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A trick to eliminate 2π (sometimes)

marci.gunyho.com

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Re: A trick to eliminate 2π (sometimes)

#71

Post by jrockway »

Misdicorl wrote: post #36
movpasd wrote: post #12

Earlier quoted context omitted.

Thing is, angles don't really have units (the technical term is they are dimensionless). They are a length (the subtended arc of a circle) divided by a length (the radius of the circle). When you want to do something like get a sine wave of period T, you inevitably have to include a 2π somewhere. Speaking as someone who had to write down many 2π's in university (especially as I find angular quantities like angular fr…

This is not true. Angles very much have units and it's why you can express the same concept with different numbers. Pi equals 180 degrees equals 0.5 turns. 1 radian has different units than 1 steradian and if they didn't there wouldn't be a need for two different words to denote them. The quantity is a ratio of two lengths, and the length measure does "drop out". But it's not just any ratio, it's a very particular ra…

Yeah, units that algebraically reduce to 1 are always very interesting to me. Consider a chart showing how many CPU seconds you're consuming per second. The unit is seconds/second, which is equal to 1, but it is still a distinct concept from radians.

Re: A trick to eliminate 2π (sometimes)

#72

Post by zerocrates »

mgunyho wrote: post #55
ctoth wrote: post #11

Unrelated to the content but complaining about the website is a popular thing to do here so I'd like to share my experience, as a blind user. Here is what my screen reader sees for this page: Recently, I came up with a trick that can get rid of in many cases. It’s pretty simple, but it has some interesting implications. This is the trick: I just define a new derivative operator, like so: That’s all. You just take the…

Author here, I'm sorry to hear that it doesn't work well with a screen reader. I tested it with the reader mode of Firefox, which renders MathML perfectly, although I don't know how that would translate to a screen reader. Safari reader mode renders the math inline, like this: I just define a new derivative operator, like so: dxđ f(x)≡2π1 ⋅dxd f(x). That’s all. while Chrome's reader mode just fails to recognize the c…

I bet the "reading" modes of the browsers are just using the HTML that's visible on the page, but that's marked explicitly as hidden from screenreaders, using the aria-hidden attribute.

Re: A trick to eliminate 2π (sometimes)

#73

Post by mgunyho »

enriquto wrote: post #17

You can also eliminate the constant in some of the integral formulas by using đx instead of dx. I'm surprised the author does not propose this. However, some constants will still remain. Most conspicuously, the 2π constant in the very definiton of the Fourier transform. I once took a personal crusade to eliminate all such constants in the elementary Fourier formulas (plancherel-parseval, convolution theorems, commuta…

> You can also eliminate the constant in some of the integral formulas by using đx instead of dx. I'm surprised the author does not propose this.

In the post I propose doing that for Gauss' theorem and Cauchy's formula, because there it's convenient, heh. But to me it feels better to use Θ^ix than a scale factor in front, since the 2pi is always present in the exponential, while the prefactor can be avoided in Fourier transforms if you keep the 2pi in the exponential (or hide it inside Θ). Does this not apply also to the elementary formulas you mention?

Re: A trick to eliminate 2π (sometimes)

#74

Post by marcosdumay »

psychoslave wrote: post #50
RogerL wrote: post #39

Earlier quoted context omitted.

But what is the answer? What should I do differently? I get don't use images, but then what? I can't imagine all screen readers have the same capabilities, or that there is a base common ability, so what should we do? Googling says MathML is the answer (e.g. https://www.washington.edu/doit/how-do-i-create-online-math-... this site uses MathML and your reader isn't handling it. So now what? (alt-tags? something else?)

It depends on what public you care about. If readability did general public is a concern, just get rid of all these symbols and go with plain prose text, possibly using images as preferred illustrations over any ideographic way to encode ideas.

You can't discuss math while getting rid of the math symbols. That's not a reasonable proposal.

Math on the web is broken, the the affected people should be up complaining about that. This site did the most accessible thing possible; the fact that every tool broke here, just like they do for every other method is not really the author's fault.

Re: A trick to eliminate 2π (sometimes)

#75

Post by patrec »

bjornasm wrote: post #48
RogerL wrote: post #39

Earlier quoted context omitted.

But what is the answer? What should I do differently? I get don't use images, but then what? I can't imagine all screen readers have the same capabilities, or that there is a base common ability, so what should we do? Googling says MathML is the answer (e.g. https://www.washington.edu/doit/how-do-i-create-online-math-... this site uses MathML and your reader isn't handling it. So now what? (alt-tags? something else?)

One option would be to do testing with screen-readers and then find out if the content works, and if not find out why.

