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:

Serendipper wrote:,,,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.

Serendipper wrote: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.

Serendipper wrote: 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?