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# How Did Mathematics Come to be Woven Into the Fabric of Reality?

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We all learned pi in school in the context of circles.  Pi is the ratio of a circle’s circumference to its diameter.  It is an irrational number approximated by 3.14.

It turns out that pi shows up all over the place, not just in circles.  Here is just one instance.  Take a piece of paper and a stick.  Draw several lines along the paper so that the lines are the length of the stick from each other.  Then randomly drop the stick on the paper.  The probability that the stick will land so that it cuts a line is exactly 2/pi, or about 64%.  If one were to perform millions of trials, one could use the results to perform a very precise calculation of the value of pi without ever considering its relation to circles.

This is just one of many places pi pops up in reality, and pi is just one of several mathematical constants that appear to be woven into the fabric of the universe. One mathematician likened it to looking out over a mountain range, where the bases of the mountains are shrouded in fog, and the symbol for pi is etched into the top of each mountain – one intuitively knows that it is all connected at some basic level even if one has no idea why.

What are we to make of what physicist Eugene Wigner called the “unreasonable effectiveness of mathematics” in describing reality?  The word “unreasonable” makes sense only in the context of expectations.  If one expects the mathematical structure of the universe to be elegant and beautiful, the fact that it turns out to be elegant and beautiful is not unreasonable at all.  It is only unreasonable if one approaches it from the perspective of the metaphysical materialist.  In his universe reality consists of nothing but particles in motion randomly bumping into each other.  In that universe there is no reason to expect any underlying mathematical order, no reason to expect mountain tops etched with pi to pop up all over the place, and no reason to suspect that those mountain tops are connected by a unifying order at the base.

Given materialist premises, none of this makes the slightest bit of sense.  It is just a brute fact.  It cannot be denied or explained.  Yet there it is.

MIT cosmologist Max Tegmark has a theory.  He says consider a character in a computer game (let’s call him Mario) that is so complex and sophisticated that he is able to achieve consciousness.  If Mario were to begin exploring his environment, he would find a lot of mathematical connections.  And if continued to explore, Mario would ultimately find that his entire world is mathematical at its roots.  Tegmark believes we live in a universe that is not just described by mathematics; he believes that mathematics defines all of reality, just as the reality of Mario’s computer game world is defined by mathematics.

Here is the interesting part.  Tegmark makes no design inference.  (He is a multiverse fanatic).  This is astounding.  All he needs to do is take his own analogy one step further.  Why is Mario’s computer game world connected mathematically?  Obviously, it is because that mathematical structure was imposed on the game by the game designer.

Why is the universe we live in connected by an unreasonably beautiful, elegant and effective mathematical structure?  Come on Max.  You are a smart guy.  I know you can figure it out.

Aleta, Very interesting. I was walking through my neighborhood the other day, and I heard the sound of a freight train "horn" or "whistle" (don't know which it is), but based on that sound, which lasted several minutes, I was able to fill in notes to make up a major triad, plus I believe a major minor 3rd above the 5th, which would have made a 7th chord. I heard it in the sound, while I don't really know if all of those notes were actually audible. They seemed to be. But having studied harmony for so many years, I begin to hear those structures even in nature.CannuckianYankee
April 30, 2016
