I’m a sucker for a kind word. But I was confused by this:
I took that to mean that when I dared to post to this thread you regretted “prodding” me. I was genuinely insulted and demoralized. I thought we were having a conversation, but apparently you prefer me to stay unprodded.
So which is it? Now that I’m going to respond to your latest post will you regret prodding me? Or will you appreciate my taking the time to provide my perspective? No way for me to know, is there. But ok what the hell. Happy New Year by the way. Here’s my response to your latest.
??? What ??? If anything I have the opposite point of view. I agree with G.H Hardy (played by Jeremy Irons in The Man Who Knew Infinity. I highly recommend it) that the best math is by definition the most useless math.
You are mischaracterizing my words and viewpoint 180 degrees. You’re attacking a strawman. That adds to my frustration with this conversation. Was I unclear? Is your reading comprehension bad? Are you just deliberately lying about what I said? Hard for me to know. Do you already regret prodding me again? Or do you wish I’d contribute? Hard to know.
Would that include every physicist since Newton? I’ve asked you this before. Modern physical science is based on infinitary math. Whether that’s a necessary or a contingent fact we don’t yet know. But the empirical fact remains. No infinitary math and you throw science back to the Middle ages. Is that your intention? I have asked you this several times now without getting a direct response.
I imagine that when you learned to drive a car, you were not first required to master metallurgy and automotive engineering. Do you take that as evidence that these disciplines do not actually underlie the act of driving a car? Or is it perhaps more likely that these disciplines are in fact essential to the very existence of cars, but that we don’t teach them to beginning drivers, in favor of simply teaching them how not to hit things?
Which it certainly does. I assume you can operate a light switch and were not first required to master the subject of electrical power generation. In calculus we teach people a rote procedure to “pull down the exponent and subtract 1.” We do not show beginning students Newton’s application of the fact that the binomial theorem can be extended to real-valued exponents.
It’s perfect clear historically that Newton worked with infinitary math. Would you really send us all back to the pre-Newtonian world?
Yet another vile mischaracterization of what I actually said. Now I’m reminded of why I quit this thread in disgust.
So now you DO agree that math underpins modern physical science? Or are you still demanding that we take science back to the year 1500 or so?
Project much?
Well now you’re contradicting yourself again. Do you or do you not agree that math is valid within itself; and does happen to be supremely useful? If you agree that math for the sake of math is valid, then exactly WHAT ARE your ideas on infinity? What do you know that all the mathematicians in the world don’t?
I perfectly well agree. But I wonder: WHY ARE YOU TELLING ME THIS? From my first post in this thread I have agreed that (as far as we know, to the limits of contemporary physical theory) there is no actual infinity instantiated in the world. Since I have long ago agreed with this point, why are you acting as if making this point again somehow counts as an intelligent comment in response to anything I’ve said?
All but mainstream mathematicians? So you know something that 140 years of professional mathematicians don’t? What would that be exactly?
What does “all but the mainstream” mean? Are you saying you’re in line with the mathematical cranks? How does that help your credibility?
You’ve already agreed that math is perfectly fine as an abstract game. That’s the philosophical doctrine of mathematical formalism. But now you claim that you oppose even the formalism. WHICH IS IT?
Yeah, that I believe.
So then why should I bother? Do you regret “prodding” me today? Or do you appreciate my point-by-point response to your remarks? How would I know what mood you’re in? You know you could always write your response in a text file and sit on it for a day to make sure you’re saying what you mean and not reacting irrationally to whatever’s going on in your life. That would be a tactic that would enable you to post more coherently.
Craig is the worst kind of sophist. Let’s not go down that road. But your Hilbert quote was about the physical world, and I’ve already said many times that I agree that (as far as we currently know) there are no actual infinities in the physical world. So your quote was totally off topic when directed to me.
Why? It’s off-topic to our discussion, which is about mathematical infinity.
Good God man, Wildberger is an absolute crank on the subject of infinity. Who are you trying to fool? Not me, since I’m extremely familiar with Wildberger’s work.
Authorities about what? You’re not making any actual point. You have said both that
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You are perfectly fine with modern mathematical formalism regarding infinity; and
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You absolutely oppose modern mathematical formalism regarding infinity.
Which is it? State your freaking thesis and defend it. Stop going back and forth on this point.
Yet you explicitly asked me for the examples of situations in which the order of a multiple integration matters. Once again you are just playing games. You ask me for the examples, I point you to the examples, you refuse to click on the link, and then you say you have no interest. THEN WHY THE F*CK DID YOU ASK??? Just playing games. Not a serious person at all.
It’s one of the examples of the need for precision and rigor in the foundations of math. The details of Fubini’s theorem are not important. The necessity of a clear and precise theorem is the point.
You ask me a question, I point to the answer, you claim you were never interested. That’s why I say you are not serious about learning or thinking or conversating.
I pointed to the link on Wiki. If I thought Wiki did a bad job I’d do a better one. In this particular case, Wiki’s presentation is spot on and I could not improve on it.
You don’t need to dive into the details. They’re unimportant. What is important is that the examples exist. The 18th and 19th centuries were all about mathematicians realizing that they desperately needed clear and logically rigorous foundations, else their intuitions would lead them astray. It’s the existence of the examples, not the details of the examples, that’s important and significant.
Learning the specific examples is totally unimportant. The fact that the examples exist is important. And all that’s needed there is a mouse click to the Wiki page.
It matters because although our intuition says the order doesn’t matter, there are actual examples in which it does matter. Showing that there is a need for logical rigor in our foundations.
Physicists find mathematical reasoning indispensable in their work. Take it up with them. Else drive us all back to 1500 when nobody knew or cared about any of it.
And I’m sure I’m resigned to reading it. But unless your thinking gets more clear it will just be more of the same.
“There is no royal road to geometry.” – Euclid.
We all have to struggle to understand the math. But in this case understanding the math is totally unimportant. All that’s needed to to accept that these examples exist, whether we drill down to the details or not. And these examples show the need for mathematical rigor.
You do NOT NEED TO UNDERSTAND THE EXAMPLES. You only need to acknowledge that the examples exist.
So bottom line, do you:
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Accept mathematical formalism as an abstract, meaningless game but perhaps an interesting one? Or
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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?