He does not believe in pi, but does he allow sqrt(2) and 1/3 even though we cannot write them down entirely in decimal form ?
>>8000985
Who is this guy and what does he do?
>>8000985
>doesn't believe in π
>has literally never seen a circle
>>8001089
Norman J "Complains math is not rigorous enough then defines numbers as strokes on a board" Wildberger
>>8001292
Pretty sure he says that math should be intuitive and people who claim it is rigorous believe in made-up things like the real numbers
>>8001321
He does have a point.
Real numbers are made up, there's nothing real about them.
>>8000985
Yes to 1/3
Not really to sqrt2
I hate that he goes out of his way to avoid reals and then when he *has* to take a sqrt he says we can approximate it
>>8001292
That may be the best possible definition. It's something entirely concrete that we can see.
>>8001321
No. He wants math to be more rigorous. He thinks adding ... to the end of a number is the least rigorous thing one could do and his entire life is dedicated to doing away with this concept and replacing it with more rigorous definitions.
>>8001336
This more rigorous means more elegant and what elegant about an infinite real number
>>8001336
He doesn't even construct his new concepts.
Anyone claiming he's rigorous, doesn't seem to know what rigor is.
I love his work, but I've yet to see any rigor behind it.
>>8001347
Lol I'm not claiming that at all.
>his entire life is dedicated to doing away with this concept and replacing it with more rigorous definitions.
I never said he was good at it
>>8000985
1/3 is rational
>>8001095
what is pi?
the ratio between a circle's circumference and its diameter
how do you prove this thing is a constant for all circles????
>>8001371
A circle is defined as having the largest area possible for a given perimeter. This will always result in the same shape, no matter what the radius is, and so all circles are similar to one another. This isn't the issue. Wildberger's problem is that he doesn't think all circles are similar just because a circle can't actually exist. It's just a definition, it's words describing an ideal. All it takes is a little imagination and you can accomplish wonders.
>>8001396
Wildberger actually defines circles parametrically
https://www.youtube.com/watch?v=bmEM75lTLes
https://www.youtube.com/watch?v=xp0H3Aw0j6E
>>8001404
ITT: brainlets
Possible pleb question here, but how can you believe or not believe in a number?
>>8001386
1/3 = .3333... only applies in some bases. sqrt(2) and pi are irrational in all bases.
>>8003165
I don't believe in 6 million.
>>8003165
I believe that the number 3 doesn't exist, fight me faggot
>>8003165
It's a philosophical question. IMHO, obviously numbers don't exist. They're just constructs of language that we've invented in order to aid us in describing the world around us in an unambiguous and precise way.
For some people, math is not a mere construct, or something. I don't really understand their position, because it looks literally incoherent to me, like "not even wrong" territory. Look up the word "Platonicist".
http://plato.stanford.edu/entries/platonism-mathematics/
See if you can make any sense of it.
>>8003450
>Light doesn't exist.
>I mean... we observe it so it's a concept of the human mind. If we weren't around there would be no light.
Space exists and matter exists so numbers exist
>>8003465
I test the existence of light. Light has observable effects. I cannot create a falsifiable test for the existence of the number 2. I don't even understand what it might mean for the number 2 to exist. Your analogy is flawed.
>>8003424
Except base pi or sqrt(2) respectively.
>>8003438
subtle, /pol/, real subtle
Burger is human trash and the cult made by a handful of /sci/ cretins is pathetic.
Whenever people refute his claims with proofs and examples he essentially puts his fingers in his ears. When this inevitably is insufficient he will end up attacking the other party personally by basically calling them a shill. This is not how you have a mathematical conversation in the adult world.
>>8000985
Well, science is a debate.
>>8004047
Not to be pedantic since this doesn't address your point, but most mathematics is not science by definition of science. There's a reason then M is separate in STEM
>>8004065
http://philosophy.stackexchange.com/questions/30865/what-is-the-relation-between-proof-in-mathematics-and-observation-in-physics
>>8004065
Yeah mathematics are not a science. Not saying that one is better than the other. Just different. Science uses mathematics shouldnt be confused with maths are a science. A mathematician will never introduce himself as a scientist
>>8004033
Pretty much. The only following he has are 17 year olds on /sci/ who can't understand him but like the memes.
