One Answer About Grabel's Law

Submitted by Ken Watts on Tue, 03/05/2013 - 14:54

The daily mull generally deals in questions which do not have final, simple, definitive answers.

This time is almost an exception.

Some time ago, I posted a little essay on Grabel's Law (you can find it here) :

"Two is not equal to three, even for very large values of two."

The law, as most of you who find your way to this post will already know, is fairly famous on the internet and even on T-shirts and mugs.

At the time I wrote about it, I had no idea who Grabel was, or what the law's origin was, and I could find no evidence of either.

The post got a lot of attention, and a lot of comments, including one from a student who claimed to have heard his professor (Arvand Grabel at Northeastern University) actually state the "law" in class:

This is quite an old topic, but since I was involved in Grabel's Law, I'll take the time to tell the story. Arvand Grabel was a professor (later Department Head) at Northeastern University.  In or about 1977 he was a visiting professor at The Cooper Union for the Advancement of Science and Art, where it was my privilege to study under him.One day he gave a small test involving a problem in which one source in a circuit nulled the current that another source would have induced.  (It was actually the theoretical model of a perfect Op Amp.)  Many of us caught on, but  few of us were determined to find a rationale for some current to remain in that branch of the circuit.In explaining the problem and the result, Professor Grabel, who was rail-thin, placed one foot on the desk in front of him (a habit which I am told helps certain back problems), stuck his chin out over his knee, raised one finger in the general direction of the light fixture, and declared "Gentlemen, Two is Not Equal to Three, Not Even for Large Values of Two!"This plays against the engineering maxim that X is equal to X plus one for sufficiently large values of X.At lunch, or perhaps on the way, one of us christened this declaration Grabel's Law.In the early 1980s, a single giant Fortune Cookie file circulated on UseNet.  I added Grabel's Law to it then.  In the years since, I have been tickled by its staying power, and doubly tickled to find it in print in daily tear-off calendars.  Every few years, I check for it on the Web, and Google turned up this article.So there's your answer: it's a Real Engineering School Story.

I did a search for an Arvand Grabel at Northeastern University, which came up blank, and so I responded to that reader's comment by cautioning other readers that it may or may not be true:

I generally don't question the veracity of my readers, and I won't this time. Let me just say to other readers that I tried to verify the existence of "Arvand Grabel at Northeastern University", and failed.

So, the delightful story above may well be true, or it may be simply a beautifully written anecdote by a remarkable storyteller.

Since I don't actually know njcommuter, I can't say which.

If it's the latter, then thanks for the entertainment. If it's the former, thanks for solving the mystery.

Subsequently another reader commented again:

I googled Grable Northeastern University and found an emeritus professor named Arvin Grable. The story seems to check out both subject- and timewise.

I followed up that lead, located Arvin Grabel, and sent him an email, asking if he could verify the story.

Here's his response:

Ken—I originally said that 8 is approximately 10 for large values of 8.  My inspiration for this remark was one of my professors—Charles Rehberg—at NYU who was one of the greatest teachers I had.


So there you have it.

We have located the real Grabel, but he seems to have created a different form of the "law".

If I read it correctly, it's a bit more ironic than the more popular version.

At least, that's what I think today.


PS: I received another note from Arvin Grabel, after posting this.


Ken—Thanks for the update.

My “law” has two motivations:

1. How to estimate the result—the easy part.

2. In regard to the OP-Amp I try to say that something very small is not negligible compared to zero.



That about sums it up.