WHY DIDN'T WE LISTEN?

[Anonymous No.10981315]

>"On August 10, 1632, five men in flowing black robes convened in a somber Roman palazzo to pass judgment on a deceptively simple proposition: that a continuous line is composed of distinct and infinitely tiny parts. With the stroke of a pen the Jesuit fathers banned the doctrine of infinitesimals, announcing that it could never be taught or even mentioned. The concept was deemed dangerous and subversive, a threat to the belief that the world was an orderly place, governed by a strict and unchanging set of rules. If infinitesimals were ever accepted, the Jesuits feared, the entire world would be plunged into chaos"
>PLUNGED INTO CHAOS

Were the Jesuits right all along?

[Anonymous No.10981945]

>>10981315
wtf I love jesuits now

[Anonymous No.10982005]

>>10981315
Finitism vs Infinitism, the oldest true intellectual argument.

[Anonymous No.10982041]

>>10981315
Yet another anecdote showing how faggy c*tholics are. What a surprise.

[Anonymous No.10982045]

>>10981315
so no calculus student would suffer with this shit until Newton
Based

[Anonymous No.10982306]

I think people are slowly realizing they were right.

[Anonymous No.10982408]

>>10981315
well they were right

[Anonymous No.10983456]

why didn't we listen

[Anonymous No.10983462]

>>10981315
>the entire world
You mean: The current surface.

[Anonymous No.10983471]

>>10982408
Who is this man?

[Anonymous No.10983491]

>>10981315
Humans are arrogant to use concepts such as infinity and claim as an AXIOM that infinite sets exist. No one understands it. It’s all pseud wankery.
>hurr but muh Cantor diagonals
It sure is easy to prove infinity by first assuming it exists to begin the proof

[Anonymous No.10983502]

foundations meme thread?
foundations meme thread

[Anonymous No.10983507]

>>10983471
He's some meme dude from youtube who contends with very basic mathematical concepts and doesn't even believe irrational and transcendental numbers can exist.

[Anonymous No.10983518]

>>10983507
to be fair, irrational numbers are unsettling. They just go off into infinity with no identifiable pattern.

[Anonymous No.10983525]

>>10983507
He’s a math professor who went to Yale. He’s not that much of a meme and is obviously intelligent

[Anonymous No.10983534]

From the same book:
>[pg 12] "Yet, useful as it was, the concept of the infinitely small was challenged at every turn. The Jesuits opposed it; Hobbes and his admirers opposed it; Anglican churchmen opposed it, as did many others. What was it, then, about the infinitely small that inspired such fierce opposition from so many different quarters ? The answer is that the infinitely small was a simple idea that punctured a great and beautiful dream: that the world was a perfectly rational place, governed by strict mathematical rules. In such a world, all things, natural and human, have their given and unchanging place in the grand universal order. Everything from a grain of sand to the stars in the sky, from the humblest beggar to kings and emperors, is part of a fixed, eternal hierarchy. Any attempt to revise or topple it is a rebellion against the one unalterable order, a senseless disruption that in any case, is doomed to failure...."

[Anonymous No.10983539]

From the same book:
>[pg 14] "From North to South, from England to Italy, the fight over the infinitely small raged across western Europe. The lines of the struggle were clearly drawn. On the one side were the advocates of intellectual freedom, scientific progress, and political reform; on the other, the champions of authority, universal and unchanging knowledge, and fixed political hierarchy. The results of the fight were not everywhere the same, but the stakes were always just as high: the face of the modern world, then coming into being. The statement that "the mathematical continuum is composed of distinct indivisibles" is innocent enough to us, but three and a half centuries ago it had the power to shake the foundations of the early modern world. And so it did: the ultimate victory of the infinitely small helped open the way to a new and dynamic science, to religious toleration, and to political freedoms on a scale unknown in human history."

[Anonymous No.10983558]

>>10983539
>>10983534
Infinity is a trick of Satan. Man, who can hardly understand the finite, thinks he can understand the infinite. It is surely the result of ego and loose thinking

[Anonymous No.10983565]

>>10983507
>>>/reddit/

[Anonymous No.10983574]

>>10983565
why?

[Anonymous No.10983576]

>>10983558
Modern man's denial of an absolute, finite truth in favor of an infinite, relative truth, has made him think as if his mind was God.

[Anonymous No.10983610]

>>10983518
chaos, chaos!

[Anonymous No.10983621]

>>10983576
Don't we have enough of this sanctimonious crap on /lit/?

[Anonymous No.10983788]

>>10982041
¿Do C*tholics worship C*-algebras?

