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September 05, 2007


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I think there might be something else wrong with Dembski's account of parsimony.

Occam's razor is for use with _competing_ hypotheses. The cat/fairy example you gave is a good one; we have to chose the best explanation from the two given. In contrast, I think what Dembski is doing is asking a question of the form:
- Which is simpler: that the cat drank the milk, or that God created life?

In Dembski's example, he's mixed two different sets of competing hypotheses. That is, when he asks us to consider "one designer or infinite universes" the two aren't alternatives in any sense, even in the context of the development of life. They're two separate hypotheses that, indeed, could be quite consistent with each other. We could have:
- one designer, one universe
- no designer, one universe
- one designer, multiple universes
- no designer, multiple universes
And, with the exception of the second in that list, all still fit into either the God camp or the evolution-through-multiple-universes camp (the second is a more traditional evolutionary outlook, I think). There's also the 'something else' option, which doesn't really come into play here, but is important to remember.

So, when we go to use Occam's razor, we should consider:
- Which is simpler: one designer, or no designer?
- Which is simpler: one universe or many universes?
and then continue as normal from there. The answer to the first is 'no designer'. The answer to the second is determined by science (once we can test it - a good quote about this above).

I'd like to know what paper the Dembski-ite is citing, because hypotheses of multiple universes don't come out of biology, nor do they arise as a response to biological improbability. To refute the anthropic principle a biologist needs only note that the argument is backwards (we evolved to fit in this universe, not that the universe is made to fit us) and ridiculous (how can you say the universe was made for us when 99.999 percent of it is uninhabitable?), or to show that it is better as an argument for evolution, as Dawkins did in The God Delusion.

No, the many worlds interpretation is one of several ideas designed to explain certain weird properties in Quantum Physics; it's merely a hypothesis at this point, and will likely remain so until there's some way to test it. Multiple universes are implied by the String and M-theory types as well, but are equally hypothetical.

You should probably invent a new term for it instead of multiverse, because by definition, the universe is everything, there can't be another universe if the universe is everything.

Definitions change. Not too long ago, "the universe" meant "the Earth, the Sun, the Moon, a couple of planets, and a sphere of tiny little stars." The universe is an expanding closed system consisting of all the matter and energy that we know exists. It may or may not be bounded, it is probably not infinite, and there may be something outside of it.

Corey -

Sort of. Calling it the "multiverse" is not really meant to be understood as "multiple instances of the universe (as maximal-set-of-everything)" but more like a structural description meant to be understood as "the universe (as MSoE) is partitioned in such a way that each partition is fully independent (i.e. can't interact with) each other."

Since we live within one of those partitions and each partition is an absolute boundary that only fiction writers can penetrate, our partition feels like the whole universe. It is merely the whole of the universe we could ever access.

         Not ever?

         Never ever.

Skeptico –

In all the time I’ve been reading your generally excellent blog, I’ve never come across such an egregious error. In your analogy w/r/t milk, cats, and fairies you made what I can only describe as a colossal blunder.

To wit, the Principle of Occam’s Razor clearly supports that conclusion “the cat drank the milk,” but not because a “milk fairy” is “more complex” than a “cat.” In fact, I would suggest that a real cat is actually much more complex than an imaginary fairy!

It is not the “complexity” of the two alternatives that tips the scale, but rather that, as everyone knows, milk fairies never drink milk but rather make it (and don’t even ask about how they get any significant volume of milk out of their tiny nipples – it’s too rude a question even to consider).

Everyone Else (and to you two, too) –

In addition to the clear commentary Dominic posted w/r/t the (sloppy) mixture of ideas that are rightly considered independently, I feel compelled to point out that Occam’s Razor is not proof of anything. It is merely a working principle that heuristically favors ideas that win out in the long term. It doesn’t even always work – that’s why it’s a heuristic, not a rule and definitely not a Law.

It is merely a working principle that heuristically favors ideas that win out in the long term. It doesn’t even always work – that’s why it’s a heuristic, not a rule and definitely not a Law.

I've got to disagree on this one. Occam's Razor only fails when there is an influx of new information.

