Mathematics - 2020-12-16 (page 2 of 3)

copper.hat

19:00

@John_Krampf sry, i haven't followed the full thread, so prob out of place. i often look for one liners when experimenting ('apl' mode :-))

John_Krampf

I do not think py folks like terseness. in a python console type `import this` and you will get the zen of python which includes:
Explicit is better than implicit.
Simple is better than complex.
Readability counts.

Black Panther

@John_Krampf It's alright, thanks a lot. Sometimes it's good to be thrown into the deep end, and learn to swim. I think in JavaScript an array with a null value evaluates to false, I'm not sure about this, I need to confirm.

Ted Shifrin

So this has turned into a python style argument room?

I miss mathematics.

John_Krampf

@BlackPanther I think you would love python, I strongly recommend learning it. I would only use C# or Java if a very particular application demanded it, but for exploration, especially the math kind, you really should use python

copper.hat

@John_Krampf i'm not exactly a newbie dev...

John_Krampf

19:02

@BlackPanther I'm not javascript expert but I think you're right

Black Panther

@copper.hat This executes places_to_check.add(p) for each p in the array of tuples, right?

If so, then the part places_to_check.add(p) in places_to_check.add(p) for p in [(x+1, y), (x-1, y), (x, y+1), (x, y-1)] is like the select clause in C# LINQ

copper.hat

@BlackPanther yes. i am not recommending it (and this is the wrong forum) it was just a terse expression if you are doing interactive exploration.

Balarka Sen

@Ted: Reading the section on curves in your differential geometry notes.

Black Panther

@John_Krampf After today, I absolutely have to learn Python. Do you know any books or written MOOCs or courses that I could use to learn Python considering I already know C# and I'm not a beginner?

Ted Shifrin

I doubt you're finding much new in there, @Balarka.

John_Krampf

19:07

@BlackPanther There's a video you should see, just a sec looking for it

Balarka Sen

No I find it interesting. We haven't seen the local canonical form so I'd like to read through that and try some exercises.

John_Krampf

@BlackPanther This is a straight dive into the beautiful expressiveness of python, I think it will inspire you youtube.com/watch?v=wf-BqAjZb8M , It's a video called "Beyond Pep8" (For context, Pep8 refers to the official Python style guide).

Ted Shifrin

Ah, we've talked about the local canonical form.

C.F.G

Hi all.

John_Krampf

I would watch several videos by Raymond Hettinger to get the idea of how to write expressive python code

nathdwek

19:15

Hey guys, me again looking for someone with a fresh pair of eyes to look at some probably stupid issue with linear algebra/quadratic optimization

copper.hat

no fresh eyes here :-)

John_Krampf

@BlackPanther this may be a better first video on beautiful python youtube.com/watch?v=OSGv2VnC0go

Ted Shifrin

Yeah, @copper, I saw that your eyes confused quotient space with complement :P

Black Panther

@John_Krampf Thanks. I usually don't learn by watching videos but I'll give this one a try. Perhaps the video you linked will change my mind. I was thinking of learning python from this data analysis course or this Python developer course, which of these two courses do you think is a better Python course and which course do you think is better for a C#/java guy like myself to learn Python?

John_Krampf

@BlackPanther Since you're hanging around on Math.SE I think the data analysis one would be better

@BlackPanther my only warning on data analysis courses is they emphasize pandas a lot, which is fine for the use case, but I have met many python programmers who inject pandas into any project when more simple idiomatic python would do

copper.hat

19:19

@TedShifrin thanks, i got stuck at the first sentence :-)

Ted Shifrin

Yup, quotient.

Black Panther

@John_Krampf I think you're right. The Python Developer course seems to be geared towards web/full stack development. I really wanted to learn Python properly from the ground up, and have a solid understanding of it so that I can use it to attack math problems instead of trying to express a mathematical solution in C# or Java.

C.F.G

Every time I read about "Axiom of choice" it makes me so uncertain about mathematics. For example, Banach–Taraski paradox is counterintuitive. One of my professors says that every time that I say it in my class, It is still weird to me! Existing such a counterintuitive in mathematics, How can we care about our proofs that seem very simple and straight?

