Archive for: September, 2011

Mathematicians are human beings

Sep 19 2011 Published by under Uncategorized

So let us begin with what seems like a curiosity: here's a pdf excerpt of a mathematical article from the Thirties. Mathematics alone can be a pain, but the addition of Fraktur for the font? That seems excessive punishment.

(An excerpt from Teichmüller's "Multiplikation zyklischer Normalringe")

But this post is not to highlight the difficulty of reading mathematics; but rather about writing it.

The article is authored by a Mr. Oswald Teichmüller; a fairly famous and influential German mathematician who died young. The mathematics and the Fraktur are not the only problem in absorbing the article; it, like much of Teichmüller's original work, is a bit difficult to get hold of. The reason for that is the journal Mr. Teichmüller chose to publish in.

Here's the cover of that journal's that particular issue.

(The cover of "Deutsche Mathematik", April 1936)

The paper's name is "Deutsche Mathematik"; German Mathematics. Pray note it is from the year 1936. The reason Oswald Teichmüller is publishing in this particular journal is that he shares a political leaning (well, tripping) with its editor, Ludwig Bieberbach --- another accomplished and important mathematician of that time.

Here's the table of contents.

(The contents page of "Deutsche Mathematik", April 1936)

It is that political leaning which explains why Deutsche Mathematik contains rabidly patriotic articles in addition to mathematical ones; why there are no Jews or foreigners publishing in it; why, generally speaking, it is of such poor quality, and why those publishing in it get ever fewer, year by year; it is the reason why such a silly and terrible thing as "German Mathematics" has even been postulated.

Mr. Teichmüller and Mr. Bieberbach are both card-carrying, uniform-wearing, hate-slinging members of the Nazi Party.

Teichmüller is a young fanatic; eventually he graduates from strutting around in a SA uniform and harassing professors to volunteering for the Eastern Front, and presumably dies there in 1943. His body is never found.

Bieberbach, an opportunistic co-founder of this German Mathematics foolishness, will survive the war, but his reputation won't. He will continue to be a teacher of mathematics; but his academic positions and inventions are done. He dies in 1982.

The journal "Deutsche Mathematik" fails in 1943; there are no reprints.

I think what I want to say here is this: mathematicians are human beings. That we deal with proof and logic doesn't need to make us any nicer or smarter. This is just one example of how we, too, can be just as vicious, misguided and small-minded as any other group. But if you want to salvage something from this gloom, consider this: the mathematical results of those two live on, and by being an indistinguishable part of the international and universal structure of mathematical creation, they deftly refute their authors' un-mathematical assertions.

(The MacTutor archive has fuller biographies of Teichmüller and Bieberbach.)

2 responses so far

What a math paper looks like: art edition

Sep 17 2011 Published by under Uncategorized

So I took a mathematical paper that I was a co-author of ---

Ah, sorry, I am a graduate student. Saying "I was a co-author" makes me feel warm and fuzzy all over, like a bear stuck to a van de Graaff generator.

--- and I crammed the paper into Wordle, pruned the result a bit, and lo and behold, this is in word art mathematics as made by professionals (and one ursine graduate student):

A math paper run through WordleMuch prettier, and just as comprehensible!
(click for bigger)

As you can see, there're a lot of words like "assumption", "depending", "follows", "condition" and the like; that's the name of the game: take some foundation, any foundation, and then just build up from that as high as you can go. Also, the "anal" in there doesn't mean what you think. We call that "rigorous".

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A dialogue on rigorous thought

Sep 16 2011 Published by under Uncategorized

"My dear mathematician friend, you must never tell anyone what you saw me do to evil dean Sharkhorn's office chair."

"Okay."

"Great! You're a true friend and a hero of the faculty, not afraid to excuse action against the evil dean Sharkhorn and his foul throne!"

"A question arises."

"Uh, sure."

"Is it okay for me to admit I've promised to never tell a certain undefined thing?"

"No!"

"So if the chair affair is denoted by X, I am to not speak of X, and to not speak of not speaking of X."

"Er, yes."

"And if someone was to inquire, say, do I have ever promised to never speak of a promise?"

"What--- who would ask something like that?"

"Little you know of mathematicians. Logicians especially; they are conversation fiends."

"Wait, look, just promise to never speak of this event, recursive."

"Okay. That's much better; we could be here for a long time otherwise. But... if I'm to not speak of the incident, or of this conversation relating to it, or of me later thinking of that or this, or of any incident relating to these earlier incidents... do you think that could become a dense subset of my future actions? If so, I couldn't speak, within the limits of easy conversational error of epsilon arbitrarily small, of anything! I would have to deny having any experiences or thought processes at all!"

"You don't have--- I--- I don't know what that means, but don't worry, won't happen. Nothing with epsilons ever happens in real life."

"Oh. Well, it's a practical matter; I trust your judgment."

"Great."

"Wait. If someone asks, 'where were you at the exact moment five minutes ago?', I would have nothing to say."

"That's the purpose."

"If they asked, was I in the loo, what should I say?"

"I... what?"

"I mean, if I'm allowed to comment on anything except the actual tacky truth, there's the possibility of excluding all other alternatives---"

"That'd take centuries! And a Sherlock Holmes!"

