Occam’s Razor has lost its edge

[Ivan Seeking]

First, we find in the skeptics dictionary that the concept is not well defined.

The original principle seems to have been invoked within the context of a belief in the notion that perfection is simplicity itself. This seems to be a metaphysical bias which we share with the medievals and the ancient Greeks. For, like them, most of our disputes are not about this principle but about what counts as necessary. To the materialist, dualists multiply pluralities unnecessarily. To the dualist, positing a mind as well as a body, is necessary. To atheists, positing God and a supernatural realm is to posit pluralities unnecessarily. To the theist, positing God is necessary. And so on. To von Daniken, perhaps, the facts make it necessary to posit extraterrestrials. To others, these aliens are unnecessary pluralities. In the end, maybe Occam's razor says little more than that for atheists God is unnecessary but for theists that is not true. If so, the principle is not very useful. On the other hand, if Occam's razor means that when confronted with two explanations, an implausible one and a probable one, a rational person should select the probable one, then the principle seems unnecessary because so obvious. But if the principle is truly a minimalist principle, then it seems to imply the more reductionism the better. If so, then the principle of parsimony might better have been called Occam's Chainsaw, for its main use seems to be for clear-cutting ontology.

http://skepdic.com/occam.html

Next, the concept predates modern physics and is no more valid than 12th century physics.
Consider Occam's original premise:

The original principle seems to have been invoked within the context of a belief in the notion that perfection is simplicity itself

Clearly the credibility of this premise died with QM.

Anyone who understands QM hasn’t studied it long enough

------ RP Feynman

Not only is this concept ill defined and out of date, it is often used as a scientific principle – like F = ma – when it fact it is a philosophical concept; not a scientific law. The use of this concept to rule out a competing theory is only valid to the extent that it is obvious; and without need of the long dead Occam or his nasty old rusty razor. The application of this principle in any practical matter is pseudoscience.

 

[Ambitwistor]

Originally posted by Ivan Seeking
First, we find in the skeptics dictionary that the concept is not well defined.

There are many versions of it; some of them are well-defined (and correspondingly limited in scope), e.g.:

http://quasar.as.utexas.edu/papers/ockham.pdf

Occam's razor, in this view, is a quantitative codification of how people consistently associate beliefs with evidence.

Clearly the credibility of this premise died with QM.

What?

Not only is this concept ill defined and out of date, it is often used as a scientific principle – like F = ma – when it fact it is a philosophical concept; not a scientific law.

Used by who? Scientists know that you can't disprove a theory on the basis of Occam's razor. You can, however, ignore a theory on that basis, if you choose.

The use of this concept to rule out a competing theory is only valid to the extent that it is obvious;

Well, what are you arguing about? Occam was stating the obvious, after all.

The application of this principle in any practical matter is pseudoscience.

Nonsense. It is not "pseudoscience" to choose which of two theories you want to pursue, on the basis of "simplicity" or any other basis, so long as both theories are scientific and not falsified.

For that matter, there is a quantitatively rigorous way in which we may compare the relative probabilities of competing hypotheses (under the assumption that the hypotheses in question are the only explanations, of course -- it's impossible to account for hypotheses that nobody has thought of yet); see the above paper.

 

[selfAdjoint]

I've always thought of OR as a proposed search strategy; don't take up the complex explanations until you have ruled out the simple ones. It surely is not constrained by whatever you happen to be talking about. The notion that it is invalidated by QM strikes me as a nonsequitur, if not a category error.

 

[quartodeciman]

OR is intended to cover real choices between totally identical situations, with no other reasons for preference involved. Sure, choose the simpler alternative. But most theories are not identical, either in method or in the choice of territory to be covered. Most new theories propose to move into distinct new territories. Two other criteria are more important: fecundity (richness of results) and plausibility (soundness of deductions).

 

[Ivan Seeking]

Originally posted by selfAdjoint
I've always thought of OR as a proposed search strategy; don't take up the complex explanations until you have ruled out the simple ones.

In this form it makes perfect sense. This is not the typical language.

The notion that it is invalidated by QM strikes me as a nonsequitur, if not a category error.

I don't see any simple explanations in modern physics. All of our simple expectations failed. This is why we have to discover the laws of physics; why we can't deduce all by logic as the Greeks tried. I see no evidence that we can anticipate the correct answers with our sense of logic or simplicity. To the point that they even exist, all explanations are complex. In fact, in the end - at the deepest levels - we have no answers.

Where is the evidence that simple answers prevail?

 

[Ivan Seeking]

Originally posted by Ambitwistor
There are many versions of it; some of them are well-defined (and correspondingly limited in scope), e.g.:

http://quasar.as.utexas.edu/papers/ockham.pdf

Occam's razor, in this view, is a quantitative codification of how people consistently associate beliefs with evidence.

Used by who? Scientists know that you can't disprove a theory on the basis of Occam's razor. You can, however, ignore a theory on that basis, if you choose.

