redesigning the railroad...

[kirby urner]

On Mon, Apr 25, 2016 at 8:48 PM, kirby urner <kirby...@gmail.com> wrote:

 

Khan Academy is a step away from chalk and talk (no chalk, more colored pens).  I haven't checked his tensor stuff yet, but I plan to.

https://youtu.be/8vBfTyBPu-4?list=PLA3C55EC6DEB58621

I did go through these in some detail.  Khan himself is not the narrator -- he has a life outside of his teaching booth no doubt. :-D

The narrator is quick to link to actual applications, such as General Relativity with its gravitational field tensor.  The linear algebra problem of using a somewhat arbitrary base gives rise to co-variant and contra-variant coordinates which may be converted into one another by matrix algebra.

Although named "Relativity Theory", Einstein's stuff is all about discovering what's invariant once we factor out the local coordinate system and deal with the phenomena more generally.  Invariance is typically modeled as a fixed distance or interval, unchanging even as basis vectors change.

Relative to my "lambda track" video, we're definitely using vectors and matrices as data structures as we tackle them in programming, studying matrix multiplication for group properties (closure, associativity, inverses, identity).

Einstein is credited in these movies for streamlining notation, mainly removing the capital sigma from the picture, as we know it's implied. 

We'd need to keep the while loop in our code though.  An L with Mx == True helps keeps us grounded in hard-numbered examples.

Mx <---- L(Mx, Hx) ----> Hx

Fig. 1  "machine-only versus human-only spectrum for language L"

The Physics department (S) will reap the rewards in being able to assume familiarity with matrix operations when bringing up tensors in connection with tiny deltas in some time-space continuum. 

High schoolers will have needed vectors to draw icosahedrons (see logo of the MAA). [1]

Per my diagram [2], a take the lambda track into S, not M, for any missing delta calculus puzzle pieces.

Kirby

[1]  The NCTM used to have an IVM for its logo but the lawyers warned they couldn't control it given our stronger hand, so they went for something more slippery, an infinity symbol, more comfortably meaningless.

[2] 

Master Plan:  https://flic.kr/p/FJPGmU

Lambda Calc:  https://flic.kr/p/bMx84t

[Joseph Austin]

On Apr 29, 2016, at 2:16 PM, kirby urner <kirby...@gmail.com> wrote:

Per my diagram [2], a take the lambda track into S, not M, for any missing delta calculus puzzle pieces.

Kirby

[2]  

Master Plan:  https://flic.kr/p/FJPGmU

Lambda Calc:  https://flic.kr/p/bMx84t

Kirby,

I'm a bit confused by the Lambda Calc link in [2].

[kirby urner]

Hi Joseph --

I was mainly using that slide decoratively, showing someone (not me) giving a talk, I think at a Python user group, and talking about what's called a "Y combinator".

The best exposition of the Y-combinator I've found on Youtube is this one from a 2012 Rubyconf: 

https://youtu.be/FITJMJjASUs
Y Not- Adventures in Functional Programming by Jim Weirich

Kirby

[Joseph Austin]

Impressive.

Did he really prove that, 

or is it a shell game and I missed the sleight of hand?

[rhetorical question].

Is "name matching" in computing the metaphysical equivalent of "action at a distance" (or "entanglement") in Physics? 

We know it works but can't really justify it?? [semi-rhetorical question]

Re the "railroad:"

Like many men my age, I grew up with toy trains and still pursue model railroading as a hobby.  Of course I enjoy trains for the trains's sake.  But the real railroads mainly care about moving freight or people for money.

Similarly with the "math" railroad.  

We academicians enjoy the railroad for the railroad's sake,

but our customers (students) really only care about getting the "answers" to their real-world "problems".

So instead of putting Science (PHYS) at "the end of the track",

I'd like to carry it along with the train from the beginning.

P=play should involve the S as well as the M.

I would teach algebra as the formulation of physics,

along with the symbol-transformation game,

both manually and machine-aided.

