# Occam's razor



## Lisa (Jun 4, 2007)

Thanks to heretic888 for his response in this thread, it brought me to explore Occam's razor a little further.

Wikipedia explains Occam's razor as:

The principle states that the explanation of any phenomenon should make as few assumptions as possible, eliminating, or "shaving off," those that make no difference in the observable predictions of the explanatory hypothesis or theory.  The principle is often expressed in Latin as the *lex parsimoniae* ("law of parisonomy" or "law of succinctness")

If we use Occam's razor that uses the idea that the simplest solution is usually the best one, how does one explain their spirituality and their beliefs in things they can not "prove"??


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## mrhnau (Jun 4, 2007)

Lisa said:


> If we use Occam's razor that uses the idea that the simplest solution is usually the best one, how does one explain their spirituality and their beliefs in things they can not "prove"??


The simplest solution does not always imply the correct solution, nor does it imply any statement regarding proof, at least from my understanding.


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## Blotan Hunka (Jun 4, 2007)

*Ellie:* Occam's Razor, the basic scientific principle. And it says... all things being equal, the simplest explanation tends to be the right one.
*Palmer: *Makes sense to me.
*Ellie:* So what's more likely--thank you.
*Palmer:* You're welcome.
*Ellie:* ...that an all-powerful mysterious god created the universe and then decided not to give any proof of its existence, or that it simply doesn't exist at all, and that we created him so that we wouldn't have to feel so small and alone?
*Palmer:* I don't know. I couldn't imagine living in a world where God didn't exist. I wouldn't want to.
*Ellie:* How do you know you're not deluding yourself. I mean, for me... I need proof.
*Palmer:* Proof. Did you love your father?
*Ellie:* What?
*Palmer:* Your dad, did you love him?
*Ellie:* Yes, very much.
*Palmer:* Prove it.

From the movie Contact.

An interesting movie exploring the differences and similarities between science and faith.


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## Callandor (Jun 4, 2007)

Lisa said:


> If we use Occam's razor that uses the idea that the simplest solution is usually the best one, ...


Usually... but not always.


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## Andrew Green (Jun 4, 2007)

I'd claim that Occam's Razor is basically a flawed concept to use in such a situation.  It works when looking at simple things, but right now I don't think our scientific knowledge points to a "simple" in terms of intuitive universe.  Theories like Quantum Mechanics and String theory which deal with the smallest (simplest) building blocks of everything are not simple in the sense most people mean by the word.

Nor is the question of the nature of and creation of the universe likely to have a simple answer.

Simplicity is also a misleading concept.  The simplest explanation to cosmology is basically earth at the center of the universe, stars a fixed distance away on a giant sphere and everything revolving around us.  With the naked eye and basic observations that is by far the simplest explnatation, in order to disprove it you need to bring in more complex things, like telescopes and more accurate measuring devices.  So which is the simpler explnatation?

Of course Occam really said that etntities should not be multiplied uneccessarily, and we could then claim that once the telescope was introduced it became neccessary to expand our explanation.

That really is the core of it.  Don't complicate your explanations of observations if you don't need to.  It says nothing about truth of a theory, just which is best.

So back to the stars, if your goal is sea navigation, then the best explanatation may very well be, stars are fixed, we are stationery and in the middle.  There is no need to complicate it beyond that.  That doesn't make it true, just "best" for the observations being made.


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## exile (Jun 4, 2007)

mrhnau said:


> The simplest solution does not always imply the correct solution, nor does it imply any statement regarding proof, at least from my understanding.



But what Ockham's Razor does give you is the default or null hypothesis. If you have a set of alternatives to cover a particular set of observations, the hypothesis which has the fewest number of components covering that set of data is, methodologically speaking, the one which has preferred status. The reason is simple: _the simplest hypothesis is going to be the one which is most vulnerable to being falsified._ Having fewer `moving parts', it has fewer resources available to evade counterexamples. The more complex the theory is, the more apparatus it can recruit in the face of `apparent' counterexamples. 

So take two hypotheses X and Y, where Y properly includes the resources of X . Suppose that the X happens to correspond to the reality we assume holds external to our own desires, beliefs and preferences. Since Y contains X, Y will not be falsified by any observations we can makeand yet, by hypothesis, it is incorrect insofar as it assumes that the extra material it contains over and beyond X is part of the reality it seeks to account for. Moreover the extra material could in principle allow Y to account for a number of phenomena that are never actually observed, which X itself could not give an account of. Hence Y is less successful in giving an account of why the world is as we observe, since it allows for possibilities that are never realizeda fact which it must remain silent about, but which X immediately explains.

Now assume that we have the same X and Y, and suppose that it's _Y_ that corresponds to that external reality. In that case, X will be fail to provide an account for those aspects of reality which correspond to the components of Y which are not part of X. Hence we will be able to jettison X, the false hypothesis, as soon as we accumulate sufficient data.

