Faith: Even mathematics depends on some unprovable assumptions

_{Denyse O'Leary

January 5, 2020

Intelligent Design, Mathematics

2}_{Categories
Intelligent Design
Mathematics}

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David Hilbert wanted all mathematics to be proved by logical steps. Kurt Gödel showed that no axiomatic system could be complete and consistent at the same time:

On Monday, September 8, 1930, Hilbert opened the annual meeting of the Society of German Scientists and Physicians in Königsberg with a famous discourse called “Logic and the knowledge of nature.” He ended with these words:
“For the mathematician there is no Ignorabimus, and, in my opinion, not at all for natural science either…
“The true reason why [no-one] has succeeded in finding an unsolvable problem is, in my opinion, that there is no unsolvable problem. In contrast to the foolish Ignorabimus, our credo avers: We must know, We shall know.”
In one of those ironies of history, during the three days prior to the conference opened by Hilbert’s speech, a joint conference called Epistemology of the Exact Sciences also took place in Königsberg. On Saturday, September 6, in a twenty-minute talk, Kurt Gödel (1906–1978) presented his incompleteness theorems. On Sunday 7, at the roundtable closing the event, Gödel announced that it was possible to give examples of mathematical propositions that could not be proven in a formal mathematical axiomatic system even though they were true.
The result was shattering. Gödel showed the limitations of any formal axiomatic system in modeling basic arithmetic. He showed that no axiomatic system could be complete and consistent at the same time.
Daniel Andrés Díaz Pachón, “Faith is the most fundamental of the mathematical tools” at Mind Matters News

So it’s not a question of faith vs. reason but faith so we can have reason.

Comments

Well, at least none of you is Spartacus.Bob O'H_{January 10, 2020
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"And I am Mary, Queen of Scots" Ed George, In an infinite number of universes you are. ;) And I'm unbiased by sheer weight of numbers. The amount of universes in which I'm unbiased is infinite. Mathematically speaking, I'm the Primus Unbias. :) Andrewasauber_{January 10, 2020
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I. AM. GROOT.ET_{January 10, 2020
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ET
I am Groot
Not likely. Everybody loves Groot. :)Ed George_{January 9, 2020
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I am GrootET_{January 9, 2020
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Andrew
I’ve been an unbiased reader here for awhile...
And I am Mary, Queen of Scots. :)Ed George_{January 9, 2020
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DiEb, I've been an unbiased reader here for awhile and watching someone engaging Bob O'H invariably results in exactly what BA77 characterizes, which is B O'H Bobbing and Weaving, Leaving and then Returning to Bob and Weave some more. Andrewasauber_{January 9, 2020
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@BA77
I’ll let the unbiased readers decide for themselves who is being forthright.
Great idea! I suppose this unbiased reader will be impressed by your oh so clever piece of repetitive humor, too: bob and weave you have me in stitches e v e r y s i n g l e t i m e !DiEb_{January 9, 2020
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Whatever Bob (and weave). You and Dieb can talk to each other and comfort yourselves in your own delusions as far as I care. My posts in 5, 16 and 17 speak for themselves and both arguments are both unscathed by your counter arguments. Again, I'll let the unbiased readers decide for themselves who is being forthright.bornagain77_{January 9, 2020
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bs77 @ 31 -
You have heard of context have you not? The CONTEXT of my post is unambiguous.