Ted Shifrin

Of course Banach-Tarski is counterintuitive. Non-measurable sets are totally counterintuitive.

C.F.G

Do you meant measure zero by "Non-measurable"?

Black Panther

19:23

@John_Krampf I see. From those two courses, which do you think would give me a stronger base/understanding of python? Frameworks/libraries like Pandas are something I can forego or don't need to be an expert at

Tobias Kildetoft

@BlackPanther What will you be using Python for?

Ted Shifrin

No, I mean non-measurable.

copper.hat

We (meaning me) have little natural intuition for infinities

Ted Shifrin

Measure zero is perfectly intuitive ;)

John_Krampf

@BlackPanther They both teach frameworks and libraries. from the description it's hard to tell. I'd say for an understanding of the language itself then I can't find much better than pycon talks like Raymond Hettinger's. But for practice then if you're interested in math the data analysis will probably be marginally more directly applicable but the python developer course will be more well rounded.

C.F.G

19:27

@TedShifrin Well, So how can we care about our proofs?

Thorgott

@TedShifrin I've seen enough people struggling with the concept of "probability 0, but not impossible"

copper.hat

@John_Krampf the video is entertaining, i like the bit about p vs np.

geocalc33

where's a good place to share heavy metal dark elixir music?

Ted Shifrin

@Thor: Yes, I suppose that distinction can be difficult.

I don't see your point, @C.F.G. Although I've taught students who would not allow the axiom of choice, I personally have never used it in my research, but I don't quibble over it.

John_Krampf

@copper.hat yep :) he's a good speaker

Black Panther

19:30

@John_Krampf by the way this problem/puzzle we are working on, is this what is called Path finding?

Karim Mansour

@TedShifrin hi

Ted Shifrin

Hi, Karim.

Black Panther

@TobiasKildetoft Sorry, my wifi or internet disconnected.

C.F.G

Another question: How mathematicians decide that an statement is a postulate or a theorem or not? This bother me a lot!!

Lukas Heger

I don't think the term postulate is used much in mathematics

if we have a proof, it's a theorem, if not, it's a conjecture

user330477

19:32

Just a quick question. Is $|\zeta'(s)| \geq 1$ for all $s \in \mathbb{C}$?

Ted Shifrin

What do you mean "decide"? One wants as few postulates as possible. For example, with the ring axioms, you prove that $0\cdot a = 0$ for every $a$ in the ring. This is not yet another axiom.

@Lukas: Well, we have axioms/postulates all over the place when we define structures.

John_Krampf

Path finding you usually have as input your start and end point already known and then find a path between them.

Here we don't really know what the end point is and what I implemented is an uninformed search strategy for doing an exhaustive search for points reachable from the origin. I didn't record the path from the origin to each point but we could have built that if we wanted though another thing to add to the program would be choosing just one path from the origin to a point which we didn't worry about here because we don't care if there's multiple paths from the origin to a point.

Lukas Heger

@Ted okay, I hadn't heard the term postulate for axioms

Thorgott

but those axioms are actually just definitions

Lukas Heger

yeah

Thorgott

19:33

not qualitatively the same thing as, say, ZFC axioms

Ted Shifrin

How is the parallel postulate different from a definition? :D

It's a semantic difference, not a mathematical difference.

Lukas Heger

Thorgott was saying that axioms are just definitions

Ted Shifrin

I thought Thor was distinguishing.

Of course, this sort of pedantic stuff is precisely what I hate.

Black Panther

@TobiasKildetoft Great question. I would not be using Python for web development, instead I would be using Python for the kind of problem we have just been working on, maybe AI, working with/processing data (for example, this, and robotics too if Python is useful there, etc.