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My spouse is a musician, and we were just talking about the overtone series, which is one of the things that makes notes based on ratios (as Pythagorus first explained) harmonious. She is reading a book called "This Is your brain on music", by Daniel Levitin, and she read me a part about how if you listen to the overtones of a note with the actual note damped, your mind fills in, so to speak, the missing note based on the overtones it's hearing. Your might like this book.Aleta
April 30, 2016
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Slightly OT Thanks everyone for the enlightening discussion. While math is not my strong suit, I appreciate that the universe is quantifiable precisely because it is finite, and as such, it had a beginning. I will have to increase my math skills this coming fall, as (at the age of 54),I continue my studies at California State University, San Bernardino. I am a music major, and have been studying music all my life, pretty much, but at the university level for the last 3 years. I decided 4 years ago that I needed to earn a degree in music, so that I could improve my composition skills, and perhaps become a music educator. What does music have to do with math? The average person would be surprised to learn that all music has a mathematical structure; particularly Western music, beginning with JS Bach and the study of "equal temperament": the realization that tonal music requires precise tuning. "a system of tuning, in which every pair of adjacent pitches is separated by the same interval. In other words, the pitches of an equal temperament can be produced by repeating a generating interval. Equal intervals also means equal ratios between the frequencies of any adjacent pair, and, since pitch is perceived roughly as the logarithm of frequency, equal perceived "distance" from every note to its nearest neighbor." https://en.wikipedia.org/wiki/Equal_temperament In addition to precise tuning, the structure of Western tonal music is based on a 12 tone chromatic scale, and the "Circle of 5ths." http://www.flupe.com/lessons/freeLessons/01_foundationLessons/L01_12Notes/12_notes.htm http://randscullard.com/CircleOfFifths/ These aren't structures that were necessarily invented by humans, although their "evolution" certainly progressed out of human ingenuity, as humans increasingly experimented with tone, rhythm, harmony and counterpoint. So I think the particular insight we can gain from this is that the structures were there to discover, but what we do with those structures is left to the imagination; to our free will in creating: the endless possibilities that we arrive at when we work with the raw material is woven into the mathematical structure of the universe. At one time (in ancient times, actually), humans understood that the basic structure of music was a part of the makeup of the universe. They called it the "Music of the Spheres.," which isn't strictly speaking, audible; but in similarity to musical structures, they are: "mathematical relationships (which) express qualities or 'tones' of energy, which manifest in numbers, visual angles, shapes and sounds." https://en.wikipedia.org/wiki/Musica_universalis So Rock and Roll, or Rhythm and Blues were never inevitable, because they are human inventions; but the rhythm and tonal structures that made them possible, were inevitable as humans continued to develop their understanding of what was musically possible. Bach, Mozart, Beethoven and so many others, merely took full advantage of their understanding of those possibilities, and they made them work in ways that are both beautiful and inspiring.CannuckianYankee
April 30, 2016
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Thank you, bornagain77. Just thinking about it, even the double-slit experiment, just as quantum tunneling, requires the wave function. As one website notes:
The two-slit experiment demonstrates better than any other experiment that a quantum wave function is a probability amplitude that can interfere with itself, producing places where the probability (the square of the absolute value of the complex probability amplitude) of finding a quantum particle is actually zero.
And another website notes:
Notice that the only explanation for quantum tunneling is if the position of the electron is truly spread out, not just hidden or unmeasured. Its raw uncertainty allows for the wave function to penetrate the barrier. This is genuine indeterminism, not simply an unknown quantity until someone measures it.
