/sci/ - Science & Math

Optimization

re-normalization

>>15044200

First the object is a collection of pixels arranged in a certain way. That is: really tiny squares. If you were zoom in far enough to see the squares you would notice that the entire thing is just a larger staircase. Using the length/width of a pixel as the unit of measure, you would see that the total length of the staircase is in fact rational. In fact, a natural number.

>>15044268
Rotate the image 45 degrees in paint and measure the diagonal again, it'll be about 40% larger. If your definition of length is that non-invariant under rotation, it's a shit definition

>>15044260
>square root 2 doesn't exist because... it can't be measured ok?
schizo shit

>>15044268
>>15044272
>pixels
>microsoft paint
yeah this is more schizo shit as well

>>15044200
The idea of a square root of two as the length of a triangle is the result of an abuse and misinterpretation of the Pythagorean theorem. First and foremost, the theorem indicates, given a triangle, the areas of its sides follow the equation A + B = H where H is the hypotenuse. In the more modern length oriented perspective, given a triangle with sides of length x, y and hypotenuse of length z, the numbers x,y,z are related via the equation [math] x^2+ y^2 =z^2 [/math]. That is the premise is a right triangle with sides of a given length and the conclusion is that they most conform to the described equation. However, the idea that you can choose two numbers x and y to find a third number has not be logically proven. Rather the result that there is no rational number [math] z [/math] satisfying [math] x^2 + y^2 = z^2 [/math] implies the assumption that one can perform such an operation is false. There is no such thing as a square root of two. Stop pretending an ancient flaw in reasoning implies there is one.

>>15044281
You just wrote a hell of a lot of nothing. You still haven't answered my question. If the hypotenuse of a right triangle with side of lengths of 1 is not square root 2 than what is it?

>>15044286
There is no such thing as a right triangle with two sides of length 1. Plain and simple.

>>15044286
>However, the idea that you can choose two numbers x and y to find a third number has not be logically proven.
Doesn't the Pythagorean theorem work on the set of all reals though? Not all the reals are "countable/measurable" though.

>>15044272
>Rotate the image 45 degrees in paint and measure the diagonal again, it'll be about 40% larger
Yes. Due to the limits of the construction of computer screens and hardware, there will be scaling issues from rotation. However if I were to physically rotate my screen 45 degrees and perform the same measurement, I'd find the same result.

>>15044294
There is no such thing as a "real" number.
>Not all the reals are "countable/measurable" though.
There is no such thing as an "unmeasurable" real number either.

>>15044299
If the sides of that triangle were 1px each, your method says that the diagonal has the same length of each side, right?

>>15044292
You implicitly assumed the existence of it when you accepted the Pythagorean theorem as true >>15044281

>>15044200
Pythagorean theorem is wrong, because it implies root(2), which doesn't exist, since only rational numbers exist.

>>15044281
Statements dreamt up by the utterly deranged

>>15044320
but we must entertain them until we reach a logical conclusion

>>15044316
Ok, for argument sake lets take the Pythagorean theorem to be false. Than what is the length of the hypotenuse of a right triangle with side lengths of 1?

>>15044326
>Than what is the length of the hypotenuse of a right triangle with side lengths of 1?
There exists no such measurable length

>>15044328
no measurable length or no length at all?

>>15044329
a measurable length may or may not exist but for some non euclidean geometry but for this euclidean system it seems to not exist
triangles do not exist in a euclidean system. we got it wrong

>>15044334
What does exist?

>>15044338
we might as well call the hypotenuse thrembo and call it a day then

>>15044200
I don't know what anyone has against sqrt(2). Defining fields with square roots is completely different from defining the field of real numbers with equivalence classes of arbitrary Cauchy sequences. A "random" real number has an infinite amount of "information". sqrt(2) has a finite amount of "information". I think you could make an algebraic structure that works perfectly well for doing geometry without any elements having infinite information. Even pi doesn't have infinite information because you can represent it as an infinite sum that follows a finite formula. It's really only "a randomly chosen real number with nothing 'special'" that we may have issues with. If all of our formulas can only, in the end, be used with concretely instantiated things anyway, then there is no point in worrying about these "random" real numbers that we could never ever specify anyway. "Side A of this triangle has length 1.28113841241982404398528375982736371827647509835............." you never have that, all problems we work with are reducible to finite information.

If irrational numbers can't be observed, but can be proven by deduction, then why can't we also prove God by deduction?

>>15044341
I'm really asking. If by "in a euclidean system" you mean R x R -- or even Q x Q if you insist -- I can still write down equations and inequalities that describe a right triangle. You're telling me those don't exist, so now I'm asking you, what does exist in this system?

>>15044353
If you can prove God by deduction then He does exist.

>>15044353
Imagine a right-angled isosceles triangle in 2-dimensional euclidean space. Congratulations, you just observed the ratio between 1 and sqrt(2).

>>15044313
Except it's not a triangle. It's a staircase.

>>15044366
And the diagonal of this staircase has the same length as each of its sides right?

>>15044355
>I can still write down equations and inequalities that describe a right triangle
You are writing down equations that don't describe the geometry in that space because they aren't measurable. Maybe points and measurable lines exists but it seems you cannot make triangles (lines that follow the rule of Pythagoras)

>>15044368
>The points (0,0), (0,1), (1,0) exist
>The line segment connecting (0,0) to (0,1) exists
>The line segment connecting (0,0) to (1,0) exists
>The line segment connecting (0,1) to (1,0) exists
which of these statements do you disagree with?

>>15044314
It's a common and elementary mistake to believe:
>You implicitly assumed the existence of it when you accepted the Pythagorean theorem as true
However. That statement is 100% false. The Pythagoreon theorem is not an equivalence theorem nor an existence theorem.

