Skip to main content

Logic: Occam's Razor

I just read the summary of Occam's Razor on Wikipedia, and it turns out that most people, including me, don't understand what he was really trying to say. Specifically, it does not mean "All other things being equal, the simplest solution is the best." Here's the quote:
Ockham's razor (sometimes spelled Occam's razor) is a principle attributed to the 14th-century English logician and Franciscan friar, William of Ockham. The principle states that the explanation of any phenomenon should make as few assumptions as possible, eliminating 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 parsimony" or "law of succinctness"): "entia non sunt multiplicanda praeter necessitatem", roughly translated as "entities must not be multiplied beyond necessity". An alternative version "Pluralitas non est ponenda sine necessitate" translates "plurality should not be posited without necessity". [1]

This is often paraphrased as "All other things being equal, the simplest solution is the best." In other words, when multiple competing hypotheses are equal in other respects, the principle recommends selecting the hypothesis that introduces the fewest assumptions and postulates the fewest entities. It is in this sense that Occam's razor is usually understood. This is, however, incorrect. Occam's razor is not concerned with the simplicity or complexity of a good explanation as such; it only demands that the explanation be free of elements that have nothing to do with the phenomenon (and the explanation).

Originally a tenet of the reductionist philosophy of nominalism, it is more often taken today as an heuristic maxim (rule of thumb) that advises economy, parsimony, or simplicity, often or especially in scientific theories. Here the same caveat applies to confounding topicality with mere simplicity. (A superficially simple phenomenon may have a complex mechanism behind it. A simple explanation would be simplistic if it failed to capture all the essential and relevant parts.)

Comments

Anonymous said…
I've been playing with some statistics related to this idea recently; specifically, the lasso:
http://www-stat.stanford.edu/~tibs/lasso.html

The idea is to fit a least squares regression with the minimum number of free parameters (i.e. the fewest assumptions). The tricky bit is weighing the number of assumptions against the quality of the fit ("with enough free parameters, I can fit you a horse") and figuring out how to interpret the complex fitting algorithm in terms of degrees of freedom.

Annals of Statistics 35:2173 gives a neat proof that the degrees of freedom are directly proportional to the number of fit parameters, and Annals of Statistics 32:407 gives an implementation with the same computational cost as a regular least squares fit.
jjinux said…
I think I just heard something flying over my head.

Sounds like fun, Mark :)
Brandon L. Golm said…
Coincidentally, right before you checked I totally made that up and put it in wikipedia.

They have since reverted my edit; it's now back to normal.

And seriously, did you really believe that complicated explanation of Occam's Razor? Obviously the simpler explanation is correct.
jjinux said…
That's hilarious!

Popular posts from this blog

Drawing Sierpinski's Triangle in Minecraft Using Python

In his keynote at PyCon, Eben Upton, the Executive Director of the Rasberry Pi Foundation, mentioned that not only has Minecraft been ported to the Rasberry Pi, but you can even control it with Python . Since four of my kids are avid Minecraft fans, I figured this might be a good time to teach them to program using Python. So I started yesterday with the goal of programming something cool for Minecraft and then showing it off at the San Francisco Python Meetup in the evening. The first problem that I faced was that I didn't have a Rasberry Pi. You can't hack Minecraft by just installing the Minecraft client. Speaking of which, I didn't have the Minecraft client installed either ;) My kids always play it on their Nexus 7s. I found an open source Minecraft server called Bukkit that "provides the means to extend the popular Minecraft multiplayer server." Then I found a plugin called RaspberryJuice that implements a subset of the Minecraft Pi modding API for B

Ubuntu 20.04 on a 2015 15" MacBook Pro

I decided to give Ubuntu 20.04 a try on my 2015 15" MacBook Pro. I didn't actually install it; I just live booted from a USB thumb drive which was enough to try out everything I wanted. In summary, it's not perfect, and issues with my camera would prevent me from switching, but given the right hardware, I think it's a really viable option. The first thing I wanted to try was what would happen if I plugged in a non-HiDPI screen given that my laptop has a HiDPI screen. Without sub-pixel scaling, whatever scale rate I picked for one screen would apply to the other. However, once I turned on sub-pixel scaling, I was able to pick different scale rates for the internal and external displays. That looked ok. I tried plugging in and unplugging multiple times, and it didn't crash. I doubt it'd work with my Thunderbolt display at work, but it worked fine for my HDMI displays at home. I even plugged it into my TV, and it stuck to the 100% scaling I picked for the othe

Creating Windows 10 Boot Media for a Lenovo Thinkpad T410 Using Only a Mac and a Linux Machine

TL;DR: Giovanni and I struggled trying to get Windows 10 installed on the Lenovo Thinkpad T410. We struggled a lot trying to create the installation media because we only had a Mac and a Linux machine to work with. Everytime we tried to boot the USB thumb drive, it just showed us a blinking cursor. At the end, we finally realized that Windows 10 wasn't supported on this laptop :-/ I've heard that it took Thomas Edison 100 tries to figure out the right material to use as a lightbulb filament. Well, I'm no Thomas Edison, but I thought it might be noteworthy to document our attempts at getting it to boot off a USB thumb drive: Download the ISO. Attempt 1: Use Etcher. Etcher says it doesn't work for Windows. Attempt 2: Use Boot Camp Assistant. It doesn't have that feature anymore. Attempt 3: Use Disk Utility on a Mac. Erase a USB thumb drive: Format: ExFAT Scheme: GUID Partition Map Mount the ISO. Copy everything from