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” atMind 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)*

Sabine Hossenfelder’s take

https://www.youtube.com/watch?time_continue=2&v=Bq9xR5PUs6s&feature=emb_logo

Did they tell him they were full?

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

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

–Albert Einstein

Of semi-related note:

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!”

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’,

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’

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.”

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

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.”

,,, 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),,,,

,, continued,,

,,, 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,,,

,,, 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.’

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.’

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,,,”

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.

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.

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.

Of supplemental note:

Verse:

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?

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

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.

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. 😆

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.

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

Not that infinity does not exist at all.