Does infinity exist?

[Serendipper]

What I don't understand about your point of view is why you reject purely mathematical infinity.

I just posted that from David Hilbert because I was listening to debate involving William Lane Craig who used a quote from David which prompted me to look it up and discover that document which I posted here solely so I would know where it is and it wasn't meant to prod you in any way. One of the purposes of this thread is to be a "junk drawer" where I can stuff articles that I randomly stumble upon in order to consolidate evidence. That's all that was about.

I don't object to the use of infinity as a "play thing" just like Christopher Hitchens didn't object to religion being a "toy" of the religious, but my objection is when the toy is asserted to be more than a toy. It's actually a funny analogy https://www.youtube.com/watch?v=d2vqwZActbQ

Studying math for the sake of math is really cool and I'm only objecting to pretending it's more than that. I think that's all I'm saying.

As David said, "In summary, let us return to our main theme and draw some conclusions from all our thinking about the infinite. Our principal result is that the infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought."

Infinity doesn't exist in nature and neither does it exist in the mind, although we can pretend it does through inference and then draw conclusions from that for whatever reason.

[wtf]

I'm only objecting to pretending it's more than that.

Who is doing that? You're making a strawman argument. You've been bitterly complaining about set theory for pages now. I'm asking you why.

And if math is only a fiction, how is it that all of modern science is based on it? You seem unable to engage with this important question.

If you need a place to store your thoughts, you could try a private blog or a pad of paper. This is a public discussion forum where you've made many claims that are open to objection, not least because many of your statements contradict each other and/or established science and math. You've gone on for weeks objecting to modern math; and when challenged directly, you claim you don't actually mean anything you say but are only using this forum as a scratchpad for your confused ideas and random quote-mining. Early on all you were capable of was throwing insults at me. At least you've stopped that. But why don't you try to learn something about the subject instead of just Googling around for quotes that are no longer even on topic? And why is it that you have the time to Google irrelevant quotes but don't have the time to click on the Wiki link that gives specific examples of the need for precise reasoning about changing the order of multiple integrals, which you explicitly asked me for? Your presentation in this thread makes you out to be an unserious person, arguing in a disingenuous manner.

Don't you want to try to learn anything?

Ah fuck it. I'm outta here. All the best.

[Serendipper]

I'm only objecting to pretending it's more than that.

I thought it was a fairly harmless thing to say. You're acting as if math studied for the enjoyment of math is somehow inferior to math studied for some goal or purpose and have therefore construed my comment as offensive. Chess is a toy, but is being good at chess a bad thing? Is describing chess as a toy a bad thing? Where is the offensiveness?

Who is doing that?

Whoever is pretending infinity applies outside of math.

You've been bitterly complaining about set theory for pages now. I'm asking you why.

The only thing I can remember bitterly complaining about was the stubbornness surrounding the definition of infinity. The only thing I remember claiming about set theory is that I couldn't find anything about it within 1200 pages of my calculus book, and that was only in response to your assertion that set theory underpins calculus. Then we transitioned to higher math where I said "math for the sake of math" then you got all pissed off because I dis'd math and here we are.

And if math is only a fiction, how is it that all of modern science is based on it? You seem unable to engage with this important question.

It's not fiction, but a tool that can be misapplied. It also can model fictitious things. Math can do more than what we would describe as "real" and just because math makes a claim, doesn't mean it will match reality. But neither can we say math is worthless because it often matches reality. It's tool to be used intelligently with proper assumptions. Garbage in = garbage out.

If you need a place to store your thoughts, you could try a private blog or a pad of paper. This is a public discussion forum where you've made many claims that are open to objection,

The reason they are public is because I want peer review, but not dogmatic digging-in in stubborn refusal to concede a point. This should be a collaboration and not a competition.

not least because many of your statements contradict each other and/or established science and math.

I know my ideas on infinity conflict with ideas of many mathematicians, but I'm not aware of other contradictions and it would be helpful if you'd point them out.

I posted an article from livescience today, written by Don Lincoln, Senior Scientist, Fermi National Accelerator Laboratory; Adjunct Professor of Physics, University of Notre Dame, that said:

Astronomers and physicists have long held that the idea of a singularity simply must be wrong. If an object with mass has no size, then it has infinite density. And, as much as researchers throw around the word "infinity," infinities of that kind don't exist in nature. Instead, 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. https://www.livescience.com/64332-black ... avity.html

As far as I can tell, I'm in sync with all but mainstream mathematicians.

