The Numbers are Awful

Ford slung the Guide sullenly back into his satchel.

"My doctor says that I have a malformed public-duty gland  and  a natural  deficiency in moral fibre," he muttered to himself, "and that I am therefore excused from saving Universes."

Nevertheless, he stomped up the stairs behind them.

What they found upstairs was just stupid, or so  it  seemed,  and Ford  shook  his  head,  buried his face in his hands and slumped against a pot plant, crushing it against the wall.

"The   central   computational   area,"    said    Slartibartfast unperturbed,  "this is where every calculation affecting the ship in any way is performed. Yes I know what it looks like, but it is in  fact a complex four-dimensional topographical map of a series of highly complex mathematical functions."

"It looks like a joke," said Arthur.

"I know what it looks like," said Slartibartfast, and  went  into it.  As  he  did  so,  Arthur had a sudden vague flash of what it might mean, but he refused to believe it. The Universe could  not possibly  work  like  that, he thought, cannot possibly. That, he thought to himself, would be as absurd as ... he terminated  that line of thinking. Most of the really absurd things he could think of had already happened.

And this was one of them.

It was a large glass cage, or box - in fact a room.

In it was a table, a long one. Around it were  gathered  about  a dozen  chairs,  of the bentwood style. On it was a tablecloth - a grubby,  red  and  white  check  tablecloth,  scarred  with   the occasional   cigarette  burn,  each,  presumably,  at  a  precise calculated mathematical position.

And on the tablecloth sat some half-eaten Italian  meals,  hedged about with half-eaten breadsticks and half-drunk glasses of wine, and toyed with listlessly by robots.

It was  all  completely  artificial.  The  robot  customers  were attended  by  a  robot  waiter,  a  robot wine waiter and a robot maetre  d'.  The  furniture  was   artificial,   the   tablecloth artificial, and each particular piece of food was clearly capable of exhibiting all the mechanical characteristics of, say, a pollo sorpreso, without actually being one.

And all participated in a  little  dance  together  -  a  complex routine  involving the manipulation of menus, bill pads, wallets, cheque books, credit cards, watches, pencils and  paper  napkins, which  seemed  to be hovering constantly on the edge of violence, but never actually getting anywhere.

Slartibartfast hurried in, and then appeared to pass the time  of day  quite  idly  with  the maetre d', whilst one of the customer robots, an autorory, slid slowly under the table, mentioning what he intended to do to some guy over some girl.

Slartibartfast took over the seat which had been thus vacated and passed a shrewd eye over the menu. The tempo of the routine round the table seemed  somehow  imperceptibly  to  quicken.  Arguments broke  out,  people  attempted  to  prove things on napkins. They waved fiercely at each  other,  and  attempted  to  examine  each other's pieces of chicken. The waiter's hand began to move on the bill pad more quickly than a human hand could  manage,  and  then more quickly than a human eye could follow. The pace accelerated. Soon, an extraordinary and insistent politeness  overwhelmed  the group, and seconds later it seemed that a moment of consensus was suddenly achieved. A new vibration thrilled through the ship.

Slartibartfast emerged from the glass room.

"Bistromathics," he said. "The most powerful computational  force known   to   parascience.  Come  to  the  Room  of  Informational Illusions."

He swept past and carried them bewildered in his wake.

The Bistromatic Drive is a wonderful new method of crossing  vast interstellar  distances  without all that dangerous mucking about with Improbability Factors.

Bistromathics  itself  is  simply  a  revolutionary  new  way  of understanding the behaviour of numbers. Just as Einstein observed that time was not an absolute  but  depended  on  the  observer's movement  in  space,  and  that  space  was  not an absolute, but depended on the  observer's  movement  in  time,  so  it  is  now realized  that  numbers  are  not  absolute,  but  depend  on the observer's movement in restaurants.

The first non-absolute number is the number of  people  for  whom the  table  is  reserved. This will vary during the course of the first three telephone calls to the restaurant, and then  bear  no apparent  relation  to the number of people who actually turn up, or to the number of people who subsequently join them  after  the show/match/party/gig,  or  to the number of people who leave when they see who else has turned up.

