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/sci/ - Science & Math

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7362615 No.7362615 [Reply] [Original]

Funniest STEM terms: go.

>Wiener measure
>Tits group
>hairy ball theorem

>> No.7362625

>>7362615
when a foreign professor says "Sine theta", it sounds like boob tits in Spanish.

>> No.7362632

>computer scientist

>> No.7362636

>>7362625
In Dutch subtraction is "aftrekken", which also means jacking off / to fap in Dutch. Everyone tries to avoid using it but sometimes they fail, quite funny when everybody does their best to ignore it, but can't help but thinking of throbbing cocks.

>> No.7362645
File: 2 KB, 210x230, 1316338075182.png [View same] [iqdb] [saucenao] [google]
7362645

>>7362632

>> No.7362647

>>7362632
kek
>>7362636
Now I want to see a Dutch qt mathematician say this on accident and blush... sounds unrealistic sadly.

>> No.7362654
File: 2 KB, 178x167, 1344172499743.png [View same] [iqdb] [saucenao] [google]
7362654

>>7362632
>>7362632

>> No.7362668

>>7362647
>I want to see a Dutch qt mathematician say this on accident and blush
It wouldn't be very hawt, since Dutch is such a harsh-sounding language.

>> No.7362677

>>7362668
>not wanting a qt who swears like a sailor as you pound her ass

>> No.7362683

>>7362668
>tfw parade is full of rain now

>> No.7362698

>>7362615
>killing fields

>> No.7362705

>theoretical computer scientist

>> No.7362711

>theoretical computer science

>> No.7362749

>>7362615
>Sonic Hedgehog gene/protein
>Robotnikinin, inhibitor of SHH
>pikachurin
>literally fucking anything found in Drosophila

>> No.7362776

>>7362615

there is literally nothing wrong with wildberger. you are just mad because he challenges your outddates "science". rational geometry is the most beautiful thing since pythagorean theorems.

>> No.7362794

>>7362749
It's not so funny if you have a fatal mutation in your "sonic hedgehog" gene.

>> No.7362804

>>7362776
Oh lord, I should have known better than use Maymay Wilberger for my filler picture. Rational geometry is just a synthetic theory made by Wildberger so that he can feed his dilusions rigorously.

>> No.7362841

>geology
dykes and cleavage

we all had a giggle in gcse geology

>> No.7362843
File: 10 KB, 251x248, smug3.jpg [View same] [iqdb] [saucenao] [google]
7362843

>>7362632

>> No.7362854

>>7362794
then why am I laughing?

>> No.7362865

>>7362804

delusions? lol this is why academia is so fucked. you jews always get buttblasted when a new innovative approach is introduced.

>> No.7362867

>>7362804
who is this wildberger? I found his math history lectures on day while bored and I recognize his face and for /sci/ memes but I don't know his whole deal.

>> No.7362877

>>7362854
because you're an autist?

>> No.7362880

>>7362867
He is trying to purge math of impure real numbers.

>> No.7362883

>>7362880
Why? Explain to a dirty engineer.

>> No.7362884

>>7362865
> innovative
lol what part?

On the subject.
I can't find a wildberger video about solving differential equations like y'=y.
The calc video I saw only applies to polynomials and as such can't really be used on anything that has an infinite taylor series

>> No.7362887

>>7362880
>impure
What kind of mathematician cares about something as stupid as that?

As long as the reals are internally consistent, there should be no problem.
Or does he actually think that the real number system is inconsistent?

>> No.7362893

>>7362883
he's a constructionist and finitist.
all constructions of reals involve assuming they exist.

he's got videos on the other constructions and why they're bad.

>> No.7362900

>>7362893
this sounds like a nebulous philosophy of math issue, rather than a issue of actual mathematics, does this actually matter or is it just philosophical wanking?

>> No.7362913

>>7362900
It's mostly wanking but sometimes tasty stuff comes out when mathematicians do it right.
The trig stuff is great. I can't get behind his approach to analysis yet however.