Science according to /sci/:
>1 is not equal to 0.999...
>irrational numbers don't exist and Pythagoras was a fraud
>Vaccine for COVID-19 don't work
Should I listen to you guy?

>>15044369
your just not guaranteed to measure one of those lines using the rules of Pythagoras tho

>>15044374
Almost forgot:
>God has been proven, by midwits are too dumb to understand the demonstration

>>15044367
Nope. If the staircase is only one pixel by one pixel, you've approached the fundamental object. There is no way of describing length beyond this.

>>15044378
>but midwits are
Fixed.

>>15044377
But all of the objects I described exist? Or no?

>>15044380
Anon >>15044268 proposed finding length by zooming in until the pixels were individually discernible, and then counting pixels. If you do this, then the length of the diagonal is the length of each side, yes?

>>15044374
>>irrational numbers don't exist and Pythagoras was a fraud
This is a red herring. Pythagoras' result is correct. You and people who abuse it to use it as an existence theorem are frauds. Pythagoras would also agree that irrational numbers don't exist.

>>15044383
>walk from A to B
>rotate body by 90 degrees every milisecond

itt: finitards argue that because sqrt(2) does not exist, length does not exist
contrapositively, any mathematical system in which lengths exist must admit the existence of irrational numbers

>>15044384
>then the length of the diagonal is the length of each side, yes?
There is no diagonal of a pixel.

>>15044382
in the axiomatic way perhaps
but the Pythagoras rule breaks down quickly once you impose measuring constraints
there may exist a subset of measurable Pythagorean triangles that exists but they don't exist for all measurable lines in the geometry

>>15044388
There is no diagonal of any square according to you

>>15044389
Any such triangle will have angles which are an irrational multiple of 90 degrees. So irrational angles are okay but not irrational lengths?

>>15044391
In pixel land, there is no such thing as a diagonal.

>>15044397
What about in reality?

>>15044395
I haven't defined angle in my geometry though...
I just have points, measurable lines, and a Pythagorean rule that sometimes works to find triangles with measurable lengths

>>15044400
Not even in reality. Everything is a messy discrete chain of atoms and at that point, it starts to become quite meaningless to describe the idea of a "diagonal" because of that.

Wtf, this is actually a thing...

>>15044369
When you try to draw the line segments, and then look at them through a microscope, you'll see the messy reality that the shape only appears to be a line segment from a distance. In reality, it's a giant fairly disorderly mess where the concept of a "line segment" no longer makes any sense. False or inadequate perspectives lead to false results.

>>15044407
interesting idea but the real world is not discrete at a fundamental level

>>15044403
Reductionism is only slightly less retarded than finitism.

>>15044409
>things only exist if you can draw them

>>15044414
Reductionism is what science is based upon. Especially physics. You take a problem and attempt try to understand why it functions this way in terms of its fundamental components.

>>15044409
You were the kid who measured the diagrams in his geometry test instead of solving them mathematically, weren't you?

>>15044419
The structural relationships between the atomic components are just as important as the atomic components themselves. The worldview that nothing exists but messy chains of atoms is incapable of distinguishing graphite from diamonds

>>15044277
Why isshe so cute? I'm gonna need sauce

>>15044430
The distinction between molecules is quite discrete. On top of that, the interacts between atoms and atomic components tend to be quite bounded and poorly understood. At best the only thing people have in actually understanding is more along the lines of boundaries and certain behavioral oddities. For example, no one knows how an electron actually behaves, nor can they, all they can do is guess that it's going to be in a particular region if its at a certain energy level. Moreover, there are fairly discrete lower bounds as far as what the theory can even talk about on top of the computational limits.

>>15044421
I didn't do that. But it would be more accurate than what the teacher wanted you to do.

>>15044440
>For example, no one knows how an electron actually behaves, nor can they, all they can do is guess that it's going to be in a particular region if its at a certain energy level.
I'm extremely skeptical that this can be proven without recourse to real numbers.

>>15044395
>angles
Not the only want to classify triangles. Angles are also quite problematic as they rely on transcendental operations if you're given a triangle. In the same way, if you're given an angle, it's also problematic since the attempt to calculate a triangle relies on transcendental operations. When you have transcendental operations, you're pretty much just pretending you can perform a calculation when you can't.

>>15044277
yo who is that

>>15044456
things that do not exist
>line segments
>lengths
>angles
things that do exist
>

>>15044452
There is no real number found in the theory either. Everything there is realistically rational numbers with something like 10 or 12 decimal places paired with an error term. Every single useful calculation is finite and rational. At best you have extendable algorithms that allow for more precise computations. Then there's the point where you can't do any measurements and its stops.

>>15044467
when you say
>the theory
you are referring to your Wildbergerian theory that only rational lengths can be measured, yes? If you're referring to the theory of quantum mechanics in general that let you conclude
>all they can do is guess that it's going to be in a particular region if its at a certain energy level
then real numbers are all over that theory -- complex numbers, too

>>15044461
>>line segments
A line segment does exist. It's simply the equation y = mx + b.
>>lengths
Rational lengths do exist. So called "irrational lengths" do not. However, areas or quadrants do exist.
>>angles
These can be said to exist in an appropriate fashion. But they certain don't exist in the explicitly circular fashion.

>>15044474
in what fashion do angles exist?

