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Re: [Phys-l] status of Occam's razor

On 3 Aug 2007, at 09:00, Stefan Jeglinski wrote:

But one major
turning point was that the Copernican system leads to the prediction
that Venus will have phases, and those were observed when the
telescope was invented.

I believe that I can see phases of Venus with the naked eye, under ideal conditions. Assuming this is not my imagination merely because I know it to be true, were there any "heretics" that claimed the same thing before the telescope, thus being another observation that drove the requirement of a new model?

It is the gibbous phases of Venus that distinguish the Copernican models from the Ptolemaic models. In Ptoemaic models Venus is always nearer Earth than is the Sun, and Venus is never seen to extend farther from the Sun than about 47 degrees. Thus crescent phases of Venus can be seen, especially near inferior conjunction where they are indeed perceptible to the unaided eye. In Copernican models Venus passes farther from the Sun and thus can exhibit gibbous phases. It was Galileo's observation of gibbous phases that lent support to the Copernican models.

Occam's razor has nothing to do with settling this question. Indeed it has no place in science; it is merely an aesthetic statement. Empirical evidence is paramount. The principal of causality, for example, is highly appealing for purely aesthetic reasons, but its validity is under close scrutiny lately, I am told. Don't introduce it to students as being scientifically useful.

Leigh

and Gary Karshner wrote:

Don,
The idea of accuracy historically in science is a moving target. In fact I think it is a moving target among our introductory students, but at least we have statistics for a model as to how to handle it. The Copernican theory was simpler on some calculations then the Ptolemaic model, but it is hard estimate which was more accurate. For example Christopher Clavius, sometimes called the last Ptolemaic astronomer, conceded that some calculation using the Copernican system were easier.
Tycho Brahe being an observer had a good grasp of observation error. He use a technique to subdivide his instruments that he knew was not precise but whose errors were less than what he thought he could measure. He even produced an error table to correct these result if he felt it was necessary.
Kepler of course built his laws on Tycho's data. He found that he could fit the Copernican model with this data to within seven minutes of arc, but he felt that Tycho's observations should be accurate to at least a minute of arc and that motivated him to through out epicycles and uniform circular motion and find another curve that would fit the data.
The deviation of the motions of the planets from Kepler's Laws is at most about fifty seconds of arc. I have wondered what if Jupiter had been more massive so the perturbations were the order of a few minute of arc, would Kepler have found his Laws? He was a real stickler for accuracy. Many astronomers would have been very happy to be within 7 minutes of arc or about one fourth the diameter of the moon.

It is important to point out that Kepler only had Tycho's data for Mars to work with. Fortunately Mars is the most eccentric of the planets that were well observed by Tycho (Mercury is hard to see). Tycho was himself a convinced supporter of a Copernican model, but the Tychonic model had a fixed Earth around which both Moon and Sun revolved. The remaining five planets orbited the Sun.

I have recently returned from a trip to Europe. I visited Tycho's observatory (on the island now called "Ven", located now in Sweden) and several other sites (Rostok where he had his famous duel, Prague and sites in its vicinity where he fled from Denmark). There is an excellent museum in Benátky (Czech Republic) where you can actually manipulate an excellent reproduction of one of Tycho's principal instruments. a large sextant which was operated by two observers. This museum is a rare treasure. Only two other English speaking parties had signed this year's guest book before I did, and the museum opened in 2006. Visit these places before you die.

On 08/02/2007 11:09 AM, chuck britton wrote:
> An Historical Question concerning Occam's Razor -
> Devil's Advocate Hat On:
>
> When did the Copernican Theory of our Solar system become as precise
> as the Ptolmeic Theory?
> Did Newton work out the perturbations required - or am I totally
> bonkers in believing someone who claimed that all the cycles and epi-
> cycles DID give more precise predictions than did Copernicus (and
> Kepler)?

(Sorry, I'm recently new to this group.)

Ptolemy's scheme was purely practical. Given elaboration to a sufficiently large number of epicycles one could generate arbitrarily accurate ephemerides. We still do things like this, using series expansions when theory does not exist or is too complicated to implement. A good example is ocean tides. The tide tables you see are generated by using years of data, not by physical theory. There is some input from astronomy that suggests periodic terms that should be looked for and used in the expectation that they will be relatively large and will simplify the harmonic sums that must be done. Still, tides are governed by other factors - distant storms and varying barometric pressure for example - and the most precise measurements will be found to be incapable of being replicated by the series.

It is obvious what the astronomical counterparts are. Tycho was merely the best observer ever at his time. He could better predict planetary positions for purposes, inter alia, of casting more accurate horoscopes! That's what was the motivation for all the Danish investment in Tycho's observatory.

and Joel Rauber wrote:
Al Bachman wrote

| My understanding of Occam's Razor is that it guides the
| choice between EQUALLY VALID models.
| If the simpler model makes incorrect predictions then we
| reject it. (Or question the experimental results more stringently!)

"Validity" is like pregnancy. Theories are either valid or they have been falsified.

This is my understanding as well as to what the current vernacular means
when referencing Occam's Razor. So two models that predict all the data
equally accurately are not necessarily equally valid, given that
"meaning" of Occam's Razor.

Perhaps Occam's razor should only be mentioned in philosophy classes!

I'll finish this by taking it one step farther. I like to ask people whom I wish to engage in conversation "Does the Sun go around the Earth or does the Earth go around the Sun?" I follow the conventional answer with the question "How do you know that?"

I was going to extend this posting, but I think it would be better to leave the questions hanging there. I will give you a hint: a common answer I get to the second question is "Everybody knows that!" To illustrate the inobvious nature of this situation let me point out that the greatest observational astronomer of his time, Tycho Brahe, thought the Sun orbited the Earth, and it is not difficult to reach that conclusion using Occam's razor.

Leigh