## perhaps *this* will refresh your memory

Posted by vlorbik on November 23, 2010

pages 4 & 5 of MEdZ #0.9.

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## vlorbik said

the seven points in the center represent

the seven “directions” from 000 on a cube.

[to wit {001, 010, 011, 100, 101, 110, 111}

(binary 1 to 7; one calls 001, 010, and 100

“unit vectors” (in the x, y, and z direction

respectively… or not… but such things

are good to know…).]

the bigger circles around (& in one case,

amongst) the seven-in-the-center “plane”…

are associated with the *lines* of

P = P_2 ({

Z}_2).These lines are then treated as the *points*…

think of the circles… of the “dual” space P^*

(“pee-star”). then there’s a

structure preserving map

(called, i suppose, “star”) from P to P^*:

a mapping P—-}P^* that not only takes

points of P (dots, say) to points of P^*

(circles), but simultaneously takes the

lines of P to the lines of P^*.

the appropriate arithmetic is modulo 2;

in the two bottom lines i’ve given examples

of “why” the points 111 and 100 do and do not

(respectively) lie on the line [110]:

the “dot product”

[xyz]abc := xa +yb + zc (mod 2)

produces 0 (it *is* on the line)

or 1 (it’s *not*).

the mod-2 addition table is given;

just remember everything is in

“remainders on division by two”.

(think “even” and “odd”, rather,

i suppose, for most people…)

this drawing was something of a breakthrough

for me. it was soon followed by

https://vlorblog.wordpress.com/2010/11/23/now-heres-something-youll-really-like-that-trick-never-works/