WILD SURMISE

August 1990 #21

AN ALMOST ANONYMOUS INFORMAL NOTE

HOW TO BE A PRODIGY AND OTHER TRICKS

From time to time, one hears of the child who was able to . -. play a bit of music after hearing it only once, do multiple digit multiplications in his head, give the day of the week for any calendar day for a thousand years and so forth. Sadly, for many such children it is their only trick, and they may be lacking in some of the normal average social abilities.

Perhaps in your inner soul you have reflected, "Such a child, is this child happy? Vrhat can be done to make him happy." Perhaps you have thought, "A waste of talent. Could I, with my otherwise magnificent intelligence and social grace, do that, I should be truly happy." Or perhaps, risigh, with my stunted social development, if I could do that, maybe people would give me a break."

Yearn no more. I shall now teach you how to tell the day of the week from the date, followed by enough other tricks to drive your most earnest friends to tears.

The Mental Calendar:

The week has seven days. This number is fixed by long custom, by religious belief and by the fact that people can't keep more than seven things in their heads at one time. The calendar we use today has been updated and altered any number of times.

The problem with calendars is that a lunar month is about twenty nine or thirty days lonq. That does not divide equally into a number of weeks. The solar year is close to being 365.25 days long. That does not divide into an even number of days, weeks or lunar months.

Sowe make some approximations. The Western calendar, named after a Pope Gregory, approximates the solar cycle. The advantage of the solar based calendar is that in the northern hemisphere the seasons generally follow the sun. When the sun is high in the sky, things are warmer: when the sun is low, things are cooler. The weather is not precise so an error of a week or so wouldn't make much difference. But a six month error would put spring in October and winter in August.

It was that sort of problem that people were dealing with when they set up the Calendar we now use. They had to skip a few days so that New Years Day would be closer to the time when the sun rose least high in the sky.

Lots of people didn't like it. It suddenly made them all a few days older than they would have been under the Julian calendar (the one set up by the flornans that had drifted out of synchrony with the sun.) In Britain, people rioted in the streets demanding their time back.

The Romans had a lunar calender that they were frequently at pains to reform since it was not exactly a solar year long. The Muslims still have a strictly lunar calendar that they scorn to reform. Depending on the century and the year, their holidays may fall in any season at all. Seasons are a bit less dramatic in the part of the world where those people tend to live.

We have not even ventured into more exotic calendars, have not dealt with half the world or a small fraction of its cultural diversity. So you see, it would take a brave person indeed to try to interrelate all the time-keeping systems there are. But for your trick, you need only relate the day of the week to the day of the months and year, Gregorian time.

Say you want to know what day of the week you were born on. You know the year and the date.

First you must find a place to start. 1989 will do. January the first fell on a Sunday that year. Then you will need to do some memorizing. (Yes, that's a little work. But you will only have to do it once in your whole life. Unless the big boys throw another calendar reform at us.) Here goes:

Sunday Wednesday Wednesday

Saturday Monday Thursday

Saturday Tuesday Friday

Sunday Wednesday Friday

You already know the months:

January February March

April May June

July August September

October November December

Look at the days you are going to memorize. Notice that they have a kind of a pattern. The first month of each quarter starts on a Saturday or Sunday. The second month on a Monday, Tuesday or Wednesday and the third month on a Wednesday, Thursday or Friday. Now go ahead and memorize them.

So far we have learned the first day of each month in 1989. It's a start, but not quite every day for a thousand years. Next, you need to look at the year for which you want a date. Say a year in the future: 2035. what you need to know is that, excluding leap years, the calendar marches right around the week. In. 1990, New Years day was Monday. In 1991, Tuesday; in 1992, Wednesday. But you do not need to count up to 2037 by sevens. Just subtract 1989 from 2035. Simple enough, just add 11 (the number of years to 2000) to 35 (the number after 2000) and get 46.

That's a big awkward number. You won't need to remember it for long, though. Now in the Gregorian calendar, every fourth year is a leap year. Instead of New Years day marching to the next day of the calendar, it jumps over one. It does this by adding a day in February, so February in 199.2 has 29 days instead of 28. So it is the NEXT year that starts one day later in the week.

How many leap years between 1989 and 2937? 46 divided by four is 11. (This tine you can drop the remainder.) So that is 46 years during which the calendar stepped once plus 11 during which the calendar leapt an extra day or 57 steps.

At this time, you must pause and think. (Have you memorized those days yet?) You must think: What are the exceptions? They are these: If leap year falls on the century, it does not leap, so you must subtract one year for each century mark crossed. That gives you 56. But if the year is a number that can be divided evenly by 400 years, it does leap even though it landed on a century, so you add one. (The year 2000 divides by 400, but not 1700 or 1000.) That gives you 57 again.

Now for the part that is fun. You divide 57 or whatever the number of steps is by seven and keep only the remainder. The easy way to do it is to glance through the number and drop out any part that is a multiple of seven. For instance, 57 and 50 will have the same remainder, so you might as well just divide 50 by seven. But then 49 is easily divisible by 7, so you might just as well subtract 49, leaving 1. 1 is less than seven so it is your remainder. Sunday plus 1 is Monday, so New Years Day on 2037 will be a Monday.

Once we have found that '1'. we own the year 2037. what day will the fourth of July be? July started on a Saturday in 1989; Saturday plus one is Sunday. July that year will start on a Sunday. The fourth? Count it on your fingers: Monday Tuesday Wednesday. Wednesday it shall be.

Suppose it is not the fourth but the fourteenth you need. Subtract seven and you are left with seven days. Get those fingers in action. It will be a Saturday.

If the year you are dealing with is a leap year. you make one more correction: Add one more day if the date you are looking at falls after February 29.

Notice that you don't actually have to know how many days there are in the month. That has already been taken care of by those days you memorized. (Don't you think it's time you did it?) The system takes a little practice, but it should be good for a lifetime, unless or course we get that calendar reform.

Lets try it going into the past. what day was Halloween in 1924?

Well 1924 from 1989 is 75. That is 75 steps backwards plus 18 leap years backwards. Don't try to add 75 and 18. The 70 doesn't make any difference. 5 and 18 make 23. Subtract 21 (7X3) and you get two days backward. Halloween is October 31. That is after February 29 so you add one day. So you have only one day to go backward. October 1989 began on Sunday, so October 1924 began on a Saturday. Subtract four weeks (28 days) from the 31'st and you have 5 days. count forward three. Sunday, Monday, Tuesday. There you are. Tuesday.

If you are going to get back before 1923, you will need to know something more. You will need to know whether you are dealing with the Julian or Gregorian calendar. The difference is that while the Julian calendar has years and months of the same length and a leap year every fourth year, it also has a leap year every century mark; the Gregorian calendar we use, you remember, has a leap year on the century only one out of every four centuries.

