A to Q

Ⓐ is for AWOL, away without leave.
Ⓑ is the Bug that is eating your sleeve.

Ⓒ is for Commissar; his ways are so set, that when asked for a favor he'll always say nyet.

Ⓓ is for Dancer, who may be exotic.
Ⓔ is for Everything wild and Erotic.

Ⓕ is for Fruitcake, a Christmas Day treat.
Ⓖ is for Goldfish, much better to eat.

Ⓗ is our Hero, Charlton Heston.
Ⓘ is the organ we call our Intestine.

Ⓙ is for Jesus, the son of a Jew.
Ⓚ is for Khrushchev, who's known for his shoe.

Ⓛ is for Let; it happens in tennis.
Ⓜ is a Merchant whose home is in Venice.

Ⓝ is for Nixon; he leads our great nation.
Ⓞ is his policy: Obliteration.

Ⓟ is for Pompey, Caesar's great rival.
Ⓠ is for Quicksand, which hinders survival.

empty promises

I promise that this blog won't always be about the empty set, but ...

Within the category of sets, Ø is what is called an initial object. That just means that for every set S there is exactly one "morphism" from Ø to S, in other words one function which associates to every member of the empty set a member of S. (The word "every" in this last phrase may take some getting used to.)

The empty set is also "initial" in a different sense. The reason why it took Russell and Whitehead hundreds of pages to get their foundations for mathematics developed to the point where they could prove that 1+1=2 was that they were defining "number", and some particular numbers, from scratch, or rather from set theory, and then defining "addition". They thought of the number 2 as, more or less, the set of all sets having exactly two elements; but in order to make sense of that idea in a non-circular fashion they had to actually define 2 to be the set of all sets of the same "size" as some particular set having just two elements. The set that they chose for this purpose was the set whose elements are the numbers 0 and 1. So they had to define 0 and 1 before defining 2. Of course, 1 was the set of sets of the same size as the set consisting of 0 alone. And of course 0 was the set of all sets having the same size as the empty set. Something like that. So the empty set was a starting point.

For me, part of the appeal of emptiness (and now I am not talking particularly about the empty set, but of empty vessels, blank minds, open-ended questions, clear skies... ) is the sense of beginning. So I'm glad that in category theory Ø is called an initial object.

On the other hand, a synonym for initial object is universally repelling object. So much for the found poetry of technical jargon.

doggerel

Ⓡ is for Rhinoceros,
Ⓢ is for his Snout,
Ⓣ is for the Trampoline on which he romps about.

Ⓤ is for his Underside;
Ⓥ's the Vest he wears,
and Ⓦ's the Woolen thread to mend it if he tears.

Ⓧ is for the Xerox which he likes to play,
Ⓨ is for the Yellow spot that always comes out gray,
and Ⓩ is for the Zero; there is nothing more to say.

- Anon

humidity, vermin, etc.

Make yourselves at home. My door is always unlocked, but it does seem to stick sometimes. I will try to solve the problem. It may just be the humidity.

It seems that by the time people had managed to push their way into the previous post all the nice fruit and cheese that I had left out had been devoured by vermin. Help yourselves to anything you find, but I would be cautious in approaching anything in the back corners of the fridge.

I will be back this evening, ready to attempt a nonempty post. Right now I have some work to do in the real world.

something

Yes, well, so it seems that this is a blog after all, since people have commented and AJP♔ has even listed it at his blog. I suppose I had better write something.

Welcome, invisible friends. The fire is lit. I hope there are enough chairs. Like Mr. Darcy's sister at Pemberley, I am a little unsure of myself in my rôle as host. Such distinguished company! Why is Mrs. Annesley making faces at me? Oh, I forgot the refreshments -- here, please help yourselves.

(Please, someone else say something.)

Nothing

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