Does infinity exist?

I’m a sucker for a kind word. But I was confused by this:

I took that to mean that when I dared to post to this thread you regretted “prodding” me. I was genuinely insulted and demoralized. I thought we were having a conversation, but apparently you prefer me to stay unprodded.

So which is it? Now that I’m going to respond to your latest post will you regret prodding me? Or will you appreciate my taking the time to provide my perspective? No way for me to know, is there. But ok what the hell. Happy New Year by the way. Here’s my response to your latest.

??? What ??? If anything I have the opposite point of view. I agree with G.H Hardy (played by Jeremy Irons in The Man Who Knew Infinity. I highly recommend it) that the best math is by definition the most useless math.

You are mischaracterizing my words and viewpoint 180 degrees. You’re attacking a strawman. That adds to my frustration with this conversation. Was I unclear? Is your reading comprehension bad? Are you just deliberately lying about what I said? Hard for me to know. Do you already regret prodding me again? Or do you wish I’d contribute? Hard to know.

Would that include every physicist since Newton? I’ve asked you this before. Modern physical science is based on infinitary math. Whether that’s a necessary or a contingent fact we don’t yet know. But the empirical fact remains. No infinitary math and you throw science back to the Middle ages. Is that your intention? I have asked you this several times now without getting a direct response.

I imagine that when you learned to drive a car, you were not first required to master metallurgy and automotive engineering. Do you take that as evidence that these disciplines do not actually underlie the act of driving a car? Or is it perhaps more likely that these disciplines are in fact essential to the very existence of cars, but that we don’t teach them to beginning drivers, in favor of simply teaching them how not to hit things?

Which it certainly does. I assume you can operate a light switch and were not first required to master the subject of electrical power generation. In calculus we teach people a rote procedure to “pull down the exponent and subtract 1.” We do not show beginning students Newton’s application of the fact that the binomial theorem can be extended to real-valued exponents.

It’s perfect clear historically that Newton worked with infinitary math. Would you really send us all back to the pre-Newtonian world?

Yet another vile mischaracterization of what I actually said. Now I’m reminded of why I quit this thread in disgust.

So now you DO agree that math underpins modern physical science? Or are you still demanding that we take science back to the year 1500 or so?

Project much?

Well now you’re contradicting yourself again. Do you or do you not agree that math is valid within itself; and does happen to be supremely useful? If you agree that math for the sake of math is valid, then exactly WHAT ARE your ideas on infinity? What do you know that all the mathematicians in the world don’t?

I perfectly well agree. But I wonder: WHY ARE YOU TELLING ME THIS? From my first post in this thread I have agreed that (as far as we know, to the limits of contemporary physical theory) there is no actual infinity instantiated in the world. Since I have long ago agreed with this point, why are you acting as if making this point again somehow counts as an intelligent comment in response to anything I’ve said?

All but mainstream mathematicians? So you know something that 140 years of professional mathematicians don’t? What would that be exactly?

What does “all but the mainstream” mean? Are you saying you’re in line with the mathematical cranks? How does that help your credibility?

You’ve already agreed that math is perfectly fine as an abstract game. That’s the philosophical doctrine of mathematical formalism. But now you claim that you oppose even the formalism. WHICH IS IT?

Yeah, that I believe.

So then why should I bother? Do you regret “prodding” me today? Or do you appreciate my point-by-point response to your remarks? How would I know what mood you’re in? You know you could always write your response in a text file and sit on it for a day to make sure you’re saying what you mean and not reacting irrationally to whatever’s going on in your life. That would be a tactic that would enable you to post more coherently.

Craig is the worst kind of sophist. Let’s not go down that road. But your Hilbert quote was about the physical world, and I’ve already said many times that I agree that (as far as we currently know) there are no actual infinities in the physical world. So your quote was totally off topic when directed to me.

Why? It’s off-topic to our discussion, which is about mathematical infinity.

Good God man, Wildberger is an absolute crank on the subject of infinity. Who are you trying to fool? Not me, since I’m extremely familiar with Wildberger’s work.

Authorities about what? You’re not making any actual point. You have said both that

  • You are perfectly fine with modern mathematical formalism regarding infinity; and

  • You absolutely oppose modern mathematical formalism regarding infinity.

Which is it? State your freaking thesis and defend it. Stop going back and forth on this point.

Yet you explicitly asked me for the examples of situations in which the order of a multiple integration matters. Once again you are just playing games. You ask me for the examples, I point you to the examples, you refuse to click on the link, and then you say you have no interest. THEN WHY THE F*CK DID YOU ASK??? Just playing games. Not a serious person at all.

