10 ms·

Khan Academy now supports tau

104 points by spicyj 14y ago

sp332 14y ago
Quite possibly because they hired Vi Hart :)
- spicyj 14y ago
  That's not the only reason, though it might have been a small factor. Many of us here at KA are tau believers. :)
  - nsfmc 14y ago
    speak for yourself, infidel!
gouranga 14y ago
I'd rather they concentrated on supporting openid so you don't need a google or Facebook account...
- spicyj 14y ago
  As we've seen with Stack Exchange, OpenID is confusing for most users, but good news: you don't need a Google or Facebook account anymore! You can sign up for a Khan Academy account with any email address here: http://www.khanacademy.org/signup http://www.khanacademy.org/signup
  - gouranga 14y ago
    Cool - when did that happen? Thanks for pointing out :)
    - spicyj 14y ago
      I don't remember exactly, but it was a few months ago. About a month ago we also launched the ability to create "child" accounts for under-13 users who aren't old enough for Google or Facebook accounts.
      - vessenes 14y ago
        It would be cool to be able to transition accounts to the new child accounts; is that possible?
        spicyj 14y ago
        Sorry, it's not possible, but the main reason to create a child account is to get around the Google/Facebook requirement -- since you've already surmounted that hurdle, a child account probably wouldn't be of any more use to you.
  - psbp 14y ago
    Off topic, but can you add the ability to check off completed videos instead of having to watch them within the website? I usually play KA videos at 1.5x or 2.0x on youtube, but then I don't receive any points :( Thanks for everything by the way.
- unconed 14y ago
  OpenID is dead. It was flawed from the beginning, they botched the deployment, and it's useless outside of the you-sitting-in-front-of-browser context. Mobile apps, delegating access, exchanging profile data... not supported.
  - gouranga 14y ago
    So what is a better solution? Genuine question.
    - unconed 14y ago
      The only thing that works well for lots of people is Facebook, twitter and google login. Mozilla's browserID might change things, but I'm neither holding my breath or expecting it to work well anytime soon. This is Mozilla after all.
nemo1618 14y ago
Just for answers? Lame. It would be noteworthy if they had an option to replace instances of pi with tau in all the practice problems.
- ramidarigaz 14y ago
  That would be unbelievably confusing...
dllthomas 14y ago
If tau means 2*pi, how do I represent torsion?
- jcurbo 14y ago
  The Tau Manifesto discusses this (perhaps not to your satisfaction, but it's there): http://tauday.com/tau-manifesto#sec:ambiguous_notation http://tauday.com/tau-manifesto#sec:ambiguous_notation
  - dllthomas 14y ago
    Consider the Frenet-Serret apparatus. We use tau to represent torsion. The Tau Manifesto proposes we replace it with N - that not only breaks the "scalars are lower-case Greek, vectors are capital Latin" pattern, but N is already used to represent the normal vector. And this is somewhere the circle constant (in whichever form) comes up frequently.
    - mhartl 14y ago
      Some people say we should use e for the base of natural logarithms, but that's crazy. The letter e is already used for the charge on an electron, for the eccentricity of an ellipse, and for orthonormal basis vectors. Oh, and it's the identity element in group theory. Exponentials and logarithms show up in all those contexts, so the risk of confusion is too great. Using e also breaks the convention of using lower-case Greek letters for fundamental mathematical constants (such as the circle constant π, the golden ratio φ, the Euler–Mascheroni constant γ, and the Feigenbaum constants α and δ). I'll keep using β = 0.367879..., thank you very much. Then the base of natural logarithms is 1/β, and 1/β^(iπ) = -1. How beautiful is that? Now, some people say that writing exponential growth as β^(-x) is confusing, but I say, come on, it's only a minus sign!
      - dllthomas 14y ago
        If that was already the convention, I'd be on board.
- 14y ago
drcube 14y ago
Tau is clearer in some domains and pi is better in others. The mental overhead from switching between the two is too much, so just pick one already. And let the rest of us know, so we can go back to having a clear standard and not requiring the mental overhead of switching while studying different authors. Oh yeah, we went through that 2000 years ago and the winner was pi. I haven't seen any compelling reason to switch yet. (Says the guy who uses "j" for the imaginary constant. :P)