>> No.7362926

>>7362913
So it worth taking a look? He has like 400+ videos on his channel, should I look at his "wildtrig" playlist

>> No.7362935

>>7362893
Calling that guy a constructivist is a disgrace to constructivism.

>> No.7362938
File: 103 KB, 602x652, image.jpg [View same] [iqdb] [saucenao] [google]
7362938

>>7362926
His algebraic topology lectures are cool. I never had the courage to sit through his trig stuff though, he would always start criticizing the reals with no real arguments (heehee), it always sounded too crackpot-y (there's nothing wrong with the material itself but when I see someone on youtube taking videos of themselves criticizing 'muh establishment', it doesn't make me want to listen)

>> No.7362940

>>7362926
I can't find the video I saw on rational trig. It was one recommended by /sci/. That playlist should cover everything eventually though.


This video is cool if you like neat calculus tricks.
https://www.youtube.com/watch?v=fKi5wGTw31g
you can pick up what a polynumber is if you skim the videos right before

>> No.7362943

>>7362940
I think I found it.
https://www.youtube.com/watch?v=dVk3CpjHR4Y

>>7362935
I've heard him called an ultra-constructionist?

>> No.7362944

>>7362940
>>7362938
So is he generally considerd a mixed bag? I thought his math history lectures where pretty interesting, I do think he made some jabs at "modern mathematics" at points in them.

>> No.7362949

>>7362944
I haven't found any videos I strictly dislike.
But I've had crackpot professors before.
They're kinda fun. You just don't swallow everything they give you.

>> No.7362963

>>7362938
His algebraic topology class barely covers any algebraic topology. In the sense that you would fail any alg top exam only having learned from those lectures

>> No.7363001

>>7362632
computation scientist pls

>> No.7363005

>>7362636
>when everybody does their best to ignore it, but can't help but thinking of throbbing cocks.
Engineer detected

>> No.7363007

>Computer Scientist

>> No.7363010

>>7362794
GOTTA GO FAST

>> No.7363985

>>7362625
Wheel I was in high school, I had a teacher from Kenya who pronounced theta as "theter" (sounds like "hater").

>> No.7364044

>>7362615
does me being so shit that i have to use a newton, einstein and pascal playing hide and seek joke to remember that pascals = N/m^2 count? other conversions and such i do fine, but can never remember that one without the joke.

>> No.7364047

>topology teacher keeps talking about balls

>> No.7364053
File: 100 KB, 575x317, Screen Shot 2015-06-30 at 08.32.56.png [View same] [iqdb] [saucenao] [google]
7364053

>>7362893
No construction of the reals assume the reals exist, that would be assuming what you want to prove. Look at the picture I uploaded, that theorem is proved by Dedekind's construction of the reals, you seriously think the proof of it goes "assume the reals exists already, QED"?

>> No.7364058

Latus rectum. hehe

>> No.7364088
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7364088

>group homo

>> No.7364098
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7364098

>>7363010
Kek

>> No.7366266

>>7362887
He's probably a dirty Pythagorean fundamentalist.

>> No.7366295

>>7362893
>all constructions of reals involve assuming they exist.
You are dumber than Wildberger, holy shit.

>>7362935
This, more or less. Wildberger is not a constructivist, he is a finitist.

>>7362943
>I've heard him called an ultra-constructionist?
ultra-constructivist and ultra-intuitionist are terms sometimes used as synonyms for finitist, however they are not the same thing as intuitionist.

The reason for the naming is that in finitist mathematics one does not assume the law of the excluded middle and one has restrictions when it comes to infinity. An example of finitist mathematics would be when dealing with the set of feasible numbers.

>>7364053
I don't like how informal this is. When using Dedekind's construction it's not really the case that Q is a subset of R. Rather there exists an isomorphism from Q to a subset of R. This is because Dedekind constructs Q as a set of ordered pairs with operations defined on them while he defines R as a set of cuts (where each cut is an ordered pair of sets of rationals) with entirely different operations defined on them.

