There's a number that shows up everywhere you look, once you know to look for it. It's in the way money grows in a bank account, the way a hot cup of coffee cools, the way radioactive atoms decay, the way a population of bacteria explodes, the way your memory of a phone number fades over a week. It's 2.71828182845..., never repeating, never resolving into a clean fraction, just rolling on forever. Mathematicians call it e. Most people meet it once in a calculus class and never think about it again.

That's a shame, because e might be the single best metaphor mathematics has ever produced for what it means to accumulate yourself. That makes it an oddly perfect mascot for a much bigger question: what is experience, actually, and could anything that "remembers" its own past, a cell, a planet, a star, be doing a primitive version of what we call consciousness?

Let's take the scenic route.

Where *e* actually comes from

Forget soul talk for a second. e was discovered by accident, by a 17th century mathematician named Jacob Bernoulli, who was staring at compound interest. If a bank pays you 100% interest once a year, your dollar doubles. If it pays 50% twice a year, compounding on itself, you end up with a little more than double. If it pays you a tiny sliver of interest continuously, every infinitesimal instant, compounding on top of compounding on top of compounding, forever, your dollar doesn't grow to infinity. It converges, beautifully, to e times itself. That's literally what the number is: the result of letting growth compound on its own output, infinitely finely, forever.

Here's the detail that matters for our story. The function built from e, written as e raised to the x, has a freakish property. Its rate of change at any moment is exactly equal to its own current value. Take its derivative, the slope, the "what happens next," and you get back the exact same function you started with. No other function in mathematics does this, except scaled copies of it. In plain English, e to the x's future depends only and entirely on everything it has already become. It doesn't grow according to some outside clock. It grows according to its own accumulated self.

If you wanted one sentence to describe how a memory bearing system works, a brain forming new thoughts out of old ones, a culture evolving out of its own history, a person becoming who they are out of everything that has already happened to them, "the next moment is proportional to everything accumulated so far" is a startlingly good one liner. It's not proof of anything mystical. It's just a strange resonance between a 300 year old banking formula and the shape of becoming itself.

Now for the soul constant leap. Read this part as a metaphor, not a theorem. Picture experience, your experience, a tree's experience, maybe even a stone's faint flicker of something, as something that compounds the way money compounds. Every moment, a system registers a difference: light hits a retina, a wave erodes a coastline, a customer's mood shifts a sales call. Most of those differences just vanish, the way a wave leaves no lasting mark on the ocean. But sometimes the difference leaves a trace, and if that trace bends the system's future behavior even slightly, you've got the seed of memory. Memory shapes the next trace. The next trace shapes the next moment. Compounding on compounding on compounding, forever, the way the bank account compounds. Except now what's compounding isn't money, it's you.

If you wanted a single number to symbolize a system whose future is built entirely out of its own accumulated past, compounding without end, e is sitting right there, looking smug, because that is exactly the mathematical situation it was born to describe. Call it poetic license, not a proof. Nobody has shown that e equals "the sum of all experience" in any rigorous sense, and you should be suspicious of anyone who claims otherwise with a straight face. But as a symbol, a number that never terminates, never repeats, and is mathematically defined by infinite self compounding, is a pretty satisfying stand in for a soul that's never finished becoming.

Now the part you actually asked about: can a rock have something like consciousness? The honest, careful answer is almost certainly not, in any meaningful sense. And it's worth being precise about why, because the why not is more interesting than a flat yes.

A stone absolutely carries traces. Scratch it, heat it, expose it to weather for ten thousand years, and it physically encodes that history in its grain, its cracks, its mineral structure. In that narrow sense, a stone has a memory the way a hard drive has a memory, just sitting there as a record. But a stone doesn't use that record. It doesn't fold yesterday's scratch into tomorrow's behavior. It doesn't correct course, defend its structure, or do anything differently because of what happened to it. The trace just sits there, inert, like a diary nobody ever rereads. Most serious frameworks for thinking about this, including the more rigorous, technical version of the theory this article is loosely inspired by, draw the line for "experience" exactly here: a trace only counts as experience if you can show, experimentally, that messing with the trace changes what the system does next. A stone fails that test completely. Erase its scratches and its future is unchanged.

A bacterium, on the other hand, barely passes. It senses a chemical gradient, registers the difference, and crucially uses that registration to swim toward food instead of away from it. That's a trace doing work, a memory of one instant steering the next. It's a flicker, not a feeling, but it's a flicker of the right shape.

So where does that leave planets and stars? Here the answer gets genuinely more interesting, because big physical systems do have real feedback loops, they're just slow and dumb compared to brains. The sun's magnetic field, for instance, runs an actual eleven year cycle in which the field of one cycle leaves an imprint that shapes the field of the next, solar physicists talk about the sun having a kind of memory of its prior cycles, expressed in sunspot patterns. A planet's climate system has feedback loops where past states, ice cover, ocean currents, atmospheric composition, genuinely constrain future states for millions of years. None of this is experience in any meaningful sense. There's no criterion being protected, no self being modeled, nothing it is like to be a sunspot cycle. But if you wanted to draw a continuum from pure dead trace, a scratch on granite, up through trace that bends the future, a thermostat, a bacterium, a sunflower tracking the sun, and all the way up to trace that models a future and includes itself in that model, you, reading this sentence, then stars and planets sit somewhere on that ladder too. Just very, very low on it, with feedback loops too slow and too uncorrelated with any preserved self to deserve the word consciousness. Philosophers who take this seriously, look up panpsychism, or Giulio Tononi's integrated information theory, which controversially assigns even a thermostat a sliver of "phi," would say maybe there's a dim ember of something everywhere. Most physicists would say that's a category error dressed up in physics vocabulary. Both camps are worth reading, and neither one has won the argument.

So what's the universe even doing? Here's the part to take with the largest grain of salt, offered in the spirit it's intended, as a thought experiment, not a finding. If experience really is what happens when trace compounds into memory, memory compounds into models, and models eventually fold the system itself back into the model, then the universe, over 13.8 billion years, has been running exactly that compounding process at every scale simultaneously: atoms into stars, stars into chemistry, chemistry into cells, cells into nervous systems, nervous systems into minds that can sit around speculating about nervous systems. Nothing about physics requires this, it's not exactly a march toward some final form of awareness. But it's tempting, emphasis on tempting, to picture the universe less like a closed box of inert stuff and more like an enormous compounding ledger, an e to the x running at cosmic scale, in which every layer of structure becomes raw material for the next layer's memory.

Push the speculation one notch further, purely for the fun of it. If you could ever sum every trace, every memory, every self model that has ever existed across the universe's entire history into one aggregate structure, a totality the way e is the totality of infinitely compounded growth, would that totality behave the way e to the x behaves? Its next moment determined entirely by everything it had already become, growing forever, never needing an outside source, because its own accumulated past is its engine? That would be a strange and rather beautiful kind of immortality, not survival in the sense of staying the same forever, but survival in the sense of never running out of past to grow from.

Is any of that true? Nobody knows, and anyone who tells you otherwise with total confidence is selling something. But it's a nice thing to think about the next time you swipe a calculator, hit the e to the x button, and watch a number climb that never, ever stops compounding on itself.

This piece takes real liberties. The resonance between e's self referential growth and the architecture of memory is a metaphor, not a derivation, and the claims about stones, planets, and cosmic purpose are explicitly speculative. If you want the rigorous, falsifiable version of the underlying theory, with an actual experimental protocol for testing when a trace becomes "experience," that's a separate, much stricter paper and we have this paper.

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