This assumes all things being equal; in the real world they never are.

Well, what are you arguing about? Occam was stating the obvious, after all.

Occam was really making a religious statement; after all.

Nonsense. It is not "pseudoscience" to choose which of two theories you want to pursue, on the basis of "simplicity" or any other basis, so long as both theories are scientific and not falsified.

Personal choices about research are one thing; dismissing all by way of Occam is another. This is the typical mentality expressed by many students and graduates in the sciences: Explanation A is simpler than B, therefore A must be the correct answer.

I see this usage as utter garbage. In my experience, in the real world the correct explanation is almost never the simple one.

 

[Ambitwistor]

Originally posted by Ivan Seeking
This assumes all things being equal; in the real world they never are.

You don't have to assume "all things equal" to apply Occam's razor.

Occam was really making a religious statement; after all.

Regardless of what Occam's intent was, his principle is still applicable.

Tell me: I have a set of 100 data points that look like a line, except there is a little bit of scatter. I want to fit a curve to it. Do I fit a line, or do I fit a 100th-degree polynomial to it with 100 coefficients? The latter can pass exactly through every data point with no error. Which theory should be preferred: the linear theory or the 100th-degree polynomial theory?

Personal choices about research are one thing; dismissing all by way of Occam is another. This is the typical mentality expressed by many students and graduates in the sciences: Explanation A is simpler than B, therefore A must be the correct answer.

Sorry, Ivan, but you do not speak for scientists. Yes, scientists do dismiss overly complicated theories when simpler alternatives exist, on the basis of Occam's Razor. But that is not because the simpler theory "must be the correct answer".

I see this usage as utter garbage. In my experience, in the real world the correct explanation is almost never the simple one.

The point is that we should not assume more than we have evidence for. If we have many competing theories, all of which explain the data, then the data cannot decide between them. But unless you have a specific reason to prefer one particular theory over any of the others, one should put the greatest degree of belief in the theory that has the fewest free parameters.

I can make up an arbitrarily complex theory to account for any data, but that doesn't mean it's a good theory. Like I said, you can come up with a theory that will explain any finite set of data exactly, by making it complicated enough, but it has no predictive power. It's like epicycles, compared to Kepler's laws.

 

[Ivan Seeking]

Originally posted by Ambitwistor
You don't have to assume "all things equal" to apply Occam's razor.

So we should apply OR when faced with evidence for a more complex hypothesis?


[quoteRegardless of what Occam's intent was, his principle is still applicable.[/quote]

Only to the extent that it is not needed.

Tell me: I have a set of 100 data points that look like a line, except there is a little bit of scatter. I want to fit a curve to it. Do I fit a line, or do I fit a 100th-degree polynomial to it with 100 coefficients? The latter can pass exactly through every data point with no error. Which theory should be preferred: the linear theory or the 100th-degree polynomial theory?

Only to the extent that it is not needed.

Sorry, Ivan, but you do not speak for scientists.

I speak from my own experience...so you speak for all scientists?

Yes, scientists do dismiss overly complicated theories when simpler alternatives exist, on the basis of Occam's Razor.

Overly complicated; when exactly does the "overly" kick in?

But that is not because the simpler theory "must be the correct answer".

I'm glad we agree.

The point is that we should not assume more than we have evidence for. If we have many competing theories, all of which explain the data, then the data cannot decide between them. But unless you have a specific reason to prefer one particular theory over any of the others, one should put the greatest degree of belief in the theory that has the fewest free parameters.

Boloney. They should each be considered on their own merit.

I can make up an arbitrarily complex theory to account for any data, but that doesn't mean it's a good theory. Like I said, you can come up with a theory that will explain any finite set of data exactly, by making it complicated enough, but it has no predictive power. It's like epicycles, compared to Kepler's laws.

Like classical physics compared to QM?

 

[Ambitwistor]

Originally posted by Ivan Seeking
So we should apply OR when faced with evidence for a more complex hypothesis?

We should apply it at all times. For a more complex hypotheses to be more plausible than a simpler one, it has to fit the data considerably better than the simpler hypothesis. If there is enough evidence in favor of the more complex hypothesis, then it will win out.

Only to the extent that it is not needed.

On the contrary, everyone uses it every day, including yourself. If you can't find your keys, do you immediately jump to the conclusion that invisible space aliens teleported into your room and stole them, or do you put more belief in the hypothesis that you misplaced them? Both hypothesis are consistent with all of the evidence, after all, but one of them is simpler than the other.

I speak from my own experience...so you speak for all scientists?

Better than you do, if you are going to maintain your ridiculous strawman position that scientists think that Occam's Razor is capable of proving or disproving theories.

Overly complicated; when exactly does the "overly" kick in?

That depends on one's judgement, of course, which is why there are arguments among scientists about what theories to prefer. In more restricted cases, it is possible to make "overly" a quantitatively precise concept; that was the point of the article I linked.

Boloney. They should each be considered on their own merit.

