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A Shout From The Attic: Impossible Dimensions

..the sons of squaws on adjacent hides being equal to the sons of the squaw on the hippopotamus hide...

Continuing his life story, Ronnie Bray recalls a geometrical joke and a puzzling, inexplicable, shrug-inducing mathematical singularity.

To read more of Ronnie's experiences please lick on A Shout From The Attic in the menu on this page. Read also his sparkling Letter From America columns.

I know you wonít believe what I am going to tell you. I would not have believed it myself if I had not seen it with my own eyes, and measured it with my own ruler, but I did see it, did measure it, drew Mr Brummittís attention to it. He knew I was right, measured it for himself with my ruler, and thatís when he shrugged his shoulders, grunted, and walked away. What more proof could you want?

We were doing geometry. They told us that it would come in handy when we went to work but I am still waiting. It has been useful for crossword puzzles in a limited way, and came in handy for one joke about the sons of squaws on adjacent hides being equal to the sons of the squaw on the hippopotamus hide, but not for much else because I didnít go into science and, being innumerate, scientific fields were closed.

We were told that the hypotenuse of a triangle was linearly inferior to the sum of the two other sides. That is not how they actually said it, but that is what it meant. For once, something I was told made sense. In the class period in question, we had to make a triangle with standard angles of 90, 60, and 30 degrees. Having done that, we had to measure the sides to calculate the relative lengths of the sides and draw some kind of conclusion that could be an arithmetical rule that would apply to all such figures.

The determination of the angles and the construction of the lines were done with little difficulty, thanks to the standard issue school ruler and protractor. But the mensuration proved problematic. In thinking about it afterwards, I have remarked at the similarity between my triangle and that other singularity, the duck-billed platypus. The duck-billed platypus is a peculiarity, because it is a mammal that lays eggs, and mammals are viviparous.

Ornithorhynchus Anatinus, as it is known to its intimati, not only lays eggs, but it also suckles its young, lives in burrows, finds food in the rivers using electrical impulses from its leather snout, and the male of the species has a poisonous spur on his hind leg. It is, therefore, decidedly extraordinary. None of which, however, has anything to do with my triangle, but I delay getting to it until you have been conditioned to accept what is considered impossible and improbable.

Other singularities include the little known fact that the British, despite the best efforts of Edwina Currie, eat enough eggs every day, twenty-six million, give or take a couple of dozen, to reach from the earth to the moon, and the almost occult verity that if you yelled at the top of your voice continuously for eight years, seven months and six days, you would have produced enough sound energy to heat one beaker of hot chocolate, or that ants can lift fifty times their own weight, pull thirty times their own weight, and always fall over on their right sides when intoxicated?

What? Ah yes, the triangle. Well, and I swear to this, I measured the hypotenuse at one and a half inches, then measured the other sides and added their sums. They added up to one and a half inches. I know that should have been two straight lines of equal length, but this was a right-angled triangle and there was nothing wrong with my measurements or my adding up.

Attracting Mr Brummittís attention, I explained my predicament, expressing to him that I knew it was impossible, but that the evidence was overwhelming. In that charming way pedagogues have, he smiled, took the ruler from my hand, and measured all sides for himself. His smile faded as he did the arithmetic, checked his measurements again, did his sums again, and obviously came to the same conclusion again. He handed me the ruler, shrugged his shoulders, grunted, and walked back to the front of the room, never to mention the oddity again.

Thus it was that the signal peculiarity when the rules of the geometric universe were suspended on my desk were put in that place where witnessed impossibilities are placed, never to be returned to, lest the insistence that the impossible happened becomes a cause for consigning the preternaturally afflicted to the house of shelter, and I have kept quiet about it until now, because I have reached an age where eccentricities are winked at by those who have not shared in the events that produced them.

No, I am not locked in a soft-walled cell, nor isolated from the general population by order of a court, nor am I on mind-altering medications for a condition that makes me think I know unknowable things, or have imagined an impossibility. I walk abroad as free as the wind, and those who know me well, can attest to my sanity, and probably will for a small fee.

But I do remember that time in form three of Spring Grove School when the immutable laws of the universe were suspended long enough for me and my teacher to witness the result when the impossible happened before my very eyes, and I wonder at it, and wonder at what must have gone through Charlie Brummittís mind as the shared a secret of impossible dimensions long held invisible from ordinary mortals.


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