mathematics absolutely btfo will they EVER recover?

>>8586124
The definition of C is as the algebraic closure of R, so this is impossible.

>>8586124
Isn't he just a nut-case, why does /sci/ care so much?

>>8586129
its only impossible if you dont realize there is no R to begin with

>>8586129
retard

What is it with him /sci/? Why does he hate infinities so much? What have they done to him?

the guy's an obvious crackpot

>>8586129
His issue on the board doesn't really have to do with the structure of C in particular; that equation is odd, obviously it has a root even just in R.

The problem is that it has a solution that is not expressible through (elementary) radicals, which makes Wildberger cry butt tears because there's no explicit form for the solution without using a limit

>>8586153
His hatred for infinities is infinite, so he is wrong.

>>8586153
>Mr. Wildberger, I very much liked the topic of your dissertation but I find the proof of your final result a bit lacking

H-how could it be?

>I realized that you implicitly assumed that this group you define here is finite when actually given some initial conditions it could turn out to be infinite, so your proof is lacking a consideration for the infinite case.

B-but

>Yes. And out of curiosity I tried to come up with a proof for the infinite case, thinking it would be trivial, but actually I hit some complications. I think that with our current mathematics a proof for the infinite case is impossible. I recommend you drop this topic for your dissertation or else you could be stuck years trying to get your PhD.

But I spent the last year working on this!

>I am sorry. As your advisor I can tell you that you would not be able to defend this thesis.

REEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

5 years later

THERE IS A CULT OF INFINITY WITHIN MATHEMATICS AND WE HAVE TO STOP IT. IT IS NOT LOGICAL.

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>>8586167
quality shit right there

>>8586153
I completely understand him.

Infinities are pseudo-mathematical unprovable trash that introduce paradoxes in fundamental areas of mathematics such as set theory. The ""axioms"" that we must assume to work with infinities counter all intuition and primal logic in our brains, and are sometimes introduced under the guise of hypothesis/conjectures to be easier to swallow (see for example the continuum "hypothesis").

Infinity does not exist and cardinalities over aleph-null are self-contradictory.

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all of this shit flinging and none of you brainiacs can actually prove him wrong

hmm

>>8586124
umm R is contained in C

>>8586135
>>8586156
If he means the algebraic numbers, he should write Qbar not C.

>>8586124
http://www.wolframalpha.com/input/?i=z%5E5+-+2z+%2B+3+%3D+0

He's wrong though

How can complex numbers be real if real numbers aren't real?

>>8586124
how can math be real when we aren't real?

>>8586193
>Infinities are pseudo-mathematical unprovable trash that introduce paradoxes in fundamental areas of mathematics such as set theory. The ""axioms"" that we must assume to work with infinities counter all intuition and primal logic in our brains, and are sometimes introduced under the guise of hypothesis/conjectures to be easier to swallow (see for example the continuum "hypothesis").
But literally all of this is why I want to do maths, because it just fucking boggles my mind and I WANT TO UNDERSTAND IT. I don't want to reject it, I want to become one with the madness. Fuck off, Wildeberger.

>>8586193
? But there is a very convenient, simple, and powerful definition of infinity in a set K with an order relation without a superior limit, like R or N.

It's the object defined as being superior (as per the order relation we defined) to any object you take in K.

For example, if K is a race of bacteria that always produce offspring and will never go extinct, if my order relation is "xRy means x is a descendant of y", then for any y, I can find an x that validates xRy.

So there is an infinite in this space I just imagined.

(disclaimer, this is me trying to apply some algebra I read. Did I do good anons ?)

>>8586193

Try doing mathematics without infinity. You wont get far,

>>8586194
You just proved you don't understand any of this shit.

There's no proving him wrong on his beliefs, you could perhaps find errors in his work, but it all starts with a belief you can't prove wrong/false.

That's exactly the same as trying to disprove the existence of souls, you can't. That doesn't make believing in souls any less retarded.

>tfw I'm sharing a board with unenthusiastic faggots who don't want to be mindblown by what infinity does to mathematics
It's a pretty bad feeling, desu.

>>8586402
This, but it's the other way around. You're the ones claiming souls.

>>8586167
my sides

>>8586363
real numbers are real

>>8586153
Infinity makes math difficult
See this book: http://press.princeton.edu/titles/10697.html
>Stillwell demonstrates that elementary mathematics becomes advanced with the intervention of infinity. Infinity has been observed throughout mathematical history, but the recent development of "reverse mathematics" confirms that infinity is essential for proving well-known theorems, and helps to determine the nature, contours, and borders of elementary mathematics.

Also this: >>8586392
So we are stuck with infinities

>>8586439
How can real numbers be real if rationals are not real?

>>8586124
Yes, by realising most polynomials of degree 5 and above generally do not have closed form solutions.

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>>8586352
BRAVO

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???

>>8586455
Give me a number which, when plugged into p(r) yields zero IDENTICALLY, not approximately.

I'll wait.

>>8586444
According to the philosophy of mathematics they are, in a sense.

i.e, '1' is not a real thing, but the concept it refers to (a single closed off thing) is real. Same with all positive integers.

Negative numbers are not real in this sense.

