Can Informality arise from Formality?

[Xonas Pitfall]

Can infinity arise from the finite? Can randomness (or noise) arise from a signal? Can informality arise from formality?

I feel like this is one of the central questions when thinking about infinity: can the finite give rise to the infinite, or is some form of infinity necessary even for a finite, mechanistic universe to exist?

Which ultimately leads to the question of bias: can something that is inherently defined, constrained, or biased ever transcend its own boundaries? Can a collection of finite, bounded things, through their interactions and collisions, generate the vast complexity and apparent openness of reality without requiring infinity at its deepest or most fundamental layer? Or does such richness ultimately depend on some form of infinity already being present at the top, bottom, or foundation of the system?

Some arguments:

Quote

For example, a finite set of rules can generate an enormous, seemingly inexhaustible space of possibilities. Human language uses a finite alphabet and finite grammatical rules, yet can produce an effectively limitless variety of sentences. Mathematics can define infinitely many numbers from a finite set of axioms. Simple programs, such as cellular automata, can generate extraordinarily complex behavior from very simple starting conditions.

Quote

In one sense, no. The whole system can never do something that is logically impossible given its underlying rules. The biases remain encoded in the system.

Quote

In another sense, yes. Interactions can produce emergent properties that are not obvious from the parts alone. A single neuron is not conscious. A single ant does not build a colony. A single water molecule is not a wave. The higher-level behavior can seem qualitatively different from the lower-level components.

Quote

Is emergence enough? If every emergent phenomenon is ultimately contained in the initial rules, then perhaps nothing has truly "undefined itself." The apparent freedom was latent all along. On the other hand, if emergence creates genuinely new levels of organization that are not reducible in any meaningful way to the underlying rules, then finite constraints may indeed give rise to something that behaves as though it transcends them.

However:

Quote

Mathematics can generate infinitely many numbers, but that's because the number system itself contains an infinite progression. A cellular automaton on an infinite grid may generate endless complexity, but the infinite grid was there from the start.

Are finite rules genuinely creating infinity, or are they merely exploring an infinity that was already implicit in the space they inhabit?

If every rule is finite and every state is finite, where does the extra room for novelty come from? Why doesn't the system eventually exhaust itself?

A finite-state system actually must eventually repeat itself. If there are only finitely many possible states, then after enough time, it cycles. No true novelty remains.

So if reality exhibits genuinely inexhaustible novelty, one might argue that somewhere there must be:

• an infinite state space,
• infinite divisibility,
• infinite time,
• infinite possibility,
• or some other non-finite feature.

Is emergence enough, or does emergence itself require an infinite reservoir of possibilities underneath it?

Quote

Can genuinely new complexity arise from simple rules?

Can finite constraints generate something that appears to transcend those constraints?

Is the richness of reality already implicit in its foundations, or does something genuinely novel emerge?

 

[cetus]

29 minutes ago, Xonas Pitfall said:

Can infinity arise from the finite?

Yes. That is what enlightenment is. Otherwise, there would be no "arising". Infinity would just 'be'. Unmoving.

Edited 4 hours ago by cetus

[Jirh]

This is the classic Chicken and Egg problem.

And the answer is yes. Because chicken and egg are not two different things, but one thing in two different forms.

So the finite and the infinite are the same, they're both abstract concepts that fail when tested against reality.

You cannot find finite, and you cannot find infinite. They're just concepts in your mind. They're ways to categorize reality.

Finite is something that ends. But when and where does anything end?

And infinite is something that never ends. But when and where is that confirmed? You have to reach the end first before you can call infinity infinite.

Edited 4 hours ago by Jirh

[cetus]

This may sound counter-intuitive, but the finite has many more parts than infinity. At the deepest level infinity is a singularity.

[Leo Gura]

38 minutes ago, Xonas Pitfall said:

can the finite give rise to the infinite,

This makes no sense.

You can get a million dollars from infinite dollars, you cannot get infinite dollars from a million dollars.

The finite must come from the Infinite.

[Jirh]

1 minute ago, Leo Gura said:

infinite dollars

Oh, yeah.

American economy in a nutshell 

But seriously, where?

[Leo Gura]

5 minutes ago, Leo Gura said:

you cannot get infinite dollars from a million dollars.

AI companies are like: hold my beer.

[cetus]

11 minutes ago, Leo Gura said:

you cannot get infinite dollars from a million dollars

Elon and Donald would disagree.

[Mellowmarsh]

36 minutes ago, Leo Gura said:

The finite must come from the Infinite.

The finite doesn’t come. The infinite closes the gap between coming and going. The infinite has no room for any thing other than the Infinite.

The infinite never moves from here to there, because the infinite cannot get there from here.

 

Edited 3 hours ago by Mellowmarsh

[Someone here]

2 hours ago, Jirh said:

And infinite is something that never ends. But when and where is that confirmed? You have to reach the end first before you can call infinity infinite.

This is not a mistake . That’s how it should be . Infinity by definition has no end . The fact that you can’t count up to infinity only confirms its definition..for if you ever reach the end it would be finite .  Just by counting up 1..2..3…4……etc you can implicitly conclude that the natural numbers are infinite . You don’t need to explicitly count them “all” because there isn’t an “all” because again it’s infinite .

[Jirh]

@Someone here

This is where I (and others, including Buddhism) disagree with Actualized.org and call this a trap.

It may seem like a small detail, but it makes all the difference.

The trap is trying to capture reality and encapsulate it into a digestible concept that we call "infinity". There's a clinging to knowledge instead of exploration. A desire for certainty over truth.

Perhaps I should use a language that makes sense in the actualized vocabulary to make the point:

The finite cannot know the infinite. Because by definition the finite is smaller, so it cannot know the larger. Then by this logic, anything we think we know about reality (or infinity if you like), including the quality of infiniteness or infinitude, is automatically invalid.

But anyway, back to Taoist wisdom:

The Tao that can be named is not the eternal Tao.