What starts out as an observed electron, becomes a mathematical function as it passes through the slits of the physical barrier, and then collapses to a wave or particle depending on whether the slits are observed! As you well know, quantum erasure simply determines the wave function collapse independent of time such that it appears to be erasing and redoing the past based on belated observation. All this is a convincing demonstration that the nature of the universe is fundamentally mathematical, and that conscious observation is also fundamental to the universe. The big bang was not observed by humans, so a non-human Mind outside of our universe must have initiated the big bang by creating and observing a wave function along with space-time, some of which God left to us to observe. Paraphrasing what others have said, the good news is that we've discovered that God created the universe, the bad news is that God turned out to be a mathematician, not a physicist. But . . . Is it possible that the universe as we observe it simply a gigantic von Neumann chain, which as it collapses forms our history? I think that the answer is perhaps, but it still requires at least an initial wave function so as not to violate cause-and-effect. -QQuerius
April 29, 2016
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As to, "then there’s the issue of what caused the wave function collapse at the initiation of the big bang. Perhaps a Mind?", this might interest you Querius: At the 8:30 minute mark of the following video, Schrodinger’s cat and Wigner's Friend are highlighted: Divinely Planted Quantum States - video https://youtu.be/qCTBygadaM4?t=512 also of note: Stephen Hawking: "Philosophy Is Dead" - Michael Egnor - August 3, 2015 Excerpt: The metaphysics of Aristotle and Aquinas is far and away the most successful framework on which to understand modern science, especially quantum mechanics. Heisenberg knew this (Link on site). Aristotle 2,300 years ago described the basics of collapse of the quantum waveform (reduction of potency to act),,, Real scientists have a meaningful understanding of natural philosophy as it relates to their work. No atheist scientist in the public spotlight today would pass a freshman philosophy class. Think Dawkins. Think Krauss. Think Myers. Think Moran. Think Novella. Think Coyne. Think Hawking. Our 21st-century scientific priesthood -- mostly atheists and materialists to the extent that their metaphysics is coherent enough to be described -- is dominated by half-educated technicians with publicists.,,, http://www.evolutionnews.org/2015/08/stephen_hawking_3098261.html “I think that modern physics has definitely decided in favor of Plato. In fact the smallest units of matter are not physical objects in the ordinary sense; they are forms, ideas which can be expressed unambiguously only in mathematical language.” Werner Heisenberg - As quoted in The New York Times Book Review (March 8, 1992). - "Uncertainty," David C. Cassidy's biography of my father, Werner Heisenberg Aquinas’ First Way – (The First Mover – Unmoved Mover) - video http://www.youtube.com/watch?v=Qmpw0_w27As Aquinas’ First Way 1) Change in nature is elevation of potency to act. 2) Potency cannot actualize itself, because it does not exist actually. 3) Potency must be actualized by another, which is itself in act. 4) Essentially ordered series of causes (elevations of potency to act) exist in nature. 5) An essentially ordered series of elevations from potency to act cannot be in infinite regress, because the series must be actualized by something that is itself in act without the need for elevation from potency. 6) The ground of an essentially ordered series of elevations from potency to act must be pure act with respect to the casual series. 7) This Pure Act– Prime Mover– is what we call God. http://egnorance.blogspot.com/2011/08/aquinas-first-way.html Or to put it much more simply: "The ‘First Mover’ is necessary for change occurring at each moment." Michael Egnor – Aquinas’ First Way http://www.evolutionnews.org/2009/09/jerry_coyne_and_aquinas_first.html Double Slit, Quantum-Electrodynamics, and Christian Theism – video https://www.facebook.com/philip.cunningham.73/videos/vb.100000088262100/1127450170601248/?type=2&theater Verse: Acts 17:28 For in him we live and move and have our being.' As some of your own poets have said, 'We are his offspring.'bornagain77
April 29, 2016
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bornagain77,
That’s why, when Peierls was asked whether a machine could be an “observer,” he said no, explaining that “the quantum mechanical description is in terms of knowledge, and knowledge requires somebody who knows.” Not a purely physical thing, but a mind.