Furthermore, no matter how you cut it we're still ultimately relying on a set of axioms. Dedekind just proves that the reals exist in ZFC set theory.

It is worth mentioning that most modern introductory analysis texts sidestep the issue by giving a list of axioms for the real numbers. Unfortunately every text I've seen (that uses axioms) foregoes the proof that the axioms uniquely define the reals (i.e. every model of the axioms is isomorphic to the reals). Coupling this with Dedekind's construction we've got existence and uniqueness in ZFC.

>> No.7366299

>>7362615
>Ctrl+F
>Cox-Zucker machine
>no results

>> No.7366303
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7366303

>> No.7366309
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7366309

>> No.7366338

>>7366295
If he is a finitist, then rather a very extreme one. As one understands finitism as Hilbert did, it's almost indistinguishable from constructivism a la Bishop.
Wildberger is rather an orthodox algebraist. But as he (hopefully) proceeds with his on-sequences, he will quickly realize how close he is to ordinary constructive math and so he wouldn't discover anything new.

>> No.7366397

Sorry, I just realized I conflated finitism with ultrafinitism. In finitism you assume the Naturals exist and in ultrafinitism you do not. Ultrafinitism is more general than intuitionism and finitism and both of those are more general than classical mathematics.

https://en.wikipedia.org/wiki/Ultrafinitism
https://en.wikipedia.org/wiki/Finitism#Other_related_philosophies_of_mathematics

I am not sure which, if either, Wildberger identifies as. I know he's often concerned with whether or not a set is recursively enumerable (i.e.it's indicator function is computable). So this makes me think he's an ultrafinitist. However other times he seems totally fine with the naturals so he may just be a finitist.
https://en.wikipedia.org/wiki/Recursively_enumerable_set

Either way, ultrafinitism is still very interesting. Here's a cool paper on feasible numbers.

http://www.researchgate.net/profile/Steven_Lindell/publication/220696482_A_Constant-Space_Sequential_Model_of_Computation_for_First-Order_Logic/links/0deec5329ef19c1308000000.pdf#page=38

>>7366338
You obviously have no understanding about the things you're talking about.

>> No.7366449

>>7363985
Holy shit Ive heard people talk like that before, biggest fucking pet peeve.

>> No.7366463

>>7362615
Cox-Box test

>> No.7366469

>>7362749
Why did they think it was good idea to call a signalling pathway "hedgehog", let alone one of the proteins "Sonic hedgehog".

>> No.7366472

>>7362636
Engineer detected

You only say aftrekken in sentences like "we trekken x van y af" or "we moeten x en y van elkaar aftrekken", it then loses its meaning of jacking off

>> No.7366481

>>7362636
>Everyone tries to avoid using it
Dutch here, you must be in elementary school.

>> No.7366483

>>7362668
krijg de tering hoerenjong

>> No.7366489

Read a paper about potato proteins
Couldn't get the image of retarded proteins out of my head

>> No.7366501
File: 575 KB, 1200x1125, 4a3518c62b8570bf3a398214f78dcc26.jpg [View same] [iqdb] [saucenao] [google]
7366501

>>7366489
Link to paper. Desire to read about potato proteins.

>> No.7366509

>>7366501
Sorry anon was a while ago and just read the abstract actually (was looking for something else)

>> No.7366517

HOMO ERECTUS.
IT IS ACTUALLY CALLED
HOMO
ERECTUS

>> No.7366522

>>7366517
Only funny until you learned a minimal amount of Latin and realized just how retarded a term 'homosexual' was. Was quite funny when you first heard of em as a youngster though.

>> No.7366545

>>7366517
So?

>> No.7366578
File: 84 KB, 600x600, bazinga.jpg [View same] [iqdb] [saucenao] [google]
7366578

>> No.7366765

Sometimes you'll see the seifert–van kampen theorem notated SvK. It's funny because S and K are commonly used names for topological spaces and v notates the topological wedge sum... Mathematicians are not known for their sense of humor.