It’s one of the examples of the need for precision and rigor in the foundations of math. The details of Fubini’s theorem are not important. The necessity of a clear and precise theorem is the point.

You ask me a question, I point to the answer, you claim you were never interested. That’s why I say you are not serious about learning or thinking or conversating.

I pointed to the link on Wiki. If I thought Wiki did a bad job I’d do a better one. In this particular case, Wiki’s presentation is spot on and I could not improve on it.

You don’t need to dive into the details. They’re unimportant. What is important is that the examples exist. The 18th and 19th centuries were all about mathematicians realizing that they desperately needed clear and logically rigorous foundations, else their intuitions would lead them astray. It’s the existence of the examples, not the details of the examples, that’s important and significant.

Learning the specific examples is totally unimportant. The fact that the examples exist is important. And all that’s needed there is a mouse click to the Wiki page.

It matters because although our intuition says the order doesn’t matter, there are actual examples in which it does matter. Showing that there is a need for logical rigor in our foundations.

Physicists find mathematical reasoning indispensable in their work. Take it up with them. Else drive us all back to 1500 when nobody knew or cared about any of it.

And I’m sure I’m resigned to reading it. But unless your thinking gets more clear it will just be more of the same.

“There is no royal road to geometry.” – Euclid.

We all have to struggle to understand the math. But in this case understanding the math is totally unimportant. All that’s needed to to accept that these examples exist, whether we drill down to the details or not. And these examples show the need for mathematical rigor.

You do NOT NEED TO UNDERSTAND THE EXAMPLES. You only need to acknowledge that the examples exist.

So bottom line, do you:

  • Accept mathematical formalism as an abstract, meaningless game but perhaps an interesting one? Or

  • Do you reject modern math?

Which is it? I wonder if you have even interrogated yourself on this issue, since you contantly whipsaw back and forth.

Please state clearly what is your objection to the mathematical formalism of infinity. And also please tell me if you have any similar objections to the rules of chess. Maybe you think the King should be able to move two squares instead of just one. Is that your point? What are you trying to say? You do understand that the entirety of set theory can be expressed in finitely many symbols, right? So what exactly is your objection? And do you want to drive physics back to pre-Newton or even pre-Galileo?

I will have to watch you use the word and learn that way, kinda like Iambiguous’ use of Dasein which evidently can’t be articulated in words.

Have you seen the movie: Iron and Silk?

I think you would like it, but fwd to 50:10 for a point I want to illustrate.

[youtube]https://www.youtube.com/watch?v=cOIbalP7dj8[/youtube]

Pan Qingfu: You have to teach me English
Mark: Sure!
Pan Qingfu: I want to learn to say these sentences.
Mark: Have you studied English before?
Pan Qingfu: No.
Mark: Then let’s start with the ABCs.
Pan Qingfu: No! That’s too slow. I want to learn whole sentences then string them together like wushu routines.
Mark: Learning English is different from learning wushu!
Pan Qingfu: No! Everything is like wushu! Now we’ll start.

Sometimes it’s easier to take things apart to figure out how it was put together than to be told how things are put together.

That’s awesome! I’ve watched them so many times that I could probably communicate in sopranos clips lol

Yeah I like Paulie.

“He killed 19 Czechoslovakians! The guy was an interior decorator!”
“Really? His apartment looked like shit.”

That was a good one!

“Yea though I walk through the valley of the shadow of death…”
“Hold that thought.”

I think I was mis-pegged after referencing BN which was only innocently meant to illustrate the colorado mountains. It was merely bad fortune that the two coincided. I don’t think I see in terms of ethnicity, but it’s more about the philosophies people hold. Everyone is a voice in the wilderness with no other special significance than that.

Yes, I’m very happy at the prospect of burying hatchets and forming an amicable relationship with a knowledgeable person.

Just talk about what you want to talk about.

He who has an ear to hear, let him hear.

What determines what the eyes want to see?

Oh I think I see what you’re saying. Like music has notes, chords, melodies which constitute different levels of resonance. My theory is desire is essentially resonance, harmony, stability. The electron is a standing wave in a location where it wants to be (a place where it naturally resonates). Atoms desire certain numbers of electrons and form molecules that desire stability of their own. Proteins, cells, organisms, communities all desire their own harmony.

Will do. Thanks!

I heard it meant “excellence”. Mindful refinement to the point of mindless reflex.

Yes I think so and I think the limits of knowledge preclude any knowledge of an absolute. A thing viewing itself could never see all of itself and any piece of knowledge known could never be a whole description of what there is.

So a method that never claims 100% certainty is no longer the subject but becomes the object? I haven’t pondered that.