Yes. hte contexct of your posts has been whether maths depends on unprovable assumptions, and specifically about the parallel postulate and whether it was an assumption or could be proved. In that context, it's difficult to see why you change the subject to relativity.Bob O'H_{January 9, 2020
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Split hairs much DiEb. I clearly was talking about the 'real world' of the non-euclidean geometry of this universe when I said the parallel postulate did not hold as being 'always' true and therefore was 'disproven'. i.e. Disproven in so far as empirical science itself in concerned. You might ought to give up Darwinian evolution and try empirical science someday. You want to quibble that it was not mathematically 'disproven'. I say, "So what?" If your mathematical model cannot hold for the real world then it is a completely useless mathematical fantasy that has no bearing on the real world as far as I am concerned! You say that the fact that the parallel postulate does not hold for the real world, and the fact that you, as a Darwinian materialist, have no right to the immaterial Platonic realm of mathematics in the first place are quote unquote "irrelevant factoids". HA! It is not surprising that you would deny that two devastating facts to your materialistic worldview are relevant. It is par for the course. Nonetheless, I am more than satisfied that the unbiased reader can clearly see who is being forthright and who who is being disingenuous,bornagain77_{January 9, 2020
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@BA77: "whatever"? As in "What ever I said before was wrong, but here are two new, irrelevant factoids?"DiEb_{January 9, 2020
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I'm curious: in what context does the sentence "And yet although Euclid’s parallel postulate was never proven it was, none-the-less, disproven" mean that Euclid's parallel postulate was not disproven?DiEb_{January 9, 2020
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Whatever DiEb, the simple point remains that the parallel postulate does not hold as being 'always' true for the 'non-euclidean' (real world) universe we live in. As a result, atheists are a completely loss to explain the 1 in 10^57 fine-tuned flatness of the universe in a ‘non-euclidean’ universe. If you, as an atheist, want to instead argue that the parallel postulate is never-the-less true in some "Platonic realm" of mathematics, I will simply refer you to post 5 and point out that you, as a Darwinian materialist, have no right to the immaterial "Platonic realm" of mathematics in the first place:
Excerpt: As David Berlinski explains, “Mathematicians are capable of grasping a world of objects that lies beyond space and time….” https://uncommondescent.com/intelligent-design/faith-even-mathematics-depends-on-some-unprovable-assumptions/#comment-690659
Thus DiEb you lose on two fronts. The parallel postulate does not hold as 'always' being true in the 'real world' 'material' universe, and you have no right, as a Darwinian materialist, to the immaterial Platonic realm. Choose your poison, both are fatal to you as a Darwinian materialist.bornagain77_{January 9, 2020
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Bob (and weave) O'Hara You have heard of context have you not? The CONTEXT of my post is unambiguous. That you failed to take it into consideration is, again, not my fault. Nor does your frivolous objection that ignores context even begin to answer the fact that atheists are a completely loss to explain the 1 in 10^57 fine-tuned flatness of the universe in a 'non-euclidean' universe. I am more than satisfied that the unbiased reader can clearly see that the atheist is, once again, at a complete loss to explain why the universe is fine-tuned such as it is.bornagain77_{January 9, 2020
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ba77 - This is what you write that I was commenting on: Post 16:
And yet although Euclid’s parallel postulate was never proven it was, none-the-less, disproven::
Which does not say that the universe is almost flat. Post 20:
Bob O’Hara, for crying out loud, I did [not] say that it did not hold by assumption for euclidean geometry. My point was exactly that it was proven not to hold for non-euclidean geometries,
Again, it does not say that the universe is almost flat. Nobody else was discussing physics here, so it was a puzzle why you were changing the subject: it simply wasn't relevant to whether the parallel postulate had been disproved, or if maths depends on unprovable assumptions. Perhaps if you had made it clear that you wanted to change the subject, and you weren't discussing the development of non-Euclidean geometry (by, for example, not commenting on the development of non-Euclidean geometry) things might have been clearer.Bob O'H_{January 9, 2020
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@BA77: In your own words
And yet although Euclid’s parallel postulate was never proven it was, none-the-less, disproven::
This is followed by a quotation which does not make this point. This lead me to the following observations: 1) you believe that the parallel postulate was disproven. 2) your quotations are only loosely connected to your statements.DiEb_{January 9, 2020
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Bob: "Once again, if that was your point, you should have written that." I did write it over and over again, It is not my fault that you either ignored it, are that you have a reading comprehension issue. To repeat:
Post16:”Where this gets interesting is when we realize that Einstein’s Relativity, (both special and general relativity) themselves are not based upon 3-Dimensional Euclidean geometry but are instead based upon non-Euclidean geometry.”,,, The result of these “non-Euclidean geometries” that undergird both theories of relativity is that spacetime itself curves, (and therefore Euclid’s parallel postulate will not hold as being true within the non-Euclidean geometry of the universe) .,,, More interesting still, although the universe itself is based upon non-Euclidean geometry and therefore “has all sorts of deformations in space-time where it varies from the perfectly flat” none-the-less when we “average all those small-scale effects out and look at the big picture’ we find that, in spite of the universe itself being based upon non-Euclidean geometry, that “within an incredibly small margin of uncertainty, is that the universe is flat.,,,”. Moreover there are “no laws of physics that predict or restrict the topology.”,,, We simply should not be living in a ‘flat’ universe where parallel lines stay parallel. As John Gribbin pointed out, “”The Universe today is actually very close to the most unlikely state of all, absolute flatness.” And, “any deviation of the Universe from flatness in the Big Bang would have grown, and grown markedly, as the Universe expanded and aged. Like the pencil balanced on its point and given the tiniest nudges, the Universe soon shifts away from perfect flatness.”,,, Moreover, it is also important to point out that the reason why Euclidean (3 Dimensional) geometry is even applicable in our science, technology, and engineering in the first place is because the 4-Dimensional space-time of our universe (General Relativity) is exceptionally, and unexpectedly “flat”. As Fraser Cain also stated in the preceding article, “We say that the universe is flat, and this means that parallel lines will always remain parallel. 90-degree turns behave as true 90-degree turns, and everything makes sense.,,,’,,, post 17 Moreover, whereas atheists have no clue why the universe should be exceptionally flat, (i.e. why parallel lines should remain parallel), so as to allow man to ‘make sense’ of the universe in the first place. The bible predicted that the universe would be exceptionally flat thousands of years before it was discovered by modern astronomy: 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_{January 9, 2020
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My point is simply that the Parallel Postulate does not hold for the actual (real world) non-euclidean geometries (General and Special Relativity) which describe our universe!