- glhaynes 14y ago
  In which domains is pi better? And was there a discussion 2000 years ago that led to pi "winning"? (If so, it'd be really fun to read its reasoning.) [Both of these are honest questions; I'm not a mathematician.]
  - drcube 14y ago
    http://www.thepimanifesto.com/ http://www.thepimanifesto.com/ The Pi Manifesto has a few examples of pi beating tau (statistics, polygons, and complex numbers mainly), while also pointing out how silly and biased some of the tau examples are. However, the argument isn't very convincing from either side. And as to your second question, I have no idea. I just know the idea has been settled for a long time now and I think this whole debate is needlessly distracting. Not that it isn't fun to watch or think about, but it confuses people who are just trying to learn and use math.
    - kmm 14y ago
      Their argument about the normal distribution is completely off though. There is completely no reason to group the two with the standard deviation. Their biggest argument seems to be that the area of unit circle is exactly pi. Sadly, there is absolutely no need to work with fractions of areas of the unit circle, while if you're working with angles the unit circle is a most natural standardisation. The normal distribution has been a lot clearer to me since I've understood the two should be grouped with the pi. Their argument about trigonometric functions is completely wrong and obviously so. Trigonometric functions work with angles and it's already shown (and pimanifesto readily admits) that tau shines there. Their argument about Euler's identity is as inane as the tauists' is. They don't understand quadratic forms. I'm guessing this site is sarcastic.
nilaykumar 14y ago
I still find it hard to see any practical, hard benefits of switching to tau. Perhaps you could argue that many things become "more natural" but at this point, pi is ingrained in mathematics, and it works perfectly well. I just can't imagine that switching to tau would allow us to reap any benefits that were previously inaccessible. I don't think there's any reason to fix what ain't broke.
- ef4 14y ago
  I think the strongest argument is pedagogical. If tau makes the underlying concepts clearer (and I believe it does), then it makes sense to use it when teaching beginners.
  - JadeNB 14y ago
    This is a dangerous argument—sure, if (I did say 'if'!) it's a win for the beginners, then why not expose them to it when there's no baggage dragging them back?; but, on the other hand, in that case, in exchange for short-term gains you're giving them a long-term loss of ability to communicate with others who weren't taught that way. (Essentially the same argument can apply to innovation; it doesn't mean that innovation is bad, just that it is rarely without cost.)
    - rlpb 14y ago
      > a long-term loss of ability to communicate with others who weren't taught that way. I'm not sure that the difference between pi and tau is severe enough to cause a communication problem. Conversion is trivial and anyone familiar with one can learn to convert to the other in about ten seconds. Existing problems with conversion from older systems into metric make a pi<->tau conversion insignificant - and even then people manage to deal with it just fine.
- vineet 14y ago
  I think their main point is not to switch to tau but to allow it in answers. I like the attitude.
nickpinkston 14y ago
This brought me back to Khan where I previous did every math exercise, and I was a bit disappointed to see that not too much has changed with the instruction they offer. I keep wanting math exercises beyond elementary calc, but they just gave the same stuff a face lift. I'm guessing they're heads down getting the Khan platform that we've heard about, but does anyone have any updates?
- spicyj 14y ago
  Right now we're focusing more on middle school–level math -- we're adding literally hundreds of new exercises in the topics that we are working on but haven't yet had time to work on calculus and beyond.
  - vessenes 14y ago