"No no no. 'Did you see anything unusual? Oh, no answer. Did you see anything unusual involving two or more humans? No, you say? Involving one human? No answer, eh? Ehhh? Who was it?'"

"...you don't need to be that obliging."

"But I don't like lying. And I don't like to get started; I don't know where to stop. Remember my cousin Jeremy?"

"Sure."

"I don't have no cousin Jeremy. He's a little white lie that got out of hand."

"But I've met... look, just say you were on the toilet. If they ask any details, say that's disgusting and shut up."

"Oh."

"Finished?"

"I guess that covers most... what if someone says they know I'm lying?"

"Then say you aren't!"

"What if they provide evidence to the contrary? Witness testimony or video or---"

"WHAT?"

"I mean, do I call that a lie? A fabricated, slanderous, untrue thing? Because I'd be arguing against the coherency of their memory, or the veracity of video imagery showing me in the dean's office's doorway talking to you. Even with the admittedly powerful position of arguing assuming a reality-contradicting premise---"

"What do you mean, video?"

"You know, from that surveillance camera in the corner of the office --- oh, and now he runs away, leaving this business unfinished. What an inconsiderate person!"

One response so far

Time, what is time?

Sep 15 2011 Published by under Uncategorized

It is one hour to midnight here in Finland, right now, when I write this. If I was in Morris, Minnesota (to pick a fringe famous place at random), it would be three hours after midday instead. That's because what a clock shows is not time, but a sun tracking system. It's a noon when the sun is overhead, or as high overhead as it's likely to get any given day.

Go out into space, and you'll see the time zones are just an illusion, though a useful illusion. It makes no sense to note the Sun being overhead when there's no turning ground beneath your feet, to make that overheadness come around at regular intervals.

If you landed on Mars, you could call the moment the Sun is overhead a midday, 12 am, too; but the next one wouldn't be along when your clock had turned 24 full hours. (You'd need to wait for an additional half an hour or so; a Martian day is around 24.5 hours.)

Worse still, if you carefully measured time from the 15th of September, 2011, to 15th of September, 2012, you would not be back in the same Martian season, no matter whether you counted days by units of 24 hours, or by suns going overhead. Years are an illusion just as much as days. Mars days and Mars years, if you define them by the planet, are not the same as those of Earth, not by length or by how many each contains of the previous unit; but if you don't define time by the planet you're on, you're in for a lot of practical trouble:

"Let's meet here at noon tomorrow."

"What? Noon tomorrow is in the middle of the night!"

"But the bus for the spring festival leaves at noon!"

"And the spring festival's in bloody December! I hate Mars!"

But if you use the local units... well, that means every planet has its own days and years. (Don't think about the moons. You'll break your mind.) Their own months too, probably, because the length of the year influences how you divide it into manageable chunks. (Our months aren't moon-ths anymore. Full moon to full moon isn't a nice integer number of days.) The Martian year is a little less than 669 local days (measured by the Sun); since the closest multiple of 30 is 660, you could start with 22 months of 30 days, and add a day to a few of them --- or you could start with 12 months of 56 days and whittle a few of them down. (Do you want to have 12 months for the old names' sake? That's a swindle waiting to happen --- "Just work here until December's over, Earth boy.")

Worse still, what do you do off-planet? Say you have a colony that floats somewhere in the asteroid belt. There you have no natural unit of a day; even if your colony rotates, that doesn't need to be the source of your overhead illumination and rhythm of life. Your colony goes around the sun, probably, but that doesn't create seasons in space. (Well, your distance from the Sun may vary, but that's unlikely to have any immediate effect.) Such a colony would probably use the "home planet's" days, months and years, and schedule their lives accordingly, at first.

But what about when the space miners complain that 24 hours is too short to contain both sleep, travel and work? (Or complain that all that one can psychologically bear to do is 4 hours of work without rest, but 20 hours of free time is economically impossible, so could they have an 18-hour schedule?) Why, that would be a temptation to retool the already arbitrary calendar. (Even more so if the home planet grew distant, and not particularly politically dominant. "Down with Earthling tyranny and the oppressive/slothful Earth day!")

Ah, but that runs into something that I know nothing about: the human animal and its ability to adapt into new day lengths. Given suitable incentives of light and darkness, could you adapt to 30-hour days? Or 12-hour days? There's probably some upper limit where one just needs to rest and sleep (whatever sleep actually is, and whether it's just another condition awaiting a cure; I don't know), and there's probably some practical lower limit where shuffling day and night, sleep and waking, becomes just silly; but what are the limits of the beast? (Related: if you have a 30-hour day, how many hours of it do you need to sleep to feel rested? The same fraction as of a 24-hour day, or more, or less?)

And what are the effects on visitors?

"The pilot wishes to welcome you to Asteroid Xena-Callisto. The local time is 12:25, the local day is 16 hours, of which the first ten are allocated as night. The food court is open; the customary dinner crush is at 15:30, and the breakfast at 10:30. We hope you enjoy your stay. Those not arriving from modulo 16 timeframes plus minus 4 are encouraged to contact the Asteroid Time Consult for advice, sleep pills and a temporal lightbulb/calculator."

