In view of the week’s events in Boston, and various pronouncements about good and evil at war on our streets, I can do little better than to quote J. Michael Straczynski, writing after 9/11:

What DO we tell the children?
Do we tell them evil is a foreign face?
No. The evil is the thought behind the face, and it can look just like yours.
Do we tell them evil is tangible, with defined borders and names and geometries and destinies?
No. They will have nightmares enough.

Perhaps we tell them that we are sorry.
Sorry that we were not able to deliver unto them the world we wished them to have.
That our eagerness to shout is not the equal of our willingness to listen.
That the burdens of distant people are the responsibility of all men and women of conscience, or their burdens will one day become our tragedy.

Or perhaps we simply tell them that we love them, and that we will protect them. That we would give our lives for theirs and do it gladly, so great is the burden of our love.
In a universe of Gameboys and VCRs, it is, perhaps, an insubstantial gift. But it is the only one that will wash away the tears and knit the wounds and make the world a sane place to live in.



Art is a way of saying what it means to be alive, and the most salient feature of existence is the unthinkable odds against it. For every way that there is of being here, there are an infinity of ways of not being here. Historical accident snuffs out whole universes with every clock tick. Statistics declare us ridiculous. Thermodynamics prohibits us. Life, by any reasonable measure, is impossible, and my life — this, here, now — infinitely more so. Art is a way of saying, in the face of all that impossibility, just how worth celebrating it is to be able to say anything at all.”

Richard Powers


While I prepare my next series of posts, which will be on the theme of torsors and similar “forgetting some structure”-type constructions in algebra and geometry (the latter including, of course, perspective and projective geometry), here’s a quote that I rather like from Terry Pratchett and Neil Gaiman’s book Good Omens:

God does not play dice with the universe; He plays an ineffable game of His own devising, which might be compared, from the perspective of any of the other players*, to being involved in an obscure and complex version of poker in a pitch-dark room, with blank cards, for infinite stakes, with a Dealer who won’t tell you the rules, and who smiles all the time.

*i.e., everybody

The next time someone tells you to get a little perspective, just take a calm breath and remember that a little perspective is all you’re likely to get: the universe is a BIG and mysterious place. 🙂

The true nature of the beast

A bit of dialogue that rings in my head a lot, from the movie Crimson Tide:

Ramsey: At the Naval War College it was metallurgy and nuclear reactors, not Nineteenth Century philosophy. “War is a continuation of politics by other means.” Von Clausewitz.
Hunter: I think, sir, that what he was actually trying to say was a little more —
Ramsey: Complicated? [Men laughing]
Hunter: Yes, the purpose of war is to serve a political end, but the true nature of war is to serve itself.
Ramsey: [Laughing] I’m very impressed. In other words, the sailor most likely to win the war is the one most willing to part company with the politicians and ignore everything except the destruction of the enemy. You’d agree with that?
Hunter: I’d agree that, um, that’s what Clausewitz was trying to say.
Ramsey: But you wouldn’t agree with it?
Hunter: No, sir, I do not. No, I just think that in the nuclear world the true enemy can’t be destroyed.
Ramsey: [Chuckling, tapping glass] Attention on deck. Von Clausewitz will now tell us exactly who the real enemy is. [Laughing] Von? [Men laughing]
Hunter: In my humble opinion… in the nuclear world… the true enemy is war itself.

Questions and Answers

Two quotations:

“In re mathematica ars proponendi pluris facienda est quam solvendi.”
(In mathematics the art of asking [questions] is more valuable than solving [them].)
— Georg Cantor (1845–1918), Doctoral Thesis, 1867


“The uncreative mind can spot wrong answers, but it takes a very creative mind to spot wrong questions.”
— Antony Jay (1930–)

It’s a common but still dispiriting experience for me to see an excellent tool being applied to the wrong problem. Conclusions are only as sound as (a) the logical reasoning used and, crucially, (b) the validity of the premises, which includes the applicability of the method itself. Both “the right answer to the wrong question” and “the wrong answer to the right question” are wrong, but the former is more devastating because it carries an aura of (false) respectability that can lead one into making bad decisions with great confidence.

Religion Types

A pseudo-quotation (I’m not willing to call it a quotation until I find a source) from Carl Jung:

“If our religion is based on salvation, our chief emotions will be fear and trembling. If our religion is based on wonder, our chief emotion will be gratitude.”

As so often with Jung, I feel that he makes a good point but ever-so-slightly misses the real underlying issue. The division of religions is not, I think, between those that are salvation-oriented and those that are wonder-oriented; the division is between those that are oriented towards the attainment of something that the practitioner does not have and can (supposedly) only attain through the medium of the religion, and the rest. The “salvation” mechanism is just a special case of this, especially so when “salvation” is something administered by a priesthood in the name of the religion. Whether it is salvation, enlightenment, life everlasting, the effect is the same: the object becomes a means of social control, is offered as a carrot and withheld as a stick — from the latter come the fear and trembling that Jung mentions.

Post-Scriptum. I’m not making a moral judgement about whether or not the use of religion for social control purposes is “a good thing”; the answer to that depends upon circumstances far too much for a brief universal answer. My point is that fear isn’t a consequence of salvation-fetishism per se, but rather (the social consequences of) attainment-fetishism more generally.