Neil deGrasse Tyson: Cosmos

Further discussion relating Euler's identity to General Relativity, Quantum Mechanics and :

in the equation e^pi*i + 1 = 0 ,,,we find that pi is required in; General Relativity (Einstein’s Equation) https://docs.google.com/File?id=dc8z67wz_52c9nxpz2h_b ,,,and we also find that the square root of negative 1 is required in; Quantum Mechanics (Schrödinger’s Equations) https://docs.google.com/File?id=dc8z67wz_51ck47zff3_b ,,and we also find that e is required for; e is required here in wave equations, in finding the distribution of prime numbers, in electrical theory, and is also found to be foundational to trigonometry.,,,this number, e, also appears in banking, because it is the maximum limit for growth of compound interest. http://www.christianitytoday.com/ct/2006/march/26.44.html?start=3 http://www.biblemaths.com/pag03_pie/img0.gif

supplemental note:

Mathematics and Physics - A Happy Coincidence? - William Lane Craig - video http://www.metacafe.com/watch/9826382/

Music and verse:

Colossians 1:17 And he is before all things, and by him all things consist. Storyside B – Be Still http://www.youtube.com/watch?v=RxwhjPF28NM

bornagain77

This following videos show that the universe also has a primary characteristic of expanding/growing equally in all places, which 'coincidentally' strongly corresponds to the 'e' in Euler's identity. 'e' is the constant that is used in equations of math for finding what the true rates of growth and decay are for any given mathematical problem trying to find as such in this universe:

Centrality of Earth Within The 4-Dimensional Space-Time of General Relativity - video http://www.metacafe.com/w/8421879

This following video shows how finely tuned the '4-Dimensional' expansion of the universe is (1 in 10^120);

Fine Tuning Of Dark Energy and Mass of the Universe - Hugh Ross - video http://www.metacafe.com/watch/4007682

Here are the verses in the Bible, which were written over 2000 years before the discovery of the finely tuned expansion of the universe by ‘Dark Energy’, that speak of God ‘Stretching out the Heavens’; Job 9:8; Isaiah 40:22; Isaiah 40:24; Isaiah 48:13; Zechariah 12:1; Psalm 104:2; Isaiah 42:5; Isaiah 45:12; Isaiah 51:13; Jeremiah 51:15; Jeremiah 10:12. The following verse is one of my favorites out of the group of verses:

Job 9:8 He alone stretches out the heavens and treads on the waves of the sea.

Towards the end of the following video, Michael Denton speaks of the square root of negative 1 being necessary to understand the foundational quantum behavior of this universe. The square root of -1 is also 'coincidentally' found in Euler's identity:

Michael Denton – Mathematical Truths Are Transcendent And Beautiful – Square root of -1 is built into the fabric of reality – video http://www.metacafe.com/watch/4003918"

Now I find it extremely strange, miraculous even, that the enigmatic Euler's identity, which was deduced centuries ago, would find such striking correlation to how reality is actually found to be structured by modern science. In pi we have correlation to the 'sphere of the universe' as revealed by the Cosmic Background radiation, as well pi correlates to the finely-tuned 'geometric flatness' within the 'sphere of the universe' that has now been found. In 'e' we have the fundamental constant that is used for ascertaining exponential growth in math that strongly correlates to the fact that space-time is 'expanding/growing equally' in all places of the universe. In the square root of -1 we have what is termed a 'imaginary number', which was first proposed to help solve equations like x2+ 1 = 0 back in the 17th century, yet now, as Michael Denton pointed out in his video, it is found that the square root of -1 is required to explain the behavior of quantum mechanics in this universe. The correlation of Euler's identity, to the foundational characteristics of how this universe is constructed and operates, is something that should be enough to send shivers down any decent mathematicians spine. Dr. William Dembski has even related 1 and 0, which are also found in Euler’s identity, to theology here:

The End Of Christianity – Finding a Good God in an Evil World – Pg.31 William Dembski PhD. Mathematics Excerpt: “In mathematics there are two ways to go to infinity. One is to grow large without measure. The other is to form a fraction in which the denominator goes to zero. The Cross is a path of humility in which the infinite God becomes finite and then contracts to zero, only to resurrect and thereby unite a finite humanity within a newfound infinity.” http://www.designinference.com/documents/2009.05.end_of_xty.pdf

Of note: I hold ‘growing large without measure’ to be a lesser quality infinity than a fraction in which the denominator goes to zero. The reason why I hold it to be a ‘lesser quality infinity’ is stated at the 4:30 minute mark of the following video:

Can A “Beginning-less Universe” Exist? – William Lane Craig – video http://www.youtube.com/watch?v=K8YN0fwo5J4

The mystery doesn't stop there, 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/ Fascinating Bible code – Pi and natural log – Amazing – video (of note: correct exponent for base of Nat Log found in John 1:1 is 10^40, not 10^65 as stated in the video) http://www.youtube.com/watch?v=Wg9LiiSVaes "Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler's Equation reaches down into the very depths of existence." Stanford University mathematics professor - Dr. Keith Devlin

bornagain77

Seeing as this thread on 'Cosmos' has ventured into extra dimensions and Leonard Euler, I think to further elaborate on Euler's Identity and how his work relates to the Cosmos in general is not too much of a stretch for this thread: First a little background so as to increase the effect of Euler's Identity and how it relates to the 'Cosmos'. It is found that mathematics is 'incomplete':

Kurt Gödel - Incompleteness Theorem - video http://www.metacafe.com/w/8462821

i.e. the 'incompleteness theorem' shows that the 'truthfulness' of any mathematical equation is not held within the equation itself but is dependent on God to derive its ultimate truthfulness:

Gödel’s Incompleteness: The #1 Mathematical Breakthrough of the 20th Century Excerpt: Gödel’s Incompleteness Theorem says: “Anything you can draw a circle around cannot explain itself without referring to something outside the circle - something you have to assume to be true but cannot prove "mathematically" to be true.” http://www.cosmicfingerprints.com/blog/incompleteness/ THE GOD OF THE MATHEMATICIANS - DAVID P. GOLDMAN - August 2010 Excerpt: we cannot construct an ontology that makes God dispensable. Secularists can dismiss this as a mere exercise within predefined rules of the game of mathematical logic, but that is sour grapes, for it was the secular side that hoped to substitute logic for God in the first place. Gödel's critique of the continuum hypothesis has the same implication as his incompleteness theorems: Mathematics never will create the sort of closed system that sorts reality into neat boxes. http://www.firstthings.com/article/2010/07/the-god-of-the-mathematicians "Clearly then no scientific cosmology, which of necessity must be highly mathematical, can have its proof of consistency within itself as far as mathematics go. In absence of such consistency, all mathematical models, all theories of elementary particles, including the theory of quarks and gluons...fall inherently short of being that theory which shows in virtue of its a priori truth that the world can only be what it is and nothing else. This is true even if the theory happened to account for perfect accuracy for all phenomena of the physical world known at a particular time." Stanley Jaki - Cosmos and Creator - 1980, pg. 49 Taking God Out of the Equation - Biblical Worldview - by Ron Tagliapietra - January 1, 2012 Excerpt: Kurt Gödel (1906–1978) proved that no logical systems (if they include the counting numbers) can have all three of the following properties. 1. Validity . . . all conclusions are reached by valid reasoning. 2. Consistency . . . no conclusions contradict any other conclusions. 3. Completeness . . . all statements made in the system are either true or false. The details filled a book, but the basic concept was simple and elegant. He summed it up this way: “Anything you can draw a circle around cannot explain itself without referring to something outside the circle—something you have to assume but cannot prove.” For this reason, his proof is also called the Incompleteness Theorem. Kurt Gödel had dropped a bomb on the foundations of mathematics. Math could not play the role of God as infinite and autonomous. It was shocking, though, that logic could prove that mathematics could not be its own ultimate foundation. Christians should not have been surprised. The first two conditions are true about math: it is valid and consistent. But only God fulfills the third condition. Only He is complete and therefore self-dependent (autonomous). God alone is “all in all” (1 Corinthians 15:28), “the beginning and the end” (Revelation 22:13). God is the ultimate authority (Hebrews 6:13), and in Christ are hidden all the treasures of wisdom and knowledge (Colossians 2:3). http://www.answersingenesis.org/articles/am/v7/n1/equation#

Now with that point established, onto Euler's Identity: The following is the very 'different' equation, from the equations normally associated with physics, that is found to have striking correspondence the 'macro' structure of the universe (Cosmos) as well as striking correspondence to how the universe (Cosmos) operates:

0 = 1 + e ^(i*pi) — Euler

Believe it or not, the five most important numbers in mathematics are tied together, through the complex domain in Euler's number, And that points, ever so subtly but strongly, to a world of reality beyond the immediately physical. Many people resist the implications, but there the compass needle points to a transcendent reality that governs our 3D 'physical' reality.

