disruptions, distractions.

so i was having dinner with my sister [0] when she asked me what i was thinking about lately. (i took this to mean mathematics.)

at first i couldn't think of anything, which was really weird,
especially since i was working on something that very morning;

i guess i've been really distracted lately.

---

to put things into perspective, the last five posts ..

(namely this, that, also this and this, and that too)

.. were dead-man's switches .. at least in erdös's sense [1]. they were compiled about a week in advance. i was away on the spur-of-the-moment holiday because .. well, the girl i'm dating was on holiday and we wanted to spend more time together. [2]

at first i thought i'd not bring any maths with me, if only as a romantic gesture .. but then i looked up my flight and it was 3 hours long: a long time, and i didn't have anything in mind to read at the time [e];

well, a laptop's not that heavy, and neither is that manuscript ..

so on the flight to rome, i idly decided to edit my $\LaTeX$. i sorted out one lemma, then another, and then in the middle of another proof, something didn't make sense.

closing the laptop, i tried to rework the proof in my mind .. only to perceive a gap. there was only an hour left in the flight to think of a patch before she and i would meet up again in the airport baggage claim .. and i started panicking ..

because the manuscript is supposed to be ready already, dammit! argh!

thus the plane touched down, decelerated [3], and arrived to its gate while i struggled without any viable ideas. dejected, i re-activated my cell phone, shuffled out of the plane and into another unfamiliar airport, and wondered ..

what kind of mathematician makes that kind of mistake, misses a gap like that?

sighing, i looked for the right baggage carousel from my flight ..

this would prove to be a distracted trip; in the mornings before we got up, i'd fumble with details in my head and feign sleepiness when she asked what was wrong.

.. to be continued?

[0] i.e. a mathematical sibling.

[1] according to this article and other accounts i've read, erdös would consider a friend "dead" if he stopped working on mathematics, so the term "dead man's switch" isn't that far off. (i wonder, then, if erdös considered "death" to be a permanent condition!)

[2] i'm leaving finland in 2 weeks. she and i haven't spoken about the future yet .. at least in much detail. suffice it to say that it's a rather turbulent time in my life. i'm pleasantly surprised that i can focus on anything mathematical, at the moment!

[e] in case you were wondering, she and i were on separate flights. now that i think about it, i don't know if she's aware of how much and often i work. (personally i don't think i work all that much, but experience with family and previous girlfriends seems to suggest otherwise.)

on an epilogical note: the laptop did help after all. i had merely a dumbphone and her smartphone wasn't connecting properly to the hotel wifi, so it came in handy with looking up various cool locations to visit.

[3] "de-celerate" shouldn't be an actual word. acceleration, being a directional quantity, can take on both negative and positive values.

thoughts, while idle: clarκe's descriptions of geometries.

so i took this past weekend off, joining friends and a special someone to idle away the days in a beach resort town. it was good fun, though i believe now that the idea of a beach is often more attractive than the actual experience.

during those sun-soaked days, i couldn't really concentrate on anything. i tried a little, but having friends around all the time turned even those peaceful periods an hour or two into unusable blocks.

then again, it's a holiday; the point is not to be working!

i did start rendezvοus with rama by arτhur c. clarκe, which made for good episodic reading; the story stretches its telling ..

.. at least until page 100, where i stopped last night..

.. and the plot isn't too intricate that you have to pay attention all the time.

i make it sound simple, but it isn't. the beauty of this book is how it points out the subtlety of human perception towards mathematical possibility.

to give you an idea, the back cover of this book reads:

Rama is a vast alien spacecraft which enters our Solar System. A perfect cylinder some fifty kilometres long, spinning rapidly, Rama is a technological marvel, a mysterious and deeply enigmatic alien artifact. It is Mankind's first visitor from the stars and must be investigated ...

yes, we all know what a cylinder is and we have all (probably) driven as far as 50km on the highway. combining those two bits of information together, however, must make for a rather unique sight. even the large hadrοn collider at CERN is only 27km in circumference, and i don't know if anyone has ever caught the entire thing within a single frame of vision ..!

a view of the LHC, courtesy of alienshift

anyway, here is an excerpt from p. 74:

"Because they were now standing on the edge of a fifty-metre cliff, it was possible for the first time to appreciate the curvature of Rama. But no one had ever seen a frozen lake bent upwards into a cylindrical surface; that was distinctly unsettling, and the eye did its best to find some other interpretation. It seemed to Dr Ernst, who had once made a study of visual illusions, that half the time she was really looking at a horizontally curving bay, not a surface that soared up into the sky. It required a deliberate effort of will to accept the fantastic truth."

moreover, clarκe does an excellent job of suggesting that, though space and its contents may be absolute, our perspectives of it can be rather relative:

from p. 42:

"And now, Karl Mercer told himself, I have to make my first decision. Am I going up that ladder, or down it?

The question was not a trivial one. They were still essentially in zero gravity, and the brain could select any reference system it pleased. By a simple effort of will, Mercer could convince himself that he was looking out across a horizontal plain [1], or up the face of a vertical wall, or over the edge of a sheer cliff. Not a few astronauts had experienced grave psychological problems by choosing the wrong coordinates when they started on a complicated job."

[1] the first two times i read this paragraph, i thought that the word was 'plane' and not 'plain.' (-:

sometimes maths is just about numbers.

well, i've been dating this girl ..

---

this morning we were talking about work. she happened to have a few blueprints(?) in her bag of what her firm was doing and how many simultaneous processes the proposed factory would be using.

it seemed very complicated to me .. like an electric circuit diagram on steroids!

then an idea came to mind .. maybe it can be my turn! .. so on her computer i showed her one of my preprints. her brow furrowed.

the basic idea's isn't that bad, i tell her.

for things that behave like mass distributions, the small-scale behavior can sometimes determine the large-scale. if, for example, there aren't enough directions when you zoom in at any given point, then the mass has to be distributed either like dust [1] or be restricted to fewer dimensions, like a line in space.

then there was a brief pause.

wait, she said, it takes 27 pages to explain that?!?

i shrugged.
well, the latest version is now 29 pages [2].

we then talked about how, at a certain point, maths no longer consists of calculating things .. not exactly, anyway.


[1] i.e. a fractal with non-integer hausdοrff dimensiοn, but not necessarily self-simιlar. at the time i was thinking about purely unrectifιable subsets of the plane.

[2] thinking about it, maybe i should have said something like: well, define "dust" ..?

*NOTE* the new label ½ × 2 is meant to tag those (few) posts which are about how mathematics, for inexplicable reasons, relates to my relationships. the idea is: once you've been with someone long enough, you are no longer 1 person. rather, you are one-half of two people. (-: