Mirror | rorriM

During a class of calculus my lecturer suddenly checked himself and
stared intently at the table in front of him for a while. Then he
looked up at us and explained that he thought he had brought six piles
of papers with him, but “no matter how he counted” there was only five
on the table. Then he became silent for a while again and then told
the following story:

“When I was young in Poland I met the great mathematician Waclaw
Sierpinski. He was old already then and rather absent-minded. Once he
had to move to a new place for some reason. His wife wife didn’t trust
him very much, so when they stood down on the street with all their
things, she said:

– Now, you stand here and watch our ten trunks, while I go and get a
taxi.

She left and left him there, eyes somewhat glazed and humming
absently. Some minutes later she returned, presumably having called
for a taxi. Says Mr Sierpinski (possibly with a glint in his eye):

– I thought you said there were ten trunks, but I’ve only counted to
nine.

– No, they’re TEN!

– No, count them: 0, 1, 2, …”

Kai-Mikael, Royal Inst. of Technology, Stockholm, SWEDEN

An assemblage of the most gifted minds in the world were all posed the
following question:

“What is 2 * 2 ?”

The engineer whips out his slide rule (so it’s old) and shuffles it
back and forth, and finally announces “3.99”.

The physicist consults his technical references, sets up the problem on
his computer, and announces “it lies between 3.98 and 4.02”.

The mathematician cogitates for a while, oblivious to the rest of
the world, then announces: “I don’t what the answer is, but I can tell
you, an answer exists!”.

Philosopher: “But what do you _mean_ by 2 * 2 ?”

Logician: “Please define 2 * 2 more precisely.”

Accountant: Closes all the doors and windows, looks around carefully,
then asks “What do you _want_ the answer to be?”

Computer Hacker: Breaks into the NSA super-computer and gives the answer.

                Hiawatha Designs an Experiment



Hiawatha, mighty hunter,

He could shoot ten arrows upward,

Shoot them with such strength and swiftness

That the last had left the bow-string

Ere the first to earth descended.

  This was commonly regarded

As a feat of skill and cunning.

Several sarcastic spirits

Pointed out to him, however,

That it might be much more useful

If he sometimes hit the target.

"Why not shoot a little straighter

And employ a smaller sample?"

Hiawatha, who at college

Majored in applied statistics,

Consequently felt entitled

To instruct his fellow man

In any subject whatsoever,

Waxed exceedingly indignant,

Talked about the law of errors,

Talked about truncated normals,

Talked of loss of information,

Talked about his lack of bias,

Pointed out that (in the long run)

Independent observations,

Even though they missed the target,

Had an average point of impact

Very near the spot he aimed at,

With the possible exception

of a set of measure zero.

  "This," they said, "was rather doubtful;

Anyway it didn't matter.

What resulted in the long run:

Either he must hit the target

Much more often than at present,

Or himself would have to pay for

All the arrows he had wasted."

  Hiawatha, in a temper,

Quoted parts of R. A. Fisher,

Quoted Yates and quoted Finney,

Quoted reams of Oscar Kempthorne,

Quoted Anderson and Bancroft

(practically in extenso)

Trying to impress upon them

That what actually mattered

Was to estimate the error.

  Several of them admitted:

"Such a thing might have its uses;

Still," they said, "he would do better

If he shot a little straighter."

  Hiawatha, to convince them,

Organized a shooting contest.

Laid out in the proper manner

Of designs experimental

Recommended in the textbooks,

Mainly used for tasting tea

(but sometimes used in other cases)

Used factorial arrangements

And the theory of Galois,

Got a nicely balanced layout

And successfully confounded

Second order interactions.

  All the other tribal marksmen,

Ignorant benighted creatures

Of experimental setups,

Used their time of preparation

Putting in a lot of practice

Merely shooting at the target.

  Thus it happened in the contest

That their scores were most impressive

With one solitary exception.

This, I hate to have to say it,

Was the score of Hiawatha,

Who as usual shot his arrows,

Shot them with great strength and swiftness,

Managing to be unbiased,

Not however with a salvo

Managing to hit the target.

  "There!" they said to Hiawatha,

"That is what we all expected."

Hiawatha, nothing daunted,

Called for pen and called for paper.

But analysis of variance

Finally produced the figures

Showing beyond all peradventure,

Everybody else was biased.

And the variance components

Did not differ from each other's,

Or from Hiawatha's.

(This last point it might be mentioned,

Would have been much more convincing

If he hadn't been compelled to

Estimate his own components

From experimental plots on

Which the values all were missing.)

  Still they couldn't understand it,

So they couldn't raise objections.

(Which is what so often happens

with analysis of variance.)

All the same his fellow tribesmen,

Ignorant benighted heathens,

Took away his bow and arrows,

Said that though my Hiawatha

Was a brilliant statistician,

He was useless as a bowman.

As for variance components

Several of the more outspoken

Make primeval observations

Hurtful of the finer feelings

Even of the statistician.

  In a corner of the forest

Sits alone my Hiawatha

Permanently cogitating

On the normal law of errors.