>>8586478
Pastebin it.

>>8586448
Lol. Nah. The dude is obsessed with the physical act of mathematics. i.e. mathematics is the physical manipulation of symbols. The symbol doesn't mean anything themselves, its how they are manipulated that matters. Guy is obsessed with physicalism, with good reason. That's why he hate infinity. You can't physically carry out the writing and manipulation of the symbols for eternity.

>>8586478
Just do a two-parter

>>8586479
>>8586485
http://pastebin.com/kSr51BQ6

>>8586488
hmm really makes you think

>>8586488
That's only approximately zero.

Anyone willing to review what I did here please ?
>>8586388

>>8586499
The function is continuous. We see only value yields 0+, the other yields 0-.

Therefore there exists a z so that f(z) = 0.

>>8586528
I am sorry but are you retarded?

Why do you use fucking continuity to disprove Wildberger? Wildberger DOES NOT have a theory of real numbers. Therefore he does not have a theory of real limits. Therefore he does not have a theory of continuity.

Questioning Wildberger is not about proving him wrong through the use of real numbers, it is arguing wether or not real numbers even have a place in mathematics.

>>8586619
YOU'RE retarded. Wildberger isn't wrong, so you can't disprove him. His theory is consistent. But so are the real numbers. His system is just a subset of math where he opts not to use reals. But using them is also perfectly fine.

who gives a fuck
god damn mathematicians are so autistic

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>tfw math undergrads on 4chan get fannyflustered by being unable to discredit you

Wildberger mathematics should replace the curriculum, because he's right. Something as simple as "angles" requires intense calculus to explain thoroughly (especially with a system as arbitrary as 360 degrees). Everything he does is built ground-up from absolute first principles, which people would understand if they watched his Math Foundations playlist from episode 1

It's been said that people learn best what they almost already know. Maths is so "confusing" and "weird" to the masses because we're asking them to "just trust us on this" as we take leaps of logic over discontinuities in the progression of mathematical topics. Norm fixes that so one thing naturally flows onto the next as you delve into deeper and deeper topics.

>>8586636
>But using them is also perfectly fine.

Using them is fine but it is kinda pointless to prove him wrong through the use of real numbers.

He will not accept your argument.

Sure, in a normal analysis class then sure. Go right ahead. Prove the FTA through the usual complex analysis tools. But don't bring that to a Wildberger discussion because it is a moot point.

>>8586656
My point is that I could say: "from now on I will only use integers. Rationals aren't allowed" and I'm not wrong, but that doesn't mean rationals are an invalid concept.

He builds on intuition instead of set theory, making for some superficial rigor. In Wildberger's math there are no equilateral triangles and Euclid's proposition 1 is false which of course makes for an interesting universe.

He's not wrong, just his arguments lack rigor

>>8586663
Are you sure about that? I thought he was all about Euclid.

>>8586665
Rational-coordinate geometry lines don't intersect circles and circles don't always intersect which basically makes that well known proposition false.

Euclid didn't use any formal rigor either so it's not the end of the world to prove some of this stuff false but that proposition has been proved with rigor countless times, I'm sure Wildberger has more info on this somewhere or the other finite mathematicians around (there's a few of them).

>>8586663
https://www.youtube.com/watch?v=ukiPO4LJqgg

26:00 he talks about equilateral triangles quite happily.

>>8586678
Oh shit by 28:00 he says there are problems. Never mind.

>>8586682
Rational-coord-geometry shits the bed for a lot of geometry but it does make sense for number theory and solves a ton of problems there.

The problem is it is not rigorous though and we had these arguments like a hundred years ago when everybody was tired of conjecture and propositions and wanted formal methods to guarantee something was T or F

>>8586124
FTA is about complex numbers. This old-fag writes about a number [math]r\in\mathbb{C}[/math]. He says no number satisfies the polynomial. Senile dementia.

>>8586687
Also when you use his intuitive ideas for number theory it freakishly 'just works' but on the other hand it can't work since equilateral triangles can't exist in this world. WTFWTF

>>8586124
How does he do Calculus without the concepts of limits and infinity?

>>8586388
the conclusion then for a finitist is that there does not exist a model that satisfies irreflexivity and transitivity (proof that there is no finite model is a nice exercise)

what you've done when you say "there is a race of bacteria etc." is construct a model that satisfies your relation R, however the finitist will deny such a model exists (precisely because there is no finite one, the reason for their reason is axiomatic and cannot be debated on mathematical grounds, and instead must be on philosophical grounds)

>>8586703
Starts around here:
https://www.youtube.com/watch?v=vyRFz8J4Y_M&list=PL5A714C94D40392AB&index=71

But you'd need to go back early in the playlist to get what polynumbers are:
https://www.youtube.com/playlist?list=PL5A714C94D40392AB

I suggest started at video 1 tbqh

What's his ethnicity? Depending on the lighting he goes from Indian to Jewish to white.

>>8586708
Why do you shill this guy so much?

>>8586730
>reply to a post
>"why do you shill so much???"

Fuck off dickhead, I answered someone's question.

>>8586712
White
t. know him in real life

>>8586795
Noice (Y)

Gently stroke his behind for me sometime. No homo though.