Thanks for posting this. And then there's the issue of what caused the wave function collapse at the initiation of the big bang. Perhaps a Mind? -QQuerius
April 28, 2016
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bornagain77, It's simple. Since it's now been conclusively demonstrated in experiments that do not directly interact with what's being observed . . . that conscious observation collapses the wave function, psi, into matter and energy waves, therefore the absence of observation leaves no possibility of an emergent consciousness. Therefore, a pre-human, conscious Mind was necessary for the existence of all mass-energy that could eventually be formed into, among everything else, conscious humans. The only way to avoid this conclusion is to scientifically demonstrate the spontaneous collapse of unobserved wave functions. What would this look like? There are two parts: 1. One has to be certain that a wave function collapse had occurred, and 2. One has to be certain that this collapse was not part of a von Neumann chain, nor an observation by any human or non-human mind. Since 2 is not possible to prove, then emergent consciousness is not logically possible, but had to have been the result of a pre-existing conscious Mind. -QQuerius
April 27, 2016
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Of related note to homodyne measurements
Quantum experiment verifies Einstein's 'spooky action at a distance' - March 24, 2015 Excerpt: An experiment,, has for the first time demonstrated Albert Einstein's original conception of "spooky action at a distance" using a single particle. ,,Professor Howard Wiseman and his experimental collaborators,, report their use of homodyne measurements to show what Einstein did not believe to be real, namely the non-local collapse of a (single) particle's wave function.,, According to quantum mechanics, a single particle can be described by a wave function that spreads over arbitrarily large distances,,, ,, by splitting a single photon between two laboratories, scientists have used homodyne detectors—which measure wave-like properties—to show the collapse of the wave function is a real effect,, This phenomenon is explained in quantum theory,, the instantaneous non-local, (beyond space and time), collapse of the wave function to wherever the particle is detected.,,, "Einstein never accepted orthodox quantum mechanics and the original basis of his contention was this single-particle argument. This is why it is important to demonstrate non-local wave function collapse with a single particle," says Professor Wiseman. "Einstein's view was that the detection of the particle only ever at one point could be much better explained by the hypothesis that the particle is only ever at one point, without invoking the instantaneous collapse of the wave function to nothing at all other points. "However, rather than simply detecting the presence or absence of the particle, we used homodyne measurements enabling one party to make different measurements and the other, using quantum tomography, to test the effect of those choices." "Through these different measurements, you see the wave function collapse in different ways, thus proving its existence and showing that Einstein was wrong." http://phys.org/news/2015-03-quantum-einstein-spooky-action-distance.html
Also of note, since the atheistic Many Worlds Interpretation (MWI) denies quantum wave collapse, the preceding experiment also effectively falsifies the atheistic MWI:
The many-worlds interpretation is an interpretation of quantum mechanics that asserts the objective reality of the universal wavefunction and denies the actuality of wavefunction collapse. https://en.wikipedia.org/wiki/Many-worlds_interpretation
also of note: Like practically everything else of significance in the atheistic worldview, their many worlds interpretation of quantum mechanics is built out of pure imagination
Too many worlds - Philip Ball - Feb. 17, 2015 Excerpt:,,, You measure the path of an electron, and in this world it seems to go this way, but in another world it went that way. That requires a parallel, identical apparatus for the electron to traverse. More – it requires a parallel you to measure it. Once begun, this process of fabrication has no end: you have to build an entire parallel universe around that one electron, identical in all respects except where the electron went. You avoid the complication of wavefunction collapse, but at the expense of making another universe.,,, http://aeon.co/magazine/science/is-the-many-worlds-hypothesis-just-a-fantasy/
bornagain77
April 27, 2016
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Does Quantum Physics Make it Easier to Believe in God? Stephen M. Barr – July 10, 2012 Excerpt: Couldn’t an inanimate physical device (say, a Geiger counter) carry out a “measurement” (minus the ‘observer’ in quantum mechanics)? That would run into the very problem pointed out by von Neumann: If the “observer” were just a purely physical entity, such as a Geiger counter, one could in principle write down a bigger wavefunction that described not only the thing being measured but also the observer. And, when calculated with the Schrödinger equation, that bigger wave function would not jump! Again: as long as only purely physical entities are involved, they are governed by an equation that says that the probabilities don’t jump. That’s why, when Peierls was asked whether a machine could be an “observer,” he