increpare games

There is a great tradition in Ireland of sending sick children away to places to reinforce fantasies proportional in absurdity to the seriousness of their illness.

For terminally ill children, Fatima, Lourdes, or other similar places of unmitigated religious daftness, are often locations of choice; for seriously ill children, particularly those with leukemia, a Christmas trip to Lapland is often considered the appropriate place of call.

Profound question: where would Santa go if he got leukemia?
Answer: Fatima.

Insensitive suggestion: tell all the kids with leukemia that Santa got leukemia and probably will be getting chemo at Christmas so won’t be able to deliver presents. But say it in the tone of voice that really means that you don’t expect him to be alive by Christmas. While molesting them.

An excerpt from the transcript of the minutes of proceedings of the first Council Système International d’Unités, which took place at Lyon in 1903:

Chair: The first proposal, put forward by Msgr. Dr de La Plebe is that we change our standard unit of length from the inch to the “meter”, defined to be the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.

Attendents: scoff scoff!

Chair takes out his cock, fluffing it to a state of erection.

Chair: Msgr. Dr de La Plebe, how long would you say my erect penis is in these “meters”, of yours? hah!

Laughter follows, and the meeting degenerates quickly, as each member of the council takes out their respective cock in order to make comparisons.

And yes, it was an all male council; I don’t know many women who want to spend all their time, nine-’til-five, year in, year out, mensurating.

(ho ho ho).

I still say that, to this day, the chief reason why respectable people went decimal was because of the fact that there was a massive turnover of workers in standards centres under the empirical system due to cock-joke-burnout.

Once, while exploring the planes of southern Africa, I came across a most astonishing civilization. The people there are highly advanced in most areas of technology (certainly relative to their savage neighbouring tribes), and yet they have not, it seems, discovered the noble art of writing.

“How then”, you ask, “can they record anything? The fallible memories of mankind alone surely cannot keep a sophisticated society functioning?”

They do have paintings and other arts and crafts, and historical event are often depicted on their pottery – but this is not their chief method of recording events – allow me to explain:

One day, shortly after my arrival, a nobleman invited me to their archives. I, having noticed the complete absence of anything like parchment or papyrus, accepted with great curiosity.

The archive itself carried the smell of a cotton mill, thick and musky, with fibres floating everywhere around. There were high sets of varnished shelves all around, and the aisles between them were quite narrow. But the shelves contained neither books nor scrolls; no, they were divided into small pigeonholes, each one maybe four inches across and two feet deep. And, in each pigeonhole, there was a knotted mass of twine.

He showed me all this before taking out one of these tangled bundles, then leading me outside so that I could see it in the open air. We sat down, and he examined it himself very intently, feeling it all around, occasionally pulling the more clotted parts of it open so that he could, somehow, “read” it more clearly, before handing it to me to examine. He said it described a battle that had happened, between other tribes, two generations ago.

The twine was not too coarse, and its ends were bound together with a small gold ring. I pointed at this ring, and asked the man what it meant. He said it did not pertain to the story in any way, and its only function was to fasten the two ends of the rope together.

Then, careful not to disturb the arrangement of the complicated mesh in my hands, I pointed to a cluster where the twine overlapped and tangled into itself much more densely than elsewhere.

“What significance does this have? Does this represent the battlefield?” I asked him.

The old man laughed, took the bundle of twine from me, and started tugging at the region I had specified, then started shaking the whole bundle rather roughly until it was in a different form to how it had been before.

“Where is that pattern now?” he asked, “What use would it be to have that represent anything if even a small child, toying with it, could alter it beyond recognition?”

This confused me greatly. “If,” I spoke, “if the section I pointed to didn’t mean anything, then what part of it has meaning? Surely any part I might assign meaning to can similarly then be pulled apart”.

He smiled; “Yes.” he said, “You see, we only ascribe meaning to the parts of the knot that cannot be changed by such trivial manipulations”.

“I do not understand then how anything can be communicated using these tangled masses”.

I had kept a notebook with me on my travels, and the old man must have seen me using it, for he then asked me to give it to him. He held it open on some pages at arm’s length on front of us.

He asked what it described. I read it out to him – it was a short note on the perennial flora of southern Italy. He then moved the book closer to us, and said “does it still describe the same thing?”

“Yes, of course”.

He stepped away from my side and turned the book away from me. “And now?”

I walked around to his side again, to see if he was playing some kind of elaborate trick, but it was still the same book, open on the same page.

“Yes, it is still the same. What are you getting at?”

“And, if posted to America and read there?”

