measured. If scaled to the size of a beach ball, it would be so round that the difference between the widest and narrow diameters would be much less than the width of a human hair.,,, They also found that the solar flattening is remarkably constant over time and too small to agree with that predicted from its surface rotation. http://www.sciencedaily.com/releases/2012/08/120816150801.htm
and this 'unexpected roundness' extends to the 'molecule of life' i.e. carbon!:
Bucky Balls - Andy Gion Excerpt: Buckyballs (C60; Carbon 60) are the roundest and most symmetrical large molecule known to man. Buckministerfullerine continues to astonish with one amazing property after another. C60 is the third major form of pure carbon; graphite and diamond are the other two. Buckyballs were discovered in 1985,,, http://www.3rd1000.com/bucky/bucky.htm
These two place where unexpected roundness is found, i.e. in stars and in the carbon molecule, is truly extraordinary. The delicate balance at which carbon is synthesized in stars is truly a work of art. Fred Hoyle (1915-2001), a famed astrophysicist, is the scientist who established the nucleo-synthesis of heavier elements within stars as mathematically valid in 1946. He is said to have converted from staunch atheism into being a Theist after discovering the precise balance at which carbon is synthesized in stars. Years after Sir Fred discovered the stunning precision with which carbon is synthesized in stars he stated this:
"I do not believe that any physicist who examined the evidence could fail to draw the inference that the laws of nuclear physics have been deliberately designed with regard to the consequences they produce within stars." Sir Fred Hoyle - "The Universe: Past and Present Reflections." Engineering and Science, November, 1981. pp. 8–12 Michael Denton - We Are Stardust - Uncanny Balance Of The Elements - and Atheist Fred Hoyle's conversion from atheism to being a Deist/Theist - video http://www.metacafe.com/watch/4003877
bornagain77
as to this comment:
"pi is also transcendental (Lindemann 1882). An immediate consequence of Lindemann’s proof of the transcendence of pi also proved that the geometric problem of antiquity known as circle squaring is impossible. A simplified, but still difficult, version of Lindemann’s proof is given by Klein (1955)."
When it is said that 'circle squaring is impossible' they basically are saying that the number pi is truly infinite in length, not finite.
Squaring the circle is a problem proposed by ancient geometers. It is the challenge of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge. http://en.wikipedia.org/wiki/Squaring_the_circle (of note: only a mathematician would try to put a square peg in a round hole :) )
Having pi being proved to be transcendent and infinite is another insurmountable problem for naturalists/materialists since the universe is found to structured upon the geometric principles of pi: For instance, the Cosmic Microwave Background Radiation (CMBR) is found to be a circular sphere:
Picture of CMBR http://new-universe.org/zenphoto/albums/Chapter4/Illustrations/Abrams47.jpg The Known Universe by AMNH – video - (please note the 'centrality' of the Earth in the universe at the 3:36 minute mark in the video) http://www.youtube.com/watch?v=17jymDn0W6U Planck's view of the Universe - Oct. 18, 2013 - video http://www.youtube.com/watch?v=Fn0FgOwyu0w
It should be noted that the roundness for the universe found in the CMBR data was predicted in the Bible centuries before it was discovered by modern science:
Proverbs 8:26-27 While as yet He had not made the earth or the fields, or the primeval dust of the world. When He prepared the heavens, I was there, when He drew a circle on the face of the deep,
It is also important to note how exceptionally round the CMBR is:
The Cosmic Background Radiation Excerpt: These fluctuations are extremely small, representing deviations from the average of only about 1/100,000 of the average temperature of the observed background radiation. The highly isotropic nature of the cosmic background radiation indicates that the early stages of the Universe were almost completely uniform. This raises two problems for (a naturalistic understanding of) the big bang theory. First, when we look at the microwave background coming from widely separated parts of the sky it can be shown that these regions are too separated to have been able to communicate with each other even with signals traveling at light velocity. Thus, how did they know to have almost exactly the same temperature? This general problem is called the horizon problem. Second, the present Universe is homogenous