You've gone on for weeks objecting to modern math; and when challenged directly, you claim you don't actually mean anything you say

Where did I say I didn't mean what I say? I guess if I said it, I obviously didn't mean it

but are only using this forum as a scratchpad for your confused ideas and random quote-mining. Early on all you were capable of was throwing insults at me.

You're insulting me by characterizing my ideas as confused and then insulting me again for formerly insulting you. I should be insulting you now in retaliation, but have recognized that you're casting yourself in a bad light with your attacks on me. Honestly, I don't want to see you go, but I just want this silliness to end. I'd prefer to have the perspective of a mathematician available.

At least you've stopped that.

Live and learn. There are other things going on in my life too that makes having patience for certain things more difficult.

But why don't you try to learn something about the subject instead of just Googling around for quotes that are no longer even on topic?

What is not on topic? I'm not rummaging around the net for random quotes. The quotes from David Hilbert came in response to William Lane Craig who quoted him in a debate, so I found the document and posted it. Other quotes came either from links you sent me or from Wildberger. The livescience quote came from google news yesterday. I'm not looking for authorities to appeal to, but will take them if they fall in my lap. And as they fall in my lap, I wanted a thread to post them into so they would be all in one place and open to discussion.

And why is it that you have the time to Google irrelevant quotes but don't have the time to click on the Wiki link that gives specific examples of the need for precise reasoning about changing the order of multiple integrals, which you explicitly asked me for?

Because I'm not interested in that topic, it's expensive in terms of neural energy, your claim is counterintuitive, and I'm not confident, even if your object were valid, that it would lead anywhere. It's a confluence of powerful forces sapping my motivation. I asked you to explain it to me and you declined. Maybe you aren't confident it would accomplish anything either, which isn't doing much for my motivation to learn about it.

So why would it matter if we integrate in the x before the y, and how do we know which is the right answer for the average temperature, and what does this have to do with practical applications of infinity? The plates aren't infinite.... the temperature isn't infinite... and there aren't even infinite slices in the plates because there is a smallest size in the universe, so where does infinity fit in?

Your presentation in this thread makes you out to be an unserious person, arguing in a disingenuous manner.

I've resigned myself to having to start a new thread eventually to consolidate what's in this thread, so perhaps I'll do better with the next iteration.

Don't you want to try to learn anything?

I'd like to learn the answer to those questions, but not enough to struggle through that wiki article.

Ah fuck it. I'm outta here. All the best.

Perhaps you'll reconsider. I'd prefer if you'd stay, but I can't say you're right if I don't think you are and I don't see why you'd want me to.

[Jakob]

Maybe we must realize a marriage between precision and vagary.

Or, we could stop believing something as limited in scope as mathematics could be expected attain any comprehensive logical precision.

Frankly mankinds deference before math is autistic. It is a direct explanation of the state of the world and man's imagined impotency to do anything about it.

The part can't encompass the whole and a thought, an idea, is a part of the universe.

Yes I think so. Thoughts are part of the universe and therefore thoughts cannot embrace the universe. Trying to embrace the universe with an aspect of the universe results in infinite regression which is evidence that the initial assumption was false.

As David said, "We have already seen that the infinite is nowhere to be found in reality, no matter what experiences, observations, and knowledge are appealed to. Can thought about things be so much different from things? Can thinking processes be so unlike the actual processes of things? In short, can thought be so far removed from reality? Rather is it not clear that, when we think that we have encountered the infinite in some real sense, we have merely been seduced into thinking so by the fact that we often encounter extremely large and extremely small dimensions in reality?

Does material logical deduction somehow deceive us or leave us in the lurch when we apply it to real things or events? No! Material logical deduction is indispensable. It deceives us only when we form arbitrary abstract definitions, especially those which involve infinitely many objects. In such cases we have illegitimately used material logical deduction; i.e., we have not paid sufficient attention to the preconditions necessary for its valid use."

