/sci/ - Science & Math

[Anonymous No.5029121]

>2012
>still thinking computer science is merely applied mathematics
>not realizing mathematics is merely a human language that distills in declarative form the computational processes of your own mind that ultimately arise and emerge from the fundamental computational nature of the Universe
>not realizing that the reason there are mathematical truths is exactly because there are computational truths
>not realizing computer scientists and software developers are wizards capable of conjuring the computational "aether" of the Universe

http://www.youtube.com/watch?v=Kcyitn0LHSM&t=11m54s
http://www.youtube.com/watch?v=zQLUPjefuWA

http://arxiv.org/abs/physics/0001020
http://arxiv.org/abs/0704.0646
http://arxiv.org/abs/1003.5831
http://arxiv.org/abs/1205.2026
http://arxiv.org/abs/1207.4803
http://arxiv.org/abs/1001.0785

http://lesswrong.com/lw/58d/how_not_to_be_a_na%C3%AFve_computationalist/

[Anonymous No.5029178]

I really like the prof in the video. Cool voice, would go to all lectures.

[Anonymous No.5029180]

[Anonymous No.5029260]

what does some bullshit math prof saying "infinite sets don't exist" have to do with anything? is he your fucking teacher or something?

[Anonymous No.5029277]

>not realizing you're using "universe" as a proper noun

But in all seriousness, we're merely scratching the surface. Rock on.

[Anonymous No.5029372]

In germany its called Informatik (- sounds just like informatics and I think it means the same). But even without a bad term with computer in it like 'computer science', the common people still think its all about computers, programming, etc. With this in mind I can understand that some people think its just applied mathematics.

So why is it this way? Well the simple automation of calculation IS a big part of computer science. So its not like these people are completely wrong. Its also the part that is the easiest to grasp, when you try to explain what a computer science concerns himself with.
Another factor I think is, that programmers, software engineers even hardware designer dominate the picture of computer science. People who actually embrace and study the wizardry on deeper levels (think meta magic) are rare. Also in my university courses about e.g. formal languages theory are held by the mathematics department. So it feels like it belongs to maths.

As a wizard myself, I would boldly state, that mathematics (as language) is applied information theory or maybe better formal languages theory.

p.s.: damn captchas; who thought pieces of text unmatchable by a (self-improving) program that tries to emulate the human recognition of words, would stay easily solvable by humans? These things a friggin' ridiculous.

[Anonymous No.5029386]

>>5029372
>p.s.: damn captchas; who thought pieces of text unmatchable by a (self-improving) program that tries to emulate the human recognition of words, would stay easily solvable by humans? These things a friggin' ridiculous.

>2012
>still thinking recaptcha hasn't been conquered with a layered approach of off-the-shelf cognitive vision algorithms
>not realizing people are making buttloads of bitcoins renting out their recaptcha bots

[Anonymous No.5029419]

>>5029121
>thinks mathematics relies on the laws of physics.
>doesn't realize that no matter how you changed the laws of physics the mathematics themselves would stay the same

>doesn't realize only a small percentage of mathematics can be computed and most mathematicians never concern themselves with it.

1/10 for making me post, come back when your computational bullshit can provide a proof for a Diophantine problem. Protip: never

[Anonymous No.5029439]

>>5029121
lol that first video is informal as fuck and the second video doesn't know shit about modern mathematics.

I see now why comp sci fags think they're relevant to mathematics. Clearly they're retarded.

[Anonymous No.5029446]

>>5029419
>stuck in the past
>unwilling to change
>not realizing that all laws of physics are emergent from an underlying information entropic force
>not realizing that all of mathematics is either computable, or can be approximated through computable means, and the stuff for which only approximations exist, such as an infinite power series expansion of a transcendental function, actually doesn't exist as per Godel's incompleteness theorem.
>didn't read any of the papers posted and drew immediate reactionary conclusions based upon cognitive biases inherent to dusty old mathematicians who are obsolete
>not understanding that the Diophantine problems are unsolvable and undecidable, by computer or human, and that understanding why one can derive a proof of Godel's incompleteness theorem
>thinking this is a proof that humans are superior and computation is inferior
>not realizing humans are embedded as computational artifacts inside of a computational reality

