Talk:Occam's razor/Archive 4

This is an archive of past discussions about Occam's razor. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

Archive 1

Archive 2

Archive 3

Archive 4

Archive 5

Archive 6

Fleshing out the justification part

I've fleshed out the justification part of this article, incorporating some text from a work of mine. This is (obviously) done with my permission -- Palthrow 02:21, 31 October 2006 (UTC)

Copernican Example

If I'm not misinformed, Copernicus's heliocentric model actually included more epicircles than Ptolemy's did (because he still assumed circular paths), so it was really not simpler. I have understood that this is a made-up after-the-fact example of an application of the razor. I will check this, but if anyone else knows, feel free to correct the article. Kronocide 21:55, 11 February 2007 (UTC)

You're right. Copernicus' model was largely no simpler than Ptolemy's, and almost as inaccurate. Copernicus was working with bad observational data from the Ancients and made his model considerably more complex than it need have been in order to accomodate this data. The claim that the Copernican model was simpler is one of those questionable examples that philosophers of science love to come up with, but which has little grounding in reality -- Palthrow 17:12, 12 February 2007 (UTC)

In Copernicus's defense as long as he stuck with circles it was going to be a complicated mess. The genius of Kepler, and one could say the science of Kepler, was to realize that one could obtain a better fit by going with ellipses even though it contradicted his earlier assertions that the heavens would only use perfect spheres. He did this not because it was "simpler" but because it did a better job of accounting for the much more accurate data he obtained from Tycho Brahe. In the end it was not considerations of what was "simple", "perfect" or "unnecessary", but which did the better job of accounting for nature as it could be observed. Perhaps the earlier models would have been better if the data of the ancients was as good as Brahe's. Kepler was doing science because he abandoned his notions of "perfection" and "simplicity" and tried to find the explanation that best accounted for the data. And it was later astronomers like Halley that saw just how good a job Kepler's explanation did of predicting the ephemerides before the fact when the predictions made from the Copernican system were no better than those of the Ptolemaic system. Gkochanowsky (talk) 22:30, 17 December 2007 (UTC)

An astronomer turned historian (can't remember his name, and he wrote a book with a title that goes something like "The book nobody read") over more than a decade managed to examine a large percentage of the copies of Copernicus's Revolutionibus. And what he discovered is that the parts of the book that appeared to be the most heavily read and notated were in the rear of the book which was dedicated to calculating ephemerides. Apparently the interest in the book had little to do with any presumed reduction in entities (Ockham’s razor) and had more to do with the simpler calculations used to produce the ephemerides. I can image just looking at the back portion of the Principia how much of a pain in the ass those calculations were and absolutely necessary if you were the court mathematician charged with creating the astrological charts. Gkochanowsky (talk) 02:33, 7 June 2008 (UTC)

Chaos Theory and Ockham's Razor

There are not really that many anti-razor theories that stand up to criticism, and often are flawed with the same limitations as the razor itself.

Except for Chaos theory. Using a common restatement of the Razor:

"When explaining a phenomena, the simplest explanation is preferable."

Well, according to Chaos Theory, the simplest explanation may be preferable ... but it is almost definitely INCOMPLETE. This puts a "logical rule-of-thumb" in an Either/Or conflict with a branch of mathematics that has and still does stand objective scrutiny. Either the Razor is true, in which case Chaos theory is false. Or Chaos Theory is true and the Razor is, while useful, almost assured to lead one to a false, or at least an incomplete, conclusion.

Ultimately this is the flaw with the Razor. And the leading cause of its misuse. Just because the simplest explanation is "prefered" ... by NO means does that imply it is true ... or even complete. And often, it is very likely that it is untrue/incomplete.

The fatal flaw with the Razor, is that *simplest* and *preferable* are both subjective. There are many of the above examples when discussing the use of the Razor to consider the existence of God by BOTH sides. This is because what is *simplest* and *preferable* depends upon the point of view of the person speaking before they even USE the razor. Any logical premise that has two subjectives in it, is by default highly flawed.