The second non-absolute number is  the  given  time  of  arrival, which   is  now  known  to  be  one  of  those  most  bizarre  of mathematical concepts,  a  recipriversexcluson,  a  number  whose existence  can  only  be  defined  as  being  anything other than itself. In other words, the given time  of  arrival  is  the  one moment  of  time at which it is impossible that any member of the party will arrive. Recipriversexclusons now play a vital part  in many  branches of maths, including statistics and accountancy and also form the basic  equations  used  to  engineer  the  Somebody Else's Problem field.

The third and most mysterious piece of  non-absoluteness  of  all lies in the relationship between the number of items on the bill, the cost of each item, the number of people  at  the  table,  and what they are each prepared to pay for. (The number of people who have actually brought any money is only a sub-phenomenon in  this field.)

The baffling discrepancies which used  to  occur  at  this  point remained  uninvestigated for centuries simply because no one took them seriously. They were at the time put down to such things  as politeness,    rudeness,    meanness,    flashness,    tiredness, emotionality,  or  the  lateness  of  the  hour,  and  completely forgotten  about on the following morning. They were never tested under  laboratory  conditions,  of  course,  because  they  never occurred  in  laboratories  -  not  in  reputable laboratories at least.

And so it was only with the advent of pocket computers  that  the startling truth became finally apparent, and it was this:

Numbers written  on  restaurant  bills  within  the  confines  of restaurants  do  not follow the same mathematical laws as numbers written on any other pieces of paper in any other  parts  of  the Universe.

This  single  fact  took  the  scientific  world  by  storm.   It completely  revolutionized  it.  So many mathematical conferences got held in such good restaurants that many of the  finest  minds of a generation died of obesity and heart failure and the science of maths was put back by years.

Slowly, however,  the  implications  of  the  idea  began  to  be understood.  To  begin with it had been too stark, too crazy, too much what the man in the street would have said, "Oh yes, I could have  told  you that," about. Then some phrases like "Interactive Subjectivity Frameworks" were invented, and everybody was able to relax and get on with it.

The small groups of monks who had taken  up  hanging  around  the major  research  institutes  singing strange chants to the effect that The Universe was only a figment of its own imagination  were eventually given a street theatre grant and went away.

"In space travel, you see," said Slartibartfast,  as  he  fiddled with some instruments in the Room of Informational Illusions, "in space travel ..."

He stopped and looked about him.

The Room of Informational Illusions was a  welcome  relief  after the visual monstrosities of the central computational area. There was nothing in it. No information, no illusions, just themselves, white  walls  and a few small instruments which looked as if they were meant to plug into something which  Slartibartfast  couldn't find.

"Yes?" urged Arthur. He had picked up Slartibartfast's  sense  of urgency but didn't know what to do with it.

"Yes what?" said the old man.

"You were saying?"

Slartibartfast looked at him sharply.

"The numbers," he said, "are awful." He resumed his search.

Arthur nodded wisely to himself. After a while he  realized  that this  wasn't  getting  him anywhere and decided that he would say "what?" after all.

"In space travel," repeated Slartibartfast, "all the numbers  are awful."

Arthur nodded again and looked round to Ford for help,  but  Ford was practising being sullen and getting quite good at it.

"I was only," said Slartibartfast with a sigh,  "trying  to  save you the trouble of asking me why all the ship's computations were being done on a waiter's bill pad."

Arthur frowned.

"Why," he said, "were all the ship's computations being done on a

wait-"

He stopped.

Slartibartfast said, "Because in space travel all the numbers are awful."

He could tell that he wasn't getting his point across.

"Listen," he said. "On a waiter's bill  pad  numbers  dance.  You must have encountered the phenomenon."

"Well ..."

"On a waiter's  bill  pad,"  said  Slartibartfast,  "reality  and unreality  collide  on such a fundamental level that each becomes the other and anything is possible, within certain parameters."

"What parameters?"

"It's impossible to say," said  Slartibartfast.  "That's  one  of them.  Strange  but  true.  At  least,  I think it's strange," he added, "and I'm assured that it's true."

At that moment he located the slot in the wall for which  he  had been  searching,  and  clicked the instrument he was holding into it.

"Do not be alarmed," he said, and then suddenly darted an alarmed look at himself, and lunged back, "it's ..."

They didn't hear what he said, because at that  moment  the  ship winked  out  of  existence  around them and a starbattle-ship the size of a small Midlands  industrial  city  plunged  out  of  the sundered night towards them, star lasers ablaze.

They gaped, pop-eyed, and were unable to scream.