They are considered on their own merit, and the simpler theory has more merit in the absence of evidence favoring the more complex theory. That's the whole point of science, after all. Otherwise we'd be fitting all our data with Nth-degree polynomials instead of coming up with predictive theories.

Like classical physics compared to QM?

That's not a complete sentence. Is what like classical physics compared to QM?

If you had proposed quantum mechanical laws in the 17th century, you would have been laughed at, and rightly so: there was no evidence that supported such a hypothesis over Newton's laws. You could equally well have proposed many other more complicated alternatives to Newton's laws, which would have been completely unsupported by the data as well. There are always infinitely many laws you can propose to replace existing laws: one of them may be right, but infinitely many others will be wrong. Without evidence, there is no way to pick one over the other, so the simplest theory is the most credible, on the basis of the evidence that exists at the time.

 

[selfAdjoint]

As a search strategy OR is useful, but in general a lot has been learned in the last few decades about searching, depth first versus breadth first, the use of frustrated systems modeled on spin glasses, etc. What I would like to see is the search strategy google uses!

 

[Ivan Seeking]

Originally posted by Ambitwistor
We should apply it at all times. For a more complex hypotheses to be more plausible than a simpler one, it has to fit the data considerably better than the simpler hypothesis. If there is enough evidence in favor of the more complex hypothesis, then it will win out.

How much is considerably? More plausible? Why needlessly rule out potentially viable options? This only increases the chance of following the wrong path ad infintum.

Both hypothesis are consistent with all of the evidence, after all, but one of them is simpler than the other.

This is silliness! You assert that it is just as likely that I lost my keys as it is that aliens took them; but the alien theory is just more complicated? This is not an example of OR; it's statistics.

Better than you do, if you are going to maintain your ridiculous strawman position that scientists think that Occam's Razor is capable of proving or disproving theories.

Ah, you're psychic also? I maintain that beyond the obvious, it has no place in science. I think the history of scientific advances supports this notion.

That depends on one's judgement, of course, which is why there are arguments among scientists about what theories to prefer. In more restricted cases, it is possible to make "overly" a quantitatively precise concept; that was the point of the article I linked.

It is still arbitrary.

They are considered on their own merit, and the simpler theory has more merit in the absence of evidence favoring the more complex theory. That's the whole point of science, after all. Otherwise we'd be fitting all our data with Nth-degree polynomials instead of coming up with predictive theories.

"in the absence of evidence favoring the more complex theory"
Not the usage that I see. This also disagrees with your first statement in this post.

If you had proposed quantum mechanical laws in the 17th century, you would have been laughed at, and rightly so: there was no evidence that supported such a hypothesis over Newton's laws. You could equally well have proposed many other more complicated alternatives to Newton's laws, which would have been completely unsupported by the data as well. There are always infinitely many laws you can propose to replace existing laws: one of them may be right, but infinitely many others will be wrong. Without evidence, there is no way to pick one over the other, so the simplest theory is the most credible, on the basis of the evidence that exists at the time

The point is that consistently we see physics increases in complexity; it does not decrease. This is in direct opposition to the implicit logic of OR. We should expect more complex solutions; not simpler ones.

Edit: If you chose to use only a limited interpretation OR, one that is really the principle of pasimony in the strictest sense, then really we agree. This is not how this principle is interpreted by many educated people; nor is this interpretation the motivation for this thread. If this were the only interpretation we would be done.

the principle that entities should not be multiplied needlessly; the simplest of two competing theories is to be preferred

Really this reads like the 2nd ammendment to the constitution: I agree with the first point but not the second. The simplest and the more complex should be considered on their own merit.

How would you define the word preferred in this context?

 

[Ivan Seeking]

Originally posted by selfAdjoint
As a search strategy OR is useful, but in general a lot has been learned in the last few decades about searching, depth first versus breadth first, the use of frustrated systems modeled on spin glasses, etc. What I would like to see is the search strategy google uses!

Perhaps we will finally obtain a TOE using random searches in super computers. Hmmmm, that would be disappointing somehow... Will the next Einstein be a Quantum Computer?

 

[Ambitwistor]

Originally posted by Ivan Seeking
How much is considerably? More plausible? Why needlessly rule out potentially viable options? This only increases the chance of following the wrong path ad infintum.

Ivan, you obviously are not a practicing scientist. There are infinitely many potentially viable options, and not that many scientists working on any specific problem. Every once in a while someone will bring up a complicated theory that was previously ignored because it was more complicated --- even today, people discussion aether theories and variable-light speed theories as alternatives to relativity, for instance --- but it is simply not possible to spend time on all "potentially viable options", nor is it reasonable to prefer more complicated theories when simpler ones work just as well.

This is silliness! You assert that it is just as likely that I lost my keys as it is that aliens took them; but the alien theory is just more complicated? This is not an example of OR; it's statistics.

But Occam's razor is statistics! Read the paper I cited.

Ah, you're psychic also?

No.

