PAPER POLYGONS, BUILDINGS, CODE-BREAKING...
...IT'S GONNA GET A LITTLE WEIRD
People ask me what I enjoy. There are many answers but they boil down to books, optics, science and patterns. Before I could read or write I was a graphomaniac: I would scribble and scribble and scribble on paper and then fold and refold and crinkle and smooth pieces of paper. A little piece of paper can become an entire world. Whether you write a story or fold it into something dimensional.
What follows zings around quite a lot. As far as a post it's like a lot of posts mashed together. If any of the math, etc. bores you scroll down a little--it changes up.
This really should have been my flagship post for Science & Optics, but was too chaotic.
A stella octangula!
Also called a stellated tetrahedron.
Father Magnus Wenninger (cute pic of him in his office/cell filled with paper
models: http://
Stella octangula is compound (the shape repeated-then turned
(roll your own: http://
I thought of making a bunch of these and leaving them around work as a mystery-but my boss (who’s also a friend) saw one tiny one and instantly knew it was me; I mean *who* else would leave something so odd behind in the library. I did see a mixed up Rubik's Cube on a professor's desk and quickly solved it at about 9:30pm. I never told anyone that. He must have just walked in and wondered who solved it for him.
By the way, I made my first paper polygon at work. My job left me alone in our library until 10pm. I also worked mornings on Saturdays. Saturdays were very mellow (usually) and I had time for experimenting with secret little paper foldings. It was very peaceful.
The 5 Platonic Solids and a few other, slightly more exotic paper polyhedrons that I made for a math display table for library help/tutoring. If you do something you like-bring it into your work if you can.
Twisted pyramid. The shape to the left is a great representation of a crystal mineral shape. I collect minerals and I've grown crystals in the past. This site provides paper diagrams for folding complex (and many times non-symmetrical) crystals out of paper : http://webmineral.com/
Much like Iron Man gets his magic powers from, uh…actually I
can't remember what his deal is…anyway, the rain gives me complex barometric migraines
*and* Master-Level Chess playing ability! Also I have a chess dictionary on my
desk. 9 moves and I smashed the computer at level 2000 with my ‘Wall of Pawns’
strategy! Basically through simple patterning I've solved the problem of
chess: no one ever need play it again. Actually this strategy worked a few more
times then I think the game ‘learned’ and I went back to being terrible at
chess. I get caught up in the patterns of the moves.
My Typewriter Art: Fourth order Magic Squares increasing by sums by 4 (except the second one which is just the first re-ordered). Sums of each horizontal, diagonal and vertical row or column are the same within each square. Essay Onion Skin paper. I started doing these in the 1970s on an early electric typewriter. This is a much later one from 2010, inspired in part by an old Manuel Morschopoulis style I typed up years before I started dating things:
I just discovered this trial magic square tucked into a box of Eaton's Essay Onion Skin typewriter paper (my favorite). I must have found it in 2010, used it to make the previous math square art and then tucked it away and forgot about it.
My paper buildings span from ancient obelisk, to a farmhouse,
German guesthaus, 19th century bridge, 20th century skyscrapers and
ultra-modern clock tower from Dubai. Why? Why not! Extreme right: Grand
Rapids Amway Grand Plaza Hotel and the Renaissance Center Building. My favorite
is still the Seagram Building (center/black). At center is the famous Dubai
Clock Tower (thing that looks like a white spider). They're a simpler (usually) version of the more advanced paper polygons...plus they're cute!
It's the Zur Glashütte Guesthouse in Crottendorf Germany. So tiny. So cute!
Skip down to the kitty if the following math blurb bores you.
When Grigory Perelman gave his lecture
solving the Poincaré Conjecture he visualized a drop of water rolling downhill:
it was a variously curved surface, but in places as it rolled it could break
off or close completely. He got rid of these pinches by using mathematical
tricks—but what if the universe wasn’t a repeating non-infinite sphere, or a
torus (donut shape), but a blob-with another blob that was separated by
‘non-existence’ that was unreachable from the blob we’re currently inside
(torus, 3-sphere or other)? If you flew in a space ship off the edge of one
blob, you’d show up at the opposite side of the same blob-never entering the
other blob(s). Kind of like the game Asteroid where you fly off one side of the
screen and show up on the other side (you’d never make it onto your neighbor’s
TV screen).