What are you left with, then, with different days and years? Well, hours, minutes, seconds obviously... but an hour is of such length that 24 of them make a full Earth day; minutes such that 60 make an hour, and seconds so that 60 make a minute. What if your planetary day is 22 hours, 31 minutes and 12 seconds? Woe the clockmaker! Woe anyone, actually, that tries to measure anything by such hours --- 48 hours will not be any integer number of days; no decent integer number of hours will be. The clocks will have 22 hours, and a half, and a bit more; that's all kinds of inconvenience.

So there is a great temptation to redefine hours too: to contain a different number of minutes, maybe. And if that is not enough --- "Our day is 1500.5 minutes!" --- then even the minutes could be redefined. The Earth day is (he said with some handwaving) 86400 seconds long; unless you are damned unlucky, your random planetary day could be measured in seconds, and divided into manageable chunks. ("What? Our day is a prime number of seconds long? Sweet bleeding cloaca of Constantine!")

Infobox: Even the Earth day is a little bit wonky. Have you heard about leap seconds? Since 1972, 24 seconds have been added to our atomic clocks to keep us up with time as measured by the position of the Sun. Leap seconds are in use because they're at the right level of coarseness: they're needed one or twice a year, tops, and nobody really notices when they're inserted into the count of time. Time that needs to be nudged like this isn't bothersome; indeed, most people don't even notice it. (Do you think your neighbor has heard about leap seconds? Hearing, would he or she say, "Seriously? There's leap seconds in my clocks? I've never noticed that thing!"?)

Our current way of counting time could no doubt be improved: 60 seconds to a minute, 60 minutes to an hour, 24 hours to a day is (to me anyway) a messy system. How may minutes in a day? 1440? Yeah, that's nice and obvious. How many hours in eight days? Hmm? If you ask me, units of time should be easy to convert, possibly just by moving the decimal separator, instead of being crawling horrors of Sumerian astrological geometry. (What? You thought the sixty-sixty and so on divisions of time came from some cool, rational consideration? Heh!)

Also, the whole base-ten system of numbers? That we talk of one hundred (ten-tens), two tens and three ones, and write 123? A blind monkey with a math degree could do better; who designs a numerical system based on a number with just two factors? A blind monkey without a math degree? Compare just 10 and 12. Ten is 2 times 5; ten marbles can be divided into either 2 or 5 equal piles. Twelve is 2 times 2 times 3; you can divide it into 2, 3, 4 or 6 piles without a knife. Having a number system with good divisibility is kinda important in practical life. ("Honey, I have 1oo muffinses and 6 guests. How do I divide them?" vs. "Honey, I have 84 muffins base twelve, and 6 guests... oh wait, 8 twelves is 8 twice-sixes, so 16 muffins each, and then 4 are left over. Base twelve is so simple even a househusband can do it!")

An hour of 100 minutes would be ugly: half of it would be 50 minutes; a third something unseemly; a fourth 25 minutes; a fifth 20 minutes, a sixth, a seventh and an eighth unspeakables. Fractions are important; and the decimal system is not particularly good with fractions.

Compare an hour of 60 minutes: a half is 30, a third 20, a fourth 15, a fifth 12, a sixth 10 --- counting and dividing something by sixties and their fractions is so fine even ancient Sumerians saw it! I blame the Egyptians for our decadic foolishness; the Egyptians, and biology. (If only we had six fingers on each hand, then base twelve would come naturally. But no --- the wrong gnathostome got crushed in the Ordovician, and five fingers it is.)

Now, this talk of different bases and different counts of time is blowing hot air, right now; there's a wee bit lot of practical stuff that is against an alteration as fundamental as these. But suppose that we one day get into space, and there's a bottleneck of a first colony, a few thousand people adjusting to an already foreign environment, and someone adds one adjustment more --- why, our distant children could laugh at us and our weird ways of handling time and numbers. Or, on widely separated islands of life, there'd be space for speciation of numbering-cultures --- have whatever expression that most pleases you.

And in the future, the handling of time... well, your mobile phone probably keeps time by querying, now and then, a server somewhere. That server might take time very seriously; and your mobile phone might actually keep you up to time with the accuracy of leap seconds; but it's not likely you notice that. Could be that in the future changing a time system is no more trouble that changing a time zone; just one of the small problems of traveling, something mainly fixed by tapping your watch-equivalent digital computer thingie, and by griping: "Oh man, this rocket lag is killing me. How can it be dark again?"

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Two old mathematician jokes

Sep 14 2011 Published by under Uncategorized

Since the topic of spherical cows came up in the comments to the previous post, I'll use that as an excuse to retell two old jokes.

* * *

There was a civil servant. (Wait, it gets better.) He set out to research ways of improving milk production. He hired three teams: one led by a physicist, one by an engineer, and one by a mathematician. (He had an excuse; his office was out of monies earmarked for biologist-hiring, so he had to improvise.)

Six months and much paperwork passed; and the civil servant called the three into his office to hear how their particular experiments had succeeded.

