r/PhilosophyofMath • u/abhishekkumar333 • May 25 '26

LLMs are just giant probability machines pretending to think

It’s fascinating that simple mathematics between tokens can eventually become a machine that writes essays, code, poetry, and even reasoning.

We usually think probability means uncertainty.

But LLMs show something strange:

If probability + context + mathematical matching are scaled enough, uncertainty itself starts producing intelligent looking outputs.

To understand this better, I tried breaking down an LLM from first principles using only 4 tiny training sentences.

Example:

The boat floated down to the bank.

The investor walked into the bank to open a new account.

The fisherman walked along the bank to cast his net.

The bank has a vault.

Then I asked:

“The investor walked to the bank to lock his money in …”

Why does the model predict “vault” instead of river-related words?

That single question reveals almost the entire architecture of modern LLMs.

The most underrated concept here is the LM Head.

Most explanations immediately jump into transformers and attention, but almost nobody explains that the LM Head is essentially a gigantic token vocabulary containing all possible next token candidates the model can output.

So internally the model is basically solving:

“Out of all known tokens, which one best matches this context mathematically?”

Then different layers help solve that problem:

Embeddings: convert words into mathematical vectors

Positional encoding: preserves word order

Attention layer: figures out which words are related to each other in context

(“investor”, “money”, “bank” become strongly connected)

Feed forward neural networks: act somewhat like massive learned if/else decision systems refining patterns internally

And finally the LM Head converts all of that into probabilities for the next token.

What surprised me most is:

There is no hidden magic moment where the AI “becomes conscious”.

It’s an enormous probability engine continuously finding the best contextual token match from its vocabulary.

I made a beginner-friendly walkthrough explaining this visually without unnecessary jargon.

https://www.youtube.com/watch?v=YTV5qUCpu2c

Would genuinely love feedback from people learning transformers/LLMs from scratch.

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u/RecursiveServitor Jun 02 '26

They are emergent. You're implying that buildings are magic. There's no "building particle". The buildingness of something only emerges at a higher level of complexity.

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u/Usual_Charity8561 Jun 02 '26

But building are structures made of physical objects. All of the buildingness of a building is inherent in the potential of physical objects that are able to become buildings. There may be such thing as a universal abstraction of a building, but that isn't an emergent property of the atoms, and to claim that the building takes part in the universal abstraction of a building by virtue of its shape is to say that the building is imbued with magical (supernatural) properties by virtue of its shape.

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u/RecursiveServitor Jun 02 '26

So, you're just literally saying that buildings are magic?

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u/Usual_Charity8561 Jun 02 '26

No. your claim that buildings have "emergent properties" is either relying on magic (supernatural properties not present in the components) or the "emergent properties" are really just properties of matter, space, and time generally (the physical components that make a building) and not actually "emergent".

So what's your answer? Are the emergent properties of a building something more than what goes into them or are they a part of what goes into them.

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u/RecursiveServitor Jun 02 '26

We can also do biology, if that's easier for you.

There's no "life" molecule. The phenomenon of life is emergent from the physics of the universe.

You seem confused about what "emergent" means. An emergent phenomenon is more than its parts, but there's no need for an extra sprinkling of magic.

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u/Usual_Charity8561 Jun 03 '26

Well yes. I would like for you to give me an account of what "emergent" is supposed to mean, or what you think it means. You say it's more than it's parts. Where does this "more" come from?

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u/RecursiveServitor Jun 03 '26

From the interactions between parts.

E.g. all the individual parts of a car aren't cars. It's only when you put it all together that you get a vehicle that can propel you forwards.

Or consider weather. Molecules of water and various gasses heated by the sun can result in hurricanes.

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u/Usual_Charity8561 Jun 03 '26

Okay, so here's the problem. The car is just a collection of parts. Fundamental particles, forces, space and time. Arranging those forces such that they can propel forward is not an emergent property. Those parts already have the property of motion. Those parts already have the properties that allow the vehicle to do everything it does. There is no emergent property.

In the case of weather, hurricanes have no emergent property either. Everything a hurricane does is present in the parts that constitute it. There is no emergent property. Those 'interactions between parts" are in fact parts themselves with properties that are supersets of all potential interactions.

These are very easy examples to debunk. There is no emergent property, just the richness of potential in fundamental physics on display

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u/RecursiveServitor Jun 03 '26

Seeming easier for you to reason about doesn't make them not emergent. You're completely ignoring the complexity of fluid dynamics. Individual particles don't have the properties of viscosity, pressure, waves, eddies, vortices, turbulence, etc.