Exactly.
For discerning what is valid use I developed value ontology.
A hell of a lot more taxing than mathematics, as it not only requires perfect exactitude but also actual experiential terms rather than only abstractions.

In other words it requires not just a sharp intelligence but also footing in the world and, for lack of a better word, a heart. I can hardly think of a weaker idea than that to understand something you need to strip it of all its actual existence.

Your ideas derived from Watts are deeply pertinent here.
Also what you said about the struggle and immersion, the rewiring of neuron webs required to get there. I've talked about that a lot too. I'm glad to see I'm not the only one.
We may just get somewhere decent as a species.

This arrived in the news yesterday:

Matter Sucked in by Black Holes May Travel into the Future, Get Spit Back Out

Astronomers and physicists have long held that the idea of a singularity simply must be wrong. If an object with mass has no size, then it has infinite density. And, as much as researchers throw around the word "infinity," infinities of that kind don't exist in nature. Instead, 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.

It's easy to give a familiar example of this. Newton's law of gravity says that the strength of the gravitational attraction changes as one over the distance squared between two objects. So if you took a ball located far from Earth, it would experience a certain weight. Then, as you brought it closer to Earth, the weight would increase. Taking that equation to the extreme, as you brought the object near to the center of Earth, it would experience an infinite force. But it doesn't.

Instead, as you bring the object close to the surface of Earth, Newton's simple law of gravity no longer applies. You have to take into account the actual distribution of Earth’s mass, and this means that you need to use different and more complex equations that predict different behavior. Similarly, while Einstein's theory of general relativity predicts that a singularity of infinite density exists at the center of black holes, this can't be true. At very small sizes, a new theory of gravity must come into play. We have a generic name for this new theory: It's called quantum gravity.

All this is just to say that when we encounter infinity, it means we've done something wrong.

Perfect.

[Jakob]

As an example of how shallow mathematicians are in their logic, I can show how easily I resolved the so called contradiction between Relativity and QM.

In fact Relativity itself produces the uncertainty principle.

A quantum like an electron is, like every amount of energy, a reference frame. It can only be properly defined in its own terms. So to approach this minuscule reference frame from the relatively massive reference frame of a technological instrumentarium could logically not produce any straightforward results about such things as "location" and "momentum".

Einstein also requested to Freud that he resolve human cruelty. Mathematicians are generally very naive about actual existence. It may have arisen as a form of escapism. In any case that is what it has become.

Existence ostensibly relies on conflict. Mathematics is of all forms of thought the least equipped to deal with this.

[Serendipper]

Maybe we must realize a marriage between precision and vagary.

Or, we could stop believing something as limited in scope as mathematics could be expected attain any comprehensive logical precision.

Math is just another tool in the toolbox and although sometimes a screwdriver can be a chisel or prybar, it's not necessarily optimized for it. Tools usually have to be implemented intelligently.

I'm beginning to think there isn't a tidy method or one particular way that works, as much as we'd like there to be, much like we can't write every situation into law and therefore we need judges with a sense of equity to fill the voids left by reaching the limits of precision. These philosophical topics are increasingly drawing me into the Middle Way.

Precision/vagary
particles/waves
prickles/goo

Frankly mankinds deference before math is autistic.

You have a remarkable skill for succinctly summarizing situations

Sopranos fan?



00:35

Tony: I need proof. I'm not gonna hurt a man that I love because some cop gossip from a degenerate fucking gambler with a badge. You understand me?

Vin: You know, you got an amazing ability to sum up a man's whole life in a single sentence: degenerate gambler with a badge, huh.

For discerning what is valid use I developed value ontology.

Help me understand what you mean by "value". Do you mean "desire"? An atom desires to have a stable electron configuration? If that is what you mean, then I think we may be on the same page, though I approached it from the eastern angle and have concluded that desire seems fundamental to everything and to be absent desire is not to exist. You've honed in from a different angle with different terminology and it could be that we've arrived at the same place, but "value" is a very confusing word for me because it has so many interpretations.

A hell of a lot more taxing than mathematics, as it not only requires perfect exactitude but also actual experiential terms rather than only abstractions. In other words it requires not just a sharp intelligence but also footing in the world and, for lack of a better word, a heart.

Hopefully 1 out of the 3 will suffice if by "heart" you mean "determination".