“I’d expect so”.

“And if I close the book, somehow the information on this page is the same?”

“Obviously”.

“So, can you not understand that your book has properties not too much different from our knots – the main difference is that the descriptions contained in our knots are simply left unchanged under a wider variety of actions”

I nodded – I still did not understand, but it was making some sense anyway

“And just as you might change the size or colour of your typeface, or the proportions or quality of your paper, we might change the length, diameter, or quality of our twine, without effecting anything.”

He handed my notebook back me.

“However, what would happen if I was to take a page from your book, tear it up, and reassemble it back into a page of the same shape, would it’s meaning be still the same?”

“No”, I said, “indeed, it may not make any sense at all”.

“So it would be the same”, he said, holding the twine in one hand in front of me, “for if I was to cut this rope, alter it’s knots, and reattach the ends, the whole meaning of the knot might be lost”.

The following isn’t intended to be a big great literary work, it was just written to contain a couple of simple things from category theory. See if you can find implicit use of any of: limits, colimits, the Category in question, image, preimage, equalizers, coequalizers, cone to the base B, cone from the base B, products, coproducts, mono-epi factorization. The idea was that, even if you don’t know the language, the below should read in a not overwhelmingly confusingly way (tediousness be damned!). And, of course, it’s all fictional. And unfinished; there was a third section planned to bring in functorial ideas …but I couldn’t think of a way to make it work nontrivially… .

The Evacuation

1. My home city of Ballina has long been a place of great peril, ravaged by famines and repeatedly decimated by earthquakes. Our governor appointed myself as the chief of evacuations, and I have spent many years in deep thought on this matter.

2. I regularly put together evacuation plans. A typical evacuation, to Foxford, say, is organised by sending out a letter to each household in Ballina, telling them of the dangers at hand, and specifying an address in Foxford where they are to go in the case of this emergency. Similarly, the houses in Foxford are notified of the residents that will be staying with them; I personally do not favour large refugee camps, preferring to house families with residents of the host city. Naturally, coordinating such a thing as an evacuation, and getting the agreement of the people who are to help our city takes a great deal of planning and diplomacy.

3. Before an evacuation, it is usual for groups of residents from the imperilled city to discuss their destinations amongst themselves.

4. Perhaps more often, neighbourhoods in the host city will meet together to discuss the households that they will be accommodating in the event of a disaster.

5. Three years ago, a great crop failure was forecasted in mid-summer. Knowing that there was nothing our citizens could do to save them, a flight to Bahola was planned. It is a far off place (the blight severely affected crops for miles around), and so we had servicemen set off in advance to build a camp-site half way. The refugees were instructed to group together with other people who were heading to the same residence in Bahola, so that they might travel in a group together and know eachother before arrival.

6. Often I do not manage the details of a whole evacuation myself, but rather I might delegate the evacuation of various districts of Ballina to local residences whom have shown themselves influential and trustworthy. Thus an evacuation can be split into many parts.

7. There is another way that an evacuation can be split into many parts: The city of Carlow was built during a particularly odd architectural era; its residential areas consist entirely of identically constructed, and rather bleak, apartment blocks, each having two hundred apartments. One rather poorly planned evacuation, from Galway I believe, was carried out in two parts; firstly, every house in Galway was sent a street and the name of apartment-block in Galway, and then, two days later, letters were sent out containing the apartment number – the number was just randomly picked between one and two hundred. Needless to say, chaos ensued. Thankfully, there are not many places like Bahola.

8. It did happen once, during an evacuation from Limerick to Cork, due to terribly bad organizing on the part of their evacuation team, that two plans were simultaneously put into action: two addresses in Cork sent to each household in Limerick.

9. Now, there were a few families who were, by chance, allocated the same residence in Cork on both occasions. These people’s evacuation was neat and orderly.

10. But, in general, it seemed everyone was left with a choice of destinations to go two. The council of Cork was appalled at this terrible administrative blunder, and insisted that it would need to know the precise numbers of refugees that would be arriving in each district of Cork. The best that the Limerick council could manage was to divide Cork up into districts such that a household’s two choices were always contained in the same zone. These zones needn’t have made much geographical sense at all, but due to the relative similarity of the two plans, such zones were relatively localised, and the Cork council was able to use this information to plan how to distribute aid to the refugees when they arrived.

Fantasy of an Evacuationist

1. Just as the orderly flowing of a stream, or the regular currents of the oceans inspire great awe and appreciate of their beauty and efficiency, so might
   the emigration patterns of a kingdom, if planned in detail and laws enforced, also be.