Borders don’t separate, but join. All borders are shared. I’d say there is no such thing as discrete.

Where do the ruptures reside? They’re dimensionless, right?

I’m having trouble understanding that one.

Thanks, I appreciate the feedback. My problem is finding time to rummage around the site, but it has been on my bucket list. I’ve been busier this winter than most.

Happy New Year! I meant that posting that didn’t have anything to do with you. I would have posted it regardless if you had existed. What I meant by prodding is I didn’t intend to provoke you. I plan to add more posts when they fall in my lap so that they’re all in one place.

I didn’t know that movie existed and I intend to watch it asap. Thanks!

Without a concrete example, those are vague accusations to me. It’s hard for me to believe I have been unfair though. Dumb maybe, but not unfair.

I’ve answered this before. Physics does not require infinity and in fact, Don Lincoln, physicist at Fermi Labs wrote that article I posted which said “when you encounter an infinity in a real, physical, science situation, what it really means is that you’ve pushed your mathematics beyond the realm where they apply. You need new math.” livescience.com/64332-black … avity.html

In other words, infinity = error. Science is not underpinned by error.

Do cars have to be made of metal? I don’t know what you’re getting at. You keep claiming infinity underpins math, but I can find no evidence to support that counterintuitive notion.

That dispatch looks like a ball of logical fallacies. Appealing to analogies for doing math without understanding the underpinnings of math does not substantiate the claim that math is underpinned by infinity. That seems like an argument from ignorance: if I don’t understand x, then y must be true; if I don’t have a theory to explain the universe, then god must exist; if I don’t understand the underpinning of math, then infinity must underpin it. I don’t see how that follows.

Then you appeal to horrors of pre-newton like any desire to avoid going back to pre-newtonian math has any relevance on what’s true.

That’s how I remember it.

I wouldn’t say math underpins science, no. A tool doesn’t underpin mechanics. Math is just another tool in the box and it is not the box nor the science.

I never was demanding that. You’re trying to make it seem like I’m demanding that.

I’m not projecting anything onto you, but revealing to you what you’re doing. You’re married to this infinity idea and are grasping at anything you can find to substantiate it. As if you can convince me that going pre-newtonian is a bad idea, and that merely because my opinion is it’s a bad idea, it must mean infinity is true. How is truth contingent on my opinion? Grasping at appeals like that reveal to me that you’re seeking to support infinity rather than being open to what exists.

No. Math is a broad category of various types of math and I can’t say any type of math would substantiate any other type. I reject ordinal infinities as fantasy, but the math is valid within the fantasy construct and independent from other constructs.

My ideas on infinity is that no one can have ideas of infinity. I don’t even know what it means to approach infinity because no matter how close we get, we’re still infinitely far away and that will always be true. Near-infinite is nonsense.

Tell me what it is that mathematicians don’t know and I’ll tell you if I know it.

Idk, I forgot the context for this one.

I’m saying I’m in sync with the greatest mathematicians and the newbies who can’t let go of infinity are who I am not in sync with.

When you call people cranks, it affects your credibility. Slander is the tool of the loser. That is more display of the grasping for anything to support infinity that I was on about above. Discrediting deniers through slander is a tactic that you believe helps substantiate the infinite, but whether he is a crank is irrelevant because even if he were credible, we’d still have to evaluate the truth of his assertions and knowing whether or not he’s a crank doesn’t aid in doing that.

You should only bother if it’s fun.

I didn’t prod you today or any other day.

It’s not a day to day mood, but general frustration with dogmatists that probably won’t be alleviated for the foreseeable future.

First, it wasn’t directed to you. Second, Hilbert said infinity cannot be basis for rational thought.

The thread is depository of all topics regarding the existence of the infinite.

A few moths ago you didn’t even know who he was. You called him “some guy” viewtopic.php?f=4&t=193794&start=25#p2705482

Yes I am. I’m not looking for authorities, but if I find a statement by someone authoritative by chance, then I will post it.

I’m not flip flopping, but those statements are too vague to answer. It depends what you mean by formalism and how it’s applied. If you want to play with toys in the abstract, that’s fine, but infinity doesn’t underpin science, math, or anything except toys in the abstract. That’s my stance and I don’t know how to make it more clear.

If you disagree, then give me example where a completed actual infinity is required for the math to work. Don’t give me analogies or wiki articles, but a specific problem we can dig into and discover beyond a doubt that a concept of infinity is required to solve the problem. You were heading in the right direction with the metal plate problem, but after I asked you to explain it to me, you got mad.

I mean, if we cannot even approach infinity, then we may as well have an extremely large finite number that we also have no method of knowing how close to it we are. Let z = a finite number bigger than any that could be represented and carryon like usual with z substituting for infinity.

