# Short story: If 1+2=3, then 2+3=4, obviously

This was a short story that I would have read in a big collection during the mid-to-late 1980s.

I'm pretty sure that the main plot involves two people (a man and a woman?) who find themselves unexpectedly in the far future. I think they were placed (by themselves or someone else) in suspended animation for an unexpectedly long time. For some reason, they don't wake up as planned and "sleep" unchanged for millions of years in a cave. (I know this sounds a lot like Buck Rogers, but I think it's just the same trope. Maybe I have this all wrong, and there's some other mode of one-way time travel or its equivalent.)

Humanity is gone, but there are other thinking creatures who live on the surface. The protagonists encounter some of these creatures, which I think were telepathic and vaguely bird-like or bat-like. The creatures communicate with the protagonists mentally, and I think later the protagonists decide to help them in a war against some other kind of competing creature.

The part that stands out is when the protagonists and the creature first establish contact. The creature is trying to gauge the humans' intelligence, and an argument crops up over "two plus three." The humans define the sum as "five," of course, but the creature explains that this is wrong. If "one plus two equals three" then "two plus three equals four" by the logic that if the first integer plus the second integer equals the third integer (i.e. 1+2=3), then the second integer plus the third integer must equal the fourth integer (i.e. 2+3=4). I think the story explains that the creatures had built an entirely different mathematics based on different first principles.

This weird math is the only thing that really stands out about the story, but it's unusual enough that it might suffice to distinguish this from other stories with similar plots and tropes.

I came across this by happenstance today while searching for another story. The one I was looking for is "The Fourth Dynasty" (1936) by R. R. Winterbotham -- much older than I expected, and very short (about 7 1/2 pages). It is available to read online in full courtesy of archive.org.

The two characters who find themselves in the future are Victor Hansen and Georgiana Johnson. They get to the future via a new type of embalming fluid (invented by Victor) that preserves living cells, which both Victor and Georgiana end up taking in a Romeo-and-Juliet-like scenario. Georgiana takes hers later after building a special tomb to hold them that is supposed to use a water-driven mechanism to wake them up after a hundred years or so, but the spring feeding it dries up while they are both in suspended animation, and they are instead woken up after 1.5 million years when an earthquake triggers the mechanism.

In the future, they are encountered by a creature named Tulor, of a race called Korans. The two humans are initially mistaken as Xubrans, which are the enemies of the Korans and described as having "savage claws, leathery hides and wings."

The passage about arithmetic (which happens after the initial encounter, and which uses a different logic for a somewhat different argument than I thought) is as follows:

During the inquiry our scientists were considerably amused at Victor's primitive mathematics. It was the first genuine proof we have had that the Einstein Fables -- which every mother reads at bedtime to her children -- were fully believed at one time.

Question: What is the sum of two plus two?

Question: Two plus two do not equal four. The correct answer is three.

Answer: What? Two plus two has always been four!

Question: Let us hear you count.

Answer: One, two, three, four --

Question: How much is one and one?

Question: That is correct. The first number doubled equals the second. It is only logical that the second number doubled should equal the third. Three follows two; therefore two doubled equals three. There is no relationship between two and four.

Answer: I suppose you will say that two and three do not equal five.

Question: Of course not. Two and three equal three and one half. Any school child knows that.

Answer: But supposing three men came into the room, and only you and I were there to begin with. Wouldn't there be five of us?

Question: We are discussing figures, not facts. Supposing that you prove that two and three make five?

Answer: I'm afraid I can't; I'm not familiar enough with mathematics.

• That's not exactly spurious math, since they don't apply it to objects, but just bad communication between the two groups. It's just another number system, related to the familiar one by M=2^(N-1). They seem to interpret fractions relative to the previous number, to interpolate between the powers of two: 3 and a half is three plus half of three, and since 3 is 4 in natural numbers 3.5 is 6, or 2+3 (2+4). It's a bit odd that they would see this as the essential number system, since it has some nasty computational properties. Commented Jun 21, 2019 at 5:52