I maintain that beyond the obvious, it has no place in science.

As I said, Occam's razor is obvious: even you seem to agree with that. So what are you arguing about?

I think the history of scientific advances supports this notion.

The history of scientific advances consists of people considering the simplest theory that fits the facts, until the evidence suggests otherwise.

It is still arbitrary.

It is only as arbitrary as you choose to make it. If you want to assign equal prior probabilities to the hypotheses under consideration, then it is completely unarbitrary and determined by the laws of probability, if you're talking about the precise version in the paper. If you're talking about human judgement, so what if it's arbitrary? You are the one who is (incorrectly) claiming that Occam's razor is used to disprove theories.

"in the absence of evidence favoring the more complex theory"
Not the usage that I see.

Well, I can hardly address some usage that you claim to see, but I have never seen among myself or my colleagues.

This also disagrees with your first statement in this post.

It does not.

The point is that consistently we see physics increases in complexity; it does not decrease.

To the contrary, the history of physics has been towards simpler, more unified theories, that predict more with fewer assumptions. The calculations may be harder, because these theories allow us to tackle more complicated

This is in direct opposition to the implicit logic of OR. We should expect more complex solutions; not simpler ones.

Occam's razor does not say that the simplest theory is always the right one!

Edit: If you chose to use only a limited interpretation OR, one that is really the principle of pasimony in the strictest sense, then really we agree. This is not how this principle is interpreted by many educated people; nor is this interpretation the motivation for this thread. If this were the only interpretation we would be done.

All right, then, I think we do agree. Even Occam himself agrees: if you read how he phrased the statement (or at least, the phrasing that is attributed to him), he said "ideas should not be multiplied beyond necessity". He didn't say anything like what you are claiming. Whether some people do claim what you say is another matter, but in my experience scientists do use Occam's razor as a principle of parsimony.

For instance, Lorentz's aether theory is exactly equivalent to Einstein's special relativity in every measurable way. If you ask a relativist why he doesn't consider LET over SR, he won't say that it's because LET is wrong. He will say that Lorentz's aether is unobservable, and SR can do everything that LET can do without an extra untestable aether lying around, so he takes the simpler theory.

Really this reads like the 2nd ammendment to the constitution: I agree with the first point but not the second. The simplest and the more complex should be considered on their own merit.

But what does that mean, "should be considered on their own merit"? Even if you assign equal prior belief in the linear theory and the 100th-degree-polynomial theory, in my previous example, after seeing the data are you really going to believe the two are equally plausible explanations?

How would you define the word preferred in this context?

Some people disagree with me, but in the spirit of Bayesian probability theory, I define it to mean that one should assign a greater belief in one hypothesis or another, given the evidence at hand.

 

[Ivan Seeking]

I got busy. I'll be back.

 

[Ivan Seeking]

Originally posted by Ambitwistor
Ivan, you obviously are not a practicing scientist. There are infinitely many potentially viable options, and not that many scientists working on any specific problem. Every once in a while someone will bring up a complicated theory that was previously ignored because it was more complicated --- even today, people discussion aether theories and variable-light speed theories as alternatives to relativity, for instance --- but it is simply not possible to spend time on all "potentially viable options", nor is it reasonable to prefer more complicated theories when simpler ones work just as well.

First, I am only a graduate in physics with a 30 year habit [what I do here at PF is mostly not included in that statement]. I do practice science at times as a function of my work and personal interests. Between my degree and my long experience with physics through books, lectures, and formal discussions, I have invested perhaps forty thousand hours into the subject. Clearly I do not qualify as a mainstream research scientist, however considering my degree and my long history with the discipline, I can hardly be considered an outsider.

by Ivan
If you chose to use only a limited interpretation OR, one that is really the principle of parsimony in the strictest sense, then really we agree. This is not how this principle is interpreted by many educated people; nor is this interpretation the motivation for this thread. If this were the only interpretation we would be done.

by Ambitwistor
All right, then, I think we do agree. Even Occam himself agrees: if you read how he phrased the statement (or at least, the phrasing that is attributed to him), he said "ideas should not be multiplied beyond necessity". He didn't say anything like what you are claiming. Whether some people do claim what you say is another matter, but in my experience scientists do use Occam's razor as a principle of parsimony.

Well, you know where I have spent my time lately. I see this concept used improperly by science and engineering students, and graduates [at least] on a fairly regular basis.

For instance, Lorentz's aether theory is exactly equivalent to Einstein's special relativity in every measurable way. If you ask a relativist why he doesn't consider LET over SR, he won't say that it's because LET is wrong. He will say that Lorentz's aether is unobservable, and SR can do everything that LET can do without an extra untestable aether lying around, so he takes the simpler theory.

If all my discussion were with you this thread would likely not exist.

But what does that mean, "should be considered on their own merit"? Even if you assign equal prior belief in the linear theory and the 100th-degree-polynomial theory, in my previous example, after seeing the data are you really going to believe the two are equally plausible explanations?