I did click the link and scanned the article then came to the conclusions I conveyed to you. I didn’t bring it up, but you brought it to the table as example of some point you were making and then bailed when I asked for a detailed explanation.

I agree, but why does it matter if we add in one direction before another?

I don’t remember asking a question that prompted the Fubini answer. I thought you were making a point that I didn’t request. I could be wrong, but that’s how I remember it.

No, wiki is actually lacking. There’s a broken link that is supposed to lead to examples that have been deleted or never added. I suspect you didn’t read it because you specifically mentioned it containing examples that were not there. Broken link → en.wikipedia.org/wiki/Fubini%27 … d_integral

Yes but I still want to know why. Extraordinary claims require evidence and that claim is quite extraordinary.

There’s the pre-newtonian appeal again.

How do you know it’s my thinking that is unclear?

This is what the theists say: you don’t need to understand, just believe! I can’t control what I believe.

Yes

That’s the same question, only negated.

I don’t know where you’re getting that impression.

I think I fulfilled all those inquisitions above. The king can move however we want it to move. In some games the king can be captured if the opponent doesn’t realize he’s in check and moves another piece. It’s all relative and arbitrary.

Everyone says “as x approaches infinity”, but what does that mean?

To approach means to get closer to, but regardless how close we get to infinity, we’re still infinitely far away.

Near-infinite doesn’t make sense.

You made a lot of specific points and I’ll try to handle them one by one rather than attempt a big bang reply. Hopefully we can bring some focus. First, Wildberger is a crank; and I’m not the only one who says so. He’s an interesting case because he has also done serious mathematical work. It’s only his ideas on infinity that are regarded (by a lot of people, not just me) as cranky.

reddit.com/r/math/comments/ … my_school/

scienceblogs.com/goodmath/2007/ … e-sets-and

math-frolic.blogspot.com/2012/0 … erger.html

reddit.com/r/math/comments/ … _goldbach/

physicsforums.com/threads/n … ra.772409/

You can Google “Norman Wildberger crank” for yourself and get a wide variety of articles on the topic.

It doesn’t reflect badly on me to label someone a crank who is (a) widely labelled a crank; and (b) happens to actually be a crank.

Please read someone other than Wildberger on the topic of infinity. It doesn’t help your cause because his ideas on infinity are generally regarded as cranky.

It’s not calling cranks cranks that affects my credibility, any more than if I called the Pope a Catholic. Wildberger’s a known mathematical crank. Rather, your quoting known cranks hurts your own credibility.

By the way whether or not Wildberger is a crank is not all that important to us. What’s important is that you’re wasting your time quoting him to me. Also I’ve known about him for several years, if I called him “some guy” in some post it’s probably because someone posted a link to a video and I didn’t bother to watch the video.

It means x gets arbitrarily large. That’s ALL it means. Didn’t they explain that in your 1200 page calculus text? No matter. “x goes to infinity” or “x approaches infinity” means that x gets arbitrarily large. It’s not bounded. It’s just a figure of speech. Although we can formalize it using the extended real numbers, in which we add a pair of symbols (+ \infty) and (- \infty) and assign them formal properties that let us use them as we need to. I’m pretty sure that’s in your calculus text too. But it’s ok if these fine points aren’t clear. Nobody is expected to learn anything in calculus beyond the basic techniques. The fine points of getting everything logically correct are taught in a subject called real analysis, taken by math majors.

In any event the use of limits at infinity in calculus is completely different than the transfinite ordinals and cardinals studied in set theory. But if you even believe in the familiar real number line taught in high school, that’s an example of an infinitely long mathematical object that’s indispensable in physical science and even social science. The familiar Gaussian probability curve, or “bell curve,” is defined over the entire real line and is one of the most important concepts in probability and statistics.

I also wanted to mention that your point about the scientist’s quote about infinity in physics is a good one and I have something substantive to say about it, but not tonight. So I hope we won’t get sidetracked on these two minor issues (Wildberger’s crankitude and the meaning of “x goes to infinity”) before I get to what I consider the more substantive and important point about infinity in physics.

Just dropped in to say I’m hard at work writing down my thoughts on the meaning of infinity as applied to physics. I’m trying to make it brief and clear. That may take a little more time. I completely take your point regarding physical infinities and I’m drafting a response that I hope will shed light.

Whether or not other people think he is a crank is completely irrelevant. It’s an appeal to popularity fallacy committed for the purpose of supporting an ad hominem fallacy. A bunch of people say he’s a crank (appeal to popularity), so he must be a crank, and because he’s a crank, his ideas on infinity are wrong (ad hominem redirection from the topic to the person).