The Julian calendar was replaced by the Gregorian in places like France in 1582 but not in Greece until 1923. You could hardly be expected to carry in mind the date every country changed, so you will have to consult an encyclopedia. Britain changed in 1752. The days in the Gregorian calendar do not correspond with the Julian. The amount of discrepancy changes one day a century for three centuries out of four. In 1752, for instance, it was 11 days.

Rather than remember a whole table of conversions, the best thing to do is just go back to the Julian calendar. From 1989 back to 1752 is 237 years, including 59 leap years, or 296 days of shift. Since we are going by the Gregorian calendar, the two years 1800 and 1900 are not leap years, so it is only 294 days shift. That is a number equally divisible by 7. So, oh best beloved, the year 1752 began on Sunday by Gregorian style, just like 1989 did. September 14, 1752 then was a Thursday, just like it was in 1989.

September 2, 1752 was a Wednesday by Julian style reckoning. That was the day they changed in Britain, between that Wednesday and that Thursday. So September 1752 began on a Thesday. When I count backwards, I find January 1, 1752, to be a Wednesday. If you really care, count it out yourself. Don't forget that 1752 was a leap year.

If 1752 began on a Wednesday, 1751 began on a Tuesday. 1750 began on Monday. And 1749 began on Sunday, just like 1989. So did 1800, which might be easier to remember but came after the English speaking world shifted to the Gregorian calendar. So remember 1402 or 1301 or 1066 - that was the year if the Norman conquest.

Start with any of those years and proceed just as you would from 1989 only remembering that in the Julian calendar, all century years are leap years just like any other fourth year.

I should like to remind you that these numbers have not been independently checked. Before trusting anything important to such a calculation, recheck all the numbers yourself. of course if you find me in error, nasty letters to the editor are welcome as usual.

By the way, don't be tempted to go back before the 8th century. Before the Venerable Bede of Jarrow not many people numbered the years anyway. Weeks were introduced by the Emperor Constantine in the 4th century. They didn't have the kinks shaken out of the Julian calendar itself before AD 4 under Augustus Caesar.

I do not suggest trying to calculate Easter. It is an attempt to reconcile the seven day week, the lunar calendar and the solar calendar all at once. They could just decide it was the second Sunday in April, but apparently somebody wants the moon to be right for sunrise services.

One last point: if a month starts on Sunday, the thirteenth will fall on Friday. Calendar reforms tend to start a lot of months on Sunday, so they produce a lot of Friday-the-Thirteenth's.

You know something? I don't think I'm ever going to memorize those days either.

Playing with knots:

Four of my favorite knots have names that sound sort of like London addresses: Fast Square, Thief Knot, Folded Arms Square and Knot-on-pen.

Get yourself a piece of string a couple of feet long. If you want to use a boot lace, fine, but the tip may get in your way.

The fast square knot is a highly specialized competition knot, useful only in competitions in which nobody has got around to making it illegal. First, you know the square knot.

The knot is symmetrical, handsome. It looks good. It is good. You can trust you life to a square knot. The granny knot looks similar.

But as you can tell the granny knot is not symmetrical. And the granny knot will slip. Try it with your bit of string if you don't believe me. It slips. So why should grannies use it? well, it turns out to be a very good knot for doing up packages. It you want to tie a string around a package, and you want that string to be tight, a square knot won't do it. The first throw you make in the square won't hold anything. The second throw makes a square knot that will not Slip so you cannot pull it tight down on the package.

With the granny knot it will slip, so you can pull the package tight Then you can put another throw on top of it and it will hold.

Yes, you can trust you life to a square knot. Sometimes.

M tells a story about a hospital that shall go unnamed where they were treating young people for drug addiction. The mood of that era was a tolerant one, and the treatment was rather enjoyable to those for whom it was designed.

Well one subject was lounging around one day and decided that the one thing he needed to complete his day lay, not in the hospital, but in his dresser drawer at home. It was, of course, the very thing he was being treated so he could do without. He could not walk out the front door as that would constitute ending his quite pleasant treatment. So he elected to lower himself from the, alas, fourth story window.

He knotted some sheets together, and out went he.

They scraped him off the ground and carried him in to have his broken bones casted. They decided that he was suicidal -treatment not permissive enouqh or something. But he insisted that it was just a mistake and that climbing down knotted sheets was a perfectly realistic way of getting out of the building.

I even used square knots," he insisted.

I trust no Wild Surmise reader will ever use a square knot for this purpose. A square knot can be tripped.

And it will trip if you try to slide over it. Instead, walk down the stairs. Or if you must use the sheet ladder, use something like a sheet bend.

Or a fisherman's knot.

You can't trust them either, but either would be better than a square.

The fast square is based on a tripped square. The competition in the old days went like this: a patrol of boy scouts stood behind a line, each scout holding a three foot piece of clothesline. At some distance was pole or small tree. The first scout ran up and tied a clove hitch around the tree. The second scout ran up with his piece of line and tied it to the first piece with a sheet bend. The third scout tied his piece to the second with a fisherman's knot. The next tied a square knot. The next put a sheepshank in the line. The last scout tied a bowline around his waist and leaned back, hoping all the knots would hold. The race was against the clock.

Now you are square man on the knot team. You are waiting for your turn to run. You already have the piece of line in your hand. what you do is to twist the line so it looks like this;

You hold the prepared knot at "A" with your left hand. You reach through the loops with your right band at "B." When your turn comes, you run up to the line already tied to the tree. You grab that line with your right hand and pull it back through the loops. still holding tension with your right hand, you let your left hand slip down to "C" and then pull the knot snug:

Now you bring your right hand over to "A" and slide it up, untripping the square knot. Try it. It is very fast.

It is also a little tricky. Suppose you hold the prepared loops backward:

Now when you complete your tie, you have a thief knot. It looks a lot like a square knot:

But the thief knot will slip far more easily than a granny knot. Why they call it a thief knot, I would not venture to say, but if you inadvertently tie a thief knot in competition, you will probably drop you buddy on his butt.

The folded arms square knot is based up the observation that when you fold your arms, you are tying them in a simple overhand knot -a half a square knot. If you take one end of a piece of line in each hand and then fold your arms, you have tied a knot in the line, although your arms remain tangled up in the knot.

If you fold your arms first thus: left hand over right armpit, right arm crossed in front of left arm, right hand tucked inside left elbow; and if you then take a piece of line in each hand and then unfold your arm, you have an overhand knot in the line. If you fold your arms again, starting right hand in front of left armpit, you will end up with the line tied in a square knot.

That is the folded arms square knot. It is sort of a solution without a riddle. what it managed to do is to tie a square knot while taking hold of each line only once and with one hand. However, it is easier to do the same thing just by looping the line around one wrist with the other hand; at least that works if you are tying both ends of the same line together.

