Back | Next
Contents

1.6

Post-Encounter Deposition

Evelyn Chang, PhD

Department of Mathematics,

Massachusetts Institute of Technology


To a mathematician, human speech is a really loose, imprecise notation. This, all by itself, makes my interaction with the Beings tough to describe. I mean, the psychedelic aspects of the Encounter have already been talked about: Yes, we smoked DMT. Yes, we were floating in zero gravity, in a big inflatable donut in the darkness of interstellar space. You don’t know your own name when you’re in that kind of a state, but that’s not really the problem. Thing is, I’m at a loss for words if I can’t start by defining what they mean. Is that all right? Can I do that?

Short version: the Beings’ communications are framed in something similar to a formal mathematical notation, but without “symbols” in the human sense. For us, a symbol might be a geometric shape, on paper or on a computer screen, or pictured in the mind. Or it’s a sound, or a burst of radio photons—some kind of container, that represents an idea. We string symbols together to form statements, and we string statements together to form proofs or, in the case of language, I suppose you’d say “stories” or “songs” or “conversations.” To make sense, we have to arrange the symbols chronologically or geometrically. The Beings don’t do it that way, but I felt like they were trying to—straining to—for us.

Longer version: they use set theory. This isn’t surprising, since all mathematics can be formulated that way. However, there are other frameworks or notations that function just as universally, so we can consider all the ways the Beings don’t speak. They don’t speak in terms of geometry, topology, arithmetic, algebra, tensors, vectors, derivatives, or integrals. Or, at least, they didn’t speak that way to me.

In simple terms, I don’t believe the Beings have any use for Boolean formal logic. It would not make sense to them to say, “IF X is TRUE, AND X OR Y is TRUE, AND X AND Y is NOT TRUE, THEN Y is NOT TRUE.” Even humans don’t think that way. We can force ourselves to, but then we’re really just using neural networks to do something, badly, that Boolean gates do well and quickly. The Beings may be even further abstracted; I didn’t get a sense that the concepts of True or False were of any interest to them at all. The Beings are clearly not made of gates, or neural networks for that matter.

I also don’t think they have a use for numbers. They might be aware of them, I don’t know, but it wouldn’t make sense to them, to talk about “two people.” Instead they might talk about a “set” that contains both Amy and Bob. However, Amy is also a set, because she’s made up of quadrillions of cells, each of which is made up of hundreds of structures and trillions of atoms. And I think they don’t even really care about the atoms or structures, except maybe in terms of how they operate on the set. So instead of “two people,” the Beings might say, “The set that contains all of this Amyness over here and all of this Bobness over there.” I think this is really important to understanding what the Beings are, and how they see themselves, and how they see us.

Can I get more formal, please? The notation isn’t difficult. In set theory, you have a relationship between an object “o” and a set “A.” If o is a member of A, then we say:

o ∈ A

If all members of A are also members of B, then either A and B are equal (A=B), or B is a “proper subset” of A:

A ⊆ B

Two very important sets, which we can define as axioms or postulates of our notation, are:

• U := The universal set (a set that contains all possible sets or objects)

• {} := The empty set (a set that contains no sets or objects)

Set theory also includes operations you can perform on sets, which are equivalent to arithmetic operators on numbers, or Boolean operators on logical expressions:


So the Beings (who always seem to be plural) might think about Amy and Bob by saying:


(A ∪ B) ⊆ U

(A ∪ B) ⊆ H

A ∩ B = {}

B\A = B

A\B = A


In other words, “Amy and Bob exist. Amy and Bob are humans. None of the objects within Amy are also within Bob, i.e., the set of Amy and the set of Bob are defined as being totally separate entities.” And where it gets interesting would be something like:


P (A) = ?


“What are all the subsets of Amy?” Or, to get closer to what they’d mean by this, something like, “Holy crap! What the hell is Amy?”

Harv Leonel swears that the Beings can split and recombine. If this is true, and if a “split” Being is identical to the “unsplit” or “combined” Being in an n-dimensional space, I could certainly see them being confused by humans. A significant portion of the stuff in a human is not really unique and is not inherent to human-ness or to that individual human’s identity. Also, all that mass-energy gets cycled through every seven to ten years anyway. Is the human a sort of wiggly standing wave, with matter washing through it, that exists only with a paired forcing function (body/environment) maintaining and tweaking it?