>>15044471
>tonly rational lengths can be measured, yes?
Actually that would be correct. Only rational length can be measured and only rational lengths are measure.
>then real numbers are all over that theory --
The only "real numbers" you see are at best the toy examples of finitely represented algorithms in while realistic calculations are actual done with only finite rational or polynomial functions. Physicists tend to treat the whole thing as a formal game to get derive some sort of prediction to run an experiment on. That is they don't care about applied math. They use everything the same way Newton did, just a little formal, very physical reasoning to try to get at a problem and don't pretend they have anything like the "real numbers" or objects mathematicians like to pretend they do. They just have the few convenient approximate tools they can use and there's nothing else to it. There aren't any "arbitrary sequences," "unmeasurable numbers," or anything other sorts of non-sense common among analysts. Plus they are constrained by physical reality and since they have to make measurements.
>complex numbers, too
The rational complex numbers are actually well defined in terms of matrices. [math] \hat{1} = \begin{bmatrix} 1& 0 \\ 0 &1 \end{bmatrix}, i = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix} [/math]. You certainly do not need to make anything up about "real numbers" or anything else along those lines to do complex numbers either.

>>15044490
>They use everything the same way Newton did, just a little formal, very physical reasoning to try to get at a problem and don't pretend they have anything like the "real numbers" or objects mathematicians like to pretend they do.
You're telling me that the theoretical physicists who study quantum mechanics do not pretend to use real numbers in their calculations, but this is false.

>>15044494
>You're telling me that the theoretical physicists who study quantum mechanics do not pretend to use real numbers in their calculations, but this is false.
They take derivatives just following the rules, then maybe plug something like e^x or cos(x) in their calculators and that's the most they do. Anything like that mostly just lipservice because it's just they learned to use from mathematicians in prereqs, everybody did it, and everything they end up doing is plugging numbers into a computer and then round to 12 decimal places (hence just rational numbers). All of the typical examples are to the point where they just involve rational arithmetic. They could care less about what a real number or anything else along those lines and they really don't care about being precise understanding that everything they do is going to be off somehow just because physical reality has its quirks and measuring things also has its quirks. Most of what they use was established long before mathematicians started doing anything related to analysis, anybody tried defining what a real number was, or even started to play the silly game Cantor invented.

For illustration, if mathematics collapsed due to the exposure of the paradoxes of set theory instead of mathematicians trying to play word games, and mathematicians moved on to look for more reasonable and less contrived modes, physicists would still use calculus because it was very successful for physical problems from when Newton and Lagrange did it. Mathematicians would just need to find much better definitions. When you read their papers even with the more recent analysis stuff, it's mostly them doing very algebraic things with operators pretty much in the fashion you'd do linear algebra. Plus there's a move more towards the algebraic geometry side of things and quite a bit of combinatorics as quantum computing as such became an issue.

>>15044538
You appear to be confusing theoretical physicists with engineers.

>>15044547
>You appear to be confusing theoretical physicists with engineers.
You appear to still imagine physicists are as retarded as the average mathematician. In general, they have a lot more in common with engineers than mathematicians. The vast majority of physicists don't care about real numbers and the vast majority of physicist only play the game as the tools and models have been convenient and successful.

"but your calculator doesn't /actually/ use real numbers, only rational numbers"
Has got to be the dumbest argument I've ever heard for anything ever.
Yeah, they use approximations. What are they approximating, hmm?

how do you explain unity, its just a sequence or state

>>15044550
>as the tools and models have been convenient and successful
Purely by coincidence of course

>>15044552
They are approximating the rational numbers created by God. We can't perfectly find them because the universe is made of pixels, but we can't see them.

>>15044567
meds

>>15044556
The success of the tools have nothing to do with modern analysis of course. It has everything to do with the fact that the tools were invented to aid physical intuition.

>>15044567
inside every finitist there are two schizos, one who insists that no concept actually exists and another who insists that the universe is made of pixels

>>15044573
And it's purely a coincidence that the tools of modern analysis give numerically a correct answer every time and a numerically incorrect answer none of the time

>>15044552
>but your calculator doesn't /actually/ use real numbers, only rational numbers
This is a fact
>Yeah, they use approximations. What are they approximating, hmm?
They're approximating physical quantities they use the models to predict. Then when they do experiments, they get actually measurements of it and it turns out close, but the math was wrong again. It was only useful for the physicists to try to get a grasp on how something works. But then, the modern mathematicians and real number apologist wants to pretend something else.

>>15044571
how spherical is a bubble anon?

>>15044590
Sphere? What's a sphere?

>>15044577
>And it's purely a coincidence that the tools of [classical calculus] give numerically a correct answer every time
I had to fix this for you. Most of the numerical tools physicists use are from prior to Cantor's birth. But it, actually it doesn't. The numerically correct answers are typically off quite a bit, and when it comes to a variety of phenomenon, there are usually a number of unpredicted features and only certain aspects of the prediction are actually seen. The more complex the phenomenon, the even more error prone the models become.

>>15044602
>The numerically correct answers are typically off quite a bit
Got an example?

>>15044604
Yeah. Search for a random paper where someone presents a model and then experiments are done related to it. Especially the ones in fluid dynamics.

how do finitards feel about negative numbers? You can't hold -5 apples in your hand

>>15044593
>It's important to realize the nature of his rebellion: not to challenge the theoretical numerical ratio between the circumference and diameter of the ideal sphere, but rather to challenge that sphere to materialize. Irrational numbers don't belong in tangible experiences. It is a question of sorting out the demonstrable from the impossible and then developing models based on the former. Essentially, Bucky is choosing not to play with 'IT, posing the question "why shouldn't mathematics deal with experience"?