Once again, if that was your point, you should have written that.Bob O'H_{January 9, 2020
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Parallel Postulate Excerpt: In 1823, Janos Bolyai and Lobachevsky independently realized that entirely self-consistent “non-Euclidean geometries” could be created in which the parallel postulate did not hold. (Gauss had also discovered but suppressed the existence of non-Euclidean geometries.) As stated above, the parallel postulate describes the type of geometry now known as Euclidean geometry. http://mathworld.wolfram.com/ParallelPostulate.html Space-Time of a Black hole – video http://www.youtube.com/watch?v=f0VOn9r4dq8 Optical Effects of Special Relativity – video (full relativistic effects shown at 2:40 minute mark) https://youtu.be/JQnHTKZBTI4?t=160
My point is simply that the Parallel Postulate does not hold for the actual (real world) non-euclidean geometries (General and Special Relativity) which describe our universe! And that atheists have no clue, via the 1 in 10^57 fine-tuned flatness within that non-euclidean geometry, why that should be so. (see posts 16 and 17) Whereas the bible predicted that the universe would be exceptionally flat thousands of years before it was discovered by modern astronomy:
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? Chuck Swindoll’s overview of Job of note: "internal clues indicate that Job lived during the time of the patriarchs, approximately 2100 to 1900 BC." https://www.insight.org/resources/bible/the-wisdom-books/job
bornagain77_{January 8, 2020
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Bob O’Hara, for crying out loud, I did not say that it did not hold by assumption for euclidean geometry. My point was exactly that it was proven not to hold for non-euclidean geometries, i.e. The actual non-euclidean geometries which describe, via relativity, our universe!
Your phrasing is somewhat unlucky: It was not proven that Euclid's fifths postulate does not hold for non-euclidean geometries - that is obvious. It was shown that the fifths postulate is independent of the other four, the same way as the continuum hypothesis is independent from ZFC. So, you can add it (or some alternate version) to your postulates and see what kind of mathematics turns out....DiEb_{January 8, 2020
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Bob (and weave) O'Hara states..
BA77: "My point was exactly that it was proven not to hold for non-euclidean geometries" Bob (and weave): "Well, perhaps you should have written that, then."
Willful blindness?
