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from “On Self-Referential Sentences” by Douglas Hofstadter, originally in Scientific American (January 1981), reprinted in Metamagical Themas (1985)
via crystilogic




via asequeltoallthethingsivedone:

October, 1971: four cesium atomic beam clocks were flown on commercial jet flights around the world, one eastward and the other westward, to test Einstein’s theory of relativity. The result: one clock lost time. The other clock gained the time that was lost.

I walk with the countenance of one who has lost a tense second, and who must catch up to you to reclaim it.

You have my second.

One second - enough for the whole engine to grind out of kilter. The lungs inhale what the body possesses in abundant supply and releases it when the body needs it most. The heart skips a beat while the mouth swallows before it chews.

I lost it in those weeks when time stood still for you and me. I was fearful of the future and you were too shy around it. We were so entirely in the present.

Now, you travel so fast.

Westward into the future.

Gaining all the seconds I am losing.




Jo Ann Beard:

[My day jobs were] Secretary and glorified secretary. For a while in my early forties I had a job stapling. It was actually fun but then it started bothering my back.

I worked once for a woman who was younger than me; she had me doing things like bringing her bagels and guarding her car when it was illegally parked. I liked her quite a lot and liked the job too, mainly because I could smoke while I guarded the car. Then she ran across a piece I had published in The New Yorker and almost had a coronary. She couldn’t adjust her idea of who this person she saw every day was. It’s like a box of paperclips had started talking to her. She just kept staring at me all day, and her friends kept coming by and laughing at her. To them this was high hilarity, that their colleague had underestimated her box of paperclips. At the end of the day she called me into her office and said: “You don’t know it, but The New Yorker is a big deal.”

I might be making it sound bad, but it was actually pretty great, all of it. The cigarettes, sitting on a fire hydrant in the sunshine, this woman’s genuine desire to let me in on my good fortune.




I view a mathematics library the same way an archaeologist views a prime digging site. There are all these wonderful treasures that are buried there and hidden from the rest of the world.

If you pick up a typical book on sheaf theory, for example, it’s unreadable. But it’s full of stuff that is very, very important to solving really difficult problems.

And I have this vision of digging through the obscure text and finding these gems and exporting them over to the engineering college and other domains where these tools can find utility.




[A] wall of fifty or sixty glass demijohns, wired tight against earthquakes, exhibit creatures from the [United East India] Company’s once-vast empire.


A pickled dragon of Kandy…a slack-jawed viper of the Celebes…A baby alligator from Halmahera…The alligator’s umbilical cord is attached to its shell for all eternity….the jar of a Barbados lamprey…[Its] mouth is a grinding mill of razor-sharp V’s and W’s.


Preserved from decay by alcohol, pig bladder, and lead, they warn not so much that all flesh perishes—what sane adult forgets this truth for long?—but that immortality comes at a steep price.




by sandydreamsinmybackpackman:

When the boat times were over

How it all came crashing down.

We couldn’t maintain

That glory, that leisure.

Something…like that

Can’t last forever.

________________

She had a muddled underbelly.

There was an iceberg.

3,000 people died, and that’s an exaggeration.

Boat times are like that.




Semigroups are like groups but semigroup elements don’t always have inverses, necessarily.

Semigroups obey the associative law:

  • a then b, then c       =       b then c, after a.

but not necessarily the commutative law (3+14=14+3). Aristotle observed that time obeys the associative law.

It is commonly agreed that time moves forward only and not backward. Not invertible means you can’t always undo what was done. (Both groups and semigroups can be noncommutative; order sometimes matters, like whether you put the couch down first or pour the concrete first.) So, John Rhodes says, we should model time with semigroups.

 

Speaking in terms of sets and sequences, (a,b,c,d,e) is equivalent to (a, ab, abc, abcd, abcde). The two representations (let’s call them events and timelines) serve different functions mathematically but are isomorphic. With this identification in hand, Rhodes launches into a tornadic discussion of groups, commutative and noncommutative:

  1. groups have fundamental constituent parts;
  2. we have found all of them;
  3. we know how they combine to form larger actions;
  4. so we essentially know everything about every group;
  5. and this bears on Life, The Universe, and Everything.

Rhodes co-invented the wreath product , which explains how to combine the fundamental units of semigroups into any semigroup at all.

 

If semigroups represent all the logical options that anyone can do with anything, then the total classification of finite simple groups is an achievement with epic implications. It would mean a mathematical theory of all the things that can be done. “Do” and “thing”, that is breaking it down pretty much to the basics.

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I read some of The Wild Book at a friend’s house a couple months ago (I haven’t bought a copy yet). Skimming throughout the text, it looks like a really fun read — jumping from abstract algebra to (mathematical) cellular automata to the Krebs cycle to religion.

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However, Rhodes draws some unwarranted conclusions, or otherwise demonstrates overly simplistic thinking.