Despite various publications of results where hand washing reduced mortality to below 1%, Semmelweis’s observations conflicted with the established scientific and medical opinions of the time and his ideas were rejected by the medical community. Semmelweis could offer no acceptable scientific explanation for his findings, and some doctors were offended at the suggestion that they should wash their hands and mocked him for it. In 1865, Semmelweis suffered a nervous breakdown and was committed to an asylum, where he died at age 47 of pyaemia, after being beaten by the guards, only 14 days after he was committed. en.wikipedia.org/wiki/Ignaz_Semmelweis

The guy who suggested hand washing was also labeled a crank and that is the argument you’re appealing to. Some people on the net who like the idea of infinity are calling Wildberger a crank specifically because he doesn’t and that is supposed to mean something? Do they also think Gauss and Hilbert are cranks??? Should it matter if they did?

From this I can learn more about you and the people calling Wildberger a crank than I can learn about Wildberger from all the slandering. And I’m probably more inclined to believe Wildberger is not a crank specifically because people insist that he is. That philosophy would have served me well in Galileo vs The Church concerning geocentrism and from my perspective it’s at least equally likely, if not more likely, that the cranks wind up being right in the end.

“All truth passes through three stages: First, it is ridiculed. Second, it is violently opposed. Third, it is accepted as being self-evident.” - Arthur Schopenhauer

The only reason to vilify people is if they’re a threat and if they’re a threat, it’s probably for good reason.

That’s why I say it does more damage to your credibility to insult his.

“Slander is the tool of the loser” - Socrates

“When you’re out of ammo, throw mud.” - Me

Mudslingers sling mud because that’s all the have to sling.

Anyway, even if you generally discredit Wildberger, it wouldn’t mean anything unless you could show that he is incapable of being correct on anything. Even the biggest fool isn’t wrong about everything.

And lastly, I don’t quote these people because I need their references, but because I’m trying to consolidate various quotes and arguments/ideas about infinity into one place.

Is it also a figure of speech to say “near-infinite”?

I’m ok with figures of speech, but Michio Kaku said “as density approaches infinity…” and it dawned on me at that moment that what he said doesn’t make sense because there is no way to approach infinity; regardless how close you get, you’re still just as far away. So the statement means absolutely nothing when taken literally, but figuratively, ok, I get it.

Take your time. It’s no problem as I’m kinda wrapped up in political threads anyway.

Can non existence exist in the absolute sense ? No it cannot which means existence has always existed [ and always will ]
This means that it exists infinitely in the past and will exist infinitely into the future

We are here discussing the existence of infinity then how can it not exist in the mind ?
It only needs to exist as a mental concept in the same way that any other thought does

He is absolutely right : the singularity as traditionally defined does not exist in nature as zero dimension and infinite density are mutually incompatible
But what is not mutually incompatible is infinitesimal dimension combined with finite density and this is therefore the true definition of the singularity

This definition also allows for time to have existed before the Big Bang because the singularity did not experience it as it [ time ] is asymptotic

Something has always existed, but I wouldn’t call that something “existence” since I define existence as a relationship between subject and object. How can something be said to exist if it doesn’t exist: in something, as a function of something, in relation to something, etc? If we talk about objective existence where the object exists only in relation to actuality, then the standpoint of actuality becomes the subject.

Like James said, that which has no affect, does not exist. So if the grand totality of everything has no affect on anything else (because there is nothing else), then we can’t talk about it as existing.

Where does the absolute exist? There is no “where”. Location is only defined inside the absolute.
What does it exist in? There is no “what” because all “what” is inside the absolute.

There is no way to talk about the absolute and any concept we think we have of it simply has to be wrong.

I think it means that time, like location, is only defined inside the thing we’re trying to measure. Time is an emergent property and a consequence of relationships between moving bodies. For instance, I could drive to the next town in 1/24 revolution of the earth… or so many billion vibrations of a certain atom. Time itself does not exist and eternity is not infinite time, but absence of time.

Well, let’s talk about squared circles. Or maybe we can discuss what the universe looks like from the outside even though there is no such thing as “look” outside the universe. This goes to show that we can talk about things without conceptualizing them. We can discuss nonsense without having a concept of the nonsense. I once had a dream where a cat had its head in its mouth. Likewise with infinity: there has never been a person who could properly conceptualize what he fools himself into believing he has. All we can do is imagine the biggest thing we can and we call that “good enough, close enough” and pretend we’ve conceptualized infinity, but we’ve only approached it and our approach is still infinitely far away.

I don’t understand. Can you unpack that a little? The way I understand it is physicists generally regard time before the big bang as north of the north pole: there is no such thing as before the big bang. Time cannot exist before there is something in existence that is moving in relation to something else that is either not moving or moving with a different velocity.

Time is internal to the universe, subjective to it, and not an objective thing existing independent of the universe which could preside over the formation of the universe and record what happened before. Whatever happened before, has no affect on anything, so it doesn’t exist :wink:

Nothing north of the north pole is only true in relation to the Earth as an isolated body but not so in relation to its position within the Universe
So this is where it fails as an analogy in trying to explain why time did not exist before the Big Bang as it assumes nothing existed before it did

It is not known what did or did not exist before the Big Bang because that is only as far as back as physics can currently go
This is demonstrably not the same as saying it cannot go any further back because the BB is the absolute beginning of time

If the singularity was a space of zero volume and infinite density then nothing could have existed before it including time

This definition is wrong because both zero volume and infinite density cannot exist in actuality
As the former would have no dimension or property and the latter can only exist in finite form

A singularity less absolute in physicality however would allow for time to exist before it as it would not be the totality of all that existed

Also if time did begin at the Big Bang it would mean absolute nothing existed before it but this is actually invalidated by quantum mechanics
As absolute nothing can only exist infinitesimally not infinitely because of the existence of quantum fluctuations which disturb vacuum states

So quantum mechanics absolutely forbids the existence of a singularity as traditionally defined

Also the Big Bang was not the beginning of the Universe as such but only local cosmic expansion

I totally agree. I totally agree. I hope saying it twice will convince you that I mean it.

When infinities arise in physics equations, it doesn’t mean there’s a physical infinity. It means that our physics has broken down. Our equations don’t apply. I totally get that. In fact even our friend Max gets that.

blogs.discovermagazine.com/crux/ … g-physics/

The point I am making is something different. I am pointing out that:

All of our modern theories of physics rely ultimately on highly abstract infinitary mathematics

That doesn’t mean that they necessarily do; only that so far, that’s how the history has worked out. There is at the moment no credible alternative. There are attempts to build physics on constructive foundations (there are infinite objects but they can be constructed by algorithms). But not finitary principles, because to do physics you need the real numbers; and to construct the real numbers we need infinite sets.

I collected some examples of the infinitary math underlying physics. I tried to be brief. Each example could be expanded to a book or the work of a lifetime. I’ll do my best to answer specific questions. As with Fubini I regret that it’s beyond me to explain any of these examples fully and in detail with perfect clarity and without requiring effort on the part of the reader. That’s what TED talks are for. /s

  1. The rigorization of Newton’s calculus culminated with infinitary set theory.

Newton discovered his theory of gravity using calculus, which he invented for that purpose. However, it’s well-known that Newton’s formulation of calculus made no logical sense at all. If (\Delta y) and (\Delta x) are nonzero, then (\frac{\Delta y}{\Delta x}) isn’t the derivative. And if they’re both zero, then the expression makes no mathematical sense! But if we pretend that it does, then we can write down a simple law that explains apples falling to earth and the planets endlessly falling around the sun.

It took another 200 years for mathematicians to develop a rigorous account of calculus from first principles; and those first principles are infinitary set theory. No set theory, no real numbers, no calculus, no gravity.

encyclopediaofmath.org/inde … f_analysis

  1. Einstein’s gneral relativity uses Riemann’s differential geometry.

In the 1840’s Bernhard Riemann developed a general theory of surfaces that could be Euclidean or very far from Euclidean. As long as they were “locally” Euclidean. Like spheres, and torii, and far weirder non-visualizable shapes. Riemann showed how to do calculus on those surfaces. 60 years later, Einstein had these crazy ideas about the nature of the universe, and the mathematician Minkowski saw that Einstein’s ideas made the most mathematical sense in Riemann’s framework. This is all abstract infinitary mathematics.

en.wikipedia.org/wiki/Differential_geometry

en.wikipedia.org/wiki/Introduct … relativity

  1. Fourier series link the physics of heat to the physics of the Internet; via infinite trigonometric series.

In 1807 Joseph Fourier analyzed the mathematics of the distribution of heat through an iron bar. He discovered that any continuous function can be expressed as an infinite trigonometric series, which looks like this:

$$f(x) = \sum_{n=0}^\infty a_n \cos(nx) + \sum_{n=1}^\infty b_n \sin(nx)$$

I only posted that because if you managed to survive high school trigonometry, it’s not that hard to unpack. You’re composing any motion into a sum of periodic sine and cosine waves, one wave for each whole number frequency. And this is an infinite series of real numbers, which we cannot make sense of without using infinitary math.

Fast forward to present time. Fourier series underlie the propagation of digital signals over the Internet. They allow us to converse in this very moment.

en.wikipedia.org/wiki/Fourier_series

  1. Quantum theory is functional analysis.

If you took linear algebra, then functional analysis can be thought of as infinite-dimensional linear algebra combined with calculus. Functional analysis studies spaces whose points are actually functions; so you can apply geometric ideas like length and angle to wild collections of functions. In that sense functional analysis actually generalizes Fourier series.

Quantum mechanics is expressed in the mathematical framework of functional analysis. QM takes place in an infinite-dimensional Hilbert space. To explain Hilbert space requires a deep dive into modern infinitary math. In particular, Hilbert space is complete, meaning that it has no holes in it. It’s like the real numbers and not like the rational numbers.

QM rests on the mathematics of uncountable sets, in an essential way.

ps – There’s our buddy Hilbert again. He did many great things. William Lane Craig misuses and abuses Hilbert’s popularized example of the infinite hotel to make disingenuous points about theology and in particular to argue for the existence of God. That’s what I’ve got against Craig.

  1. Cantor was led to set theory from Fourier series.

In every online overview of Georg Cantor’s magnificent creation of set theory, nobody ever mentions how he came upon his ideas. It’s as if he woke up one day and decided to revolutionize the foundations of math and piss off his teacher and mentor Kronecker. Nothing could be further from the truth.

Cantor was in fact studing Fourier’s trigonometric series! One of the questions of that era was whether a given function could have more than one distinct Fourier series. To investigate this problem, Cantor had to consider the various types of sets of points on which two series could agree; or equivalently, the various sets of points on which a trigonometric series could be zero. He was thereby led to the problem of classifying various infinite sets of real numbers; and that led him to the discovery of transfinite ordinal and cardinal numbers. (Ordinals are about order in the same way that cardinals are about quantity).

In other words, and this is a fact that you probably will not find stated as clearly as I’m stating it here:

If you begin by studying the flow of heat through an iron rod; you will inexorably discover transfinite set theory.

I do not know what that means in the ultimate scheme of things. But I submit that even the most ardent finitist must at least give consideration to this historical reality.

ias.ac.in/article/fulltext/ … /0977-0999

Conclusion

I hope I’ve been able to explain why I completely agree with your point that infinities in physical equations don’t imply the actual existence of infinities. Yet at the same time, I am pointing out that our best THEORIES of physics are invariably founded on highly infinitary math. As to what that means … for my own part, I can’t help but feel that mathematical infinity is telling us something about the world. We just don’t know yet what that is.

Most definitely, and one that I would never personally use. Nothing is “near infinite,” I agree with you about that. Physicists and others use it to mean “really big.”

When physicists talk about infinity they often have NO IDEA what they’re saying in terms of math. Physicists misuse the word infinity terribly; and of all the physicists who do that, the celebrity physicists do it the worst.

You’re reading way too much into words people are using very informally.

I almost don’t feel like this needs saying…

To be accurate about infinite sets, it’s proper to say, “the sequence approaches 2”. Rather than, “the sequence is 2”

If there is no time, then what does “before” mean?

If time had a beginning, then there is no before. If there were a before, then after the before would not be the beginning of time.

Oh I see. But in order to have time, we need things in motion through a spacial construct. How can there be things in motion if the universe is so small?

But time doesn’t exist relative to light, yet there is not nothing.

Yes that makes sense.

That could be true.

That was an excellent post and qualifies as a treasure to be found on this site! :obscene-drinkingcheers:

Thanks for the link and I would have showcased it all on its own had I seen it first :slight_smile:

I see what you mean, but as Max pointed out when describing air as seeming continuous while actually being discrete, it’s easier to model a continuum than a bazillion molecules, each with functional probabilistic movements of their own. Essentially, it’s taking an average and it turns out that it’s pretty accurate.

But what I was saying previously is that we work with the presumed ramifications of infinity, “as if” this or that were infinite, without actually ever using infinity itself. For instance, y = 1/x as x approaches infinity, then y approaches 0, but we don’t actually USE infinity in any calculations, but we extrapolate.

Hilbert pointed out there is a difference between boundless and infinite. For instance space is boundless as far as we can tell, but it isn’t infinite in size and never will be until eternity arrives. Why can’t we use the boundless assumption instead of full-blown infinity?

I didn’t know he developed calculus specifically to investigate gravity. Cool! It does make sense now that you mention it.