First came the physicist. He reported a 20% increase in milk production; he had fed the cows raw chemical elements in the exact combination that milk is made of; and milk production had gone up 20%. Unfortunately, 20% of the cows had died, making this an exercise in running in place.

Hearing this, the mathematician sniggered.

Second, the engineer told her results. At her farm, the milk production had gone up 50%, thanks to a revolutionary new cow-exercising obstacle course and a milking machine made of surplus jet engine parts. (Thanks to one of them, anyway.) Unfortunately, 50% of the cows had been lost in jet engine-related mishaps; though in addition to milk, the farm now also produced bottled cow. Still, overall, the civil servant judged this as running in place.

Hearing this, the mathematician smirked.

Finally, the mathematician came in, and turned at the blackboard, and raised a piece of chalk --- only to be interrupted by an inquiry for the increase in milk production.

"Oh, an increase of 300%", the mathematician mumbled, and drew on the blackboard.

The physicist made an incredulous noise. The engineer choked. The civil servant expressed cautious approval.

And the mathematician said: "However, I did lose 300% of the provided cows."

* * *

I know, the canonical endquote is, "Ah yes, my method was very simple. Let us assume all cows are identical spheres of constant density..." --- but what's the fun in telling the joke you expect?

Oh, and the mathematician is naturally smirking not because she's smug and doing better; indeed, she's doing something horribly wrong; but she's amused because 80% times 120% and 50% times 150% are both less than 100%.

Now, the second joke.

* * *

A pair of physicists got into trouble, as physicists usually do. This time they got into a balloon, and went flying; there rose a great amount of mist, and obscured their view; there rose a greatly variable wind, and confused their senses of direction and location; and soon, drifting along at altitude, location and velocity unknown, they were forced to yell towards the sound of an accordion they heard rising from far below.

"Hello!" they cried. "Help! Please tell us where we are!"

After a while, a faint voice answered: "You're in a balloon!"

At this, one of the physicists pulled a cord, and the balloon collapsed; as the other howled in terror, they plunged downwards --- and with desperate steering just barely fell, with a great though safe splash, into the lake that was just next to their university's math department.

"Why", the second physicist, the terror-stricken one, gasped, "you lunatic! You could have killed us! What if it had been the Tall Spiky Biology Building below us!"

"Relax", the first physicist said, "it was perfectly safe. I knew a mathematician answered us, and the time of day being the working hours, she was at the department, right next to this lake."

"Why, how did you know she was a mathematician?"

"Perfectly simple. The answer she gave us was absolutely, indubitably, irrefutably true... and absolutely useless."

2 responses so far

Cowed by mathematics

Sep 13 2011 Published by under Uncategorized

In the following, I will try to popularize mathematics by replacing scary words ("tensoriffic polynome productions!") with cows.

I will not go into primes, probability or neat-o tricks of geometry. Instead, I will try to explain how mathematics is written; how mathematicians think; and how this terrible machine of pattern description moves forward... with cows.

Mathematics is statements like this:

A: "We define a cow as that which has four legs, eats grass, and gives milk."

B: "If you have something that has four legs, eats grass, and is called Daisy, it is a cow."

Statement A is a definition; in mathematics you want to know exactly what you are talking about; you can't talk about it otherwise. This is different with other subjects; in politics, it actually helps if your words have no fixed definitions. In mathematics, every word should have a meaning, and should only be used to mean that.

Thus, from now on, for the duration of this post and as far beyond that as you want, a cow is anything for which the three conditions of Definition A hold. Whether it moos or not is irrelevant; it is a cow if it has four legs, and eats grass, and gives milk. If even one of those three doesn't hold, then it isn't a cow.

Statement B is a proposition; it is your suggestion for something that might be true for your definitions of "cow", "legs", "Daisy", "four" and the like.

If you add a proof to a proposition, you get a theorem: the proof is something that shows your proposition is actually true, and a theorem is a true statement. So:

Theorem B: "If you have something that has four legs, eats grass, and is called Daisy, it is a cow."

Proof (of Theorem B): "The first two details of the definition of a cow (four legs, eats grass) hold already, so it is enough to prove milk-giving. It is well known (see Farmer's Guidebook 2011) that that which has four legs and is called Daisy gives milk. Thus we are done."

Kindly note that we could write a stricter theorem ---

Theorem BS: "If you have something that has four legs, eats grass, and is called Daisy, and also says "Moo!", it is a cow."

This is not something a mathematician would do, because the same proof would do, and the assumption of mooing would be unnecessary, not being used in the proof. It would be a sloppy theorem; an inelegant one; one that is not beautiful. If you've already proven something for all fourlegs-grasseating-Daisies, you don't need to reprove it for the fourlegs-grasseating-Daisies that moo.

What a mathematician would be interested in would be something looser, something that gives more (or equal) bang for less (or equal) buck, like this:

Theorem BL: "If you have something that has four legs, eats grass, and is called D-something, it is a cow."

If you could prove Theorem BL, you wouldn't need Theorem B; you would just note that "Daisy" is D-something, and by Theorem BL, you know Theorem B holds.

Very rashly speaking mathematics is done doing four things:

  1. Thinking up and proving new theorems;
  2. Finding better (shorter, simpler, more beautiful, more evocative) proofs for old theorems;
  3. Proving better versions of already proven theorems (as in, BL inspired by B); and
  4. Making horrible cow-horse hybrids and seeing if they will live.