>>8586712
canadian

>>8586839
Funny, he doesn't look Asian.

>>8586193
>intuition
b8

>>8586130
memes

>>8586392
http://www.springer.com/gp/book/9789400713468

>>8586703
Algebraic/Geometric point of view. Basically algebraic methods for obtaining a function's associated tangent line, tangent conic, tangent cubic, etc at a point.

Lots of brutal parametric descriptions and he sneaks in a lot of advanced stuff like the algebra of differential forms and changing domain to higher dimensions where infinities in one variable vanish.

>>8586460
>Give me a number x which, when plugged into f(x)=x^2, yields two IDENTICALLY, not approximately.

>I'll wait.

>>8586402
s/believing in souls/not believing in qualia/

>>8587245
Wildberger's entire point is to reformulate math without using irrationals.

>>8587255
Which is to say that Wildberger intends to disregard natural thought processes that produce axioms that require the existence of irrationals in an effort to reformulate math.

>>8587257
Dude, realize he compensates by introducing hardcore shit way early. He is nuts especially since he actually wants this taught to kids but he basically falls back on tensors (especially bilinear forms and symplectic forms) and a lot of group theory over rings in order to make shit work.

Yet he things sin and cos are too hard for our kids.

>>8587257
>natural thought processes
In what regard they are "natural"?

>>8587266
Oh and knot theory. Lots of knot theory.

>And what about explicit examples? Is this not the way to sort out the wheat from the chaff? Yes it is, and all we need to do is open our eyes clearly and look beyond our wishful dreaming to see things as they really are, not the way we would like them to be in our alternative Polyanna land of modern pure mathematics!

Down with the false prophets of infinitesimals !
I mean, his theory is logically consistent, yes, but what's the point ? Without inifinitesimals, don't you "lose" all previous results in analysis, and since almost everything in math is related, almost everything in Algebra and number theory as well ?

>>8587278
Yeah his life work is to reformulate much of that work. The only part he wants thrown out is the infinite set theory of Cantor, etc. Too bad that's the foundation of... everything.

He has dozens of papers and a few hundred videos building up his new math. He uses tensors and linear algebra as his foundations instead of sets (with funky names of course like maxels and such) and it appears he will soon tackle group theory.

He already has a theory of geometry (this is his research area) he even has the start of a geometric theory of Fourier Analysis.

He admits analysis is his biggest challenge, especially measure theory/probability

>>8587285
How can you even use Newton's definition of calculus with his theory ? What about the physics ?

>>8586193
But math doesn't deal with infinities, it deals with things that can be proven to be true for arbitrarily large quantities.

>>8587307
I'd say set theory is all about dealing with infinities.

>>8587312
How so?

>>8587316
All detailed here https://www.scientificamerican.com/article/infinity-logic-law/ (from a Quanta journal article reprinted)

You can also pick any present day math journal you want, search for infinity and read the articles by pasting in their link or DOI# into sci-hub there's always infinity dissenters around

>>8586402
>That's exactly the same as trying to disprove the existence of souls, you can't. That doesn't make believing in souls any less retarded.
PS: You can. It's not that hard. The fundamental physics of everyday life is known. The Standard Model accurately describes every experiment that has ever been done on Earth. If QFT is right, and it almost certainly is concerning what happens in our brains, then we know that there are no more particles or forces that have a measurable effect on the human brain, because QFT says that if there was such a thing, we would have noticed it already in particle accelerators.

If there was a soul that did something, it would have to nudge atoms in the brain from time to time. We know that there is no such force, because we've looked really hard, and it's not there. It's the same kind of reasoning that allows us to positively claim that there are no T Rex's walking the planet.

Any rebuttal misses the point, and it's probably fallacious special pleading.

>>8586484
You got Wildberger very wrong. He objects strongly to the view that math is just symbol manipulation. The view "math is just symbol manipulation" is the opposite position of his particular brand of ultra-finitism and mathematical Platonicism.

>>8586619
I'm pretty sure you can have a theory of limits with just Q. Q is dense. Of course, in this system, a Rational-valued function could converge at a point according to the Cauchy definition, but it would not have a Rational-value limit. Other points, the function could converge, and the limit could be defined, and the limit would be a Rational value.

>>8587344
Physicalism

>>8587335
But again, is it infinities that are studied in set theory, or is it rather that "infinity" is just a short-hand way to talk about stuff that can be proven to hold true for arbitrarily large quantities? (similarly to mathematical induction)

>>8587350
I don't know what that word means.

I am a philosophical naturalist, but that is not taken on faith. Rather, by applying the scientific method to the available evidence, philosophical naturalism is an undeniable /conclusion/ (and like all scientific conclusions, it is tentative, and subject to being overturn with new evidence).

>>8587360
Try to explain sentience in terms of matter, then.

>>8587365
??
It's just the standard materialist position. I'm pretty sure you know it. The human brain is just physical machine, albeit vastly more complicated than most physical machines. Can we just skip ahead to your supposed "defeater" for my position?

>>8587370
Imagine an entity which is not sentient: for example, a rock*. Now imagine a human. Imagine taking the rock and making it more and more like a human physically. Do you believe that a point comes, at which the physical structure of your entity is at some particular stage of arrangement and/or complexity, when the entity suddenly becomes sentient? (Sentient as in "having a subjective experience") If so, can you conceive of what particular arrangement of matter is necessary in order to "activate" sentience? And where does the sentience come from? Why would it appear? Why are humans sentient rather than being so-called "philosophical zombies" that look and behave exactly as humans but have no subjective experience?

To be technical, there's no way to say whether it is a human body that is sentient or the entire universe that is sentient... but I'll talk about a rock to simplify things.

>>8587370
oops, the last sentence should start with an asterisk - it was supposed to be a footnote

>>8587380
(You) assume that the people who make these materialist arguments treat sentience as the equivalent of the soul, some magical different position for humans, when the logical viewpoint is that our perception of consciousness is simply how the machine that is a brain interprets information and makes decisions based on it.

>>8587380
>Do you believe that a point comes, at which the physical structure of your entity is at some particular stage of arrangement and/or complexity, when the entity suddenly becomes sentient?

I'm not sure. I suspect that as you continue this gradual process, one gets more and more subjective experience.

> And where does the sentience come from?

I don't know.

> Why would it appear?

I don't know.

> Why are humans sentient rather than being so-called "philosophical zombies" that look and behave exactly as humans but have no subjective experience?

I don't know if it's possible for p-zombies to exist. I suspect not, given the likely truth of the proposition that first-person experience is a result of a particular kind of physical configuration.

Regardless, this is a non-sequitir. I agree that these are interesting questions, but they do very little to nothing to address the massive wealth of evidence in favor of the Standard Model of particle physics, which leaves zero room for human souls except by very bad arguments like special pleading. To go from "I don't know", to "I don't know, and therefore there's a non-material magic soul that does it" is fallacious. It's textbook argument from ignorance.
http://tvtropes.org/pmwiki/pmwiki.php/Main/AWizardDidIt

>>8587387
What is the difference between a philosophical zombie and an actual human being?

>>8587392
philosophical zombies don't exist.

>>8587388
> one gets more and more subjective experience.
Remember the last time you woke up from sleep. Becoming sentient was binary, not gradual. You were completely not sentient, then you were sentient - only aware of a certain sluggish warmth, probably, not thoughts or visual stimuli (for the first second or so) - but already aware. Therefore I think sentience is binary. Either I am sentient or I am not.

regarding your latter point - it is irrelevant whether the SM leaves any room for souls. The key fact is that it does not exclude them.

By the way, I am only arguing about sentience, not about souls - I'm not trying to prove that souls exist, unless we just mean "sentience" by "soul".

>>8587396
Then it is logical to say that we live in a universe in which certain physical arrangements are correlated with subjective experience. I agree with that. However, then the question remains - why those particular arrangements and not others? What is the connection between a few pounds of neural tissue and qualia?

>>8587398
>regarding your latter point - it is irrelevant whether the SM leaves any room for souls. The key fact is that it does not exclude them.

Yes, the Standard Model does exclude them. In order for souls to exist, they must materially interact with the atoms in your head. At the very least, they must be passive observers of state in order to "see" the outside world, and they must also manipulate, nudge an atom here, nudge another atom there, etc., in order to allow your decisions to be acted upon by your body. Can you will your arm to move? That's an action by your purported soul on your physical body. That violates the Standard Model. We know that there is no such thing, because the math of QFT says that if there was, then we would have created it in a particle accelerator already, and we haven't. Claiming that there is a soul is a huge special pleading to the math of QFT and the Standard Model.

>>8587398
>By the way, I am only arguing about sentience, not about souls - I'm not trying to prove that souls exist, unless we just mean "sentience" by "soul".

That's a separate question. "Sentience" is entirely compatible with materialism. "Sentience" is just a property of certain physical machines.

>>8587404
Sentience can exist without being the cause of physical effects - a "passive observer", as you put it.

>>8587407
Ah well, that is the interesting question... I assumed that any discussion of souls would only be interesting if we turned it into a discussion of sentience.

>>8587365
If by "sentience" you don't mean "magic" or "souls", then I don't see the problem. Do I need to explain the internal working of Firefox, my OS, the TCP IP stack, etc. to you too? It's a very long and complicated story, and unlike for my computer posting on 4chan, we know very little about the story about how the human brain does what it does. It's a very, very complicated thing. (But we do know that the basic parts obey the Standard Model.)

>>8587407
Here is the mystical part, though... imagine we figure out exactly which configurations of matter are sentient and which are not. Imagine we have total control over matter. We can change the insentient configuration into the sentient one by an act of will. We do so. Sentience appears "in" the matter. The mystery consists in this: that if we did this, it is possible that looking at the patterns of matter that had to be changed would tell us nothing that had any connection to what subjective experience is like. We would be able to perfectly abstract, for example, mathematical patterns from the physical phenomena being studied - we could even reduce the preconditions for sentience to a set of mathematical-physical axioms. But that incredible understanding could well (and I suspect, would well) tell us nothing about why suddenly subjective experience

>>8587417
I'm saying that it's perfectly possible that understanding sentience is orthogonal to understanding the physical workings of the brain. Even if we knew where every atom in the brain was, we might be no closer to explaining sentience.