    Hey, nice work. My daughters do Khan Academy at home in the mornings for a bit rather than their elementary school math class. They love it. I wanted to tell you guys a story though, about your UI transition. I walked in a few months ago to my 8 year old daughter slumped at the desk next to her computer, nonresponsive. When I was like "Oh my God, are you okay?" She told me, with many tears, that she was no longer to obtain I believe they were called "Master" badges in some future subjects, like Geometry. She had earned one of the Master badges at great effort, and when the UI changed, you guys retired them for more granular badges. Overall, I'd say it was the right decision to make; gaining subject mastery is done on a smaller slice of content now, and feels more achievable. That said, she was totally devastated that she wouldn't be able to earn those future badges. Oh man, it was tough. She recovered nicely and loves the new interface, but I was thinking what an impact a UI change had, and thinking that a) probably many adults feel the same way with a change, but don't communicate it as well, and b) some sort of way to notify / slowly introduce / help transition kids who use the tool intimately as changes happen would be pretty awesome. Thanks for all the work! I wish I'd taken some video for your UI guys, she was really bummed, the sort of response you can't get out of a focus group. :)
    - spicyj 14y ago
rsanchez1 14y ago
Tau is a fad.
wazoox 14y ago
So let's see. There's pi, used for ~2300 years, or tau, some niche US-only fad (check for the tau wikipedia page in every language BUT english). It makes absolutely no fscking sense. Now could we move on?
Xion 14y ago
The proponents of tau that cite the ubiquity of the 2pi factor in maths seem to forget that it's an exceedingly huge swath of knowledge and thus any notion of ubiquity might as well be moot, or totally dependent on the region of maths this person frequents. I wouldn't be surprised if there are some domains of maths where even natural numbers are used rarely or almost never (formal logic springs to mind). That's why it's possible to cherry-pick favourable examples which support either side of pi-tau debate. But you might say, of course, that those fields of mathematics which tau makes "easier" are the ones important in early math education (especially below the university level). Hence adopting tau would make them substantially friendlier and more intuitive to many people. While the idea of "fixing" math concept to make them more bearable to laymen should not be dismissed automatically, I would like to point out that the question of tau vs. 2pi is by no means the only issue of this kind. Indeed, there are a couple of more "warts" in everyday maths that could also warrant "fixing". Consider: * The direction in which positive and negative angles on two-dimensional, Cartesian plane are measured [1]. Counter-intuitively, the measure increases when going counterclockwise, while going clockwise decreases it. * The main diagonal [2] of a matrix goes from upper-left to lower-right corner, which coincides with the shape of backslash character. * The established order of indices for matrix' elements is row-column, so that A_xy refers to element in x-th row and y-th column of matrix A. This goes against the habit of specifying the horizontal coordinate before the vertical coordinate when talking about XY planes [3]. * Definition of convex [4] and concave [5] functions (for R->R ones) do not agree with the intuitive associations based on plots of those functions. Clearly, the convex one looks like a valley, and the concave one resembles a hill or mountain. I'm sure there are many more examples of such unreasonable, counter-intuitive conventions, so we really have a lot of work ahead of us. So, anyone fancies writing the Slash Diagonal Manifesto?... [1] http://en.wikipedia.org/wiki/Angle#Positive_and_negative_angles http://en.wikipedia.org/wiki/Angle#Positive_and_negative_ang... [2] http://en.wikipedia.org/wiki/Main_diagonal http://en.wikipedia.org/wiki/Main_diagonal [3] http://en.wikipedia.org/wiki/Cartesian_coordinate_system#Cartesian_coordinates_in_two_dimensions http://en.wikipedia.org/wiki/Cartesian_coordinate_system#Car... [4] http://en.wikipedia.org/wiki/Convex_function http://en.wikipedia.org/wiki/Convex_function [5] http://en.wikipedia.org/wiki/Concave_function http://en.wikipedia.org/wiki/Concave_function
- jacobolus 14y ago
andrewingram 14y ago
I'm still on the fence as to which is more correct, though I do find that tau eliminates a lot of the silly brainfarts I used to make at school. But I do think this is actually quite important. Mathematics has a few 'special' values including; 0, 1, i, pi/tau and e, special because they turn up everywhere, so it'd be nice to know which of pi and tau is the 'correct' special number.