The difference in the two situations is that a more complex false hypothesis incorporating a correct simpler hypothesis can never be falsified, whereas a simpler false hypothesis which is part of a more complex correct hypothesis can be straightforwardly falsified. Hence, methodologically, the only way to arrive at the correct hypothesis is to start from the simplest theory that accounts for the available data and increase the range of observation until one encounters a contraindication. This may or may not actually suffice to falsify the simpler hypothesis, but if it does, then the next most simple hypothesisthe one only more complex enough than the simplest one to account for the problematic dataachieves the priviliged status accorded by Ockham's Razor. And so on. 

Application of this approach in a variety of sciences has repeatedly shown that earlier, `gold-standard' hypotheses and the theories that provide interpretations for these hypotheses are not actually wrong, but rather limiting cases of the hypotheses and theories which supplant them in the face of novel, often baffling phenomena. The array of independent domains of evidence which are correctly predicted by modern physical theories identifies these theories as the gold standard of our understanding of that vast reality beyond our senses which we will never have direct access to, but which we can capture abstract models of by the exercise of observation and reason.


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## Steel Tiger (Jun 4, 2007)

exile said:


> But what Ockham's Razor does give you is the default or null hypothesis. If you have a set of alternatives to cover a particular set of observations, the hypothesis which has the fewest number of components covering that set of data is, methodologically speaking, the one which has preferred status. The reason is simple: _the simplest hypothesis is going to be the one which is most vulnerable to being falsified._ Having fewer `moving parts', it has fewer resources available to evade counterexamples. The more complex the theory is, the more apparatus it can recruit in the face of `apparent' counterexamples.
> 
> So take two hypotheses X and Y, where Y properly includes the resources of X . Suppose that the X happens to correspond to the reality we assume holds external to our own desires, beliefs and preferences. Since Y contains X, Y will not be falsified by any observations we can make&#8212;and yet, by hypothesis, it is incorrect insofar as it assumes that the extra material it contains over and beyond X is part of the reality it seeks to account for. Moreover the extra material could in principle allow Y to account for a number of phenomena that are never actually observed, which X itself could not give an account of. Hence Y is less successful in giving an account of why the world is as we observe, since it allows for possibilities that are never realized&#8212;a fact which it must remain silent about, but which X immediately explains.
> 
> ...


 
Yeah! What he said! What did he say?


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## exile (Jun 4, 2007)

Steel Tiger said:


> Yeah! What he said! What did he say?



C'mon, you know what I'm saying!! 

If it's true that 

_Robin is a spy_

corresponds to everything we know about Robin's behavior, 

then it's also true that 

_Robin is a spy and exactly seven completely undetectable entities are present in every shopping line Robin is in_

corresponds to exactly the same data about Robin's behavior...

Hell, I fell for it. You're just funnin' me, ST!


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## Callandor (Jun 5, 2007)

Steel Tiger said:


> Yeah! What he said! What did he say?


Dunno either, but it sounds right.


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## Lisa (Jun 5, 2007)

Steel Tiger said:


> Yeah! What he said! What did he say?





exile said:


> C'mon, you know what I'm saying!!
> 
> If it's true that
> 
> ...





Callandor said:


> Dunno either, but it sounds right.



Occam's razor is, simply put, the KISS theory.

*K*eep *I*t *S*imple *S*tupid...


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## heretic888 (Jun 5, 2007)

Actually, Occam's Razor is pretty simple enough (no pun intended).

If you have two explanations that can equally account for the same observations (or datum), the explanation that requires the fewer hypotheses to support it is most likely the correct one. That's it.

I don't really buy into the whole 'simple' versus 'complex' angle, because to me it leads to imprecise language and understanding. Parsimony has to do with number of hypotheses, so if that's what you mean by 'complexity' so be it.

A few points I'd like to elaborate:

1) If a more 'complex' explanation accounts for the evidence better than a more 'simple' explanation, then Occam's Razor no longer applies (because there is a disparity in explanatory power between the two). Parsimony is only relevant if two explanations can equally account for all the available evidence.

2) People actually use parsimony all the time. Most people take it for granted that the less 'complex' (i.e., fewer hypotheses) explanation is probably the correct one for most things (i.e., when I was blinded a moment ago, was it because I looked up into the sun or because an undetectable alien projected a mind probe into my brain?). Comments like "well, parsimony isn't always right!" or "the simplest explanation isn't always the best one!" are true enough in and of themselves, but they tend to be directed toward personal beliefs rather than general methodology (i.e., people have no problem discarding the myths of Zeus and Heracles as fables, but 'magically' the same parameters do not apply to Biblical tales). There is almost always Special Pleading behind the critique of parsimony.

I think Occam's Razor is invaluable because it really cuts through the intellectual dishonesty, special pleading, and cognitive double-standards that human beings regularly set up for themselves.