>> No.7366769

>>7366765
Oh yeah, and the siefert van kampen applies to the wedge sum most of the time. So you can name your spaces S and K beforehand and set up a joke where you say SvK because SvK QED.

>> No.7367000

>>7366522
And then when you get into your 20's you're usually secure enough to laugh at silly things again

>> No.7367005

>>7366397
He doesn't believe that there "are" an infinite amount of prime numbers, arguing with the finite ways of encoding stuff, so yeah

>> No.7367056

>>7367000
I saw a whole classroom laugh when it was time to discuss the "hairy ball theorem."

>> No.7367919

>>7366303
I just top lel'd at that one, friend.

>> No.7367927
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7367927

>>7363005
top kek

>> No.7367933
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7367933

>>7362804
>that feel when the meme image you created is posted by someone else and derails the thread

>> No.7367934

>>7364053
Show me a dedekind cut then without just stating that there is such a set.

>> No.7367942

>>7367934
>google is haaaaaaaaaaaaaard
https://en.wikipedia.org/wiki/Dedekind_cut

>> No.7367945

>>7367942
Are you illiterate or just stupid?

>> No.7367949

>>7367945
Neither, you drooling mongoloid.

>> No.7367950

>>7367933
Damnit anon.

>> No.7367954 [DELETED] 

>>7367933
It's a good image.
>>7367949
cool have fooled me.

>> No.7367956

>>7367949
could have fooled me.

>> No.7367958

>>7367933
Fuck you steve, I created that image first,

>> No.7367971

>>7367942
Chaitin's constant is a real number. Please write down its Dedekind cut for me.

>> No.7367973

>>7367934
>>7367942
>>7367971
Goddammit, just use fucking Cauchy Sequences.

>> No.7367980

>>7367973
Please write down a Cauchy sequence in the equivalence class of the "real" number <span class="math"> \Omega [/spoiler], where <span class="math"> \Omega [/spoiler] is Chaitin's constant associated with the programming language of your choice.

>> No.7368003

>>7367971
OK, The cut is between A and B where A is the set of all rationals approximating the probability of a random program halting from below and B is the set of all rationals approximating the probability of a random program halting from above.

>> No.7368018

>>7368003
This is a circular definition. You haven't written anything down.

You claim to have constructed the reals. In standard mathematics, it is assumed that Chaitin 's constant is one of your so called "reals". That means that you should be able to write down the Dedekind but for it without referring to the object you're constructing. So do it.

>> No.7368040

>>7368018
How is it a circular definition? Are you going to argue that Chaitin's constant isn't well defined? Because it is: the probability of a random program halting. What is circular about this?

This is a rather bad argument to use because it seems you are confusing computability with definability.

http://web.maths.unsw.edu.au/~jim/newsteadcontinuum.pdf

>That means that you should be able to write down the Dedekind but for it without referring to the object you're constructing.
The entire point of the Dedekind cut is to describe the object, so there is no way for me to not refer to the object. What would make it circular logic is if I referred to the number itself. But I'm not. I'm referring to approximations of a defined probability, whether or not that probability is real. This is no different from referring to the number which equals 2 when squared.

>> No.7368043

>>7368040
*approximations of the number which equals 2 when squared

>> No.7368049

>>7362636
>but can't help but thinking of throbbing cocks.
>>7362677

the first thread i go to on this board and i cant stop laughing

>> No.7368053

>>7368040
Incorrect. If you cannot see why you the definition of <span class="math"> \sqrt{2} [/spoiler] as the set of all rational numbers less than <span class="math"> \sqrt{2} [/spoiler] is circular, then you may need to have your head examined, as it assumes the existence of what you are attempting to construct.

<span class="math"> \Omega [/spoiler] IS CLAIMED to be a real number, that satisfies some property, namely it is the "probability" that a random program in a given language halts.

