"Oh, thank God" was the thought in my head as I turned the last page of the 17th story in this section to find that there were no more. A few of the stories amused or interested me, but I found none of them exciting. In addition, almost all of them (or so it seemed) were about bleeding topology. It got to the stage where I actually had to put the book down and do deep breathing when I saw any of the words "topology", "fourth dimension", "Moebius strip" or "Klein bottle" on the first page of a new story.
All right, then. Let's look at the ones that are not about topology. The Devil and Simon Flagg by Arthur Porges was one which amused me. A professor of mathematics strikes a deal with the Devil over an impossible maths problem and (inveitably) wins. The plot was a little predictable, but it's a dear little story with no serious faults.
Inflexible Logic by Russell Maloney was not a great story by any means. It dealt with the old question of six chimpanzees on typewriters creating all the literary works of the English language. In this stories the chimpanzees actually wrote all the books in question, but not in the random manner dictated by probabilites - instead they wrote down all the works as if they'd known them by heart all their lives. Nothing actually happened (with the small exception of an insane mathematician murdering all the chimpanzees and their keeper).
This topic is treated much better in Kurd Lasswitz's The Universal Library. In this story the books are created, not in a random fashion, but by an orderly mechanised process. There is also some discussion of just how many books would be created, the problems that would result from the multitudes of half-nonsensical manuscripts that would result, and what I consider to be the biggest fallacy in the whole chimpanzee thing: the question of length of manuscript. I don't believe that two books of exactly the same number of characters have ever been written in the English language. Even if this is not the case, the wildly different lengths of all the manuscripts render the puzzle ridiculous. Probabilities can only be calculated and/or used practically when such crucial details are held constant.
I'm afraid that Superiority is the first Arthur C. Clarke story that I have found lacking. This one is severely lacking. The basic point of the story seems to be that the losing side of an interstellar war claim to have been defeated by their enemies' "inferior science". In fact, it is apparent in the description of the war that their defeat was due to their utterly screwed up strategiess. They withdrew their old weaponry and concentrated all their resources on building the new weapons that were being developed. This gave the enemy time to gather forces and launch a new attack, and did not allow for unforseen technical hitches in the new weapons. They were left with no backup plan at all. This is a spectacularly stupid way to fight a war, and it is not at all the fault of the enemies' inferior technology that they lost. Rather, it is the fault of the losing side's ridiculous tactical errors.
However, I was amused by the mention of one machine using a million vacuum tubes. Of course, this story was written just three years after the invention of the transistor, so the little devices would not yet have been useful or prevalent. It's highly possible that Clarke had not even heard of them, and if he had, he must have considered them too unreliable (which they were back then) to be the switches, amplifiers, rectifiers, etc, of the future.
The Mathematical Voodoo by H. Nearing, Jr. is another sweet little story with no obvious faults. A mathematical idiot is made a genius by his professor teaching maths to a voodoo doll in the student's image. I like the rather different angle, and the twist that comes at the end regarding the fate of the doll, and thus of the student.
Frederic Brown's Expedition actually made me smile. It briefly tells the story of the so-called "Mighty" Captain Maxon, who seems to have impregnated the 29 women on his Martian expedition in two days. The stories brevity is its strength, but it would have done much better as a small piece of a larger story - like Arthur C. Clarke's story about the imagined first moon landing. This story consited of many lovely smaller stories.
God and the Machine by Nigel Balchin is the sweetest so far of the sweet little stories. A mean and miserable physicist, unable to understand why his wife has left him, builds a machine that can play draughts. The machine is his pride and joy, but is confused when its opponent makes foolish and unpredictable moves, and finally cheats rather than losing. The creator is horrorfied, but his friend helps him to see the funny side of the incident. What I like is the change in the physicist when he gets so excited over his machine. I compare my own excitement over my first (rather pathetic) computer program, and can entirely understand this man's delight. However, I must warn those after Balchin's heart not to knock the physicists. Physics is the future and the purest of the three sciences (mathematics, of course, being the only truly pure science), and those who disagree are apt to find themselves fed into machines designed to create infinitely dense matter. I should add that most physicists tend to be quite impatient and unreasonable people, although they cannot rival IT personnel, especially technicians, in their lack of people skills.
Back to the book. The mathematics in The Tachypomp, by Edward Page Mitchell, does not impress me. I'm unsure whether the idea would have been novel in 1873. (Essentially, the idea is to mount a number of trains on top of each other with the longest on the bottom and the shortest on the top. The relative velocities will result in the shortest train achieving a ridiculously high speed relative to the ground.) But I do like the protagonist's eccentric tutor. With a skeletal chair for frightening his creditors into submission and a tunnel to the center of the earth for disposing of them if they do not submit, this wonderful Frenchman is my ideal nutty genius. I would sit up all night drinking "aqua fortis" with a man like this if I thought it would give me the remotest glimpse of the depths of him intellect.
And finally, John Jones's Dollar by Harry Stephen Keeler. This is a pretty good first draft. However, it's disordered, there are too many gratuitous futuristic details (I suppose that was what they public liked in 1927) and the point of the story is not clear. When I did figure out what the point was, it appealed strongly to the socialist in me. (I was once idealistic also.) In 1921 John Jones deposited a dollar in a bank to the credit of his fortieth descendent. This descendent would have been born in 2921, to inherit the largest store of wealth in the solar system. In fact, the fund had become so enormous that John Jones's 40th descendent would have inherited the entire solar system, because the cash had been invested in literally every enterprise in existence. Unfortunately, John Jones's 39th descendent died childless, ending the line of John Joneses, so the Government took over the fund. In this way John Jones, an idealistic socialist, caused absolute socialism without even thinking of it.
Of course something has been overlooked here, and that is the spreading effect. It is quite possible, after 40 generations, that John Jones's descendents would have ended up marrying each other and there would have been many possibilities for the 40th descendent - even in different centuries, if the family tree became tangled enough. However, we must assume that the Jones line somehow died out, leaving only this one 39th descendent.
Sorry, it's not over yet. I must comment on a few of the topological ones. The best one (and probably my favourite from this section) is A Subway Named Moebius by A. J. Deutsch. I like it because it uses topology to enrich the story, rather than merely illustrating the weird and all-too-familiar possiblities associated with topological problems. A subway system turns out to have "infinite connectivity", meaning that trains can jump over into non-spatial dimensions with no warning and effectively disappear. When this first happens, the day after the subway opens, it seems impossible to get the train back. It reappears several months later, only to be suceeded by another mysterious disappearence. Worst of all, the city's only topologist appears to be continually on board the disappeared trains, so he can't be consulted. Oh dear, how lovely.
I like the other topological story for exactly the same reason. It's A. Botss and the Moebius Strip by William Hazlett Upson. In this story, Botts wants to steal another man's tractor. He achieves this by distracting the tractor's owner, who is painting a pump belt red to reduce the risk of injury. The belt-painter says he will paint only the outside of the belt so the paint won't cause it to slip. Unbeknown to him, Botts has twisted one end of the belt, turning it into a Moebius strip (a figure that has only one side and one edge), so he ends up painting "both" sides, then attempting to remove the paint from "both" sides. For more on Moebius strips see Math Forum.