Just so I get this straight:
Euclidean and Pythagorean, but he reject anything later than Archimedes?
No PhD in mathematics is that stupid.
I'm missing something.
>>8004091
[Different anon]
I like to think of mathematics as existing as an exploration of representational axioms and theoretical axioms, and science as an exploration of the physical world based on theories posited in both philosophy and mathematics.
Is that fucked? It's probably fucked.
>>8004103
exactly
science and specificly physics is the "child" of philosophy and mathematics. Ancient Greek "scientists" were philosophers.
With Archimedes being the first one to distinct the two
>>8004065
The real million dolla question is why is there a T.
>>8004103
>>I like to think of mathematics as existing as an exploration of representational axioms and theoretical axioms
this is mathematics seen as a logician.
mathematics are about formalizations of your speculations (which you form from your desire to see things that you experience [the empirical world], through induction, as similar or dissimilar) to the point that you have a structure more formalized than your speculations structured in natural languages.
Logic is just a the formalization of your speculations about *validity of inferences*, so here logic is a formal part of mathematics.
It turns out that plenty of mathematical structures are cast into some formal deductive logic (like set theory formalizes your structures of numbers).
Philosophy is just structuring and formalizing in natural languages.
Science is just claiming that your formalized structures (in formal languages or not) gives you access to some *reality*, more or less hidden with respect to what you are conscious of[=<the empirical world].
Same thing for the religions which go beyond empiricism.
Some mathematicians, typically Brouwer, think that mathematics should, equally to the speculations (however formalized) of the scientists, talk about the empirical world. So typically, your formal symbols are real entities: these entities belong to some world and they connect or not back to the empirical world.
>>8001089
kek is that really piper?
>>>>8004161
The construction of all of R is literally in chapter 1 of rudin.
Clearly you haven't studied any math beyond the engineering curriculum. Off yourself, grown ups are talking
>>8003522
Bases must be wholes brainlet
>>8004192
>It turns out that plenty of mathematical structures are cast into some formal deductive logic (like set theory formalizes your structures of numbers).
I meant your usual set theory cast in FOL.
Set theory is just a structure too and it turns out that you can interpret a part of this structure as some kind of numbers.
>>8004197
>The construction of all of R is literally in chapter 1 of rudin.
>>8004168
Technology?
>>8004261
what's that?
>>8000985
A word that starts with the letter T
>>8004266
and ends with Y?
>>8004268
Yeah.
It sounds pretty cool and it's fancier if you say STEM instead of SEM, so just throw it in there.
this is how R is built in Hott
>>8004192
>Some mathematicians, typically Brouwer, think that mathematics should, equally to the speculations (however formalized) of the scientists, talk about the empirical world. So typically, your formal symbols are real entities: these entities belong to some world and they connect or not back to the empirical world.
to be clearer,
the symbols are names of real entities and, since you begin always from the empirical world, this world constrains you on the creation and usage of these real entities. then these real entities can or cannot belong to some other world as well.
[For brouwer, you never leave the empirical world I think]
I think that wildberger might be like brouwer
>>8003438
Undercooked roast.
>>8000985
>He does not believe in pi, but does he allow sqrt(2) and 1/3
This is reasonable. If you allow integers then you might as well allow fractions, and it's not unrealistic to include algebraic numbers as well. This is still a countable set so the Berg can avoid sperging out over uncountability.
>>8004404
he spergs out over any infinite set at all
>>8004254
This the level of argumentation you get when dealing with Burger and his 17 year old precal brainlet
>better us le ebin maymay arrows since I have no counterpoint lefevere xddd
>>8004194
Piper Perri, yes.