The knot on the pen evolved one day while someone who will go nameless was fidgeting with a tethered pen. You have seen them, of course, a pen tied to a desk by a length of chain like they use to keep bathtub plugs from getting lost.

The device invites one to tie a knot in the pen. But before we do, let us take a square knot apart.

As you see it comes apart to form to overhand knots.

Now let us tie a knot on the pen.

The question is, will there be a knot on the chain when you pull the pen out. Obviously, if you pull. the pen out to the right, there will be a knot, but if you pull the pen out to the left, there will not be.

Now put two knots on the pen.

Again if you pull the pen out to the left there will be no knot. Pull the pen out to the right, and if you choose there will be two knots:

But of course a square knot can be taken apart into two knots, so the same two can be put together into a square knot. With a little practice, you can do it as you take the knots off the pen.

Now how have your choice. When you take the pen out, you can wind up with no knot, two overhand knots or a square knot.

Spotting the green flash:

One of the pleasures of living on the west coast of Florida is to view sunsets over the Gulf of Mexico. The most splendid sunsets occur when there are lots of high cumulonimbus clouds. A severe and prolonged drought his reduced the cloud formations in recent years, but the clear air has permitted another kind of sunset observation. These days, you can see the "green flash."

As light enters the atmosphere of the earth from the near vacuum of space, the light is slowed down. Just why that happens is a big of a mystery to me, but assume the mechanism is something like this. Light, being electromagnetic radiation, encounters the electrons in the outer shell of a molecule of atmospheric gas. The electromagnetic force of the light wave distorts the position of the electrons for an instant. The electrons then snap back into their original position and the light wave proceeds on its way without having lost any energy but after an infinitesimal delay. Why this interaction should not make the light change its direction, I do not know.

X-ray wave length radiation and ultra-violet light are energetic enough to break electrons loose, so they do lose energy and tend to get absorbed by the atmosphere. The blue light actually does get scattered as it passes through the air. That is why the sky is blue in the day time.

The rest of the light, the red, orange, yellow and green, continue on their way, slowed down, but not grossly scattered. The red, orange and yellow look a lot alike, so think of sunlight coming through the atmosphere as being of two colors, red and green, with a lot more red than green.

As the red light and green light are slowed down, the green light is slowed down more. It is more energetic than the red. Imagine a heavy person and a light person running across a lot of mattresses. The heavy person is slowed down more.

when light hits the atmosphere, it is turned as well as slowed down. Imagine a car running off the road. The left wheel, say, runs off into the grass of the median. That wheel slows down. The car turns away from the road and onto the median. Similarly, as the light hits the air at an angle, it turns to descend more steeply, more nearly vertical.

As the green light is slowed more by the atmosphere, so it is turned more as it enters the atmosphere.

If the sun is straight overhead, light enters the air without turning, just as the car would not turn particularly if it ran into the median squarely. But when the sun is close to the horizon, the amount of bending of the light is substantial. The sun looks higher than it actually is.

More strictly, the direction you see the sun is is not where the sun would appear to be if suddenly the earth's atmosphere were taken away. Although the sun may be optically above the horizon, the geometrical position of the sun may be below the horizon. Since the green light is bent more, the green light from the sun will seem to be higher than the red light. In other words, as the sun sets, there are two partially overlapping suns: a big bright red one and a smaller dimmer green one just above it.

One reason you don't see the green sun is that it is so much dimmer. For another thing, the blue light scattered from the sun acts as a blue mask behind which the green sun is hidden. No imaging system, not even the fabulously refined human eye, can perceive the green sun while the red sun is above the horizon or even when half of the red disc is still visible.

But just as the red sun sets, just as the sky become abruptly darker and the forward scattered blue light fades away, ah then, then, if the observer is alert, then if the horizon is bare, then if the air is crystal clear, just as a sliver of the red sun is melting away, there is an instant of green light.

Only you still probably can't see it. You've watched the sun set any number of times, of course. The red sun sets, and it gets dark. Period. Ever since people started eating food, picnickers have watched the sun set without seeing~the sun turn green.

You see, it's a poor idea to look at the sun. The sun will blind you very quickly and quite permanently if you look up at it at noon. The lens focuses all the energy of the sunlight onto the incredibly sensitive cells of the fovea, and those cells are destroyed. The iris, the colored part of the eye, will give you some protection, but not enough to let you look straight at the sun.

Over a longer period of time, the ultra violet light of the sun will do the same thing, destroy those cells. The lens of the eye, however, is a pretty good ultra-violet shield. with normal use, the fovea will give satisfactory performance for a lifetime.

But the lens itself can be ruined by the ultra violet light. The lens becomes cloudy, a state called a "cataract.~' Modern surgery is able to replace the lens with a serviceable substitute. But you would rather not ruin the original one. And in a reasonably long lifetime with a fair amount of time outdoors, the sun's ultraviolet will produce cataracts.

So any avoidable exposure to ultraviolet is bad for the eye. Cheap sun glasses can absorb visible light, making they eye more comfortable, but let the ultraviolet through. with the light dimmer, the iris contacts, dilating the pupil and letting more ultra violet light get into the eye.

At sundown, people who know better than to gaze on the noonday sun will be seen reclining on green hillsides gazing contentedly at that same sun for many minutes as it sets. It does make you wonder about people. Of course, the sunlight coming in through the atmosphere is very strongly filtered. So it does not hurt the eyes. nut no one has yet persuaded me that the effect is much different from cheap sun~glasses.

Now you know why people don't generally see the green flash. They have been out there blinding themselves. On a very clear day with a very sharp horizon, when viewing conditions are best, they are blinder than ever. You wonder how they think they are going to be able to see well enough to drive home.

But if you promise you will only do this once and never again abuse your eyes, I'll tell you how to see it. High down to the drug store and buy yourself a good pair of expensive sunglasses: something that says "Guaranteed 100% Uv absorbing." Wear them any time you are out in the sun, driving or sitting by a big sunny window, or when you are at one of those dives where they put on UV lights that make people's clothes light up. If the glasses start to get worn out, replace them.

Also put on sun screen, but that is a different story.

Find yourself a beach or a desert with an unobstructed horizon and go there at sundown on a clear day. Keep the glasses on. Don't even look toward the sun until it is at the horizon. Now, glasses still on, glance at the sun only briefly from time to time until most of the disc has set. Now, take hold of the glasses, keeping them on still, and watch the sun go down. It will seem to go faster and faster until there is only a tiny rim which is rapidly getting shorter. Now, with seconds to go, lift the glasses and look. The green flash lasts less than a second.

Now don't do it again.

"Why not ?"

I had a friend in high school who was afflicted the usual degree of adolescent woe, but who was unusually articulate. From time to time he would sigh and ask, '¹Why?¹' Why were we so bored, melancholy, unglamorous and unsurrounded by girls. Hut why on a deeper level too. Why everything? Why anything?