[Anonymous No.10983822]

I mean, they Jesuits right. Space itself is discritized. Infinitesimals don't exist in nature

[Anonymous No.10983837]

>>10983507
>talking shit about Wildberger

[Anonymous No.10983839]

we were too cocky

[Anonymous No.10983871]

>>10983837
GO AWAY REALS

[Anonymous No.10984022]

>>10983837
GO AWAY REALS

[Anonymous No.10984167]

infinity doesn't exist. Smallest parts compose everything. without smallest parts, nothing could coalesce together to become larger objects.
an infinite amount of 0's is still 0, and nothing.
conversely, an infinite amount of even smallest parts would add up to an infinite whole, so there everything is coalesced into a single object.

so there is a finite amount of matter in the universe, and it's composed of finitely small smallest parts.

if we assume the smallest part is on the scale of planck units at [math]1.616255(18)×10^{-35}m[/math], this gives us 35 decimal places of [math]absolute[/math] accuracy required for using pi to define a 1 meter diameter circle. Any more accuracy is lost between planck units.

pi has an end and its end is 35 decimal places, so not even pi is infinite.

[Anonymous No.10984170]

>>10983471

[Anonymous No.10984187]

>>10983502
Math is better without the axiom of choice, but when a result can only be obtained by using it, then we should use the tools at hand.

[Anonymous No.10984188]

>>10984167
to clarify, if the diameter of the universe is [math]8.8×10^{26}m[/math] in 8.8 septillion meters, we only need to know pi accurate to 61 decimal places to accurately measure the circumfrence of the universe to planck unit accuracy. so 61 is actually as many decimal places of pi that can even exist.

[Anonymous No.10984199]

Read Spengler's connection of the infinitesimal calculus to the foundations of the modern culture. Just as geometry was the foundation of ancient culture, and algebra the foundation of medieval culture.

[Anonymous No.10984227]

>>10984188
what the heck bros i thought we needed 31 trillion digits of pi

[Anonymous No.10984238]

>>10984199
Didn't know Spengler touched on this.
A question arises, then. What's next?

[Anonymous No.10984244]

>>10984188
The sum of the first 61 digits of pi is 300...does this mean anything?

[Anonymous No.10984259]

>>10984244
it must mean [math]\pi = 3[/math]

[Anonymous No.10984284]

>>10984238
Unification and differentiation of the very spaces in which mathematics operates in.
https://www.glass-bead.org/article/the-theory-of-topos-theoretic-bridges-a-conceptual-introduction/?lang=enview

If the Greeks saw the world as the walls in the cave, and the medieval Christians saw the world as the what the cavern was as shown by the light of God (stars piercing through), and our faustian civilization saw the cavern as an infinite expanse. Then, whatever is next must see reality as a network of interconnected each operating with it's own set of rules, and the morphisms between them as a tunnel from one to the next.

If the information overload of the internet has shown us anything, its that globalistic ideological totality will never work. Universalism is dead, but that doesn't imply a complete semantic apocalypse.
https://youtu.be/gpeAdsNjM2w
Information can still be translated between representations while still persevering at least some of its structure.

[Anonymous No.10984314]

>>10984284
Wondering what the effect would be on our current understanding of physics...

[Anonymous No.10984318]

>>10984244
It's actually 301

[Anonymous No.10984367]

>>10984314
The basic idea would be that instead of laws being universal, instead each reference frame would understand reality as a translation of information from causally connected reference frames.
A reference frame is a representation of the structure of the information which has interacted with it. A translation of this representation is part of causality. I would assume that if aspects of structure are not preserved in this translation, this would likely contribute to entropy of a system.

[Anonymous No.10984560]

>>10984188
>physics
>cosmology
not math

[Anonymous No.10984623]

>>10983837
GO AWAY "REALS"

[Anonymous No.10984688]

>>10982005
infinitesimals have nothing to do with finitism/infinitism.

The real numbers and the standard approach to analysis do not use infinitesimals.

An infinitesimal number is a non-real number that is smaller than every real number but also not equal to 0.

This thread is full of brainlets.

[Anonymous No.10984711]

>>10984688
>Its isomorphic to 1/inf but I am going to pretend its not the same thing

[Anonymous No.10984774]

>>10984560
pi isn't math either, its the unit ratio defining the circumference of a 1 unit diameter circle at [math]1_{m}:\pi_{m}[/math], and that is equal to exactly [math]3.14159265358979323846264338327950288[/math].
Relative to the diameter of the universe, it's instead [math]1*10^{26}_{m}:3.1415926535897932384626433832795028841971693993751058209749445*10^{26}_{m}[/math]

using the 1m:πm ratio, a pi meter describes
3 meters
14 centimeters
1 millimeter
592 micrometers
653 nanometers
589 picometers
793 femtometers
238 attometers
462 zeptometers
and
643.038327950288 yoctometers; or 643 yoctometers and 236,592,285 planck lengths.