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## Xue Sheng (Jun 5, 2007)

And her all these years I thought Occam's razor was a Gillette


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## exile (Jun 5, 2007)

heretic888 said:


> Actually, Occam's Razor is pretty simple enough (no pun intended).
> 
> If you have two explanations that can equally account for the same observations (or datum), the explanation that requires the fewer hypotheses to support it is most likely the correct one. That's it.



That's the content of O's R, sure enough; but the reason why O's R is a crucial methodological constraint is just that unless you assume the most restricted set of hypotheses consistent with the fact, you have no way to tell whether some of the hypotheses you _do_ assume are unmotivated by observation. If hn denotes hypothesis n, and then you assume A={h1,...h10} because this set of hypotheses is consistent with observation, but there is a simpler story B={h1,...h5} which will do the same work, then the data involved will not contradict A, in spite of the fact that there is no justification for h6 through h10. So even though B may in principle be the complete truth, you'll never have any reason to reject A, although nothing supports h6 through h10. But if you assume B, then the appearance of anything any of h6 through h10 are needed for shows you (in the ideal case) that B cannot be right (since it lacks at least one crucial hypothesis). So you are in effect required to assume B over A because if B is wrong, it'll show; but if you assume A, when B is correct, you'll never have any reason based on observation to reject A.

That's why considerations of falsification and confirmation pretty much _drive_ you to O's R&#8212;they make it clear _why_ it is that the minimal account of the given data set has pride of place.



heretic888 said:


> If a more 'complex' explanation accounts for the evidence better than a more 'simple' explanation, then Occam's Razor no longer applies (because there is a disparity in explanatory power between the two). Parsimony is only relevant if two explanations can equally account for all the available evidence.



Of course; O's R is always evaluated with respect to a fixed set of observations. 



heretic888 said:


> I think Occam's Razor is invaluable because it really cuts through the intellectual dishonesty, special pleading, and cognitive double-standards that human beings regularly set up for themselves.



The problem is, in practice O's R isn't so easy to apply. Because, for example, sometimes what looks like counterevidence turns out not to be; it's rather that there is a hidden causal factor interacting with your simplest hypothesis which is consistent with that hypothesis, but which creates seemingly disconfirming data. The discovery of the planet Neptune, based on perturbations in the orbit of Uranus which were inconsistent with classical mechanics, may be the most famous and certainly one of the clearest examples of this sort of thing (see http://en.wikipedia.org/wiki/Neptune, e.g.). So often, when two hypotheses are in disagreement in science, what one finds is that one of them, which appears contraindicated, is nonetheless maintained by its supporters,  on the grounds that there's an alternate account of the anomaly which is claimed to be independently justified. And then you have to pursue the credibility of the alternative causal hypothesis. In this way, things can get very complex in a hurry...


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## Andrew Green (Jun 5, 2007)

heretic888 said:


> If you have two explanations that can equally account for the same observations (or datum), the explanation that requires the fewer hypotheses to support it is most likely the correct one. That's it.



I'm going to disagree a little here, I think this is a minor misunderstanding of the principle, at least as I read it.

It is in picking the "best" explanation, not the most correct one.  The best is not always the correct one, even when a more correct one is available.

Above I gave the example of navigation and assuming the earth is fixed with other bodies rotating around it.

Another example would be using Newtonian physics for calculations, despite Relativity being "more correct"

Or treating light as either a wave or a particle, depending on your goal.

To me Occam's razor is about practicality, not truth.


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## heretic888 (Jun 5, 2007)

exile said:


> The problem is, in practice O's R isn't so easy to apply.



Sometimes it is. Most of the time its not.

Like I stated in my first post, most people use Occam's Razor _all_ the time, in their day-to-day observations. When I look up into the sun and am temporarily blinded, is it because my eyes are sensitive to the sun's light or is it because a solar alien projected a mind probe into my brain that rendered me temporarily unable to see?? When I can't seem to find my keys in my home, is it because I put them somewhere else or is it because an undetectable gremlin made off with them during the night??

This shouldn't come as a shock to anyone. We use parsimony _every_ day of our lives, on millions of mundane observations that we take for granted.

There are just those odd sacred cows --- almost always tied to religion or supernaturalism --- that certain people refuse to apply Occam's Razor to. They're just "special". Why? Just because. This is an intellectual double-standard to the millions of actions we undertake every day, to be sure.


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## heretic888 (Jun 5, 2007)

Andrew Green said:


> To me Occam's razor is about practicality, not truth.



Nope.

Occam's Razor is about probability, because the "truth" as understood in science does not operate in absolutes (including the absolute I just stated  ).

When all other things are equal, do you go with the answer that has to "prove" (again, something that can't really be done in science, but y'know) one claim or the answer that has to "prove" five claims? 

Well, duh. The answer's obvious. You go with the one that's only dependent on one what-if. Why? Because its a safer bet.

This, of course, is just an analogy and it assumes that all things are indeed equal (which is the only time parsimony is even relevant). But, the point holds. The answer that has the most to prove also has the best chance of being wrong.

As for the nature of "truth" and whatnot, I leave that to the sophists....


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