Now a normal healthy cynic will answer that question, "Because," and will think himself very clever. But to us it seemed brutish to leaap to the conclusion without first examining the question.

There are two obvious questions about the question "Why?" They are: "why not?" (or what makes you think it could have been otherwise in the first place) and "Why, 'why?"' (or why do you ask, even given that it could have been different.)

So we could have had amiable conversations of this form:

"Why?"

"Why, 'Why?'?"

"Why, 'Why, "'Why'"?'?"

"Why , 'why, "'why, ""why?""?'"?'?"

However, we had enough Scotch Irish between us not to let well enough alone. You will remember, of course, that it was not the A bomb that won the Pacific war for the U.S. The pressure of the Japanese fighter pilots was so intense that we were close to being unable to maintain a presence in the Pacific that would let us deliver a bomb.

But then there was the U.S. intelligence outfit. Their job was to intercept and interpret Japanese messages. I would not for a moment discount the importance and courage of the men who went out and fought, but it was a big war a long way off and the enemy had extraordinary determination. Without the ability to read the Japanese intentions often literally better than they could understand each other, it might all have been different. And those code boys were, to a large extent, Southern - Scotch Irish.

Even to this day, with our economy reeling from the onslaught of Japanese camcorders, VCRs, cameras, cars, film, medical equipment and what have you, the U.S~ is still secure in one field. That is the creation of super-computers.

Certainly there are other things that the U.S. does more of and better, but in the field of super-computers, the Japanese have made an enormous investment. But all in vain. The abstract reasoning that such things require does not really appeal to them. If their pride were not in it, it would be no problem. They could go hire some Gurkhas. Gurkhas really go in for that sort of thing when they are not fighting. And it doesn't take many people to makea super-computer: somebody to design the components and somebody to put them together.

We were not curkhas, but we were not above a little competition on an abstract level. I thought things out to go in a pattern, such as:

"Why?"

"Why not?"

"Why, 'Why not'?"

"Why not, 'why not?'?"

"Why 'Why not, '''why not?'"?'?"

"Why not, 'Why not, "'Why not?'"?'?"

But we would get into conversations like this:

I: "Why?"

He: "Why not?"

"Why, 'Why not?'?"

"Why, 'Why, "'Why not?'"?'?"

"Not 'Why, "'Why, ""Why not??""?'"?'. 'Why not, "'why not?'"?'."

"Why, ''Not "'Why, ""'Why not?'""?""?'". "'Why not, ""Why not?""?'".'? Why not, 'Why, '"Why, ""Why not?""?'"?'?"

"Wh ... wh...wh...."

He would cock his head to one side, let his tongue loll out and look at the ceiling. He seemed to think it concentrated his mind if he pretended he was being hanged.

"Why, 'Wh....'; why, 'Wh... wh....';

"why,

"Why?'

'Why, "'Why?'?'

"Why, "'Why, ""Why?""?'"?'

'Why, "'Why, ""Why, ""'Why?'""?""?'"?';

"Why,

'Why?'

'why not?'

'Why, "'why not'"?'

'Why not, "'why not?'"?'

'Why, "'Why not, ""Why not?""?'"?'

"Why,

'Why?'

'Why not?'

'Why, "'Why not?'"?'

'Why, "'Why, ""Why not?""?'"?'

'Not "'Why, ""Why, ""'Why not?'""?""?'". "'Why not, ""Why not?""?'".'

'Wh ... wh... wh....';

"WHY?"

Only he said it fast, so it came out like this:"Why wh..why wh.. wh. why why why why why why why. why why why why why why why not why why not why not why not why why not why not why not why not why not why why why not why why not why why why not not why why why not why not why not why not why why why not why not why not why not why why why not wh..wh..wh..why?"

Today one of us is designing components for super-computers and the other one of is publishing anonymously in an obscure journal. I will leave it to you to figure out who does which.

And why.

Hot computers:

Maxwell's Demon is the brainchild of the same Scot who invented the partial differential equations for electromagnetic radiation and placed serious physics forever out of the reach of us ordinary mortals who do not use partial differentials. The "demon" is an unblushing perpetual motion device. It used to be an intellectual curiosity. It should not be any longer.

The way the demon works is like this: Imagine two chambers tilled with gas with a little door between them. The door weiqhs nothina so that it can be opened and closed without any work. A little demon stands at the door. When he sees a fast-moving gas particle traveling on a course that will take it through the door and into chamber A, he opens the.door. When he sees a slow moving particle on a course for chamber B, he opens the door. At other times he keeps the door closed. In time, all the hot qas is in one chamber, and the temperature difference can be used to run a little steam engine and get some work done for free.

Since work is energy and energy is interconvertable with matter, free work is exactly the same as creating matter out of no matter or energy, is like waving a wand and having an entire working steam calliope materialize in thin air. It can't be done.

More modern attempts to make Maxwell's demon work ... I'm not kidding. They are still talking about making it work ... center around the notion of having a cylinder holding one gas molecule with a piston at each end and a partition with door in the middle. when the door is closed, the piston on the side with no gas is moved effortlessly inward. The other piston is pushed forcibly outward, doing work. The cycle can then be repeated.

People who think about such things generally concede weightless and frictionless pistons, but objec~ at the point where the cycle is repeated. At that point a bit of information (the information as to what the machine was just doing) must be erased. Erasing information wastes work, and the machine makes no net gain.

But what if there were several molecules? The machine is told to open and close the door until it chances to get all of the molecules on one side. Then it does its work cycle, getting out more energy than before, but erasing no more information.

I trust no Wild Surmise reader is amused. There are three questions: Why doesn't it work? Why should they care why it doesn't work? If they do care, why isn't it obvious to them?

The reason it doesn't work is this. In the original design, the demon stands at a door and gazes at gas molecules. Each molecule has energy. If the molecule is a single helium atom, that energy will be its kinetic energy. The kinetic energy of any object is related to its speed and mass (energy = 1/2 times mass times velocity tines velocity). The kinetic energy an object at some velocity is the amount of work you would have to do on the object to lift it high enough so that when you dropped it it would reach that same velocity by the time it fell back to where it started.

A helium atom is a single atom. It has three degrees of freedom:

up-down, left-right and front-back. Adding the kinetic energy along each axis gives you the atom's total kinetic energy.

But when you say "molecule," you generally mean more than one atom. A simple case would be ordinary hydrogen, H₂. Two atoms bound together. They can have kinetic energy, just like Helium. They can also spin. Also the bond between then can be stretched. Water, H₂0, has two bonds that can stretch and the angle between them can bend. I will let you work out butyric acid vapor, CI!₃-cH₂-CH₂-COOH, for yourself.

If the molecules of qas are in thermal equilibrium (which will happen very quickly if they are allowed to bump into each other), they will have a single average total energy. some will have more energy for brief periods and some less. But if you take any group of them, say all the molecules in the northeast corner, or all the H₂0 vapor molecules, all the molecules in any group will have the same average energy. That is just what temperature means. Average energy of particles.

