I highly recommend watching the entire dialogue on Philoctetes if you haven't already. I'm working my way through Kreyszig's 'Functional Analysis' right now and I might be catching the operator bug as well. Fun stuff ^_^
Complex numbers spring to mind for me as something we know so much about even though the main thing introduced, i, is a number know nothing of other than it squares to -1. You can really dig so much deeper into a topic when you remove the need for computation and just think about the implications of what ever new idea you’re introducing.
This is true for all numbers though, the natural numbers are just most intuitive. Negative numbers are the result of asking for the solution to x + 1 = 0, i of course comes from x^2 + 1 = 0, even natural numbers are just the implications of a set of rules; 1 is S(0). The way mathematics is taught really ruins people's perception of it by making them see numbers as the result of calculations, calculations are just useful algorithms for computing values, not the values themselves. "What is i?" or "what is -1?" is not a question that makes sense. Mathematics is the study of rules and their consequences and doesn't really have anything to do with "things", contrary to everyone calling everything a "mathematical object".
Great stuff! Thanks for posting. I just wish the video weren't so fuzzy! Or just maybe, the fuzziness is a metaphor for the content! (Or: The real video is in a velvet bag, but we can make out the outlines here...)
3:55-4:16 I have something similar but different; the concept of ablation. To ablate is to remove. This walks hand-in-hand with negativity bias, we don't normally see presences, we see absences, "flaws", contrasts, and we typically define something on the basis of what it is not. Case in point, as he said earlier, what are the two other lines in the right triangle besides the hypotenuse? It's the non-hypotenuses. He removed hypotenuseness instead of naming the two lines. The essence of ablative processes is that, in mathematical rather than philosophical language, they tend to approach a limit but never reach it. Like digging into a fruit and never reaching the center. A related concept is that of negative definition. The Viktor guy speaks of a "languageizing" of, and "abstracting" away from an object, as in, plain old abstraction - whereas this one is a human activity and property of language, of which abstraction is one part.
@@sthetatos It's a neologism of mine. There is no bibliography. If you want something rather than nothing, you should look into the concepts of Negative bias (psychology), Positive & Negative definitions (ontology, philosophy), Hermeneutic Circle (ontology), Asymptotes (I think that was mentioned in this video), Problem of Induction (philosophy of science), Apophaticism (theology). I'd say, it's closest to "negative definition", and refers to the process of negatively defining something. A slippery, endless endeavor.
This is exactly what I thought when going into group theory. I wish they had attempted to convey this idea in high school as to not make math so boring.
What a great video, thanks for posting! I have often wondered about the interplay between meaning and structure. It feels like SICP, that "data" and "program" are not separate, they are indistinguishable, and freely "transform." Algebra is program, values are data! It's too bad that Professor Greene laughed off applications to literary/artistic abstractions at the end. Can there be bijections between algebraic statements and literary expressions? Why not? That literary expressions are sometimes inconsistent is not a flaw in the idea, it only demonstrates that one can make mappings between inconsistent statements. (One might argue that the inconsistencies in literature carry their own meaning - often, the tragic flaw of a hero figure is that is math is bad.) Mathematics has no problem considering many systems of algebraic rules. All we demand of the system of rules is that they remain consistent, regardless of which rules we apply to "symbols on a page." Very provacative discussion. I'll check out Philoctetes and Shklovsky.
Yes it's a talk called Math and Beauty I believe. The TH-cam channel is called Philoctetes. I've been meaning to upload the talks featuring Barry as well as other clips of his monologues. Such profound metaphorical insight and great fun at that.
![Barry Mazur "A Lecture on Primes and the Riemann Hypothesis" [2014]](http://i.ytimg.com/vi/way0jAWpjZA/mqdefault.jpg)
![Barry Mazur "A Lecture on Primes and the Riemann Hypothesis" [2014]](/img/tr.png)
This is wonderful! Brilliantly illustrates why algebra, number theory, and operator theory are my favourite branches of mathematics!
I highly recommend watching the entire dialogue on Philoctetes if you haven't already. I'm working my way through Kreyszig's 'Functional Analysis' right now and I might be catching the operator bug as well. Fun stuff ^_^
@@Israel2.3.2 still have a long way to go... I have a keen interest in higher mathematics but I still need to start my undergraduate level.
the student’s arrow is also a sign
I love this insight/perspective so damn much.
This was nice. I was expecting him to discredit “algebraization” in favor of intuition, like Feynman did in that one interview
Complex numbers spring to mind for me as something we know so much about even though the main thing introduced, i, is a number know nothing of other than it squares to -1. You can really dig so much deeper into a topic when you remove the need for computation and just think about the implications of what ever new idea you’re introducing.