>>8587420
It seems that you have basic misunderstanding of science, and epistemology.

https://www.youtube.com/watch?v=MO0r930Sn_8

The only way that we ever show causation in science is by correlation, and by trying to remove all confounding variables. That's all a "controlled experiment in a lab" is.

If you ask "how do magnets work?", there is no good answer. I can explain how they work in terms of Maxwell's equations or the Standard Model and QFT, but for example, you could just ask "but why do the fields of QFT interact in the ways that they do?", and I do not have an answer. Asking for that kind of explanation is ultimately impossible. Every explanation of mechanism is an explanation in terms of another model, and eventually you will arrive in a model where there is no known mechanism, such as current QFT.

We know that certain configurations of matter do "cause" certain subjective experience. How? We don't know, and we don't need to know "how?" in order to know something, just like we don't need to know "how?" the particular fields of QFT interact in order to properly model and predict a magnet and its effects.

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>>8586124
>has polynomial p(x) = x^5 - 2x + 3
>can't find the solution
>"hurr durr the fundamental theorem of algebra is wrong"
When are you guys going to stop shilling for this crackpot?

>>8587428

>We know that certain configurations of matter do "cause" certain subjective experience.
I agree with the quotes. We know that certain configurations of matter are correlated with subjective experience. We do not know if there is any sort of causal relationship.

What about this as a possibility: QFT is true and sentience is real. But QFT does not, and in principle cannot, explain sentience. Then sentience is a real property of the universe, yet one which our physical understanding has no room for.

>>8587442
>We do not know if there is any sort of causal relationship.
Yes we do.

I can damage a certain part of your brain, and you lose the ability to do basic math. I can destroy another part of the brain, and you lose the ability to form long term memories. I can stimulate a part of the brain, and you will hear music. I can stimulate another part of the brain (optic nerve), and I can make you see things. I can do all sorts of things to your subjective experience with various drugs, such as LCD, alcohol, etc. We know damn well that there is causation.

I can take apart your entire mind, piece by piece, by taking apart your brain.

>>8587442
>What about this as a possibility: QFT is true and sentience is real. But QFT does not, and in principle cannot, explain sentience. Then sentience is a real property of the universe, yet one which our physical understanding has no room for.

I don't know what you mean by sentience. Do you mean first person experience aka qualia? Whatever. Do you mean "passing the Turing test" and similar? In principle, we can totally explain "passing the Turing test".

>>8587445
You are completely right about that... I should have worded things better. What I mean is that we do not know of any mechanism that connects material arrangements to qualia.

>>8587445
Yeah that's bullshit though, the brain isn't that simple. Multiple areas of the brain are involved with those actions, it's not so compartmentalized that your brain has a "math module" and a "memory module". Some parts focus more on certain tasks more than others but they all work together to accomplish those tasks. This is particularly true for math and memory forming.

>>8587447
Qualia

>>8587450
What the hell are you talking about? I just gave many examples on how we do know that changing the "configuration" in certain ways does affect your qualia. I don't know what you're talking about.

>>8587451
And yet, there are real people in the real world that have suffered particular kinds of brain injury where exactly that has happened.

I didn't say that the functioning of those things happens only in one part of the brain. I did say that I can remove that ability by removing certain parts of the brain. Totally different things.

>>8587453
But you cannot explain how the causation works.

>>8587452
As I already said, I have no mechanism for how particular physical configurations of matter cause/affect qualia. And as I also said, it's irrelevant to the well established conclusion that there are no souls.

>>8587454
See here again:
>>8587428
We can never explain how causation works. Never. That's just not what science does.

>>8587453
Well you said "part" not "parts". Just felt like I had to clear up that common misconception about there being a "math center" and "reading center" in the brain

>>8587457
Please. Thank you for the clarification / correction.

>>8587456
I'm not interested in souls. I'm interested in sentience.

As for "that's not what science does". Yes, that's technically true that science does not explain how causation works. But generally there are observable phenomena that behave continuously. I push on a continuous rod that at its other end pushes on some other object it thereby sets in motion. I generate an electric field and then there is a measurable continuous gradation of phenomena throughout space as a result. And so on. Between brain structure and qualia, on the other hand, there is an abrupt leap. There is a point at which the whole chain of explaining one thing in terms of another simply stops, and you just have to say: "Look, there is sentience!" It is dropped into the situation as if by magic. And it is not measurable.

>>8587402
Qualia is an illusion. The way we perceive things is nothing more than how our brain operates.
captcha: stop objec

>>8587462
>Qualia is an illusion
Please. Don't try to define your way out. Qualia is obviously real - unless you are a p-zombie.

>The way we perceive things is nothing more than how our brain operates.
No proof.

>>8587456
I should clarify, I do not mean "continuous" in the pure math sense. It's a metaphor. What I mean is that, I can explain why pushing a rod on one end also pushes the other end by explaining how one atom pushes another... and so on (roughly speaking). With neurons -> sentience, there is an explanatory gap, and the two sides of the gap are utterly different.