said no, explaining that “the quantum mechanical description is in terms of knowledge, and knowledge requires somebody who knows.” Not a purely physical thing, but a mind. https://www.bigquestionsonline.com/content/does-quantum-physics-make-it-easier-believe-god The Measurement Problem in quantum mechanics – (Inspiring Philosophy) – 2014 video https://www.youtube.com/watch?v=qB7d5V71vUE also of note: Interaction-free measurements by quantum Zeno stabilization of ultracold atoms - 2015 After early work of Renninger1, Elitzur and Vaidman2 showed that the presence of an absorbing object in one arm of a Mach–Zehnder interferometer can be detected with a single photon, even if it passes through the other arm (see Fig. 1a). In the absence of the object, constructive and destructive interference lead to a bright and a dark output port. However, if an object blocks the upper arm, the interference is absent and the photon can exit from the formerly dark output port—witnessing the existence of the object. In the literature, this has been termed an ‘interaction-free measurement’ (IFM) of the object, although the quantum mechanical description actually includes an interaction. The detection is only ‘interaction free’ when the photon leaves the dark output port, whereas a photon in the bright output port yields no information and a photon hitting the object corresponds to the case with interaction. Because of these unwanted results, the efficiency of IFM is, at most, 50% (refs 2, 3). It can be increased by exploiting the Zeno effect4, as proposed5 and experimentally verified6 with polarized photons (see also refs 7, 8 for an alternative proposal exploiting the resonance condition of a high-finesse cavity). Here, we exploit the quantum Zeno effect to suppress the decay of an unstable system and use this principle for IFMs with an ideal efficiency of 100%. In the generic formulation of the quantum Zeno effect, an unstable system does not decay if its state is continuously measured. This continuous measurement can also be replaced by a continuous absorption of the decay products. An object that continuously absorbs the decay products therefore strongly suppresses the decay of the unstable system. In the limit of strong absorption, decay products are never generated. Therefore, the presence of the object can be detected interaction free by monitoring whether the system decayed or not. In our implementation, the system is realized by a Bose–Einstein condensate (BEC) in an unstable spin configuration. The decay products are atoms that are generated in pairs with opposite spin orientation. Hence, our experiments present a demonstration of the Zeno effect in a truly unstable many-body system9, 10. The ‘absorbing’ object is realized by a resonant laser beam, which removes the decayed atoms with one spin orientation from the system. The interaction-free character of the measurement is proven by a detection of the atoms with the opposite spin direction using a homodyne detection method11. Our implementation in principle allows for an arbitrarily high probability for an IFM of the object, when monitoring the system for sufficiently long times. From our experimental data, we extract confidence levels of 90%, well beyond previous optical experiments. Our experiment also realizes a long-standing proposal for indirect Zeno measurements12, 13. It presents an IFM with a many-particle probe and opens the field of counterfactual quantum information14, 15, 16, 17, 18 to atom optics. Moreover, our setup opens the possibility to investigate open-system dynamics in the Zeno and anti-Zeno regime19, 20. http://www.nature.com/ncomms/2015/150414/ncomms7811/full/ncomms7811.html?WT.ec_id=NCOMMS-20150415
bornagain77
April 27, 2016
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Querius @ 91
You just got owned by bornagain77! And all you can come up with is further unsupported assertions? I hate to break it to you, but your naked assertions do not constitute irrefutable proof
Instruments don't have consciousness. Quantum effects are observed by instruments. Unless you believe instruments are conscious, your assertions don't work. The interaction free measurement which is being used to claim effect of consciousness by using Zehnder interferometer is not really 'interaction free'. Like many terms in QM (Nothing is not Nothing), 'interaction free' is not interaction free! Avshalom C. Elitzur and Lev Vaidman clearly state that in their paper. In fact many QM researchers have avoided using the term as it gives the wrong connotation. Here's direct quote from Avshalom C. Elitzur and Lev Vaidman
The argument which claims that this is an interaction-free measurement sounds very persuasive, but is, in fact, an artifact of a certain interpretation of quantum mechanics. (The interpretation which is usually adopted in discussions of Wheeler’s delayed-choice experiment.) The paradox of obtaining information without interaction appears due to the assumption that only one “branch” of a quantum state exists.
Considering your continued evasion of my simple questions in the Do You Believe in Evolution post, your confusion between squaring velocity with doubling it in the equation for kinetic energy, and your being owned in that thread by RexTugwell has pretty much established your low credibility, not to mention that your style reminds me a lot of someone else here with a lot of sock puppets who once posted some fundamental errors in computing statistics.