"Nature Isn't Using Pi"
Nature can have no perfect spheres because she has no continuous surfaces. The mathematician's sphere calls for all points on its surface to be exactly equidistant from the center. This "sphere," explains Fuller, has no holes. It is an absolutely impermeable con-tainer sealing off a section of Universe, a perpetual energy-conserv-ing machine defying all laws of nature. The illusion of a physical continuum in any spherical system is due to the limitations of the human sense

>>15044608
>thread

>>15044612
from "a fuller explanation pg 16"

>>15044612
Hmm, what is being approximated in that gif? I wonder what it could be. I guess we can never know what the circumference of a perfect circle is because some people are confused by infinity :( So sad.

>>15044607
Oh that's different from what I'm asking. I'm asking if anybody has ever used modern analytic techniques to obtain a rational number which was incorrect. Like using cauchy sequences to obtain 2+2 = 3 (though it would certainly be more subtle.)

>>15044608
Negative numbers are just a consequence of defining subtraction in terms of addition. A negative number is just an extension of natural numbers and is not outside of the domain of finitism.

>>15044632
Negative numbers can never exist in nature. If you're allowed to just willy-nilly take extensions of natural numbers, the reals are also an extension of natural numbers

>>15044636
>Negative numbers can never exist in nature
What is a negative and positive charge? What are references to direction? Left v. Right. Why not create a numerical representation of this? Surplus and deficit? Below or above a point. Introducing negative numbers provides a numerical way to describe this.
>If you're allowed to just willy-nilly take extensions of natural numbers, the reals are also an extension of natural numbers
Nope. You are not allowed to pretend something like real numbers exist. There is no such thing as real number in any tangible or logical sense.

>>15044622
The point is clarity in mathematics when we say 1+1 = 2 we are not comparing apples to oranges. In code monkey terms they are all the same type.

When you dawn your mathematical garb fascinates, dazzles and blinds those to the underlying errors by [math]1 + \infty[/math] one commits a greivous error in communication! one insinuates that infinity has the same type as the unity, which is not the case. 1 can be represented in finite memory, infinity will sooner consume all the heat in the universe that show you her final digit, to cope we stick a function that resolves at iteration, but these are not the same

I offer this rosetta stone to aid in bridging these two worlds,

>>15044643
Negative numbers are a simplified mathematical tool which can conveniently model charge and direction, but they are only a formal game, they do not actually exist. There is no physical intuition for them. The only objects that exist in nature are positive rational numbers -- you can't just pretend negative numbers exist because they provide a convenient numerical way to describe things

>>15044623
>I'm asking if anybody has ever used modern analytic techniques to obtain a rational number which was incorrect
The vast majority of numerical techniques predate modern analysis and usually even predate Cauchy.
>Like using cauchy sequences to obtain 2+2 = 3
With series, you can always get something like 1/2 = infinity or something like that. But that's usually handwaved away in the books.

>Negative numbers are a simplified mathematical tool which can conveniently model charge and direction
No. They are derived from such a thing.
>There is no physical intuition for them
This statement contradicts
>Negative numbers are a simplified mathematical tool which can conveniently model charge and direction
As this statement does state that negative numbers give physical intuition.

>>15044646
There is no such thing as [math] \sqrt{-1} [/math]. There is a matrix [math] i = \begin{pmatrix} 0 & -1 \\ 1 & 0 [/math] however.

>>15044674
They are derived from the physical intuitions behind change and direction, just as real numbers are derived from the physical intuition of changing continuously from one quantity to another. But that doesn't mean real numbers exist, and it doesn't mean negative numbers exist. The only numbers that actually exist are positive integers (rational numbers don't exist either -- you can't have 1.5 atoms)

>>15044678
very, very based

>>15044692
kek wildbergerbros itt

>>15044692
>>15044674
seems my theory is not yet complete, back to the drawing board

how does one characterize a matrix in terms of precision and length, by its half trace? hubris it seams

>>15044678
There is no such thing as salt. There is sodium chloride however.

>>15044703
sodium chloride is just a subset of all salts however

>>15044704
yes, sodium chloride is a subset of all sodium chlorides

>>15044709
potassium chloride is a salt

>>15044713
No, potassium chloride is potassium chloride. "Salt" is an abstraction, a fiction which does not actually exist in nature

>>15044719
proof?

>>15044686
>just as real numbers are derived from the physical intuition of changing continuously from one quantity to another
How exactly is a number going to "continuously change" to another number. There are only a few alleged sources of "real" numbers. First, from assuming there are solutions to equations which it isn't really clear that there's a solution, like [math] x^2 =2 [/math] or [math]x^7 = 19 [/math]. Then there are some hypothesized ratios like [math] \pi [/math] or [math] \varphi [/math]. Finally there are a few extendable polynomials like [math] e^x [/math], [math] \cos(x) [/math], etc. that are fairly common and used to "derive" numbers. However, in practice non one has calculated any of these numbers and or even proven they really exist.

What did come from physical intuition was more of the idea of a differential (Liebnitz) and a hyperior (Newton), which were numbers smaller than any number but still non-zero. So you'd see the typical formula for a differential [math] dx [/math] like [math] dx^2=0 [/math] or in Newton's case, he wrote his derivative as [math] f'(x) = \frac{f(x+o) - f(x)}{x-o} [/math] where o was a hyperion. The other thing was the idea of a limit in terms of Weierstrauss, but this, though physical, didn't lead to the concept of a "real" number as in these "irrational numbers" or these "uncalculable," "unmeasurable" "numbers" that are claimed to somehow exist in real analysis nor does it necessitate such a thing. Besides the term "Real" number was more as a contrast to the term "imaginary number."

>>15044686
> it doesn't mean negative numbers exist. The only numbers that actually exist are positive integers (rational numbers don't exist either -- you can't have 1.5 atoms)
Negative number and rational numbers are human description of oriented activities while rational numbers are directly related to the process of dividing up collection of objects or objects. Negative numbers and rational numbers are directly tied to human actions and therefore do exist. Whereas real numbers are purely a mathematical hypothesis.