Tobias Kildetoft

Ahh, I suppose Python is indeed the goto for many when it comes to AI

at least as the outer layer

John_Krampf

19:37

@BlackPanther check out this aima.cs.berkeley.edu

Thorgott

yeah, I was trying to distinguish

Lukas Heger

~~just add everything you can't prove as an axiom~~

Balarka Sen

@TedShifrin Quick question. If $S$ is a regular surface, $p$ is an umbilic, then we can choose coordinates $(u, v)$ around $p$ such that $\partial_u$ and $\partial_v$ form a basis of eigenvectors for the shape operator. In particular $\mathbf{n}_u = -k_1 \partial_u$ and $\mathbf{n}_v = -k_2 \partial_v$. Equating mix partials and using $k_1(p) = k_2(p)$, I get $\partial_u k_2(p) = \partial_v k_1(p) = 0$.

Thorgott

I don't think an axiom such as "there exists a set" is structurally the same thing as a definition

Balarka Sen

Do you understand this in an intuitive way or is it just some identity

Thorgott

19:38

but of course, I'm not a logician, so I probably better keep shut

Black Panther

@John_Krampf I see, that makes it hard because now I have 3 good resources to choose from :D.

Tobias Kildetoft

@BlackPanther You should also check out mit.edu/~puzzle/2020/puzzle/hackin_the_beanstalk (not that you will learn anything, but it is fun to try to solve)

John_Krampf

@BlackPanther look trhough AIMA first, it's the best textbook on AI and although the principles are language neutral, the code they use to implement their AI algorithms is written in python

Ted Shifrin

@Balarka: The beginning is wrong. Oh, are you assuming every point is an umbilic? Or just some point? If every point is an umbilic, then any coordinates work. If it's an isolated point, you cannot necessarily choose coordinates.

If every point is an umbilic, why are you writing $k_1$ and $k_2$ when it's just $k$?

Lukas Heger

are umbilic points related to the umbilical cord?

Balarka Sen

19:40

Only $p$ is an isolated umbilic. Why not? You're saying coordinates under which the coordinate lines are lines of curvature does not exist in general?

Ted Shifrin

Yes, @Lukas ... equally curved in all directions, like the umbilus.

Yeah, when you have an umbilic, you do not necessarily have local coordinates adapted.

You can blow up the point and then do it.

Balarka Sen

But why? You can still choose a frame of principal directions, and locally that should integrate to a chart, in my mind.

I don't understand the obstruction I think.

Black Panther

@John_Krampf Yes, I'll be starting this MIT programming competition in a couple of weeks, which I suspect uses path finding, so I'm hoping what I learned today from you would be relevant to that MIT programming competition, or at least a building block for anything I have to learn or do when I compete.

Ted Shifrin

What says the frame extends smoothly across $p$?

Balarka Sen

I see your point.

Ted Shifrin

19:44

This is actually a big deal and one of the failures of moving frames. :P

Balarka Sen

Simultaneous diagonalization for a family of quadratic forms should be problematic precisely when your eigenvalues are crossing, I see.

Ted Shifrin

If you look at my paper with McCrory that I sent you, this sort of problem is why we had to pass to a double-cover to do stuff with asymptotic directions (projective geometry).

Balarka Sen

@TedShifrin Ah OK

Ted Shifrin

Well, diagonalizing one when the eigenvalues come together is the issue.

Black Panther

@John_Krampf Wow, thanks for the link. I've not heard of that book until you linked to it. Is that a book on just AI or does it teach you Python too?

@TobiasKildetoft Thanks, I'm not sure what that is, but it looks fun.

Balarka Sen

19:48

@TedShifrin But yeah I was wondering about where I get stuck trying to say something about an isolated umbilic in the proof that all points umbilic => part of sphere

Mike Miller

@TedShifrin The point is just that there is no smooth map $D: \text{DMat}_{2 \times 2} \to \Bbb R^2$, where the first is the space of diagonalizable 2 x 2 matrices, and the latter the space of diagonal 2 x 2 matrices, so that $D(M)$ is conjugate to $M$.

Ted Shifrin

@Balarka: We should be able to make an example where the principal directions spiral as you come in to the origin.

John_Krampf

@BlackPanther It's a book on AI, the code repo examples happen to be in Python

Tobias Kildetoft

@BlackPanther That is pretty much the feeling any puzzle from the mystery hunt gives you

(looking forward to next years hunt which will be fully online)

Black Panther

@John_Krampf You mean I can learn Python through this book you linked?

