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0 pointsgodelski8mo ago0 comments

Honestly it's difficult to understand exactly what you're arguing. Because I understand laymen not understanding your argument about infinities not being real (and even many HN users don't understand code is math bit a CS degree doesn't take you far in math. Some calc and maybe lin alg) but are we concerned about laymen? I too am frustrated by nonexperts having strong opinions and having difficulties updating them, but that's not a culture problem. We're on HN and we know the CS stereotypes, right?

If instead you're talking about experts then I learned about what you're talking about in my Linear 2 course in a physics undergrad and have seen the topic appear many times since even outside my own reading of set theory. The axiom of choice seems to have even entered more main stream nerd knowledge. It's very hard to learn why AoC is a problem without learning about how infinities can be abused. But honestly I don't know any person that's even an amateur mathematician that thinks infinities are physical

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btilly8mo ago· 2 in thread

The fact that you think I'm talking about the axiom of choice, demonstrates that you didn't understand what I'm talking about. I would also be willing to bet a reasonable sum of money that this topic did not come up in your Linear 2 course in physics undergrad.

The arguments between the different schools of philosophy in math are something that most professional mathematicians are unaware of. Those who know about them, generally learned them while learning about either the history of math, or the philosophy of math. I personally only became aware of them while reading https://www.amazon.com/Mathematical-Experience-Phillip-J-Dav.... I didn't learn more about the topic until I was in grad school, and that was from personal conversations. It was never covered in any course that I took on, either in undergraduate or graduate schools.

Now I'm curious. Was there anything that I said that should have been said more clearly? Or was it hard to understand because you were trying to fit what I said into what you know about an entirely unrelated debate about the axiom of choice?

godelskiOP8mo ago

  > The fact that you think I'm talking about the axiom of choice, demonstrates that you didn't understand what I'm talking about.

Dude... just a minute ago you were complaining about ZFC... Sure, I brought up AoC but your time to protest was then.

The reason I brought up AoC is because it is a common way to learn about the abuse of infinity and where axioms need be discussed. Both things you brought up. I think you are reading further into this than I intended.

  > Now I'm curious. Was there anything that I said that should have been said more clearly?

Is this a joke?

When someone says

  >> Honestly it's difficult to understand exactly what you're arguing.

That's your chance to explain. It is someone explicitly saying... I'm trying to understand but you are not communicating efficiently.

This is even more frustrating as you keep pointing out that this is not common knowledge. So why are you also communicating like it is?! If it is something so few know about then be fucking clear. Don't make anyone guess. Don't link a book, use your own words and link a book if you want to suggest further reading, but not "this is the entire concept I'm talking about". Otherwise we just have to guess and you getting pissed off that we guess wrong is just down right your own fault.

So stop shooting yourself in the foot and blaming others. If people aren't understanding you, try assuming they can't read your mind and don't have the exact same knowledge you do. Talk about fundamental principles...

btilly8mo ago

I've had a lot of chances to explain. I've posted a lot of explanations. For example see https://news.ycombinator.com/item?id=45435534 for an explanation that I posted 11 hours ago. See https://plato.stanford.edu/entries/mathematics-constructive/ for a link that I gave. See https://news.ycombinator.com/item?id=45434701 for someone with a different point of view, attempting to explain the same key point.

That point being that what we mean by "exists" is fundamentally a philosophical question. And our conclusions about what mathematical things exist will depend on how we answer that question. And very specifically, there are well-studied mathematical philosophies in which uncountable sets do not have larger cardinalities than countable ones.

If none of those explanations wind up being clear for you, then I'm going to need feedback from you to have a chance to explain this to you. Because you haven't told me enough for me to make any reasonable guess what the sticking point is between you and understanding. And without that, I have no chance of guessing what would clarify this for you.

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