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of mathematics, psychedelics, and dreams Below are the 9 most recent journal entries recorded in the "arrhybtun" journal:
March 18th, 2008
02:17 pm
[gaspaheangea]

[Link]

on the subject of jivas...
Jim Woodring's jiva look like quaternion julia sets.

Here's one I made with chaoscope:

jivaCollapse )

The constant is -1.

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02:15 pm
[gaspaheangea]

[Link]

new book! (media alert)
John Horton Conway has a The Symmetries of Things -- hasn't been released yet but you can preorder through Amazon.

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December 2nd, 2006
11:15 pm
[gaspaheangea]

[Link]

commentary on previous posts (1)
curves of constant width and pursuit curvesCollapse )

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December 1st, 2006
09:59 am
[jackdavinci]

[Link]

LSD sketches
strange and sloppy but interesting to me at least... comment with questions for explanations. for gaspaheangea - i actually did see/draw a 120-cell, although each face had a vibrating pentangular spiral on it. sketches below cut:

the amazing adventures in jack landCollapse )

Current Mood: Trippy
Current Music: Touch the Sound

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November 30th, 2006
07:11 pm
[jackdavinci]

[Link]

equation for the path of a point on a spinning gyroscope?
i was watching the movie Contact the other day in which there is a giant gyroscopic device with three wheels thus. a normal gyroscope's job is i guess to keep the interior stable, but in this device, the outermost ring is fixed, and each interior ring is fixed to a motor such each on it own would only spin at a constant speed around one axis.

so i'm wondering, how would you graph the path that a point on the inner most ring takes as it traces along the surface of an imaginary sphere whose radius is the same as the innermost ring? how would you graph it if there were only two rings spinning? one ring?

i have and would like to use the graphing program grapher for max OS X. i suspect the equations would be something similar to what that page shows for a torus knot, although i surmise that the torus is using a cylindrical equation and what i need here is some kind of spherical equation. grapher gives two basic equation set ups besides cylindrical, one is a cartesian matrix of x,y,z - and the other a spherical matrix of r,φ,θ. but what equations do i use? i imagine r is just a constant since it's only moving along the surface of an imaginary sphere. but i'm not sure what to put for φ and θ, and for t and u.



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March 11th, 2006
12:33 am
[gaspaheangea]

[Link]

stretchy language, the birdscape, a conference of idiots, and cats made of words
My usual territory is way more visual (meaning solely concerned with geometry to the point that linear descriptions are rather limiting, but I thought I'd say the following)


Some I knew once described language getting stretchy on mushrooms.
Gracie and Zarkov's visible language experience

Somehow the description of visible language vaguely reminded me of David Keenan's little essay about logical combinators

At this point, I recall a dream in which I was in my old room in my old house reading a book. The book was mathematical/scientific in character. As I read it, the formatting of the paragraphs changed into that of indented computer code. (like any one of the variants that you'd see with C or perl and so on)


Sometimes I think Senor McKenna is unneccessarily messianic in character, and a little silly. But let's take
three things together:
The classic gnomes essay
his visible language essay

I think that in the case of the second essay, mathematicians have a striking advantage.
Have you ever worked on a completely nonvisual problem for hours on end only to get math-high
dreams that were startlingly visual in character? I did this once. Kind of a reminder that I should
get my head firmly around group theory. It's like dealing with mathematics is dealing in terms
of something highly visual for which the easiest current representation is not terribly visual.
Take Julia sets. Gaston Julia only vaguely hinted at their bizarre properties in his paper, but didn't
have the computational resources at the time to see them displayed in brilliant color.
(the paper was Mémoire sur l'itération des fonctions rationnelles (I seem to recall
a very rough sketch sampled from his paper in some other book). What happens when you find
yourself dreaming or tripping of looking at an an exotic R^4
sphere
from a vantage point in some fifth dimensional space. If somone doesn't have the written language
or the experience to see it as an exotic R4, their mind might try to fit it into the categories it's accustomed to.

Rapidly changing tacks (okay, not really, and you'll see how in a bit), I was
reading John Baez's website, and came across his description of one
of the conferences he recently attended. It was about the geometry of computation ... turning various computational processes into higher dimensional forms (one morphisms, two morphisms and so on, not the vagaries that McKenna produces!)

I was poking through Pharyngula and found this analogy for the genome as a villiage of idiots.

wacky hypothesis time!
space travel is exorbitantly expensive. in terms of social and mechanical costs it is insanely expensive.
it takes years to send probes to other parts of the solar system, and no human being now alive is going to
get to other stars. I think I remember some part of Douglas Hofstadter's Metamagical Themas where
he talks about a machine designed to search logological space for pangrams. (aside: if the universe
were a piece of fiction, then the speed of light might be one of its constraints, Oulipo style).
Mathematics explores space the same way that physics explores space. They're just different, equally valid
types of space exploration.

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February 27th, 2006
01:58 am
[gaspaheangea]

[Link]

a transformation
Imagine that you're holding a pencil in your hand, and you rotate it, and
just as it finally rests in a new position, it does that optical illusion trick, you
know, like the one from the old-lady/young-woman or rabbit/duck illusions,
and you're holding a bowl of soup in your hand.

I had this occur in a dream quite a long time ago, and only now do
I have good words for it.

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August 7th, 2005
09:53 pm
[gaspaheangea]

[Link]

dreams about mathematics...
some think they're dry and unemotional, others have sphere wars

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August 4th, 2005
08:52 pm
[gaspaheangea]

[Link]

complex dreams
Last night I dreamt I was in front of a mirror and a friend of mine and myself
were watching ourselves diffeomorph
into each other. Then he started getting silly and changed into a 3d julia set though it wasn't obviously
the 3d cross section of a 4d julia set -- just kind of imagine that each one of the "sub blobs"
in this:
julia setCollapse )

Is kind of more like one of Jim Woodring's jivas rather
than the cross section of a four dimensional quaternion
julia set. (incidentally I found this gem
while looking for pictures of Woodring's jivas)

The next part of the dream involved randomly grabbing food at a cafeteria and
then because of some strange legal rule, having to go in these chutes/linear roller
coasters in which it seemed like the vertical dimension was being compressed
very fast, until +i∞ and -i∞ were joined up, and the next step involved
connecting up +∞ and -∞ so that you had the Riemann sphere. (this part
started out with a bar that I held onto and then the motion in the
environment seemed to be part of the bar)

Now the next step was kind of weird, and involved seeing a grid of longitude
and latitude imposed on the sphere. Somehow I was aware that 1, -1, i, and -i
were being mapped to tetrahedrally symmetric points on the sphere, though
this isn't the way that the Riemann sphere is usually done. (zero at one pole,
point of infinity at the other pole, and -1, 1, -i, i along the equator)

I can hardly remember the way that the whole scheme was quaternionified, but
it did happen.

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