As an example of the fourth, you could try to prove something like Theorem B for horses, replacing "cow" with "horse" and "Daisy" with "Charlie". It seems intuitive that the theories of various animals should have similar parts in them. That analogue might be true, and might be something that could be proven. The maddening part is that you can't quite know something can be proven until you've done so; intuition is useful, but not infallible, and it's really easy to spend a lot of time trying to show something false as being true.

Thus with the two odd ones of those four activities, you have to include their "negatives" as well, because they generate knowledge of the game of ifs and thens you're playing: Thinking up statements that aren't true (so no sense in trying to prove them), and trying to see how far a theorem can go. For example, this:

Would-be Theorem BLL: "If you have something that has four legs and eats grass, it is a cow."

That would be a revolution in cow studies, if you could prove it; it would make our very definition of a cow inelegant. Anything that had four legs and ate grass would be a cow, and by being a cow, also give milk; and thus demanding those two and milk-giving of would-be cows would be kind of a stupid definition. It would be better to define cows as four-legged grass-eaters, and then note and rewrite Theorem BLL as an exciting property of all such creatures: "All cows give milk." (Compare "A chair must have more than two legs and exactly four legs.")

Now, would and would; this wannabe-Theorem BLL cannot be proven, and a counterexample will show it. Take this horse here, named Charlie. Charlie has four legs and eats grass; Charlie is not a cow. If BLL was a theorem, Charlie would be a cow; hence, BLL cannot be true; it cannot be a theorem. Thus away with this B(u)LL, and towards more meaty bovinistics!

Now, if you look at Theorem B or BS or BL, you see they all are of this form:

Form 1: "If (X), then (Y)."

(More exactly, "If a thing is (X), then it is also (Y).")

There are mathematical statements that aren't that form. The first example could be this:

Form 2: "If (X), then not (Y)."

A mathematician would quibble at that, and say that if you choose "not (Y1)" as (Y) in Form 1, you get "If (X), then not (Y1)", that is, Form 2. This is not pure contrarianism, because doing mathematics can be a complex business; and mathematicians, being very simple human beings, tend to demand as few extra complications as possible.

These are a few more of the kinds of things mathematics can express:

Form 3: "If (X), then there is a (Y)."

Form 4: "There is no (X)."

Form 5: "For all (X), (Y) holds."

Coming up with an example of Form 4 isn't exactly of earth-shattering difficulty: "There is no five-legged cow." For proof (because "d'oh!" isn't enough), this will do: "Assume there is a five-legged cow. Because it is a cow, it has four legs. An animal cannot have both four and five legs; thus there can be no such animal, that is, there are no five-legged cows."

Next, Form 5 is just a more general form of Form 1; an example would be, "For every cow, there is a corresponding cowshed." Or, stretching the form a bit, "For any collection of cows, there is a cowshed that can house that collection."

The suitable definition of "a cowshed" is left as an exercise to the reader.

Now, what about Form 3? That's something new. Consider this:

Theorem C: "If you have a herd of cows, the herd has a biggest cow."

This is not a statement about what you can say about a particular cow by examining it closely; it says that under particular conditions, there is a cow of a certain quality. Which cow? The theorem need not say.

Theorem C could be proven by giving a procedure that, for any herd you might choose, winnowed out of it the biggest cow in it.

Just as well the proof could be like this: "Assume there is a herd which doesn't have a biggest cow. Then (something outrageous and impossible follows). Thus it can't ever be the case that there is no biggest cow, that is, there is a biggest cow in every herd." Which cow that is, is a separate and possibly much harder problem.

So much for structure; next, a bit of formality. Some mathematical theorems are called lemmas; they're "small theorems", usually bits of a crawl towards a bigger theorem. Some theorems are called rules or laws; this is just chest-beating. Some theorems are called corollaries; they're "sisters", theorems that are easy once you've proven a related theorem. For example:

Lemma D: "If a collection of animals has a biggest animal, it has a smallest animal, too."

Corollary E: "If you have a herd of cows, the herd has a smallest cow."

Assuming we have proven Theorem C, we can collide it with Lemma D, and Corollary E immediately follows.

Now this post could be continued and made more rigorous and informative by adding all kinds of verbiage about logic and the derivation of ABBA strings; but my goal here was just to explain the parts of which mathematical exposition is made. (The other parts, such as lists of references, page numbers and breathlessly hypeful abstracts, are not particularly unique.) Now, if you ever see a mathematics textbook, or an article on the properties of even primes, you can sort of see its structure.

(Advice is gratefully accepted on whether this was a d'oh-fest of obviousness. Mathematicians need not answer this; I can guess.)

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The Secrets of the Advisors

Sep 12 2011 Published by under Uncategorized

Hello. I am called Masks of Eris, the same as my blog; I think introductions are tiresome.

I am a graduate student of mathematics; I don't know when it is socially correct to start calling myself a mathematician.