>>15044700
Try using the following matrices in your number system

[math] \hat{1} = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0& 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix} [/math]
[math] \hat{i} = \begin{pmatrix} 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \\ 1& 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \end{pmatrix} [/math]
[math] \hat{j} = \begin{pmatrix} 0 & -1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0& 0 & 0 & -1 \\ 0 & 0 & 1 & 0\end{pmatrix} [/math]
[math] \hat{k} = \begin{pmatrix} 0 & 0 & 0 & -1 \\ 0 & 0 & 1 & 0 \\ 0& 1 & 0 & 0 \\ -1 & 0 & 0 & 0 \end{pmatrix} [/math]

See what you get from there. Derive the multiplication rules for the matrices. Then you can work with formula [math] q = t\hat{1} + x\hat{i} + y\hat{j} + z\hat{k} [/math] where [math] t, x, y, z [/math] are rational numbers.

>>15044724
Anon is wrong, because he's pretending sodium chloride exists.
As the enlightened are aware, the square root of two is NOT the length of the diagonal of a unit square. In the first place, there is no such thing as a unit square, because any square in nature will be uneven on a small enough scale. Secondly, the length of a diagonal can not be measured precisely, but only approximated. Approximations can be made better, but at the cost of increased effort and computation
The exact same situation holds with fictions like "sodium chloride." In reality, any sample of sodium chloride will have additional impurities. Nobody has ever obtained a block of material consisting exclusively of sodium chloride molecules. Secondly, we are unable to determine with 100% whether a compound is made exclusively of sodium chloride. We can only obtain results to a nonzero degree of error. This error can be made small, but at the expense of increased effort and computation.
So we have this material which is impossible to obtain and impossible to determine if we've obtained it. This situation is patently ludicrous. "Sodium chloride" is a fiction and if there are any holes in my argument, I would love to hear them.

>>15044738
Real numbers are directly tied to the human action of getting up and moving in any direction, although neckbearded armchair mathematician finitists may not be familiar with this action

>>15044764
Incorrect. All motions are discrete if observed in sufficiently small time periods.

>>15044733
I see no reason why a hyperion is less fictitious than a real number

>>15044769
Incorrect. All motions are continuous and infinitely differentiable if observed in sufficiently small time periods.

>>15044770
It is fictitious and the people in calculus during the period got called out for it by a prominent Bishop for their bullshit. Because of this, the direction of math and physics changed for a time.

>>15044292
>There is no way of quantifying this triangle even if it existed
FTFY

>>15044281
>The idea of a square root of two as the length of a triangle is the result of an abuse and misinterpretation of the Pythagorean theorem
No it's the result of using the exact same fucking theorem and not being able to quantify the answer.

>>15044323
>entertain lunacy

>>15044622
>some people are confused by infinity :(
We have an omniscient being here everyone. Ask this anon the big questions. Like how to quantify the side of a simple triangle with more than half the blanks already filled out for you.

>>15044421
You were the kid that never understood why "Geometry" and "Math" are two different topics. Protip: This fucking triangle is one of the main reason they're not (because math can't describe it where geometry can).

>>15044773
>All motions are continuous
Nope. Discrete at the smallest scales.
>infinitely
No such thing as infinite
>differentiable
have you ever taken an infinite number of derivatives before? That's right, you can't. So the term "infinitely x" is meaningless.

>>15044733
>How exactly is a number going to "continuously change" to another number
Like this, *moves hand from one position to another*

>>15044763
>In reality, any sample of sodium chloride will have additional impurities.
Okay but there exists a neighborhood of purely sodium chloride atoms such that it is theoretically possible to construct a pure crystal if one could practically remove the impurities. So it does exist its just hard to purify.

>>15044782
>Nope. Discrete at the smallest scales.
No such thing as smallest scale(s)
>No such thing as infinite
Set of all numbers
>have you ever taken an infinite number of derivatives before?
Yes, of e^x

>>15044788
I see no reason this should be true.

>>15044798
its true theoretically and experimentally
its just really hard to remove all impurities but there exists parts of the crystal that are pure

>>15044803
What experiment are you referring to?

>>15044780
>>There is no way of quantifying this triangle even if it existed
>>The idea of a square root of two as the length of a triangle is the result of an abuse and misinterpretation of the Pythagorean theorem
Holy shit you're retarded. You're posting without even understanding the theorem. The NECESSARY condition of the Pythagorean theorem does not give you license to pretend that you can plug any two numbers willy-nilly into the necessary condition and third length of a triangle since if a rational number cannot be found satisfying the equation, i.e. 1^2 + 1^2= 2 = h^2, it absolutely does not exist. If you're relying then on geometric constructions to assert this, the reality is that you're off 0.000001 cm from the ends of each line segment and you actually drew a rational length and don't realize it.

>>15044791
>No such thing as smallest scale(s)
The smallest scale is discrete so therefore motion is discrete at the smallest scale.
>Set of all numbers
There is no such thing as a "set of all numbers"
>Yes, of e^x
Except you haven't. How do I know? Because a human being can only do a finite number of things.

>>15044807
>you're off 0.000001 cm from the ends of each line segment and you actually drew a rational length and don't realize it
if he was 0.000001 cm off and obtained an irrational number, the actual length would be irrational as well

>>15044814
>The smallest scale is discrete so therefore motion is discrete at the smallest scale.
You're asserting this like it's a fact but it isn't.
>There is no such thing as a "set of all numbers"
Prove it
>Except you haven't. How do I know? Because a human being can only do a finite number of things.
Don't presume to speak for all human beings, you're really just confirming that you can only do a finite number of things. I took an infinite number of derivatives of e^x and got e^x, ezpz.