What it is:

In science, it is a useful guide to help lead the experimentation on fewer paths that are *likelier* to provide reliable results. In logic, it is almost without a doubt not useful except as a tool to keep the thinker focused. But for truth, or for any possible use as a methodolgy to *decisevely* show when an idea should or should not be considered? Worthless.

64.167.48.200 22:21, 12 February 2007 (UTC) Chrome

I don't see how chaos theory applies to Occam's Razor in any way. The main focus of chaos theory is that some complex patterns cannot be reduced to linear patterns, at least not in the obvious straightforward sense we are used to. The only way I can see this being relevant at all is if you accept precisely the interpretation of the razor that the article points out again and again as an oversimplification. If you're going that way I don't see a reason to go all the way into higher mathematics. If the razor fails on the account of the wondrous, incredibly complex nature of chaos theory defying the simplicty of how the world is supposed to work from the limited perspetive of the human race, it just as well may fail on the account of 64/16 not equalling 4 by cancelling out the 6s because the wondrous, incredibly complex nature of the fundamental theorem of arithmetic defying the simplicity of how the world is supposed to work from the limited perspective of a misguided first-grader.

As for the razor ultimately relying on subjective opinions, I beg to differ. A crucial aspect of the Razor and of logic in general is precisely that you cannot simply pick some confabulated opinion and say, "well, I hereby define this PREFERABLE and SIMPLE", magically making it thus in the process; and it should go without saying that ongoing disputes on any subject can result from a plenthora of different catalysts that have nothing to do with logical difficulties of determining which side has the better case, if any. Theories become better by taking less for granted - minimising needed axioms and "self-evident truths", and then in turn minimizing gratuitous improbabilities within the tangled webs of belief they weave. "There is an all-powerful, conscious being, so it decides to create the world and then men and so on" is NOT on the same starting line as "there is lots of condensed matter, it goes boom, and generally speaking everything else follows". Consider this being - How and why is it conscious, given a simplistic definition of consciousness? Why would it decide to create the world and men and so on rather than do any of the myriad of other things it could have decided to do? Not all axiomatic frameworks were born equal. That some people insist they were is proof of something, but a problem with Occam's razor is not it. --AceMyth 21:07, 13 February 2007 (UTC)

Thankyou Ace. You stated the exact word I was attempting to use. As this is a discussion I won't go back and re-edit what I orignally wrote.

Ockham's razor is an oversimplification.

As far as subjectivity. Yes there is. Let us take a non-religious example, to keep those ideoligies out.

I was reading on Science.com a discussion of experts regarding life on other planets. One scientist stated that while it is perfectly concievable that life could have occurred on other planets, what little we know about life in general suggests that the chances of such life having the perfect environment to develop into intelligent life-forms is statistically improbable. Another scientist countered by stating that according to Ockham's Razor, since it simpler to believe we are not alone, due to the unbelievability that we are a unique circumstance, then there is intelligent life on other planets, thus the statistics only show how little we know about biology. Of course, the big problem there is that Ockham's Razor is a tool not a proof. So this isn't a perfect example.

A final problem with Ockham's Razor -- actually I think *Danger* is a better word -- could be stated as the "Broken Radio Syndrome" (I made this term up from a science fiction story I once read in an old Isaac Asimov magazine I got a bunch of years ago). It can limit you to certain thoughts, kind of like a radio that has the dial broken so the user can only use the buttons. There is lots of music out there ... but they can never hear it.

An example: There is no reason to believe that the moon has any effect on Human Birth Patterns. Statistically, since a woman has her period three days a month, the likelihood of her having her period on any one of the three days of the full-moon would be a around 11% (3/28). Yet several studies have shown that in fact 27%-29% of women have a period on those days. Now that is statistically significant, too significant to ignore. And since women are much more likely to get pregnant 2 weeks after their period. The moon DOES have an effect on Human Birth Patterns.

Now, the counter to this argument is that once we know these statistics, Ockham's Razor would require us to include it.