There are many others things I don't know, which sometimes affects, or even inspires, my blogging. Indeed, sometimes it seems an education in mathematics consists of nothing but decreasing your relative amount knowledge (relative to all you know exists), even as your absolute amount of knowledge slowly increases.

But this one thing I know: how a graduate student's advisor, that guide of thesis-work and toil, is chosen. The method is a die roll; a fair, impartial die roll; and the role the advisor plays is taken from the table below. It is a grim, adventurous tale how I got hold of it, and what happened to the brave assistant who annotated it; but that is a tale which this introductory margin is too narrow to contain.

* * *

Roll (1d100) : Result

1-2 : Nice

3-12 : Raving lunatic psycho (Yes, this is the actual proportion. The thing is, those that roll 1 or 2 have a disproportionately larger probability of survival; i.e. their advisor is not a raving lunatic psycho.)

13-14 : Nice on the surface, raving lunatic psycho below. (As you know, graduate students aren't told their roll; sometimes even the advisor doesn't know, but is just given subtle behavioral nudges by the Secret Department Committee.)

15-17 : Nice on the surface. Nice below it. Actually all nice, except that one mortal enemy whose name calls up a black storm of rage. Unfortunately, that's a semi-major author on your thesis topic.

18-21 : Charles Manson (with a roll of 21 and the subject of Modern Religions, literally.)

22-23 : Quaintly old-fashioned. As in, "You sent me electronic mail? Oh, turn my machine on and check if I got it. Usually the secretary does, but he is still procuring the fine vellum I requested for your official study plan."

24-25 : Aggressively old-fashioned. As in, "You sent me electronic mail? Why? I don't have a computer. Use paper! And cursive longhand!"

26-27 : Really, really old-fashioned. With a beard and all, no matter the sex; in the old-fashioned days every academician had a beard and a black robe. Don't goggle, for professors are subtle and quick to anger. And also have magical powers; did you really think the money came from sources other than the gibbering dark demons of the rites of De Fundiis Mysteriis and The Book of Bloody Grants?

28-29 : Affable but clueless (What, elaboration is needed on this? Sure! Um, it's fairly simple. If you just take a person that's as one usually is, and them um proceeds by the usual tricks and methods and does the jump sideways, that's as it is in the book of that one person. Easy, you can do it!)

30-32 : Feedback enthusiast ("Ah, but what do you think about what you thought about what I said about your feelings?")

33-35 : Unstable ("And this form of an integer is, is fine, because it decomposes better than the rotting body of a..." (blinks) "I didn't mean anything by that.")

36-38 : Stalker ("This is normal academic supervision. Now proceed with the lady, please.")

39-42 : Recursion tasker ("Easy. You prove Lemma A with Theorem C, just add that. C is proven with E --- add that --- that's a corollary of Theorem 5.1, easy to add, which follows from chapters 1-4...")

43 : Law savvy ("Well, actually, I do own you. Study plan section 5-C.")

44 : Genre savvy ("Of course I knew you would be here. Do you think this wrinkled face never contorted in a graduate student's lazy despair? Do you think these feet never took the route not past the Door of Doom? I know you, for mere half a century ago I was you!")

45-46 : Zen ("When the pupil is ready to learn, a teacher will appear. You clearly aren't ready yet.")

47-48 : Believer ("Problems with your thesis? Let us pray. Oh Pythagoras, we turn at thee---")

49-51 : Publicity hound ("That's a good thesis topic, provided we could make it a bit more international. You think you could put some controversy into it? The fine properties of even primes and the government is full of Nazi criminals! Excellent!")

52-54 : Fund-a-mentalist ("Ah yes, you... I have funding for you from the Imperial Zoo of Hamburg. The cage arrives tomorrow.")

55 : The advisor is a substance abuser --- this, however, is no reason to be (s/gl)ad since this means he daily pours ketchup into his underpants while blissing out over the feeling. (Here "he" is used deliberately, as according to the Heinz theory of humors ketchup is the male condiment; a woman would use mustard.)

56 : Substance abuser, harmless. While you're in his/her smoky office, it seems nothing is difficult and all the secrets of the universe are within your reach, moons and planets of titillating possibilities whirling round and round in your head, emitting blue moans and intoxicating tastes --- but when you get back to your room and take up a pencil, nothing but a headache remains.

57 : Substance abuser, almost harmless. Your thesis draft comes back with notes written in some messy red liquid. The advisor giggles, then assures you of not being the kind of a lunatic that'd write notes in one's own blood. You sigh in relief, but then see the other graduate student walking around, looking wan, with his arm in a sling...

58 : Mildly eccentric (Has an irrational fear of cellphones and computers. Attends official functions in a tinfoil suit. Likes the administration.)

59-61 : Technohazard (She enters your room and your thesis is replaced by the Blue Screen of Death. If you don't use Windows, a hamster runs in instead, dives inside your machine, and spontaneously combusts. Then she asks: "Any new developments?")

62-65 : A fan of different ways of learning ("I cannot help you. You must seek the answers from Beyond.")

66-67 : Yoda ("Mudhole? Slimy? My office this is!")

68-69 : Chewbacca (Has some communication problems.)

70-74 : The Emperor ("Everything that has transpired has done so according to my design.")

75-77 : Darth Vader ("You have failed me for the last time!" --- also, all modern lists of archetypes include several Star Wars characters; this is known as the Campbell-Lucas law, as you surely know, and now can't gracefully admit not having known.)

78-81 : Saruman ("And yet you did not have the wit to see it. Your love of the Halflings' leaf has clearly slowed your mind.")

82-84 : Sauron (Secretary tells you that "My Master, Sauron the Great, bids thee welcome. Remember, he doesn't allow his name to be spoken or expressed in any form. And don't say anything about the eye.")

85-89 : Gollum ("My preciousss... Precious funding... Gone! All gone! The grad student! We hates it! We hates it forever! It shall pay!")

90 : Cthulhu ("Ph'nglui mglw'bhok Cthulhu R'lyeh wgah'nagl fhtagn" or "In his office at R'lyeh dead Cthulhu waits dreaming". Which is to say, the graduate student that wakes him/her/it will end up screaming.)

91 : Conan the Barbarian ("Black-haired, sullen-eyed, [...] a thief, a reaver, a slayer, with gigantic melancholies and gigantic mirth." That's the reputation, so there's the constant risk of becoming an anecdote.)

92-93 : Sadist ("Pain is the breaking of the shell that encloses your understanding." Enough said.)

94 : Humorless twit ("I, for one, find this list to be unrealistic and offensive.")

95-96 : The advisor is elsewhere, and did not take you with him/her/it. No worries, for there is Skype; much worries, for there also is a twelve-hour time difference.

97 : The advisor is dead, but the department can't afford losing the prestigious name. The secretary recommends using an Ouija board.

98 : The advisor is held in the local correctional facility. He apparently did something to his previous grad students. You have to remove your tie and shoelaces before you're allowed to see him.

99 : The advisor is nice, but you keep having a terrible hunch that she keeps spiders in her room and you can't quite say why.

100 : The advisor is a difficult person.

* * *

Now that I have the younger audience in my grip, and the elders in an uproar over me revealing the Secrets of the Tenured Ones of the Tenureous Darkness --- and those in between thinking this post has been thoroughly meh --- I can tell a bit more of myself: I am Finnish, and in Finland, in Unnamed-Small-University-X, and I usually blog about whatever; the above is an example of my subtle style, vast erudition and stolid realism. I am a fan of George Carlin and heavy metal, a Discordian, and equipped with delusions of humility.

Oh, and I'll be blogging here for the next two weeks. Nice to meet you all; I am honored and somewhat giddy to be here.

Feel free to protest below, or to discuss the question of when one can with good conscience call oneself a mathematician, a biologist or even, oh shudders, an academician. I don't know, and as can be seen above, my guesses tend towards the unrealistic.

2 responses so far

So Great to Meet You!!

Sep 11 2011 Published by under Uncategorized

Dearest Friends,

Today is the final day of my two week guest blog extravaganza here at Scientopia.  I can't tell you enough about how much fun I had, and how wonderful it was to make new friends and hear terrific new ideas.  Many of your suggestions will live on here at Suburban Stone Age.  I hope you stop by to visit us, and join us in our further adventures.

If you'd like to keep abreast of what we're up to, you can subscribe to our blog at www.suburbanstoneage.com.  I'll also be posting pictures of our projects, such as our upcoming compost bin (based on your suggestions), on SSA's Facebook page.  We always love to hear from all the great folks out there who are looking for and finding solutions, so I hope you'll come play with us.

In the meantime, we'll keep looking to the Information Age, the Agricultural Age, and the Stone Age to build a more sustainable modern life.  We'll keep you posted!

Take care and be well from all of the gang,

Becky Simpson & Crew

Suburban Stone Age

 

 

2 responses so far

What a Crock!: On Containers and Storage

Sep 11 2011 Published by under Uncategorized

One of the challenges I've been facing with producing my own food is the issue of storage.  There are three types of storage I woefully lack, and it makes for mess, frustration and inefficiency.  One of this winter's projects is to get myself all set up for next year, so my house doesn't explode with food that becomes clutter, I don't loose food to rot, and there aren't any pest problems.

The first of storage is what I think of as "fresh" storage.  I am looking for stack able bins where I can keep fresh fruits on hand for immediate use in the kitchen.   Right now, I am finding that scrap cardboard boxed full of tomatoes are stacking up all over the counter, and that has to stop.  I need bins that are easily accessible yet out of the way where I can have a meal or two's supply of onions, potatoes, garlic, tomatoes, and carrots.  In addition, I'd like another set to hold apples, bananas, oranges and any fresh fruits.  These need to be on hand for the kids to grab as snacks.   Cost will be a factor, I figure I'll need at least 10.  I'll check into building some, and also be checking Craig's list to see if any come up for sale cheap.

The second type f storage I need is what I call "dry" storage.  Think root cellar area.  I have wanted a real root cellar for many years now, but most plans call for a lot of building, expense or both.  That may end up happening, but it will be a few years, and until that day, I'll have to settle for the linen closet.  I currently have pumpkins in my bedroom closet, and they are doing really well.  I think I'll adapt the hall closet to cool long term storage of potatoes, onion, carrots, and other roots, as it turns out the closets are the most temperature stable rooms in the house and on the property.