Mike Miller

19:49

@TobiasKildetoft I forgot about that math puzzle website, Ill go back there after grading is doone

Ted Shifrin

@MikeM: Yeah, smoothness is definitely an issue, but I'm not even sure you can do it continuously in general. I haven't thought about this recently.

John_Krampf

@BlackPanther Given you already know C# then I think yes you can learn python by reading the example code as you learn more about AI. For example the book covers path finding

Tobias Kildetoft

@MikeMiller I never really got around to looking at it either

Ted Shifrin

@Balarka: How is there is an isolated point if every point is such?

Mike Miller

@TedShifrin I think you can do it continuously in the 2 x 2 case but not after that.

Ted Shifrin

19:50

I'm not even sure of that, @MikeM. I think I can visualize a spiraling road up to the top of a mountain.

Balarka Sen

@TedShifrin No I mean to say it seemed like the proof should say $(k_2)_u = (k_1)_v = 0$ but I was wrong.

At an isolated umbilic

I wasn't trying to specialize

Mike Miller

Nevermind, this fails in the 2 x 2 case.

Black Panther

@John_Krampf Thanks :D. I am really interested in AI, if I can learn AI and at the same time learn Python then I will definitely read AIMA from start to finish.

Ted Shifrin

I appreciate that viewpoint, though, @MikeM.

Mike Miller

I remember the example now.
[x x]
[x x]

for positive x.

[x 0]
[0 0]
for negative x.

Ted Shifrin

19:52

@Balarka: If you have coordinates, it probably does. I guess we can look at Codazzi-Mainardi and see what comes out.

Black Panther

@John_Krampf the book is free, right?

John_Krampf

@BlackPanther nope

Mike Miller

Every book is free at the russian bookstore

Ted Shifrin

@MikeM: So the point is that the eigenvectors do not patch continuously at the origin. Right.

Very instructive for Balarka :D

Mike Miller

Right. The eigenvalues do. But not the eigenvectors in any useful sense.

Balarka Sen

19:54

Cool

Ted Shifrin

This is the sort of thing that got me into singularity theory, @Balarka.

Trying to do differential geometry where things drop rank.

Mike Miller

Yeah that's good stuff

Too bad it died

Balarka Sen

Yeah, this is automatically my favorite thing of the week now.

Ted Shifrin

I don't think it's completely dead, @MikeM, but it was never exactly main-stream.

Balarka Sen

Too bad we'll both die @Mike

Ted Shifrin

19:55

Too bad we never wrote our final series of papers ... years of work never published.

Balarka Sen

"good stuff" - living people about dead us

Mike Miller

More of a compliment than I expect to receive

Alessandro Codenotti

@BalarkaSen smbc-comics.com/comic/die

Mike Miller

I found a write-up that explicitly mentions the above example. I wonder if that's where I first saw it

faculty.tcu.edu/richardson/Seminars/Efton_GAGA_lectures.pdf

Balarka Sen

@Ted: An inspiring quote from the foreword of Eliashberg-Mishachev: "Dedicated to V. I. Arnold, who introduced us to the world of singularities, and M. Gromov, who taught us how to remove them"

Ted Shifrin

19:57

Anyhow, @Balarka, do you agree with me that you can construct a surface with an isolated umbilic (presumably a planar point, but I'm not even sure)?

Nice quote :)

Balarka Sen

Yeah I agree. I'll have to construct one which shows this kind of behavior but it shouldn't be too hard.

Thanks @MikeMiller

Ted Shifrin

I tried to be pretty careful in my text, @Balarka, about explicitly referring to the ODE result when you are away from umbilic points, but I didn't go into details why.

copper.hat

i think a lot of authors 'assume away' awkward issues like singularities.

Ted Shifrin

You have to, @copper. They're a whole mess of trouble.

C.F.G

@MikeMiller: Hi. Which Russian bookstore?

