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Tag Archives: stories

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You cannot enumerate the lies in this post. (ho ho ho)

Letters, lies, and more lies.

While I was in Egypt, I bought a book of letters by Florence Nightingale that she wrote when she was touring about.

Pablo, darling!

Greeting from Thebes; I cam across this, like, totally sweet anecdote; it’s maybe not really your cup of tea (great observer of geometry that you are), but I simply must communicate it to someone or else I will burst!

So, I was walking through the literature souk (on the banks of the nil, oh how very pre-romantic!), and came across a delightful volume of correspondence between Pharoah Rameses the Third and Albrecht Durer (Oh just imagine it! Having your personal letters published for all the world (or it’s literate portion, at any rate) to peruse!), that are curious in several respects.

So, it seems that in this episode with the volume covers, the Pharoah had developed an interest in engravers of the northern-renaissance and, consequently, had decided to write to Durer, secretly hoping to kindle up a relationship so that he might be able to commission some naughty little engravings of tearful clowns or the like from him at a later date.

Albrecht, needless to say, was quite excited at receiving such royal (arguably divine) correspondance, and enclosed with his reply a copy of his recently published treatise on perspective.

Rameses was delighted to receive such a delightful work of science, and studied this book intently

One thing, in particular, that took his attention, was a section illustrating a particularly practical (and rather simple) application of perpspective and projective geometry; he was saying that if you want to write on the side of a building, that it really makes sense to have the letters higher up be smaller than the ones lower down, so that they all appear roughly the same size. This was not rocket-science, nor, indeed, did it involve wheels, but it was remarkable nonetheless, and it was something he could work with. He was something of a trickster, you see, and he thought of an excellent joke to play on Albrecht – not the sort of joke that would be at Durer’s expense, but rather one that he was sure to appreciate.

He thought of a new type of structure – one that would be enormously tall, towering many stories high, and tapering at the top to about half the size of its base: this was the first obelisk. The trick was though, to keep the writing the same size all the way up. Thus, the writing occupies half of the faces lower down, but, as the obelisk narrows upwards, it grows to fill its full width.

And, it seemed, this did indeed win Durer’s eternal affections; he, upon completion of this monument, sent out a convoy to find Durer and bring him to Egypt, without telling him exactly what the reason for this was excepting that it did not involve him being put in to slavery. After a month’s travel, he was arrived in Cairo, the cart stopped directly on front of the obelisk. Nothing, apparently, could exceed his amusement; what delightful humour this Pharaoh had!

And they all, essentially, lived happily ever after. Further collaboration, stretching the notions of perspective to extremes, resulted in the pyramids, designed, in some or hyper-Georgian manner, to seem to be stretching up to infinity.

And, well, it seems like such a delightful story I simply must share it with you.

I heard you have been terribly ill; I will kiss everything better when I get back;

Yours,

xxx

Florence

This got me thinking about a particular chapter of invisible cities, where there is a city whose buildings are built according to the arrangements of the stars, and they keep on adding on more and more stories in the hope that they will some day be able to reach them, and the fact that the pyramids around Giza are laid out to resemble the Orion constellation, that Giza might be an artist’s construction of what such a city might look like if completed.

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No no, I mean the *other* sort of fault. (ho ho ho)

An argumentative fallacy

A class of reasoning I’ve observed in heated arguments between irritable people:

Person A does something that person B doesn’t like. Person B will commonly first remark something like “What’s this mess, did *you* do this?”, before going to say something like “This mess is all *your* fault”. This leads, logically enough to them saying “It’s all *your* fault”.

Now a piece of magic occurs, and the emphasis changes, resulting in “It’s *all* your fault”. They will repeat this again, using it as one might when saying “It’s raining”, so: “It’s *ALL* your fault”. This inevitably leads them to defensive conclusions of the form of “I’ve *never* done anything wrong”, with the intended scope being absolute and universality. There is a certain ingenuity involved in this sort of reasoning, I’m sure you’ll agree.

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Feeling trapped? Oh, then come read my stories what I will be putting up here nexte Woche!

Introducing some stories short.