I mean that rather than use words like “belief”, I prefer to consider things strictly in terms of probabilities. I may comment on your paper later. It is most interesting.

There is still the deeper objection to Occam’s motivation. The original thesis that motivates OR - the religious belief that simplicity is perfection, and since the universe was made by God, it must be simple – appears to be incorrect. You pointed out that physics reduces complexity with simpler models. My objection is that nature keeps forcing more complex models; physics only responds to this requirement. So at its core, the belief in ultimate simplicity appears to be contraindicated by modern physics. For this reason, I argue that in the face of the evidence, the core philosophy of OR is statistically unlikely.

 

[Ambitwistor]

I mean that rather than use words like "belief", I prefer to consider things strictly in terms of probabilities.

To someone who subscribes to the Bayesian interpretation of probability theory, as I do, a probability is a degree of belief. Janyes's book Probability Theory: The Logic of Science has a good discussion of this perspective.

There is still the deeper objection to Occam's motivation. The original thesis that motivates OR - the religious belief that simplicity is perfection, and since the universe was made by God, it must be simple - appears to be incorrect.

Occam's motivation and the validity of Occam's razor are independent issues; I'm not too interested in debating the former.

You pointed out that physics reduces complexity with simpler models. My objection is that nature keeps forcing more complex models;

Well, then we appear to disagree on whether models get simpler or more complex.

So at its core, the belief in ultimate simplicity appears to be contraindicated by modern physics. For this reason, I argue that in the face of the evidence, the core philosophy of OR is statistically unlikely.

Occam's razor doesn't state that the simplest theory is right. It states that we should place the most belief in the simplest theory consistent with the evidence, in the absence of any evidence favoring the more complicated theories. I would still like to see you address the question of why you wouldn't prefer a 100th-degree polynomial fit instead of a linear fit, since it's "statistically unlikely" that the linear theory is right.

 

[Ivan Seeking]

Originally posted by Ambitwistor
To someone who subscribes to the Bayesian interpretation of probability theory, as I do, a probability is a degree of belief. Janyes's book Probability Theory: The Logic of Science has a good discussion of this perspective.

If you choose this as a definition, fair enough.

Occam's motivation and the validity of Occam's razor are independent issues; I'm not too interested in debating the former.

I think the implicit philosophy does matter. This is clearly what motivates many common interpretations of this concept. Also, this is a philosophy forum. I didn't post this in mathematics or physics for a reason.

Well, then we appear to disagree on whether models get simpler or more complex.

You seem to have the wrong idea. If we consider that modern physics began with Newton, clearly we have seen a tremendous increase in the complexity of the physical models required to describe that observed. The latest data point to add complexity to the curve appears to be dark energy.

Occam's razor doesn't state that the simplest theory is right. It states that we should place the most belief in the simplest theory consistent with the evidence, in the absence of any evidence favoring the more complicated theories. I would still like to see you address the question of why you wouldn't prefer a 100th-degree polynomial fit instead of a linear fit, since it's "statistically unlikely" that the linear theory is right.

As I said, in my first post:

The use of this concept to rule out a competing theory is only valid to the extent that it is obvious

I have never disputed this point. Why do you keep ignoring this?

 

[Ambitwistor]

I think the implicit philosophy does matter. This is clearly what motivates many common interpretations of this concept.

Many common interpretations of Occam's Razor are based on Occam's theological motivations?? I doubt that!

You seem to have the wrong idea. If we consider that modern physics began with Newton, clearly we have seen a tremendous increase in the complexity of the physical models required to describe that observed.

We see complexity go up and down. When more phenomena are discovered, more complex models tend to be proposed, but then people find a way of fitting these proposals into an elegant framework and the models get simpler again.

I have never disputed this point. Why do you keep ignoring this?

You seem to be ignoring my response to your point, which is that all uses of Occam's Razor are obvious.

 

[Ivan Seeking]

Originally posted by Ambitwistor
Many common interpretations of Occam's Razor are based on Occam's theological motivations?? I doubt that!

On a superficial level, no. But at the deepest level, any belief based premise, such as the more general notion taken from OR that we should expect simplicity in nature is ultimately theological in nature. Physicist do practice philosophy daily. It is argued that this is often not unrecognized. Here is a link to an article that discusses this notion. I have posted this in the past but it has been a while.

http://physicsweb.org/article/world/15/4/2/1#2

We see complexity go up and down. When more phenomena are discovered, more complex models tend to be proposed, but then people find a way of fitting these proposals into an elegant framework and the models get simpler again.

A macroscopic view - the complete history of physics - yields a more and more complex curve...thus far. How many dimensions do we work with now? Up to twelve? I think your Newtonian line in three dimensions has morphed into a hypervolume.

You seem to be ignoring my response to your point, which is that all uses of Occam's Razor are obvious.

I don't agree. Please see the link in the first post.

There is a philosophy implicit in a thousand decisions a day. The article linked above describes the basis for this premise. This however is another discussion altogether.