104 points by spicyj 14y ago

sp332 14y ago

Quite possibly because they hired Vi Hart :)

spicyj 14y ago
That's not the only reason, though it might have been a small factor. Many of us here at KA are tau believers. :)
- nsfmc 14y ago
  speak for yourself, infidel!

gouranga 14y ago

I'd rather they concentrated on supporting openid so you don't need a google or Facebook account...

spicyj 14y ago
As we've seen with Stack Exchange, OpenID is confusing for most users, but good news: you don't need a Google or Facebook account anymore! You can sign up for a Khan Academy account with any email address here: http://www.khanacademy.org/signup http://www.khanacademy.org/signup
- gouranga 14y ago
  Cool - when did that happen? Thanks for pointing out :)
  - spicyj 14y ago
    I don't remember exactly, but it was a few months ago. About a month ago we also launched the ability to create "child" accounts for under-13 users who aren't old enough for Google or Facebook accounts.
    - vessenes 14y ago
      It would be cool to be able to transition accounts to the new child accounts; is that possible?
      - spicyj 14y ago
        Sorry, it's not possible, but the main reason to create a child account is to get around the Google/Facebook requirement -- since you've already surmounted that hurdle, a child account probably wouldn't be of any more use to you.
- psbp 14y ago
  Off topic, but can you add the ability to check off completed videos instead of having to watch them within the website? I usually play KA videos at 1.5x or 2.0x on youtube, but then I don't receive any points :( Thanks for everything by the way.
unconed 14y ago
OpenID is dead. It was flawed from the beginning, they botched the deployment, and it's useless outside of the you-sitting-in-front-of-browser context. Mobile apps, delegating access, exchanging profile data... not supported.
- gouranga 14y ago
  So what is a better solution? Genuine question.
  - unconed 14y ago
    The only thing that works well for lots of people is Facebook, twitter and google login. Mozilla's browserID might change things, but I'm neither holding my breath or expecting it to work well anytime soon. This is Mozilla after all.

nemo1618 14y ago

Just for answers? Lame. It would be noteworthy if they had an option to replace instances of pi with tau in all the practice problems.

ramidarigaz 14y ago
That would be unbelievably confusing...

dllthomas 14y ago

If tau means 2*pi, how do I represent torsion?

jcurbo 14y ago
The Tau Manifesto discusses this (perhaps not to your satisfaction, but it's there): http://tauday.com/tau-manifesto#sec:ambiguous_notation http://tauday.com/tau-manifesto#sec:ambiguous_notation
- dllthomas 14y ago
  Consider the Frenet-Serret apparatus. We use tau to represent torsion. The Tau Manifesto proposes we replace it with N - that not only breaks the "scalars are lower-case Greek, vectors are capital Latin" pattern, but N is already used to represent the normal vector. And this is somewhere the circle constant (in whichever form) comes up frequently.
  - mhartl 14y ago
    Some people say we should use e for the base of natural logarithms, but that's crazy. The letter e is already used for the charge on an electron, for the eccentricity of an ellipse, and for orthonormal basis vectors. Oh, and it's the identity element in group theory. Exponentials and logarithms show up in all those contexts, so the risk of confusion is too great. Using e also breaks the convention of using lower-case Greek letters for fundamental mathematical constants (such as the circle constant π, the golden ratio φ, the Euler–Mascheroni constant γ, and the Feigenbaum constants α and δ). I'll keep using β = 0.367879..., thank you very much. Then the base of natural logarithms is 1/β, and 1/β^(iπ) = -1. How beautiful is that? Now, some people say that writing exponential growth as β^(-x) is confusing, but I say, come on, it's only a minus sign!
    - dllthomas 14y ago
      If that was already the convention, I'd be on board.
14y ago