Hmm. Okay. Here’s a part where I try to do somehing like preface what’re going to be a series of very short stories (10, I think, which translates to a solid 3 weeks worth of material which is, I think, not to be sniffed at, given my absence over the summertime) with something of an apology/explanation.

I had this small idea over the weekend of trying to write a sequence of geometrically inspired (very) short stories with themes of claustrophobia/agoraphobia (in, respectively, geometrical/incorrectly eometrical senses). Anyway, they’re definitely not toooooooo good, but, so far as I’ve thought of them, there’s a different phonomon at play in each one, so none of them will be entirely without meaning/point; but some are terribly weak.

As to why, this follows from a conversation that I had with someone last friday, with a mention (on my part) of this drawing by Fomenko,

,

one I am particularly fond of, depicting the contraction of a space onto a subspace of parallelepipeds in some intuitive/surreal way.

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Come on dude! Don't split the band up; we're all on the same side here! If you do that, we mightn't be on the same side anymore. (If you split us up again after that, we mightn't even be in the same band... : ( )

Before I get into things…the book of sand

Okay…want to talk about the Book of Sand, only it seems the the wikipedia entry on it is really, really bad. So, look at it if you will, but don’t take it too seriously – the actual story is only a couple of pages long, so might be worth tracking down.

Anyway, so the book in the story has, it seems, an infinite number of pages whilst being of finite size. Other than the uncomfortable situation that Borges says that the pages are numbered.

He says that all the pages are numbered – that is to say that we have some division of the interval into a countable number of segments that, assuming homogeneity, are everywhere dense. These sorts of foliations leave me feeeeling queasy I have to say.

It is a suprisingly nontrivial to think of this mathematically – my initial reaction to it was due to a misthinking, that he was foliating the interval perfectly – that is to say that each page would be of zero thickness and correspond to a point on the interval – but then it would be impossible to number, well, (almost) any of them. This, whilst not being exactly what he meant, would link up well to another story, Odin’s Disk, where the chief artifact of concern was an infinitely thin disk (the translator calls it a circle, the only shape with exactly one side; I don’t know where these terminological/factual errors crept in).

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See wikipedia if you don't get the reference.

A burger or, something more than a burger?

So, I made a funny a few weeks ago

Friend:’A friend of mine used to go to burger king on a semi-regular basis and he always used to get really annoyed because they’d put the burger box (with the burger inside it) on to his tray upside down. And, one time when I was there with him he had just got given his tray – he opened the burger box thing, to find it was upside down, and he said to the dude who had given it to him “Dude, what do you think I am, left-handed?”‘

And we all laughed, and I was, like, “Well, what if it was a pseudo-burger?”

Some people laughed anyway. At least I did.

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"plum" line, geddit?
(ho ho ho)

A torment for the purchasers of glasses.

That is to say, a torment for those of us in their company, of course, but that doesn’t give as snappy a title, and in this modern world of snappy titles, I feel that the reorientation of tormentations about the tormentors (as opposed to the tormented) doesn’t seem to fit well. But if you have any suggestions for titles, then please, by all means, write them on a postman, and send them in, and I will do my best to give them a jolly reception.

So, a little torment for today:

Let’s say that somebody has bought a new pair of glasses, just, and that they are terribly proud of them, showing them around and the like. If they are weak of character, then to spoil their burgeoning pride can take but a single sentence, spoken in a “tactful” (not necessarily discrete), carefully-metered tone:

“They look lovely only, aren’t they just, just a little lopsided?”

of course, whether they are or not isn’t the point; all you wish is to foist an embryonic torment onto their souls in the hope that it will germinate and blossom into something altogether wonderful.

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Yeah, haven't been feeling the most inspired updatewise recently. Oh well. You guys all still totally love me though, so that's okay.

A torment for the “Mobile Generation”.

Restaurants and mobile telephones. No person of any class or breeding will ever leave their mobile telephone active while sharing a repast with somebody in one of our city’s fine establishments; it’s one of the big etiquette no-nos.

However, those of us who like to torment are not interested in these social conventions except as a means to irk and perpetually torment those nearest and dearest to us. So let me offer a suggestion how best to capitalize on this rule:

Either before you enter the restaurant, or just when you do arrive at the said establishment, your partner should in some way discretely turn off their phone. Check for this, and when they do, make some show of sending a text message from yours, and then comment to them that you hope they will reply quickly.