Post16:"Where this gets interesting is when we realize that Einstein’s Relativity, (both special and general relativity) themselves are not based upon 3-Dimensional Euclidean geometry but are instead based upon non-Euclidean geometry.",,, The result of these “non-Euclidean geometries” that undergird both theories of relativity is that spacetime itself curves, (and therefore Euclid’s parallel postulate will not hold as being true within the non-Euclidean geometry of the universe) .,,, More interesting still, although the universe itself is based upon non-Euclidean geometry and therefore “has all sorts of deformations in space-time where it varies from the perfectly flat” none-the-less when we “average all those small-scale effects out and look at the big picture’ we find that, in spite of the universe itself being based upon non-Euclidean geometry, that “within an incredibly small margin of uncertainty, is that the universe is flat.,,,”. Moreover there are “no laws of physics that predict or restrict the topology.”,,, We simply should not be living in a ‘flat’ universe where parallel lines stay parallel. As John Gribbin pointed out, “”The Universe today is actually very close to the most unlikely state of all, absolute flatness.” And, “any deviation of the Universe from flatness in the Big Bang would have grown, and grown markedly, as the Universe expanded and aged. Like the pencil balanced on its point and given the tiniest nudges, the Universe soon shifts away from perfect flatness.”,,, Moreover, it is also important to point out that the reason why Euclidean (3 Dimensional) geometry is even applicable in our science, technology, and engineering in the first place is because the 4-Dimensional space-time of our universe (General Relativity) is exceptionally, and unexpectedly “flat”. As Fraser Cain also stated in the preceding article, “We say that the universe is flat, and this means that parallel lines will always remain parallel. 90-degree turns behave as true 90-degree turns, and everything makes sense.,,,’,,,
post 17
Moreover, whereas atheists have no clue why the universe should be exceptionally flat, (i.e. why parallel lines should remain parallel), so as to allow man to ‘make sense’ of the universe in the first place. The bible predicted that the universe would be exceptionally flat thousands of years before it was discovered by modern astronomy: 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_{January 7, 2020
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ba77 -
My point was exactly that it was proven not to hold for non-euclidean geometries
Well, perhaps you should have written that, then.Bob O'H_{January 7, 2020
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correction, "Bob O’Hara, for crying out loud, I did NOT say that it did not hold by assumption for euclidean geometry. ,,,,"bornagain77_{January 7, 2020
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Silver Asiatic at 19, thanks for fleshing that out. I like the fact that you used a triangle to flesh it out. (A triangle happens to be the same exact example I used in conversation with a friend yesterday to prove to him that his thoughts must be 'spiritual' instead of material)bornagain77_{January 7, 2020
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Bob O'Hara, for crying out loud, I did say that it did not hold by assumption for euclidean geometry. My point was exactly that it was proven not to hold for non-euclidean geometries, i.e. The actual non-euclidean geometries which describe, via relativity, our universe! I went on to show, via the 1 in 10^57 fine tuned flatness of the universe, how atheists, such as you yourself, have no clue why euclidean geometry should even hold for our universe and thus for why humans should even be able to 'miraculously' describe the universe with mathematics, nor any clue for why we can apply mathematics in such a way so as to intelligently design scientific instruments so as to be able to even 'do science' in the first place. The Theistic implications of the entire situation, which I made clear in posts 16 and 17, are overwhelming. Missing the forest for the trees is too subtle a rebuke for your mistake.bornagain77_{January 7, 2020
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BA77 @ 10 I had not seen that before - yes, it's great. There are similar concepts to that also. Here, we have truths which are eternal. It could also be universals which would exist even if there was no human life on earth. Or immaterial forms of objects. Like a triangle. Everyone who knows what a triangle is, can think of a triangle. This triangle in thought, is the form - it is not a physical object, but it conforms to the geometric formula for a triangle. 1. Form or pattern of individual objects exist (the form of a triangle) 2. The form is a universal, and not a physical object but a mental object. 3. The form would exist even if there were no human beings on earth. 4. So, the form cannot be the product of human minds. 5. Therefore the form, essence or pattern of the object is immaterial and the product of a transcendent, universal mind.Silver Asiatic_{January 7, 2020
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ba77 @ 16 -
And yet although Euclid’s parallel postulate was never proven it was, none-the-less, disproven::
No it wasn't. It was shown that it's possible to construct geometries where the parallel postulate does not hold. In Euclidean geometry, the parallel postulate is true (by assumption), so can't be dis-proven.Bob O'H_{January 7, 2020
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The author of the preceding article should be very grateful that the universe is ‘ever-so-boringly flat’. If the universe were not so ‘ever-so-boringly flat’ science and technology simply would not be possible for humans in the first place. Without some remarkable degree of exceptional, and stable, flatness for the universe, (as well as exceptional stability for all the other constants), Euclidean (3-Dimensional) geometry would not be applicable to our world. or to the universe at large, and this would make science and engineering for humans, for all practical purposes, all but impossible. As Michael Schirber explains, if any of the constants varied, (or the spacetime of the universe varied for that matter), then, "The speed of light, for instance, might be measured one day with a ruler and a clock. If the next day the same measurement gave a different answer, no one could tell if the speed of light changed, the ruler length changed, or the clock ticking changed."
