Why parsimony?

[Politesse]

It tends to tick off many a theist right quick.

So if your goal is petty inter-religious bickering, parsimony is a useful principle?

 

[Politesse]

The goal is not to be lazy. . . But to challenge assumptions.

For example, medieval astronomers were required to use some pretty complicated ideas to describe the movements of the planets. But that was because they presupposed a geocentric model of the solar system:

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Once it was accepted that the sun was the center, and the earth was only another planet in orbit around it, did the model become much simpler.

To me, that is the core of parsimony, the rejections of presuppositions that lead to unnecessary compexity.

I see how that establishes that questioning assumptions is prudent. But how does it prove that parsimony is wise? The astronomers weren't wrong because their model was too complicated. The complications were a side effect of an incorrect assumption.

 

[Sapiens]

Parsimony goes back (at least) to Aristotle (3rd century BCE) where he writes in his Posterior Analytics, "We may assume the superiority ceteris paribus [other things being equal] of the demonstration which derives from fewer postulates or hypotheses." That has proven to be good advice for more than two millennia.

 

[Kuzcotopia]

I see how that establishes that questioning assumptions is prudent. But how does it prove that parsimony is wise? The astronomers weren't wrong because their model was too complicated. The complications were a side effect of an incorrect assumption.

I made no attempt to prove it was wise.

Overly complex explaintions or outcomes can be motivators to test assumptions and presuppositions.

Do you have an example of parsimony not leading to a proper conclusion? Maybe I can understand your point better?

 

[Rick O'Shez]

A heuristic shorthand applied in many human endeavors is the principle of parsimony. In simple terms, parsimony suggests that when you have multiple competing ideas, you should select the one with the fewest steps, or the least amount of complexity.

Why should one opt for parsimony? In what situations might this be appropriate, and in what situations might it be inappropriate? Does our tendency to gravitate towards simplicity or complexity say something about our personalities?

(as an aside, this topic was inspired by a lecture I attended today, and it's now on my list to find some references somewhere for the history of this idea as it pertains specifically to the sciences; on the odd chance that folks have good academic references in the philosophy of science for this, please throw them at me)

There is an elegance to simplicity.

 

[9-10ths_Penguin]

A heuristic shorthand applied in many human endeavors is the principle of parsimony. In simple terms, parsimony suggests that when you have multiple competing ideas, you should select the one with the fewest steps, or the least amount of complexity.

Why should one opt for parsimony? In what situations might this be appropriate, and in what situations might it be inappropriate? Does our tendency to gravitate towards simplicity or complexity say something about our personalities?

(as an aside, this topic was inspired by a lecture I attended today, and it's now on my list to find some references somewhere for the history of this idea as it pertains specifically to the sciences; on the odd chance that folks have good academic references in the philosophy of science for this, please throw them at me)

Why would you include factors in a model when you don't know whether they have an effect or what sort of effect that might be?

In the sciences, we have statistical tests to tell us how well the factors we've assumed explain the data we have. If the data is well explained by some set of factors, why add others?

I see parsimony in the sciences as just an extension of the principle that we shouldn't assume things without justification.

 

[BSM1]

To make this as simple as I can at the moment: As far as I can see, all symbols have the same set of relationships to a reality as maps have to a terrain. Furthermore, all ideas or concepts about a reality are symbolic. That is, ideas or concepts are a subset of symbols. Hence, all ideas or concepts about a reality have the same set of relationships to a reality as maps have to a terrain.

The set of relationships that symbols, including ideas, can have to a reality (ideally) range anywhere from complete correspondence to complete non-correspondence. Moreover, the degree to which an idea significantly corresponds to a reality can be thought of as its "truthfulness". The degree to which an idea significantly does not correspond to a reality can be thought of as its "falsity". That is analogous to saying that the degree to which a map corresponds to a terrain can be thought of as its accuracy, and the degree to which it doesn't correspond can be thought of as its inaccuracy.

Thus, suppose we have two competing ideas. Let's call the first idea "A", let's call the second idea "B", and let's call the reality that A and B compete to most perfectly or completely correspond to, "R".

Furthermore, suppose for the sake of illustration that A consists of the notion that R is red, hard, and hot, while B consists of the notion that R is red, hard, hot, and throbbing. In other words, A is a less elaborate description of R than is B.