Again, this is a philosophical discussion. A rigorous mathematical treatment such as the one posted by you may or may not have anything to do with the premise my argument.

 

[NateTG]

Occam's Razor:
If there are two theories that make the same prediction, then the simpler theory is better.

So, for example, according to OR, on classical physics scales - i.e. non-relativistic/non-quantum masses and speeds - classical physicis is the best theory.

When you are dealing with domains where the theories differ, then you use the theory that is more consistent with your experimental data. (OR does not apply here.)

So let's take a look at the example of lost keys:

Theory 1: I lost my keys
Theory 2: Space aliens stole my keys.

Theory 1 makes the prediction that my keys will turn up somewhere that I've been.
Theory 2 makes the prediction that there were aliens near me, so the aliens should have been observable.

Clearly experience (for most people) is not consistent with theory 2. That eliminates theory 2 before OR really comes into play.

There are several problems with the application of OR in general -- the notions of theory, the same, and better are not rigorously stated, and it is entirely concievable that a theory can trade conceptual simplicity for computational complexity. An example of this might be the standard model (a catalog of particles and interactions) vs. string theory (conceptually elegant, computationally painfull).

A good example of Occam's Razor being applied is the history of the motion of the planets: Although Keppler's work is equivalent on the motion of the planets, it's usually not covered in favor of Newton's equations because Newton's equations are simpler, and make the same predictions.

 

[Ambitwistor]

Originally posted by Ivan Seeking
On a superficial level, no. But at the deepest level, any belief based premise, such as the more general notion taken from OR that we should expect simplicity in nature is ultimately theological in nature.

This is nonsense. Belief is not theology, nor is probability theory or logic.

Physicist do practice philosophy daily.

So? Nobody is denying that Occam's Razor is a philosophical principle: it can't be used to prove or disprove physical theories.

A macroscopic view - the complete history of physics - yields a more and more complex curve...thus far. How many dimensions do we work with now?

I don't know about you, but I work with the same four that Newton did.

 

[Ivan Seeking]

Originally posted by Ambitwistor
This is nonsense. Belief is not theology, nor is probability theory or logic.

Belief is always faith based. Where do we define faith in science? Faith is for the religious.

So? Nobody is denying that Occam's Razor is a philosophical principle: it can't be used to prove or disprove physical theories.

So, it applies in many more ways than as in the one paper you cite.

I don't know about you, but I work with the same four that Newton did.

Now you are either being ridiculous or you don't know nearly as much as I had assumed.

 

[Ivan Seeking]

Originally posted by NateTG
Occam's Razor:
If there are two theories that make the same prediction, then the simpler theory is better.

So, for example, according to OR, on classical physics scales - i.e. non-relativistic/non-quantum masses and speeds - classical physicis is the best theory.

When you are dealing with domains where the theories differ, then you use the theory that is more consistent with your experimental data. (OR does not apply here.)

So let's take a look at the example of lost keys:

Theory 1: I lost my keys
Theory 2: Space aliens stole my keys.

Theory 1 makes the prediction that my keys will turn up somewhere that I've been.
Theory 2 makes the prediction that there were aliens near me, so the aliens should have been observable.

Clearly experience (for most people) is not consistent with theory 2. That eliminates theory 2 before OR really comes into play.

thank you.

There are several problems with the application of OR in general -- the notions of theory, the same, and better are not rigorously stated, and it is entirely concievable that a theory can trade conceptual simplicity for computational complexity. An example of this might be the standard model (a catalog of particles and interactions) vs. string theory (conceptually elegant, computationally painfull).

A good example of Occam's Razor being applied is the history of the motion of the planets: Although Keppler's work is equivalent on the motion of the planets, it's usually not covered in favor of Newton's equations because Newton's equations are simpler, and make the same predictions.

How would you characterize the case of the old wave-particle paradox?

 

[NateTG]

Originally posted by Ivan Seeking
How would you characterize the case of the old wave-particle duality paradox?

I would say that there were two theories - light as particle and light as wave and that the theories make different predictions in some situations. When there are theories that make different predictions, the appropriate approach is to experiment (use the razor to shave).

I don't personally know enough of the history/theory to have a whole lot of insight.

 

[Ambitwistor]

Originally posted by Ivan Seeking
Belief is always faith based.

Hardly. I can believe something, knowing full well that I might be wrong, without "taking it on faith".

So, it applies in many more ways than as in the one paper you cite.

So, you're ignoring the original point, which is that Occam's theology has nothing to with how Occam's Razor is commonly intepreted. I would wager that most people don't even know anything about Occam other than the statement of his Razor --- and many of those who say they are applying Occam's Razor probably don't even know his original wording.

Now you are either being ridiculous or you don't know nearly as much as I had assumed.

If you are implying that Newton didn't use three space and one time dimension in his theories, you're mistaken. It's just that space and time were absolute in Newton's theory, whereas they were unified and relative in Einstein's.