Scientists Question Nature’s Fundamental Laws – Michael Schirber – 2006 Excerpt: “There is absolutely no reason these constants should be constant,” says astronomer Michael Murphy of the University of Cambridge. “These are famous numbers in physics, but we have no real reason for why they are what they are.” The observed differences are small-roughly a few parts in a million-but the implications are huge (if they hold up): The laws of physics would have to be rewritten, not to mention we might need to make room for six more spatial dimensions than the three that we are used to.”,,, The speed of light, for instance, might be measured one day with a ruler and a clock. If the next day the same measurement gave a different answer, no one could tell if the speed of light changed, the ruler length changed, or the clock ticking changed. http://www.space.com/2613-scientists-question-nature-fundamental-laws.html
Moreover, this exceptional flatness for the universe allows us to see that the ‘tiny temperature variations (in the Cosmic BackGround Radiation) correspond to the largest scale structures of the observable universe.’
How do we know the universe is flat? Discovering the topology of the universe – by Fraser Cain – June 7, 2017 Excerpt: “And here’s the part that blows my mind every time I think about it. These tiny temperature variations correspond to the largest scale structures of the observable universe. A region that was a fraction of a degree warmer become a vast galaxy cluster, hundreds of millions of light-years across.” – per physorg
And what is interesting in regards to ‘these largest scale structures of the observable universe’, is that astronomy now reveals a surprising rotational coincidence for Earth in relation to the quasar and radio galaxy distributions in the universe, i.e ‘these largest scale structures of the observable universe’:
Is there a violation of the Copernican principle in radio sky? – Ashok K. Singal – May 17, 2013 Abstract: Cosmic Microwave Background Radiation (CMBR) observations from the WMAP satellite have shown some unexpected anisotropies (directionally dependent observations), which surprisingly seem to be aligned with the eclipticcite {20,16,15}. The latest data from the Planck satellite have confirmed the presence of these anisotropiescite {17}. Here we report even larger anisotropies in the sky distributions of powerful extended quasars and some other sub-classes of radio galaxies in the 3CRR catalogue, one of the oldest and most intensively studies sample of strong radio sourcescite{21,22,3}. The anisotropies lie about a plane passing through the two equinoxes and the north celestial pole (NCP). We can rule out at a 99.995% confidence level the hypothesis that these asymmetries are merely due to statistical fluctuations. Further, even the distribution of observed radio sizes of quasars and radio galaxies show large systematic differences between these two sky regions. The redshift distribution appear to be very similar in both regions of sky for all sources, which rules out any local effects to be the cause of these anomalies. Two pertinent questions then arise. First, why should there be such large anisotropies present in the sky distribution of some of the most distant discrete sources implying inhomogeneities in the universe at very large scales (covering a fraction of the universe)? 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
Moreover, when the tiny temperature variations are averaged, ‘smeared’, and/or smoothed out, they were able to detect the anomalies in the CMBR, which ‘strangely’ line up with the earth and solar system,
Large-scale alignments from WMAP and Planck – 2013 We revisit the alignments of the largest structures observed in the cosmic microwave background (CMB) using the seven and nine-year WMAP and first-year Planck data releases. The observed alignments — the quadrupole with the octopole and their joint alignment with the direction of our motion with respect to the CMB (the dipole direction) and the geometry of the Solar System (defined by the Ecliptic plane) — are generally in good agreement with results from the previous WMAP data releases.,,, both the WMAP and Planck data confirm the alignments of the largest observable CMB modes in the Universe. http://arxiv.org/abs/1311.4562
Here is an excellent clip from the documentary “The Principle” that explains, in an easy to understand manner, how these ‘anomalies’ that line up with the earth and solar system were found, via ‘averaging out’, in the tiny temperature variations in the CMBR data.
Cosmic Microwave Background Proves Intelligent Design (disproves Copernican principle) (clip of “The Principle”) – video https://www.youtube.com/watch?v=htV8WTyo4rw
In other words, the "tiny temperature variations" in the CMBR, to the largest scale structures in the universe itself, reveal teleology, (i.e. a goal directed purpose, a plan, a reason), that specifically included the earth from the start. ,,, The earth, from what our best science can now tell us, is not some random cosmic fluke as atheists had presupposed.
Genesis 1:1 In the beginning God created the heavens and the earth.