>>8001319
Fuck off, I always avoid sci memes like Langan and this faggot
so what's his deal? he doesn't believe in real numbers?
what does he say about cantor's work
>>8004197
He's already covered the relevant materials in Rudin
>>8000985
sqrt(2) and 1/3 can be written in systems other than Base 10 so they're okay
Kripke's thesis is that objects have essences, properties that belong to them of necessity, not accidentally, these properties single out "natural kinds" of objects that "carve nature at the joints" rather than according to our cultural biases, practical needs, etc., those would be the "artificial kinds". This provides a semantic framework for a realist ontology, as opposed to semantic theories of Quine and Wittgenstein that reduce meaning to use in a language game, which requires no realist referents, or deny such referents to "natural kinds", which only acquire meaning as placeholders in a theoretical "web of belief". E.g. gold, water, etc., only mean in the context of chemistry, which relates to experience only as a whole, and reflects pragmatic human considerations as much as nature. Of course, if "natural kinds" do "carve nature at the joints" then there is something "in nature" corresponding to them, even if we do not yet discern it fully and precisely. This provides a framework where Kripke-Putnam reference is preserved across scientific revolutions despite Kuhn's "incommensurable paradigms", this promise of continuity is what attracted Putnam, when he was still a realist, and others. Rigid designation is tangential to this, it enters only in that if we believe in nature given "essential properties" then it makes sense to keep them fixed across possible worlds when analyzing "physical" counterfactuals.
>>8005818
However, Kripke's essentialism is not "a path back to scientific realism", that would be putting the cart before the horse. It works if we presuppose a form of scientific realism, that would be scientific essentialism, but in itself it is a semantic theory that purports to describe use of language based on speakers' "linguistic intuitions" (similarly rigid designation purports to account for "modal intuitions"), not metaphysics. Ironically, Kripke himself is partial to Wittgenstein, and Putnam apparently discarded even his very weak "internal realism", which was of Quinean pseudo-variety. That folk intuitions are faithful to "reality" is also highly doubtful, or as Cummins put it "there is no more reason to think that innate philosophy is a good basis for philosophy than that innate physics is a good basis for physics". Cummins's Reflections on Relective Equilibrium is a sharp critique of Kripke-Putnam's approach in general:"It is commonplace for researchers in the Theory of Content to proceed as if the relevant intuitions were undisputed. Nor is the reason for this practice far to seek. The Putnamian take on these cases is widely enough shared to allow for a range of thriving intramural sports among believers. Those who do not share the intuition are simply not invited to the games". Recently even semantic adequacy of Kripke-Putnam's theory of natural kinds has come under fire, see Ben-Yami's Natural Kind Terms.
>>8004431
>This the level of argumentation you get when dealing with Burger and his 17 year old precal brainlet
Why don't you comment on NJ's videos and get a reply from the man himself. You think that beating a straw man here means anything, it really doesn't.
Also you have not written [math]\pi [/math] like that post asked you to, and I presume you cannot and let's be honest no one can.
>>8004161
[eqn] \pi = \frac{4}{1} - \frac{4}{3} + \frac{4}{5} - \frac{4}{7} + \frac{4}{9} - \frac{4}{11} + \frac{4}{13} - \cdots[/eqn]
Just one way, though there are many.
>>8001386
Irrational isn't a property of the number base at all. It basically says whether or not the number is an integer ratio
>>8001386
>yes but the decimal form of 1/3 is not ending
It is in base 3. Why should we give a shit about a base 10 expansion?
>>8000985
If this guy is serious then why isnt he giving lectures at top mathematical institutes rather than youtube viedeos to procrastinating 18 year olds?
>>8006412
You don't get to lecture at top mathematical institutes just because you're serious.
>>8006202
https://youtu.be/lcIbCZR0HbU
>>8000985
We need an Institute of Advanced Crank Studies. Some billionaire needs to fund this.
>>8006478
That was, without question, one of the most retarded videos I've ever watched.
>He doesn't believe in π
>pic related has π being used in the bottom right courner
I don't even think you tried.
>>8004290
>inhabited
Who the fuck says "inhabited" instead of "non-empty"?
>>8006684
Judging by the the YouTube shit I just watched he believes in pi, just not pi as an infinite string of numbers, no he seems to believe that the only true definition of pi is that which can be computed. So for example he only takes a computation by a couple of Asians as the current definition of pi because thst value actually exists somewhere, in this case on a hard drive.
It's more than a bit strange, since he doesn't seem to think that you can just keep applying the same algorithm again and again. Anyway fuck this guy.
>>8006698
The wild burger is only a /sci/ meme, fortunately. I do admit his videos on algebraic topology are good though.