Now, you should spend a good deal of the first course completely occupied with the operation of your phone, sending text messages and completely ignoring your partner, and not touching your food for the most part – this works better if they are paying, but is satisfactory by other arrangements as well. This should leave them feeling rather tired with your behaviour before they’ve even gotten to the main course. And, of course, be sure to hold the phone as follows: both elbows on table, phone, held in both hands, raised to your eye level.

Now, in the wait between courses you should send a message to a family member asking them to call you when they are free to, somebody who you expect will reply to your request within the next ten minutes. Then put your phone away, and begin to talk to them in some seemingly earnest way, apologizing profusely for your ignoring of them.

Then your phone rings (Oh, make sure that your ring-tone is truly obnoxious). Now, you do all the things that you feel might annoy him – talk loudly, say that you are in a restaurant, indeed feel free to complain about the food. Now, and this is the piece de resistance: ask the person who called you if they would like to speak to your partner, and that you are sure they would like to talk to them. Then thrust the contraption in their faces and say to them, “Here, so and so wants to talk to you”.

Works a treat.

If you’re stuck for something to try during dessert, if things get that far, I can heartily recommend a course of constant mobile-phone photograph taking. Especially if you have the anti-pervert camera shutter sound on your phone.

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In brief: equivalent configurations must be obtainable by geometrical congruences, and all congruences aught to give equivalent configurations. Viva l'representations!

A fantasy on unordered “enumeration”, part the second.

Where I do add another journalistic account of a tribe I visited before, that had a system of unordered counting quite remarkable.

I came across a village some forty days south of where I met that tribe tribe whose inhabitants were, astoundingly, even more puritanical in their approach to counting – or rather to assigning cardinalities.

These people had accepted the arts of reading and arithmetic into their culture with great success but, when I told them of the nomadic tribe from the previous article, they broke into laughter at the very naivety of the idea!

This had me taken aback – not only had they seemed to have completely comprehended what I had told them, but they had simultaneously judged the idea to be worthless, or so I thought. When I asked them to explain themselves, I learned that such ideas had reached them long ago, and that they had advanced such trains of thought far further than the northerners I had thought so exceptional.

The most respected of the village elders, over evening meal, explained to me their philosophy of counting. He made clear that they did not ridicule the notion of an unordered set in and of itself, but rather of a large unordered set. He declared fully that unordered sets could only consist of either one, two, or three items and that indeed the only numbers were one, two, and three.

Immediately after stating this, I inquired if he did believe in the empty set. He shrugged nonchalantly; such matters did not seems to prick at his philosophical conscience much as it did those of us in the Western world. I then asked him to explain his rather grandiose claim.

He came to sit closer to me and asked how many colours were there, essentially. I replied that there were three: red green and blue. He asked me if I thought there to be any fundamentally important relationships amongst those three colours, if I thought any larger or more important than any other, if there was any ordering to them, and I replied that I did not.

He went over to fetch a small box containing coloured chalk, and a perfectly smooth & symmetrical triangular piece of slate, asking me to draw them on the slate.

I picked three pieces of chalk and drew three small circles in a row, red green and blue, forming a line from one of the corners down the middle of the triangle to side opposite.

He asked me why I did put red on the small side and blue on the large side. I said that I had no reason for doing so. He said then, that if I had a slate that was instead a rectangle, that the information I sought to communicate, namely the three colours, might come across more clearly if there were no ways of distinguishing the colour on one side from the colour on the other.

On the triangular slate, if picked up, one could be told to hold the slate so that the line was horizontal, and that the pointed side was facing left, and so be able to talk in some way of a “left” and “right” colour, but one could not be given such commands if there was no way of distinguishing left from right on the slate. I thought that a curious idea, but there was some reasoning to it, so I said yes.

He then asked me why I did put green in the middle. I said that I had no reason, but that one always had to put some colour in the middle if one was drawing three colours in a row. He said that he did not find such arrangements satisfactory. He said, if there is no meaning to the middle, then why should one have a middle at all? I thought about this – clearly, the fact that green was in the middle couldn’t be remedied by changing the shape of the tile.

