Intelligent Design Mathematics

At Mind Matters News: 1. Why Infinity Does Not Exist in Reality

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Robert J. Marks: A few examples will show the absurd results that come from assuming that infinity exists in the world around us as it does in math:

Cantor’s theory of the infinite can be explained, starting with the lowly shepherd tending sheep. Imagine a shepherd who does not count well. He gathers stones until the number of stones is equal to the number of sheep he is tending. The set of stones is said to have the same size, or cardinality, as the set of sheep. If there are ten sheep, the size of the set of sheep is ten and the shepherd picks up ten stones. The size of the set of sheep is the same as the size of the set of stones because there is a one-to-one correspondence. At the end of the day, the shepherd compares the number of stones to the number of sheep. If the number of the stones is the same as the number of sheep, no sheep have been lost. Sheep #1 corresponds to stone 1, sheep #2 to stone 2, sheep #3 to stone 3 all the way up to the tenth sheep…

A set with a true infinite size is the set of counting numbers.

{ 1,2,3,4,…}.

The infinite size of this set is said to be the Hebrew letter aleph: . Let’s play around. Take away the first number in this set, namely 1, to get the set

{2,3,4,5,…}.

Even though we’ve made the original set smaller in one sense, both sets have the same size. Think of sheep and stones. Sheep number 1 now maps to stone #2. Sheep number 2 maps to stone #3. Sheep 3 to stone #4 etc. The sets never end so this correspondence goes on forever. There is a one-to-one correspondence between the elements of the two infinite sets so the size of both sets is identical.

This result should strike you as ludicrous. The infinite size of the sets might be the same, but the diminished set is clearly smaller than the set of counting numbers in another sense. This is weird. Let’s apply this same simple idea to the infinite. We’ll show that doing so leads to ludicrous conclusions. Such conclusions are common when dealing with infinities.

Robert J. Marks , “1. Why Infinity Does Not Exist in Reality” at Mind Matters News

But this is nothing compared to what happens when Dr. Marks gets to Hilbert’s Hotel …

Takehome: Robert J. Marks: In a series of five posts, I explain the difference between what infinity means — and doesn’t mean — as a concept.

Next: Infinity illustrates that the universe has a beginning. The age of the universe is shown to necessarily be finite if ridiculous properties of infinity are to be avoided.

You may also wish to read: Yes, you can manipulate infinity in math. The hyperreals are bigger (and smaller) than your average number — and better! (Jonathan Bartlett)

12 Replies to “At Mind Matters News: 1. Why Infinity Does Not Exist in Reality

  1. 1
  2. 2
    Bob O'H says:

    But this is nothing compared to what happens when Dr. Marks gets to Hilbert’s Hotel …

    Did they tell him they were full?

  3. 3
    kairosfocus says:

    Yes, cardinality of transfinites is counter intuitive. I often show that the trick is for countablesets, find a structured way to put it in a map to N or equivalently transform it into N. The case shown, n-1, in succession from n = 1 will give N. KF

  4. 4
    chuckdarwin says:

    “Only two things are infinite, the universe and human stupidity, and I’m not sure about the former.”
    –Albert Einstein

  5. 5
    bornagain77 says:

    Of semi-related note:

    “Every number is defined by its own character so that no number is equal to any other. They are unequal to one another and are different, and the individual numbers are finite, but as a class they are infinite. Does that mean that God does not know all numbers, because of their infinity? Does God’s knowledge extend as far as a certain sum, and end there? No one could be insane enough to say that.
    Now those philosophers who revere the authority of Plato will not despise numbers and say that they are irreverent to God’s knowledge, For Plato emphasizes that God constructed the world by use of numbers, while we have the authority of Scripture, where God is thus addressed, “You have set all things in order all things by number, measure, and weight.” And the prophet says of God, “He produces the world according to number’. And the Savior says in the Gospel, “Your hairs are all numbered”.
    Never let us doubt then that every number is known to him “whose understanding cannot be numbered”. Although the infinite series of numbers cannot be numbered, this infinity of numbers is not outside the comprehension of him “whose understanding cannot be numbered”.”
    – St. Augustine – “City of God” – 12th Book, 19th Chapter
    – Infinity: Aristotle, St. Augustine, Cantor, Gödel – video – 31:29 minute mark
    https://youtu.be/SMt2VtjMfrU?t=1889

    And indeed, that the Judeo-Christian belief that the infinite Mind of God has “set all things in order all things by number, measure, and weight” is obviously an integral belief that played an essential role in the founding of modern science in Medieval Christian Europe. This essential belief is testified to by Kepler’s statement upon discovering the mathematical laws of Planetary motion, “O, Almighty God, I am thinking Thy thoughts after Thee!”

