

Khan Academy now supports tau - spicyj
http://www.khanacademy.org/about/blog/post/26083003300/happy-tau-day

======
drcube
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
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
<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
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.

------
Xion
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 _counter_ clockwise, 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 _back_ slash 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_ang...](http://en.wikipedia.org/wiki/Angle#Positive_and_negative_angles)
[2] <http://en.wikipedia.org/wiki/Main_diagonal> [3]
[http://en.wikipedia.org/wiki/Cartesian_coordinate_system#Car...](http://en.wikipedia.org/wiki/Cartesian_coordinate_system#Cartesian_coordinates_in_two_dimensions)
[4] <http://en.wikipedia.org/wiki/Convex_function> [5]
<http://en.wikipedia.org/wiki/Concave_function>

~~~
jacobolus
* Counter-clockwise angles comes from making charts and graphs with the independent variable going from left to right, and the dependent variable from bottom to top. This is far too ingrained in the way we teach and learn about mathematics to change now, much more than the choice of pi or tau (though we do make y go from top to bottom in many computer graphics contexts). There’s no reasonable way that we could integrate direction of reading on a clock with direction of reading typical charts with direction of reading text into a uniform system, and I don’t consider changing all the clocks, texts, and charts in the world to be a reasonable possibility.

* What does the shape of the slash character have to do with anything? A slash is a fraction bar. Fractions and matrix diagonals are entirely unrelated, though in both cases numbers are read from top left to bottom right, in accordance with our typical reading direction in western texts.

* Matrix index ordering is a pain in the butt and will be confusing whichever way they’re labeled. The logic behind the current system is to use the first index for the component that results when multiplying by a vector, and using the second index within that component. Picking the opposite convention would also end up confusing. Figuring out the proper ordering when dealing with non-commutative “number” systems in general is a pain, and I don’t think there’s any easy answer. We have matrices multiply column vectors on the left, because that’s typically how we notate operators acting on some input. But it means that composition is multiplication from left to right, which is a bit confusing. There’s no way to make the order be always left-to-right or always right-to-left. But much more importantly, matrices are a kind of painful abstraction to use in general. Mathematics education would be much improved in many ways if we used Geometric Algebra instead of matrix representations a lot more of the time. <http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf>

* It’s much easier to just call these “concave up” and “concave down”. Problem solved.

------
nickpinkston
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
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
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. :)

~~~
kamens
Email me your daughter's email address used on Khan and tell her to keep her
eye out for a special badge.

ben@khanacademy.org

~~~
vessenes
Aww, thanks!

------
nilaykumar
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
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
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
> 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.

------
nemo1618
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
That would be unbelievably confusing...

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

~~~
spicyj
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>

~~~
gouranga
Cool - when did that happen?

Thanks for pointing out :)

~~~
spicyj
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
It would be cool to be able to transition accounts to the new child accounts;
is that possible?

~~~
spicyj
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.

------
sp332
Quite possibly because they hired Vi Hart :)

~~~
spicyj
That's not the only reason, though it might have been a small factor. Many of
us here at KA are tau believers. :)

~~~
nsfmc
speak for yourself, infidel!

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

~~~
joshAg
overloading variables is nothing new in math/science/engineering. Usual
methods include picking a different variable to represent torsion, or
appending a subscipt or superscript of some kind to differentiate between the
two taus. you could also use a bar (like hbar and h in physics) or an
apostrophe.

~~~
jmharvey
In macroeconomics, pi is commonly used to represent the rate of inflation.
And, as in many fields, i is used as an iterator.

Which means that in your math, if you're assuming constant inflation, you need
to deflate prices in year i by a factor of e^(i*pi).

~~~
joshAg
beautiful, just beautiful.

------
wazoox
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?

------
andrewingram
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.

------
rsanchez1
Tau is a fad.

