28. MATHEMATICS

Ahmed, his first understudy, and his second understudy.

The two understudies make their entrance, in the middle of a lively discussion that began backstage.

FIRST UNDERSTUDY. I am the one and only Ahmed.

SECOND UNDERSTUDY. I understand everything. I am the one and only Ahmed.

FIRST UNDERSTUDY. Imbecile! If I say, “I am the one and only Ahmed,” you’re supposed to say, “You are the one and only Ahmed.”

SECOND UNDERSTUDY. Of course I know that! You are the one and only imbecile.

FIRST UNDERSTUDY. What a cretin! You don’t even know basic arithmetic. You never passed kindergarten!

Ahmed has entered and listens to them without being seen.

Look carefully. We are two. Yes or no?

SECOND UNDERSTUDY. We are two.

FIRST UNDERSTUDY. And two is one plus one.

SECOND UNDERSTUDY. I understand everything. Since we’re two, we’re two times one. Two times one Ahmed. And since you’re an Ahmed, it’s because the Ahmed that you are is one. Now everything that’s one is unique. Therefore I am the only Ahmed.

FIRST UNDERSTUDY. Not you, me! You said, “Since you are an Ahmed one and because everything that’s one is unique.” You ought to conclude, “Therefore, you are the only Ahmed.”

SECOND UNDERSTUDY. I understand everything very well. But! But! I used silent reasoning.

FIRST UNDERSTUDY. What the hell does that mean? Reasoning should always be audible.

SECOND UNDERSTUDY. I understand you perfectly. Reasoning should always resonate! Oh, resonate, silent reasoning!

FIRST UNDERSTUDY. Are you completely hammered or something?

SECOND UNDERSTUDY. Indeed, isn’t it precisely on an anvil that one makes reasonings resonate? Get an earful of this:

Improvisation: as if the second understudy were forging his reasoning on an anvil.

We were two Ahmeds, each of us being one Ahmed. Therefore, I am one and, one being unique, I am the only Ahmed.

FIRST UNDERSTUDY. And what about me, what am I? Any ideas?

AHMED (intervening suddenly). That’s the whole problem right there. It relates to higher mathematics.

SECOND UNDERSTUDY. It must be very high. I understand our master perfectly.

FIRST UNDERSTUDY. You don’t understand anything at all, you pretentious cretin! How does it change what we’re talking about that this gentleman here, who claims to be Ahmed, shows up once again and sticks his nose into our business?

SECOND UNDERSTUDY. Because there were two of us being a single one, and now we’re three. Now three is much more than two. Three is transcendent.

FIRST UNDERSTUDY. Transcendent! What the hell is this jargon?

AHMED. He’s right! Three is enormously more than two. Because in three there’s eight.

FIRST UNDERSTUDY. In three there’s eight? Well, in that case, in me there’s what I ate. Oysters on a plate. Plus their pearls. This gentleman is dishonoring Ahmed with his ridiculous song and dance.

SECOND UNDERSTUDY. I understand everything! He’s an imbecile too.

In what follows, Ahmed organizes the reconfigurations on the stage in such a way that all the subsets become visible.

AHMED. You’ll see if there isn’t eight in three. Let’s say that my name is A1, like Ahmed one, that he (pointing to the first understudy) is named A2, like Ahmed two, and that he’s A3. Do you agree that A1, A2, and A3 are all three in the three? Since there are in fact three Ahmeds.

SECOND UNDERSTUDY. I understand everything! Each Ahmed, who is one, is in the three, because one plus one plus one makes three.

AHMED. So we already have three in the three. Now I’m going to join Ahmed two, I’m going to stick with him, I’m going to drop Ahmed three. It’s A1 and A2 together. That makes something else that’s in the three.

FIRST UNDERSTUDY. What are you talking about, in the three?

AHMED. Where else do you think we should be? We’re two Ahmeds inside the three, if you put them together. They’re still inside the three. How could they get out?

SECOND UNDERSTUDY. How true! The two of A1 and A2 is made up of pieces of the three, so it’s necessarily stuck inside the three.

AHMED. So we’ve already found four things in the three. But if now I stick with A3, this guy, the one who always understands everything, that makes yet another thing that’s in the three. Because it’s made up of what’s in the three and of nothing else. So now we have five things in the three.

FIRST UNDERSTUDY. I’m starting to feel like I’m being had, with this three that fabricates five.

SECOND UNDERSTUDY. Yes, we’re being had big time. I completely get that. And I even get it big time, because there’s at least a sixth thing in the three.

FIRST UNDERSTUDY. You, the imbecile, you see a sixth thing? And where exactly would it be?

SECOND UNDERSTUDY. If we stick together, you and me, while dropping our revered master, that makes one more thing that’s in the three, since it’s now two Ahmeds out of three.

AHMED. He’s not bad, this kid! And now let’s all three of us stick together, nice and tight. That makes one more group that’s in the three.

FIRST UNDERSTUDY. That’s it! I’ve figured out how you keep duping us! You’ve already counted this last group! From the beginning! When you said there’s A1 and A2 and A3, and that makes three things in the three.

AHMED. No, that’s so wrong! What a dope you are! At the beginning, I counted us separately, and the proof is that that made three things. Now I’m counting us as a whole, and that makes one thing completely different from the three others.

SECOND UNDERSTUDY. I understand everything. Each Ahmed makes one, but the three Ahmeds taken together makes one too, which isn’t one bit like the other one, since, instead of there being one Ahmed, there are three stuck together.

FIRST UNDERSTUDY. I’m being had! I’m being duped! What the hell is this three that’s in the three?