>>8587461
This is part of the general misunderstanding of science, which is all too common. In your mind, you are unable to distinguish "science" from "materialism" and "naturalism".

I don't see those "abrupt leaps" and stark differences. To me, the way that a magnet works, and gravity works, is just as spooky as how certain configurations of matter cause qualia.

For further reading, I strongly suggest this peer reviewed philosophy of science paper:
https://sites.google.com/site/maartenboudry/teksten-1/methodological-naturalism

>Between brain structure and qualia, on the other hand, there is an abrupt leap. There is a point at which the whole chain of explaining one thing in terms of another simply stops, and you just have to say: "Look, there is sentience!"

Again, do you mean qualia? If you mean "qualia", then please use the correct term. "Sentience" is more ambiguous, and it could refer to an entirely materialistic concept, such as a description of a machine that can pass the Turing test.

Finally, you have yet to demonstrate whether the gap is really that big. For example, on my laptop, I can turn it on and off. Vast changes in behavior with very small configuration changes. Yet, many of the things that my laptop can do can also be done by a small pocket calculator. Maybe qualia is the same way. Maybe dogs have qualia. (I think that they do.) Maybe ants have qualia. I don't know. Maybe there is a smooth gradient, much smoother than you realize.

And finally, again, there are still no souls.

>>8587466
>With neurons -> sentience, there is an explanatory gap, and the two sides of the gap are utterly different.
Again, do you mean "passing the Turing test"? If so, then that can be explained /in principle/ step by step, in exactly the same way that I can explain that pushing on the end of a rod is pushing on one atom, which pushes on another, which pushes on another, etc.

It would be like explaining the internal operation of my laptop to run FFXIV. There are many, many, many steps, but every step is descriable, explainable, and materialistic. For a human brain to pass the Turing test, there is another story, which has many many steps, but every step is simple and materialistic.

We don't yet know the whole story for the human brain like we do for the laptop, but I do know that the story is there, based on the overwhelming evidence that I have in favor of SM and QFT.

>>8587464
>disprove god exists

>>8587468

>Misunderstanding
No, I understand perfectly well what you mean... I agree with your distinction. I just see others who cannot, and who fall into naive materialism.

>"Sentience" is more ambiguous, and it could refer to an entirely materialistic concept, such as a description of a machine that can pass the Turing test.
Not the way I use the word... I've never seen it used to describe just passing the turing test. Yes, I mean by it what you mean by qualia.

>To me, the way that a magnet works, and gravity works, is just as spooky as how certain configurations of matter cause qualia.
Then we agree. All I want to do is draw attention to this weirdness. Our subjective experience, which is so important to who we are - indeed, without which we would not be in any sense significant for ourselves - is as weird
as gravity. It's not just a matter of putting wires together in a certain way - or if it is in the sense that putting the wires together in that way correlates with sentience arising, it is nonetheless mysterious that sentience is what arises and that such a thing even is.

>gradient of qualia
But there is either awareness, or no awareness - the presence or absence of awareness is binary. Any bit of awareness, and you're already aware as opposed to unaware.

>>8587470
no, I mean subjective experience/qualia, not passing the turing test. to me there's nothing mysterious about being able to pass the turing test. i believe that insentient matter could pass the turing test.

>>8587473
That would be a valid request

>>8587474
>But there is either awareness, or no awareness - the presence or absence of awareness is binary. Any bit of awareness, and you're already aware as opposed to unaware.
I'm not convinced this is true. I slightly suspect that it's too confused and too simplistic to be true or false. However, I offer no contest at this point.

For example, let me take something from Dennett (<3). In a room full of college professors who study philosophy of mind, he did the change blindness test on the audience of professors.

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

Afterwards, Dennett said, paraphrase: "At some point, you saw the images, quickly changing from one to the other. Your optical nerves registered the difference from the start, but it took most of you a second or more to 'consciously recognize' the difference in a way that would allow you to vocalize and describe the difference in English. So, did you have qualia of the difference before this moment, or not?"

A third of the professors said "obviously yes, I had qualia of the difference before I noticed it", and another third said "obviously no, I didn't have qualia of it if I didn't notice it", and the last third said "oh my god, I never thought about it like that".

I similarly suspect that the term "aware" is not rigorous enough for the discussion, and I suspect that we don't have enough understanding, in order for what you wrote to be really meaningful.

>>8587481
>So, did you have qualia of the difference before this moment, or not?
They had whatever qualia they had at each moment... the particular nature of qualia and how the change in qualia is timed compared to physical phenomena does not factor into "big" the question of the nature of sentience. I fail to see what Dennett's point was.

>>8587481
oops, I mean: does not factor into the "big" question of the nature of sentience.

Another note: The professors who said "yes, I had qualia of the difference before I noticed it" don't understand what "qualia" means.