>>8006418
>"muh conspiracy!"
>"jooos!"
>>8001396
>A circle is defined as having the largest area possible for a given perimeter.
yeah, no, that's not the definition of a circle, merely a property (that you can't prove).
>>8006690
They are not equivalent without EM
>>8004192
good post
is there a good /sci/ faq anyway?
>>8006678
check out his video on infinite sequences where he says that the classic proof of the infinitude of primes is incorrect
bii
>>8000985
>He does not believe in pi
Is he a friend of James Anderson (of "nullity" fame) and/or John Gabriel (of "new calculus" fame), mostly enjoying a reputation of cranks?
>>8007575
The circle is the unique thingy with that property so it's just fine as a definition.
>>8001386
Any rational number has finite-length representations in certain bases. Try base 3, you'll see that one-third will be represented as "0.1".
Base 10 is not inherent to maths in any way whatsoever. It's just what we use because we have ten fingers. As a matter of fact, any base is just a representation. It's "form" rather than "substance".
>>8008618
Also pi has a finite length in base pi.
Is the circle the only topological space with homotopy group Z?
>>8001396
>Wildberger's problem is that he doesn't think all circles are similar just because a circle can't actually exist.
Most (if not all) mathematical objects "don't actually exist". That's what separates maths form physics and other sciences which assume a physical world and its inherent limitations.
>>8008621
Can you have fractional (let alone irrational or even transcendental) bases?
>>8008632
Yes.
Pretty sure he doesn't into circles because circles are defined as the locus of points equidistant from a single point.
Its a set of infinite points and requires transcendental/analysis methods to get any properties.
And why stoop to using such methods for teaching trig when your high school students can't even into real numbers (as shown by all the .999=1 threads)
Circles are boring anyway. Triangles erryday
>>8008642
But that violates the rule to construct the naturals first and then everything else. Also, there would be non-equal distances between numbers represented by the glyphs of a number system (i.e. "digits"), and or the number "one" wouldn't be "1". All in all, it's really hard to make sense of it (let alone, practical usability).
PS anyone else tired of "click-a-mole until there's none left"-captchas?
>>8008658
Yes.
Fucking thing takes forever to fade with the next pic
>>8000985
So is Wildberger just a finitist?
>>8008658
Most mathematicians don't construct the reals as the set of infinite decimal numbers.
Re-writing a number as some weird base isn't part of some construction
>>8008658
>But that violates the rule to construct the naturals first and then everything else.
That's just a convention, not a fundamental law of all mathematics.
It is possible to believe the Peano axioms to be inconsistent, but only if you believe all models of Robinson arithmetic to be nonstandard.
In other words, if you believe every model of arithmetic has infinite descending chains.
Of course, even if you believe the latter, you can still believe PA to be consistent. There exist nonstandard models of PA.
Also, even if all models of arithmetic are nonstandard, if you believe in the consistency of ZF you believe in the consistency of PA.
So basically you have to be really daft to reject PA. You have to both reject set theory and visualize the natural numbers as having an infinite descending chain.
>>8008686
>peano axioms
the peano axioms are a simplification for people who are just studying math and need to work with N without having a set theory background
they're absolutely irrelevant
>>8006698
can you add algorithms?
try adding [math]\pi [/math] + [math]\pi [/math]
https://youtu.be/ScLgc_98XxM
>>8006678
retard here is (you).
>>8001328
>there's nothing real about them
There probably is. We don't know if the universe is continuous or discrete at the smallest scale. Since he's so hung up on things that are "intuitive," it definitely seems intuitive that the universe is continuous, hence, made up of real numbers.
>>8008669
Yeah, but this only became clear in a video 2 years ago.
Beyond that, from his finitist dogma he doesn't seem to even understand that if you don't adopt it, non-constructive theory can work out. He seems to be of the opinion that they are faulty.
>>8001371
You can prove it using logic. But he would throw out your proof for one of two reasons:
1) it uses axioms
2) a perfect mathematical circle doesn't exist in nature
>>8008764
2π?
