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It Takes Two Neurons to Ride a Bicycle (2004)

paradise.caltech.edu

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Re: It Takes Two Neurons to Ride a Bicycle (2004)

#51

Post by dahart »

> There is not a direct or fixed correspondence, but as a general rule, during stable riding, a higher clockwise torque on the handlebars will cause the bicycle to start leaning more to the left

It's counter-steering! I was glad to read that counter-steering is accounted for and works in their physics simulation like it does in the real world.

I don't have a source handy, but I believe that there is a fixed correspondence between steering angle and the resulting turn that depends on the bike's speed, lean & steer. (And maybe tire radius counts too.) A bike riding in a stable constant clockwise turn will have a slight right lean & clockwise steer in steady-state. Steering clockwise from there will turn the bike left, or increase the turning radius until it's straight and then start turning counter-clockwise. Steering counter-clockwise from steady state clockwise turn will turn turn the bike right, increase the lean and decrease the turning radius.

Re: It Takes Two Neurons to Ride a Bicycle (2004)

#52

Post by GoToRO »

There are no secrets to riding a bike:

1. Do no try to go straight. Move the handlebars violently left and right when you feel you are falling left or right.

2. Going slow is hard. Go fast. The wheels spinning will behave as stabilizers, making it easier to stay on the bike.

3. Moving your body will make you fall at first if you do not counteract by moving the handlebar. Start by going downhill, without pedaling.

Re: It Takes Two Neurons to Ride a Bicycle (2004)

#53

Post by chestervonwinch »

lucb1e wrote: post #50
chestervonwinch wrote: post #31

Earlier quoted context omitted.

1) Sometimes it's actually helpful to use greek letters when a convention is used. For example: capitals for matrices (A), lowercase for column vectors (a), and Greek for scalars (α). 2) I agree with the gist of your point, but I'm guessing you're being down-voted because you come off as sort of flippant. Anyhow, I've long thought that mathematics should have hover-text to help remove the mental overhead of translati…

> Obviously, using variables names like `velocity_of_thing` is much too verbose in mathematics That is not obvious to me. Perhaps in a purely mathematical paper with dozens of formulas, but that's not my field of study. In any paper I read of any discipline, I never came across any paper filled with enough formulas that it would make sense to compress at the cost of clarity. I fully agree, though, on following conven…

> I never came across any paper filled with enough formulas that it would make sense to compress at the cost of clarity

Fair point, but with this approach, even simple formulae could really clutter up a page if the variable names are long and descriptive (imagine just a rational function!). Also, as with programming, folks might abbreviate (e.g., `vel_thg`) and then we're nearly back at square one.

Re: It Takes Two Neurons to Ride a Bicycle (2004)

#54

Post by tajen »

pje wrote: post #39

This is now my favorite scientific paper headline, beating out the previous champion, "How Many Birds Are There?" https://link.springer.com/article/10.1023/A:1018341530497

In that case, if you lay outdoors with your mouth open, how long does it take until a bird ... in it? Depending on the worldwide bird density and the relative size of the mouth: https://what-if.xkcd.com/11/

Re: It Takes Two Neurons to Ride a Bicycle (2004)

#55

Post by lucb1e »

andars wrote: post #26
lucb1e wrote: post #20

Earlier quoted context omitted.

But then it wouldn't look as "scientific" (i.e. anyone could understand it, it wouldn't look complicated). At least that's what I feel like, reading and writing a bunch of papers for my master's. We are encouraged to put math stuff in ours just because it looks more theoretical that way. Whenever I do something of worth I also make sure to blog about it so I can write down in normal terms what we did and found, with…

Would you mind sharing your field of study?

Security, software and network engineering. (Previous study was software and security, this one is security and network; and I've always liked to play with tech in those three subfields.)

Re: It Takes Two Neurons to Ride a Bicycle (2004)

#56

Post by jmkirby »

Joe-Z wrote: post #29
lucb1e wrote: post #20

Earlier quoted context omitted.

But then it wouldn't look as "scientific" (i.e. anyone could understand it, it wouldn't look complicated). At least that's what I feel like, reading and writing a bunch of papers for my master's. We are encouraged to put math stuff in ours just because it looks more theoretical that way. Whenever I do something of worth I also make sure to blog about it so I can write down in normal terms what we did and found, with…

I got the same feeling while I was still in university. I mean if the mathematical notation would at least make it more concise, because there are definitely computations which are easier explained using this notation. But more often than not I look at papers, where I know what they were doing and how and just have to ask myself: Why would you go through the work of translating what you did back into formulas, which…

I'm old enough to have never been tested for dyslexia, because I scored high in average tests..

But come high school years, or in British sixth form studying for"A levels", I scored in the top decile for my class and for Applied Math, but the bottom dectile for Pure Math.

I think you can make a very good argument that math notation is not doing the potentially career changing job it could be doing, by not expanding the keys. Darn, even a key table index alongside would be night and day better. Edit - didn't remember the length of my comment after coming back to it after a break, so culled the excess. The punchline was that when we got a new young and enthusiastic Pure tutor, who was French, so he in true anger would explain to us in great eloquent depth, my marks equalized in two semesters.

There's surely something like a formal study of students to show if comprehension is the main reason math is hard?

Re: It Takes Two Neurons to Ride a Bicycle (2004)

#57

Post by lucb1e »

chestervonwinch wrote: post #53
lucb1e wrote: post #50

Earlier quoted context omitted.

> Obviously, using variables names like `velocity_of_thing` is much too verbose in mathematics That is not obvious to me. Perhaps in a purely mathematical paper with dozens of formulas, but that's not my field of study. In any paper I read of any discipline, I never came across any paper filled with enough formulas that it would make sense to compress at the cost of clarity. I fully agree, though, on following conven…

> I never came across any paper filled with enough formulas that it would make sense to compress at the cost of clarity Fair point, but with this approach, even simple formulae could really clutter up a page if the variable names are long and descriptive (imagine just a rational function!). Also, as with programming, folks might abbreviate (e.g., `vel_thg`) and then we're nearly back at square one.

Also in programming, when my girlfriend (the mathematician[1]) used single letters in code and I helped her with the coding part of it, she had to remind me what some letters stood for. With acronyms or abbreviations I might need to ask a first time (or maybe not even that, especially if you put a comment with the full version upon declaration), but it's definitely easier to remember what is what.

But anyway that's programming. Papers are a little different of course, with limited space so usually there are no big code parts with declarations and comments. Which is also why I like blog posts: things are clickable and interactive. A PDF is super static and you can't expect a reader to click through to the code or to be able to zoom in.

[1] well, she claims not to be, but from my POV it's math even if she says it's a subfield.

Re: It Takes Two Neurons to Ride a Bicycle (2004)

#59

Post by slavik81 »

slavik81 wrote: post #42
chestervonwinch wrote: post #31

Earlier quoted context omitted.

1) Sometimes it's actually helpful to use greek letters when a convention is used. For example: capitals for matrices (A), lowercase for column vectors (a), and Greek for scalars (α). 2) I agree with the gist of your point, but I'm guessing you're being down-voted because you come off as sort of flippant. Anyhow, I've long thought that mathematics should have hover-text to help remove the mental overhead of translati…

Just the other day I spent a solid 30 minutes trying to distinguish between I and Iⱼ in an equation of motion. Turns out that the former was the identity matrix and the later was the inertial matrix of body j. If there's a way to add that sort of hover annotation in LaTeX, I'd gladly use that for my thesis.

It seems there is a method to add tooltips, though it looks a little rough. Worth a shot, I suppose. https://tex.stackexchange.com/q/155518/77180
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