[Anonymous No.10984813]

>>10984774
a standard 32-bit float register in a computer can render 6 decimals accurately.
>3.141592
This allows for 1micrometer accuracy relative to a meter with only 6 decimals, which more or less lines up with how smoothly 3D rotations have been handled in video games over the past 20 years.

[Anonymous No.10984905]

>>10983462
kek

[Anonymous No.10984940]

>>10984188
Are you telling me my crypto rig isn't helping the human race?

[Anonymous No.10984962]

I don't understand how infinitesimals are able to describe anything in what appears to be a finite universe.

[Anonymous No.10985238]

>>10984711
1/inf is 0, retard.

[Anonymous No.10987049]

>>10985238
does that mean 0*inf is 1?

[Anonymous No.10987054]

>>10987049
checkmate.

[Anonymous No.10987102]

>>10984688
math is not metaphysics you brainlet.

[Anonymous No.10987125]

>>10987102
math is an abstraction of metaphysics.

[Anonymous No.10987180]

>>10987125
just because we can model infinity with limits or in non-standard analysis with infinitismals doesn't mean that is how reality actually works.

after all, doesn't quantum physics show distance is actually discrete?

[Anonymous No.10987363]

>>10983837
GO AWAY REALS

[Anonymous No.10987409]

>>10983491
Is everyone on sci a retard? The Cantor diagonals proof is NOT to prove that infinity exists, it is to prove that there exists a level of infinity greater than the countable infinity.

[Anonymous No.10987509]

>>10987409
I don't think that was his point.
Cantor's argument relies on this idea of 'containing infinity' with magical elipses.

>Suppose you have a real number 3.14 . . .

That's not a real. That's a rational number. It can be written as 314/100. If you were able to contain an infinitely random sequence of digits then it would not be infinite by definition.

>Well what about 1/3 = 0.333 . . .?

Wrong. No mater where you stop you will be off by a little bit. If mathematicians are okay with this then would they have issue with saying that there exists such a thing as the largest integer? Simply 999 . . .?

[Anonymous No.10987594]

>>10981315
I am somewhat sceptical of the claims of this book. the author fails to explain the problem the authorities had with infinitesimals. he just keeps repeating that ‘the idea threatened the established order’, without explaining why should this be so. my guess is that there were such arguments over the divisibility of the continuum as described, but that the political aspect is most likely made up, and the real reason, as gleamed from the quotes, was that the claims were a reformulation of atomism. infinitesimals are divisible, and the author either misunderstood the concerns the authorities stated clearly, or he just tried to emulate and hence avoid mentioning Greenberg’s ‘Swerves’, which brings a similar claim (of having turned the world towards modernity) about atomism.

[Anonymous No.10987596]

>>10987180
No it doesn't.

t. Physicist

[Anonymous No.10987682]

>>10983507
>very basic mathematical concepts
>infinity
yeah, nah. Fuck off with that noise and go bitch about the scary math "cranks" on reddit.
>>10983491
This. Cantor is the biggest faggot fraud in the history of mathematics.
>>10983558
>>10983576
These but unironically
>>10987409
>it is to prove that there exists a level of infinity greater than the countable infinity.
The shit that I took this morning proved that there exists a level of leprechauns Xx~greater~xX than the purple leprechauns. Wow math is ez with my turdagonalization argument. Now I'll throw in a bunch of Hebrew letters, whoooa fuckin revolutionary new maths
>>10987594
>he just keeps repeating that ‘the idea threatened the established order’,
Well thank goodness that progress moves ever forward, we just have to accept orders of infinity and cut our dicks off

[Anonymous No.10988079]

>>10987682
>Well thank goodness that progress moves ever forward, we just have to accept orders of infinity and cut our dicks off

It's great to hear that even mathematics must be classified as either pro or anti trannies.

[Anonymous No.10988382]

>>10987509
Well obviously infinity is an axiom, bit nothing about cantor's argument is about proving infinity, it assumes infinity, because math is axiomatic. We can't prove infinity that's why it's an axiom.

[Anonymous No.10988386]

>>10981315
>WHY DIDN'T WE LISTEN?
Because we never listen. What a stupid question.

[Anonymous No.10988393]

>>10983507
Nah, he believes undefinable real numbers can't exist. He's fine with algebraic irrationals and even definable transcendentals like e and pi.

[Anonymous No.10989678]

>>10988393
Are you basically saying he only believes in computable (There's some algorithm that could in theory calculate it with infinite time) real numbers?
This would include sqrt(2) btw.

[Anonymous No.10989837]

>>10989678
No, there are definable numbers which are not computable.