Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Why Momentum Works

distill.pub

Post reply on HN
Print view View original

81–90 of 100 posts

Re: Why Momentum Works

#81

Post by yorwba »

xapata wrote: post #6

> The added inertia acts both as a smoother and an accelerator momentum = mass * velocity force = mass * acceleration momentum = (force / acceleration) * velocity So, it looks to me like momentum is inversely related to acceleration. It doesn't seem right to call momentum an "accelerator".

But velocity is the integral of acceleration, and for constant acceleration, this means

    velocity = 1/2*acceleration*time^2
    momentum = 1/2*force*time^2 = 1/2*mass*acceleration*time^2
So momentum is actually proportional to acceleration in this case.

Re: Why Momentum Works

#82

Post by colmvp »

I have to say that the dynamics of momentum diagram is a thing of real beauty. The whole paper felt a little NYTimes like and then of course, I see that Shan Carter helped a little bit with it!

Re: Why Momentum Works

#83

Post by xapata »

yorwba wrote: post #81
xapata wrote: post #6

> The added inertia acts both as a smoother and an accelerator momentum = mass * velocity force = mass * acceleration momentum = (force / acceleration) * velocity So, it looks to me like momentum is inversely related to acceleration. It doesn't seem right to call momentum an "accelerator".

But velocity is the integral of acceleration, and for constant acceleration, this means velocity = 1/2*acceleration*time^2 momentum = 1/2*force*time^2 = 1/2*mass*acceleration*time^2 So momentum is actually proportional to acceleration in this case.

Hmm. Think of the response that acceleration would have, all else equal, if momentum increased.

There's two ways to change momentum -- velocity or mass. If mass increases, acceleration decreases. If velocity increases, acceleration remains the same.

Edit: You've got a bit of an endogeneity problem in your equation. And I guess I do, too.

    momentum = 1/2 * mass * acceleration * time ^ 2
Since momentum is equivalent to mass times velocity, one of its components is on both sides of the equation simultaneously. My original equation had the same problem, except with velocity instead of mass.

So... I think "momentum" here is leading us a bit in the wrong direction. What the author should have been saying is "mass". After all, the metaphor was "a heavy ball", emphasizing the weight. The initial velocity was unchanged across the comparison.

It bugs me that so many domains misuse the term "momentum". Business people confuse momentum for velocity. Now machine learning folks are confusing momentum for mass. It's common for people to use a component of the whole as a stand-in term, like "my wheels" instead of "my car". Less common to go the other way: "my arm hurts" instead of "my elbow hurts". In this machine learning case the imprecision of the metaphor harms understanding.

Re: Why Momentum Works

#86

Post by xapata »

xapata wrote: post #79
arjie wrote: post #62

Earlier quoted context omitted.

To the author: I found the sentences quoted above quite clear. Please do not change them. They helped me rapidly comprehend what the article was going to be about.

You don't find the idea that increased momentum causes increased speed a bit strange?

I think I've figured out my confusion. I'm thinking of momentum as mass, not the product of mass and velocity. To an extent, the authors seem to have the same confusion.

Re: Why Momentum Works

#87

Post by tempodox »

I was fully expecting an article about some braindead product that nobody needs, called Momentum. Imagine my surprise finding physics and a healthily low percentage of BS.

Re: Why Momentum Works

#88

Post by throwaway71958 »

Some of the multi-author articles on Distill have a very important (IMO) innovation. They quantify precisely the contribution each author has made to the article. I would like to see this become norm in scientific papers, so on the one hand it'd be clear who to ask questions if they arise, and on the other the various dignitaries won't get their honorary spot on the authors list of papers they were barely involved with scientifically.

Re: Why Momentum Works

#90

Post by jast »

throwaway71958 wrote: post #88

Some of the multi-author articles on Distill have a very important (IMO) innovation. They quantify precisely the contribution each author has made to the article. I would like to see this become norm in scientific papers, so on the one hand it'd be clear who to ask questions if they arise, and on the other the various dignitaries won't get their honorary spot on the authors list of papers they were barely involved wi…

Other journals, e.g. Nature, already had this. It's not a Distil innovation. But I agree, this should be the norm in journals/confs/etc.
Post reply on HN