"Nothing in the world can take the place of Persistence. Talent will not; nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not; the world is full of educated derelicts. Persistence and Determination alone are omnipotent. The slogan “Press On” has solved and will always solve the problems of the human race."- Calvin Coolidge

I can hardly think of a weaker idea than that to understand something you need to strip it of all its actual existence.

Another insightful summary!

Your ideas derived from Watts are deeply pertinent here. Also what you said about the struggle and immersion, the rewiring of neuron webs required to get there. I've talked about that a lot too. I'm glad to see I'm not the only one.

That probably explains the old adage of "sleeping on it" to make important decisions. The brain may need time to grow or somehow arrange itself to better model or conceptualize a situation which can then be seen clearer for a better decision. From my own experience with Watts, I feel I had to grow eyes to see what he was presenting and it wasn't easy. I listened to some presentations 30 times and still learned something, which meant that nuggets flew right over my head 30 times without my noticing. Birds that fly high indeed look small! But now I can see clearer and spot those birds because I grew the tools necessary to do so.

I think the brain can be rewired and neurons can grow, so I believe (contrary to popular opinion) that intelligence can be taught. Just like muscles can be trained to support heavier loads, the brain can be trained to support heavier ideas by forming the necessary neural network, which is the supporting framework capable of modeling what previously couldn't be conceived. The problem is often the ego... people can't let go of what they already think is right, either due to self-esteem issues or narcissism. If true, then intelligence is mainly a function of humility or the extent to which one can be wrong and switch sides.

We may just get somewhere decent as a species.

I know what you mean.

The Catholic Church issued apology in 1992 for persecuting Galileo and in 1995 for burning people at the stake,,,, 400 years later! https://en.wikipedia.org/wiki/List_of_a ... hn_Paul_II

[Serendipper]

As an example of how shallow mathematicians are in their logic, I can show how easily I resolved the so called contradiction between Relativity and QM.

In fact Relativity itself produces the uncertainty principle.

A quantum like an electron is, like every amount of energy, a reference frame. It can only be properly defined in its own terms. So to approach this minuscule reference frame from the relatively massive reference frame of a technological instrumentarium could logically not produce any straightforward results about such things as "location" and "momentum".

Yes, it doesn't makes sense to probe an electron with something bigger than an electron.

Einstein also requested to Freud that he resolve human cruelty. Mathematicians are generally very naive about actual existence. It may have arisen as a form of escapism. In any case that is what it has become.

Existence ostensibly relies on conflict. Mathematics is of all forms of thought the least equipped to deal with this.

In 1983 an American developmental psychologist Howard Gardener described 9 types of intelligence:

Naturalist (nature smart)
Musical (sound smart)
Logical-mathematical (number/reasoning smart)
Existential (life smart)
Interpersonal (people smart)
Bodily-kinesthetic (body smart)
Linguistic (word smart)
Intra-personal (self smart)
Spatial (picture smart)

https://blog.adioma.com/9-types-of-inte ... fographic/

[Jakob]

Serendipper - I've used the term value because all of its meanings apply as the same principle in different contexts. Indeed desire is a main human context. But I see loyalty (when taken in the same semantic manner as you propose we take desire) as at leat as fundamental. Stability, consistency. For me terms like consciousness and desire are rather too specific but it is clear we aren't in contradiction.

I've spent some 20 years with rigorous meditation, Zen to begin with, yoga and later western occultism on top of that, coupled with martial arts, Shaolin and Tai Chi, the first years that was many hours each day. And it's absolutely the case that this has formed the background to my emerged understanding.

I am a Sopranos fan and I much enjoyed that compliment. A memorable character, that detective. I think its around the same time whem Tony has to deal with these Hasidic Jews
"Hasidim but I don't believe 'em" in Paulies immortal words.
Or: "and the Romans, where are they now? "
"You're looking at em asshole."
But then, " this guy is a bull. If we don't kI'll him we should put him to work."
Fantastic show. No wonder Gandolfini couldn't live on after it was done.
I mention the Hasids as a playful reference to our earlier clash on BTL. I'm very much a Zionist, for reasons more complex and dark than can be said aloud. It's very nice that we do see eye to eye on philosophy proper. Politics is nasty by nature, philosophy is not.