Mike Miller

20:00

gen.lib.rus.ec

the phrasing "russian bookstore" was a joke I have seen before

Now we see how long until someone flags that link into oblivion

Ted Shifrin

I have given up objecting to illegal s***.

C.F.G

But it isn't illegal?

Ted Shifrin

I mean, when the whole government engages in it ...

Yes, @C.F.G, absolutely.

And they certainly do not have the permission of the authors or publishers.

Balarka Sen

@TedShifrin Thanks, I'll check the precise statement from your text tomorrow.

Astyx

It was Alessandro's expression at first I believe

Ted Shifrin

20:02

At one point, I asked my publisher to go after one of those sites, but eventually I gave up.

Mike Miller

Lol

Loser

Ted Shifrin

Me?

Alessandro Codenotti

I'm sure I've been using this expression for a long time, but I don't remember whether I saw it somewhere or I came up with it

Balarka Sen

People are flagging Mike's messages

Alessandro Codenotti

@MikeMiller It has been flagged btw

Ted Shifrin

20:03

I didn't do it.

C.F.G

I didn't too.

Thorgott

Feb 28 '18 at 10:24, by Alessandro Codenotti

How fortunate, my favourite Russian bookstore had a copy with fast delivery, it just arrived

Alessandro Codenotti

@C.F.G This message has been flagged too

Thorgott

first mention in the logs

user193319

2

Q: McDuff Groups and McDuff Factors

Let $G$ be a countable, infinite conjugacy class (ICC) group (i.e., if $g \in G \setminus \{1\}$, then the conjugacy class of $g$ is infinite). This will insure that the group von Neumann algebra $L(G)$ is a so-called $II_1$ factor von Neumann algebra. Recall that a $II_1$ factor von Neumann alge...

John_Krampf

20:04

@TedShifrin I am sorry to hear that.

user193319

Is this question more suitable for mathoverflow?

Ted Shifrin

@John_Krampf This is partly why I turned down about 6 offers to turn my free diff geo book into a published book.

Astyx

Under which jurisdiction is this chat anyway ?

John_Krampf

@TedShifrin I think it's terrible that your hard work was stolen from you without consent. It disincentivizes people from producing great work when they aren't allowed to productize it how they want.

Ted Shifrin

Yeah, but the flip side is that publishers charge six arms and three legs for books. When my coauthor and I wrote our linear algebra book, our editor swore that they would keep the price at the bottom of the range of prices for such books. A year later, it flew up, and he innocently said that his bosses would not allow it.

Tobias Kildetoft

20:08

Yeah, math books on introductory topics are a strange breed. Many of them are clearly being essentially exploited by the publishers who put out new editions with just enough changes to be incompatible with previous ones, but no actual new content

Ted Shifrin

That's in every field, @Tobias. Every field.

Alessandro Codenotti

@TedShifrin And all that money magically disappeared between the publisher and you leaving cents per copy as it often happens?

Ted Shifrin

In things like biology and political science, where things are changing every week, I can see its validity. But ...

Tobias Kildetoft

Unfortunately, this has made a lot of people think that it is OK to skip the paying part

John_Krampf

@TedShifrin I want to be empathetic about price but I feel that good presentations of technical topics really are worth that much. Take someone who understand linear algebra vs someone who doesn't, they have so much more technical (and career $$$ if that matters) potential

Ted Shifrin

20:09

@Alessandro: Well, our royalties may have gone up a little. I honestly do not remember.

Tobias Kildetoft

@TedShifrin No doubt (I just have only seen it in math myself)

Ted Shifrin

The sad thing, @John_Krampf, is how many horrible books there are. And many of them sell better than the good ones. pats self on back

robjohn

Hats do not show up on the attendee board.

Ted Shifrin

Did they used to?

John_Krampf

@TedShifrin I think when this happens it is often because some publishers aggressively market their books including with kickbacks to decision makers. But stealing IP and putting it for free on the net mainly punishes the honest author who puts effort into their book instead of their marketing. The marketing focused people can always print up a new edition that switches question order to keep the money flowing

copper.hat

20:13

unfortunately the market for math books is not like the market for mp3s...

