About Tauism

This Khan Academy classic is worth projecting in a classroom.  I know I would be eager to share it, if back in high school teaching, like in the good old days

I'm not suggesting I'd turn my whole curriculum over to Sal, just that I'm up for sampling choice pieces by authors I admire, Vi Hart another one (good at math video as an art form).  This retrospective by Khan, combined with a polemic at the end, seems a great high point to cite.

The math classroom of the future, in one of its many forms, casts the teacher in the role of VJ (video DJ) in a lot of ways.

Most clips might be of lesser length than Khan's average, although some teachers might invest in a full series of something, with their own time at the podium, as emcee and expert, to apply local spin, relate it to actual students more directly (personalize, make it real, take questions).

It's up to the teachers and lesson planners to glue the samplings into coherent pathways that come together to produce whole concepts.  The teacher may improvise a good portion of the presentation, yet there's a known terrain, the school's agreed-upon curriculum, what it's known for.

The fact remains that "citing video" is a lot like a VJ's job and editing video is the "anime" equivalent of doing "manga" or "stills" (picture Jupyter Notebooks with still graphics courtesy of matplotlib).

In the graphical arts, manga equals comic books, anime equals cartoons.

In mathematics, one needs both.

Sal covers a lot of ground in the above video, looking back, reviewing trig functions, radians, the whole idea of pi. 

Then comes his impassioned defense of tau (as 2 pi).  He uses tau's appearance on the stage as an excuse to quickly review the whole board once again, having set us up the first time with a critique of Euler's Formula, arguably the most beautiful in math, but having a flaw, a blemish.

I don't see any either/or here really.  Use tau in place of pi when it's prettier.  Why not?

However at this juncture it's worth mentioning another low intensity tug-o-war in which tau is involved.  Versus Phi.  There's been some debate about whether tau stands for .618... i.e. the reciprocal of 1.618... 

Some authors use tau for the latter, however the convention I'm most familiar with assigns Greek letter phi to 1.618... and tau to its reciprocal (0.618...).  In English or other romanized ("ascii-fied") texts, we may use phi in place of the Greek letter.  Then comes the low intensity debate whether to pronounce it "fee" or "fie".  A contingent says it both ways.  Maybe one should say "fee" on odd days of the week?

Quoting from Wikipedia:

Since the 20th century, the golden ratio has been represented by the Greek letter φ (phi, after Phidias, a sculptor who is said to have employed it) or less commonly by τ (tau, the first letter of the ancient Greek root τομή—meaning cut).

What I suggest coming from a liberal arts background is we remind students of mathematics that debate is a feature (not a bug) of their discipline and circle these simple examples, in preparation for investigating bigger debates in lessons to come.

When Sal comes back around again, reviewing the board, the trig functions, the unit circle, he shows that Euler's formula may be made even more beautiful.   By that time some of us are ready to vote for Sal's argument, especially with the caveat that pi is not hereby banned.  These constants do not compete so much as reinforce one another.

As for phi versus tau, I think we've pretty much settled on tau being the reciprocal of the golden mean, which golden mean is itself > 1, i.e. is 1.618... or (1 + rt2(5))/2 -- note that I sometimes replace sqrt() with rt2() as I don't want to push the mental model to favor "squares" too prejudicially, given the triangle-friendly balance of this curriculum (Martian Math inspired)).

Especially if tau is going of to do yeoman's service as 2 pi, replacing 2 pi r with tau r in many a Jupyter Notebook, all the more reason, then, to not force it to do double duty as the golden ratio as well.

That'd only add to the post Babel confusion, not that I expect any posting by me to serve as an edict.  The post Babel confusion (not everyone on the same page) is more what I'm drawing attention to, as another lens for viewing math.

Tune in the debates for a change.  Listen to arguments.

Kirby

Additional reading / links


[originally a post to mathfuture, a Google Group]

1-2-3 Testing

I just purchased Camtasia for Mac, a product for making screencasts especially.

The above represents my fresh out-of-the-box use of this tool, which I've used in a previous incarnation on Windows.

Snake Escape!

The Achilles Heel of a large snake aquarium is the lid, made of some kind of mesh with seams applied to four edges.  The other five sides are glass, but the lid has to be porous.  If a seam comes loose, good bye secure holding tank.  Barry got out.

Joel passed the news from Lindsey, staying in the Snake Room, that a python was on the loose near the deck door.  I'd cleaned the aquarium Friday before picking up Lindsey at PDX International.