>>8008804
1) you gotta start with some axioms, you can't define everything as you'll run out with notions usable in your definition otherwise;
2) maths is not physics, most (if not all) mathematical objects "don't exist in nature", (which should be pretty obvious I think).
>>8008655
He has a definition for circles idiot. And no, he doesn't define circles in that stupid way. Read the thread
>>8000985
Does this video pass the Wildberger filter?
https://www.youtube.com/watch?v=SrU9YDoXE88
>>8009187
he would be mad that "Vsauce Micheal here" sells his philosophical stance (that you can and should just make up axioms and study them for fun) as fact.
>>8004197
He made a video like 2 years ago pointing out the flaws of the construction of R on most popular analysis books. Including Rudin.
>>8008956
How does he define triangles?
As three functions?
>>8009386
The construction of [math]\mathbb{R} [/math] as the set of dedekind cuts modulo the canonical equivalent relation, endowed with the inherited order and algebraic structure, is literally completely unambiguous. There is no possible flaw, and no real mathematician thinks there is any possible flaw.
>>8009187
Even sauce man is catching onto the meme axioms.
>>8008831
math is so easy with [math]\rm I\!R[/math]s
Someone needs to go to a lecture and ask wilderberger what the biggest natural number is.
When he says, respond: but good sir, what about your number plus 1?
>>8010381
Wildberger disagrees:
https://www.youtube.com/watch?v=fXdFGbuAoF0
https://www.youtube.com/watch?v=jlnBo3APRlU
>>8010453
Neither video shows a flaw.
>>8010420
That's not Wildberger's view, watch the beginning of this video
https://www.youtube.com/watch?v=wPEYoW0Mj1U
https://www.youtube.com/watch?v=XKy_VTBq0yk
>>8006478
The Absolute Madman
Wildberger should read this.
But I heard that he does not like the axiomatic approach.
>This page is to provide non-technical or maybe semi-technical discussion of the nature and role of the foundational system for mathematics known as homotopy type theory. For more technical details and further pointers see at homotopy type theory.
https://ncatlab.org/nlab/show/homotopy+type+theory+FAQ
>>8011134
that was an interesting read, thanks.
>>8000985
I think in general he doesn't believe in infinite sets so in general no. However, I think that in his arguments (where he gives non-existence of infinite sets the benefit of the doubt) he says that these example irrationals aren't really a problem because you can describe them with computable functions. However given that the set of computable functions is countable then we can't describe all reals in this way and in fact the majority of reals end up on a very shaky foundation.
>>8003015
new picture, nice
Kant only had three epistemic categories, analytic a posteriori are highly problematic (even Kripke talks only about necessary a posteriori). As for π it was originally defined as a ratio of the circumference to diameter, and only two thousand years later related to numbers and decimal expansions. Still, one could define it as a number using one of many series expansions, continued fractions, etc., known in Kant's time. Regardless, like all arithmetic and geometry all such definitions (or rather constructions implied in them) are synthetic a priori, the difference would only be whether it is a priori synthesis in space (geometry), or in time (arithmetic).
Kant gives a famous example of a similar synthetic a priori in the Critique of Pure Reason, 7+5=12:"The concept of twelve is by no means thought by merely thinking of the combination of seven and five; and analyze this possible sum as we may, we shall not discover twelve in the concept. We must go beyond these concepts, by calling to our aid some concrete image [Anschauung], i.e., either our five fingers, or five points (as Segner has it in his Arithmetic), and we must add successively the units of the five, given in some concrete image [Anschauung], to the concept of seven. Hence our concept is really amplified by the proposition 7 + 5 = 12, and we add to the first a second, not thought in it. Arithmetical judgments are therefore synthetical, and the more plainly according as we take larger numbers...". Obviously, as we take larger numbers a live human may run out of time to synthesize the requisite intuition. But our understanding also has the capacity to project indefinite extensions of our intuitions (as with mathematical induction for instance), so we can intuit that it is possible in principle. This last part was developed systematically by Kant's mathematical descendants, Hilbert and intuitionists, see Is there a Kantian influence on Hilbert's formalist programme?