Ted Shifrin

Anyhow, I never started in the book business expecting it to make me wealthy. I just wanted to contribute some high-quality texts. Some of the students haven't necessarily appreciated said "high quality."

robjohn

@TedShifrin I don't remember. I was just looking at the board and I noticed that it was not showing.

Alessandro Codenotti

I don't think they ever did but I'm not sure

John_Krampf

@TedShifrin For me money is just a guide to help me focus on one activity vs another. Math activities don't make me rich at all but I'm not picky so instead of working on recreational problem X I can work on problem Y if there's an incentive attached to it

Tobias Kildetoft

I kept being surprised how hard it was to write good exposition. Even when I knew the topic really well

Ted Shifrin

20:16

Ah, I don't think I ever did that, @John_Krampf, but very interesting.

@Tobias: My view is that most math authors do not write well. Papers, books, whatever.

But the culture of journals discourages good exposition, sadly.

Tobias Kildetoft

Yeah. I was certainly never really satisfied with any of the expository stuff I wrote

John_Krampf

@TobiasKildetoft Yeah that's why having a good exposition from someone who knows what they're talking about is worth its weight in... silver

Tobias Kildetoft

The research stuff I found to be fine generally

Ted Shifrin

Oh, I've struggled through some horridly written papers.

copper.hat

unfortunately there is the reality of publish or perish.

John_Krampf

20:19

@TedShifrin Yeah of course my definition of what I consider mathematical is pretty broad, so if someone is stuck on only focusing on their favorite subarea of their favorite subdiscipline then there might not be any money to be found.

Ted Shifrin

Yes, but quality of writing isn't part of that.

copper.hat

perhaps the quality quantity product is some sort of publishing uncertainty principle...

Tobias Kildetoft

Sure, I have struggled through terrible writing too. But for my own writing I was mostly satisfied with the research stuff and never really with the expository stuff.

John_Krampf

How would you guys describe the difference between Math.SE and MathOverflow?

Astyx

One is research grade, the other has ignorant people like me contributing

Ted Shifrin

20:27

MathOverflow is supposed to be advanced grad students and researchers. I have answered only one question on MO. I've answered zillions here.

(But that's mostly because I just don't hang out at MO much at all.)

John_Krampf

My background is in analysis so I rarely see anything of interest on MO, which seems to be about algebra, number theory, maybe some combinatorics problems? It seems weird to me to tackle research questions in such a format but perhaps in those disciplines research happens in shorter cycles? When I was in grad school the top analysis professors published 2-3 papers a year and the top combinatorics professors seemed to put out 1 every 6 weeks.

Ted Shifrin

Oh, there's plenty of analysis and geometric analysis on MO, too.

Black Panther

20:43

@John_Krampf if I read and understand that AIMA book from start to finish will I be able to get a job in the AI field in robotics etc.?

@John_Krampf And how much time should it take me to get through that book?

copper.hat

there is a big gap between reading and getting a job!

Black Panther

I meant understanding what I read

Maybe not a super high paying job, but at least entry level or something

Tobias Kildetoft

Reading (and even understanding) any book will not be enough to land a job

Employers look for something that actually demonstrates that you can do stuff. And anyone can claim to have read and understood a book

copper.hat

an employer needs to have some idea that you can actually apply stuff, unfortunately just declaring that you understand will not convince many. no judgement on you, just a reality.

Tobias Kildetoft

So generally it will take more to get an interview. But once at such an interview, having understood the book will obviously be a great bonus

Black Panther

20:50

@copper.hat No worries, I'll just have to practice the concepts I learn from that book

@TobiasKildetoft Maybe I'll put exercises I do on GitHub.

Tobias Kildetoft

That is certainly a good idea, yes

Anything (of decent quality) on GitHub is a big plus for getting an interview

Black Panther

As for how long the book should take me, what do you think?

copper.hat

good luck. i don't know you so take the following with a grain of salt, but getting any software work would be a good start. unfortunately the 'learn it and they will see it' is not a good approach.