Moreover, whereas atheists have no clue why the universe should be exceptionally flat, (i.e. why parallel line should remain parallel), so as to allow man to 'make sense' of the universe in the first place. The bible predicted that the universe would be exceptionally flat thousands of years before it was discovered by modern astronomy:
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?
As both Einstein and Wigner pointed out, the fact that mathematics should even be applicable to our universe in the first place, is, by all rights, a "miracle" that is inexplicable for atheists:
On the Rational Order of the World: a Letter to Maurice Solovine - Albert Einstein - March 30, 1952 Excerpt: "You find it strange that I consider the comprehensibility of the world (to the extent that we are authorized to speak of such a comprehensibility) as a miracle or as an eternal mystery. Well, a priori, one should expect a chaotic world, which cannot be grasped by the mind in any way .. the kind of order created by Newton's theory of gravitation, for example, is wholly different. Even if a man proposes the axioms of the theory, the success of such a project presupposes a high degree of ordering of the objective world, and this could not be expected a priori. That is the 'miracle' which is constantly reinforced as our knowledge expands. There lies the weakness of positivists and professional atheists who are elated because they feel that they have not only successfully rid the world of gods but “bared the miracles." -Albert Einstein http://inters.org/Einstein-Letter-Solovine The Unreasonable Effectiveness of Mathematics in the Natural Sciences - Eugene Wigner - 1960 Excerpt: ,,certainly it is hard to believe that our reasoning power was brought, by Darwin's process of natural selection, to the perfection which it seems to possess.,,, It is difficult to avoid the impression that a miracle confronts us here, quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions, or to the two miracles of the existence of laws of nature and of the human mind's capacity to divine them.,,, The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning. http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html
Supplemental notes:
And whereas, atheists have no compelling evidence for all the various extra dimensions, parallel universe and/or multiverse scenarios that they have put forth, Christians, on the other hand, (as is shown in the following video), can appeal directly to the higher dimensional mathematics behind Quantum Mechanics, Special Relativity and General Relativity to support their belief that God upholds this universe in its continual existence, as well as to support their belief in a heavenly dimension and in a hellish dimension. Quantum Mechanics, Special Relativity, General Relativity and Christianity - video https://www.youtube.com/watch?v=h4QDy1Soolo Moreover, allowing the Agent causality of God ‘back’ into physics, as the Christian founders of modern science originally envisioned,,,, (Isaac Newton, Michael Faraday, James Clerk Maxwell, and Max Planck, to name a few of the Christian founders),,, and as quantum mechanics itself now empirically demands (with the closing of the free will loophole by Anton Zeilinger and company), rightly allowing the Agent causality of God ‘back’ into physics provides us with a very plausible resolution for the much sought after ‘theory of everything’ in that Christ’s resurrection from the dead provides an empirically backed reconciliation, via the Shroud of Turin, between quantum mechanics and general relativity into the much sought after ``Theory of Everything”. Here are a few posts where I lay out and defend some of the evidence for that claim: January 2020 https://uncommondescent.com/intelligent-design/welcome-to-the-brave-new-world-of-science/#comment-690569
Verse:
Colossians 1:15-20 The Son is the image of the invisible God, the firstborn over all creation. For in him all things were created: things in heaven and on earth, visible and invisible, whether thrones or powers or rulers or authorities; all things have been created through him and for him. He is before all things, and in him all things hold together. And he is the head of the body, the church; he is the beginning and the firstborn from among the dead, so that in everything he might have the supremacy. For God was pleased to have all his fullness dwell in him, and through him to reconcile to himself all things, whether things on earth or things in heaven, by making peace through his blood, shed on the cross.
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At 2 Bob O'Hara states
Of course maths depends on unprovable assumptions, and this was known long before Gödel. That’s why they are assumptions not theorems or lemmas. The history of Euclid’s parallel postulate is a great example of this.