AHMED. Where should this three be, if not in the three? If it were supposed to be somewhere else, it would be at least a four!

FIRST UNDERSTUDY. I’m being duped up the wazoo.

AHMED. In any case, we’ve found seven things in the three.

FIRST UNDERSTUDY. Seven, and not eight! Maybe there are seven in the three, but you’d said eight! So where is thing eight? Can you show it to us, this famous eighth thing?

AHMED (acting confused). Can I show it, can I show it … It exists, but showing it is another kettle of fish.

SECOND UNDERSTUDY. It’s true that I don’t see where the eighth thing can be. Where are you, thing eight?

He looks everywhere.

I don’t see anything.

FIRST UNDERSTUDY. OK, imbecile, let’s start all over, and this time let’s count carefully.

SECOND UNDERSTUDY. At your service, Ahmed.

The two understudies redo all the possible arrangements of the three bodies onstage, counting noisily each time.

FIRST UNDERSTUDY. Seven. No two ways about it. Seven. The gentleman here doesn’t know transcendental arithmetic.

AHMED. Sarcastic understudy! Ahmed number 2! Get up on the platform. Good. You’re there, one of the things in the three. Right? OK, now come back down. What operation have we performed? There was one Ahmed on the platform, and we’ve removed one Ahmed from the platform …

SECOND UNDERSTUDY. I know, master, I know! We performed a subtraction! We did one Ahmed minus one Ahmed.

AHMED. And one Ahmed minus one Ahmed makes …

SECOND UNDERSTUDY. Zero Ahmeds.

AHMED. And zero Ahmeds, since it’s produced from the Ahmeds of the three, since it’s A2 minus A2, well, it’s also in the three. It’s the eighth thing in the three.

SECOND UNDERSTUDY. It’s luminous. Zero Ahmeds being produced with things from the three Ahmeds is itself a thing in this three.

FIRST UNDERSTUDY. We’re being duped! “A thing, a thing”! Look at the platform: there’s nothing there at all! Zero isn’t a thing.

AHMED. Careful! Not just any old zero! Zero Ahmeds! If it’s zero Ahmeds, it comes from the three Ahmeds. And, as for the fact that the stage is empty, I warned you: you can’t show the eighth thing, you can only think it.

SECOND UNDERSTUDY. I completely understand how this reasoning resonates on the anvil of our master. I think! I think Zero Ahmeds! Boy, is this good!

FIRST UNDERSTUDY. Now we’re being taken for another ride! Look! I put this stick on the platform, then I remove it. Stick minus stick makes zero sticks, right? And can you tell me how, looking at the empty platform, I can tell the difference between zero Ahmeds and zero sticks? Zero is always zero, whether it comes from three Ahmeds or from a rabbit cage. Zero isn’t in three.

AHMED. All you’ve proven is that zero sticks is also a thing that’s in the one of the stick, just as zero Ahmeds is in three Ahmeds. As for rabbit cage zero, it’s in the rabbit cage.

SECOND UNDERSTUDY. Therefore, zero is a rabbit.

FIRST UNDERSTUDY. Sure looks like it. A rabbit pulled out of a hat.

AHMED. It remains the case that in three there’s eight, which means that three is vastly greater than two.

SECOND UNDERSTUDY. And in four what is there?

AHMED. In four there’s sixteen. Yes, sixteen. But it would take too long to show, and, besides, there are only three of us. What if we did some geometry instead?

FIRST UNDERSTUDY. Good idea. I’m great at geometry, I won’t let myself be had like in arithmetic.

SECOND UNDERSTUDY. I’m a complete dope when it comes to geometry. But I won’t let myself be had either.

AHMED. And how’s that?

SECOND UNDERSTUDY. Because nobody wants to have me. Even my mother used to say to me: we would rather not have had you. Being had happens only to people that people want to have, so being had is still what I don’t have and won’t have.

FIRST UNDERSTUDY (pointing to Ahmed). Haven’t we just been watching him having you?

AHMED. Let’s move on to geometry. The three of us together, on this square platform, form a triangle. A triangle whose apexes are A1, A2, and A3. Question: can the triangle that we form be bigger than a square?

The first understudy takes charge of operations, arranging the three bodies in different key points.

FIRST UNDERSTUDY. The triangle is by definition smaller than the square. I can even show that it’s never greater than half the square. It’s equal to half the square when, for example, we occupy three of the angles of the square. It’s the maximum.

SECOND UNDERSTUDY. I understand everything. It’s the maximum.

AHMED. Is that what you think? Go stand at the two corners of the platform toward the front. Good.

Ahmed disappears and then suddenly reappears at the top of the rear of the stage, standing up, towering over the two other characters.

And now? If you route the triangle through my head and your feet, what’s it like?

SECOND UNDERSTUDY. It’s about as big as the square. I understand everything: it wasn’t the maximum at all, just now.

FIRST UNDERSTUDY. Miserable imbecile! He’s had us again! His triangle isn’t on the same plane as the square!

AHMED. And when did I ever say that it was supposed to be?

SECOND UNDERSTUDY, (to the first understudy). And when did he ever say that it was supposed to be?

AHMED. You’ve always got to read statements precisely. Don’t leave out anything of what’s said and don’t add anything. That’s what makes the Ahmed! And you too (to the audience), take a leaf from my book. In mathematics, of course, but in everything else too, especially in politics: listen to statements, listen to what gets said, without taking anything away and without adding anything of your own whims or hopes. What gets said as it gets said. And never forget anything! Life is a lot more mathematical than you think.