The problem is, Ockham's Razor would prevent us from ever even looking -- we would never see it. Because there would never be any reason for us to even consider such a connection. But as I said, this is a *Danger*, more in the usage of the razor versus the razor itself.

And probably, this is more my concern regarding the Razor, and how it is taught in colleges at the undergraduate levels. There are traps that using the Razor can lead one into ... traps that are there due mostly to human limitations.

The above example also is an interesting variation of Chaos Theory, the moon is not linearly connected to the concept of Human Birth Patterns.

207.214.111.136 13:14, 19 February 2007 (UTC) Chrome

I agree, "Ockham's Razor" is of little use in science. Perhaps it plays some important role in philosophy but I am not sure you could the philosophers to agree on it. Gkochanowsky (talk) 02:41, 7 February 2008 (UTC)

Well, you always need some sort of principle of parsimony in order to constrain theories. Otherwise, we might just as well maintain that "acceleration of an object is proportional to the force applied, and inversely proportional to the mass of the object, unless that object is a pink space elephant" -- which is equally well confirmed. The need for a parsimony principle in science can easily be demonstrated. Let us suppose that a series of observations give us the following values for two related variables, x and y:

x: 0 1 2 3 4 5 6

y: 0 2 4 6 8 10 12

Interpret these numbers as representative of some scientific measurements we have obtained. A formula immediately suggests itself concerning the relationship between the two variables:

y = 2x.

This formula yields data in accordance with the evidence obtained so far, and should allow us to extrapolate the value of y based on any value for x, e.g. x = 7 -> y = 14. However, the following formula also satisfies our criterion:

B) y = x7 -21x6 +175x5 -735x4 +1624x3 -1724x2 +722x

If we compare formulas A and B, it is mathematically clear that they account equally well for the evidence while making drastically different projections concerning the value of y for values of x other than the ones obtained. Which theory is more plausible? -- Palthrow (talk) 13:28, 7 February 2008 (UTC)

This justification of Ockham’s always stupefies me. Apparently we need a principle to discard things that no one thinks exist until of course someone thinks it exists. If you had applied Ockham’s to the neutrino we would not have discovered it because at the time it was the equivalent of "a pink space elephant". The only criterion that science uses to prefer one explanation over another is prediction, observation and experiment on nature. If you apply Ockham’s to itself you would find that it is superfluous when it comes to science. Your example is also stupifying since in science if one explanation accounts for and predicts more than another than that is the preferred explanation. I don't need Ockhams to discard an expanation that is correct for only one observation and wrong for the rest when there is an explanation that does a better job on more obseravations. You can play with your equations all you like. Until you go to nature you will not know. I have often found that theorists are brilliant before the experiment is done. And usually not so brilliant after the experiment is done. Gkochanowsky (talk) 23:53, 13 May 2008 (UTC)

Mechanical scientist? I don't think so

One possible conclusion from mixing these concepts - Kolmogorov complexity and Occam's Razor - is that an ideal data compressor would also be a scientific explanation/formulation generator. A compressed logarithm table would be output as the logarithm formula and the data set's intervals; a compressed falling object's space x time graphic would be output as the gravity formula for the involved objects, and so forth. Though such a compressor does not seem practical to manufacture in the foreseeable future, the implications of its conception would be dramatic.

The problem the editor describes is undecidable, as the Kolmogorov complexity of a given string is in general undecidable. Imagine that you want to build this mechanical scientist. You get a set of datapoints of size S, so you merrily go about testing all algorithms with length less than S (plus however many characters it takes to write print(""); in your language). Except it turns out that algorithm number 13 doesn't terminate. Oops. You get stuck in an infinite loop. No worries, you say, I'll just check all the terminating algorithms first. But to do so, you would need to know which ones terminate. And you can't, because of the Halting problem. This is not a watertight proof, I think, but it should provide the intuition.

The good news is that you can enumerate all algorithms that provably terminate in certain logics, and I think that you use this approach to extend the class of algorithms you are looking for to one large enough to encompass most (all?) of known science. But in general, this is exactly the reason why Wikipedia articles ought to cite sources, and not contain random ideas you came up with under the shower this morning. That's all. —The preceding unsigned comment was added by Sjeng (talk • contribs) 02:36, 14 February 2007 (UTC).

