*Playing around with polaroid screens at Google.*

If you shine light through

- a light polariser
`A`

- another light polariser
`B`

that’s perpendicular to`A`

(i.e.,`A ⊥B`

or`A×B=0`

) - i.e.,
`AB`

represents “shine the light through`A`

then through`B`

which`⊥A`

” - then no light comes through (it’s black.)

If you shine light through

- a polaroid
`A`

- another polaroid
`B ⊥ A`

- a third polaroid
`C`

that’s halfway between`A`

and`B`

(either halfway)

then no light comes through (it’s black.)

So far, formulaically, we have:

`AB=0`

`BA=0`

- whence it follows
**ABC**=(AB)C=(0)C**=0****CBA**=C(0)**=0**`BAC=0`

`CBA=0`

But! This is surprising to watch and surprising to see the formula.

- If you shine through
`A`

then`C`

then`B`

, it’s kind of light! `ACB≠0`

- furthermore
`BCA≠0`

Woo-hoo, Noncommutativity!

Earlier in the talk Ron Garret does a two-slit experient with two mechanical-pencil leads and a laser pointer. Wave-particle duality with an at-home science kit.

(Source: twitter.com)