wtf wrote: ↑Thu May 23, 2019 12:17 am
Earlier you claimed to be studying Homotopy Type Theory, or HOTT. I found that interesting since I'm studying a related discipline, category theory.
Here's the problem. Metaphysically - the notion of "studying" means two entirely different things to you and me.
You have already made it clear that to you "studying mathematics" means nothing more than "amusing yourself". So perhaps maximum amusement means maximum understanding?
To me it means something like "constructing useful mental models". USEFUL being key here. Working back from a real-world problem to derive a Mathematical solution. Because empirical validation of my models means that I have a selection criterion that's a little more stringent than my own amusement.
Quite literally you have no way to confirm or falsify the epistemic claim "I understand mathematics". Your notion of "understanding" lacks contact with the ground. It's a castle in the sky - it means anything you want it to mean. At best - you are calibrated to some notion of "understanding" that is accepted amongst Mathematicians (e.g it's social acceptance), yet the moment you ask a mathematician about N-th order side-effects (or anything non-deterministic really) they start babbling some nonsense about "purity" and "beauty".
And if that's what mathematicians optimise for - great, but it's really difficult to setup any objective system of determining whether you actually "understand mathematics". You have read mathematics? You have adopted the language of Mathematicians? You can say things about abstract objects that don't upset other members of your tribe?
From where I am standing, Mathematicians produce useful algorithms from time to time and entirely by accident. Is just - luck is not a strategy in my game.
You have certainly admitted that you don't want to APPLY mathematics outside of the abstract, so it's really difficult to arbitrate your knowledge-claims. But that's not even the worst systemic issue at play.
If you don't know how to test/falsify your own claim of "understanding", how are you going to test somebody else's?
And if you aren't testing another's "understanding" (because you don't know what "understanding" means) then what are you testing for?
When you use a ruler to measure the table, you are also using the table to measure the ruler...
wtf wrote: ↑Thu May 23, 2019 12:17 am
I asked you if you knew about category theory and you claimed you did. I probed that by asking you what a universal property was. Your completely off-topic response convinced me that not only don't you know any category theory, but you are someone who claims to understand things rather than simply admit they don't.
What you were testing is whether I SPEAK the language a category theorist USE to talk about "category theory'.
Which is pretty weird, considering you know that:
1. I am more familiar with Type theory
2.
Type theory is equivalent to Category Theory
And when the response that I gave you didn't arrive in the language that you expected it to arrive in, you concluded what you concluded.
So yeah. You aren't very bright when you keep missing the point: our INTUITIONS are the same. Our LANGUAGE is different.
What Feynman said rings true. If you can't explain it to somebody else - you don't understand it.
If you want to convince me that you 'understand category theory'. Translate your understanding of 'universal properties' into Type theory and see if you arrive at
identity types
Similarly - if you asked me if I know anything about "proof theory" It would be a lie if I told you that I don't.
Because I have written more proofs than you have.
Only, I don't call them "proofs". I call them programs. So when you keep using your language to test my understanding - you are setting yourself up for failure.
You might find some truly useful insights about this problem in the first chapter of a book called "The Mathematical theory of Communication" by one, Claude E. Shannon. That is - if you actually care about applied Mathematics.
wtf wrote: ↑Thu May 23, 2019 12:17 am
And now I ask you what's a homotopy, and you have no idea. So you're not actually studying HOTT.
So are you claiming that my concrete example of APPLIED homotopy (parallel computation) in the real world is "me having no idea"?
Tell us all about how HOTT is a pure discipline, reserved only for the higher echelons of the Mathematical elite, and how my empirical intuitions and practical understanding of distributed systems is not transferable knowledge.
I can understand how it's upsetting to you. That a 22 year old DOING real-world computer science can develop the same intuitions about homotopy which takes 30+ years to acquire through the usual scholastic methods.
wtf wrote: ↑Thu May 23, 2019 12:17 am
And YOU are the one who chose Univalence as your handle, and you don't even know what the word means or what is its significance in modern alternative approaches to math foundations.
Sounds to me like you got triggered. Few weeks back you claimed that words have no meaning, and look at you now - defending the meaning of a word!
Observe how you are interpreting the significance of Univalence to the sub-culture of Mathematics. Still refusing to step outside that box and attempt to compute the consequences from a broader perspective.
Further observe, that despite the significance of the Curry-Howard-Lembek isomorphism, you insist on talking about Mathematics as if it has absolutely no relevance to Computation, or as if my empirical knowledge about large-scale computation is somehow not transferable into the world of Mathematics. That's just tribal thinking.
And you continue to repeat the tribal error of most humans "If you don't speak my language - you aren't one of us".
That's one way of refusing to acknowledge that all of your precious Mathematics boils down to a computational system that is less than 200000 lines of code. For some perspective. The Linux kernel alone is +- 20 million.
All you "understand" is Mathematics. If you can even call that "understanding".
wtf wrote: ↑Thu May 23, 2019 12:17 am
I'm perfectly justified in calling you out on your bluster. If you clearly don't know what you're talking about regarding subjects I'm familiar with
Yep... there it is. Because you spend time reading books about it, you have deemed yourself an expert.
Your ability to measure others understanding ends with your ability to measure your own.
Because your understanding is only scholastic you only know how to test for LANGUAGE. Somebody who TALKS about category theory.
Not somebody who BUILDS SYSTEMS that USE category theory.
Pretend you and I don't share a conversational language, then come up with an experiment to "test my understanding" of your field.
You can't? Because it's entirely abstract? Sucks to be you.
So, I guess I am going to continue "not know what I am talking about" when I point out that relational databases are the analog equivalent of your abstract area of expertise.
This is yet another example as to how and why my understanding is calibrated by reality. If you want to prove any sort of "familiarity" about category theory you should have absolutely no problem pointing us to the Mathematical equivalent of the CAP theorem?
wtf wrote: ↑Thu May 23, 2019 12:17 am
, then that causes me to doubt that you know what you're talking about on subjects I don't know anything about but that you claim to.
Because your ONLY test for asserting one's "knowledge" and "understanding" boils down to "Can you talk about X the way I talk about X"?
Your very own notion of "understanding" (or how to test for it) is. Well. Absent.
The way I test for "understanding" is if people can apply their knowledge to the real world.
If you can't - it's not knowledge.
wtf wrote: ↑Thu May 23, 2019 12:17 am
Yes I do see you managed to regurgitate some stuff you just hurriedly looked up. You simply have not convinced me.
Then come back to me when you have convinced yourself that relational databases are applied category theory.
wtf wrote: ↑Thu May 23, 2019 12:17 am
As an example, when I pointed out that I learned that the lambda calculus is an example of a Cartesian closed category, I expected that you might say something like, "Cool, can you tell me more about what that means?" Or, "Thanks but I'm not interested in that." What I did NOT expect was for you to pretend to understand the remark when it's so painfully obvious that you don't. That's where I'm losing my enthusiasm for this conversation.
Q.E.D What you are TESTING is whether I SPEAK your language.
If you are looking to speak about category theory in the abstract then you should probably look for other people who aspire to Mathematical purism/idealism. I am not one of those people.
If you want to talk about the APPLICATION of Mathematics ( e.g real-world problems!) Talk to me.
Because I have made it quite clear (and you keep proving my point). The patterns from your field are the patterns from my field.
And you have failed to convince me that you have anything remotely resembling of "understanding" when you can't even see how a relational database are APPLIED category theory.
You are the epitome of the pet-peeve I have with academics. You aren't interested in understanding the world. You are interested in abstract ideas.
So how about the abstract idea of "understanding what it means to understand the world"?