I've been winding down my forum activities after 17 years, so Im wary of going all the way again into explaining this logic I developed between East and West, I've done this hundreds f times across the Web with different names and I'm very satisfied that a lot of my focus on valuing now echos in all kinds of media. I'm all about grassroots insurgency of ideas.

The thread "the Philosophers" in nonphilosophical chat has become a kind of archive of some of my work. I think of online writing as scattering seeds knowing that some of them will take root. I don't believe in directly convincing people. "You only see what your eyes want to see" , with Madonna, an unlikely person to quote. But since you're able to understand much I'll give one last summary here.

I've called this phenomenon of selectivity self-valuing logic, though this is misleading as one only vales oneself through ones external values such as first of all oxygen and other unconsciously held values, of which one only becomes conscious when they fall away - or when one practices meditation. On a conscious leven we get desires and on an even more conscious level, moral values.
Some say oxygen isn't a value. But let's see them discard it in favour of some money before we believe them.
So I see breathing as valuing. And valuing, if it amounts to the perpetuation of the being, as self-valuing. Not the valuing of a self (the self is an illusion) but the valuing of valuing.

It's tough to put into grammar. Grammar itself is a presupposed structure that is false. There is no fundamental difference between the subject, the verb, the object; the being is artificially split into this trinity for the sake of communicating some utilitarian messages. But utility itself is a specific value.
I recommend a look at the thread "the ontological thranny" started by without-music, a poster of some genius who was here for a short while in 2011.
Beyond all this I wish you good "demon days" as the Vikings called this solstice time, and take care of yourself, and keep up your kung fu, meaning literally, as far as my knowledge of Cantonese goes, good work.


PS tying the thought of infinity to the expression "sleeping on it", a bit I wrote to a friend recently;

"Any selfvaluing is an epistemic standard, meaning a limited holder of truth. Its being relies on its limitedness, as you explain. Knowledge is obviously reliant on being limited. Too many ways to clarify that. And that's at the genesis of my own understanding of being as selfvaluing; seeing the scientific method as a form of severe limitation of what constitutes knowledge. Precisely because it refuses almost every form of knowing, it becomes almost indistinguishable from knowledge itself.

There is no negation of continuity in the absence of it. Continuity of what? Continuity in life also doesn't exist. We must sleep precisely because of the ruptures that [lie] between literally everything. We must negate the positive being and lose ourselves each day just in order to not contradict the contents of own consciousness by putting them into some vessel."

I think this is what Spinoza tried to get at. Or maybe he did, I never finished the Ethica, and I know only one old poster here who did, a guy named Dunamis. He was banned long ago, but it's worth looking into some of his posts. There is a lot of treasure hidden on the site. Your own posts are always substantive and with interesting references and must be counted among such treasures.

[wtf]

Perhaps you'll reconsider. I'd prefer if you'd stay ...

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

,,,it wasn't meant to prod you in any way.

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.

I thought it was a fairly harmless thing to say. You're acting as if math studied for the enjoyment of math is somehow inferior to math studied for some goal or purpose and have therefore construed my comment as offensive.

???? 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.

Chess is a toy, but is being good at chess a bad thing? Is describing chess as a toy a bad thing? Where is the offensiveness?

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.

Whoever is pretending infinity applies outside of math.

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.

The only thing I can remember bitterly complaining about was the stubbornness surrounding the definition of infinity. The only thing I remember claiming about set theory is that I couldn't find anything about it within 1200 pages of my calculus book ...

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?

..., and that was only in response to your assertion that set theory underpins calculus.

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?

Then we transitioned to higher math where I said "math for the sake of math" then you got all pissed off because I dis'd math and here we are.

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

It's not fiction, but a tool that can be misapplied. It also can model fictitious things. Math can do more than what we would describe as "real" and just because math makes a claim, doesn't mean it will match reality. But neither can we say math is worthless because it often matches reality. It's tool to be used intelligently with proper assumptions. Garbage in = garbage out.

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?

The reason they are public is because I want peer review, but not dogmatic digging-in in stubborn refusal to concede a point. This should be a collaboration and not a competition.

Project much?

I know my ideas on infinity conflict with ideas of many mathematicians, but I'm not aware of other contradictions and it would be helpful if you'd point them out.

