increpare games

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.