I see your point (I'm not responsible for that part of the article, just for minor rephrasing). Though I'd like to point out that human scientists are as mechanical as anything. --AceMyth 16:05, 14 February 2007 (UTC)

This in no way contradicts the point, because humans do not have a deterministic decision algorithm for coming up with the most compact theory for a set of data points in finite time either. Rather, they try to reach the most compact theory consistent with the data so far by a process of trial and error that we call science (which is, or ought to be, if they are honest, further complicated by the continuous arrival of more data). In particular cases they may even be able to show that a scientific theory is the most compact possible (although they'd probably prefer to debate indefinitely what universal Turing machine to use for defining Kolmogorov complexity), but in general all we now is that the present understanding is the best we've got so far. Machines can be built that try to have a go at this theory-building problem, just like we do, with no guarantee of success even in the long run, and in fact people try to do this. It used to be called artificial intelligence, but now machine learning seems more fashionable. These machines (or rather, programs) are better than humans in some well-defined learning domains, but we still beat them by far when it comes to versatility. Sjeng 22:56, 17 February 2007 (UTC)

AID -misuse of the razor - deciding which is simpler

Some users have noted that the arguments about God are a misuse of the razor--both theories don't predict the same thing so "all things are NOT equal". Occam is commonly missapplied in this way, usually by psuedoskeptics.

Deism presumably makes the same predictions.1Z 20:18, 28 February 2007 (UTC)

Deism makes no predictions about the here-and-now other than 'It's God's will.'WolfKeeper 20:28, 28 February 2007 (UTC)

In the context of theology "prediction" means "retrodiction".1Z 21:31, 28 February 2007 (UTC)

The article needs to mention the problem of controversy over which explanation is actually the simpler one. Occam is referenced all over wiki paranormal articles. . . ie. which is simpler mass hallucination or the extraterresrial hypothesis?

Maybe this article could benefit from the Article Improvement Drive. Puddytang 21:27, 22 February 2007 (UTC)

Trivia

I'd like the people here who are informed and concerned about this page to consider the value of the "Trivia" section at the bottom of the page. In my opinion it is the worst kind of fancruft (eg, quotes from the Simpsons that not even Simpsons fans would care about) and should be removed entirely from a serious and useful article. It's not my article, though; I'll leave it up to y'all.. 70.121.157.246 16:21, 19 March 2007 (UTC)

Trivia could easily be renamed "Ockham's Razor in Popular Culture" after merging the first point into the article body. [unsigned/undated]

Occam's view of the razor and Christianity

Currently, the last paragraph in the Religion section reads:

Considering that the razor is often wielded against theism, it is somewhat ironic that Ockham himself believed in God. He apparently considered Christianity to be outside the scope of his rule, once writing, "No plurality should be assumed unless it can be proved (a) by reason, or (b) by experience, or (c) by some infallible authority." The last clause "refers to the Bible, the Saints and certain pronouncements of the Church" (Hoffmann 1997).

I corrected this to read as follows:

Considering that the razor is often wielded as an argument against theism, it is somewhat ironic that Ockham himself was a theist. He considered some Christian sources to be valid sources of factual data, equal to both logic and sense perception. He wrote, "No plurality should be assumed unless it can be proved (a) by reason, or (b) by experience, or (c) by some infallible authority"; referring in the last clause "to the Bible, the Saints and certain pronouncements of the Church" (Hoffmann 1997). In Ockham's view, an explaination which does not harmonize with reason, experience or the aforementioned sources, cannot be considered valid.

However, I was reverted with statement "requires citation". I'm confused as to how my change requires a citation -- the citation which supports my change is given in the above by Ockham himself, as expounded by Hoffman.

"No plurality should be assumed unless it can be proved..." (a general statement of the principle of the razor) "...by [the Bible, the Saints and certain pronouncements of the Church]" (Christian sources of knowledge). In other words, don't multipy reasons / causes / components / etc unnecessarily; where necessity is determined by harmony not only with reason and experience, but in Ockham's view, with Christian sources of knowledge as well.