If you are telling me that this number is a so called "real", and you are also telling me that you have constructed all "reals", then you can construct the "real" a priori without assuming it has the properties this number is supposed to have. i.e. without assuming the existence of <span class="math"> \Omega [/spoiler], construct a "real" <span class="math"> X [/spoiler] and show me that this <span class="math"> X [/spoiler] satisfies the property that in fact <span class="math"> X=\Omega [/spoiler]

>> No.7368055

>>7368040
> This is no different from referring to the number which equals 2 when squared.
exactly. You cannot construct a real number equaling the sqrt(2) until you assume that such a number could exist.

There's nothing wrong with this and there's plenty of math that finds this useful.

>> No.7368072

>>7368043
I see you corrected your mistake. Now make a similar correction for <span class="math"> \Omega [/spoiler] without assuming its existence and I'll be happy.

i.e. if I doubted the existence of <span class="math"> \sqrt{2} [/spoiler] you could show me a sequence of rationals that when squared approach two with arbitrary precision, and I would be happy to identify this sequence as <span class="math"> \sqrt{2} [/spoiler] because it satisfies all the relations I expect from a so-called "square root of 2".

I challenge you to come up with a similar solution to <span class="math"> \Omega [/spoiler]

>> No.7368074

>>7368053
>Incorrect. If you cannot see why you the definition of 2 as the set of all rational numbers less than 2 is circular
But that's not my definition you numbskull. Square a rational number. Is it less than 2? Then it goes in set A. Is it great than 2? Then it goes in set B.

The analogous process for Chaitin's constant would be to guess some rational number as the digits of Chaitin's constant and calculate the halting problem for all programs up to the size in bits of your guess. Depending on the halting of the program, each guess can be placed into its proper set. Thus we have a definable process, but one that can't be computed due to the halting problem.

>> No.7368083

>>7368074
>This is no different from referring to the number which equals 2 when squared.
This amounts to referring to <span class="math"> \sqrt{2} [/spoiler]

>Thus we have a definable process
I didn't ask you to define a process. I asked you to produce its Dedekind cut, or Cauchy sequence. You claim to have constructed all of them, so where is it.

>> No.7368090

>>7368083
>This amounts to referring to sqrt2
I corrected myself, so quoting my uncorrected sentence is just misleading.

>I didn't ask you to define a process. I asked you to produce its Dedekind cut, or Cauchy sequence. You claim to have constructed all of them, so where is it.
Defining a process is producing a Dedekind cut. This is like saying "You have to compute every rational which is below 2 when squared". My definition of the set is the construction. Again, learn the difference between computability and definability. Computability has nothing to do with construction.

It's well known that there is an algorithm that can enumerate all rationals less than Chaitin's constant, this is all you really need to construct the cut, and I did describe it.

>> No.7368105

>>7368090
>Computability has nothing to do with construction.
I didn't say anything about computability, I just asked you to produce the cut for <span class="math"> \Omega [/spoiler]. You gave me an interesting answer.

The difference for <span class="math"> \sqrt{2}[/spoiler] is that from each rational I have a thousand algorithms to produce another one in the the cut that when squared will be closer to 2. I am able to predict how closely I will emulate the ideal property I desire. For your process, there is no such guarantee. So why should I be happy identifying the rationals that come of this process with a number that satisfies the supposed properties of Omega?

> My definition of the set is the construction
well, I define Bob's constant <span class="math"> B [/spoiler] as the the cut of all rationals such that when those rationals take their dogs for walks, they clean up after it when it takes a shit on someones lawn.

>> No.7368114

>>7368105
>I didn't say anything about computability, I just asked you to produce the cut for . You gave me an interesting answer.
Which I did.