BEEP BEEP BIOLOGIST HERE

>You cannot empirically validate subjectivity
>You cannot invalidate solipsism
>You're currently having a semantics debate because you're using different definitions for common terms, which is a massive waste of time that will inevitably end in a pissing contest over whose definition "wins"

Love,
>antapex of the quantitative hierarchy

>>8586460
>Number exists if and only if it has finite and easy to write representation in arbitrarily chosen notation

>>8586643
Radian and degrees measure of angle gives us unique angle, that is, given the measure of some angle in radians or degrees we know exactly what angle does it describe, while wildburger's spread describes two complimentary angles and there's no way to distinguish them, you can't say you mean the bigger or smaller one because, in wildburger's world they are both the same. This very facts says wildberger's theories are shit and real maths is superior to what he does

>>8586656
It's impossible to disprove wildberger's theories because they're not facts but emotions. He doesn't give any proofs for his claims, he just says "I don't like reals and infinity makes me sad, so they're wrong". It's not an argument you can't discuss or try to disprove. In fact, it's impossible to disprove, because it's true he doesn't like reals. But his feelings don't mean anything in maths.

>>8587668
he needs a rational safespace

>>8586703
He defines limits of rational functions, but his definition is inconsistent with his other theories because he defines them as n tends to infinity, but as we know, it can't because there's no infinity. Also his definition of limit has the exact same flaws he claims "regular" definition has, so his definition is invalid by his own claims

>>8587266
He defines naturals as strokes on board, so I'd call that kid's intuition rather than hardcore shit or anything close to rigorous definition

>>8586130
Do you ever wonder why you and others react this way to Wildberger and others like him? You think that if enough people sneer at someone that invalidates their ideas? Wildberger has the courage to confront what he believes is an error in mathematical thinking. Retards such as yourself laugh at this because it assures you that are smart. Have you ever studied the history of mathematics, science, or any human endeavor? There are countless examples of the majority opinion being wrong and the most enlightened minds of the time being ridiculed. Indeed, this does not serve as evidence that any one renegade is correct. It should, however, make you reassess whether you know what you claim to know. If you think that our ideas about infinity are certain, you are kidding yourself. The number of academics being certain of something has no bearing on the truth. They are sheep and frauds like you. You will all continue believing in the things that will signal to other people that you are smart. You don't care about knowledge or even thinking. You wouldn't pursue an academically unpopular thought because you care more about acceptance than substance. Wildberger may be completely "wrong," but at least he questioned what he was told and formulated his own thoughts are much more robust than you and any sneering academics give them credit for. One Wildberger is worth 1000 of your kind.

>>8587272
They arise while solving real life problems. You may not have encountered this if all the maths you need is basic rational arithmetics for giving the change

>>8587278
His theory is not consistent and standard analysis doesn't use infinitesimals

>>8587344>>8587360

holy shit you know nothing about epistemology

>>8587686
-you do not need consistency to have a theory
-you do not even know why you require consistency
-you have not established the lack of consistency.

>>8587668
you really stick to undergrad math don't you

>>8587703
>you have not established the lack of consistency

>he defines limits in infinity whilst claiming infinity doesn't exist
>he says standard definition of limit of a sequence is invalid because the term sequence is undefined, while he defines limit of rational sequences, or as he calls them "rational polynumbers" without defining them
>in video where he claims his rational geometry can solve problems without the use of irrationals he solves some problem and his method gives answer involving square root of 6

>>8587703
Theory has to be consistent to be even called a theory, his are not so it's not worth time discussing them. They are self contradictory, so he disproved his own theories

>>8587704
Wildberger didn't even make it to high school maths with his definition of naturals basing on counting sticks

>>8586130
There is literally only 1 guy who cares about his shit, and like 2 guys who pretend to agree with him who are only in it to troll the other 1 guy.

4chan is the country of faggots, brainlets and trolls.
Your stupidity is inifinite.

>>8588080
*Our stupidity

>>8586382
The number O is a completely random number that reads as a different random number at every one of its instances.

The mathematical implications of this are interesting but nonetheless there is no parallel to this in real life so it is completely useless.

A similar case can be made for infinity.

>>8587676
No.

"n towards infinity" is just informal shorthand for a symbolic logic definition with no infinity. Take calc 1. His problem is not with limits. It's with the usual constructions of Reals, which depend on infinite sets.

>>8588088
No, thanks. It's yours. Really.

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>>8588093
>completely useless

http://www.stat.yale.edu/Courses/1997-98/101/ranvar.htm

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Axioms

>>8586124
If this guy was something different than a troll, the world would have long known...
Let him troll, but please OP, don't troll /sci ever again with this dumbass.

>>8588333
The concept of limit depends on existence of infinite sets. Finite sets have no limit points. Please, follow your own advice.

>>8587682
>may be completely wrong
>more robust
What did he mean by this??

>>8588380
I don't know exactly the asshats position. However, this is true:
Even Naturals are an infinite set, but he doesn't have problems making statements about all Naturals. Rationals are trivially constructable from Naturals in a constructivist way: every Rational can be named. The Reals cannot be positively constructed and enumerated. Most Reals cannot be named or specified.

I can define "limit" just fine without resorting to infinite sets.

For a function f : Q -> Q,
for c,L∈Q,
if (∀e∈Q)(∃d∈Q)(∀x∈Q)(e>0 ∧ d>0 ∧ |x-c|<d → |f(x)-L|<L,
then lim x→∞ f(x) = L

Obviously, I'd have to spruce it up a little bit with "limit points" to include functions that have a domain that is a subset of Q.