Now consider our cylinder with two pistons and one gas molecule all in thermal equilibrium. If the weight of each piston is zero, then its speed must be infinite. We will not have the slightest chance of finding it, much less controlling it. If the weight of each piston is exactly equal to the weight of the contained molecule, then the piston will be rattling around much faster than the molecule. Remember, it has to have the same total energy and while the molecule at the very least has three degrees of freedom, the piston is constrained to but one. It will be slamming back and forth so fast that it will be much harder to find than the molecule was.

Ah, but the piston is latched into place. Fine, and the latch is in thermal equilibrium so the latch is slamming back and forth, so eventually the piston is free. So we put a latch on the latch, but the latch on the latch is in thermal equilibrium

We will thus have to content ourselves with pistons that are much heavier than our molecules. But now moving them about is no longer effortless.

But of course things would never get so far anyway. We are looking at molecules. Visible light consists of waves that are simply too long to detect anything as small as a gas molecule. Imagine trying to pick up a tiny metal ball by groping for it with a hand wrapped in layers of cotton batting. You would not be able to feel it. If you use shorter wave length light, the energy will be great enough to break up molecules or strip electrons off individual atoms. Imagine trying to do an inventory in a china shop by swinging a hammer around.

If it is a piston instead of a gas molecule you are looking for, you still have the same kind of problem.

So, granted that everyone knows that the Maxwell Demon device cannot work, why are people interested in just why it cannot work? It has to do with computers. Everyone knows that information and energy are interconvertable. Everyone knows that computers store and handle information. The question is: just how do you quantity the energy value of the information in a computer.

The standard equation is easy. If the temperature of the computer is T on the Kelvin or absolute temperature scale, and if loq~2 is the natural logarithm of 2, and if k is Boltzmann's constant, then the energy represented by one bit of information is:

KTloge2.

You might well ask, "what is Boltzmann's constant?" I miqht well say, "It is a number that relates temperature to energy?" And you might well start throwing things at me and shouting, "I knew that, dummy." But the point is that it is a constant. So is log~².

And how much work can a molecule do for you, once you know where it is? Well, of course that is kTlog~2 also. Hence the appeal of having one bit of information in the computer represent more than one molecule. Since the computer can represent anything with a bit, and since one bit that represented 10 molecules would not cost as much as the 10 molecules can bring you, and since we know the machine can't work, obviously there is something wrong with the way me estimate the information value of a computer.

Obviously.

One bit of information is equivalent to kTlog~2 indeed. Are we to believe that? Take a simple computer like an abacus, a frame with a bunch of wires on it and little beads on the wires. The position of the beads represents numbers. Make the thing out of jet engine grade titanium. Set the beads on the abacus to some number, say 127. Heat it up to two thousand degrees. What does it say? 127. Drop its temperature to one degree above absolute zero. (Do not attempt to handle your abacus at such extreme temperatures.) What does it say? 127. Has the information content of the abacus changed more than a thousand fold? No. The information content has not changed at all.

There is something wrong about the way we estimate the energy value of the information content of computers.

That is why people think and care about such things.

So what is the problem with coming up with the right measure? The problem is that we use something called the "metric system." Now the metric system, like the "theory of evolution" is constantly being altered. And altering something as basic as a system of measures is expensive at just the point where it hurts the most.

Imagine that you changed the length of the football field from 100 yards to 100 meters. It would affect the game. It would throw every player off at the instinct level. Things he knew without laYing to think about them would no longer be true. Little harm n a game, except injury rates would probably go up~ A game is a ~et sum proposition; one side loses and the other wins. If it is fair contest, that's all that matters.

But science is not a net sum game. It is human dancing with the Iniverse. It is extending human understanding of the universe. xtending the universe's understanding 6f itself. It is not the )nly noble enterprise, but it is a very noble one. When you 'hange little things like "chrone's disease" to "Chrone disease" md · 'degrees Kelvin" to "xelvins~' and "tidal wave" to "tsunami" md "panda bear" to "panda" and "turkey buzzard" to "turkey rulturell and "cycles per second" to "Hertz," it hurts. It hurts he scientist's instinctive feel for things, a feel he has [eveloped by long years of experience. To that extent, such a hange hurts the universe.

There comes a time when a fundamental change must be considered. A time when a form has outworn its content. A time of change. Pace it, the English system with its yards and quarts

as formalized in the eighteenth century. It still works very eli for buying cloth and milk. The metric system, with its teters and liters was also invented in the eighteenth century. It no longer a state-of-the-art system.

It is quite proper that quarts and yards be different. Milk and 'loth are different. But energy in the metric system is measured .n ergs or joules. Temperature is measured in centigrade. And as re well know, energy and temperature are one and the same.

Imagine a system of weights and measures that reflects more modern ~inking. Take a unit of mass. Say an isolated hydrogen atom. 'onvert that into energy by Einstein's equation E=Mc~. That gives unit of energy. It also is a unit of temperature. Take that nit of energy and turn it into a photon. The photon will have a enqth. At the speed of light, the photon will pass a point in a ertain period of time. That is unit time. Acceleration is unit

peed divided by unit time. Of course that will be a colossal egree of acceleration, which brings one to a point. Must of hese numbers will be much too large or much too small for veryday use. No problem. The is already a scale that goes, Thousand, million, billion, trillion" and so forth. Alas, it is ifferent in England, but you can't make omelets without breaking ggs. Use that scale to bring your unit into the range you want .0 use power is unit energy per unit time. Electric current is electrons er unit time. Electric potential (now measured in volts) is ower divided by current. By building things up this way, you get id of all those constants like Boltzmann's constant.

This permits the scientist to discard an enormous amount of istorical baggage and dimly remembered numbers. A bright child ould be able to tell you how fast the oxygen molecules in the room were moving about and how much faster the water molecules were moving. Unless you have looked up Holtzmann's constant while reading this, you will probably not be able to.

Now let us look at the Maxwell's flemon question aqain, knowing that everything can be converted to everything else. The molecule is moving toward the door. The demon must decide whether to open the door.

Well, first he will have to figure out just what kind of molecule it is. Tn order to study the molecule, the demon will have to evaluate each and every component, each atom, bond and bond angle. It is only reasonable he do so. Suppose a trichloroctane (C8H15c13) molecule is coming at the door at some temperature, that is total energy, equivalent to 500 degrees. The demon inspects only one hydrogen atom sticking out at him. since it is highly unlikely that all the energy of the molecule be residing at any one time in that atom, he will in all likelihood make a drastic underestimate of the energy of the.molecule.

Next, he will have to figure not only whether the molecule is proceeding toward the door, but whether it is on course to enter the door. A ship at sea may be truly said to be on course even though it will need a rudder correction before it actually enters the harbor. The demon must assure himself that no such correction will be needed.