>>15044815
>obtained an irrational number
He hasn't obtained an "irrational number." NO ONE has ever obtained or seen an irrational number and no one ever will. The only thing you will see is a charade or sleight of hand on the part of mathematicians as they pretend there is one because they want it to exist.

>>15044819
I've never seen any number before. what do they look like?

>>15044818
>You're asserting this like it's a fact but it isn't.
The opposite it false, therefore this is true.
>Prove it
Sure. Mail me a box containing all possible numbers written down in their complete decimal form or in a rational form. Oh what's that? You can't even write down alleged sufficiently large integers? You're the one who stuck their foot in their mouth.
>Don't presume to speak for all human beings, you're really just confirming that you can only do a finite number of things. I took an infinite number of derivatives of e^x and got e^x, ezpz.
Except in your case, you have done anything of the sort. You've only taken one derivative and then fucked off pretending that concluding from it being possible to write down a formula for some nth derivative. You still haven't done an infinite number of things and you never will. Fucking retard.

>>15044825
If you weren't blind, you would have seen one before. You can feel one in your braille.

>>15044827
>Sure. Mail me a box containing all possible numbers written down in their complete decimal form or in a rational form. Oh what's that? You can't even write down alleged sufficiently large integers? You're the one who stuck their foot in their mouth.
Nah I can do that, what's your address?
>Except in your case, you have done anything of the sort. You've only taken one derivative and then fucked off pretending that concluding from it being possible to write down a formula for some nth derivative. You still haven't done an infinite number of things and you never will. Fucking retard.
limit as n goes to infinity of nth derivative of f(x), ezpz

>>15044831
No, I can feel a numeral. If we're allowed to just write down symbols and say "look, a number", then check it out, [math]\sqrt{2}[/math]

>>15044836
I guess being blind really does make you retarded. There is no such thing as a number called the square root of 2.

>15044835
>no self-awareness
>no social senses
Retard

>>15044841
I'm not the one opining about philosophy of math who can't distinguish between numbers and numerals.

>>15044807
>If you're relying then on geometric constructions to assert this, the reality is that you're off 0.000001 cm from the ends of each line segment and you actually drew a rational length and don't realize it.

No the fact is the "magnitude", the device used to construct DOES NOT CHANGE WHATSOEVER. It is "itself". Math? Math uses silly symbols "undefined" and decimals that expand infinitely as a coping mechanism for being unable to actually quantify it. It the most "accurate description" you're going to get, but even then you're right. It's constructing an idealism that "doesn't exist".

>>15044836
Yeah lets just write down symbols and forget what they mean. In fact lets just shit all over math: the language of quantification and add all sorts of expressions and meaningless woo to complicate what "number" means and refers to.Bbecause we're materialists anyway right? Yeah it must not exist unless it can be described using standardized units and probing devices.

>>15044844
Not an argument. Here's what a proper argument looks like

things that don't make sense:
>real numbers
>sets
things that do make sense:
>reality is made of pixels
>only certain lengths are measurable and you can't measure any length
>calculus should be done with numbers that are smaller than every number

>>15044780
>you have to be omniscient to not be absolutely baffled by the concept of infinity
lmao. This is called telling on yourself, dimwit.

>"Geometry" and "Math" are two different topics
This retard is from bizarro-earth where geometry and arithmetic aren't the two oldest branches of mathematics.

>>15044855
>lmao. This is called telling on yourself, dimwit.
Go peddle you rehashed buddhism elsewhere Ramir.

>two oldest branches of mathematics.
>geometry
>math
So when you're done quantifying your incommesurable magnitude (you never will be), here's your next homework assignment. Then maybe on march 14th while you're still pounding away at the calculator I'll come drop by with one of my coffee mug stains and we can quantify that shape.

>>15044874
https://en.wikipedia.org/wiki/Geometry
Are you genuinely from a different universe?

>>15044874
You've lost the plot and got stuck on socially constructed human definitions as axioms of reality.

Congrats. You schizo'd yourself.

>>15044887
>>15044905
>N-no you're mad and arguing over definitions!

It's "undefined". Deal with it

>>15044200
sqrt(2) is finite THOUGH
>inb4 "buh muh it goes on forever"
infinite precision is just a null assumption about the number line. it doesn't require an infinity, it just appears that way because of our choice of number system. sqrt(2) is a finitely precise number of sqrt(2)s

interesting none of you are interested in the lone exception to the Pythagorean Theorem; the one where the route to the hypotenuse is cubed and not squared.. Pythagoras himself never intended for his theorem to be an axiom of geometry. but rather it was a challenge; for someone, anyone, to stand up and say, no, this theorem is not correct, for it is wanting of an exception.. he waited all his life for this.. but the prestige of his achievement had garnered only blind followers; students who could only repeat what he had said, never taking it upon themselves to challenge him, and go further.. Pythagoras, to his own detriment, had become the source for which all would be cited.. for this reason he would refuse further meetings, and retired from teaching.. Timaeus would come the closest, with his most beautiful of all the triangles.. perhaps one day soon, a new Pythagorean will emerge, and change forever the axiom, that Pythagoras himself never intended.

>>15044941
meds.

>>15044941
a^2 + b^2 = c^3 is an elliptic curve in c and a or b

>>15044944

>>15044949
of the numbers below ten, which one is a cube? when is the hypotenuse equal to that number?