What Occam's Razor says, explicitly, is that when all other things (i.e., evidence) are equal between two hypotheses, the one which relies on the fewest hypothetical entities is most likely to be the correct one. The only time the other hypothesis ends up being correct is when some evidence comes in to suggest the existence of the previously hypothetical entity. In that case, the two hypotheses are no longer on equal evidentiary grounds, and so Occam's Razor no longer applies. It can lead us to the incorrect conclusion, but we would be foolish to accept an unparsimonious hypothesis until there is evidence to suggest its accuracy.

It's not that Occam's Razor isn't always correct, it's just that Occam's Razor only applies in situations with two hypotheses that are equally well-supported by the evidence. If there's a preponderance of evidence in favor of one hypothesis, then we choose that one, and Occam's Razor is unnecessary.

You're right that it's not proof of anything; the whole reason you apply Occam's Razor is because of a lack of proof.

[Off Topic]
I have a proposition to make. No one link to UD anymore. I think screen shots are a better alternative.
[/Off Topic]


just me, having re-read Skeptico's article I really can't reconcile your criticism to it. I can't see where he writes about the relative complexity of alternatives with regard to how or when to use Occam's Razor, and which you appear to take issue with.

One thing to remember is that an 'entity' isn't necessarily a physical thing. The multiverse hypothesis is actually more parsimonious than the single universe because it doesn't presuppose an arbitrary limit of 1 to the number of universes - the entity in this case being the limit itself.

pv - At least one of us has missed something here... my "criticism" of Skeptico's initial posting was, as I hoped was clear, intended to be “comedical” rather than “intellectical.”

On the other hand, my hopes might have been just that - hopes.

On the other-other hand, you may be responding beyond the vale of my comment’s (apparently poorly constructed) hyperbolistical spew. Really, I was just trying to generate some cyber-yuks.

On the other^3 hand, Tom Floss seems to have missed the target w/r/t the third (To Everyone Else) part, which was really the only (almost-) serious part of my response of 2007-06-06. (In fairness to Tom, I should say that I have missed the target w/r/t getting my point across to him and likely to others, as well – THUS:)

SPECIFICALLY IN RESPONSE TO TOM FLOSS’S POST: I believe that we are mostly in agreement w/r/t Occam’s Razor but have some minor issues in how we language both the Razor and issues of proof, probability, heuristic, etc.

First, the agreement: the Razor is not proof of anything. It cannot be used as such and efforts to do so merely highlight the failings of an argument displaying such attempt.

Second, the disagreement: You say that “[the Razor] only fails when there is an influx of new information.” To me, this is like saying that chances of selecting a King of Hearts, for example, from a full standard deck change once I remove all other picture cards. On first blush, they do seem to change, from 1-in-52 to 1-in-41 – but this is wrong. The chances of the stated scenario are always 1-in-52, since it clearly says “from a full standard deck.”

Moving back to Occam, I don’t see that the application of the Razor when we are “information poor” can be made wrong at a later time when we are “information rich.”

Back to the playing cards: Even when I relax the stipulation and I were to just consider the chance of pulling a K-h from any deck, I would say are also 1-in-52. Why? Consider how many decks of cards there are in the world. Don’t you see that most of them are actually “full standard” decks?

Once more, back to Big-O... The Razor is a principle that applies like the relaxed “Chances of K-h from a deck.” It’s a general principle that’s accrued whatever merit it has from being useful across many choices, across many domains, and across many years.

Even were I to find out that a specific deck was really a trick deck that was made up of only K-h cards (giving 1-in-1 chance, i.e. 100%) and then was presented with second deck of unknown content it still makes sense to say there’s a 1-in-52 chance of pulling a K-h. After all, it’s a different deck and virtually all decks are “full standard.” (Oh yeah, this was back on the playing card side of the analogy...)

And finally resting with the O of O’s: Just like any given deck of cards should be considered, in the absence of other information, to be a “full standard” deck, each situation where Occam’s Razor could be meaningfully applied should be considered, in the absence of other information, to be a “standard choice about the complexity exhibited by our models of reality.” That standard choice is to choose the less complex model. That standard choice is exactly Occam’s Razor. That choice, as a predictor, is never wrong, even when a subsequent “influx of information” has us revise the models under consideration. All the new info does is change the models under consideration (or at least the context for evaluation of said models) – but this is substantially distinct from making the earlier application of the Razor “wrong.”

