What can we gain by losing infinity?
quantamagazine.org
What can we gain by losing infinity?
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Re: What can we gain by losing infinity?
#2[deleted]
Re: What can we gain by losing infinity?
#3In school I developed a strong hunch that continuity and infinity are "convenient delusions" we have that allow us to process the otherwise horrific complexity of the world. Experiencing time, sound, or visual motion as continuous, rather than discrete signal inputs is so much simpler. Similarly, the mathematical tricks and shortcuts we can use on well behaved continuous functions are both "unreasonably effective" and... probably not grounded in actual reality[1]? But damn are they convenient.
[1] EDIT: the reasoning is simple, if naive: the largest quantities we can measure are not, in fact, infinitely large, and the smallest ones we can measure are not, in fact, infinitesimally small. So until you show me an infinitesimal or an infinity, you're just making them up!
Re: What can we gain by losing infinity?
#4finite moments. cherish them.
Re: What can we gain by losing infinity?
#5Normally amps only go up to ten… but this one goes to eleven.
…it’s one louder ain’t it!?!
Re: What can we gain by losing infinity?
#6> To Zeilberger, believing in infinity is like believing in God. It’s an alluring idea that flatters our intuitions and helps us make sense of all sorts of phenomena. But the problem is that we cannot truly observe infinity, and so we cannot truly say what it is.
I'm hoping this is just bad writing from Quanta rather than something "ultrafinitists" truly believe.
I really don't think it's that complicated. Even pre-schoolers, competing to see who can say the highest number, quickly learn the concept of infinity. Or elementary school students trying to write 1/3 as a decimal.
Of course you need to be careful mapping infinity onto the physical world. But as a mathematical concept, there is absolutely nothing wrong with it.
> Mathematicians can construct a form of calculus without infinity, for instance, cutting infinitesimal limits out of the picture entirely.
This seems like a useful concept that also doesn't require denying the very obvious concept of infinity.
Re: What can we gain by losing infinity?
#7It's not a new idea, and it's a challenging one to investigate. Without real numbers (that are infinitely long) most of the calculus stops working. And everything that depends on it.
Perhaps we can recover some of it by treating the infinitely variable values as approximations of the more discrete values and then somehow proving that the errors from them stay bounded, for at least some interesting problems.
Re: What can we gain by losing infinity?
#8The article doesn’t really tell us what is gained by rejecting infinity.
And in general, why not also reject zero, negative numbers, irrational numbers, complex numbers, uncomputable numbers, etc.?
Seems like an article about quacks that can’t even agree on what the bounds and rules of their quackery are.
Re: What can we gain by losing infinity?
#9> To Zeilberger, believing in infinity is like believing in God. It’s an alluring idea that flatters our intuitions and helps us make sense of all sorts of phenomena. But the problem is that we cannot truly observe infinity, and so we cannot truly say what it is. I'm hoping this is just bad writing from Quanta rather than something "ultrafinitists" truly believe. I really don't think it's that complicated. Even pre-s…
I’m pretty certain a finite number of pre-schoolers can only recite a finite number of numbers.
Yes, they could on indefinitely, but will they ever?
Re: What can we gain by losing infinity?
#10> To Zeilberger, believing in infinity is like believing in God. It’s an alluring idea that flatters our intuitions and helps us make sense of all sorts of phenomena. But the problem is that we cannot truly observe infinity, and so we cannot truly say what it is. I'm hoping this is just bad writing from Quanta rather than something "ultrafinitists" truly believe. I really don't think it's that complicated. Even pre-s…
I’m pretty certain a finite number of pre-schoolers can only recite a finite number of numbers. Yes, they could on indefinitely, but will they ever?
> Yes, they could on indefinitely
Only if they live forever, which they won't. They can only count so fast, and there are only so many of them. Even if every atom in the observable universe was counting at, idk, 1GHz, that's still a finite number. The universe is not (as far as we know for certain) infinitely old. Time may extend infinitely into the future, or it may not. We don't know. So far as we know for sure everything is in fact finite.