## Grist for the Mull

Ken Watts - Tue, 2007/08/21 - 11:10am

Some time ago I posted, as one of the Daily Quotes, Grabel's Law:

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

I posted it because I found it particularly funny, and then forgot about it. But recently, I've had a run of visitors to the site, all through searches for Grabel's law, and that has raised two questions for me:

- Why the sudden interest in Grabel's law?

If you've come to this post by searching for Grabel's law, leave a comment below. - Who was Grabel?

If you know, or if you can find out, please tell us all about that, as well. - Why is Grabel's law funny?

I'm open to other views on this, too, but I actually have a theory of my own.

I think the humor lies in the combination of two elements. First there's the nonsensical mathematical jargon—treating a number, 2, as though it were a variable, x or y—which is slightly amusing in itself.

But added to this is a basic trait which we've all seen in our fellow humans—the tendency not to give up in the face of a simple fact. How many times have you heard someone advance a theory in conversation, only to be proved wrong. How often do they immediately give up? How often do they grasp at straws? You know the kind of conversation:

Guy with martini: "Winter is colder because the light from the sun hits the earth at an angle and bounces off."

Science teacher: "Actually, that's only partly right. The light does hit at an angle, but it doesn't 'bounce'. It's just that the angle means the light gets spread over a greater area."

Guy with martini: "Yeah, it gets spread over a greater area, but I think it bounces a little, too."

Science teacher: "Actually, bouncing has nothing to do with it."

Guy with martini: "Well, I think it depends on your point of view..."

I suspect that when we first hear Grabel's Law there's a faint subtext in our brain, a very subtle echo of a conversation that goes something like:

Guy with martini: "Very few people know this, but they've recently proved that two can sometimes equal three."

Math teacher: "Math happens to be my field, and nobody has proved any such thing. Two does not equal three."

Guy with martini: "Well, not ordinarily. But for very large values of two...(For surprising news

about the real Grabel

see the next post...)

## Comments

bazkie replied on Permalink

"If you've come to this post by searching for Grabel's law, leave a comment below."

i did, i read the quote on my igoogle page (it displays random quotes from some quotations page). it captured my interest because of the mathematics/nerd-factor ;) as an information sponge, i usually google anything i find the least bit interesting :)

anyway, nice post! :)

timeofnick replied on Permalink

Ditto the above comment. I also have a daily quotes app on my igoogle page and googled Grabel's law for the same reason: curiosity about who Grabel is.

someguy replied on Permalink

A slight tangent, but....

You can actually prove that 0.9999.. is equal to 1 with some very simple proofs.

Any calculator (or basic understanding of long division) can show that:

1/9 = 0.1111..

And anyone familiar with the basics of fractions can see that:

9*(1/9) = 9/9 = 1

but, writing the same thing slightly differently:

9* 0.1111.. = 0.9999..

You get something that doesn't appear to be the same at first glance. But by the transitive law we can legally rewrite it as:

1 = 0.9999..

Or for another proof:

Let c = 0.9999.. and thus 10*c = 9.9999..

Easy so far...

But if we subtract 'c' from both sides:

(10*c) - c = 9.999.. - c

We get:

9*c = 9

which is easily solved to give:

c = 1

Which again implies that 1 = 0.9999..

-Just some guy

g31110 replied on Permalink

I saw it on igoogle as well.

Nice site, though.

chihuahuab replied on Permalink

Same here, I saw it on IGoogle, thats why I'm here LOL

Abhoth the Unclean replied on Permalink

This is not about maths or about who Grabel might or might not be. The first is useful for high precision stuff and might even lead us in an interesting direction regarding the meaning of life, the universe and everything. The second is the messenger and not to be confused with the message. The beauty of this quote lies in the absurdity and in its usefulness to the modern political leader who continually try to tell us that black is white, red is blue and that 1 + 1, if there are enough votes in it, equals 3.

Abhoth

``

jayflight replied on Permalink

As with the others, Daily Quotes brought this up and I thought it was amusing! A similar quote I found was:

"1 + 1 = 3, for large values of 1."

As someone who has been using the Weight Watchers Points system and found that eating 1 item worth one point twice lead to a total of 3 points... lead me to the following thought...

1.4 + 1.4 = 2.8

and if you apply rounding principals...

1 + 1 = 3.

Darn math!

Ken Watts replied on Permalink

Thank you all for your interest, insights, and wit!

-Ken

njcommuter replied on Permalink

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.

Ken Watts replied on Permalink

I'll leave my original apply to njcommuter intact below, but for those who want to skip to the conclusion of the search for the real Grabel, check here.

I generally don't queston 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.

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