    “O, Almighty God, I am thinking Thy thoughts after Thee!”
    – Johannes Kepler, “The Harmonies of the World.”, book five – 1619 – best known for his three laws of planetary motion,

    Moreover, that the infinite Mind of God must be behind any mathematics that describe this universe is not just some archaic Christian belief that is left over from the ‘dark ages’ of Medieval Christian Europe, but the belief that the infinite Mind of God must be behind any mathematics that describe this universe is also testified to by modern physics. Especially by both Eugene Wigner and Albert Einstein calling the applicability of mathematics to the universe a quote-unquote ‘miracle’.

    In fact, Eugene Wigner, (who’s insights into the foundations of quantum mechanics have fostered a ‘second quantum revolution’; per A. Zeilinger), went so far as question Darwinism’s ability to produce our ‘reasoning power’, when he called the applicability of mathematics to the universe a ‘miracle’,

    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.
    https://www.maths.ed.ac.uk/~v1ranick/papers/wigner.pdf

    and Albert Einstein, who needs no introduction, even went so far as to chastise ‘professional atheists’ in the process of calling the applicability of mathematics to the universe a ‘miracle’

    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

    That both Eugene Wigner, a giant in Quantum Mechanics, and Albert Einstein, who discovered both Special and General Relativity, would both, in essence, hold that the infinite mind of God must be behind any mathematics that describe this universe, by both of them calling the applicability of mathematics to the universe a quote-unquote ‘miracle’, is very interesting.

    The reason that it is very interesting is because in the quest to find a mathematical ‘theory of everything’, (a theory where General Relativity and Quantum Mechanics are hypothetically brought into a single overarching mathematical framework), theoretical physicists are stymied at every turn by the fact that there apparently exists an ‘infinite mathematical divide’ between the two theories that can’t be bridged.

    Professor Jeremy Bernstein states the ‘infinite mathematical divide’ between the two theories as such, “there remains an irremediable difficulty. Every order reveals new types of infinities, and no finite number of renormalizations renders all the terms in the series finite.The theory is not renormalizable.”

    Quantum Leaps – Jeremy Bernstein – October 19, 2018
    Excerpt: Divergent series notwithstanding, quantum electrodynamics yielded results of remarkable accuracy. Consider the magnetic moment of the electron. This calculation, which has been calculated up to the fifth order in ?, agrees with experiment to ten parts in a billion. If one continued the calculation to higher and higher orders, at some point the series would begin to break down. There is no sign of that as yet. Why not carry out a similar program for gravitation? One can readily write down the Feynman graphs that represent the terms in the expansion. Yet there remains an irremediable difficulty. Every order reveals new types of infinities, and no finite number of renormalizations renders all the terms in the series finite.
    The theory is not renormalizable.
    https://inference-review.com/article/quantum-leaps
    Jeremy Bernstein is professor emeritus of physics at the Stevens Institute of Technology.

    And as theoretical physicist Sera Cremonini noted, “You would need to add infinitely many counterterms in a never-ending process. Renormalization would fail.,,,”

    Why Gravity Is Not Like the Other Forces
    We asked four physicists why gravity stands out among the forces of nature. We got four different answers.
    Excerpt: the quantum version of Einstein’s general relativity is “nonrenormalizable.”,,,
    In quantum theories, infinite terms appear when you try to calculate how very energetic particles scatter off each other and interact. In theories that are renormalizable — which include the theories describing all the forces of nature other than gravity — we can remove these infinities in a rigorous way by appropriately adding other quantities that effectively cancel them, so-called counterterms. This renormalization process leads to physically sensible answers that agree with experiments to a very high degree of accuracy.
    The problem with a quantum version of general relativity is that the calculations that would describe interactions of very energetic gravitons — the quantized units of gravity — would have infinitely many infinite terms. You would need to add infinitely many counterterms in a never-ending process. Renormalization would fail.,,,
    Sera Cremonini – theoretical physicist – Lehigh University
    https://www.quantamagazine.org/why-gravity-is-not-like-the-other-forces-20200615/

    And although theoretical physicists have been stymied for 40 plus years now in their quest to find a purely mathematical theory of everything, a theory that can bridge the ‘infinite mathematical divide’ that apparently exists between the two theories, all hope is not lost.