Last, the demon must watch the molecule up until the last instant, lest a collision with another particle change the picture altogether. He will have to be able to. recompute very fast.

And that, of course, is the essence of the matter. The value of the information is not a function of the number of bits and the temperature of the medium in which it is recorded. The value is a function of the number of bits and the speed at which they are accessed.

There is a mathematical term they use called a "floating point operation." It is a sort of standard sized piece of arithmetic. A rate of one floating point operation per second is a FLOP. A million floating point operations per second is referred to cheerfully as a megaflop.

If we are evaluating the energy needed to record the position of a gas molecule with

energy = kTloge2

first we ditch the constant and say energy - T (using our own temperature scale) energy = 1/2 m v² which is true if all the energy is kinetic energy. (m is mass of the atom. V is its velocity. Ke is kinetic energy. f is force. a is acceleration. t is time.)

From high school physics we remember

f = m times a;

a = v divided by t~

So of course So

m = f divided a.

Ke = 1/2 C~ divided by a) v2

If we want to convert that into flops, well 1 flop = 1 bit/sec. so:

and

flop = 1 bit/sec = 1/2 f times t times v 1 bit = 1/2 f times v.

No surprise. The energy value of a bit of information is not a function of the thermostat in the room where the computer is sitting; the energy value is a function of how fast that bit of information can be moved around.

What, you ask, is FORCE doing in there? Well of course, force is an acceleration function. It is a measure of how fast the whole system can be turned on and oft.

Oh I may have made an error in there, but the point is you see how simple it is, once you shake the old metric system and all its ghastly conversion constants and its implicit assumption of the disconnectedness of reality out of your head.

We can still use the English system for footfall and milk. But we very much need a new scientific system of weights and measures.

Editor's note:

WILD SURMISE is an occasional newsletter on speculative matter.

After last issue's article on split infinitives, we got a total of 2 notes (unsigned of course) pointing out proof reading errors. That means less than one per thousand of you confuses splitting an infinitive as a proof reading error (which we have done, too) and doing so as policy. Keep up the good work.

M's last Christmas story took him about three years to write. He always said he couldn't finish it unless there was a white Christmas. That doesn't happen often here in Florida, but M was in Gainesville when he was working on the final draft on Christmas eve, and sure enough it snowed.

There have been some other omens. On New Years eve this year, Jupiter was at the zenith at midnight. That makes it a New Years Star, just as Venus sometimes the Morning Star.

On April 4 of this year, there was an astronomical arrangement that looked like a four handed clock face with Procyon at the center surrounded at equal distances by the moon, Jupiter, Betelgeuse and syrius standing respectively at twelve o'clock, four, six and eight. That is either the peace sign or Nero's cross, depending on your mental set. That, in turn, is either good news or bad news depending on your mental set.

The other day Cooter came in with a couple pictures of cloud formations. One of them looked like a cross. In a few minutes it had turned into the dove of peace. We were feeling quite cheered until M pointed out that the cross in that position is just the Ogham symbol for 'in." Ogham, apparently, is one of the numerous Neanderthal dialects that N grunts.

For those of you looking for something to read, Albion's seed, by David Hackett Fisher, NY, Oxford University press 1989 is intensely interesting. A must for any American or anyone who must deal with Americans.

Then there is Southern by the Grace of God, by Michael Andrew Grissom, available from The Rebel press, p.o. Box 158766, Nashville, Tennessee 37215. We have not read it, but we love the title and pictures.

If you can lay your hands on it, there is God's Frontiersmen: The Scots-Irish Epic, by Rory Fitzpatrick published in 1989 by George Weidenfeld and Nicolson Ltd, 91 Clapham High Street, London SW4 7TA, United Kingdom.

If you are going as far as England to find something to read, and have oodles of time, we have found NATURE, c/o Macmillan Magazines Ltd, 4 Little Essex street, London WC2R 3LF, united Kingdom to be more and more charming. It is the prestigious science journal Einstein selected to publish his theories of relativity. Recently they have hinted, as no one else has dared, that the current plans to unify European currency and economy while leaving questions of sovereignty ambiguous darkly shadow the adoption of the American constitution, which did the same thing for the same reasons. The ambiguity (to put it mildly, one might well say the total distortion) of the Constitution led to America's bloodiest war. Until this plan for monetary union came up, it could well be believed that Europe had her bloodiest war in the past.

On a pleasanter note, NATURE devoted a whole page to the work of one Stefan Marinov who, along with Booty, remains one of Einstein's few remaining critics. Booty has never been mentioned in NATURE. At one point they report with satisfaction, '¹Mercifully, he cMarinov) has not threatened to immolate himself of NATURE's account for many months." At least we now know how to get noticed. But no one on the WILD SURMISE staff is threatening to set himself alight.

Another publication that flinches not to challenge widely held beliefs is MENSA LECThflES, self published by Pene', 12195 Matlacha Blvd., Matlacha FL 33991. Rene' is a scientist in the sense that he obverses things, develops theories and then does experiments to test those theories. You will find much in his writing that provokes thought. We would be far from endorsing everything he says. However, one of his point deserves special mention. It is generally said, "Like electrical charges repel each other." Rene' contradicts this and says, "Two bodies with like electrical charge but with electrical charge of sufficiently different magnitude may attract each other." He has tested this and found it to be the case. Unless someone repeats his work and finds something different, we believe him. Details in his book.

Copyright August, 1990, WILD SURMISE

Points of Light

Points of light

Late one Christmas night

Began to glide and glitter

Among the gold and crimson ornaments.

A gold horn-of-plenty spilled its ruby wealth Onto the pine needles and the emerald holly leaves, Gilded with love.

Their gilt was reflected in the windowpane And from the icicles beyond, hanging from the eaves.

Suddenly a blanket of snow fell past the window,

Released from a slow slide down a canopy

where, carefully hoarded, the snow

Had waited till warmth from out house

Caused the little avalanche.

The many points of light on the tree glowed, For a second, in the falling snow. Then the tree resumed its Christmas vigil.

Only I, a child of three

Watching through the night,

Saw, past the tree,

The little avalanche

And the thousand points of light.

Gerald Baker (2119 college St.,Cedar Falls, TA 50613) was kind enough to send a facsimile of a postcard sent last April from Russia. The card says (after an apparently unrelated introduction) "Do you know anything about spacecraft? In September Voronezh (the town the postcard came from) was visited by extra-terrestrine civilization. If you have some questions about this write down to me. I witnessed this event and even managed to make some photo. all the best ....'

Gerald Baker is a faithful correspondent and a phenomenal networker. If anyone has any further knowledge of the event, I sure he would be delighted to hear.

The correspondent who sent what follows is not one of our regular staff. However, he says he would rather not be named. The issue is a sad one, unquestionably with multiple sides.