This is true for all numbers though, the natural numbers are just most intuitive. Negative numbers are the result of asking for the solution to x + 1 = 0, i of course comes from x^2 + 1 = 0, even natural numbers are just the implications of a set of rules; 1 is S(0). The way mathematics is taught really ruins people's perception of it by making them see numbers as the result of calculations, calculations are just useful algorithms for computing values, not the values themselves. "What is i?" or "what is -1?" is not a question that makes sense. Mathematics is the study of rules and their consequences and doesn't really have anything to do with "things", contrary to everyone calling everything a "mathematical object".
'It was during office hours'... "Good!"😂
Great stuff! Thanks for posting. I just wish the video weren't so fuzzy! Or just maybe, the fuzziness is a metaphor for the content! (Or: The real video is in a velvet bag, but we can make out the outlines here...)
3:55-4:16 I have something similar but different; the concept of ablation. To ablate is to remove. This walks hand-in-hand with negativity bias, we don't normally see presences, we see absences, "flaws", contrasts, and we typically define something on the basis of what it is not.
Case in point, as he said earlier, what are the two other lines in the right triangle besides the hypotenuse? It's the non-hypotenuses. He removed hypotenuseness instead of naming the two lines.
The essence of ablative processes is that, in mathematical rather than philosophical language, they tend to approach a limit but never reach it.
Like digging into a fruit and never reaching the center.
A related concept is that of negative definition.
The Viktor guy speaks of a "languageizing" of, and "abstracting" away from an object, as in, plain old abstraction - whereas this one is a human activity and property of language, of which abstraction is one part.
Great comment. Can you elaborate a little more about the concept of ablation? I know the term from medicine. Some bibliography? Thanks.
@@sthetatos It's a neologism of mine. There is no bibliography.
If you want something rather than nothing, you should look into the concepts of Negative bias (psychology), Positive & Negative definitions (ontology, philosophy), Hermeneutic Circle (ontology), Asymptotes (I think that was mentioned in this video), Problem of Induction (philosophy of science), Apophaticism (theology).
I'd say, it's closest to "negative definition", and refers to the process of negatively defining something. A slippery, endless endeavor.
This is exactly what I thought when going into group theory. I wish they had attempted to convey this idea in high school as to not make math so boring.
What a great video, thanks for posting! I have often wondered about the interplay between meaning and structure. It feels like SICP, that "data" and "program" are not separate, they are indistinguishable, and freely "transform." Algebra is program, values are data! It's too bad that Professor Greene laughed off applications to literary/artistic abstractions at the end. Can there be bijections between algebraic statements and literary expressions? Why not? That literary expressions are sometimes inconsistent is not a flaw in the idea, it only demonstrates that one can make mappings between inconsistent statements. (One might argue that the inconsistencies in literature carry their own meaning - often, the tragic flaw of a hero figure is that is math is bad.) Mathematics has no problem considering many systems of algebraic rules. All we demand of the system of rules is that they remain consistent, regardless of which rules we apply to "symbols on a page." Very provacative discussion. I'll check out Philoctetes and Shklovsky.
If you search "STEM diagrams be like" you'll find another internet meme this reminded me of.
looked like robert downey junior
I often joke: Everyone's talkin' about `politics` - yet, nobody has read the book.
As I can see, you have 😉
Is the whole video available somewhere?
Yes it's a talk called Math and Beauty I believe. The TH-cam channel is called Philoctetes. I've been meaning to upload the talks featuring Barry as well as other clips of his monologues. Such profound metaphorical insight and great fun at that.
th-cam.com/video/kdUkqW7m5-A/w-d-xo.html
@@Israel2.3.2 I can't find the channel. Are you referring to "Philoctetesctr"?
@@vwwvwwwvwwwvwwvvwwvw Yes that's the one, I just searched Philoctetes center and the channel came up.
so true
As a programmer I think a slightly more elegant way to put it is to see the class, not the instance.
Is that Robert Greene?
Brian Greene
So no, it's not Robert Greene. 😂
isnt that just meta? Elevate root(2) to another level in the discourse?
Imagine calling yourself a mathematician and forgetting -sqrt2 as a solution to x^2-2=0
What a bunch of nerds
Barry Mazur Is Greater Than You Are Friend.
@@Israel2.3.2 Free Palestine ✊
My man you're in the wrong comment section
Tell me about it...
jesus is lord