[flubert]

I figured this was a riff on Jayes. From Chapter 10, section 8 of "Probability Theory: The Logic of Science" (starting on page 329).

     10.8  Mechanics under the clouds

"We are fortunate that the principles of Newtonian mechanics could be developed and verified to great accuracy by studying astronomical phenomena, where friction and turbulence do not complicate what we see. But suppose the Earth were, like Venus, enclosed perpetually in thick clouds. The very existence of an external universe would be unknown for a longtime, and to develop the laws of mechanics we would be dependent on the observations we could make locally.

Since tossing of small objects is nearly the first activity of every child, it would be observed very early that they do not always fall with the same side up, and that all one’s efforts to control the outcome are in vain. The natural hypothesis would be that it is the volition of the object tossed, not the volition of the tosser, that determines the outcome;indeed, that is the hypothesis that small children make when questioned about this.

Then it would be a major discovery, once coins had been fabricated, that they tend to show both sides about equally often; and the equality appears to get better as the number of tosses increases. The equality of heads and tails would be seen as a fundamental law of physics; symmetric objects have a symmetric volition in falling (as, indeed, Cramer and Feller seem to have thought). Of course, physicists continued discovering new particles and calculation techniques – just as an astronomer can discover a new planet and a new algorithm to calculate its orbit, without any advance in his basic understanding of celestial mechanics.

With this beginning, we could develop the mathematical theory of object tossing, dis-covering the binomial distribution, the absence of time correlations, the limit theorems, the combinatorial frequency laws for tossing of several coins at once, the extension to more complicated symmetric objects like dice, etc. All the experimental confirmations of the theory would consist of more and more tossing experiments, measuring the frequencies in more and more elaborate scenarios. From such experiments, nothing would ever be found that called into question the existence of that volition of the object tossed; they only enable one to confirm that volition and measure it more and more accurately.

Then, suppose that someone was so foolish as to suggest that the motion of a tossed object is determined, not by its own volition, but by laws like those of Newtonian mechanics,governed by its initial position and velocity. He would be met with scorn and derision; for in all the existing experiments there is not the slightest evidence for any such influence. The Establishment would proclaim that, since all the observable facts are accounted for by the volition theory, it is philosophically naıve and a sign of professional incompetence to assume or search for anything deeper. In this respect, the elementary physics textbooks would read just like our present quantum theory textbooks.

Indeed, anyone trying to test the mechanical theory would have no success; however carefully he tossed the coin (not knowing what we know) it would persist in showing head and tails about equally often. To find any evidence for a causal instead of a statistical theory would require control over the initial conditions of launching, orders of magnitude more precise than anyone can achieve by hand tossing. We would continue almost indefinitely,satisfied with laws of physical probability and denying the existence of causes for individual tosses external to the object tossed – just as quantum theory does today – because those probability laws account correctly for everything that we can observe reproducibly with the technology we are using.

After thousands of years of triumph of the statistical theory, someone finally makes a machine which tosses coins in absolutely still air, with very precise control of the exact initial conditions. Magically, the coin starts giving unequal numbers of heads and tails; the frequency of heads is being controlled partially by the machine. With development of more and more precise machines, one finally reaches a degree of control where the outcome of the toss can be predicted with 100% accuracy. Belief in ‘physical probabilities’ expressing a volition of the coin is recognized finally as an unfounded superstition. The existence of an underlying mechanical theory is proved beyond question; and the long success of the previous statistical theory is seen as due only to the lack of control over the initial conditions of the tossing.

Because of recent spectacular advances in the technology of experimentation, with increasingly detailed control over the initial states of individual atoms (see, for example,Rempe, Walter and Klein, 1987), we think that the stage is going to be set, before very many more years have passed, for the same thing to happen in quantum theory; a century from now the true causes of microphenomena will be known to every schoolboy and, to paraphrase Seneca, they will be incredulous that such clear truths could have escaped usthroughout the 20th (and into the 21st) century"

http://www.med.mcgill.ca/epidemiology/hanley/bios601/Gaussia...

[mannykannot]

It is an amusing story, but the Venusian-Newtons could show that their principles would allow one to calculate the behavior of non-symmetric objects, and that the statistics of both symmetric and non-symmetric projectiles can be predicted by their theory - and it also explains gyroscopic precession!

[leto_ii]

Great passage!

You may be closer to the source of inspiration, although I feel that Feynman may have been part of it too. Maybe it was a combination of the two :)

I like that Jaynes' alegory highlights really how difficult it may be IRL to move from a simplistic theory to the next level of depth.