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 posted an article from livescience today, written by Don Lincoln, Senior Scientist, Fermi National Accelerator Laboratory; Adjunct Professor of Physics, University of Notre Dame, that said: ...

(quote omitted)

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?

As far as I can tell, I'm in sync with all but mainstream mathematicians.

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?

Where did I say I didn't mean what I say? I guess if I said it, I obviously didn't mean it

Yeah, that I believe.

Live and learn. There are other things going on in my life too that makes having patience for certain things more difficult.

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.

What is not on topic? I'm not rummaging around the net for random quotes. The quotes from David Hilbert came in response to William Lane Craig who quoted him in a debate,

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.

so I found the document and posted it.

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

Other quotes came either from links you sent me or from Wildberger.

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.

The livescience quote came from google news yesterday. I'm not looking for authorities to appeal to, but will take them if they fall in my lap.

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.

Because I'm not interested in that topic,

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 expensive in terms of neural energy, your claim is counterintuitive, and I'm not confident, even if your object were valid, that it would lead anywhere.

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.

It's a confluence of powerful forces sapping my motivation.

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 asked you to explain it to me and you declined.

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.

Maybe you aren't confident it would accomplish anything either, which isn't doing much for my motivation to learn about it.

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.

So why would it matter if we integrate in the x before the y, and how do we know which is the right answer for the average temperature, and what does this have to do with practical applications of infinity?

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.

The plates aren't infinite.... the temperature isn't infinite... and there aren't even infinite slices in the plates because there is a smallest size in the universe, so where does infinity fit in?

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.

I've resigned myself to having to start a new thread eventually to consolidate what's in this thread, so perhaps I'll do better with the next iteration.

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.

I'd like to learn the answer to those questions, but not enough to struggle through that wiki article.

"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?

[Serendipper]

Serendipper - I've used the term value because all of its meanings apply as the same principle in different contexts. Indeed desire is a main human context.

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.



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.

I am a Sopranos fan and I much enjoyed that compliment.

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

A memorable character, that detective. I think its around the same time whem Tony has to deal with these Hasidic Jews
"Hasidim but I don't believe 'em" in Paulies immortal words.

Yeah I like Paulie.

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

Or: "and the Romans, where are they now? "
"You're looking at em asshole."

That was a good one!

But then, " this guy is a bull. If we don't kI'll him we should put him to work."

"Yea though I walk through the valley of the shadow of death..."
"Hold that thought."

Fantastic show. No wonder Gandolfini couldn't live on after it was done.
I mention the Hasids as a playful reference to our earlier clash on BTL. I'm very much a Zionist, for reasons more complex and dark than can be said aloud.

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.

It's very nice that we do see eye to eye on philosophy proper. Politics is nasty by nature, philosophy is not.

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

I've been winding down my forum activities after 17 years, so Im wary of going all the way again into explaining this logic I developed between East and West, I've done this hundreds f times across the Web with different names and I'm very satisfied that a lot of my focus on valuing now echos in all kinds of media. I'm all about grassroots insurgency of ideas.

Just talk about what you want to talk about.

The thread "the Philosophers" in nonphilosophical chat has become a kind of archive of some of my work. I think of online writing as scattering seeds knowing that some of them will take root.

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

I don't believe in directly convincing people. "You only see what your eyes want to see" , with Madonna, an unlikely person to quote. But since you're able to understand much I'll give one last summary here.

What determines what the eyes want to see?

I've called this phenomenon of selectivity self-valuing logic, though this is misleading as one only vales oneself through ones external values such as first of all oxygen and other unconsciously held values, of which one only becomes conscious when they fall away - or when one practices meditation. On a conscious leven we get desires and on an even more conscious level, moral values.

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.

I recommend a look at the thread "the ontological thranny" started by without-music, a poster of some genius who was here for a short while in 2011.

Will do. Thanks!

Beyond all this I wish you good "demon days" as the Vikings called this solstice time, and take care of yourself, and keep up your kung fu, meaning literally, as far as my knowledge of Cantonese goes, good work.

