Is there a limit to what we can understand?

Economics, at its best, looks past labels and asks what actually happens: what causes what, which assumptions are being smuggled in, and whether a model describes reality or merely rearranges its own premises.

Terms like “bonds,” “notes,” “bills,” and “borrowing” mean something entirely different when applied to the private sector vs. a Monetarily Sovereign government. That this is not well understood by the public or even by economists is one of the great failings of that would-be science.

In science, calling something “entanglement,” “gravity,” or “consciousness” does not tell us what it is. It only tells us what category we have placed it in.

Everything we learn, we learn by analogy. Visualize an atom. You see something that’s like a miniature solar system. Visualize magnetism. You visualize something pulling on something, like a rubber band. And space-time is like a rubber sheet with a bowling ball in the middle. Those are your analogies for learning, but they are wrong.

An atom is not a bunch of point particles circling a nucleus like a solar system, nor does magnetism attract. It is more like a grid with numbers at each crossing, telling the grid what to do. Except, it’s not like that either.

Mathematics may be the greatest analogy ever invented. It gives us structures that can match observed behavior with astonishing precision. But a successful mathematical description is not necessarily reality itself.

It may be more like a map that predicts every turn while remaining silent about what the landscape actually is. Nature does not follow equations. Nature behaves. We invent equations that imitate that behavior.

Aerial view of a man standing in vast desert stretching to the left, a colossal ancient wall dominating the center. The ...
He may physically be incapable of seeing or even imagining all that is on the other side.

The danger comes when prediction is mistaken for explanation. If an equation tells us exactly what entangled particles will do, physics may congratulate itself for having solved the problem. Yet the equation still may not tell us why entanglement exists, what physical reality produces it, or what the equations are equations of.

The oft-quoted term, “Shut up and calculate,” meaning “don’t worry about ‘why’ or even ‘how’; just determine ‘what’,” may be useful advice for getting results, but it becomes destructive when it is treated as the limit of legitimate curiosity.

Suppose we could perceive spacetime and gravity directly. Would spacetime appear smooth, granular, turbulent, knotted, flashing, layered, or alive with patterns invisible to us? Would gravity behave differently within an atom than between stars? Would it fragment near concentrations of energy? Would it respond to stimuli?

These questions sound speculative only because our present language and senses are so limited. They are attempts to imagine the hidden reality beneath our mathematical summaries.

The hardest question in physics is not “what?” or “how?” but “why?” Even discovering what spacetime looks like would not answer why it looks that way. If it consists of microscopic knots, why knots? If the knots minimize energy, why that form of energy? If some deeper field produces spacetime, why does that field exist and behave as it does?

Every answer generates another meaningful “why.” Knowledge may not be a mine with a bottom. It may be an endlessly branching structure in which every explanation becomes the premise of a deeper “why?” question.

This suggests a boundary more profound than ordinary ignorance. There are things we do not know but could learn. There also may be things our minds are not built to understand.

A dog cannot understand calculus, not because nobody has explained it clearly enough, but because the dog lacks the mental architecture in which calculus could exist. Human beings may stand in the same relationship to some aspects of reality.

Entanglement may be our first clear encounter with that possibility. We know what it does with extraordinary precision. We can calculate correlations and verify them experimentally. But every familiar analogy fails. No picture drawn from ordinary space, objects, signals, or causes seems capable of containing the phenomenon without distortion.

Perhaps entanglement is not merely difficult. Perhaps it lies beyond the range of concepts the human brain evolved to represent.

I wrote a short story titled, “The Meaning of Awareness,” that turns on one’s ability to visualize the phrase. “I know that you know.” Then, another level, “I know that you know that I know.” Then another level, “I know, that you know, that I know, that you know.”

The challenge was for the narrator to see how many levels he could visualize.

In the climactic paragraph, he says:

“Then in one all-consuming burst, I discard my fear, and organizing my structure, I exert my every mental effort. “I know, that you know, that I know, that you know, that I know, that you know . . .” Yes. There. I saw it. Only for a second, but I did see it. From here I see infinity. Triumph. I have attained level six. Yet in my triumph I feel despair, for I see now that I never shall understand level seven. It is beyond my aptitude.”

And then, a voice says,

“Then know this: There are those who have achieved level one hundred.”

“No,” I cry. “That cannot be. One hundred. What glories can such incredible creatures know? What is their universe?”

“They know beyond an infinity of infinities. They see all the multitude of dimensions. They visualize this cosmos and all the others beside it. They understand time before the beginning and time after the end.”

The human mind has limits It eventually loses its ability to hold the nested structure as a whole. The protagonist barely and briefly manages six levels, then learns that another entity can visualize one hundred. His limitation does not doom him to stupidity. It dooms him to ignorance. It dooms him to being human.

If an artificial intelligence can visualize, one eventually might visualize a thousand levels. We cannot imagine what knowing this would be like.

Mathematics has no such difficulty visualizing. A formula can represent one hundred, one thousand, or a million recursive levels with ease. The structure can be defined perfectly even though no human ever can visualize it. This separates mathematical description from human understanding.

Two people looking at more and more mountains receding into the distance
After several thousand years climbing one mountain, humanity sees that many more exist, and wonders whether there will be the time or the ability to climb them.

Mathematics may continue far beyond the point at which intuition collapses. We may know that something exists, prove how it behaves, and still remain unable to conceive what that existence is like.

The same may be true of dimensions, infinities, and the ultimate structure of reality. Georg Cantor showed that infinity is not a single final vastness. There are larger infinities beyond smaller ones, and infinitely larger ones beyond those.

The unknown may possess a similar architecture. There may be an infinite universe of questions within human conceptual reach and an even larger infinity beyond it—followed by an infinite succession of still greater conceptual worlds.

Other creatures in the universe may be greater than we are. A different biological intelligence, or perhaps a future artificial intelligence, might hold structures that collapse inside a human mind.

Such a being would not merely calculate faster or remember more facts. It might perceive relationships that do not exist for us as conceivable objects. What we call paradox might appear to it as plainly as a circle appears to us.

But even that intelligence may encounter its own wall. Beyond its “hundred levels” may lie an entity capable of ten thousand. Beyond every conceptual horizon may be another horizon inaccessible to the mind below it.

Intelligence, then, would not be a division between those who understand and those who do not. It would be an endless hierarchy of what each kind of mind is capable of understanding.

Once you stop being able to answer, or even ask, the next meaningful “why,” you have reached the boundary of your conceptual world. The universe may continue beyond it, but your understanding does not. That boundary is not the edge of reality. It is only the edge of the mind doing the asking.

There may be an entire universe on the other side of the “WHY?” wall, and we are not yet tall enough to see over it. Mathematics may tell us that the universe is there. It may describe its outlines and predict its effects. But description is not vision, calculation is not comprehension, and “what” is not “why.”

The haunting possibility is not merely that there are truths we do not yet know. It is that there may be truths which are perfectly coherent, perfectly lawful, and perfectly describable, but which no human mind ever can understand.

We cannot imagine what we cannot imagine.

Rodger Malcolm  Mitchell

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