I don't need to refer to anything that Wildberger doesn't like, AFAIK. I am quantifying over "infinite" sets, but Wildberger implicitly does that in other cases, and he doesn't seem to care, as long as the infinite set is constructible like Q.

>>8588414
> if (∀e∈Q)(∃d∈Q)(∀x∈Q)(e>0 ∧ d>0 ∧ |x-c|<d → |f(x)-L|<e),
Also, fixed.

>>8588414
Undergrad.

>>8588538
Yes, and?

He and anyone who agrees with him act like lowly undergraduate physics students learning quantum mechanics for the first time.

The universe doesn't care whether you agree with it or find it intuitive or not. Just because you have a hard time wrapping your head around concepts like infinity doesn't mean they don't exist, it just means our brains aren't tailored to understand literally everything because we evolved to only need to understand how many fucking bananas we need to stay alive and not the difference between countable and uncountable sets.
Fuck.

>>8587682
>Wildberger has the courage to confront what he believes is an error in mathematical thinking.
See this is actually why people don't like Wildberger. There are plenty of constructivists and finitists that people respect. The issue is that Wildberger uses political rhetoric in discussing mathematics in order to convince naive students. Framing finitism as "courageous" or correcting "an error" is non-mathematical and misleading.

>There are countless examples of the majority opinion being wrong and the most enlightened minds of the time being ridiculed.
This is a classic internet fallacy. There are even more examples of actual crackpots and fools being ridiculed. Being contrarian or using conspiracy logic will rightfully gain you scorn.

>If you think that our ideas about infinity are certain, you are kidding yourself. The number of academics being certain of something has no bearing on the truth.
They are certain. Mathematics is unique in that we can absolutely prove something based on axioms, and the axioms themselves are neither true nor false. It is not Wildberger's finitist axioms that are the issue, the issue is his claim that he does not use axioms at all, that his intuition is the truth, etc. Again, this is non-mathematical political rhetoric.

>They are sheep and frauds like you. You will all continue believing in the things that will signal to other people that you are smart. You don't care about knowledge or even thinking
And this is why people laugh at you. Until you grow up you will not be able to see how ridiculous you are being and how you are missing the point.

>>8586135
u gotta be smart af to put ur last name on a /sci post *slow claps*

>>8586167
Is that really what happened?

>>8588580
Go ask an analysis professor about your "theory".

>>8588717
?
You seem confused. I dislike Wildberger's stuff. However, you can still talk about limits in Rationals. For example, limits on Rational-valued functions is necessary to define Cauchy sequences, which is used as part of the common Cauchy construction of the Reals.

>>8588414
It should be [math]x\rightarrow c[/math] but whatever. Okay, we talking limits of functions. What you wrote is not a definition of a limit of a function, because [math]c[/math] should be a limit point of [math]Q[/math]. And every neighborhood of a limit point contains infinite amount of points. Just because the definition of a limit doesn't mention the word "infinite", doesn't mean it doesn't depend of existence of infinite sets.

>>8588605
you really have not done math beyond a HS level

>>8589461
Don't shoot me. I'm just the messenger. Take it up with Wildberger.

>>8588414
>Naturals are an infinite set
Wrong, there are only about 10^200 natural numbers.

>>8589618
>there are only about 10^200 natural numbers
Take the greatest number of those numbers.
Add 1.
So, anon ? Ya don't know your classics of proofs, do ya?

>>8587520
>biologist here

Thanks for the warning, filtered.

>>8586414
Yes indeed, there is no proof that infinity exist or doesn't exist. However assuming it exists is what allow us to do maths the easiest way. So we assume it exists.

The same way there is no way to proof that the earth isn't hollow, until we go to earth's core. Still, a non-hollow earth is a way simpler way to explain seismics waves in inner earth. So, until a better theory is provided' we stick to it.

That's called scientific reasoning boya.

>>8589463
>reply full of perfectly reasonable arguments
>he resorts to ad hominem in hopes of getting unBtfo
nice

>>8590197
> Take the greatest number of those numbers.
> Add 1.
prove that you can do that

>>8586124
his handwriting is really sexy

>>8590756
>prove that you can do that
Give me the greatest number of the approx 10^200 that have been mentioned. Because you know there is a finite number of integers, you are able to give it to me. Or at least you can state you know it. Can't you.

I'll just add 1 to it.
If you're not happy with that, I'll even write your number in whatever basis you wish.
And I'll still add 1.
And I will have done it.
I will have thereby proven I can do it.

Anything else I can do for ya, anon?

>>8587344
>PS: You can. It's not that hard.
Retard. You can't prove a negative. That's why the burden on proof lies on the positive claim.

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>>8586124
This board clings to myths. They do not care about critical thinking. They're grad school sheep with no other skills

>>8586167
max(kek)

>>8587266
>Yet he things sin and cos are too hard for our kids.
They are. Try making 5 year olds rediscover CORDIC. Protip: you can't

>>8586193
How many digits are un pi?

>>8586443
>Also this: >>8586392
>So we are stuck with infinities
not an argument.