That’s how I see it, but maybe that’s

Just Me.


It's really not that hard to spell my name correctly. Just like the Christmas carol, there's no "L."

Moving back to Occam, I don’t see that the application of the Razor when we are “information poor” can be made wrong at a later time when we are “information rich.”

I'm not entirely sure what you're trying to say here. What I mean to say is that Occam's Razor is essentially a last resort for evaluating between competing hypotheses. Ideally, we would judge them based on the preponderance of evidence; when the evidence suggests that one of the hypotheses is true, we accept it and discard the other. It's when we don't have a preponderance of evidence--when two hypotheses explain the observed phenomena equally well--that we're forced to apply Occam's Razor.

Take, for instance, the problem of luminiferous aether. In 1887, we knew a few things about light, specifically that it was made up of electromagnetic waves. We could then proceed to apply our knowledge of all other types of waves, such as the fact that they all require a medium through which to propagate. Water waves propagate through water, seismic waves propagate through matter, and sound waves propagate through the air. Light, being a wave, must propagate through some medium, even though we can't see that medium.

So, let's say we have two hypotheses: 1) there exists a medium, termed luminiferous aether, through which electromagnetic waves propagate; 2) electromagnetic waves are special, unlike any other kind of waves, and do not require a medium.

Based on the evidence available in 1887, these hypotheses explained the observed phenomena equally well. However, Hypothesis 2 requires us to engage in what looks like special pleading, proposing some completely different sort of wave from all other known types of waves. Using Occam's Razor, we would discard Hypothesis 2 as unparsimonious.

That year saw Michelson and Morley perform an experiment to prove the existence of the luminiferous aether, which failed spectacularly. The new evidence suggested that Hypothesis 1 was incorrect; the two hypotheses no longer explained the observed phenomena equally well, and Occam's Razor would no longer apply (since there would now be a preponderance of evidence against the first hypothesis). Thirty years later Al Einstein did the work to show why Hypothesis 2 was, indeed, the correct one.

In this case, and in some scant few others, the hypothesis which seemed less parsimonious under one set of evidence turned out to be the correct one when new evidence arose. Put simply, the evidence is the first line of attack; it's only when you can't determine which hypothesis is correct according to the evidence that you resort to the Razor.

I don't know that I'd agree that Occam's Razor derives its merit from being frequently useful; I think it's useful because it forces us not to make unsupported assumptions or accept unsupported claims.

It seems we're in less disagreement than either of us might think; I agree that, at the time and given any current set of evidence, no valid application of the Razor is "wrong," it may only seem that way in hindsight. The late 19th Century scientists proposing the existence of the aether weren't wrong, based on their existing body of knowledge. It's only once we've gathered more evidence and formed better models that we're able to say "that was wrong."

But, speaking from a position where we can look on the past, we can see situations where reason, the Razor, and occasionally even the evidence, led to initial conclusions which later turned out to be wrong.

Technically, I'd say that you'd need two examples of something before you can assume that there are more than that, but still, deadon. I was meaning to do a little Occam talkin at some point, but I'll probably cover more the rather confused idea of "elegance" in science now that you've covered the essentials of this particular point so well. Also...


Big-O, Big-O: Big-O!

Ye Not guilty!

I have a question for the Razor...

Which theory would Occam select for the milk hypothesis between:

A - The milk fairy drank it.


B - The goldfish rose out of the fishbowl and swam in thin air outside to drink the milk, then returned back to the goldfish bowl.

The ball is in Occam's court.


Seems to me like they're both made-up explanations so Occam would say there's no reason to believe either A or B.

Sometimes you have to say "I don't know". The religious have trouble with this idea though - they usually need to make up a "God" explanation, when the answer is really "I don't know".

I'm surprised no-one has pointed out that "probability (of) less than 1 in 10 raised to the negative 1,018" is complete gibberish, since a probability can't be greater than 1.

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