>>8013113
Hume would equally have no problem, logic and mathematics for him are relations of ideas, and everything in them is analytic a priori, i.e. tautological. Kant was overly optimistic when he wrote "For he would then have recognized that, according to his own argument, pure mathematics, as certainly containing a priori synthetic propositions, would also not be possible; and from such an assertion his good sense would have saved him", he should have read Hume's Treatise, not just his Enquiry. It would be a more interesting question for Frege, for whom arithmetic was a priori analytic, and geometry a priori synthetic, but he'd probably say that equating geometric and analytic π is where it becomes synthetic. Practical considerations generally did not preoccupy traditional epistemologists, be it Plato, Hume, Kant, Frege or Husserl.
>>8013113
>it is a priori synthesis in space (geometry), or in time (arithmetic).
Can you explain why arithmetic is viewed as [math] a [/math] [math] priori [/math] synthesis in time?
>>8001089
>>8013148
all maths seems a priori to him
http://plato.stanford.edu/entries/kant-mathematics/
In both the Preamble to the Prolegomena to Any Future Metaphysics and the B-Introduction to the Critique of Pure Reason, Kant introduces the analytic/synthetic distinction, which distinguishes between judgments the predicates of which belong to or are contained in the subject concept and judgments the predicates of which are connected to but go beyond the subject concept, respectively.
>In each text, he follows his presentation of this distinction with a discussion of his claim that all mathematical judgments are synthetic and a priori.[4]
There he claims, first, that “properly mathematical judgments are always a priori judgments” on the grounds that they are necessary, and so cannot be derived from experience (B14). He follows this with an explanation of how such non-empirical judgments can yet be synthetic, that is, how they can serve to synthesize a subject and predicate concept rather than merely explicate or analyze a subject concept into its constituent logical parts.
>Here he famously invokes the proposition “7 + 5 = 12” and argues negatively, claiming that “no matter how long I analyze my concept of such a possible sum [of seven and five] I will still not find twelve in it”, and also positively, claiming that “One must go beyond these concepts [of seven and five], seeking assistance in the intuition that corresponds to one of the two, one's five fingers, say…and one after another add the units of the five given in the intuition to the concept of seven…and thus see the number 12 arise” (B15).
>He takes it to follow that the necessary truth of an arithmetic proposition such as “7 + 5 = 12” cannot be established by any method of logical or conceptual analysis (Anderson 2004), but can be established by intuitive synthesis (Parsons 1969).
>>8013152
He follows this discussion of arithmetic reasoning and truth with corresponding claims about Euclidean geometry, according to which the principles of geometry express synthetic relations between concepts (such as between the concept of the straight line between two points and the concept of the shortest line between those same two points), neither of which can be analytically “extracted” from the other. The principles of geometry thus express relations among basic geometric concepts inasmuch as these can be “exhibited in intuition” (Shabel 2003, Sutherland 2005a).
for the time and arithmetic:
====================================
In the Transcendental Analytic, Kant deduces the table of twelve categories, or pure concepts of the understanding, the first six of which he describes as “mathematical” (as opposed to “dynamical”) categories because of their concern with objects of intuition (B110). The concept of number is treated as “belonging” to the category of “allness” or totality, which is itself thought to result from the combination of the concepts of unity and plurality (Parsons 1984). But, Kant claims further that difficulties that arise in the representation of infinities—in which one allegedly represents unity and plurality with no resulting representation of number—reveal that a concept of number must require the mediation of “a special act of the understanding” (B111). (This special act is presumably the synthesis that Kant describes as a function of both imagination and understanding, and which it is the business of the full theory of judgment—including the Transcendental Deduction and the Schematism—to explain (Longuenesse 1998).)
>>8013156
>So, though he also claims that arithmetic “forms its concepts of numbers through successive addition of units in time” (4:283), it is misleading to infer that arithmetic is to time as geometry is to space, since a formal intuition of time is inadequate to explain the general and abstract science of number.[5] (In fact, Kant declares mechanics to be the mathematical science that is to time what geometry is to space.)
>>8013158
>5. It is, of course, the use of such a science of arithmetic that is more general than a science of time. The individual propositions of arithmetic, or what Kant calls “numerical formulas,” are in fact singular, which is why he claims that arithmetic does not have axioms as geometry does. (A164/B205)
>>8013152
thanks
