Proof by Analogy

I often post comments on my Twitter or Facebook feed that are a little.. untrue, or jarring. For example, I once claimed that “Ignorance can lead to the better outcome” (expanded upon in a blog post – Left Hand Don’t Know).

Other times, I try to post a comment which might elicit some responses, like the time when we got a chorus of Princess Bride quotes all over my Facebook wall after I posted a series of updates with blanks to be filled in. Fun for all!

I was trained at college as a mathematician, and I know the basics (and many of the nuances) of various forms of proof. I know, for example, that if you accidentally take an untruth to be true, you can then go on to prove anything else in the World you want. In other words, once you assume a contradiction, you can also prove that unicorns and everlasting gobstoppers exist.

Similarly, proof by analogy is invalid. This one often irks me since
you will often see folks in the news making arguments based on analogy,
and then standing back proudly as if they had proven something. They
are being persuasive, but they are not proving anything. And persuasion
is important and useful (I use it myself every day). But every day I
see folks mistaking persuasive arguments for valid proofs, and acting
on the conclusions as if they were mathematical truths. No such thing.

Keep in mind, please, that the word “proof” can be applied, with very different meanings, to mathematics or science. In math, something proven is unquestionably true. In science, “proof” simply means that you have repeated your experiment so many times with (arguably) identical results that you (and everyone else) should believe that your “theory” is true. Very different.

The word “proof” as applied to debate and persuasion is again very different. It simply means that you won over the hearts of your audience. Congrats, that’s not easy to do!

Goofing on Facebook

So as a goof recently I claimed on Facebook that I could “prove anything by analogy”, and challenged my friends to test me.

Immediately came back three commonly accepted “truths” – wanting a proof for each:

  • You cannot trisect a straight line (from an engineer)
  • E = mc2 (c’mon!)
  • We park on driveways and drive on parkways (hmm..)

I did not say it would be easy for me to come up with the proofs. While not valid in arriving at truth, arguments which prove by analogy are still exceedingly difficult to craft and sell to the public. This is gonna take some work.

Back in the Office

What does this have to do with our day?

I would like to think that it used to be that there might be one or two people in our life or community who made unsubstantiated claims in a persuasive way, or who was kooky enough to believe and convince others of things that were either mere opinion, or just plain not universally true. We might say the person was “kissing the blarney stone” or “just a curmudgeon” or “had an axe to grind”. It might be the mythical town drunk or the elder grandparent who rambles on about back when we used to “wear an onion on the belt” (Grandpa Simpson). Disclaimer: I, in fact, DID used to wear an onion on my own belt, since it was the “fashion at the time”.

But today the situation is different. It seems like everyone has access to more information than is helpful, and everyone thinks they have a valid proof for whatever they believe. PLEASE NOTE: I am just as guilty of this, in my worse moments, and I really try to avoid it when possible.

My own personal belief is that the reason for the current plethora of proofs is that folks think they must have proof for their beliefs. Somehow, it seems like many folks are not comfortable just holding a belief, unless they can also argue it as true. And beliefs, being just that – beliefs, can never be proven, unless you resort to the invalid forms – proof by analogy or proof based on an assumed contradiction.

So the next time someone approaches you with an idea or a new project, and builds a wall of absolutism around it, seemingly backed by proofs and truths – take a step back. See what other things you might be able to prove, simply by drawing analogies to unrelated (but similar) ideas. It gets goofy.

Here goes – “E = mc2”. Well, this is saying that the energy inherent in an object is equivalent to the mass of the object, multiplied by the square of the speed of light (which is a helluva big number). In other words, a small mass can result in a lot of energy. This is the basis for the destructive nature of an atomic bomb.

That’s easy. It’s like when you go to a party at a club. All the people are the masses. Multiplying is like adding lots and lots, so you add more people and lots of lights, and BINGO – lots of energy. More energy than you ever could have imagined, right? Ever got that feeling, where you are just taken over by the music and the lights and don’t know what caused you to have that kind of fun?

Proof by analogy. Pretty lame. Q.E.D.