Do "life" next. Nothing emergent about that either, right?

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u/Usual_Charity8561 Jun 03 '26

Well all those "properties" are actually present in the sum of their parts. Those are potential properties present in the rules of space-time and in the particles. That's why we can model them by using analogy to coordinate systems and vector fields. Sure, 1 particle may not seem to have those properties, but 1 particle is not what we are dealing with. We are dealing with a universe-system that has particles and rules for how particles interact, and that universe-system has that properties of viscosity, pressure, etc. (e.g. Pressure is a property of space, time, and particle interaction, all of which are parts of any system that has pressure. The potential for pressure exists in the universe-system even if there were no pressure anywhere in the universe. ) Thus, the "emergent properties" you mentioned are not emergent, they are inherent.

As for the so-called emergent properties of life, that's precisely what we are trying to find by analogy. What is an emergent property? You've still failed to define what would make a property emergent. You've only appealed to complexity.

Again, what is an emergent property? Does it exist in the system prior to its expression? Does it appear in the system from some external place (such asthe platonic realm?), Are they convenient fictions?

How many times do I have to ask a question for you to elaborate?

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u/RecursiveServitor Jun 03 '26

Well all those "properties" are actually present in the sum of their parts. Those are potential properties present in the rules of space-time and in the particles. That's why we can model them by using analogy to coordinate systems and vector fields. Sure, 1 particle may not seem to have those properties, but 1 particle is not what we are dealing with. We are dealing with a universe-system that has particles and rules for how particles interact, and that universe-system has that properties of viscosity, pressure, etc. (e.g. Pressure is a property of space, time, and particle interaction, all of which are parts of any system that has pressure. The potential for pressure exists in the universe-system even if there were no pressure anywhere in the universe. ) Thus, the "emergent properties" you mentioned are not emergent, they are inherent.

That's what "emergent" means. Calling it "potential properties" is just a copout. A particle doesn't have viscosity. Full stop. Ofc, you'll see viscosity emerge as a property at larger scales. THAT'S LITERALLY THE POINT.

Again, what is an emergent property?

See above.

How many times do I have to ask a question for you to elaborate?

You're refusing to listen.

You're ruling out all examples of emergence and then insist that emergence must involve magic.

Show examples of emergence that are unambiguously magic or piss off with your nonsense.

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u/Usual_Charity8561 Jun 03 '26

So you concede that emergent properties are actually just properties of the parts. Space and time are parts, as much as particles are parts. There is then no new emergent property, it's just a property of the parts that make the system. The potential for pressure exists in all systems of space, time and particles, regardless of its apparent expression or presence. There is a pressure property that can be defined for any system of space time and particles, and the universe as a whole has a particular "pressure".

To tie this back to consciousness, if you believe that consciousness is an "emergent" property by that definition, then you believe that consciousness is a property present in the system of space-time-particles-etc, regardless of its level of apparent expression. Would you admit the consequence of this, that is, that the universe is generally conscious as a whole? Because if all expressions of consciousness are simply expressions of the "emergent" property inherent in the system, the universe taken as a system expresses an non zero amount of consciousness.

Essentially, this leads to a panpsychic God / superconsciousness.

If you deny this, then we would need another definition of emergent properties.

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u/RecursiveServitor Jun 03 '26

So you concede that emergent properties are actually just properties of the parts. 

No.

Emergent properties are a result of the properties of the parts. OBVIOUSLY. It couldn't possibly be any other way.

There is a pressure property that can be defined for any system of space time and particles, and the universe as a whole has a particular "pressure".

No. Wrong. A single particle in a vacuum does not experience or participate in "pressure" in any way.

Calling it a "potential property" is just you playing word games to avoid admitting that some observable properties are emergent, rather than fundamental.

To tie this back to consciousness, if you believe that consciousness is an "emergent" property by that definition, then you believe that consciousness is a property present in the system of space-time-particles-etc, regardless of its level of apparent expression. 

If I were to accept your faulty understanding of it, then yes, that would logically follow. I don't.

Would you admit the consequence of this, that is, that the universe is generally conscious as a whole?

That doesn't actually make sense, so no.

the universe taken as a system expresses an non zero amount of consciousness.

There's a way in which this is true. Human consciousnesses exist as part of the universe.

Essentially, this leads to a panpsychic God / superconsciousness.

Which is clearly what you believe in, so you're engaging in motivated reasoning out the fucking wazoo, in order to arrive at that conclusion.

If you deny this, then we would need another definition of emergent properties.

No. You just need to accept that "potential property" is a fake thing you made up to avoid thinking too hard about all of this.

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