I really don't have a problem with - of all people- you thinking I have low credibility ! I gave you a homework.Please do it. If you can't even do multiplication and see 20,000 years x 6 days is not anywhere near 13.8 billion years or can't understand that to equate bya to biblical days in the first three days of calculations by Schroder (7.1 bya, 3.6bya, 1.8bya), God's speed would have to be above light speed, you can't really be taken seriously, and no, I certainly don't go by any other handle here at UD.Me_Think
April 27, 2016
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Querius, for me personally, the fact that consciousness is integral to quantum mechanics is not really even a matter of philosophical debate anymore but is now simply an established empirical fact despite how much atheists bitch and moan to the contrary:
A Short Survey Of Quantum Mechanics and Consciousness Excerpt: Putting all the lines of evidence together the argument for God from consciousness can now be framed like this: 1. Consciousness either preceded all of material reality or is a ‘epi-phenomena’ of material reality. 2. If consciousness is a ‘epi-phenomena’ of material reality then consciousness will be found to have no special position within material reality. Whereas conversely, if consciousness precedes material reality then consciousness will be found to have a special position within material reality. 3. Consciousness is found to have a special, even central, position within material reality. 4. Therefore, consciousness is found to precede material reality. Four intersecting lines of experimental evidence from quantum mechanics that shows that consciousness precedes material reality (Wigner’s Quantum Symmetries, Wheeler’s Delayed Choice, Leggett’s Inequalities, Quantum Zeno effect) https://docs.google.com/document/d/1uLcJUgLm1vwFyjwcbwuYP0bK6k8mXy-of990HudzduI/edit
bornagain77
April 27, 2016
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Bornagain77, Thanks for your posts and links. It will take me a while to go through them. As you probably know, quantum theory has been the most intensively challenged and validated area in all of science to a precision of up to 10 parts per billion. The wild controversy is in the interpretations---what does it all mean to existence and consciousness. Is the interpretation of quantum effects exclusively the domain of faith and philosophy, or can the scientific method extend to these interpretive areas, and to what extent? -QQuerius
April 27, 2016
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Wow, Me_Think. You just got owned by bornagain77! And all you can come up with is further unsupported assertions? I hate to break it to you, but your naked assertions do not constitute irrefutable proof. As I said, you might want to read up on quantum theory, including some of the latest experimental evidence, before you post something contrary. Considering your continued evasion of my simple questions in the Do You Believe in Evolution post, your confusion between squaring velocity with doubling it in the equation for kinetic energy, and your being owned in that thread by RexTugwell has pretty much established your low credibility, not to mention that your style reminds me a lot of someone else here with a lot of sock puppets who once posted some fundamental errors in computing statistics. Goodbye. -QQuerius
April 27, 2016
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God can count, to suggest otherwise is silly. By definition there can only be one true absolute God, and in whatever essence God exists; and as the Alpha and Omega of eternal space and eternal time. Mathematics, while dealing with infinity, cannot prove or disprove eternal infinity exists, or God. It seems God wills to be found primarily by means of faith. Jesus said, His miracles were the sign of who He is. Philosophically or theologically speaking, such an all powerful uncreated, uncaused Creator may select a point in eternal time to create the cosmos. Therefore, He would choose the exact time to create, otherwise, God would not be in control. It follows, once a predetermined, fixed point occurred intelligently, no matter what that point consisted of, then there is a case for every point that follows to be ordered. Speed would be ordered, design would be ordered. Material would be delivered to order, all to a higher law initially, that is by an unknown process; a super science known only as a miracle. Darwin