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Dimensions 1, 8 & 24 have universally optimal configurations; 3 is a zoo

offline EpicMegatrax from Greatest Hits on 2019-06-01 05:17 [#02578902]
Points: 12566 Status: Regular


Dimensions 1, 8 & 24 have universally optimal
configurations; 3 is a zoo

non-math readable

me, previously, on spheres.

i actually remember going off on an insane tangent about the
sphere packing problem. it was 2016 or so; i was on the
porch with a cigarette. the original source, to me, was a
passage from neal stephonson's book "cryptonomicon," which
featured an extended passage about the optimum consumption
of captain crunch cereal; how it was ship-shaped to satisfy
marketing but effectively spheroid for packaging purposes.

the "what is the optimal way to cram a number of spheres
into a space?" is one of my favorite fings, really. it seems
so simple at first, but, no, it's nuts. a very fascinating
sphere of context.


offline EpicMegatrax from Greatest Hits on 2019-06-01 05:30 [#02578903]
Points: 12566 Status: Regular

Randy takes the red box and holds it securely between
his knees with
the handy stay closed tab pointing away from him. Using both
hands in unison
he carefully works his fingertips underneath the flap,
trying to achieve
equal pressure on each side, paying special attention to
places where too
much glue was laid down by the gluing machine. For a
few long, tense
moments, nothing at all happens, and an ignorant or
impatient observer might
suppose that Randy is getting nowhere. But then the entire
flap pops open in
an instant as the entire glue front gives way. Randy hates
it when the box
top gets bent or, worst of all possible words, torn.
The lower flap is
merely tacked down with a couple of small glue spots and
Randy pulls it back
to reveal a translucent, inflated sac. The halogen down
light recessed in
the ceiling shines through the cloudy material of the sac
to reveal gold
everywhere the glint of gold. Randy rotates the box ninety
degrees and holds
it between his knees so its long axis is pointed at the
television set, then
grips the top of the sac and carefully parts its heat
sealed seam, which
purrs as it gives way. Removal of the somewhat milky plastic
barrier causes
the individual nuggets of Cap'n Crunch to resolve, under
the halogen light,
with a kind of preternatural crispness and definition that
makes the roof of
Randy's mouth glow and throb in trepidation.


offline EpicMegatrax from Greatest Hits on 2019-06-01 05:31 [#02578904]
Points: 12566 Status: Regular

On the TV, the dancing instructors have finished
demonstrating the
basic steps. It is almost painful to watch them doing
the compulsories,
because when they do, they must willfully forget everything
they know about
advanced ballroom dancing, and dance like persons who have
suffered strokes,
or major brain injuries, that have wiped out not only the
parts of their
brain responsible for fine motor skills but also blown
every panel in the
aesthetic discretion module. They must, in other words,
dance the way their
beginning pupils like Randy dance.
The gold nuggets of Cap'n Crunch pelt the bottom of
the bowl with a
sound like glass rods being snapped in half Tiny fragments
spall away from
their corners and ricochet around on the white porcelain
surface. World
class cereal eating is a dance of fine compromises. The
giant heaping bowl
of sodden cereal, awash in milk, is the mark of the
novice. Ideally one
wants the bone dry cereal nuggets and the cryogenic milk to
enter the mouth
with minimal contact and for the entire reaction between
them to take place
in the mouth. Randy has worked out a set of mental
blueprints for a special
cereal eating spoon that will have a tube running down
the handle and a
little pump for the milk, so that you can spoon dry cereal
up out of a bowl,
hit a button with your thumb, and squirt milk into the
bowl of the spoon
even as you are introducing it into your mouth. The next
best thing is to
work in small increments, putting only a small amount of
Cap'n Crunch in
your bowl at a time and eating it all up before it
becomes a pit of
loathsome slime, which, in the case of Cap'n Crunch,
takes about thirty


offline EpicMegatrax from Greatest Hits on 2019-06-01 05:32 [#02578905]
Points: 12566 Status: Regular