 

[Ambitwistor]

Originally posted by NateTG

Theory 1: I lost my keys
Theory 2: Space aliens stole my keys.

Theory 1 makes the prediction that my keys will turn up somewhere that I've been.
Theory 2 makes the prediction that there were aliens near me, so the aliens should have been observable.

I said they were invisible space aliens, and you haven't found your keys yet. The evidence --- namely, that you can't find your keys --- is equally consistent with both theories. If you find your keys nearby, then I agree that theory 1 is preferred by the evidence alone. (Unless I postulate that the invisible space aliens also like to secretly return keys somewhere nearby.)

It is Occam's Razor why we don't construct elaborate ad-hoc modifications to an already-complicated theory to keep it alive.

 

[NateTG]

Originally posted by Ambitwistor
I said they were invisible space aliens, and you haven't found your keys yet. The evidence --- namely, that you can't find your keys --- is equally consistent with both theories. If you find your keys nearby, then I agree that theory 1 is preferred by the evidence alone. (Unless I postulate that the invisible space aliens also like to secretly return keys somewhere nearby.)

And I said observed not seen. The aliens might still be smellable, hearable, or touchable.

If you have a situation where there is no opportunity for experimentation then theory is pointless.

 

[Ambitwistor]

Originally posted by NateTG
And I said observed not seen. The aliens might still be smellable, hearable, or touchable.

That doesn't mean they were smelled, heard, or touched. For that matter, we can just postulate your mortal enemy snuck in and stole the keys because they didn't like you; if they were careful, you might not be able to obtain physical evidence.

If you have a situation where there is no opportunity for experimentation then theory is pointless.

Yes, that's exactly why Lorentz ether theory was rejected in favor of special relativity on the basis of Occam's Razor; not because it was wrong, but because it was more complicated and no evidence in its favor.

 

[Ivan Seeking]

Originally posted by Ambitwistor
Hardly. I can believe something, knowing full well that I might be wrong, without "taking it on faith".

A belief is an internal thought or memory which exists in one's mind. Most people accept that for a belief to be knowledge it must be, at least, true and justified. The Gettier problem in philosophy is the question of whether there are any other requirements before a belief can be accepted as knowledge.

http://en.wikipedia.org/wiki/Propositional_knowledge

So typically belief does imply an intellectual choice beyond mere probabilies. At the least, in the common usage belief cannotes extreme bias. You have selected an obscure and rigorous defintion of belief; this does not apply to everyone.

So, you're ignoring the original point, which is that Occam's theology has nothing to with how Occam's Razor is commonly intepreted. I would wager that most people don't even know anything about Occam other than the statement of his Razor --- and many of those who say they are applying Occam's Razor probably don't even know his original wording.

There are at least two parts to OR:

First, "plurality should not be posited without necessity."
No objections.

A Popular usage: "The simplest explanation tends to be the correct explanation".
If you never see this interpretation, then no wonder we don't agree.

Earlier you said: "but it is simply not possible to spend time on all "potentially viable options", nor is it reasonable to prefer more complicated theories when simpler ones work just as well."

My point is that evidence is often rejected or ignored because it represents challenges to the simple explanations. This results from belief based bias.

If you are implying that Newton didn't use three space and one time dimension in his theories, you're mistaken. It's just that space and time were absolute in Newton's theory, whereas they were unified and relative in Einstein's.

Are you arguing that the whole of modern physics is no more complex than 17th century physics? 18th century? 19th Century?

Also, you are clearly familiar with String Theory. Why do you seem to evade my reference to the 10 or 12 dimensions that appear to be required to explain all forces in nature?

 

[Ambitwistor]

Originally posted by Ivan Seeking
So typically belief does imply an intellectual choice beyond mere probabilies. At the least, in the common usage belief cannotes extreme bias.

This is certainly not true. I can believe it will rain tomorrow without being anywhere even close to certain that it will rain tomorrow, or "accepting it on faith".

Moreover, whether I define a probability to be a degree of belief is independent of the question of whether "belief" is the same as "faith".

A Popular usage: "The simplest explanation tends to be the correct explanation".
If you never see this interpretation, then no wonder we don't agree.

The interpretation I use is that one should put greater belief in the simpler theory, in the absence of any evidence favoring the more complex theory.

My point is that evidence is often rejected or ignored because it represents challenges to the simple explanations.

Really? "Often"? Says who?

Are you arguing that the whole of modern physics is no more complex than 17th century physics? 18th century? 19th Century?

I'm arguing that in the history of scientific development, there is not a universal replacement of simpler theories with more complicated ones. Sometimes theories get more complicated, and sometimes they get simpler.

Also, you are clearly familiar with String Theory. Why do you seem to evade my reference to the 10 or 12 dimensions that appear to be required to explain all forces in nature?

I'm not "evading" your reference, I'm ignoring it. String theory says that 10 or 11 dimensions are needed to describe nature, but that doesn't mean that I agree with that claim. We really have no idea of whether extra dimensions either exist or are necessary to explain anything.