Next, for the two ideas to be in genuine or true competition, what we know about A's correspondence to R must be the same as what we know about B's correspondence to R. That is, A and B must have the same set of known correspondences. Say, for the sake of illustration, that set is "red, hard, and hot". Why the same set? Because if they had a different set of known correspondences, then one or the other idea would more completely correspond to R, and the two would not be in genuine competition (although some folks, speaking loosely, might still call them in competition).

Now, the rule of parsimony basically states that whenever we have two competing ideas about a reality, we go with the idea that is the simplest or most parsimonious. If we apply the rule to our illustration, then we would pick A over B as the most parsimonious idea. But picking A over B is logically the same as picking the idea which introduces the least unfounded speculation over the idea which introduces the most unfounded speculation, for we know that A's "red, hard, and hot" is less speculative than B's "red, hard, hot, and throbbing", since "throbbing" is not in our set of known correspondences.

Thus, to sum up all of the above, one reason someone might choose to apply the rule of parsimony to pick between genuinely competing ideas is in order to pick the idea that is least speculative. Of course, someone else might prefer the more speculative idea for personal reasons (e.g. they just darn well like the notion that R is "throbbing", and don't care that "throbbing" bears no known correspondence to R). The choice between parsimonious and greater complexity is somewhat a matter of taste.

At least that's how I see it. Of course, I just woke up from a nap, my head is still a little groggy, and so my thoughts on this matter are less than parsimonious, and probably garbage anyway.

Yeah, what he said...

 

[9-10ths_Penguin]

Something else occurs to me: anything other than Occam's Razor ends up with unjustified arbitrary conclusions.

There's only one simplest explanation, but there uncountably many "unnecessarily complex" explanations. How do you choose between them to pick your working hypothesis?

 

[Quintessence]

To add unnecessary complexity is typically to....
- Make something more difficult to understand.
- Introduce error.
- Risk being led astray.

How is it determined that a particular element is "unnecessary complexity?"

I mean, I don't know about you guys, but I find simplistic storytelling hella boring. Seen more simplistic "good vs evil" morality stories than I want to shake a stick at.

 

[Papoon]

I see how that establishes that questioning assumptions is prudent. But how does it prove that parsimony is wise? The astronomers weren't wrong because their model was too complicated. The complications were a side effect of an incorrect assumption.

Actually those astronomers weren't entirely wrong.

Just for a moment, assume earth as reference point, and the diagram is accurate - or at least any map of relative motion assuming earth as coordinate 0,0,0 would produce a similar 2D representation.

That's not the sun going down, it's the horizon moving up !

 

[Quintessence]

People will most often choose the path of least resistance unless really, really motivated to do otherwise. I'm not sure why that is, but I think it might be a cost benefit analysis skill left over from ye olden hunter gatherer days. The more effort (energy, resources) you invest in an uncertain outcome, the greater the loss if the intended outcome isn't achieved.

Hmm. Does the "path of least resistance" look the same for all people? Sorry, that's a bit rhetorical - it seems to me the answer to that is no. How does that end up impacting things, we might wonder?

 

[Quintessence]

Thus, to sum up all of the above, one reason someone might choose to apply the rule of parsimony to pick between genuinely competing ideas is in order to pick the idea that is least speculative. Of course, someone else might prefer the more speculative idea for personal reasons (e.g. they just darn well like the notion that R is "throbbing", and don't care that "throbbing" bears no known correspondence to R). The choice between parsimonious and greater complexity is somewhat a matter of taste.

A fair point to make, if one's concern is about the supposed correspondence between sets of ideas (maps) and the "real" of it (territory). The purpose is to simplify hypothesis testing to make it more manageable At the same time, though, if you leave important variables out of your model, you end up with a bad model. Garbage in, garbage out, so they say.

There are many people who prefer simpler explanations and who are not "simple-minded" or dullards. For instance, Einstein and Feynman come to mind...

Yeah, I was mostly being facetious with that post.

 

[Quintessence]

What a great OP!

(BTW tree-hugger Quint, I probably never mentioned that the house I live in, is in a redwood grove?)

Lots of possible answers here, but one idea is that humans are pattern-matching machines. A child of 3 or 4 can reliably tell you whether a given picture is a picture of a dog or a cat. This seemingly simple feat is just now barely possible for a computer to do. I'd say that valuing parsimony is consistent with relying heavily on pattern matching. Parsimonious observations will tend to fit patterns more readily.