And yet although Euclid’s parallel postulate was never proven it was, none-the-less, disproven::
Parallel Postulate Excerpt: In 1823, Janos Bolyai and Lobachevsky independently realized that entirely self-consistent "non-Euclidean geometries" could be created in which the parallel postulate did not hold. (Gauss had also discovered but suppressed the existence of non-Euclidean geometries.) As stated above, the parallel postulate describes the type of geometry now known as Euclidean geometry. http://mathworld.wolfram.com/ParallelPostulate.html Euclid's Postulates 1. A straight line segment can be drawn joining any two points. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center. 4. All right angles are congruent. 5. If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough. This postulate is equivalent to what is known as the parallel postulate. Euclid's fifth postulate cannot be proven as a theorem, although this was attempted by many people. Euclid himself used only the first four postulates ("absolute geometry") for the first 28 propositions of the Elements, but was forced to invoke the parallel postulate on the 29th. In 1823, Janos Bolyai and Nicolai Lobachevsky independently realized that entirely self-consistent "non-Euclidean geometries" could be created in which the parallel postulate did not hold. (Gauss had also discovered but suppressed the existence of non-Euclidean geometries.) http://mathworld.wolfram.com/EuclidsPostulates.html
Where this gets interesting is when we realize that Einstein's Relativity, (both special and general relativity) themselves are not based upon 3-Dimensional Euclidean geometry but are instead based upon non-Euclidean geometry.
Four-dimensional space - history Excerpt: In 1908, Hermann Minkowski presented a paper[8] consolidating the role of time as the fourth dimension of spacetime, the basis for Einstein's theories of special and general relativity.[9] But the geometry of spacetime, being non-Euclidean, is profoundly different from that popularised by Hinton. - per wikpedia Spacetime Excerpt: In 1908, Hermann Minkowski—once one of the math professors of a young Einstein in Zurich—presented a geometric interpretation of special relativity that fused time and the three spatial dimensions of space into a single four-dimensional continuum now known as Minkowski space. A key feature of this interpretation is the definition of a spacetime interval that combines distance and time. Although measurements of distance and time between events differ for measurements made in different reference frames, the spacetime interval is independent of the inertial frame of reference in which they are recorded. Minkowski's geometric interpretation of relativity was to prove vital to Einstein's development of his 1915 general theory of relativity, wherein he showed that spacetime becomes curved in the presence of mass or energy.,,, Einstein, for his part, was initially dismissive of Minkowski's geometric interpretation of special relativity, regarding it as überflüssige Gelehrsamkeit (superfluous learnedness). However, in order to complete his search for general relativity that started in 1907, the geometric interpretation of relativity proved to be vital, and in 1916, Einstein fully acknowledged his indebtedness to Minkowski, whose interpretation greatly facilitated the transition to general relativity.[10]:151–152 Since there are other types of spacetime, such as the curved spacetime of general relativity, the spacetime of special relativity is today known as Minkowski spacetime. https://en.wikipedia.org/wiki/Spacetime
The result of these "non-Euclidean geometries" that undergird both theories of relativity is that spacetime itself curves, (and therefore Euclid’s parallel postulate will not hold as being true within the non-Euclidean geometry of the universe) . And whereas the curvature of the 4-dimensional spacetime that undergirds Einstein's general relativity is fairly well known,,,
Space-Time of a Black hole - video http://www.youtube.com/watch?v=f0VOn9r4dq8
,,, and whereas that non-Euclidean geometry associated with general relativity is fairly well known, what is far less well known is that special relativity also has spacetime curvature associated with it, In the following video clip, which was made by two Australian University Physics Professors, we find that the 3-Dimensional world ‘folds and collapses’ into a tunnel shape as a ‘hypothetical’ observer approaches the ‘higher dimension’ of the speed of light.
Optical Effects of Special Relativity - video (full relativistic effects shown at 2:40 minute mark) https://youtu.be/JQnHTKZBTI4?t=160
More interesting still, although the universe itself is based upon non-Euclidean geometry and therefore "has all sorts of deformations in space-time where it varies from the perfectly flat" none-the-less when we "average all those small-scale effects out and look at the big picture' we find that, in spite of the universe itself being based upon non-Euclidean geometry, that "within an incredibly small margin of uncertainty, is that the universe is flat.,,,". Moreover there are "no laws of physics that predict or restrict the topology."
Yes, the world (universe) really is flat - December 8, 2016 Excerpt: The universe has all sorts of deformations in space-time where it varies from the perfectly flat. Any place where there’s mass or energy, there’s a corresponding bending of space-time — that’s General Relativity 101. So a couple light beams would naturally collide inside a wandering black hole, or bend along weird angles after encountering a galaxy or two. But average all those small-scale effects out and look at the big picture. When we examine very old light — say, the cosmic microwave background — that has been traveling the universe for more than 13.8 billion years, we get a true sense of the universe’s shape. And the answer, as far as we can tell, to within an incredibly small margin of uncertainty, is that the universe is flat.,,, ,,, but there are also no laws of physics that predict or restrict the topology. https://uncommondescent.com/intelligent-design/yes-the-world-really-is-flat/
We simply should not be living in a 'flat' universe where parallel lines stay parallel. As John Gribbin pointed out, ""The Universe today is actually very close to the most unlikely state of all, absolute flatness." And, "any deviation of the Universe from flatness in the Big Bang would have grown, and grown markedly, as the Universe expanded and aged. Like the pencil balanced on its point and given the tiniest nudges, the Universe soon shifts away from perfect flatness."