dismissed miracles, the biggest mistake he would ever make. The biggest blindfold consensus science will ever use. That God can make something instantly perfect, must be the case; therefore, the first matter would be delivered perfectly, complete in its first state; the action of a perfect being. It follows, therefore, that any first material substance could be created mature, or immature. We have it on record, that God calculated, six days would do the job to complete a perfect creation, that is, to suit humans. You may disagree with that figure. However, a vexing question then remains, if you were all powerful and all intelligent, how then would you create, for love’s sake, and with every atom to be able to be created and numbered to do your will. God wrote intelligently, plain and simple, and in stone, He created in six days. An important point is, He in no way gave an explanation to how miracles affect certain data. We have his word, recorded as divine law, which should be enough! He created a cosmos fit for gods, a home to move in straight away. The fittest is God, who would, you think, have created all in a fit and proper manner. That is, Good enough to generate perfectly fit children of the Most High. According to Darwin, who ignored such priceless data; that is, a true recorded miraculously embedded history of a developing nation, from whom the creator God would be born. An unbroken chain of worship every seven days back to the miracle of Sinai. A test of pure faith. God counted Ten Commandments, He therefore knew how to count up to six. Mathematically, the God-Man said even the hairs on our heads are numbered. Every hair circumference honed with pi. In evolutionary terms, how did pi get to the attention of the illusive phantom natural selector! Creation in six days is equal to Jesus saying he would generate himself from dead matter, as six days divided by two days equals three yom(s). Of course, historic miracles have all gone pie in the sky in this day and age. Today, such is dismissed and thoroughly done over, as calculated by the number of ‘darwins.' I darwin, is mathematically greater than any intelligent designed miracle, as there are none: the equation mathematically proves it - http://blackwellpublishing.com/ridley/tutorials/Rates_of_evolution2.aspmw
April 27, 2016
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I can google. I just also happen to know what the Fibonacci series and golden spirals are. When I google your search term so I find a lot of photos of nautlius shells, which are not golden spirals. And lots of spiral galaxies, which vary greatly in how tightly they turn. There are good examples (pinecones, sunflower seeds) but don't appear "for no reason" as Barry claims, but just as a result of very simply growth processes.wd400
April 27, 2016
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wd400 @41: Google "Fibonacci sequence in nature" and select 'images'. You'll have plenty of examples. Oh, wait, you're an atheist, so if I gave you 100, you'd require 101.AnimatedDust
April 27, 2016
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I propose a thought experiment. We start with two identical sand beaches, and set up two scenarios. In the first scenario, we bury gold bars a the same relative location on each beach. In scenario 1, we ask two participants to locate the gold bars. In scenario 2, we ask the two participants to build sand castles. What do we expect? In scenario 1 we expect each participant to have no clue where the gold is until an eureka moment happens, he declares that he is done, and he reports the known location of the gold bar. In the second scenario, we expect to find two very different looking sand castles. We will not be surprised at all if someone declares that they are done, then goes back and makes a few changes. What is the fundamental difference between these two scenarios?bFast
April 27, 2016
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News liked my comment at 81 :-) , so I've replied on the thread she started at https://uncommondescent.com/intelligent-design/either-science-or-naturalism-will-win/Aleta
April 27, 2016
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News (at #83): Either man is observing something that underlies the universe and working within those given results or mathematics is an adaptation for survival (it could be completely irrational and is only tangentially related to how the universe works).