Tobias Kildetoft

(I have some stuff on GitHub, and that does not qualify as being of decent quality)

Black Panther

Understood. I better not put all my eggs in one basket then

Nowadays it's better to be a generalist, than a specialist

John_Krampf

20:54

whoa boy the snow is here

Black Panther

:D

Where you at?

Tobias Kildetoft

Being a specialist can be fine, as long as you specialize in something a lot of people want

John_Krampf

@BlackPanther Long Island (NY)

Black Panther

I see just rain :(

@TobiasKildetoft Very true.

copper.hat

just to get a job, someone needs to know that you know stuff :-)

John_Krampf

20:56

@BlackPanther I find the book fascinating and keep going back to it. Could take a few weeks if it's sporading nights and weekends like I do. I guess if you have literally nothing else to do and amazing focus you could read it in a few days.

Black Panther

@John_Krampf The snow arrived for you just before Christmas :). Happy days

John_Krampf

@BlackPanther I would hire someone who read that books 10 x over someone from a data analysis course. That being said I'm not hiring and people with the money to hire are often more impressed by buzzwords than understanding.

Black Panther

@John_Krampf :D Reading it is one thing, comprehending and retaining what you read at that speed is very difficult, in fact I would like to see someone do it just to know it's possible. Of course if you have already covered the topic before then it's not impossible to do.

John_Krampf

@BlackPanther By "reading" I definitely think you should program the things in the books for yourself, also try to do some of the exercises as you go, they will confirm that you understood what you read

Black Panther

@John_Krampf That's good to know :). Yup, your soft skills take you further, without it you're not getting promoted to management positions which always pay more.

@John_Krampf I see, a practical approach.

If I'm reading that book then I guess I'll be here a lot more often.

Thank you everyone, and have a nice day. I have a phone call to make, and an early day tomorrow

copper.hat

21:08

there may be better rooms for data science type discussions?

John_Krampf

@BlackPanther good luck have fun!

@copper.hat depends on the data science. if it's the kind of data science where you want to understand what you're doing then math people are second to none. but conversation about "what pre-fabricated library and I plug and play with" then that's for somewhere else

copper.hat

@John_Krampf makes sense, but things here tend to a little more topological/analysis focused...

or random comments as in my case :-)

John_Krampf

@copper.hat I'm one of those people who sees very rigorous reasoning as equivalent to math. If anyone has a differing conception of math I would like to know it.

copper.hat

@John_Krampf this is more of a discussion over a bottle of wine... i have found that i have two modes in this regard: a 'math mode' and a 'developer mode'. both are rigorous, but require (for me!!!, not generalising) a different way of thinking and it takes me time (hours+) to switch.

John_Krampf

@copper.hat hm... have you ever written code in prolog? it bridges the gap between the two modes

copper.hat

21:30

@John_Krampf back in the 80's :-(. my preferred coding is lisp (well scheme really) which worked for me as a bridge.

generally i prefer exploratory programming...

John_Krampf

@copper.hat 80's were a wild time for prolog. I'm jealous I wish I could have been there. I liked prolog a lot recently but the support just isn't there. I'm just happy that python is pretty and well supported. Great video on prolog for those unfamiliar youtube.com/watch?v=G_eYTctGZw8

@copper.hat lisp, python, and some others are good for this. Prolog is good for this too (I love how search algorithms are a built-in primitive) though it can be tricky to inspect a result if you don't plan for that in advance.

For the record I was there in the 80s but a little too young to be programming prolog

copper.hat

@John_Krampf that was the unexpected thing for me with s/w, that for any 'real' work you need libraries and fairly active support (commercial or community).

(unexpected in the 80's timeframe i mean :-). i have done commercial dev in scheme, but its harder to come by now :-(

a lot of chips are still designed with a system that has lisp as its 'extension language'.