"At a time when a public debate is going on about continuing life for seriously brain-damaged accident - and stroke victims, the mental retardation facilities in the country are spending over $40,000 per bed year on profoundly retarded persons who require total care and are fed by gastrostomy tube. An annual review, in which their "program" for the coming year is discussed (typical toileting objective: "will keep diapers dry for three hours") has been expanded to fill three hours, and one of the questions discussed is their "right" to citizenship so they can vote. Profoundly retarded people have IQ's of 19 or less; this measure is usually based on adaptive behavior tests, since intelligence tests don't measure accurately in sucb low ranges.

"I have come to the conclusion that a "mystique" has grown up because a large group of people all over the country cannot afford to speak for fear of losing their jobs. The Federal government pays the bill and lays down regulations with which state institutions must comply or lose the money. This is worse than any farm subsidy scandal. It involves what I regard as harassment of helpless people: insisting that they have "active treatment," i.e.. "training," during almost all their waking hours instead of just leaving them to lie comfortably in bed. The "training" is called "sensory st4mulation," and the objective usually reads something like "will respond to a sweet odor (strawberry) 5 out of 6 times." That means they move their heads or smile or blink. It would be better to get some facilities converted to 'nursing home" type states, which is the kind of care these people really need, but it would mean the facility giving up a large amount of money.

"The bill for the taxpayer is high. There is one facility where about 80 out of a 240 population are in this condition. Nursing home care would cost $30,000. The extra $10,000 a year for training comes to $800,000 a year for this one facility. Since 2.6% of the general population of the U.S. is in the profound category, and using 1% as an estimate of the ones who are in this persistent vegetative state, you can figure the amount spent all over the country.

"This kind of program is arguably "good" for higher levels of retardation; severely retarded people can be taught to eliminate in the toilet and feed themselves, but even there expense must be weighed. A move is underway to place these people in the community, in what amount to small institutions, which are more expensive, and entrepreneurs have been quick to see a profit.

"Surely there are other needs. Educating normal children for one."

Reflections of Jerry Cox

Box 40-A, Rt. #1

Woodbine, Ky. 40771

BE FREE OF THE GOD-MONSTER

A God has earned no praise who isn't passionately interested in your happiness.

A God has earned no praise who sees you only as a means to an end, such as helping other.

A God has earned no praise who has superhuman requirements for mere human being.

A God has earned no praise who readily resorts to punishment.

A God has earned no praise who sends messengers, but does not send Himself.

A god has earned no praise who gives you the examination without first teaching you the course.

A God has earned no praise who saves some and damns other.

A God has earned no praise who cannot be pleased.

A God has earned no praise who bring you to your knees.

A God has earned no praise who must COMMAND worship.

A God has earned no praise who thinks so little of your heart that he ORDERS you to love.

Such a God is not God at all, but the God-Monster that has

been handed down by unreflecting people for generations. whoever would know God must be free of the God-Monster.

A LIFETIME'S LEARNING IN SIX QUOTES

"There is only God."--Da Love-Ananda.

"Therefore, be perfectly and exclusively devoted to happiness itself."--Da Love-Ananda (typography revised).

'Understand your unhappiness. This is the first thing that must occur."--Da Love-Ananda.

The individual is an aperture through which the whole energy of the universe is aware of itself."--Alan Watts.

The reality of my life cannot die, for I am indestructible consciousness. "--Paramahansa Yoganada.

You can no more have too much self-esteem than you can have too much health."--Nathaniel Branden.

A FINAL THOUGHT FREE FOR THE SHARING:

God, show the world how happy you can make a human being~ You may use me as an example.

MILD SURPRISE

There is a place of geometric forms. Parallel lines. Sheer vertical planes. Polygons. Congruent figures. Close set columns of stone. Pattern without life. Relationships purely abstract. Crystals that are big, bigger than a man, bigger than a whale, at least the whole pattern is. It proves that an abstract mathematical relationship can be bigger than any living thing. Western thought has been criticized as being opposed to nature. The oriental is much more comfortable with natural things. But the Giants Causeway is nature too, a cold, dry intellectual nature. A cerebral nature. Certainly crystals exist elsewhere, but tiny ones, nothing like these packed basalt columns beside the North Irish sea. They challenge one to think about thinking.

I walked up the road from Giants Causeway. At the souvenir shop I fell to chatting with the lad behind the counter. Taller and thinner than most folk of the south, he had on a dress shirt and tie rather than the loose southern sweater. His hair was brown. The most distinctive, not the most common, hair color in the north is sort of slate, almost teal. I think it is so they look less conspicuous on the rooftops.

"While you're here, you can visit the Bushmills distillery."

"Bushmills?"

"It's bad stuff. Gives you a hangover." (He was pulling the time honored Scotch Irish trick of bad mouthing something he liked.)

"Maybe if you just drank a little."

"Buy I drink a lot. It was the first whiskey ever distilled."

"I knew the Scotch Irish invented Bourbon. I never knew they invented whiskey."

"The Scots Irish invented everything. Too bad they didn't just invent good things. Think about it."

On the way to Dublin there would be time for one more night in the north. That turned out to be in Newcastle, county Down, under the very shadow of the Mountains of Morne. They had The put the car in back, where it would be kept behind a locked iron gate. That was a first. Very reassuring. And the hotel wasn't damaged. All the others had had plaster off the lobby, wires hanging from the ceiling, glass door broken, signs saying; "Renovations. Sorry for the inconvenience." No army choppers overhead. I collected the room key.

"You won't want a front door key unless you go out," said the girl. OK, woman maybe. Looked like a girl to me, younger than I, as young as that is.

"Sure."

"You're not going . . . OUT ... are you?"

"Might."

"Then you have to leave your car keys."

"I need to get into the car to get stuff out."

"Or your driver's license."

"Nu uhn."

"OK. Five pounds then."

"Fine."

The evening was cool, damp and raw, but I thought it would be my only chance to visit a pub in the north. Now in the south pubs are very friendly and it's easy to chat. I thought it couldn't be too different here. A brief stroll on the street convinced me that the only serviceable pub was the one right in the hotel. I went thither. The same girl was now tending bar.

"What would you like to drink?"

"Well now I understand you've got something called Bushmills that is distilled right here in Northern Ireland, and it's the first whiskey in the world."

"We've got it. Do you want regular or black label? Regular is cheaper."

"First time. Why don't you give me black label."

It came with a large pitcher of water. I tried it straight. "That will do. I won't need the water."

I strolled to the back of the pub. A soccer game was on TV. There were a half dozen teenagers, three boys three girls, who clearly were more interested in each other than in anything I might have to say. Two thin men sat at the front of the pub, elbows on knees, heads together. No invitation to talk there.

Presently I went to the bar for another black label. "Tell me something, ma'am. I notice everybody you see around here, total strangers, they look at you and shake their heads like this."