drcube 14y ago

Tau is clearer in some domains and pi is better in others. The mental overhead from switching between the two is too much, so just pick one already. And let the rest of us know, so we can go back to having a clear standard and not requiring the mental overhead of switching while studying different authors. Oh yeah, we went through that 2000 years ago and the winner was pi. I haven't seen any compelling reason to switch yet. (Says the guy who uses "j" for the imaginary constant. :P)

glhaynes 14y ago
In which domains is pi better? And was there a discussion 2000 years ago that led to pi "winning"? (If so, it'd be really fun to read its reasoning.) [Both of these are honest questions; I'm not a mathematician.]
- drcube 14y ago
  http://www.thepimanifesto.com/ http://www.thepimanifesto.com/ The Pi Manifesto has a few examples of pi beating tau (statistics, polygons, and complex numbers mainly), while also pointing out how silly and biased some of the tau examples are. However, the argument isn't very convincing from either side. And as to your second question, I have no idea. I just know the idea has been settled for a long time now and I think this whole debate is needlessly distracting. Not that it isn't fun to watch or think about, but it confuses people who are just trying to learn and use math.
  - kmm 14y ago
    Their argument about the normal distribution is completely off though. There is completely no reason to group the two with the standard deviation. Their biggest argument seems to be that the area of unit circle is exactly pi. Sadly, there is absolutely no need to work with fractions of areas of the unit circle, while if you're working with angles the unit circle is a most natural standardisation. The normal distribution has been a lot clearer to me since I've understood the two should be grouped with the pi. Their argument about trigonometric functions is completely wrong and obviously so. Trigonometric functions work with angles and it's already shown (and pimanifesto readily admits) that tau shines there. Their argument about Euler's identity is as inane as the tauists' is. They don't understand quadratic forms. I'm guessing this site is sarcastic.

nilaykumar 14y ago

I still find it hard to see any practical, hard benefits of switching to tau. Perhaps you could argue that many things become "more natural" but at this point, pi is ingrained in mathematics, and it works perfectly well. I just can't imagine that switching to tau would allow us to reap any benefits that were previously inaccessible. I don't think there's any reason to fix what ain't broke.

ef4 14y ago
I think the strongest argument is pedagogical. If tau makes the underlying concepts clearer (and I believe it does), then it makes sense to use it when teaching beginners.
- JadeNB 14y ago
  This is a dangerous argument—sure, if (I did say 'if'!) it's a win for the beginners, then why not expose them to it when there's no baggage dragging them back?; but, on the other hand, in that case, in exchange for short-term gains you're giving them a long-term loss of ability to communicate with others who weren't taught that way. (Essentially the same argument can apply to innovation; it doesn't mean that innovation is bad, just that it is rarely without cost.)
  - rlpb 14y ago
    > a long-term loss of ability to communicate with others who weren't taught that way. I'm not sure that the difference between pi and tau is severe enough to cause a communication problem. Conversion is trivial and anyone familiar with one can learn to convert to the other in about ten seconds. Existing problems with conversion from older systems into metric make a pi<->tau conversion insignificant - and even then people manage to deal with it just fine.
vineet 14y ago
I think their main point is not to switch to tau but to allow it in answers. I like the attitude.

nickpinkston 14y ago

This brought me back to Khan where I previous did every math exercise, and I was a bit disappointed to see that not too much has changed with the instruction they offer. I keep wanting math exercises beyond elementary calc, but they just gave the same stuff a face lift. I'm guessing they're heads down getting the Khan platform that we've heard about, but does anyone have any updates?