John_Krampf

@copper.hat " i have done commercial dev in scheme, but its harder to come by now" you're giving me nostalgia for a time I wasn't around in. " that was the unexpected thing for me with s/w, that for any 'real' work you need libraries and fairly active support" Yep for all the cool features another language can give you, nothing beats googling your problem and having 5 stack overflow responses of people working through the same problem

copper.hat

@John_Krampf i like the symbolic nature of lisp which py doesn't really have. (actually my most recent scheme dev was maybe 5 years ago). also, keep in mind that i do contract/consulting work, so it is easy to misconstrue some of my comments :-)

John_Krampf

I'm just thankful I got into my career in such a way that I can work in Python and not have to work in the statically typed compiled languages. that workflow sounds so painful and code so obtuse.

copper.hat

21:39

i have developed in c++ for decades and thoroughly hate the way it has evolved.

John_Krampf

@copper.hat " i like the symbolic nature of lisp which py doesn't really have." yep from not having macros to even small things like not having symbols. Some recent code I wrote is using interned strings instead of symbols which I guess is ok but really out of the way method of doing things

Of course, macros are a double edged sword, I do some work in R and there's already enough syntax hackery they're doing there where it's difficult to interpret what the code is doing

copper.hat

@John_Krampf a lot of what i did would be fairly described as grunt work, and the symbolic nature of lisp meant a lot of stuff could be done or experimented with really quickly. but it is much slower than compiled for intensive stuff (which should be pushed to c++ and its ilk).

i can't really discuss it here, but i did have a lisp->py project, and it was painful.

John_Krampf

I disagree that intensive stuff should be pushed to c++. I mean, _maybe_ one person should do this every 10 years, but in my experience I go with what Norvig says in points 21 to 24 here https://norvig.com/Lisp-retro.html

There are four general techniques for speeding up an algorithm: caching, compiling, delaying computation, and indexing. [p. 269]
We can write a compiler as a set of macros. [p. 277]
Compilation and memoization can yield 100-fold speed-ups. [p. 307]
Low-level efficiency concerns can yield 40-fold speed-ups. [p. 315]

copper.hat

21:55

@John_Krampf nice article! the speed discussion is too involved to get into here. but you need low level (even assembler and/or gpus) to handle some tasks (place & route, design rule checking, formal verification, simulation) in a commercial environment. this includes being able to hire people who know the stuff.

John_Krampf

@copper.hat haha I will defer to you on that. For my work though I find a much bigger problem than execution speed is making sure my subordinates don't get distracted going down rabbit holes as if something being asked of them requires them to go out and learn C in order to speed up their code instead of just not using double for loops where they aren't necessary

copper.hat

@John_Krampf no question there. order of magnitude first before constants :-)

John_Krampf

@copper.hat it's the curse of working in tech startups when we hire inexperienced 20 somethings who will look for any excuse to play with new technology rather than build new features or fix bugs on an existing code base

copper.hat

this could be a very interesting discussion , but the right forum involves wine :-)

@John_Krampf this is true, but unfortunately you need to go with the flow unless you have a large supply of hires :-)

John_Krampf

@copper.hat If only Everyone Listened To Me!!

copper.hat

22:04

:-)

user2103480

22:32

@John_Krampf there are a lot of great analysts on MO from what I've seen; the people who ask questions there tend to ask about the topics you mentioned, though. So be the change you want to see in the world and ask good analysis questions on MO

@John_Krampf interestingly, my logic professor had to program a lot in prolog and hated it

John_Krampf

22:52

@user2103480 yeah... "logic programming" is a bit of a pipe dream forcing logic on to programmers and programming onto logicians. I wish people just learned prolog as a programming language with cool features as opposed to the AI friend you wished existed but really doesn't

user2103480

Why learn something technical if you don't need it, or the skills attached to it, regularly?

Or why learn it when the abstract skills you gain can also be learned from a topic that's more useful to oneself

Thorgott

good question, why did I learn measure theory again

John_Krampf

@Thorgott of all things I learned measure theory is one of the most useful

user2103480

@Thorgott not only did you learn it, I think you learned it and remember it pretty well for just taking one course (and analysis III)

John_Krampf

@user2103480 pretty fair to be honest. unless you find some intrinsic beauty to it, though there's a limit to that because learning something for its intrinsic beauty is a luxury

Transcript for

$Mathematics$ Mathematics