If any loop can be shrunk to a point on a
manifold sphere-then it is ‘simple’; a 3-sphere, like the Earth or a tying a
string around a greasy watermelon: the tighter you pull the knot, the more it
slips down and off—making a single point (the knot off the watermelon);
meanwhile if you try it with a torus (think donut) and you tie it around the
center you can make a donut necklace, and no matter how tight you make the chain, the donut will not slip off,
unlock when you try to tie a chain around a baseball or watermelon or other
spheroid-thus the torus is not simple. There was ONE historian who LIED and
said that people thought the Earth was flat; untrue, for over 3000 years people
have known the earth was roughly spheroid.
The argument Columbus had about
going around the world was NOT about falling off the edge-it was about who big
a circumference he’d have to navigate: Queen Isabella’s people thought anywhere
from 18,000 miles to 26,000 miles around (it’s a smidge under 25,000 at the
bloated equator). Now, if you took every available map of the Earth at the time
you could assemble them into a sphere (paste the flat paper maps onto a globe),
but you could have also pasted them onto a Torus (donut shape) or a globe that
looked a bit more like a pear-in fact our Earth bloats out at the equator due
to centrifugal/rotational force, much like how a dragster’s rear wheels get all
elongated and huge vertically when the drover whomps on the gas. Columbus
worried that at the top of the pair the circumference was less than the bottom
of the pear—and thus run out of supplies on his voyage. Columbus worried about a smart thing--not the dumb thing your teachers thought.
Okay, wake back up: the fancy-smanshy maths are over!!!!!!!!
BTW, The cat is called Harbooz which is Ukrainian for melon, watermelon, cantalope...she is very jealous if anyone carries a melon into the house and must be calmed by cradling her just like she was a melon being brought in with the rest of the groceries.
Patterns and little private worlds in paper, math, writing, coding, etc.
I've written about patterns and also creating little worlds.
This is my train set, it's T-Gauge. T = 3mm between the left and right wheels (axle length). It is 1:450 scale. This is not to be confused with TT-Gauge which is way bigger!
There are little people.
There are even smaller people.
These are (huge by comparison) Z-Scale train people next to a penny.
So tiny.
TRULY SECRET WORLDS: CRYPTOGRAPHY
People are encrypting the dumbest things these
days-but it's always fun to hit the button and feel like James Bond, if only
for a second. Cryptography (and decoding) follow algorithms and patterns. I've kept notebooks since getting a secret code book (which I still have) as a very young child.
In 1401 the Duke of Mantua Leon Battista
Alberti invented a frequency blurring cryptographic algorithm. In 1999 two
books were published with an error in the plaintext portion of that code.
Tonight I found *both* of them. Basically an 's' was were a '5' should have
been in the ciphertext, so that the word "Deepfreeze" was decoded (by
me) as "Neepfreeze".
Frequency blurring is where a letter can be coded as more than one symbol:
t = x,
q or 3;
h = y,
i or 9;
e = z,
m or 22
This way
you can just count the number of times a symbol was used and match that to a
simple chart of English Letter usage frequencies (where 'e' is the most used
letter, etc.). I've already broken 3 other codes in these books using simple
frequency counting. You count the usage of the symbols and list them from most
used to least and then line it up against the English (or whatever) frequency
chart--in single substitution it's usually only 1 or 2 letters off and very
easy to decode.
Not surprisingly, when I was an undergrad at Wayne State University and spending lots of time in their photographic darkrooms I got interested in spy cameras, properly called subminiature cameras. I also always wanted one since seeing (what I think was) a Minox subminiature spy camera being used in an episode of Laverne & Shirley. I think they were trying to steal the secret recipe from a rival brewery or something. LOL!
Anyway, as you can see above-I got a Minox spy camera. It's from the Cold War Era. The bumps on the chain correspond to settings on the focus dial. You put a document on a desk; hold the camera above it; count the bumps and set the focus dial to the corresponding settings: easy copying of top secret documents! This is the famous camera that advances the film by holding it like a pair of binoculars and pulling/pushing on the left and right sides: click-click. It is a fine piece of machinery, like a Rolex watch. I even obtained a film slitter for it to cut 35mm film down to 8.5mm size.
This is a teeny-tiny subminature camera from the Cold War era. It came with a dozen rolls of 8.5mm film. Penny shown for size. Nice faux-alligator leatherette covering. I like how the (original!) box seems to imply that, 'yes, you too can create something as colorfully saturated and blurry as the Zapruder Film!!!" Actually it seems to show an Asian car stopping at a security gate. It i very light and cheap feeling but cool. It's like a neat digital watch versus a Rolex.
At some point I'll post about: my crystal radio sets made with old razor blades and pencil leads (I even made my own pencil after reading a book about the history of pencils); shortwave radio, CBs and my Rubiks Cube and Knock-off Rubik-like puzzle collection.
Well, that's the tail end of the snake--good night!
