Einstein in Heaven
Einstein dies and goes to heaven only to be informed that his room is not yet ready. "I hope you will not mind waiting in a dormitory. We are very sorry, but it's the best we can do and you will have to share the room with others." he is told by the doorman (say his name is Pete). Einstein says that this is no problem at all and that there is no need to make such a great fuss. So Pete leads him to the dorm. They enter and Albert is introduced to all of the present inhabitants.
"See, Here is your first room mate. He has an IQ of 180!"
"Why that's wonderful!" Says Albert. "We can discuss mathematics!"
"And here is your second room mate. His IQ is 150!"
"Why that's wonderful!" Says Albert. "We can discuss physics!"
"And here is your third room mate. His IQ is 100!"
"That Wonderful! We can discuss the latest plays at the theater!"
Just then another man moves out to capture Albert's hand and shake it.
"I'm your last room mate and I'm sorry, but my IQ is only 80."
Albert smiles back at him and says, "So, where to you think interest
rates are headed?"
Subject: All you wanted to know about science
The beguiling ideas about science quoted here were gleaned from essays, exams, and classroom discussions. Most were from 5th and 6th graders. They illustrate Mark Twain's contention that the "most interesting information comes from children, for they tell all they know and then stop."
A physics joke:
"Energy equals milk chocolate square"
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)
See also "Applied Dynamic Programming" by Bellman and Dreyfuss, prior to 1962.
Problem: To Catch a Lion in the Sahara Desert.
(Hunting lions in Africa was originally published as "A contribution to the mathematical theory of big game hunting" in the American Mathematical Monthly in 1938 by "H. Petard, of Princeton NJ" [actually the late Ralph Boas]. It has been reprinted several times.
1. Mathematical Methods
1.1 The Hilbert (axiomatic) method
We place a locked cage onto a given point in the desert. After that
we introduce the following logical system:
Axiom 1: The set of lions in the Sahara is not empty.
Axiom 2: If there exists a lion in the Sahara, then there exists a
lion in the cage.
Procedure: If P is a theorem, and if the following is holds:
"P implies Q", then Q is a theorem.
Theorem 1: There exists a lion in the cage.
1.2 The geometrical inversion method
We place a spherical cage in the desert, enter it and lock it from inside. We then perform an inversion with respect to the cage. Then the lion is inside the cage, and we are outside.
1.3 The projective geometry method
Without loss of generality, we can view the desert as a plane surface. We project the surface onto a line and afterwards the line onto an interior point of the cage. Thereby the lion is mapped onto that same point.
1.4 The Bolzano-Weierstrass method
Divide the desert by a line running from north to south. The lion is then either in the eastern or in the western part. Let's assume it is in the eastern part. Divide this part by a line running from east to west. The lion is either in the northern or in the southern part. Let's assume it is in the northern part. We can continue this process arbitrarily and thereby constructing with each step an increasingly narrow fence around the selected area. The diameter of the chosen partitions converges to zero so that the lion is caged into a fence of arbitrarily small diameter.
1.5 The set theoretical method
We observe that the desert is a separable space. It therefore contains an enumerable dense set of points which constitutes a sequence with the lion as its limit. We silently approach the lion in this sequence, carrying the proper equipment with us.
1.6 The Peano method
In the usual way construct a curve containing every point in the desert. It has been proven [1] that such a curve can be traversed in arbitrarily short time. Now we traverse the curve, carrying a spear, in a time less than what it takes the lion to move a distance equal to its own length.
1.7 A topological method
We observe that the lion possesses the topological gender of a torus. We embed the desert in a four dimensional space. Then it is possible to apply a deformation [2] of such a kind that the lion when returning to the three dimensional space is all tied up in itself. It is then completely helpless.
1.8 The Cauchy method
We examine a lion-valued function f(z). Be \zeta the cage. Consider the integral
1 [ f(z)
------- I --------- dz
2 \pi i ] z - \zeta
C
where C represents the boundary of the desert. Its value is f(zeta), i.e. there is a lion in the cage [3].
1.9 The Wiener-Tauber method
We obtain a tame lion, L_0, from the class L(-\infinity,\infinity), whose fourier transform vanishes nowhere. We put this lion somewhere in the desert. L_0 then converges toward our cage. According to the general Wiener-Tauner theorem [4] every other lion L will converge toward the same cage. (Alternatively we can approximate L arbitrarily close by translating L_0 through the desert [5].)
2. Theoretical Physics Methods
2.1 The Dirac method
We assert that wild lions can ipso facto not be observed in the Sahara desert. Therefore, if there are any lions at all in the desert, they are tame. We leave catching a tame lion as an exercise to the reader.
2.2 The Schroedinger method
At every instant there is a non-zero probability of the lion being in the cage. Sit and wait.
2.3 The Quantum Measurement Method
We assume that the sex of the lion is ab initio indeterminate. The wave function for the lion is hence a superposition of the gender eigenstate for a lion and that for a lioness. We lay these eigenstates out flat on the ground and orthogonal to each other. Since the (male) lion has a distinctive mane, the measurement of sex can safely be made from a distance, using binoculars. The lion then collapses into one of the eigenstates, which is rolled up and placed inside the cage.
2.4 The nuclear physics method
Insert a tame lion into the cage and apply a Majorana exchange operator [6] on it and a wild lion.
As a variant let us assume that we would like to catch (for argument's sake) a male lion. We insert a tame female lion into the cage and apply the Heisenberg exchange operator [7], exchanging spins.