spicyj 14y ago
Right now we're focusing more on middle school–level math -- we're adding literally hundreds of new exercises in the topics that we are working on but haven't yet had time to work on calculus and beyond.
- vessenes 14y ago
  Hey, nice work. My daughters do Khan Academy at home in the mornings for a bit rather than their elementary school math class. They love it. I wanted to tell you guys a story though, about your UI transition. I walked in a few months ago to my 8 year old daughter slumped at the desk next to her computer, nonresponsive. When I was like "Oh my God, are you okay?" She told me, with many tears, that she was no longer to obtain I believe they were called "Master" badges in some future subjects, like Geometry. She had earned one of the Master badges at great effort, and when the UI changed, you guys retired them for more granular badges. Overall, I'd say it was the right decision to make; gaining subject mastery is done on a smaller slice of content now, and feels more achievable. That said, she was totally devastated that she wouldn't be able to earn those future badges. Oh man, it was tough. She recovered nicely and loves the new interface, but I was thinking what an impact a UI change had, and thinking that a) probably many adults feel the same way with a change, but don't communicate it as well, and b) some sort of way to notify / slowly introduce / help transition kids who use the tool intimately as changes happen would be pretty awesome. Thanks for all the work! I wish I'd taken some video for your UI guys, she was really bummed, the sort of response you can't get out of a focus group. :)
  - spicyj 14y ago

rsanchez1 14y ago

Tau is a fad.

wazoox 14y ago

So let's see. There's pi, used for ~2300 years, or tau, some niche US-only fad (check for the tau wikipedia page in every language BUT english). It makes absolutely no fscking sense. Now could we move on?

Xion 14y ago

The proponents of tau that cite the ubiquity of the 2pi factor in maths seem to forget that it's an exceedingly huge swath of knowledge and thus any notion of ubiquity might as well be moot, or totally dependent on the region of maths this person frequents. I wouldn't be surprised if there are some domains of maths where even natural numbers are used rarely or almost never (formal logic springs to mind). That's why it's possible to cherry-pick favourable examples which support either side of pi-tau debate. But you might say, of course, that those fields of mathematics which tau makes "easier" are the ones important in early math education (especially below the university level). Hence adopting tau would make them substantially friendlier and more intuitive to many people. While the idea of "fixing" math concept to make them more bearable to laymen should not be dismissed automatically, I would like to point out that the question of tau vs. 2pi is by no means the only issue of this kind. Indeed, there are a couple of more "warts" in everyday maths that could also warrant "fixing". Consider: * The direction in which positive and negative angles on two-dimensional, Cartesian plane are measured [1]. Counter-intuitively, the measure increases when going counterclockwise, while going clockwise decreases it. * The main diagonal [2] of a matrix goes from upper-left to lower-right corner, which coincides with the shape of backslash character. * The established order of indices for matrix' elements is row-column, so that A_xy refers to element in x-th row and y-th column of matrix A. This goes against the habit of specifying the horizontal coordinate before the vertical coordinate when talking about XY planes [3]. * Definition of convex [4] and concave [5] functions (for R->R ones) do not agree with the intuitive associations based on plots of those functions. Clearly, the convex one looks like a valley, and the concave one resembles a hill or mountain. I'm sure there are many more examples of such unreasonable, counter-intuitive conventions, so we really have a lot of work ahead of us. So, anyone fancies writing the Slash Diagonal Manifesto?... [1] http://en.wikipedia.org/wiki/Angle#Positive_and_negative_angles http://en.wikipedia.org/wiki/Angle#Positive_and_negative_ang... [2] http://en.wikipedia.org/wiki/Main_diagonal http://en.wikipedia.org/wiki/Main_diagonal [3] http://en.wikipedia.org/wiki/Cartesian_coordinate_system#Cartesian_coordinates_in_two_dimensions http://en.wikipedia.org/wiki/Cartesian_coordinate_system#Car... [4] http://en.wikipedia.org/wiki/Convex_function http://en.wikipedia.org/wiki/Convex_function [5] http://en.wikipedia.org/wiki/Concave_function http://en.wikipedia.org/wiki/Concave_function

jacobolus 14y ago

andrewingram 14y ago

I'm still on the fence as to which is more correct, though I do find that tau eliminates a lot of the silly brainfarts I used to make at school. But I do think this is actually quite important. Mathematics has a few 'special' values including; 0, 1, i, pi/tau and e, special because they turn up everywhere, so it'd be nice to know which of pi and tau is the 'correct' special number.