Do they? My experience learning how to identify various plants makes me wonder about that. Minimalist or simplistic observations won't do it for you, especially if you're trying to identify something from the grass family. A grass will look like a grass.... particularly to non-botanists. Hell, non-botanists call things that are actually sedges or rushes "grasses" even though they are not. That brings up the issue of presumed patterns being erroneous (did you know that birds are reptiles from a phylogenetic and evolutionary standpoint?), mistaken attributions (that moment when that person you identified as a male turned out to be a female), and so on and so forth. But I'm getting rambly now.

And dang you, I wish I lived in the forest. All the forest properties in my area are way over my price range. *sniffles*

 

[9-10ths_Penguin]

How is it determined that a particular element is "unnecessary complexity?"

If it doesn't improve the explanatory value of your theory, it's unnecessary.

If it affects the outcome, but not at a magnitude that's distinguishable from random background noise, it's unnecessary.

 

[Quintessence]

There is an elegance to simplicity.

There is. And also, boringness (as I said earlier with those darned "good vs evil" stories - so sick of those).

 

[Quintessence]

If it doesn't improve the explanatory value of your theory, it's unnecessary.

If it affects the outcome, but not at a magnitude that's distinguishable from random background noise, it's unnecessary.

Well, that's great if you are talking about theories. What about other things in life? Keep in mind I did not intend to limit this topic to some particular human endeavor. If you're a storyteller writing a novel, what makes a story element "unnecessary" because it is complex? Just as an example.

 

[ADigitalArtist]

What a great OP!

(BTW tree-hugger Quint, I probably never mentioned that the house I live in, is in a redwood grove?)

Lots of possible answers here, but one idea is that humans are pattern-matching machines. A child of 3 or 4 can reliably tell you whether a given picture is a picture of a dog or a cat. This seemingly simple feat is just now barely possible for a computer to do. I'd say that valuing parsimony is consistent with relying heavily on pattern matching. Parsimonious observations will tend to fit patterns more readily.

Though human pattern-matching can get quite beyond parsimonious, which makes sense from a naturalist view. We evolved as bigger brained prey and pattern-matching arose from a survival technique to match sounds and sights to predators. Since there was little down side to assuming that stick was a snake and that sound was a lion and erring on caution, we tend to insert patterns where they often don't exist, or Pareidolia. So a sort of natural proclivity to overcomplicate what we are seeing in an effort to find patterns.

 

[beenherebeforeagain]

Please be so kind as to list something that we know ALL the options.

Sure. When my car starts having problems, while I myself do not know whether it's a simple or complex/complicated problem, I take the car to my mechanic, who can figure it out because they know all the options...and how to decide which is the correct explanation for the problem.

But I do get your point, and I admit my wording was over-broad. "All the options we're considering right now" might be a better phrasing. The key is, even if there is a "best" option out of the three or however many options we're considering to explain a problem, that we recognize that we might be wrong, and that further consideration needs to be given, more information collected. And what seemed simple at first might not be simple on further study.

 

[9-10ths_Penguin]

Well, that's great if you are talking about theories. What about other things in life? Keep in mind I did not intend to limit this topic to some particular human endeavor. If you're a storyteller writing a novel, what makes a story element "unnecessary" because it is complex? Just as an example.

Why would Occam's Razor apply to storytelling?

 

[Fireside_Hindu]

Hmm. Does the "path of least resistance" look the same for all people? Sorry, that's a bit rhetorical - it seems to me the answer to that is no. How does that end up impacting things, we might wonder?

I guess it really depends. For some things I think people look to what others are doing or have done and base their behavior on that rather than reality until something changes.

For example, when cities try to put into place a plastic bag ban, there is initially a lot of resistance because the alternative to plastic bags is seen as more effort. (I have spend more money (initially) on reusable bags, then i have to remember to bring them, then I have to find a pace to store them etc). It's very hard to get people to see the big picture.

Once the laws pass though, and the stubborn ones see their neighbors not only using the reusable bags, but enjoying it and having no problem with it, suddenly they start to change their tune. Maybe it isn't so bad? They realize that it's not really that much more thought, just an alteration of a habit. It takes some adjustment, but it soon becomes as natural as it was before.

But for more personal thing I imagine the path looks different to different people, yes. A lot depends of experience and temperament probably.