But, for that matter, as I said earlier and you ignored, a string theorist would claim that string theory, even with extra spacetime dimensions, is fundamentally simpler than the existing Standard Model. That's why string theorists like string theory.

 

[Ivan Seeking]

Originally posted by Ambitwistor
This is certainly not true. I can believe it will rain tomorrow without being anywhere even close to certain that it will rain tomorrow, or "accepting it on faith"./quote]

Aside from your mathematical reference, what then is the difference between belief and expectations?

Moreover, whether I define a probability to be a degree of belief is independent of the question of whether "belief" is the same as "faith".

I understand; and this is a very reasonable approach.

The interpretation I use is that one should put greater belief in the simpler theory, in the absence of any evidence favoring the more complex theory.

Again, this comes down to our personal exposure to this question.

[quoteReally? "Often"? Says who?

I see this frequently. Perhaps you don't see this because you don't explore the fringe.

I'm arguing that in the history of scientific development, there is not a universal replacement of simpler theories with more complicated ones. Sometimes theories get more complicated, and sometimes they get simpler.

Still, complexity does increase. Based on the evidence, we should drive for the simplest theory, and we should expect more complexity.

This also speaks to the assumption that a TOE can even exist. This assumption in itself reflects the philosophy of William of Ockham.

I'm not "evading" your reference, I'm ignoring it. String theory says that 10 or 11 dimensions are needed to describe nature, but that doesn't mean that I agree with that claim. We really have no idea of whether extra dimensions either exist or are necessary to explain anything.

That fine. So you ignored a legitimate reference to a, or the leading contender for a unified theory becuase you don't know if its neccesary.

But, for that matter, as I said earlier and you ignored, a string theorist would claim that string theory, even with extra spacetime dimensions, is fundamentally simpler than the existing Standard Model. That's why string theorists like string theory. [/B]

True. The fact remains that to the best of our knowledtge, the universe is not simple and we should not expect it to be. The significance of this implicit philosophy, one that is counter to that of the philosophy OR, is discussed in the Physics Web Link.

 

[Ambitwistor]

Aside from your mathematical reference, what then is the difference between belief and expectations?

I don't make much distinction between them. Although there is some distinction based on context: If I say that I believe something, that just means I think there's a reasonable chance that it's true. But when people speak of their "beliefs", that often implies a greater strength of conviction.

Again, this comes down to our personal exposure to this question.

Really? "Often"? Says who?

I see this frequently. Perhaps you don't see this because you don't explore the fringe.

There are many reasons why fringe claims are often ignored, but I don't think Occam's Razor is necessarily one of them.

Still, complexity does increase. Based on the evidence, we should drive for the simplest theory, and we should expect more complexity.

I don't know that we should. The recent modern trend in physics has been towards unification.

That fine. So you ignored a legitimate reference to a, or the leading contender for a unified theory becuase you don't know if its neccesary.

Yes.

True. The fact remains that to the best of our knowledtge, the universe is not simple and we should not expect it to be.

I think an important distinction has not yet been made in this thread: a theory might be simple, but its solutions might be arbitrarily complex.

 

[Ivan Seeking]

There are many reasons why fringe claims are often ignored, but I don't think Occam's Razor is necessarily one of them.

I didn't say claims, I said evidence.

Otherwise, I guess I have made my argument.

I think an important distinction has not yet been made in this thread: a theory might be simple, but its solutions might be arbitrarily complex.

This is an interesting point. Could you elaborate?

 

[Ambitwistor]

I didn't say claims, I said evidence.

I don't think it's the case that contradictory evidence is ignored, if that evidence is well-established. If it's on the edge of measurement, maybe. More rigorous evidence is required to cast doubt upon a well-established theory, after all. This can also be phrased rigorously in the language of probability theory.

This is an interesting point. Could you elaborate?

Well, take Newton's law of gravity. It's pretty simple, but the dynamics of many gravitationally-interacting bodies can be chaotic and enormously complex. Or the Navier-Stokes equations ... not as simple as Newtonian gravity, but still not horrendously complicated. However, the turbulent solutions of fluid dynamics still evade our best efforts to understand them. Or, take string theory. It is derived uniquely from a few simple axioms, but it could in principle describe the dynamics of everything in the entire universe, if only you could solve the equations ...

 

[Mentat]

Originally posted by Ivan Seeking
Belief is always faith based.

I heartily disagree with your take on OR, Ivan (no offense), but will explain my disagreement on another post. This one is directed at the quoted sentence. You see, this is actually not true. Belief can be based on credulity, or it can be based on faith, or it can be without basis at all.

"Faith is the assured expectation of things hoped for, the evident demonstration of realities, though not beheld" [Italics mine] Hebrews 11:1, New World Translation of the Holy Scriptures. It's the best definition I've heard so far .

Thus the difference between faith and mere belief is established.