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

PS tying the thought of infinity to the expression "sleeping on it", a bit I wrote to a friend recently;

"Any selfvaluing is an epistemic standard, meaning a limited holder of truth. Its being relies on its limitedness, as you explain. Knowledge is obviously reliant on being limited.

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.

Too many ways to clarify that. And that's at the genesis of my own understanding of being as selfvaluing; seeing the scientific method as a form of severe limitation of what constitutes knowledge. Precisely because it refuses almost every form of knowing, it becomes almost indistinguishable from knowledge itself.

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

There is no negation of continuity in the absence of it. Continuity of what? Continuity in life also doesn't exist.

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

We must sleep precisely because of the ruptures that [lie] between literally everything.

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

We must negate the positive being and lose ourselves each day just in order to not contradict the contents of own consciousness by putting them into some vessel."

I'm having trouble understanding that one.

I think this is what Spinoza tried to get at. Or maybe he did, I never finished the Ethica, and I know only one old poster here who did, a guy named Dunamis. He was banned long ago, but it's worth looking into some of his posts. There is a lot of treasure hidden on the site. Your own posts are always substantive and with interesting references and must be counted among such treasures.

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.

[Serendipper]

Perhaps you'll reconsider. I'd prefer if you'd stay ...

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

,,,it wasn't meant to prod you in any way.

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.

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 thought it was a fairly harmless thing to say. You're acting as if math studied for the enjoyment of math is somehow inferior to math studied for some goal or purpose and have therefore construed my comment as offensive.

???? 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.

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

Chess is a toy, but is being good at chess a bad thing? Is describing chess as a toy a bad thing? Where is the offensiveness?

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.

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.

Whoever is pretending infinity applies outside of math.

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'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." https://www.livescience.com/64332-black ... avity.html

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

The only thing I can remember bitterly complaining about was the stubbornness surrounding the definition of infinity. The only thing I remember claiming about set theory is that I couldn't find anything about it within 1200 pages of my calculus book ...

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?

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.

..., and that was only in response to your assertion that set theory underpins calculus.

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?

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.

Then we transitioned to higher math where I said "math for the sake of math" then you got all pissed off because I dis'd math and here we are.

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

That's how I remember it.

It's not fiction, but a tool that can be misapplied. It also can model fictitious things. Math can do more than what we would describe as "real" and just because math makes a claim, doesn't mean it will match reality. But neither can we say math is worthless because it often matches reality. It's tool to be used intelligently with proper assumptions. Garbage in = garbage out.

So now you DO agree that math underpins modern physical science?

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.

Or are you still demanding that we take science back to the year 1500 or so?

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

The reason they are public is because I want peer review, but not dogmatic digging-in in stubborn refusal to concede a point. This should be a collaboration and not a competition.

Project much?

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.

I know my ideas on infinity conflict with ideas of many mathematicians, but I'm not aware of other contradictions and it would be helpful if you'd point them out.

Well now you're contradicting yourself again. Do you or do you not agree that math is valid within itself;

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.

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?

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.

What do you know that all the mathematicians in the world don't?

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

I posted an article from livescience today, written by Don Lincoln, Senior Scientist, Fermi National Accelerator Laboratory; Adjunct Professor of Physics, University of Notre Dame, that said: ...

(quote omitted)

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?

Idk, I forgot the context for this one.

As far as I can tell, I'm in sync with all but mainstream mathematicians.

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?

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.

Live and learn. There are other things going on in my life too that makes having patience for certain things more difficult.

So then why should I bother?

You should only bother if it's fun.

Do you regret "prodding" me today?

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

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.

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

What is not on topic? I'm not rummaging around the net for random quotes. The quotes from David Hilbert came in response to William Lane Craig who quoted him in a debate,

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.

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

so I found the document and posted it.

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

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

Other quotes came either from links you sent me or from Wildberger.

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.

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

The livescience quote came from google news yesterday. I'm not looking for authorities to appeal to, but will take them if they fall in my lap.

Authorities about what? You're not making any actual point.

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.

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.

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.

Because I'm not interested in that topic,

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.

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.

it's expensive in terms of neural energy, your claim is counterintuitive, and I'm not confident, even if your object were valid, that it would lead anywhere.

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.

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

It's a confluence of powerful forces sapping my motivation.

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 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.

I asked you to explain it to me and you declined.

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.