Please explain why any further citation is needed to correct the misrepresentation of Ockham as placing Christianity outside the razor, when it is clear from his own words that he placed Christianity as a source of knowledge which informs the application of the razor. —The preceding unsigned comment was added by 64.234.1.144 (talk) 07:38, 10 April 2007 (UTC).

I think your edit does a better job of explaining Ockham's views (i.e., Christianity was a part of his razor, not an exception), so I've restored your wording. Thanks for the edit and the comment. — Elembis (talk) 17:18, 10 April 2007 (UTC)

Science by Razor Alone?

There is a reference to the use of Ockham's Razor for preferring the Copernican model over the Ptolemaic model. This may become yet another fine example where philosophers in their determination to show how philosophy drives science got both the history and the science wrong. It would be great if philosophers would stick to what they know best, philosophy, and leave science to the scientists and history to the historians.

It turns out that what convinced people was the Rudolphin tables created by Kepler. And not because they were simpler but because they did a much better job at computing the ephemeredes than either the Ptolemaic or Copernican system. Philosophers completely ignore that the Copernican system still included epicycles and they also create a historically inaccurate and false dichotomy by ignoring that there were actually three competing explanations. It would be nice if philosophers actually engaged in scholarship when they try to foist lame philosophical principles like Ockham’s razor onto science and leave science to the scientists and history to the historians. Gkochanowsky 02:56, 31 May 2007 (UTC)

Oh, how I want to get into this argument again. How I yearn to question the quantifications behind the term "better job" and wonder whether perhaps these tables did not really have "KEPLER IS RIGHT" written on them in super special a-priori gospel ink but rather made predictions that were closer to reality and thus appeared more likely, likely as in probable, probable as in math, math as in philosophy with numbers in it. But we've been through this already, I'm afraid, and the article was not affected in any positive way (or, to be fair, at all). As my views on Occam's Razor are such that I don't consider the Ptolemaic model any more a prominent example of its application than any other theory which has ever been thrown into the garbage can of history on grounds of not outright impossibility but rather high improbability, which is most of them really, I don't care much for this example either way- it serves more to highlight the traditional, ontological, almost naive connotations associated with the history of this concept than to demonstrate how or why it holds water in the context of modern science. If you can find citations for your claim- that is, that ontological simplicity had nothing to do with the dismissal of those aforementioned inferior astronomical models by the questionably-fickle scientific consensus- you are more than welcome to pour them into this section and enhance it with another perspective. --AceMyth 03:30, 31 May 2007 (UTC)

Better job in that many years later the Rudolphin tables predicted the positions of the planets much more accurately than those of the Ptolemaic or Copernican systems. They were so accurate that Halley commented on it and took it to Newton because he thought that Kepler was on to something. Also I was incorrect in that there were three competing explanations. There were four. Brahe proposed a system as well. There were probably many more, but not as well known.

But go look for yourself. Some of the information is right here in Wikipedia. The actual history of what happened is far more informative about science, its history and how it works than any lame philosophical principle. Gkochanowsky 23:11, 8 June 2007 (UTC)

Probability theory and statistics

This article is reasonably understandable until the section on "probability theory and statistics," which is somewhat technical and should be clarified for a lay audience. 69.140.164.142 15:21, 22 April 2007 (UTC)

Not to mention that William of Ockham would have no idea what it was. At best it is it's own mathematical claim on reality that it's advocates like to call Ockham's razor. And as far as I can tell they do this for reasons that are not exactly clear to even them. Gkochanowsky 22:30, 30 November 2007 (UTC)

So now Bayes' Theorem is "at best a mathematical claim on reality". I suppose you're implying that reality is at bottom a social, linguistic construct, or something to that extent... -AceMyth 08:36, 3 December 2007 (UTC)