[Anonymous No.5029460]

>>5029446
>doesn't understand godel's incompleteness theorems.
>doesn't use the term "existence" in any meaningful way to a mathematician.
>thinks mathematics is bound to the physical world when most of the shit done in mathematics could never exist in the physical world.
>doesn't know what mathematics is, thinks it's one single axiomatization (classical algebra).
>doesn't realize that tons of diophantine problems are solvable and have been solved such as fermat's last theorem, but it is impossible for a non-mathematician to do it.
>thinks this is a human vs machine argument when it's arguable that really sophisticated systems built on learning algorithms may be capable of deriving proofs.
>thinks mathematics is computational
>is actually the person stuck in the past (mathematics from the 1800s).

[Anonymous No.5029470]

>>5029460
>doesn't understand human brains are really just complex computers constrained by what's possible under Universal Computation
>doesn't understand the rest of his arguments are thus invalid

[Anonymous No.5029472]

>>5029470

>doesn't understand that mathematics work doesn't involve computation, only science.
>doesn't understand the rest of his arguments are thus invalid

[Anonymous No.5029514]

>>5029446
>the stuff for which only approximations exist, such as an infinite power series expansion of a transcendental function, actually doesn't exist as per Godel's incompleteness theorem.

What?

[Anonymous No.5029517]

>>5029470
The human brain can be a computational artifact without that having any bearings on foundations of mathematics. Also you don't understand what Godel's incompleteness theorems state.

Don't get me wrong, computationalism is almost certainly right. You just don't have a well-informed background regarding it.

[Anonymous No.5029521]

>>5029514
He's a retard. Dude thinks stuff that can't be computed doesn't "exist" and that this is somehow (incorrectly) related to godel's incompleteness theorems. Probably because he believes that mathematics is a system founded on logic (wrong) and via godel's incompleteness theorem there are things that are true but can't be proven (he probably misconstrued this to somehow mean that there are things in mathematics that don't exist or some shit).

I wouldn't want to watch such a feeble mind try to reconcile their worldview when confronted with constructivist geometry.

[Anonymous No.5029601]

Wait wait wait. What do you guys mean by saying math (or XYZ) is not computational? I would argue that the act of thinking or (broader) processing information is computational - as in can be described as multiple calculation steps. I don't talk about the 'real' world here; that would be a another discussion what this might be. But I don't understand what you want to express by saying that.

As a related note on physics: Every interaction is expressed as calculable rule, isn't it? E.g. by defining an unitary operator when dealing with quantum mechanics.
If you say, that there is something, that can't be described/behaves in a computational fashion, how does it even make sense to talk/study/think about it. Such thing could only exist if the world does not follow invariant/stable rules.

[Anonymous No.5029657]

>What sense does it make to talk about things that cannot be constructed in the physical world through computation?

Well, there's a couple problems with the approach.

1) It only talks about things that can be quantified. For example, suppose you have a jar full of water and a cup full of water. You don't know the actual quantity of the water but you can still make meaningful statements about it. Such as 'cup of water < jar of water'. If you take it further and acquire a third thing to compare either to then you can possibly use the transitive property to derive a new meaningful statement about the third. This example is a little contrived because you can quantify the amount of water in each object if you really want to, but there are instances in the physical universe where you cannot and you are forced to rely on bounds.

2) Computation is a bad approach at construction for a number of reasons. Here is an example of geometric construction (picture attached). The idea is that through thales theorem any circle with a triangle inscribed where one of the sides bisects the circle is a right triangle. This can be abused to construct any sqrt(n) value (where 1 is defined as part of the construction). In the picture sqrt(2) is constructed.

Continued in next post

[Anonymous No.5029677]

>>5029657

As stated before this can be used to construct any sqrt(n) number, this picture shows a more detailed construction of sqrt(5) in the same way.

If you use your pre-constructed sqrt(n) as the basis for another construction then you can construct forth roots and so on. However, you cannot construct cube roots, and well as it turns out, there are a ton of "numbers" that cannot be constructed through geometric means. This in turn leads to a ton of regular polygons and other shit that can similarly not be constructed (heptagon for example cannot whereas 17-gon can). So the question 'do these things exist' now stares us in the face and we're forced to define what existence means. OP is saying that only things that can be constructed through computation exist in the physical world and that mathematics is ONLY those things and nothing more (horseshit). This mixes up three definitions.