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 -> https://en.wikipedia.org/wiki/Fubini%27 ... d_integral

So why would it matter if we integrate in the x before the y, and how do we know which is the right answer for the average temperature, and what does this have to do with practical applications of infinity?

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.

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

The plates aren't infinite.... the temperature isn't infinite... and there aren't even infinite slices in the plates because there is a smallest size in the universe, so where does infinity fit in?

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.

There's the pre-newtonian appeal again.

I've resigned myself to having to start a new thread eventually to consolidate what's in this thread, so perhaps I'll do better with the next iteration.

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.

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

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

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

So bottom line, do you:

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

Yes

* Do you reject modern math?

That's the same question, only negated.

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

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

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 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.

[Serendipper]

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.

[wtf]

When you call people cranks, it affects your credibility.

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.

https://www.reddit.com/r/math/comments/ ... my_school/

https://scienceblogs.com/goodmath/2007/ ... e-sets-and

https://math-frolic.blogspot.com/2012/0 ... erger.html

https://www.reddit.com/r/math/comments/ ... _goldbach/

https://www.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.

[wtf]

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

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.

[wtf]

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.

[Serendipper]

When you call people cranks, it affects your credibility.

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.

https://www.reddit.com/r/math/comments/ ... my_school/

https://scienceblogs.com/goodmath/2007/ ... e-sets-and

https://math-frolic.blogspot.com/2012/0 ... erger.html

https://www.reddit.com/r/math/comments/ ... _goldbach/

https://www.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.

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. https://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.

[Serendipper]

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

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.

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.

[Serendipper]

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.

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

[surreptitious75]

Infinity doesnt exist in nature and neither does it exist in the mind although we can pretend
it does through inference and then draw conclusions from that for whatever reason

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

[surreptitious75]

I posted an article from livescience today written by Don Lincoln Senior Scientist Fermi National Accelerator Laboratory
Adjunct Professor of Physics University of Notre Dame that said :

Astronomers and physicists have long held that the idea of a singularity simply must be wrong . If an object with mass has no size
then it has infinite density . And as much as researchers throw around the word infinity infinities of that kind dont exist in nature

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

[Serendipper]

Infinity doesnt exist in nature and neither does it exist in the mind although we can pretend
it does through inference and then draw conclusions from that for whatever reason

Can non existence exist in the absolute sense ? No it cannot which means existence has always existed [ and always will ]

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.

This means that it exists infinitely in the past and will exist infinitely into the future

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.

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

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 posted an article from livescience today written by Don Lincoln Senior Scientist Fermi National Accelerator Laboratory
Adjunct Professor of Physics University of Notre Dame that said :

Astronomers and physicists have long held that the idea of a singularity simply must be wrong . If an object with mass has no size
then it has infinite density . And as much as researchers throw around the word infinity infinities of that kind dont exist in nature

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

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

[surreptitious75]

I posted an article from livescience today written by Don Lincoln Senior Scientist Fermi National Accelerator Laboratory
Adjunct Professor of Physics University of Notre Dame that said :

Astronomers and physicists have long held that the idea of a singularity simply must be wrong . If an object with mass has no size
then it has infinite density . And as much as researchers throw around the word infinity infinities of that kind dont exist in nature

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

I dont 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

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

[wtf]

I posted an article from livescience today, written by Don Lincoln, Senior Scientist, Fermi National Accelerator Laboratory; Adjunct Professor of Physics, University of Notre Dame, that said:

"Astronomers and physicists have long held that the idea of a singularity simply must be wrong. If an object with mass has no size, then it has infinite density. And, as much as researchers throw around the word "infinity," infinities of that kind don't exist in nature. Instead, 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. "https://www.livescience.com/64332-black ... avity.html

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.

http://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.

https://www.encyclopediaofmath.org/inde ... f_analysis


2) 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.

https://en.wikipedia.org/wiki/Differential_geometry

https://en.wikipedia.org/wiki/Introduct ... relativity

3) 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.

https://en.wikipedia.org/wiki/Fourier_series

4) 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.


5) 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.

https://www.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.

[wtf]

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

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."

I'm ok with figures of speech, but Michio Kaku said "as density approaches infinity...."

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.

[Ecmandu]

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"