"The Universe today is actually very close to the most unlikely state of all, absolute flatness. And that means it must have been born in an even flatter state, as Dicke and Peebles, two of the Princeton astronomers involved in the discovery of the 3 K background radiation, pointed out in 1979. Finding the Universe in a state of even approximate flatness today is even less likely than finding a perfectly sharpened pencil balancing on its point for millions of years, for, as Dicke and Peebles pointed out, any deviation of the Universe from flatness in the Big Bang would have grown, and grown markedly, as the Universe expanded and aged. Like the pencil balanced on its point and given the tiniest nudges, the Universe soon shifts away from perfect flatness." ~ John Gribbin, In Search of the Big Bang
In fact, in so far as measurement accuracy will allow, "astronomers estimate that the universe must have been flat to 1 part within 1×10^57 parts."
How do we know the universe is flat? Discovering the topology of the universe - by Fraser Cain - June 7, 2017 Excerpt: With the most sensitive space-based telescopes they have available, astronomers are able to detect tiny variations in the temperature of this background radiation. And here's the part that blows my mind every time I think about it. These tiny temperature variations correspond to the largest scale structures of the observable universe. A region that was a fraction of a degree warmer become a vast galaxy cluster, hundreds of millions of light-years across. The cosmic microwave background radiation just gives and gives, and when it comes to figuring out the topology of the universe, it has the answer we need. If the universe was curved in any way, these temperature variations would appear distorted compared to the actual size that we see these structures today. But they're not. To best of its ability, ESA's Planck space telescope, can't detect any distortion at all. The universe is flat.,,, We say that the universe is flat, and this means that parallel lines will always remain parallel. 90-degree turns behave as true 90-degree turns, and everything makes sense.,,, Since the universe is flat now, it must have been flat in the past, when the universe was an incredibly dense singularity. And for it to maintain this level of flatness over 13.8 billion years of expansion, in kind of amazing. In fact, astronomers estimate that the universe must have been flat to 1 part within 1×10^57 parts. Which seems like an insane coincidence. https://phys.org/news/2017-06-universe-flat-topology.html
Moreover, it is also important to point out that the reason why Euclidean (3 Dimensional) geometry is even applicable in our science, technology, and engineering in the first place is because the 4-Dimensional space-time of our universe (General Relativity) is exceptionally, and unexpectedly “flat”. As Fraser Cain also stated in the preceding article, “We say that the universe is flat, and this means that parallel lines will always remain parallel. 90-degree turns behave as true 90-degree turns, and everything makes sense.,,,’
How do we know the universe is flat? Discovering the topology of the universe – by Fraser Cain – June 7, 2017 Excerpt: We say that the universe is flat, and this means that parallel lines will always remain parallel. 90-degree turns behave as true 90-degree turns, and everything makes sense.,,, Since the universe is flat now, it must have been flat in the past, when the universe was an incredibly dense singularity. And for it to maintain this level of flatness over 13.8 billion years of expansion, in kind of amazing. In fact, astronomers estimate that the universe must have been flat to 1 part within 1×10^57 parts. Which seems like an insane coincidence. https://phys.org/news/2017-06-universe-flat-topology.html Why We Need Cosmic Inflation By Paul Sutter, Astrophysicist | October 22, 2018 Excerpt: As best as we can measure, the geometry of our universe appears to be perfectly, totally, ever-so-boringly flat. On large, cosmic scales, parallel lines stay parallel forever, interior angles of triangles add up to 180 degrees, and so on. All the rules of Euclidean geometry that you learned in high school apply. But there’s no reason for our universe to be flat. At large scales it could’ve had any old curvature it wanted. Our cosmos could’ve been shaped like a giant, multidimensional beach ball, or a horse-riding saddle. But, no, it picked flat. https://www.space.com/42202-why-we-need-cosmic-inflation.html
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