I think most people are fine with the idea that some of the costs (monetary and otherwise) arising from disabilities should be transferred from the people suffering from them to society at large. But I don't think it's reasonable for producers and users of broken screen readers to expect everyone (including authors of private blogs posts) bending over backwards to accommodate them, nor is it a remotely efficient use of societal resources. It also creates completely perverse incentives.

Re: A trick to eliminate 2π (sometimes)

#76

Post by marginalia_nu »

psychoslave wrote: post #50
RogerL wrote: post #39

Earlier quoted context omitted.

But what is the answer? What should I do differently? I get don't use images, but then what? I can't imagine all screen readers have the same capabilities, or that there is a base common ability, so what should we do? Googling says MathML is the answer (e.g. https://www.washington.edu/doit/how-do-i-create-online-math-... this site uses MathML and your reader isn't handling it. So now what? (alt-tags? something else?)

It depends on what public you care about. If readability did general public is a concern, just get rid of all these symbols and go with plain prose text, possibly using images as preferred illustrations over any ideographic way to encode ideas.

I don't think it's really viable to just stop posting equations altogether. Yeah it's more accessible, but it would also completely cripple any sort of discussion between mathematicians, physicists, etc.

Equations and mathematical notation aren't simple illustrations. They're in many ways more important than the stuff around them.

Re: A trick to eliminate 2π (sometimes)

#77

Post by linuxdude314 »

6gvONxR4sf7o wrote: post #38
movpasd wrote: post #12

Earlier quoted context omitted.

Thing is, angles don't really have units (the technical term is they are dimensionless). They are a length (the subtended arc of a circle) divided by a length (the radius of the circle). When you want to do something like get a sine wave of period T, you inevitably have to include a 2π somewhere. Speaking as someone who had to write down many 2π's in university (especially as I find angular quantities like angular fr…

Angles aren't dimensionless any more than lengths are dimensionless (feet per second makes just as much sense as rpm). It's just that angles have symmetries that lengths don't, which is where 2 pi comes in. Do you want units where your symmetries are expressed in multiples of 1, 2, or 2 pi (for turns, half-turns, and radians, respectively)?

If you mean units instead of dimensions I agree.

There is a natural reason for pi occurring in physics that makes little sense to ignore.

Treating it as something to be dealt with misses the forest for the trees.

Radians are the naturally occurring Euclidean unit of angular measurement.

Re: A trick to eliminate 2π (sometimes)

#78

Post by gbear605 »

marcosdumay wrote: post #74
psychoslave wrote: post #50

Earlier quoted context omitted.

It depends on what public you care about. If readability did general public is a concern, just get rid of all these symbols and go with plain prose text, possibly using images as preferred illustrations over any ideographic way to encode ideas.

You can't discuss math while getting rid of the math symbols. That's not a reasonable proposal. Math on the web is broken, the the affected people should be up complaining about that. This site did the most accessible thing possible; the fact that every tool broke here, just like they do for every other method is not really the author's fault.

It’s not entirely impossible; mathematicians did it for thousands of years (just read Newton’s Principia). It does use very specific language to do so, and some of the language might not exist for some advanced mathematical concepts, but I think that this whole article could be written that way.

Re: A trick to eliminate 2π (sometimes)

#79

Post by marcosdumay »

gbear605 wrote: post #78
marcosdumay wrote: post #74

Earlier quoted context omitted.

You can't discuss math while getting rid of the math symbols. That's not a reasonable proposal. Math on the web is broken, the the affected people should be up complaining about that. This site did the most accessible thing possible; the fact that every tool broke here, just like they do for every other method is not really the author's fault.

It’s not entirely impossible; mathematicians did it for thousands of years (just read Newton’s Principia). It does use very specific language to do so, and some of the language might not exist for some advanced mathematical concepts, but I think that this whole article could be written that way.

Yeah, let's talk about the difference in accessibility between the text on this site and Newton's Principia...

Re: A trick to eliminate 2π (sometimes)

#80

Post by jraph »

ctoth wrote: post #11

Unrelated to the content but complaining about the website is a popular thing to do here so I'd like to share my experience, as a blind user. Here is what my screen reader sees for this page: Recently, I came up with a trick that can get rid of in many cases. It’s pretty simple, but it has some interesting implications. This is the trick: I just define a new derivative operator, like so: That’s all. You just take the…

Wow, I'd be interested in knowing how to fix this. I don't currently write math on the web but if I had to, I would be tempted to do it exactly like this: bare HTML with MathML, no JavaScript. And would do it thinking about blind people relying on accessible content to read it.
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