The Left Hand of the Electron - Arvind Gupta

223 Pages·2007·0.91 MB·English

by  Isaac Asimov

CONTENTS
INTRODUCTION
A—The Problem of Left and Right
1—ODDS AND EVENS
2—THE LEFT HAND OF THE ELECTRON
3—SEEING DOUBLE
4—THE 3-D MOLECULE
5—THE ASYMMETRY OF LD7E
B—The Problem of Oceans
6—THE THALASSOGENS
7—HOT WATER
8—COLD WATER
C—The Problem of Numbers and Lines
9—PRIME QUALITY
10—EUCLID'S FIFTH
11—THE PLANE TRUTH
D—The Problem of the Platypus
12—HOLES IN THE HEAD
Vlll CONTENTS
E—The Problem of History
13—THE EUREKA PHENOMENON 159
14—POMPEY AND CIRCUMSTANCE 172
15—BILL AND I 186
F—The Problem of Population
16—STOP! 201
17 BUT HOW? 214

THE LEFT HAND OF THE ELECTRON
.
A—The Problem of Left and Right
1 ODDS AND EVENS
I have just gone through a rather unsettling experience. Ordinarily
it is not very difficult to think up a topic for these chapters.
Some interesting point will occur to me, which will quickly lead
my mind to a particular line of development, beginning in one
place and ending in another. Then, I get started.
Today, however, having determined to deal with asymmetry
(in more than one chapter, very likely) and to end with life and
antilife, I found that two possible starting points occurred to me.
Ordinarily, when this happens, one starting point seems so much
superior to me that I choose it over the other with a minimum of
hesitation.
This time, however, the question was whether to start with
even numbers or with double refraction, and the arguments raging
within my head for each case were so equally balanced that I
couldn't make up my mind. For two hours I sat at my desk, pon
dering first one and then the other and growing steadily un-
happier.
Indeed, I became uncomfortably aware of the resemblance of
my case to that of "Buridan's ass."
The reference, here, is to a fourteenth-century French philoso
pher, Jean Buridan, who was supposed to have stated the follow
ing: "If a hungry ass were placed exactly between two haystacks
in every respect equal, it would starve to death, because there
would be no motive why it should go to one rather than to the
other."
Actually, of course, there's a fallacy here, since the statement
does not recognize the existence of the random factor. The ass,
no logician, is bound to turn his head randomly so that one hay
stack comes into better view, shuffle his feet randomly so that one
4 THE PROBLEM OF LEFT AND RIGHT
haystack comes to be closer; and he would end at the haystack
better seen or more closely approached.
Which haystack that would be, one could not tell in advance.
If one had a thousand asses placed exactly between a thousand
sets of haystack pairs, one could confidently expect that about
half would turn to the right and half to the left. The individual
ass, however, would remain unpredictable.
In the same way, it is impossible to predict whether an honest
coin, honestly thrown, will come down heads or tails in any one
particular case, but we can confidently predict that a very large
number of coins tossed simultaneously (or one coin tossed a very
large number of times) will show heads just about half the time
and tails the other half.
And so it happens that although the chance of the fall of heads
or tails is exactly even, just fifty-fifty, you can nevertheless call
upon the aid of randomness to help you make a decision by tossing
one coin once.
At this point, I snapped out of my reverie and did what a lesser
mind would have done two hours before. I tossed a coin.
Shall we start with even numbers, Gentle Readers?
I suspect that some prehistoric philosopher must have decided
that there were two kinds of numbers: peaceful ones and warlike
ones. The peaceful numbers were those of the type 2, 4, 6, 8, while
the numbers in between were warlike.
If there were 8 stone axes and two individuals possessing equal
claim, it would be easy to hand 4 to each and make peace. If there
were 7, however, you would have to give 3 to each and then either
toss away the 1 remaining (a clear loss of a valuable object) or
let the two disputants fight over it.
The fact that the original property that marked out the signifi
cance of what we now call even and odd numbers was something
like this is indicated by the very names we give them.
The word "even" means fundamentally, "flat, smooth, without
unusual depressions or elevations." We use the word in this sense
ODDS AND EVENS 5
when we say that a person says something "in an even tone of
voice." An even number of identical coins, for instance, can be
divided into two piles of exactly the same height. The two piles
are even in height and hence the number is called even. The even
number is the one with the property of "equal shares."
"Odd," on the other hand, is from an old Norse word meaning
"point" or "tip." If an odd number of coins is divided into two
piles as nearly equal as possible, one pile is higher by one coin and
therefore rears a point or tip into the air, as compared with the
other. The odd number possesses the property of "unequal
shares," and it is no accident that the expression "odds" in betting
implies the wagering of unequal amounts of money by the two
participants.
Since even numbers possess the property of equal shares, they
were said to have "parity," from a Latin word meaning "equal."
Originally, this word applied (as logic demanded) to even num
bers only, but mathematicians found it convenient to say that if
two numbers were both even or both odd, they were, in each case
"of the same parity." An even number and an odd number,
grouped together, were "of different parity."
To see the convenience of this convention, consider the fol
lowing:
If two even numbers are added, the sum is invariably even.
(This can be expressed mathematically by saying that two even
numbers can be expressed as zm and zn where m and n are whole
numbers and that the sum, zm + zn, is still clearly divisible by
two. However, we are friends, you and I, and I'm sure we can dis
pense with mathematical reasoning and that I will find you willing
to accept my word of honor as a gentleman in such matters. Be
sides, you are welcome to search for two even numbers whose
sum isn't even.)
If two odd numbers are added, the sum is also invariably even.
If an odd number and an even number are added, however, the
sum is invariably odd.