Do not fail me again

>>15044941
>>15044951
>>15044962
The set of solutions to x^3 + y^3 = r^3 isn't round. There is no single point from which all such solutions are equidistant. Therefore you can't use it to calculate the hypotenuse, because if you did, its length would vary if you rotated the triangle

>>15044969
when can a hypotenuse be divided into three equal parts? what must occur with the other two sides?

>>15044974
>when can a hypotenuse be divided into three equal parts?
That's not what exponentiation is.

>>15044962
2^2+2^2=2^3

>>15044979
That's not a right triangle.

>>15044976
what about the two equal sides? what happens if they are both equal to two?

this is your last chance to make the team

>>15044982
>what happens if they are both equal to two?
Then the length of the hypotenuse is sqrt(8).
You incorrectly believe this to be wrong because you've found some special exception. But your exception is an equilateral triangle, not a right triangle, so it's irrelevant. It's not even correct to call the third side the hypotenuse in this case.
Btw, your proposed alternative means for calculating the length of the third side doesn't apply to other side lengths for equilateral triangles. Consider: in an equilateral triangle with side lengths 3 and 3, the third side's length should be 3, but 3^2 + 3^2 = 18, and the cube root of 18 is not 3.

>>15044987
test over. you were not selected.

>>15044993
Wasn't a test, it was just half an hour of people proving you wrong

>>15044980
The square corner means 90 degrees

>>15044997
I know, but the side lengths given contradict the square corner.
If you insist that's a right triangle then it's not in euclidean geometry, that triangle is on the surface of a sphere. In that case, the formula anon proposes for the hypotenuse is still incorrect, because the cube root of 18 isn't 3

>>15044987
>>15044995
>>15045002
Nigger

>>15045006
>t. buttmad retard

ITT: people who dont understand what finitism is

>>15045019
OP didn't say finitism, he said finitards.

real numbers don't exist, only p-adics

>>15045002
That right triangle doesn't have side lengths 3, it has side lengths 2, proving anon's formula correct in almost all cases

>>15045026
Padics are just as fake as real numbers.

>>15045028
It's not correct for side length 1 either. 1^2 + 1^2 = 2, cube root of 2 is not 1. It's also not correct for side length 4: 4^2 + 4^2 = 32, cube root of 32 is not 4.

>>15045031
Some tribes in the amazon count exclusively in 2-adics

>>15045033
My triangle doesn't have side lengths 1 or 4, it has side lengths 2

>>15045038
A formula has to be general to be useful or worth discussing

>>15045040
This just proves that there is no right triangle with side lengths 1, 1, and 1, but there is one with side lengths 2, 2 and 2

>>15045043
Wrong, it's self-evident that for any side length L there's an equilateral right triangle with that side length inscribed on the sphere with radius r = 2L/pi.

>>15045040
It is general

>>15045053
That picture is inherently incorrect, it's impossible for a non-equilateral isosceles right triangle with the hypotenuse as one of the two equal sides to exist in any elliptical geometry.

>>15044929
READ MF;
>got stuck on socially constructed human definitions as axioms of reality

Fake Mathematician, Dialectic thats all linguistic, CONFUSINF HUMAN DEFINTIONS FOR REALITY.

If I simply have to repost my first post you clearly didnt understand it, as a legit mathematician would.

>Its "undefined"
Liguistics. You are not a mathematician.

CHARLATAN.

>>15045058
And yet there it is

>>15045066
No, there it isn't.
If you're saying the triangle pictured actually has side lengths 5,5,10 in the configuration posited -- no, it doesn't. If you measure the sides, they won't measure to that.
If you're saying the triangle pictured is an actual *representation* of a non-equilateral isosceles right triangle with the hypotenuse as one of the equal sides: sure it is, but you can *represent* anything you want, doesn't make it true. The text "0 = 1" is a representation of the claim that 0 and 1 are the same number. There it is, it's very real text, right there for all to see. Doesn't make it true. Better yet, for something that's undeniably false by its very definition: the text "bottom" represents the bottom truth value, ~T, also called "false," "not true," "contradiction," etc. In layman's terms, the text "bottom" represents the claim that some hypothetical arbitrary statement which is objectively false is in fact true instead. It represents a claim that is definitely untrue and cannot be true no matter what. And yet, I can type "bottom" all I want, and the universe doesn't collapse in on itself (yet).

>>15045073
>If you measure the sides, they won't measure to that.
That's because it's an imperfect rendering on a computer screen. You can never attain the numbers exactly by measurement, you can only approximate them

>>15045078
My post you just replied to is an adequate response to the reply you wrote to it, so I'm just gonna copy paste the part that's still relevant and unaddressed.
>you can *represent* anything you want, doesn't make it true. The text "0 = 1" is a representation of the claim that 0 and 1 are the same number. There it is, it's very real text, right there for all to see. Doesn't make it true. Better yet, for something that's undeniably false by its very definition: the text "bottom" represents the bottom truth value, ~T, also called "false," "not true," "contradiction," etc. In layman's terms, the text "bottom" represents the claim that some hypothetical arbitrary statement which is objectively false is in fact true instead. It represents a claim that is definitely untrue and cannot be true no matter what. And yet, I can type "bottom" all I want, and the universe doesn't collapse in on itself (yet).

>>15045081
I agree with all of that

>>15045083
Point is you can't just make up impossible triangles and say they prove anon's retarded trick question is actually general. General to what? If you have to fold and twist and crumple space to pretend a formula is useful, maybe it's not. Better stated, all you've managed to prove is the tautological claim that the formula a^2 + b^2 = c^3 applies generally to all tuples a,b,c s.t. a^2 + b^2 = c^3.