"No. They nod their heads like this."

"I'm sure they shake their heads like this."

"Sometimes they shrug their shoulders like this."

I shrugged, tipped her again and went back to my seat, spread my arms out along the back rest. The flushmills slowly vanished. Back to the bar.

"I hope the troubles haven't bothered you."

"No, it's no worse than in our country. In Washington, once or twice a day somebody gets killed. It isn't that bad here. Same problem. It's a matter of having your own country. The Black people don't have one. Think of it as a war. At any one time, one out of four young Black American males is in jail, on probation or parole. Conservatively, half die of violence or go to jail at some time in their lives. If you were righting a war, and half your male population had been killed or captured, you'd surrender. Only they don't have anybody to surrender to." Actually, the Scotch Irish are notorious for not surrendering under such circumstances, but I had been drinking.

The Then near the door left.

"Do you want another Black Label, sir?"

"No, it would be wasted on me. Give me the regular." As she poured it, one of the men came back

"I can't get into my room, number 27."

"But that's your key right in your hand," she said.

"I can't get the door open."

She bustled away. I sat again. Should have accepted that water. When she came back, I went to the bar.

"Drunk," she said. I let the remark pass, assuming she meant that other guy and not me.

"It finally made me thirsty. could I have a beer?"

"Half pint, right?" she said. I took the hint. As I sipped, she said. "Were you in flelfast? Belfast is supposed to be all right as long as you stay out of the neighborhoods."

The neighborhoods? "The neighborhoods?"

"The east and the west. The Shank, that's the protestants and the Falls, that's Catholic." She said "Shank" and "Falls" with identical emphasis. I was too mellow to make anything of that at the time, but it is hard to say the two in the same tone.

"Un huh."

"You know the leaders. The leader of the IRA and the UDL. They're just like that." Holding her index and middle fingers together.

"What's UDL mean?"

"Ulster Defense League."

"Yes, one side kills somebody. The other side kills somebody. They just want to keep it going."

"Sure. But you said the east and west were protestant and Catholic. which is which?"

"Really, Sir." Her voice was suddenly miserable. anything about Belfast geography."

"Sure, of course."

"I don't know

She went on rapidly. "There really isn't anything to it, sir. why half my friends are protestants."

Thud.

"So," think I. "You are Catholic. This is a Catholic pub. Pretty tacky of me bragging about Bushmills." I tipped her one last time, gave my best easy smile. It was late after all. I went to bed.

My room smelled of tobacco. It wasn't as if somebody had been smoking in it. But somebody who smoked had been in it since I had last. Cleaning person, probably. I checked my things. Nothing missing. T opened the window to air the place out, undressed and stretched out.

Presently I hear noise in the hall. Two men. They are talking to each other angrily. I look upward in the dark. Ah, two Gaelic buddies back from a night out, fussing and carrying on. Soccer game maybe. r hear a word like "2'x~ '" any number of times. Mostly I can't catch what they are saying at all. But then I make out: "... knocking back Bushmills one right after the other..."

Wells'r, it woke me right up. "They must be talking about me. I was the only one drinking Bushmills. But these guys have been drinking. You can tell from their voices." I guessed they were the two men from the pub.

I slipped out of bed and stood away from the door. It was time to go into full paranoid hyper drive. Just now that consisted only of listening. More palaver and then · '.... that door right off its hinges . . .1'

OK, they are talking about my door. That means they have gone to the trouble of checking the hotel registry to find out where the foreigner is staying. The can't-open-door trick. That was to nail down where the girl would be for a few minutes. "Off its hinges?" Bomb? Not in a Catholic hotel. Gun maybe. That's why I'm standing over here even though it's harder to hear. Knock it down with their bare hands? I wish they'd try.

More excited talk. "... every been with the ARMY boy? Ever been to Dublin and seen what the ARMY can do?...~' I don't think he means the Ulster Defense League, somehow.

All right, I've been warned. It's time to take action. There is no phone in the room. Somehow screaming out the window doesn't seem right. I'll have to arm myself.

T turned on the lights; might as well make them think I'm up to something. I dig in my bag and get out ... a pair of nail clippers. It is called bathos; the very depth of absurdity.

A tiny little folding pair of scissors. All right. You guys are in trouble now. I stood naked beside the door. The little engine on my fingers ends.

I thought about the situation. First, there is something missing. where is the lump in my throat? The dry mouth? The racing pulse? The quick breath? where's my adrenaline? I have just, for the first time in my entire life, picked up an instrument and planned to kill somebody with it. It shouldn't come as such a matter of course.

I guessed I just about weighed as much as the two of them. So

that was a wash. They were in a narrow hall, which worked for me.

I could open the door at my own time, so I had the initiative.

Even if they shot the lock out, one of them would still have to

put his head in sooner or later if they wanted to do any more.

But most of all I was thinking: They haven't got a prayer. I don't think they can take this door, much less me.

Had I been fresh I might have got out the Polaroid camera. I could open the door and take a picture of them. The flash would blind them. Before they recovered, I could take a couple more pictures, offer them as presents, "Two old buddies coming home after a night out." Pretend I hadn't understood a word and close the door. Then let them wonder if they are going to be able to find and destroy every picture. But I was not fresh. I was not being clever. But I was clever enough to stand my ground.

Speaking of ground, where was the middle ground around here? If a stranger approaches you on the street and offers you a unlabeled pill to swallow, common sense dictates that you neither murder the stranger nor accept the pill. Yet within minutes, I have dealt with a person to whom differences mean nothing and two to whom they mean life and death.

There was another issue. Except for the words I have quoted, I had not understood a single thing they had said. And they had been doing a lot of talking. Suppose I had not understood at all. Suppose they didn't know I existed, but were talking about something else entirely, and there I was, nail clipper at the ready, poised to burl myself through the door and start dismantling them. Who was the hunter? who the hare?

Meanwhile, they are not going away. They are getting more and more excited. Don't they realize they don't have a chance? Is there something I don't know?

Then I heard a voice. I couldn't understand this voice either, but I could tell two things~ It was the girl's voice, and she was saying, 'Pipe down and go to bed." Either their voices had reached her all the way through the mostly empty hotel or she had come by to check on me.

That was it. Suddenly I had a friend in their camp. A member of their own tribe whom they could not possibly intimidate. If anything happened to me, there was a hostile witness. It was checkmate.

Silence outside. I turned off the light and went back to bed.

Next morning, I ran into the fellow coming out of room 27. He had dark glasses on and was carrying a suitcase. I flashed a broad grin, noticed I had left my light on and locked the door of my room. When I got back, the door was unlocked and the light off. He just wanted to show me he really could have got in. I checked the car for bombs before leaving. They got to me that far, anyway.

Tonight I hope they are in some warm dry pub where there are no outsiders. One of them is saying, "He was this big."