2. I picture this: an entire kingdom, meticulously construct, all places of business and dwellings alike built and planned by the ruling King. Each city will have designated it several other cities “downstream”, where people may migrate to. However, families will not have freedom where they will live in the cities. In each house there will be a golden plaque; engraved on it will be an address in each of the cities downstream – the inhabitants may only move to these residences. Of course, the river metaphor isn’t terribly useful, as it can be nice to allow circulations: for people to be eventually able to move back to a city they once departed tearfully, or to allow people to move to different residences in the same city (For a city to be downstream from itself).

3. Now, if a ruler fair be, he would not torment his subjects by having them agonise that maybe they would end up in a better house in Cork if they moved first to Clare and then after a few months on to Cork, rather than just move directly. This would create great inefficiency in the Kingdom I do believe. Better that people be allocated, and know that they be allocated, at most one house in any city (this does rule out the notion of a city being downstream from itself). But perhaps not; when one takes one’s fantasies this far it becomes difficult to gauge fairness.

4. In a similar vein to the botched evacuation from Limerick to Cork described in the previous section, it can be useful to divide up such a kingdom into \emph{streams}, that is, groups of residences spread out over different cities, where you cannot migrate from one stream to another. If it was possible for people to move anywhere, then this would not be a useful conceptualization, but it is possible to plan one’s kingdom in a way that you will get a good number of streams.

5. Let us dream that England is such an orderly migratorial-utopia as the one described above, and let it be Dublin that is terribly imperilled.

6. In planning an evacuation from Dublin to England, if I just designate you one house in one city, you might, upon arrival, see the address of a much nice house in a much nicer city on your gold plaque. Or you might think that you may be able to get to a better house in your current city by moving around a few other cities then coming back (this is assuming England did not agree with the argument that I presented some paragraphs back). Such unnecessary movement would stir up great trouble amongst the local residents no doubt, and I believe that the refugees should not have to worry about issues such as this in any event! Thus, I would have it that every Dublin household is sent one address in each English city, which have been chosen so that if you move to the Nottingham address, you will know that however you migrate, you will always be residing in one of the addresses in that list. Thus people would only have to choose once where to evacuate to, and not ever worry about moving around England in their time there. This amounts to injecting people into the agreeable streams that I argued for.

7. If there world was ideal, we would not have to impose two households of refugees on an English family, and we would make use of all the agreeable streams in England.

8. Similarly, if I was to plan an evacuation of England to New York, I would allocate addresses to residences in such a way that an English family, disappointed that they have been told to move to an industrial district of New York, would not find that by migrating to another city they would be allocated an address in a more prestigious place. No, if an address is allocated to a particular residence, it will be the same address that is allocated to it all places downstream from it.

A prelude

It took me a long long time to cop on to what the deal was with resolutions. But, I was, a bit ago, walking somewhere, and I saw something, or thought of something (I can’t remember what), and was like “oh, that’s just like a projective resolution”. I also had a dream about the Hilbert Syzygy theorem a few weeks ago. Can’t remember the details of that either, surely they were fascinating, though. I should probably take more descriptive notes. Ho hum… .

A difference in usage

Here’s a simple word which has markedly different connotations to mathematicians and non-mathematicians (in that the technical sense of the word can be, roughly, applied to the same situations as the non-technical one).

If you, as a nonmathematics-exposed person, say that Anne tends to project her misery onto everyone else, you would probably mean that she goes around believing everyone else to be exactly as miserable as she is.

However, to a mathematician, projection has a different intuitive feeling – projecting A onto B connotes the action of “picking out” what elements of A are common to B. That is, if you said to me that Anne tends to project her misery onto everyone else, I would be likely to feel that she only sees in other people is misery – and not only any misery, but a misery that resonantes with her own, if any. So, if I project my happiness onto you as a mathematician, I see in you what aspects of your happiness are similar to mine.

(this came out of a chat with greg).

A geometric fantasy

I was walking down the street about two weeks ago, and I thought “what if I think about myself as living in projective space?”. And I tried. Projective space is a “compactification” of our normal “affine” space, and corresponds to adding some points and calling them “infinity” (in some strikingly pleasant way), without really changing much of their local structure. But the thing is it turns spaces infinite in extent, like our “affine” space, and turns them into objects that are finite in extent (it turns the infinite line into a circle, for example). But yes, it made things feel different. The sky was no longer so far away, and everything felt as if brightly illuminated and indoors – intimate, being an appropriate word, perhaps.