    Dr. William Dembski in this following comment, although he was not directly addressing the ‘infinite mathematical divide’ that exists between General Relativity and Quantum Mechanics, offers this insight into what the ‘unification’ of infinite God with finite man might look like mathematically:, Specifically he states, “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.”

    The End Of Christianity – Finding a Good God in an Evil World – Pg.31
    William Dembski PhDs. Mathematics and Theology
    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.....of_xty.pdf

    ,,, and when we rightly allow the Agent causality of God ‘back’ into physics, (as the Christian founders of modern science originally envisioned, Johann Kepler, Isaac Newton, Michael Faraday, James Clerk Maxwell, and Max Planck, to name a few of the Christian founders),,,,

    “Newton’s Rejection of the “Newtonian World View”: The Role of Divine Will in Newton’s Natural Philosophy – (Davis, 1991)
    Abstract Excerpt: Finally, Newton held that, since the world is a product of divine freedom rather than necessity, the laws of nature must be inferred from the phenomena of nature, not deduced from metaphysical axioms — as both Descartes and Leibniz were wont to do.
    http://home.messiah.edu/~tdavis/newton.htm

  6. 6
    bornagain77 says:

    ,, continued,,

    “That (contingency) was a huge concept (that was important for the founding of modern science). The historians of science call that ‘contingency’. The idea that nature has an order that is built into it. But it is an order that is contingent upon the will of the Creator. It could have been otherwise. Just as there are many ways to make a timepiece, or a clock,,, there are many different ways God could have ordered the universe. And it is up to us not to deduce that order from first principles, or from some intuitions that we have about how nature ought to be, but rather it is important to go out and see how nature actually is.”
    – Stephen Meyer – 5:00 minute mark – Andrew Klavan and Stephen Meyer Talk God and Science
    https://idthefuture.com/1530/

    ,,, and when we rightly allow the Agent causality of God ‘back’ into physics as quantum mechanics itself now empirically demands with the closing of the “freedom-of-choice” loophole by Anton Zeilinger and company,,,

    Cosmic Bell Test Using Random Measurement Settings from High-Redshift Quasars – Anton Zeilinger – 14 June 2018
    Excerpt: This experiment pushes back to at least 7.8 Gyr ago the most recent time by which any local-realist influences could have exploited the “freedom-of-choice” loophole to engineer the observed Bell violation, excluding any such mechanism from 96% of the space-time volume of the past light cone of our experiment, extending from the big bang to today.
    https://arxiv.org/abs/1808.05966

    ,,, then that very reasonable concession on our part to rightly allow the Agent Causality of God ‘back’ into physics then 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”.

    In regards to gravity being dealt with in the Shroud of Turin, the following article states that ‘The bottom part of the cloth (containing the dorsal image) would have born all the weight of the man’s supine body, yet the dorsal image is not encoded with a greater amount of intensity than the frontal image.’

    Particle Radiation from the Body – July 2012 – M. Antonacci, A. C. Lind
    Excerpt: The Shroud’s frontal and dorsal body images are encoded with the same amount of intensity, independent of any pressure or weight from the body. The bottom part of the cloth (containing the dorsal image) would have born all the weight of the man’s supine body, yet the dorsal image is not encoded with a greater amount of intensity than the frontal image. Radiation coming from the body would not only explain this feature, but also the left/right and light/dark reversals found on the cloth’s frontal and dorsal body images.
    https://academicjournals.org/journal/SRE/article-full-text-pdf/CC774D029455

    And in the following video, Isabel Piczek states,,, ‘The muscles of the body are absolutely not crushed against the stone of the tomb. They are perfect. It means the body is hovering between the two sides of the shroud. What does that mean? It means there is absolutely no gravity.’