Wondering in idle moments

If perhaps increased precision

Might perhaps be sometimes better

Even at the cost of bias,

If one could thereby now and then

Register upon a target.

W. E. Mientka, “Professor Leo Moser — Reflections of a Visit”

American Mathematical Monthly, Vol. 79, Number 6 (June-July, 1972)

A bunch of Polish scientists decided to flee their repressive
government by hijacking an airliner and forcing the pilot to
fly them to a western country. They drove to the airport,
forced their way on board a large passenger jet, and found there
was no pilot on board. Terrified, they listened as the sirens
got louder. Finally, one of the scientists suggested that since
he was an experimentalist, he would try to fly the aircraft.

He sat down at the controls and tried to figure them out. The sirens
got louder and louder. Armed men surrounded the jet. The would be
pilot’s friends cried out, “Please, please take off now!!!
Hurry!!!!!!” The experimentalist calmly replied, “Have patience.
I’m just a simple pole in a complex plane.”

Theorem : All positive integers are equal.

Proof:

Sufficient to show that for any two positive integers, A and B,
A = B. Further, it is sufficient to show that for all N > 0, if A
and B (positive integers) satisfy (MAX(A, B) = N) then A = B.

Proceed by induction.

If N = 1, then A and B, being positive integers, must both be 1.
So A = B.

Assume that the theorem is true for some value k. Take A and B
with MAX(A, B) = k+1. Then MAX((A-1), (B-1)) = k. And hence
(A-1) = (B-1). Consequently, A = B.

The USDA once wanted to make cows produce milk faster, to improve the dairy
industry.

So, they decided to consult the foremost biologists and
recombinant DNA technicians to build them a better cow.
They assembled this team of great scientists, and gave them
unlimited funding. They requested rare chemicals, weird
bacteria, tons of quarantine equipment, there was a
God-awful typhus epidemic they started by accident,
and, 2 years later, they came back with the “new, improved cow.”
It had a milk production improvement of 2% over the
original.

They then tried with the greatest Nobel Prize winning chemists
around. They worked for six months, and, after requisitioning
tons of chemical equipment, and poisoning half the small town
in Colorado where they were working with a toxic cloud from
one of their experiments, they got a 5% improvement in milk output.

The physicists tried for a year, and, after ten thousand cows were
subjected to radiation therapy, they got a 1% improvement in output.

Finally, in desperation, they turned to the mathematicians. The
foremost mathematician of his time offered to help them with the problem.
Upon hearing the problem, he told the delegation that they could come back
in the morning and he would have solved the problem. In the morning,
they came back, and he handed them a piece of paper with the
computations for the new, 300% improved milk cow.

The plans began:

“A Proof of the Attainability of Increased Milk Output from Bovines:

Consider a spherical cow……”

Theorem: a cat has nine tails.

Proof:

No cat has eight tails. A cat has one tail more than no cat. Therefore,
a cat has nine tails.

Von Neumann and Nobert Weiner were both the subject of many dotty
professor stories. Von Neumann supposedly had the habit of simply
writing answers to homework assignments on the board (the method
of solution being, of course, obvious) when he was asked how to solve
problems. One time one of his students tried to get more helpful
information by asking if there was another way to solve the problem.
Von Neumann looked blank for a moment, thought, and then answered,
“Yes.”.

Weiner was in fact very absent minded. The following story is told
about him: When they moved from Cambridge to Newton his wife, knowing
that he would be absolutely useless on the move, packed him off to
MIT while she directed the move. Since she was certain that he would
forget that they had moved and where they had moved to, she wrote down
the new address on a piece of paper, and gave it to him. Naturally,
in the course of the day, an insight occurred to him. He reached in
his pocket, found a piece of paper on which he furiously scribbled
some notes, thought it over, decided there was a fallacy in his idea,
and threw the piece of paper away. At the end of the day he went
home (to the old address in Cambridge, of course). When he got there
he realized that they had moved, that he had no idea where they had
moved to, and that the piece of paper with the address was long gone.
Fortunately inspiration struck. There was a young girl on the street
and he conceived the idea of asking her where he had moved to, saying,
“Excuse me, perhaps you know me. I’m Norbert Weiner and we’ve just
moved. Would you know where we’ve moved to?” To which the young
girl replied, “Yes daddy, mommy thought you would forget.”

The capper to the story is that I asked his daughter (the girl in
the story) about the truth of the story, many years later. She
said that it wasn’t quite true — that he never forgot who his
children were! The rest of it, however, was pretty close to what
actually happened…

Richard Harter, Computer Corp. of America, Cambridge, MA

A doctor, a lawyer and a mathematician were discussing the relative merits
of having a wife or a mistress.

The lawyer says: “For sure a mistress is better. If you have a wife and
want a divorce, it causes all sorts of legal problems.”

The doctor says: “It’s better to have a wife because the sense of security
lowers your stress and is good for your health.”

The mathematician says: ” You’re both wrong. It’s best to have both so that
when the wife thinks you’re with the mistress and the mistress thinks you’re
with your wife — you can do some mathematics.”

Russell to Whitehead: “My Godel is killing me!”