Fortunately for us, I didn't have to turn the house upside down searching and had another much smaller aquarium at the ready that I could at least secure.  Tomorrow I'll need to check with the pet store on my options.  Barry can spend the night in this smaller tank.

In other news, the HTC One M9 came with Lollipop, which sent me into a First World Problem tizzy.  I was expecting Marshmallow.  Upgrading does not seem that hard.  William Brown, a former O'Reilly School student, came by and rescued me from my blue funk, treating me to 10 Cloverfield Lane at The Bagdad.

Sometimes one's karma gets heavy, like in said movie, wherein disaster is the theme.  What if the ETs do come?  They might not be friendly.  How friendly would we be if left to spread unchecked, across the galaxy?  Checking historical precedents, one might conclude "not very".

Those who specialize in the "science of worry" (risk management) try to prioritize what to fear.  Should we be defending against machines taking over?  Depends on what that means.  In many dimensions they already have.

Taking over where drudgery was the norm is not necessarily a bad thing.  But what counts as "drudgery" and so on.  Will humans be smart enough to let themselves not work at meaningless tasks, just to "earn the right" to have a life.

Engaging in useless tasks for no reason is called "not having a life" where I come from.

Lindsey was very calm about the snake on the loose.  She asked how long it had been free.  "At least a day" I speculated.  "Cool" she said.

Walker is feeling pretty weak in the meditation department.  I transferred her to friends in the FNB network for healing.  She needs to recover her strength.

Thanks to Ron Braithwaite for dropping by this afternoon and joining me on an errand.

Men's Retreat

I managed to overlap with the Quaker guys, plus the Great Bear Camp owners, all in one day this year.  I was rolling out of the driveway at 4:06 AM and back before midnight the same day.

Getting some time in the rain forest, seeing the cougar scratching posts, the new bridge and so on, made it worth all that driving.

Also, the Quaker men were good at telling life stories, talking about what it's been like for them to be dads, fathers, husbands, single men, boys, soldiers or whatever roles they've played.

Thanks to Carl Thatcher and Joe Snyder for setting the tone.  The theme:  Making Our Lives Count.

Tom Wittick reminded me to study the life of Houdini more.  Houdini knew Lovecraft, Teddy Roosevelt, Arthur Conan Doyle.  Tom is a font of interesting historical information.

On the way back from our hike to see the cougar scratch posts (trees whereon cougars sharpened their claws), the camp owner joked he was so off the grid that when he turned on the radio, he heard words the broadcasters took for granted, that he'd never heard.  Like "meme" (on NPR).

We talked about "memes" after that, singing commercial jingles as we emerged from the forest.  "Winston tastes good like a cigarette should".  There's no smoking at Bear Camp.

Sound Check

Trinkets are interactive / editable.  We're sharing about them on edu-sig this month.  Naomi and I are the new listowners.

Smoking Gun?

So what about taking the show on the road in a Bizmo (business mobile) and sending a heads up to the hinterlands that "code school" might be an option.  Consider a future in IT (part of STEM or STEAM).

I was ready to start with recruiting a couple decades ago at least, and started sharing my designs.   Later I started articulating the vision in my on-line journals (blogs), getting it out there.

A Control Room, or Dispatching Center, would keep the Bizmos busy.  Sounds like fun.

On the road with Global Data (or Global Matrix as the case may be).

However, the GNU Math meme (a pun on "new math") was also deeply tied to those stream-linings in spatial geometry, where we get all those pretty whole number volumes and a quantum leap in sophistication, in terms of being able to think geospatially, with more than just XYZ as a scaffolding (matrix).

We had the IVM (another matrix), we had Quadrays (different basis vectors).

Everything was published, in color, with animations, including to Wikipedia and Wikieducator.

Sources were cited, proofs were made.

Even H.S.M. Coxeter, King of Infinite Space, said the sphere packing formula as worth crowing about.  We did some crowing.

We've seen almost no interest, however, in any of the above.   Search the web, check if I'm right.  No need to take my word for it.  My fellow humans have other priorities, no time for follow-through.

I shared about Quadrays with PSU's Math Learning Center (MLC).

I delivered talks on the concentric hierarchy to any math class that'd let me in (quite a few did), as well as at Pycons, Europythons etc.

But all this flint clicking failed to start a fire apparently.  How soggy was the fuel?

Lets hope some future student of our time, maybe in a hundred years, comes up with some theories, as to why a promising future was disowned and disavowed.

I bet there's some story to unearth, maybe even a "smoking gun".