    “When you look at the image of the shroud, the two bodies next to each other, you feel that it is a flat image. But if you create, for instance, a three dimensional object, as I did, the real body, then you realize that there is a strange dividing element. An interface from which the image is projected up and the image is projected down. The muscles of the body are absolutely not crushed against the stone of the tomb. They are perfect. It means the body is hovering between the two sides of the shroud. What does that mean? It means there is absolutely no gravity. Other strange you discover is that the image is absolutely undistorted. Now if you imagine the clothe was wrinkled, tied, wrapped around the body, and all of the sudden you see a perfect image, which is impossible unless the shroud was made absolutely taut, rigidly taut.”
    Isabel Piczek –
    Turin shroud – (Particle Physicist explains the ‘event horizon’ on the Shroud of Turin) – video
    https://www.youtube.com/watch?v=27Ru3_TWuiY

    Kevin Moran, an optical engineer who studied the Shroud, describes the Shroud Image in this way, “The unique front-and-back only image can be best described as gravitationally collimated. The radiation that made the image acted perfectly parallel to gravity. There is no side image. The radiation is parallel to gravity,,,”

    Optically Terminated Image Pixels Observed on Frei 1978 Samples – Kevin E. Moran – 1999
    Discussion
    Pia’s negative photograph, from 1898, showed what looked to be a body that was glowing, but slightly submerged in a bath of cloudy water. This condition is more properly described as an image that is visible, at a distance, but by locally attenuated radiation. The unique front-and-back only image can be best described as gravitationally collimated. The radiation that made the image acted perfectly parallel to gravity. There is no side image. The radiation is parallel to gravity and, if moving at light speed, only lasted about 100 picoseconds. It is particulate in nature, colliding only with some of the fibers. It is not a continuum or spherical-front radiation that made the image, as visible or UV light. It is not the X-ray radiation that obeys the one over R squared law that we are so accustomed to in medicine. It is more unique,,,
    Theoretical model
    It is suggested that the image was formed when a high-energy particle struck the fiber and released radiation within the fiber at a speed greater that the local speed of light. Since the fiber acts as a light pipe, this energy moved out through the fiber until it encountered an optical discontinuity, then it slowed to the local speed of light and dispersed.
    Discussion
    The fact that the pixels don’t fluoresce suggests that the conversion to their now brittle dehydrated state occurred instantly and completely so no partial products remain to be activated by the ultraviolet light. This suggests a quantum event where a finite amount of energy transferred abruptly. The fact that there are images front and back suggests the radiating particles were released along the gravity vector. The radiation pressure may also help explain why the blood was “lifted cleanly” from the body as it transformed to a resurrected state.”
    https://www.shroud.com/pdfs/moran.pdf

    Moreover, besides gravity being dealt with on the Shroud of Turin, the Shroud also gives us evidence that Quantum Mechanics itself was dealt with. In the following paper, it was found that it was not possible to describe the image formation on the Shroud in classical terms but they found it necessary to describe the formation of the image on the Shroud in discrete quantum terms.

    The absorbed energy in the Shroud body image formation appears as contributed by discrete (quantum) values – Giovanni Fazio, Giuseppe Mandaglio – 2008
    Excerpt: This result means that the optical density distribution,, can not be attributed at the absorbed energy described in the framework of the classical physics model. It is, in fact, necessary to hypothesize a absorption by discrete values of the energy where the ‘quantum’ is equal to the one necessary to yellow one fibril.
    http://cab.unime.it/mus/541/1/c1a0802004.pdf

    Moreover, the following rather astonishing study on the Shroud, found that it would take 34 Trillion Watts of what is termed VUV (directional) radiation to form the image on the shroud.

