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My Mathematical Regression

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Re: My Mathematical Regression

#151

Post by ranit »

aj_hackman wrote: post #143
ranit wrote: post #85

Earlier quoted context omitted.

>> He eventually got bored. He retired and joined a seminary. Wow, got bored and joined a seminary - Do you know how does he feel there? A genuine question - Did he expect to get excited and challenged in a seminary?

"The first gulp from the glass of natural sciences will turn you into an atheist, but at the bottom of the glass, God is waiting for you."

A good quote. I didn’t mean the question as “atheist vs believer argument”, but rather as an environment where ideas are accepted and flourish. Because I understood the parent comment: “He eventually got bored.” as "He got bored by the corporate environment not getting his ideas and thus went to a better organization in that regard."

So now, how was he, the one with brilliant and unorthodox ideas, got accepted in an institution like seminary? How he felt having arguments there, etc. …

Re: My Mathematical Regression

#153

Post by dhosek »

shenberg wrote: post #34
dhosek wrote: post #24

There’s a bit of hand-waving in the jump to 2 n choose n solution, which I suppose is fine, and my ex–math teacher brain really wants to have a proper proof or at least solid reasoning rather than “it follows the pattern” based on three observations. But I am reminded of how during my engagement 24 years ago, my future father-in-law raised an issue of being able to determine whether they were getting the full amount…

You always either go left or down so total 40 steps, choose 20 to be down (or 20 to be right)

Which suggests another approach to the solution; you have 20Ls and 20Rs which can appear in any order so it’s a permutation with repetition problem and thus 40!/(20!20!)

That approach has the advantage that it’s easily adapted to non square rectangular grids (n+m)!/(n!m!)

Re: My Mathematical Regression

#154

Post by eru »

kleiba2 wrote: post #142
eru wrote: post #133

Earlier quoted context omitted.

Just the opposite: he was very smart; but most people don't consider his overall life choices to be something you would want to copy.

Ah, got it! Thanks for the clarification.

Sorry, I was perhaps being too indirect.

Re: My Mathematical Regression

#155

Post by eru »

kj4211cash wrote: post #131
eru wrote: post #97

Earlier quoted context omitted.

> I managed a guy like that. He was capable of very complex thinking, but he wasn't in love with complexity, he was in love with simplicity. His solutions tended to be of the form, "we can ignore all these things, and just focus on X, and it will provide all the value." He'd notice something and simplify it and the benefit to the company would be measured in multiples of his salary. I did some of that a few times in…

This is basically my professional career. I've stayed 5+ years at the same place now and it's gotten to the point where people ask for me to build an optimization before it's even clear they have a problem amenable to optimization. Yay! My work has a good rep. But also I'm called upon entirely too frequently to explain work I did years ago or to answer questions like which constraint "comes first". Honestly it's gett…

> I guess it's just sophisticated enough.

Maybe, though just applying a commercial or open-source off-the-shelf solver is a lot easier than most of what they ask you to figure out in your average programming interview. Probably about as hard as doing some SQL queries, which we even entrust semi-technical people with.

Of course, when your first naive modelling attempt doesn't work (eg can't be solved in any reasonable amount of time), there's a bag of more complicated tricks and some real ingenious engineering you can do; but again, the lower rungs of that aren't all that dissimilar from what your local database guru does when she tells you to add more indices.

Re: My Mathematical Regression

#157

Post by dhosek »

gobdovan wrote: post #37
dhosek wrote: post #24

There’s a bit of hand-waving in the jump to 2 n choose n solution, which I suppose is fine, and my ex–math teacher brain really wants to have a proper proof or at least solid reasoning rather than “it follows the pattern” based on three observations. But I am reminded of how during my engagement 24 years ago, my future father-in-law raised an issue of being able to determine whether they were getting the full amount…

You can go down or right at any point. To go in bottom-right corner, you need n down steps and n right steps. In how many ways can you arrange n things on type A and n things of type B? In C(2n, n). The problem is about modeling, once you model it correctly, you get the definition of combinations.

C(2n, n) isn’t about permutations, but choosing subsets of a set without order, but as I’ve thought about it, the model here is that there are 2n moves to be made and you need to choose n of them to be down (or right, depending on your preference).

Re: My Mathematical Regression

#158

Post by mbowcut2 »

mb7733 wrote: post #3

An intuitive motivation for the solution in the article (2n choose n). For an n*n grid you have to you will take 2n steps, n "over" and n "down". All that matters is the order of the steps. So if you think of there being 2n "slots", you have to pick n to be "over", and the rest are forced to be "down". So it's n choose 2n indeed. You can also think of it another way, without using the formula combinations, and only t…

I made myself reason it out, and came up with the exact same intuition. You need a sequence of 2n moves (n down moves, n over moves), but the sequence is completely determined by which moves are down (the others must be over). So it's 2n (moves) choose n (over).

Re: My Mathematical Regression

#159

Post by lajarre »

i often hear this frustration, been hit by it first-hand and am just recovering

my keys to overcoming this frustration:

* capture (focus on) the joy of doing math; this doesn't get better the more you know (i'd argue, to the contrary); a child figuring out that 2+2 = 3+1 is as profoundly moved as Tao doing his most advanced ones

* be responsible and figure out what parts of the maths journey have lastingly influenced your way of thinking about the world; if you trust math is really beautiful or "it's the language of the universe" or something, then it _must_ have an influence on how you see things; not because of the theorems, but because of the practice; isolate this, nurture it

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