and isotropic, but only on very large scales. For scales the size of superclusters and smaller the luminous matter in the universe is quite lumpy, as illustrated in the following figure. ,,, Thus, the discovery of small deviations from smoothness (anisotopies) in the cosmic microwave background is welcome, for it provides at least the possibility for the seeds around which structure formed in the later Universe. However, as we shall see, we are still far from a quantitative understanding of how this came to be. http://csep10.phys.utk.edu/astr162/lect/cosmology/cbr.html Wilkinson Microwave Anisotropy Probe - Main result Excerpt: The microwave background is very homogeneous in temperature (the relative variations from the mean, which presently is still 2.7 kelvins, are only of the order of 5x10?5.) http://en.wikipedia.org/wiki/Wilkinson_Microwave_Anisotropy_Probe#Main_result
From initial entropic considerations, the precision of the initial isotropic (uniform) condition of the 'sphere of the universe' really stands out:
The Physics of the Small and Large: What is the Bridge Between Them? Roger Penrose Excerpt: "The time-asymmetry is fundamentally connected to with the Second Law of Thermodynamics: indeed, the extraordinarily special nature (to a greater precision than about 1 in 10^10^123, in terms of phase-space volume) can be identified as the "source" of the Second Law (Entropy)." Roger Penrose – How Special Was The Big Bang? “But why was the big bang so precisely organized, whereas the big crunch (or the singularities in black holes) would be expected to be totally chaotic? It would appear that this question can be phrased in terms of the behaviour of the WEYL part of the space-time curvature at space-time singularities. What we appear to find is that there is a constraint WEYL = 0 (or something very like this) at initial space-time singularities-but not at final singularities-and this seems to be what confines the Creator’s choice to this very tiny region of phase space." How special was the big bang? - Roger Penrose Excerpt: This now tells us how precise the Creator's aim must have been: namely to an accuracy of one part in 10^10^123. (from the Emperor’s New Mind, Penrose, pp 339-345 - 1989)
As well, corresponding to the transcendent and infinite number of pi (dividing the circumference of a circle by its diameter), the universe is also found to be exceptionally 'flat':
Did the Universe Hyperinflate? – Hugh Ross – April 2010 Excerpt: Perfect geometric flatness is where the space-time surface of the universe exhibits zero curvature (see figure 3). Two meaningful measurements of the universe’s curvature parameter, ½k, exist. Analysis of the 5-year database from WMAP establishes that -0.0170 less than 1/2k less than 0.0068.4 Weak gravitational lensing of distant quasars by intervening galaxies places -0.031 less than 1/2k less than 0.009.5 Both measurements confirm the universe indeed manifests zero or very close to zero geometric curvature,,, per Reasons to Believe Refutation Of Oscillating Universe - Michael Strauss PhD. - (Boomerang results) video http://www.metacafe.com/watch/4323673 Why astronomers say we live in a remarkably flat universe—and what that really means - January 2014 Excerpt: the universe appears remarkably flat. It takes a lot of effort to find any curvature at all, https://uncommondescent.com/intelligent-design/why-astronomers-say-we-live-in-a-remarkably-flat-universe-and-what-that-really-means/ The curvature of the space time of the universe is 'flat' to at least 1 in 10^15 places of accuracy http://books.google.com/books?id=O_beAVEoR7sC&pg=PT88&lpg=PT88&dq#v=onepage&q&f=false
bornagain77
PPS: Why -- and I consciously echo Wigner et al -- is Mathematics so uncannily effective in analysing and predicting the behaviour of reality? Could reality have been built on a foundation of Mathematics instantiated as physics? Complete with fine tuning? (BA, swing for 6, but don't sky de ball, slips is waiting for an edge . . . wid gully and silly mid on and off backing them up [and all of this is Cricket Jargon]) kairosfocus
Then, there's that signature equation discovered by Euler: 1 + e^ (i*pi) = 0 This joins the major operations of Math, with the five most pivotal numbers, all in the eqn voted the most beautiful gem of all. If ever you wanted a signature of Reason Himself at the root of reality, this is it. KF PS: BA77, have fun, mon! kairosfocus
Is this tent big enough for a Tauist? :) Phinehas
Being abstract, mathematics can get away with being irrational. You know, like abstract artists. For your average Joe during a traffic stop, however, not so much.... :D jstanley01