And so on along whichever track you choose.

I'm not even convinced there is necessarily Y at the end.

A LOGO program is basically a finite "differential" equation,

and the path is it's initial-boundary-value integral.

If kids can understand LOGO, why do we wait until 4th semester college

to introduce differential equations?

I guess my point is, if you master the principles of mathematical reasoning,

and it's relationship to applications, you don't need to master all the individual mathematical areas or applications to be functionally educated.  Just as, if I master the principles of programming, I don't need to learn all the programming languages to be able to do any programming job--I can learn any new language or paradigm if/when I need it.

[Although I admit convincing HR can often be a bigger challenge.]

Joe

On Apr 29, 2016, at 11:55 PM, kirby urner <kirby...@gmail.com> wrote:

Hi Joseph --

I was mainly using that slide decoratively, showing someone (not me) giving a talk, I think at a Python user group, and talking about what's called a "Y combinator".

The best exposition of the Y-combinator I've found on Youtube is this one from a 2012 Rubyconf: 

https://youtu.be/FITJMJjASUs
Y Not- Adventures in Functional Programming by Jim Weirich

Kirby

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[kirby urner]

On Wed, May 4, 2016 at 11:58 AM, Joseph Austin <drtec...@gmail.com> wrote:

<< EDIT >>

 

So instead of putting Science (PHYS) at "the end of the track",

I'd like to carry it along with the train from the beginning.

P=play should involve the S as well as the M.

I should clarify that the diagram to which you refer is meant to

be somewhat a map of what's true today, but juxtaposed with

new terminology.

Today, K-8 usually does not feature "subject teachers" as

much as "home room" teachers i.e. the students tend to

have the same teacher for all subjects and there's just

the one main track, not forgetting special needs tracks.

I'm not really challenging this status quo and understand

when teachers of that age level say they're teaching students,

not subjects.

It's around middle school that the faculty starts to differentiate

more, and students begin to travel from room to room at

the sound of a bell.  That's when we encounter "subject

teachers" perhaps for the first time.

Starting around middle school, and definitely by high
school, you get Math from the Math teacher, English from
the English teacher, Science from the Science teacher,
whereas in K-8, or at least K-6, you more likely had one
teacher for all subjects.

That's why I show only the one track for K-8. 

Then I put a Y or fork to mirror what used to be the
pre-college versus not pre-college tracks, also known
as pre-college and vocational respectively. 

This is where I start to superimpose new terminology, and

at the same time speak more specifically about a "math track"
(because in high school we need three or four years of
something called "math" to get that diploma).

I'm suggesting that you could still be intending to go to

college and yet not necessarily stick to the conventional

pre-calculus / calculus track.  That's no longer the only

pre-college math track.  We offer a choice.

Because there's more than one important calculus in this
world, and it this level lets just say we have two main
ones:  delta (analog) and lambda (digital).  Yes, it's my

innovation to shop talk it this way.  I'm applying spin.

I'm meaning something more by my delta and lambda,

roughly analog versus digital.

In other words, Instead of college prep versus vocational,
the pre-existing two tracking, I'm suggesting analog versus
digital.  Delta calc is very analog in the sense that continuity
is key.  Delta calc is all about differentiation and integration
in a world of smooth / continuous functions.  Lambda calc
is more about discrete / finite / on-or-off digital logic.  So I'm
distinguishing two flavors and suggesting Math teachers

should be covering both.

Of course we need to be teaching Science at all levels.

STEM is really one integrated ball of wax, or should we

say STEAM, adding Anthropology? [1] 

The idea of "subject areas" and distilling everything into
disciplines, is more about culture / ethnicity than anything
(it's something we study in Anthropology).  How the distilling

is done depends on the school and/or ambient culture.

Kirby

[1]  adding an A to STEM to spell STEAM is nothing new,

however the vast majority want A to mean Art.  I prefer to

have my A mean Anthropology under which Art is subsumed.