The third type of storage I need I call "wet" storage.  This is the happy place where I can leave crocks of pickles to ferment, ginger ale to mature, and the like.  It needs to be cool and stable, yet accessible, a many of these projects-in-progress require attention daily.  This will be the most challenging area, which explains why my pickling career has yet to be started.  So far I am thinking of clearing off a special shelf in the pantry, but it gets quite warm there and that could be a problem.  Perhaps with winter coming, it will be a different situation.

I think the first priority will be the fresh storage.  I'm going to get busy sourcing the bins, and let you know what I come up with.  If I find any spectacular deals or ideas, I'll be sure to share.  If you have any solutions too, I'd love to hear it!  I'll keep you posted!

 

 

2 responses so far

here be monsters

Sep 09 2011 Published by under Uncategorized

Since the stores are already decking themselves in Halloween finery, it seems appropriate to indulge in a little monster talk.   More appropriately for this venue: monster-versus-scientist talk.  By way of gothic literature.

Gothic lit emerges in the late 18th century, morphs eventually into what is often labelled horror, then splinters into many subgenres. Conventions, motifs, and tropes of the gothic include the following: wild landscapes; remote or exotic locales;  dimly lit, gloomy settings (contrast of light and dark); ruins or isolated crumbling castles or mansions (later cities and houses); crypts, tombs, dungeons, torture chambers, dark towers, hidden rooms, secret corridors/passageways; dream states or nightmares; found manuscripts or artifacts; ancestral curses; family secrets; damsels in distress; marvellous or mysterious creatures, monsters, spirits, or strangers; enigmatic figures with supernatural powers; interest in evil, its origins;  specific reference to noon, midnight, twilight (the witching hours); use of traditionally “magical” numbers such as 3, 7, 13; unnatural acts of nature (blood-red moon, sudden fierce wind, etc.); murder, suicide, torture, madness (especially persecution and paranoia), lycanthropy (werewolves), ghosts, vampires, doubles and doppelgängers, demons, poltergeists, demonic pacts, diabolic possession/exorcism, witchcraft, and voodoo.  So, to sum up: scary stuff.

In gothic lit, there's typically a battle between reason and unreason, which can manifest as some sort of tension between science and the supernatural.  (See?  I was getting to the science part.  Thanks for bearing with me.)  In some cases, the division between the science fiction (or speculative fiction) genre and the gothic genre can seem thin indeed.  Mary Wollstonecraft Shelley's Frankenstein is hailed as one of the first important examples of both science fiction and gothic fiction, which makes sense given that Dr. Victor Frankenstein uses his scientific knowledge to build the Monster from "parts" in a lab.  And those parts?  Come from dead people.  (Think of the plethora of horror films we have today that would never have existed without such a blueprint.)

But wait!  There are more scientists in gothic lit!

Sometimes scientists are the heros, sometimes they are the catalysts, and sometimes they are the monsters.  But no matter which character role they inhabit, they are always interesting.  The desperate characters in Bram Stoker's Dracula turn to Dr. Van Helsing when the vampires have made it impossible to ignore their blood-thirsty mayhem any longer.  In H.G. Wells's The Time Machine, the invention of the time machine by the enthusiastic scientist protagonist is what brings him face to face with a pack of (hungry) subterranean Morlocks.  (And in Wells's The Island of Doctor Moreau, it's the doctor himself performing vivisections that becomes monstrous.)   Nathaniel Hawthorne's "The Birthmark" focuses on a scientist insistent upon removing his wife's birthmark in order to make her perfect, which leads to [*spoiler alert*] her death because, of course, no one can be perfect.  In Margaret Atwood's Oryx and Crake, a scientist determined to try out his own "elegant concept" leads to worldwide catastrophe.  And we musn't forget Dr. Jekyll and Mr. Hyde, Robert Louis Stevensons's cautionary tale about using the self as test subject.

Even in many gothic texts that aren't focused on science, per se, the protagonist takes a rather scientific approach in studying some kind of terrifying phenomenon.  Fantastic events are observed empirically.  For example, in Ambrose Bierce's "The Damned Thing," a group of men try to reason out the actions of an invisible force through the paper records left behind by one of its victims.  In Charlotte Perkins Gilman's "The Yellow Wallpaper," a woman forbidden to do anything (oppressed by the "rest cure") becomes obsessed with analyzing the pattern on her wallpaper.  Finally, Ursula K. LeGuin's "Schrodinger's Cat" demands that we readers do the scientific thinking ourselves; we must entertain the possibilities of quantum mechanics in order to make sense of the story itself, which is a sort of postmodern gothic apocalyptic scenario.

Whew.

To my way of thinking, gothic's persistent use of science seems fitting because gothic texts--like science, in my humble opinion, though correct me if I'm wrong--are all about pushing boundaries, crossing borders, challenging the status quo, and forcing us to question our perceptions in powerful and profound ways.

Which leaves me with the following questions: If you read gothic texts, what did you make of the "science-esque" qualities?  Or, more generally, do literary representations of science hold any interest for you, and if so, what sorts of reading are you drawn to?

8 responses so far

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