>The difference for 2 is that from each rational I have a thousand algorithms to produce another one in the the cut that when squared will be closer to 2. I am able to predict how closely I will emulate the ideal property I desire. For your process, there is no such guarantee.
The only guarantee needed is that the set of the rationals exists. Dedekind cut has nothing to do with the order in which you produce these rationals. This is only for your peace of mind, but it has nothing to do with the problem at hand.

>So why should I be happy identifying the rationals that come of this process with a number that satisfies the supposed properties of Omega?
Because that's the Dedekind cut.

>well, I define Bob's constant B as the the cut of all rationals such that when those rationals take their dogs for walks, they clean up after it when it takes a shit on someones lawn.
Again, it seems like you are implying the halting problem is not well defined. It is not random concepts attached to numbers.

>> No.7368130

>>7368114
>The only guarantee needed is that the set of the rationals exists. Dedekind cut has nothing to do with the order in which you produce these rationals. This is only for your peace of mind, but it has nothing to do with the problem at hand

I didn't say there was a problem. I don't claim cuts aren't well defined. I have asked many people to construct the cuts they're talking about you're the first of many to actually explain how its done.

>Because that's the Dedekind cut
Not really good enough, as I only have access to a finite number of the members of the cut, and no algorithm to get me rationals closer and closer to satisfying the property the cut is defined to satisfy.

Ultimately I want to do arithmetic with real numbers. Depending on the language being used, the rationals may never even be good enough for me to write down the first digit in base 10.

>> No.7368151

>>7368130
>Not really good enough, as I only have access to a finite number of the members of the cut
So what?

>and no algorithm to get me rationals closer and closer to satisfying the property the cut is defined to satisfy.
The cut is not defined to satisfy computability.

>Ultimately I want to do arithmetic with real numbers
What exactly is arithmetic with an uncomputable supposed to prove?

>> No.7368163

>>7368151
>So what?

Because I am being charitable in allowing a potential process to stand in for a cut. In reality, when I can only look at a finite amount of rationals in the cut, which rationals they are becomes important to me. That problem can be remedied for <span class="math"> \sqrt{2} [/spoiler], not so for Omega.

>What exactly is arithmetic with an uncomputable supposed to prove?

What do you mean prove? Real numbers come defined with laws of arithmetic, no? There is no arithmetic with uncomputable numbers if I can't write down the first digit of it. For each language, at a certain point I can never produce another digit and hence cannot tell it apart from any other number within that "vicinity". If the vicinity happens to be the first fucking digit, that's even more asinine because I like to have at least 1 digit accuracy when I do arithmetic.

>> No.7368179

>>7368163
>Because I am being charitable in allowing a potential process to stand in for a cut.
*facepalm* What exactly do you think a Dedekind cut is? How do you define a particular infinite set if not by a potential process of choice?

>In reality, when I can only look at a finite amount of rationals in the cut, which rationals they are becomes important to me.
You can only look at a finite amount of anything. This has zero bearing on what mathematically exists though. And again, the order of the rationals is irrelevant to the cut. We are not talking about anything mathematical now.

>There is no arithmetic with uncomputable numbers if I can't write down the first digit of it.
Writing down digits has nothing to do with arithmetic. Since the Dedekind cuts are defined, the Dedekind cut of the sum must also be defined. What is the sum of pi and e? Pi+e. Notice how no digits are involved.

>For each language, at a certain point I can never produce another digit and hence cannot tell it apart from any other number within that "vicinity".
Luckily we are not using digits to show the uniqueness of reals. That's what Dedekind cuts are for. None of your complaints are relevant.

>> No.7368198

>>7368179

>This has zero bearing on what mathematically exists though. And again, the order of the rationals is irrelevant to the cut. We are not talking about anything mathematical now.
yes we are talking about something mathematical. We are talking about, at least implicitly, about what kind of objects one wants to admit into their consideration. Pathological objects are not particularly interesting to me, nor are objects that I can never specify with a desired precision in any reasonable system of representation.

>Writing down digits has nothing to do with arithmetic
> What is the sum of pi and e? Pi+e
Pi and e can be easily computed to arbitrary precision.

>Luckily we are not using digits to show the uniqueness of reals
I didn't say they aren't unique. It's just that if I have a number but can in principle never know whether its first digit is 0 or 1, then I cannot do anything meaningful with it. If you find a use for such a number let me know

>> No.7368222

>>7368198
>We are talking about, at least implicitly, about what kind of objects one wants to admit into their consideration.
How is what YOU want to consider mathematical? Is your favorite number a field of mathematics?

>Pathological objects are not particularly interesting to me, nor are objects that I can never specify with a desired precision in any reasonable system of representation.
No one cares.

>Pi and e can be easily computed to arbitrary precision.
And what does that have to do with arithmetic?

>It's just that if I have a number but can in principle never know whether its first digit is 0 or 1, then I cannot do anything meaningful with it. If you find a use for such a number let me know
Yes, the halting problem is so useless! It's so uninteresting! All these mathematicians are just pretending to be interested by it!

The only useless, boring object here is your feeble finitist jabbering.

>> No.7368266

>>7368222
>How is what YOU want to consider mathematical? Is your favorite number a field of mathematics?

It's a shared discipline. We agree more or less upon what objects we are going to study. We are also finite. Whenever we move from abstract descriptions to concrete representations we have to do make do with finite strings of symbols. How nimbly one can move from definitions to calculations of objects that approximately or exactly respect the properties of the definition is something that matters in mathematics.

If everything that can be defined easily satisfied that criteria this would not come up. Some objects are questionable, so we discuss it. One may argue, though I haven't and wont, that it is not wise to talk about things that can never be specified satisfactorily in such a language.

>And what does that have to do with arithmetic?
You are just being deliberately obtuse. You know perfectly well that the inability to specify the first digit of a number in a finite language means you cannot calculate it within a rather large range of error. I understand that you can specify an algorithm to produce rationals in their respective cuts and add those rationals together, but that by itself is not enough for a satisfactory theory of arithmetic in <span class="math"> \mathbb{R} [/spoiler]. Symbols commuting around a "+" sign is not arithmetic.

>Yes, the halting problem is so useless! It's so uninteresting! All these mathematicians are just pretending to be interested by it!
It's solved, no? The answer is it's not decidable. That's why it is interesting. I'm not saying don't study computability.

Also, I'm not a finitist. I look at things from different perspectives. Since you're becoming increasingly dismissive and insulting, goodbye.

>> No.7368990

>>7366303
top lel

>> No.7369033

>>7368266
>How nimbly one can move from definitions to calculations of objects that approximately or exactly respect the properties of the definition is something that matters in mathematics.
No it really isn't. Not in the way you're discussing it. No mathematician besides Wildburger is saying that we should abandon the reals because some reals are incomputable. It just makes no sense and you are parroting him without even having an underlying argument or position. Why is this interesting if you think it is not a criterion for what should be discussed?

>You know perfectly well that the inability to specify the first digit of a number in a finite language means you cannot calculate it within a rather large range of error.
Yes, and I'm asking why you are pointing this out. Why is this relevant? You pointed out that an incomputable number is incomputable. Woopdeefuckingdo. Where is the point?

>but that by itself is not enough for a satisfactory theory of arithmetic in R.
It is though. It's easily proved that arithmetic of the reals, including incomputables, is directly implied by the definition of the reals through Dedekind cuts. You are simply pointing out that something you can do with the rationals cannot be done with the reals, but this does not mean you can't do arithmetic, it just means we are talking about two different things. It's simply the incorrect application of your expectation to a definition that doesn't require what you expect. Do you complain also that you can do things with integers that you can't rationals? Oh no there's no successor of 3/4, I guess that means rationals are not "satisfactory".

>It's solved, no? The answer is it's not decidable. That's why it is interesting. I'm not saying don't study computability.
You just said uncomputables are useless because you can't add their digits. Do you not see how this is stupid and not mathematically valid?