I asked him then what he proposed be done about it. He took the slate from me, rubbed out the three colours, and put them on the slate again himself, but this time there was one at each edge. Now there was no colour on the inside, and no colour to the left or right of any colour. But then something came to my mind.

“Is not green located counterclockwise from red?” I asked.

He smiled warmly. “Yes,” he said “there is still a problem here. There is no way to talk about three on the side of a slate or parchment”.

“But one can display sets of size two to your satisfaction?” I asked – he nodded.

I was still puzzled. “So why, then, do you still believe that three is a number?”

He grinned at me; “Thankfully, we do not live on the sides of slates or scrolls”. He turned around the slate, and drew the three colours by each of the edges, with the colours back to back matching.

“Now,” he said, pointing to the other side, “green is located clockwise from red on this other side – now no sense of chirality can be used to evince any patterns from this arrangement, nor indeed is there any way at all to”.

“And”, he added, “one cannot produce any patterns to display any larger sets where there are no interrelations. This is why I say that the only numbers are one, two, and three: any larger collection simply must, by the geometry of this universe, have some structure to it’s contents rendering it undescribable by a mere number. Of course, not every collection of size three has no internal structure, but it is a physical impossibility that there be any collection of size greater than three with no internal structure”.

Then I responded “just because one cannot represent such things geometrically, that does not mean that they do not exist”.

He laughed at what he perceived to be the dim-wittedness of my suggestion.

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Now! Let's see if you can't learn something today.

A stylish varation on a classical torment: playing favourites.

(Also ideal for teachers, parents, or anyone whose approval carries weight).

Playing favourites — it’s one of the oldest ways of tormenting those under your command, and one of the best. Deserved or undeserved, so long as those in your employ are honest workers who take pride in their job, it’s sure to breed malaise in the work-environment as well as any other method of wickedness.

But it can get a little boring, you know? Year in year out, the same sausages on the plate; sometimes you just want to spice things up a little! So, here’s an elaboration of the classic-to-beat-all-classics, perfect for the winter 06/07 season:

Say you are managing a project involving two workers, both kind honestly people. Pick on one of them, the weaker of the two. Don’t be directly destructive in their criticism, but take every opportunity you can to take over or suggest obvious ways of doing even the simplest of tasks, as if you do not trust them in any way; be overwhelming in your control and never utter a positive word their way. Pay not much attention to the other worker.

Now, eventually, and here’s what you’re pushing for, the other worker will say something to you in a very direct manor saying that the other is capable of doing work without your constant interference in the presence of the other party (if they say it to you in private, simply ignore it).

This is your cue: from that moment, do nothing but praise the fellow you initially harassed so much; laud his diligence, eulogize his adroitness – whatever you can. And don’t for a moment make mention of his co-worker, who did stand up for him.

The torments in this strategy are manifold. For one, the worker you plagued so much at the start will not in any way believe your criticism. More than this, if he comes to you privately asking that the other have his efforts acknowledged, you should ignore him; he will not say it in front of his co-worker for implicit in such a strategy would be the assuming of a position of superiority, something which he will not want to do. But he will consider doing so, and that will be an extra little torment.

The other fellow, well, he is the victim of the torment of playing favourites, but the additional fact that it seems to be punishment for backing up a coworker will damage his spirit in a far more general and long-lasting way.

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These may or may not be communications of grevious crimes committed against yours truly.

Two torments on gratuities.

Given that I’ve cleared my conscience, I feel that I can offer some advice on how to torment people you are going to dinner with when it comes to the paying of gratuities.

Scenario the First:
It’s been a really good dinner. Both of you are paying for yourselves. The other person leaves a hefty tip. What you do is not only to not give any gratuity, but indeed to pay under what you actually should, so that their generous gratuity is completely nullified or, even better, reduced it to an insulting amount. If they do not notice this, let them know as soon as you have left the restaurant.

Scenario the Second:
It’s been a really good dinner. Both of you are paying for yourselves. The other person leaves a hefty tip. You say “Oh, that’s far too much of a tip”, take most of the tip-money from the tray, and put it back into your wallet.