I’m going to need some help with this one. If dx = 0, then it contains no information about the change in x, so how can anything result from it? I’ve always taken dx to mean a differential that is smaller than can be discerned, but still able to convey information. It seems to me that calculus couldn’t work if it were based on division by zero, and that if it works, it must not be. What is it I am failing to see? I mean, it’s not an issue of 0/0 making no mathematical sense, it’s a philosophical issue of the nonexistence of significance because there is nothing in zero to be significant.

Isn’t this the same problem as previous? dx=0?

I can’t make sense of it WITH infinitary math lol! What’s the cosine of infinity? What’s the infnite-th ‘a’?

Well, thanks to Hilbert, I’ve already conceded that the boundless is not the same as the infinite and if it were true that QM required infinity, then no machine nor human mind could model it. It simply must be true that open-ended finites are actually employed and underpin QM rather than true infinite spaces.

Like Max said, “Not only do we lack evidence for the infinite but we don’t need the infinite to do physics. Our best computer simulations, accurately describing everything from the formation of galaxies to tomorrow’s weather to the masses of elementary particles, use only finite computer resources by treating everything as finite. So if we can do without infinity to figure out what happens next, surely nature can, too—in a way that’s more deep and elegant than the hacks we use for our computer simulations.”

We can claim physics is based on infinity, but I think it’s more accurate to say pretend or fool ourselves into thinking such.

Max continued with, “Our challenge as physicists is to discover this elegant way and the infinity-free equations describing it—the true laws of physics. To start this search in earnest, we need to question infinity. I’m betting that we also need to let go of it.”

He said, “let go of it” like we’re clinging to it for some reason external to what is true. I think the reason is to be rid of god, but that’s my personal opinion. Because if we can’t have infinite time, then there must be a creator and yada yada. So if we cling to infinity, then we don’t need the creator. Hence why Craig quotes Hilbert because his first order of business is to dispel infinity and substitute god.

I applaud your effort, I really do, and I’ve learned a lot of history because of it, but I still cannot concede that infinity underpins anything and I’d be lying if I said I could see it. I’m not being stubborn and feel like I’m walking on eggshells being as amicable and conciliatory as possible in trying not to offend and I’m certainly ready to say “Ooooohhh… I see now”, but I just don’t see it.

Craig is no friend of mine and I was simply listening to a debate on youtube (I often let youtube autoplay like a radio) when I heard him quote Hilbert, so I dug into it and posted what I found. I’m not endorsing Craig lol

I still can’t understand how one infinity can be bigger than another since, to be so, the smaller infinity would need to have limits which would then make it not infinity.

Right, because of what Max said about the continuum model vs the actual discrete. Heat flow is actually IR light flow which is radiation from one molecule to another: a charged particle vibrates and vibrations include accelerations which cause EM radiation that emanates out in all directions; then the EM wave encounters another charged particle which causes vibration and the cycle continues until all the energy is radiated out. It’s a discrete process from molecule to molecule, but is modeled as continuous for simplicity’s sake.

I’ve long taken issue with the 3 modes of heat transmission (conduction, convention, radiation) because there is only radiation. Atoms do not touch, so they can’t conduct, but the van der waals force simply transfers the vibrations more quickly when atoms are sufficiently close. Convection is simply vibrating atoms in linear motion that are radiating IR light. I have many issues with physics and have often described it as more of an art than a science (hence why it’s so difficult). I mean, there are pages and pages on the internet devoted to simply trying to define heat.

quora.com/What-is-heat-1
quora.com/What-is-meant-by-heat
quora.com/What-is-heat-in-physics
quora.com/What-is-the-definition-of-heat
quora.com/What-distinguishes-work-and-heat

Physics is a mess. What gamma rays are, depends who you ask. They could be high-frequency light or any radiation of any frequency that originated from a nucleus. But I’m digressing…

It just means we’re using averages rather than discrete actualities and it’s close enough.

I think it means there are really no separate things and when an aspect of the universe attempts to inspect itself in order to find its fundamentals or universal truths, it will find infinity like a camera looking at its own monitor. Infinity is evidence of the continuity of the singular universe rather than an existing truly boundless thing. Infinity simply means you’re looking at yourself.

Anyway, great post! Please don’t be mad. Everyone here values your presence and are intimidated by your obvious mathematical prowess :sunglasses: Don’t take my pushback too seriously :slight_smile: I’d prefer if we could collaborate as colleagues rather than competing.

Small is a relative term and from a classical perspective the quantum is incredibly so but this does not mean motion is not actually possible at this level
Three of the four fundamental forces operate at the quantum level inside of an atom in relation to the motion of its protons and neutrons and electrons
Also motion is a universal constant so any space no matter how small will feature motion even if it is just quantum fluctuations disturbing vacuum states