Reality Has an Inside

Even mathematics seems to accept perspective

Multiple times now we have discussed how:

• The world tries to build the inside from the outside, deduce the interior from the exterior;

• Many falsely reason that from knowing the body we certainly know the soul, that from knowing brain, we must know mind, that there’s nothing else to soul and mind than body and brain in the first place;

• In a way, the entire notion of interiority is ruled out a priori by the materialist worldview.

However, there is an idea from the sciences that to me seems deeply concerned with interiority.

Without trapdoor functions, which enable public key cryptography, the internet as we know it would be largely unworkable. They are a key mathematical principle underlying your ability to send secure messages between, say, your web browser and your bank without allowing anyone in between, even your internet provider, to read the messages. These trapdoor functions rely on the fact that multiplying prime numbers together is far easier than factoring numbers into their constituent primes. Hence, they are “trapdoors”—they “open” only one way. In other words, there is a practical computational asymmetry in mathematics that allows us to construct secure digital barriers of a sort, encryption that your phone can easily “unlock” if you have the key but that a supercomputer would struggle to break without one.

The trapdoor function could be thought of as a weaker, more perspectival, computational version of the Second Law of Thermodynamics, which establishes that physics is directional and thus has time. Computational asymmetry implies that mathematics for situated knowers—and is there another kind?—can have perspective. We are able to securely purchase goods online largely because composite numbers contain their factors but do not disclose them equally to every standpoint.

One of the concerns about the emerging technology of quantum computing is that quantum computers may be exceptionally good at this kind of factoring and thus render much of our current-day trapdoor-function-based encryption ineffective. (This is one reason why trapdoor functions are weaker than the Second Law of Thermodynamics, which no computer will violate any time soon.) However, asymmetry and “situatedness” may have the last laugh. Quantum technologies may also enable secure, widespread use of the “one-time pad,” an encryption technique that if executed properly is mathematically unbreakable without holding the keys. The relevant technique is called quantum key distribution, which is based on yet another intersection of physics with perspective, the fact that at the quantum level there is no observation without participation. All knowers are situated, and their situatedness can be harnessed to strengthen encryption.

What’s more, the one-time pad is mathematically unbreakable because the encrypted message is equally consistent with every possible cleartext of the same length. This is a different way of saying that technically, messages encrypted by a one-time pad contain no information about the original message. The meaning lives entirely in its relation with the key; in effect, the message has no determinable outside, only an inside.

So even in our coming sci-fi future, there will be numbers that are accessible to those on the “inside” and denied to those on the “outside.” A single string of ones and zeros can be eternal gibberish to an eavesdropper and a prayer to the one who wrote it; the history of the number, or, in other words, the other knowledge of the one who wrote it, makes a difference.

This all sounds suspiciously similar to certain Chassidic metaphors for the Divine act of Creation. In the Torah, being derives from G-d’s speech. A teacher contracts his vast personal understanding into a dense metaphor that the student can only grasp superficially, from the outside, but that from the teacher’s perspective transparently contains all the depth of his intellect. If the trapdoor function firmly distinguishes informational inside from outside, and the one-time pad eliminates the outside entirely, then Chassidus questions whether the entire distinction between inside and outside is itself one of the effects of createdness. What if “outside” is not where G-d is absent, but merely that disclosure of G-d which is unrecognizable without the key?

The secret to G-d’s closeness is not another being beyond the object or an encounter beyond all we have encountered, but the relationship of createdness that makes this object and all encounters Divine. We should be looking to understand the teacher and how He spoke, not sulking because we don’t hold the keys. Genesis is genuinely epistemically superior to mere inspection from within the creation. The outside is not as outside as it first appears, given G-d. Even science doesn’t entirely concede a view from nowhere. Reality has an inside. So let’s delve.