Anyway, you don’t need to understand all that. It’s just a notation. It’s an example, to give you the flavor of what I’m talking about. So, now I can explain: What I got from the Beings was a series of mathematical proofs. A lot of them! A firehose of them, smashing into me. More than I could process, or count, or remember. Here’s an example:


• B := Beings

• H := Humans

• U := Universe

• UB := Native Scope of Existence of the Beings within the

Universe

• UH := Native Scope of Existence of the Humans within

the Universe

• pH := Perception of Humans

• pB := Perception of Beings

• iBH := Interaction/communication between Beings

and Humans (commutative?)


B ∈ UB

H ∈ UH

UB ∪ UH ⊆ U

pH ⊆ UH ⊆ pB ⊆ UB

pB ∩ pH ⊆ iBH


Or something like that. What I think it means—what it meant to me at the time—was that the Beings themselves exist, but that their existence looks nothing like ours. By analogy: the universe is a simulation, and we’re computer graphics dancing on a screen somewhere. Not just human beings, but everything we see and feel: graphics. But the Beings aren’t on the screen at all; they’re maybe something like data structures in raw machine language, like a background process on the CPU itself. That’s my analogy, not theirs.

But you ask me: What did they look like, what did they feel like, what did they sound like? And it’s just nonsense. They’re not on the video screen with us. They can interact with our weird slice of the universe, but only from a remove, by manipulating energy in the CPU. Now, I know everyone’s Encounter was different. All one hundred of us, completely different. I can’t explain that, and it’s not my job to explain it. This is what the Beings told me. This is what they said, which is actually an interesting philosophical point all by itself.

One bedeviling question in mathematics has always been, is math an invention or a discovery? Or a mixture of the two, in which case, which parts are which? I personally lean toward the discovery side of the argument, because some internally consistent frameworks can be used to describe the universe, and some can’t. You don’t “invent” a hammer made of soap bubbles, because that doesn’t do anything. What you do is discover the art of hammering things, and then invent a better and better hammer.

Set theory certainly avoids some human-y thoughts about math, but then so would topology. You could come up with equivalent proofs in a few different math points of view like analysis, topology, set theory type, just like there are equivalent definitions of continuity. The Beings might even know how to do that, but it isn’t how they think. For so long, the SETI people, and the astronomical community generally, have assumed that alien intelligences would have to know about number theory, but why should they? What are they trying to communicate? If the medium is the message, then the Beings have told us groupings are more important than numbers, for understanding the universe. If we assume they know more about the universe than we do, this is something where we should sit up and take notice.

Let’s say, for the sake of argument, that a Being, or at least the avatar of a Being on our computer screen, can be represented as a four-dimensional (or n-dimensional) hyperellipsoid. From the Analects of Brother Michael (ha!), we get a general sense that the ellipsoid has a fixed total volume, or some equivalent, non-geometric constraint. It can stretch in one dimension, but then it has to shrink in at least one other dimension in order to meet that boundary condition.

How would such numerically, materially, topologically naïve Beings approach mathematics? Their thoughts on the subject might be the aspiration of all pure mathematicians! In linear algebra (another form they don’t seem to use), the big divide isn’t three or more dimensions, it’s between finite and infinite dimensions. That’s what changes which theorems hold. And in analysis, there’s a lot of discussion about the size of infinites—countable, uncountable and bigger infinities (which relates to power sets, interestingly enough). Topology doesn’t even have ways to measure time or distance, and of course sets are about whatever you want them to be about (ha again!).

Geeking out a bit, I’ll say (just for the benefit of my colleagues and for reasons too complicated to explain here) that the Beings, even if “smooth” in three or even four dimensions, must be self-similar in n dimensions at differing scales of measurement. Assuming the solutions are nondegenerate, are the Beings spacetime fractals that can be categorized with respect to the particularities of the details of self-similarity? Do you have to shift position slightly in n-space to perceive a difference in scale, and what increment before B(x,t) = B(x+delta_x,t +delta_t)? Ah, they reveal periodic wave structure as well. Are they something like time crystals, but periodic in dimensions other than our linear time?

Much work ahead.

I suppose writing this for a lay audience is something I’ve failed to do, but using English to talk about alien math is like hitting rocks with that hammer made of soap bubbles. We humans invented math because there was no other way to get certain kinds of things done. And yes, I’m thinking maybe communicating with alien Beings is one of those things.


Back | Next
Framed