    Astonishing discovery at Christ’s tomb supports Turin Shroud – NOV 26TH 2016
    Excerpt: The first attempts made to reproduce the face on the Shroud by radiation, used a CO2 laser which produced an image on a linen fabric that is similar at a macroscopic level. However, microscopic analysis showed a coloring that is too deep and many charred linen threads, features that are incompatible with the Shroud image. Instead, the results of ENEA “show that a short and intense burst of VUV directional radiation can color a linen cloth so as to reproduce many of the peculiar characteristics of the body image on the Shroud of Turin, including shades of color, the surface color of the fibrils of the outer linen fabric, and the absence of fluorescence”.
    ‘However, Enea scientists warn, “it should be noted that the total power of VUV radiations required to instantly color the surface of linen that corresponds to a human of average height, body surface area equal to = 2000 MW/cm2 17000 cm2 = 34 thousand billion watts makes it impractical today to reproduce the entire Shroud image using a single laser excimer, since this power cannot be produced by any VUV light source built to date (the most powerful available on the market come only to several billion watts)”.
    Comment
    The ENEA study of the Holy Shroud of Turin concluded that it would take 34 Thousand Billion (trillion) Watts of VUV radiation to make the image on the shroud. This output of electromagnetic energy remains beyond human technology.
    – per predator

    So thus in conclusion, when we rightly allow the Agent Causality of God back into physics, as the Christian founders of modern science originally envisioned, then a very plausible solution to the number one unsolved mystery in science today, of finding a reconciliation between General Relativity and Quantum Mechanics, readily pops out for us in that, as the Shroud of Turin itself gives witness to, both Gravity and Quantum Mechanics were dealt with in Christ’s resurrection from the dead.

    Verses.

    Matthew 28:18
    Then Jesus came to them and said, “All authority in heaven and on earth has been given to me,”

    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.

    Of supplemental note:

    ,,, the Copernican Principle and/or the Principle of Mediocrity has now been overturned by both General Relativity and Quantum Mechanics, our two most powerful theories in science, as well as by several other lines of scientific evidence (i.e. we are NOT ‘chemical scum’ as Stephen Hawking once infamously claimed.)
    March 2022
    https://uncommondescent.com/evolution/neil-thomas-on-evolutionary-theory-as-magical-thinking/#comment-748883

    Verse:

    Matthew 10:30-32
    …And even the very hairs of your head are all numbered. So do not be afraid; you are worth more than many sparrows. Therefore everyone who confesses Me before men, I will also confess him before My Father in heaven.…

  7. 7
    jerry says:

    and human stupidity

    As exemplified by the commenter.

    Not quite infinite but you are batting so close to zero such that no matter how small a number one offers, Chuchdarwin’s batting (correct things said) average is less.

    Question: Do you comment here to make ID look good?

  8. 8
    Pater Kimbridge says:

    So much for the people who think mathematics was discovered, rather than invented. How did we discover infinity if it does not really exist?

  9. 9
    kairosfocus says:

    PK, I suggest that actual physical instantiation of a transfinite number of discrete items (such as Hilbert’s Hotel would be) is a problem, utterly different from that in any distinct possible world, von Neumann’s succession on { } logically leads to N, Z, Q, R, C, R* etc as abstract entities, driven by the logic of structure and quantity. For example, C, relabelled, gives us the Euclidean Plane or we can retain coordinates as the Cartesian one, readily. This is why mathematics at its core has universal power: any distinct possible world. Which, is a branch on which we all sit phenomenon. KF

    PS, there is no possible world in which 2 + 3 != 5, i.e. this is an example of discovery that is then incorporated into wider frameworks until we have a vast structure.

  10. 10
    Lieutenant Commander Data says:

    Chuckdarwin
    “Only two things are infinite, the universe and human stupidity, and I’m not sure about the former.”
    –Albert Einstein

    Chuckdarwin that is a human cites Einstein that is a human about infinity of human stupidity .The irony is that Chuckdarwin didn’t think that quote include him and Einstein. 😆

  11. 11
    jerry says:

    So much for the people who think mathematics was discovered, rather than invented

    Mathematics is a form of logic.

    Just because it can be applied to make believe concepts which are invented does not make logic itself invented. Literature is real just like logic, but many of its topics are invented for a purpose just as in mathematics.

    Is logic discovered? Or just a part of reality that is obvious. Not that the results of logic are obvious, but the process is obvious. There is plenty of examples here that illustrate that logical processes are rarely applied.

    The interesting thing is why so few people use logic in their thinking even though all will say they do. The answer: emotions rule most of our thinking not logic. That is the only explanation for anti ID people.

  12. 12
    Silver Asiatic says:

    The proposal in the OP is that infinity does not exist …

    in the world around us

    Not that infinity does not exist at all.

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