1) If it is constructable/provable in a certain formal system/axiomatization, then it exists in that formal system/axiomatization.
2) If it should exist in mathematics as a whole from a philosophical (of math) perspective. Also called Morality by mathfags, occasionally (but it has nothing to do with the term morality in philosophy, which allows mathfags to troll the shit out of philosofags).
3) Whether or not it can physically exist (be constructed) in the physical world.

continued in next post

[Anonymous No.5029679]

>>5029677
forgot my picture

[Anonymous No.5029693]

>>5029679

Looking back at our geometric constructions with our new definitions a couple things become clear. Some values only exist in the constructable sense, some values should exist in the moral sense, and because of quantum properties and overall just the nature of the physical universe, none of these values can exist in the physical universe (can a perfect circle exist? how about a triangle? a line? a point even?).

Isn't it now just as dangerous, if not more to try and make the sweeping generalizations that OP is making? Sure, the brain may deal with computation. It may even turn out it does all of it's decision making through sophisticated game theory quantization processes. The problem is that if one tries to say that values that can only be approximated do not "exist" just because they cannot be computed, what form of "exists" are they talking about? If they're saying that they can't exist in the physical universe, then this may seem rational, but roots that manifest in the physical universe do not do so by computing themselves recursively. Worse still, irrational numbers themselves can only be approximated through computation, so from this perspective it's even weaker than geometric construction. If they're talking about morality then they are just flat out wrong or they have to redefine mathematics. If they're talking about it existing in the constructable sense, then at best they're only talking about computation and not anything else.

[Anonymous No.5029695]

>>5029677
>>5029679

Sorry, that picture is sqrt(4), not sqrt(5).

[Anonymous No.5029724]

>>5029446
>not realizing that all of mathematics is either computable, or can be approximated through computable means, and the stuff for which only approximations exist, such as an infinite power series expansion of a transcendental function, actually doesn't exist as per Godel's incompleteness theorem.
you should really visit an intro course to mathematical logic

[Anonymous No.5029733]

Are you all simply trolling or just retarded?

Computer science, sure, involves mathematics, but those two are very different.

And no, mathematicians, you don't know anything about computer science. You can't just say "it's math, therefor I understand it." QM also involves a lot of math, but simply knowing math doesn't imply that you also magically know anything that uses math. Get your shit together.

[Anonymous No.5029740]

>>5029733
I've always said computer science isn't mathematics. It uses the scientific method for shit like algorithms and shit. If anything it's science.

The only people saying it's math are the physicists.

[Anonymous No.5029741]

>And no, mathematicians, you don't know anything about computer science. You can't just say "it's math, therefor I understand it."
who claimed that exactly?

[Anonymous No.5029746]

>infantile cartoon
reported

[Anonymous No.5029765]

>computer science
>science

http://www.youtube.com/watch?v=lL4wg6ZAFIM

[Anonymous No.5029768]

Mill's fallacy itt........
Just because salt tastes salty in the past IS NO GUARANTEE that salt will taste salty in the future. This is a basis of Pragmatism, just like Hume's doubt - you can't see cause and effect. Regardless of how you define computation,,,,you are only TRYING TO PREDICT AND MANIPULATE THE FUTURE,,,a trick we are especially good at compared to other plants and animals, but still have a long way to go before we become gods.

[Anonymous No.5029789]

>>5029657
Hat off for explaining in such detail.

Maybe my definition of computation is too broad. E.g. the geometric steps you described could also be seen as computations.

I think what OP was getting at is, that since the world (and therefore humans and therefor our language) work under laws, which work by taking some input and transforming it to some result = computation. Therefor he states, that math is based on computations (done by humans). Thus at the very core you would have to deal with computations to understand stuff.
Then OP goes all herpaderp Comp. Sc. > Math since comp. sc. is all about computation.

[Anonymous No.5029795]

>>5029746

please stop using the word 'infantile' or I shall have the waiter spit in your yogurt.