No, I am not making any such statement. To restate it in another way, a Beysian claim should be called just that, not Ockham's razor, since Ockham would have no idea what it was. I have no idea why advocates of Baysian statistics are not willing to attribute it to Bayes. Gkochanowsky 18:23, 4 December 2007 (UTC)

Religion - Occam's Razor supporting theism

Added a brief paragraph mentioning that some people (myself included) view Occam's razor as actually supporting the idea of theism. Is it okay as is, or would a citation or two be preferred? NigelCunningham 05:25, 2 May 2007 (UTC)

Citations are always helpful. Of course, O. himself though the razor was compatible with theism.1Z 21:48, 14 May 2007 (UTC)

Huh. I am extremely interested in what sort of criterion could possibly render intelligent design- intelligent design- a simpler model than anything. Intelligent design makes no predictions, it just looks at whatever already happened and lets the ad-hockery commence, which is exactly not working with Occam's razor. The oh-wow-this-is-so-improbable argument draws its conclusion from the marginal probability being low while completely ignoring the conditional probability being low as well (see Bayesian inference) - I mean, assuming an intelligent designer, what is the probability of a fly? Yeah. --AceMyth 10:47, 16 May 2007 (UTC)

Indeed it is quite parsimonious, and some have termed it a "thought-terminating cliché". (Cladistics is too complicated anyway, too many jawbreakers like plesiomorphy and synapomorphy and such. Created kinds is much simpler. Baraminology is simpler too; check results against scripture, boom, done, go home and relax. Sorry to sound sarcastic.) ... Kenosis 14:31, 18 May 2007 (UTC)

ETA: I removed this because I noticed that the teleological argument for the existence of God is already mentioned earlier in the section. But you mentioned the possibility of citations so if you have some go ahead and plug them there, as currently they're sorely missing. --AceMyth 11:06, 16 May 2007 (UTC)

About moving "Occam" to/from "Ockham"

I notice there was a debate on whether the article should be Occam's razor or Ockham's Razor (notice how the latter has "Razor" capitalized, because Ockham's razor (small "r") is a redirect to Occam's razor). This debate was closed with no consensus. I have notice, too, that this lack of consensus has led to TWO different pages, being edited in parallel. Please, stop that! Choose one friggin name, and make all the other spellings redirects! The present situation is silly. — Isilanes 15:26, 16 May 2007 (UTC)
Not only that, but Talk:Occam's razor redirected to Talk:Ockham's razor while the article remained at Occam's razor. I've moved the talk page (this one) back to the occ spelling, squashing the redirect. — Feezo (Talk) 19:23, 21 May 2007 (UTC)

Good job! — isilanes (talk|contribs) 19:41, 21 May 2007 (UTC)

William of Ockham on Religion

From the Internet encyclopedia of Philosophy:

"At bottom, Ockham advocates simplicity in order to reduce the risk of error. Every hypothesis carries the possibility that it may be wrong. The more hypotheses you accept, the more you increase your risk. Ockham strove to avoid error at all times, even if it meant abandoning well-loved, traditional beliefs. This approach helped to earn him his reputation as destroyer of the medieval synthesis of faith and reason."

"Despite his departures from orthodoxy and his conflict with the papacy, Ockham never renounced Catholicism. He steadfastly embraced fideism, the view that belief in God is a matter of faith alone. Although fideism was soon to become common among Protestant thinkers, it was not so common among medieval Catholics."

And on to various examples, including Ockham going as far as to assert that the concept of the Holy Trinity is a logical contradiction. It seems clear that we have misinterpreted him on the relationship between Religion and Philosophy to the point of attributing to him a view absolutely contrary to the one he actually held. --AceMyth 01:46, 6 June 2007 (UTC)

It is my humble belief that it was not Ockham who was the "destroyer" but that his theory had entitled him to the position. As AceMyth said/implied, Ockham embraced theology and agreed that it was 'acceptable' to use as a means of an answer. Ockham himself became the victim of his own machine, thus personifying other's use in his razor, which was contrary to his beliefs. Re-wording should suffice most of the changes. --FuriousCactus (talk) 19:30, 17 April 2008 (UTC)