At this point in the videotape he always wonders if
he's inadvertently
set his beer down on the fast forward button, or
something, because the
dancers go straight from their vicious Randy parody into
something that
obviously qualifies as advanced dancing. Randy knows that
the steps they are
doing are nominally the same as the basic steps
demonstrated earlier, but
he's damned if he can tell which is which, once they go
into their creative
mode. There is no recognizable transition, and that is
what pisses Randy
off, and has always pissed him off, about dancing
lessons. Any moron can
learn to trudge through the basic steps. That takes all of
half an hour. But
when that half hour is over, dancing instructors always
expect you'll take
flight and go through one of those miraculous time lapse
transitions that
happen only in Broadway musicals and begin dancing
brilliantly. Randy
supposes that people who are lousy at math feel the same
way: the instructor
writes a few simple equations on the board, and ten
minutes later he's
deriving the speed of light in a vacuum.
He pours the milk with one hand while jamming the
spoon in with the
other, not wanting to waste a single moment of the magical,
golden time when
cold milk and Cap'n Crunch are together but have not yet
begun to pollute
each other's essential natures: two Platonic ideals
separated by a boundary
a molecule wide.


offline EpicMegatrax from Greatest Hits on 2019-06-01 05:33 [#02578906]
Points: 12566 Status: Regular

Where the flume of milk splashes over the spoon handle,
polished stainless steel fogs with condensation. Randy of
course uses whole
milk, because otherwise why bother? Anything less is
indistinguishable from
water, and besides he thinks that the fat in whole milk acts
as some kind of
a buffer that retards the dissolution into slime process.
The giant spoon
goes into his mouth before the milk in the bowl has even
had time to seek
its own level. A few drips come off the bottom and are
caught by his freshly
washed goatee (still trying to find the right balance
between beardedness
and vulnerability, Randy has allowed one of these to
grow). Randy sets the
milk pod down, grabs a fluffy napkin, lifts it to his
chin, and uses a
pinching motion to sort of lift the drops of milk from his
whiskers rather
than smashing and smearing them down into the beard.
Meanwhile all his
concentration is fixed on the interior of his mouth,
which naturally he
cannot see, but which he can imagine in three
dimensions as if zooming
through it in a virtual reality display. Here is where a
novice would lose
his cool and simply chomp down. A few of the nuggets would
explode between
his molars, but then his jaw would snap shut and
drive all of the
unshattered nuggets straight up into his palate where
their armor of razor
sharp dextrose crystals would inflict massive collateral
damage, turning the
rest of the meal into a sort of pain hazed death march
and rendering him
Novocain mute for three days. But Randy has, over time,
worked out a really
fiendish Cap'n Crunch eating strategy that revolves
around playing the
nuggets' most deadly features against each other. The
nuggets themselves are
pillow shaped and vaguely striated to echo piratical
treasure chests.


offline EpicMegatrax from Greatest Hits on 2019-06-01 05:34 [#02578907]
Points: 12566 Status: Regular

Now, with a flake type of cereal, Randy's strategy
would never work.
But then, Cap'n Crunch in a flake form would be suicidal
madness; it would
last about as long, when immersed in milk, as snowflakes
sifting down into a
deep fryer. No, the cereal engineers at General Mills had
to find a shape
that would minimize surface area, and, as some sort of
compromise between
the sphere that is dictated by Euclidean geometry and
whatever sunken
treasure related shapes that the cereal aestheticians
were probably
clamoring for, they came up with this hard to pin down
striated pillow
formation. The important thing, for Randy's purposes, is
that the individual
pieces of Cap'n Crunch are, to a very rough
approximation, shaped kind of
like molars. The strategy, then, is to make the Cap'n Crunch
chew itself by
grinding the nuggets together in the center of the oral
cavity, like stones
in a lapidary tumbler. Like advanced ballroom dancing,
verbal explanations
(or for that matter watching videotapes) only goes so far
and then your body
just has to learn the moves.
By the time he has eaten a satisfactory amount of Cap'n
Crunch (about a
third of a 25 ounce box) and reached the bottom of his
beer bottle, Randy
has convinced himself that this whole dance thing is a
practical joke. When
he reaches the hotel, Amy and Doug Shaftoe will be
waiting for him with
mischievous smiles. They will tell him they were just
teasing and then take
him into the bar to talk him down.
Randy puts on the last few bits of his suit. Any
delaying tactics are
acceptable at this point, so he checks his e mail.


offline w M w from London (United Kingdom) on 2019-06-02 19:06 [#02579065]
Points: 21331 Status: Lurker

The sphere packing problem was referenced on Nigga Turtles
(soon to be shadow banned by oligopoly tube if not already)
when michaelangelo (probably) said "then... we're gonna pack
your mouth full of nuts" to April on the telephone.


offline EpicMegatrax from Greatest Hits on 2019-06-02 20:04 [#02579108]
Points: 12566 Status: Regular

this math is everywhere


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