I'll go with the second of those, except for the "completely irrational" part. Science is highly systematic. Mathematics is the study of systematicity and systematic methodology. The mathematics does not come from the universe itself, but from the highly systematic nature of the methods used by the scientists. And please note that many scientists were/are mathematicians. Using a systematic methodology is a highly rational approach to exploring our world.Neil Rickert
April 27, 2016
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Aleta, I note again, the definition that mathematics as practised is the study of the logic of structure and quantity (including of course space). Structure and quantity in material part are necessary facets of any possible world and as such are necessary beings. I pointed to twoness and its involvement in distinct identity, pivotal to a world being possible. I would suggest that this lies at the heart of possibility and being, manifesting a world of mathematical realities as necessary to reality. A very obvious longstanding view is that such realities are eternally contemplated by the inherently good necessary and maximally great being at the root of an actual world existing, i.e. God. KFkairosfocus
April 27, 2016
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Aleta at 81: Sorry, that won't work. Either man is observing something that underlies the universe and working within those given results or mathematics is an adaptation for survival (it could be completely irrational and is only tangentially related to how the universe works). The second position saves naturalism (and its creation story, Darwinism) at the price of science. But naturalists are increasingly eager to dump falsifiability and evidence-based thinking. Many are cool with criminalizing dissent. See also: Tyson bombshell: Universe likely just computer sim Science will pick up where it left off, with a hiatus of naturalism in between.News
April 27, 2016
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Aleta, everything man-made is woven into the fabric of reality. That includes mathematics. So back to the original question by Mr A - how did it happen. Just atoms & void & oops?ppolish
April 26, 2016
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Well, yes, at least from one point of view, all of mathematics is man-made: there is a fascinating history of it from the first numbers system and geometry up to calculus and beyond. Any math we know about must have been formalized by humans someplace in history. (I wrote a couple of posts about some of this over in one of the infinity threads.) On the other hand, because new results in math seem inevitable, in some sense, being logically connected consequences, especially after we have worked them out, there is a sense that there we already there and we just discovered them. As one of my students once said as we discussed this in class, she thought that perhaps math was discovered (that is, existed somehow separate from us), but we invented the means of talking and writing about it. And as my Game of Life example was meant to illustrate, there is some math that clearly was just invented, and then the logical consequences of it was explored. So I don't think it's unreasonable to say that math is man-made in the sense that we have chosen the starting points (the axioms, definitions, and logical rules) and then continued the process as we worked out more and more results. That has been the result of the work of human beings, and thus, in that sense, made by man.Aleta
April 26, 2016
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Neil Rickert, "Personally, I think ... Mathematics is entirely man made." Hmmm, is this the opinion that popped into your head one day, or is it something you determined with reason? If so, please share your reasoning.bFast
April 26, 2016
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Conway's Game of Life is man-made mathematics. There are an infinite number of initial patterns, and the only way to know the resulting end pattern is to step though the generations. I can't imagine that every result of the Game of Life has some metaphysical counterpart. See https://en.wikipedia.org/wiki/Conway%27s_Game_of_LifeAleta
April 26, 2016
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Aleta @ 59 writes: "Another possibility is the more Western idea of an engaged deity specifically creating this world and ultimately human beings, with whom he has a special relationship. I don’t believe this is very likely at all, but it is possible" Aleta, the second sentence is not logical or sensical. The use of the word "(un)likely" assumes you have a "matrix of possibilities" (cf Dembski) from which to choose or refer to. The lingo and thought is part of your mathematical training. The subject of God can't be talked about in mathematical or statistical terms. This is a heart issue. Belief, faith, whatever. You are basically saying you don't "feel" there is a personal God. I "feel", to the point of knowing, there is a personal God.juwilker
April 26, 2016
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News,
Just a question: Do people who think mathematics is manmade mind if it is reorganized so as to consistently give someone else more money for the same job? People typically base their case for fairness on the theory that the mathematics is not manmade, but is an external standard to which one can appeal.
I'm not sure that all of mathematics is human-made, but I believe at least some (probably most) is. But how would this reorganization work in the real world? Can you give us more specifics? I really don't see any way it could be accomplished.daveS
April 26, 2016
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WD400 @ 64. If I had to resort to evasion, dissembling, and bad faith to defend my position, I hope I would rethink my position. It does not seem to bother you. It should.
lol. Stop evading and just give some examples.wd400
April 26, 2016
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WD400 @ 64. If I had to resort to evasion, dissembling, and bad faith to defend my position, I hope I would rethink my position. It does not seem to bother you. It should.Barry Arrington
April 26, 2016
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Barry Arrington: How Did Mathematics Come to be Woven Into the Fabric of Reality? It's all about symmetry.Zachriel
April 26, 2016
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