  • He equates “religion" with beliefs about the afterlife.
    image
    And he’s an Egyptologist or something?
  • His example of a semigroup loses all knowledge right away rather than things being gradually more covert depending on ingenuity.
  • Does the semigroup therefore model our understanding or the progress of the physical world?
  • He says that scientific understanding is equivalent to the introduction of spacetime coordinates. Um, dissection & anatomy? Synthesis of urea? Germ hypothesis, periodic table, polio vaccine?
    image


    image
    Also, by existence I think he means experience. Existence does not imply feedback.
  • Just because there are many different “models” of time or space, doesn’t reduce the credibility of any religion. Unless the religion specifically stated “The body moves around in ³ forever — throughout time, which is ¹.” I can’t remember reading that in Scripture.
    image
  • And semigroups are supposed to be unpopular because they controvert religion? I assume it’s just because they’re abstruse.

Has it really been proven that information is lost when a person dies and is buried or cremated? The smoke from the funeral pyre is in a lower entropic state than the atoms of the nervous system were, but doesn’t the specific configuration parametrise the smoke which affects the wind and so on? Information may be chaotically scrambled but is that the same thing as lost?

 

I’m not insulting what John Rhodes produced: a rare jewel that looks at scientific and philosophical questions through the lens of abstract algebra. These questions are meant to provoke further discussion of his ideas.




"The whole is more than the sum of the parts"

Who says scientists are reductionistic? Any superadditive system—due to complexity, interaction terms, valuation by an Lₚ norm with 0<p<1, or some other reason—adds up to more in total than the pieces individually do.

(Such Lₚ norms are semimetrics but not seminorms.)




Using the Gutenberg Project’s free text of Don Quijote + Unix for Poets, here are the most used (non-short) words in Miguel de Cervantes’ famous work:

  • 2167 Quijote
  • 2145 Sancho
  • 1331 porque
  • 1053 respondió
  • 1027 había
  •  900 merced
  •  813 vuestra
  •  796 todos
  •  711 cuando
  •  625 donde
  •  614 quien
  •  577 decir
  •  573 caballero
  •  535 hacer
  •  525 aunque
  •  482 aquel
  •  464 aquí
  •  462 estaba
  •  450 sobre
  •  431 está
  •  416 tanto
  •  414 verdad
  •  409 allí
  •  398 tengo
  •  393 mundo
  •  385 tiene
  •  383 alguna
  •  377 hasta
  •  371 dicho
  •  363 parte
  •  361 entre
  •  359 todas
  •  358 buena
  •  353 luego
  •  346 cosas
  •  344 menos
  •  344 lugar
  •  342 tenía
  •  328 manera
  •  328 aquella
  •  327 tiempo
  •  325 Panza
  •  310 ahora
  •  304 puesto
  •  292 caballeros
  •  289 ellos
  •  287 mucho
  •  285 fuera
  •  283 puede
  •  282 antes
  •  281 mejor
  •  281 algún
  •  280 visto
  •  279 Dulcinea
  •  272 tierra
  •  269 otras
  •  258 padre
  •  258 otros
  •  258 hombre
  •  257 hecho
  •  254 haber
  •  253 quiero
  •  252 cielo
  •  250 habían
  •  248 amigo
  •  247 saber
  •  246 historia
  •  245 camino
  •  242 tener
  •  240 escudero
  •  239 parece
  •  239 manos
  •  238 días
  •  234 muchas
  •  231 estas
  •  222 mujer
  •  222 desta
  •  221 será
  •  219 mesmo
  •  219 cuanto
  •  219 cómo
  •  215 quién
  •  214 cabeza
  •  211 punto
  •  211 noche
  •  207 veces
  •  207 replicó
  •  205 cuenta
  •  203 Rocinante
  •  202 parecer
  •  200 razones
  •  199 también
  •  198 fuese
  •  198 duque
  •  198 diciendo
  •  197 andante
  •  196 muchos
  •  196 estos
  •  196 caballo
  •  195 vuesa
  •  195 nuestro
  •  193 podía

CODE: tr -sc '[A-Z][a-z][áéíóú]' '[\012*]' < quijote.textfile | perl -e 'while (<>) { print if length($_)>5; }' | sort | uniq -c | sort -rn > quijote.hist

Here’s the power law distribution of non-short words in Don Quijote:

CODE:  tr -sc '[A-Z][a-z][áéíóú]' '[\012*]' < quijote | perl -e 'while (<>) { print if length($_)>5; }' | sort | uniq -c | sort -rn | perl -e 'while (<>) { print $1 if $_ =~ /(\d+)/; print "\n"; } ' | uniq -c > quijote.countofcounts.powerlaw.hist

> par(bg="#fafaff", col="#111177")
> plot(quijote.countofcounts.powerlaw, log="y", type="s", lwd=4, xlab="Number of times a word appears in the text", ylab="Number of words with this frequency", main="Word Frequency in Don Quijote de la Mancha", col="#111177")

And including short words retains the power law distribution.

CODE: tr -sc '[A-Z][a-z][áéíóú]' '[\012*]' < quijote | uniq -c | sort -rn | perl -e ‘while (<>) { print $1 if $_ =~ /(\d+)/; print “\n”; } ’ | uniq -c > quijote.countofcounts.powerlaw.hist.shortwordstambien

(Source: gutenberg.org)




As David Foster Wallace saw it, irony could critique but it couldn’t nourish or redeem.

(Source: newyorker.com)