2.5 A relativistic method
All over the desert we distribute lion bait containing large amounts of the companion star of Sirius. After enough of the bait has been eaten we send a beam of light through the desert. This will curl around the lion so it gets all confused and can be approached without danger.
3. Experimental Physics Methods
3.1 The thermodynamics method
We construct a semi-permeable membrane which lets everything but lions pass through. This we drag across the desert.
3.2 The atomic fission method
We irradiate the desert with slow neutrons. The lion becomes radioactive and starts to disintegrate. Once the disintegration process is progressed far enough the lion will be unable to resist.
3.3 The magneto-optical method
We plant a large, lense shaped field with cat mint (nepeta cataria) such that its axis is parallel to the direction of the horizontal component of the earth's magnetic field. We put the cage in one of the field's foci . Throughout the desert we distribute large amounts of magnetized spinach (spinacia oleracea) which has, as everybody knows, a high iron content. The spinach is eaten by vegetarian desert inhabitants which in turn are eaten by the lions. Afterwards the lions are oriented parallel to the earth's magnetic field and the resulting lion beam is focussed on the cage by the cat mint lense.
[1] After Hilbert, cf. E. W. Hobson, "The Theory of Functions of a Real
Variable and the Theory of Fourier's Series" (1927), vol. 1, pp 456-457
[2] H. Seifert and W. Threlfall, "Lehrbuch der Topologie" (1934), pp 2-3
[3] According to the Picard theorem (W. F. Osgood, Lehrbuch der
Funktionentheorie, vol 1 (1928), p 178) it is possible to catch every lion
except for at most one.
[4] N. Wiener, "The Fourier Integral and Certain of its Applications" (1933),
pp 73-74
[5] N. Wiener, ibid, p 89
[6] cf e.g. H. A. Bethe and R. F. Bacher, "Reviews of Modern Physics", 8
(1936), pp 82-229, esp. pp 106-107
[7] ibid
4. Contributions from Computer Science
4.1 The search method
We assume that the lion is most likely to be found in the direction to the north of the point where we are standing. Therefore the REAL problem we have is that of speed, since we are only using a PC to solve the problem.
4.2 The parallel search method
By using parallelism we will be able to search in the direction to the north much faster than earlier.
4.3 The Monte-Carlo method
We pick a random number indexing the space we search. By excluding neighboring points in the search, we can drastically reduce the number of points we need to consider. The lion will according to probability appear sooner or later.
4.4 The practical approach
We see a rabbit very close to us. Since it is already dead, it is particularly easy to catch. We therefore catch it and call it a lion.
4.5 The common language approach
If only everyone used ADA/Common Lisp/Prolog, this problem would be trivial to solve.
4.6 The standard approach
We know what a Lion is from ISO 4711/X.123. Since CCITT have specified a Lion to be a particular option of a cat we will have to wait for a harmonized standard to appear. $20,000,000 have been funded for initial investigations into this standard development.
4.7 Linear search
Stand in the top left hand corner of the Sahara Desert. Take one step east. Repeat until you have found the lion, or you reach the right hand edge. If you reach the right hand edge, take one step southwards, and proceed towards the left hand edge. When you finally reach the lion, put it the cage. If the lion should happen to eat you before you manage to get it in the cage, press the reset button, and try again.
4.8 The Dijkstra approach
The way the problem reached me was: catch a wild lion in the Sahara Desert. Another way of stating the problem is:
Axiom 1: Sahara elem deserts
Axiom 2: Lion elem Sahara
Axiom 3: NOT(Lion elem cage)
We observe the following invariant:
P1: C(L) v not(C(L))
where C(L) means: the value of "L" is in the cage.
Establishing C initially is trivially accomplished with the statement
;cage := {}
Note 0:
This is easily implemented by opening the door to the cage and shaking
out any lions that happen to be there initially.
(End of note 0.)
The obvious program structure is then:
;cage:={}
;do NOT (C(L)) ->
;"approach lion under invariance of P1"
;if P(L) ->
;"insert lion in cage"
[]not P(L) ->
;skip
;fi
;od
where P(L) means: the value of L is within arm's reach.
Note 1:
Axiom 2 ensures that the loop terminates.
(End of note 1.)
Exercise 0:
Refine the step "Approach lion under invariance of P1".
(End of exercise 0.)
Note 2:
The program is robust in the sense that it will lead to
abortion if the value of L is "lioness".
(End of note 2.)
Remark 0:
This may be a new sense of the word "robust" for you.
(End of remark 0.)
Note 3:
From observation we can see that the above program leads to the
desired goal. It goes without saying that we therefore do not have to
run it.
(End of note 3.)
(End of approach.)
For other articles, see also:
A Random Walk in Science - R.L. Weber and E. Mendoza
More Random Walks In Science - R.L. Weber and E. Mendoza
In Mathematical Circles (2 volumes) - Howard Eves
Mathematical Circles Revisited - Howard Eves
Mathematical Circles Squared - Howard Eves
Fantasia Mathematica - Clifton Fadiman
The Mathematical Magpi - Clifton Fadiman
Seven Years of Manifold - Jaworski
The Best of the Journal of Irreproducible Results - George H. Scheer
Mathematics Made Difficult - Linderholm
A Stress-Analysis of a Strapless Evening Gown - Robert Baker
The Worm-Runners Digest
Knuth's April 1984 CACM article on The Space Complexity of Songs
Stolfi and ?? SIGACT article on Pessimal Algorithms and Simplexity Analysis
Go back to Uberkoder's Jokes page.