>>15045095
You still haven't debunked >>15045053, all you did is claim without evidence that if you measured it, the numbers would be different

>>15044200
GAHAHAHA

behold! hold the infinitist slithers back into the cave from whence it came, observe the changes to the real number wikipedia from this pic related to now

https://en.wikipedia.org/wiki/Real_number

no long does it claim a real number can represent a distance along a line

we are winning

Godspeed

>>15045150
no longer can such erroneous notions be found

>>15044386
You don't do this?

What even is 1?

>>15045065
>READ MF;
Ironic because that's what you're saying part of the problem is when you shit on linguistics.

>got stuck on socially constructed human definitions as axioms of reality
...you mean math? No see that's one of the reasons why I keep saying math can't solve it.

>CONFUSINF HUMAN DEFINTIONS FOR REALITY.
"Math" is a confusing human way of defining things using quantity. It is the confusion, it is the psychosis. So don't be surprised when it confuses stupid humans.

>Its "undefined"
So stop defining it. Retard.

>Liguistics. You are not a mathematician.
No it's "undefined" according to math retard. You literally cannot quantify it. It's the equivalent of taking another word from another language that has no literal translation into yours and making up a definition for it. Your throwing shit at the wall and hoping it sticks, but the problem is you can't hit the target.

>>15045521
"1" is "the principle of number". It too is not even a number, but explaining that to people like this would ensure you pull your hair out by 30 because they like to argue over what "number" means instead of relying on the source like they should be doing.

>>15044410
>interesting idea but the real world is not discrete at a fundamental level
Evidence for this? I know that some of the mathematical models used to make predictions to non-arbitrary precision are continuous, but this says nothing of ontic physical continuousness. How would you even ever prove ontic continuousness of physicality anyways? No matter how for you zoomed in, there would always be finer resolution. It's not as if you would get to an infinite resolution and be able to declare that you have demonstated it. It's a purely metaphysical claim and not empirically provable or demonstrable.

>>15045978
>No matter how for you zoomed in, there would always be finer resolution.
if this is true then the world would not be discrete

>>15045988
Right. I don't believe physical world is continuous. I was making an argument that the physical world is discrete in every way, energetically, materially, temporally, spacially. I was making the argument that physical continuousness does not exist. mathematical continuousness is grounded in minds, not in physicality. I was making an argument that continuousness exists in models of the physical world which have utility in some instances, but the models themselves being continuous do not say anything about the existence of actual physical infinities. They work to make predictions to a limited number of decimal places because the planck scale is so small that some physical things are EFFECTIVELY continuous for all practical purposes.

>>15045988
By the way, I know some will try to deny planck units, but I find the arguments, such as picrel peer reviewd by the American Journal of Physics paper compelling. Even if one goes into denial about planck units or any other minimum resolution, this still doesn't change the fact that physical continuities are not empirically verifiable, for the reasons mentioned here
>>15045978
Six easy roads to the Planck scale
https://arxiv.org/pdf/1001.1205.pdf

>>15045988
whoops, forgot picrel here
>>15046066

>>15046066
the existence of planck units =/= discreteness. Just because it is impossible to measure at that level of precision does not logically imply that all distances are integer multiples of Planck length

>>15045988
>if this is true then the world would not be discrete
Yes. But it certainly still follows order.

If math leads to this flurry of autism, maybe nothing mathematicians talk about should be taken seriously anymore and math departments across the world should be defunded.

>>15044200
Sqrt(2)=1.414

>>15046072
In the case of space, it's a resolution for spacetime at which point if you don't postulate discreteness absurdities in predictions arise, just as in the case of the ultraviolet catastrophe which led planck to invent quantum physics. picrel. Everything physical is discrete. By the way, another reason infinite resolution can never be verified by the players immersed in the simulation
>At the scale of Planck length, it is meaningless to try to distinguish two points (positions) apart based on the calculation according to the uncertainty principle. Moreover, on the empirical level, if we attempt to investigate any distance smaller than one Planck length with physical experiments, i.e., sending a photon to the space to be studied, a black hole would form due to the high energy/mass (of the aforementioned photon) in comparison to the limitedness of the space we try to confine it in. Thus, no information can ever be revealed if we attempt to investigate any shorter distance than a Planck length

>>15044200
Imagine a drawing of a circle and you label it's diameter to be bigger than the circumference, kind of the same thing

>>15044326
What is the circumference of a square circle?

>>15046165
again, what you just said does not imply the discreteness of space -- in fact it negates it by considering the theoretical possibility of sending a photon to the space to be studied

>>15045932
>So stop defining it. Retard.
Thats the purpose of Mathematics. You have utterly lost the plot in Linguistics thats melded via Logic/Philosophy into Math.

Youre a high functioning Autist. You do not have Aspergers.

>>15044200
Simple.
that shape does not exist. It's impossible.
Only approximations of that shape can exist.

>>15047321
>Thats the purpose of Mathematics
You have to take a diarrhea dump on math to quantify an irrational. It's like you took the "Absence of evidence" meme argument and completely forgot about the part where it mentions known unknowns. This is a known unknown, Math knows it cannot know it. Otherwise math becomes unknown because you have to break the axioms for one special case.

>You have utterly lost the plot in Linguistics thats melded via Logic/Philosophy into Math.
It's not going to be defined. Dish out whatever coping mechanism your peabrain can conjure.

>Youre a high functioning Autist. You do not have Aspergers.
You could make tea from how hard you're clenching straw. It's not difficulty with a word problem. It's "undefined".

>>15044403
Lol literally incorrect. Spacetime can't be discrete

Some numbers cannot be in one place.

What's so bad about having numbers that can't be written as ratios of other numbers?

>>15044260
the idea of someone using geogebra to 'prove' anything in math is hilarious to me