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.) Moreover Euler’s Identity, rather than just being the 'most enigmatic equation' in math, finds striking correlation to how our 3D reality is actually structured,,, The universe is found to actually be a circular sphere which 'coincidentally' corresponds to the circle of pi within Euler's identity:

The first full-sky image (Cosmic Microwave Background Radiation - CMBR) from Europe's Planck telescope - video http://www.youtube.com/watch?v=e5BeGg4xWVM The Known Universe by AMNH – video - (please note the 'centrality' of the Earth in the universe in the video) http://www.youtube.com/watch?v=17jymDn0W6U 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,

The finely tuned 'flatness' of the entire universe, which 'coincidentally' corresponds to the diameter of pi in Euler’s identity, is found on this following site:

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 < ½k < 0.0068.4 Weak gravitational lensing of distant quasars by intervening galaxies places -0.031 < ½k < 0.009.5 Both measurements confirm the universe indeed manifests zero or very close to zero geometric curvature,,, http://www.reasons.org/did-universe-hyperinflate 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 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?

bornagain77

Neil, Check out Brian Greene's fabulous PBS series on string theory, entitled The Elegant Universe. You can stream it for free online. The 10, and eventually 11 dimensions which Ed Witten's mathematics used to unify the theory, clearly imply extra-cosmological realities, since our cosmos is by definition a space-time (i.e., four-dimensional) realm. Actually, I expect that those extra dimensions do exist -- a realm in which our timeless and spaceless souls exist. Of course, the notion that random errors filtered by natural selection can produce the complex information-processing technology found in living systems is simply absurd. It is for such things that the term no-brainer was invented. GilDodgen

"If these people maintained the slightest rigor, the slightest taste for the truth, it would be quite easy to steer them away from their errors; but their tendency towards stubbornness makes this completely impossible." Leonard Euler After years of dealing with a few fairly dogmatic, and pretty rude, atheists that quote from Euler rings especially true for me. Indeed, if some of the more entrenched atheists were open to reason even in the least then the argument from reason should at least give them pause for thoughtful consideration: “One absolutely central inconsistency ruins [the popular scientific philosophy]. The whole picture professes to depend on inferences from observed facts. Unless inference is valid, the whole picture disappears… unless Reason is an absolute, all is in ruins. Yet those who ask me to believe this world picture also ask me to believe that Reason is simply the unforeseen and unintended by-product of mindless matter at one stage of its endless and aimless becoming. Here is flat contradiction. They ask me at the same moment to accept a conclusion and to discredit the only testimony on which that conclusion can be based.” —C.S. Lewis, Is Theology Poetry (aka the Argument from Reason) C.S. Lewis, Reason, and Naturalism: An Interview with Dr. Jay Richards - audio http://www.idthefuture.com/2012/12/cs_lewis_reason_and_naturalism.html The Argument From Reason - resource page http://www.reasonsforgod.org/the-argument-from-reason/ The Argument from Reason - video http://www.youtube.com/watch?v=xKX-QtEo2fI bornagain77

PS: SO, you are citing Euler -- one of the greatest ever mathematicians -- in his reply to the freethinkers, regarding a defense of revelation. Let me link: http://www.math.dartmouth.edu/~euler/docs/translations/E092trans.pdf kairosfocus

Gil, after seeing how the challenge of a bright red ball on a table has been responded to, you have a point. SteveO, So do you. KF kairosfocus

Gil:

Trying to convince people, who choose to believe otherwise, that random errors cannot produce complex computer programs, as in living systems, is a hopeless task

Leonard Euler, often praised here for the genius of his mathematics, also had some insights into people who are beyond the reach of reason:

(they) have yet to produce any objections that have not long been refuted most thoroughly. But since they are not motivated by the love of truth, and since they have an entirely different point of view, we should not be surprised that the best refutations count for nothing and that the weakest and most ridiculous reasoning, which has so often been shown to be baseless, is continuously repeated. If these people maintained the slightest rigor, the slightest taste for the truth, it would be quite easy to steer them away from their errors; but their tendency towards stubbornness makes this completely impossible.

But we should keep in mind that the debate is not for those but for others who are less fixed in their ideology and who can be shown clearly the behaviour Euler described. steveO

So nature gave rise to nature. The sad part is there are people who buy into that. Joe

That opening statement "The cosmos is all there is ..." was Carl Sagan, probably from the original Cosmos TV series. I recognize the voice.

By the way, if “the cosmos is all that is, or ever was, or ever will be,” wouldn’t that completely invalidate String Theory, which depends on 10 or 11 dimensions of space-time in order that its mathematics make sense?

I expect that astrophysicists take those dimensions to be part of the cosmos. Neil Rickert

It is useless to argue against tautologies such as particular definition of "cosmos". nightlight