The Infinite monkey VS reality

[Morphsnorkle]

If the infinite monkey theorem provides proofs for the probability of order's emergence from chaos, is there a way to measure the probability of order in our universe i.e. matter/anti-matter, snowflakes, DNA?
I just wonder because if there was, you could compare the two values and see if we observe a higher rate of order in reality than in a theoretical chaos based situation.

 

[Drakkith]

One key thing to realize is that many natural phenomena are not entirely random. Snowflakes are assembled from water molecules arranged in a certain pattern. This pattern is not entirely random, but obeys certain laws. The same goes for DNA.

 

[Chronos]

The eternal question has always been is there a pattern embedded in the apparent randomness of nature? While uncertain, it is clear that disorder [randomness] still holds its own in physics.

 

[Morphsnorkle]

I'm not sure if you guys get me.
Drakkith, I'm already pointing out that these natural phenomena don't appear to be entirely random, their inherent ordered features are objectively observable and mathamatically functional. But do they appear at a rate greater than the order we see emerge in the infinite monkey equations? (see: https://en.wikipedia.org/wiki/Infinite_monkey_theorem#Direct_proof)
Chronos, I agree, disorder obviously has some part to play in the opperation of the tangible universe. But that's what I'm asking is, what would you see if:
1.) You could extrapolate from a chaos based probability calculation, a value that represented the frequency that a given threshold of order would be surpassed inside that model i.e. how long would it take the system to produce 'Hamlet'
2.) Using a supercomputer and some really bright people, calculate the rate (given the approximate age of the universe) that an order threshold would be/has been surpassed in our universe ie. when did life on Earth begin.
3.) compare the two values and see if order emerges faster in the natural world than in a theoretical model like the monkey typists model which is purely and certainly based on chaos.
If you could produce results that show there is a disparity leaning towards nature showing faster emergent order than a chaos model, then you could conclude that the laws of nature are purpose-based with their function being to accelerate the formation of complex, universally inherent, ordered systems.

BTW, I'm totally open to anyone telling me this whole idea is disfuntional, I'd just appreciate some detail/further reading on why.

 

[PeterDonis]

But do they appear at a rate greater than the order we see emerge in the infinite monkey equations?

Unless I'm missing something, these don't say anything about "the rate at which order appears".

how long would it take the system to produce 'Hamlet'

This brings up a more important reason why the infinite monkey theorem is irrelevant here: it assumes that all of the events in question are statistically independent. The events of Shakespeare writing each letter of Hamlet are not statistically independent, so calculations like the one in the infinite monkey theorem are irrelevant.

 

[256bits]

observe a higher rate of order in reality than in a theoretical chaos based situation.

Chaos has a different meaning than complete randomness. I am not sure if you are transposing the two words to mean the same thing.

See,
https://en.wikipedia.org/wiki/Chaos_theory

 

[Chalnoth]

If the infinite monkey theorem provides proofs for the probability of order's emergence from chaos, is there a way to measure the probability of order in our universe i.e. matter/anti-matter, snowflakes, DNA?
I just wonder because if there was, you could compare the two values and see if we observe a higher rate of order in reality than in a theoretical chaos based situation.

There's no way to arrive at the universe we observe by simple reference to a random, stochastic process.

The way that this is properly codified is through entropy: entropy is a sort of measure of "order" in a system. A more specific way in which to state it is that entropy is a count of the number of ways that you can rearrange the components of the system and still have it come out looking the same. To take a simple example, consider a glass. If we have a whole glass, sitting on a table, there are some number of ways to rearrange the atoms in that glass and still have it coming out looking like the same glass.

But if we drop the glass off that table and let it shatter on the floor, then the number of ways we can rearrange the atoms increases exponentially: now not only can we rearrange the atoms within the shape, but the pieces of the glass themselves that are now spread across the floor can be rearranged in a multitude of ways without changing the fact that it looks like a bunch of shards of glass.

With this view, things tend towards higher entropy simply because there are more ways for the system to exist in a higher-entropy state. Sometimes it will drop to a lower-entropy (more ordered) configuration, but only occasionally. Still, if we wait long enough, there will be a drop in entropy as large as we like.

You might think, at first blush, that this could explain our universe: every once in a while, there's a big drop in entropy, occasionally big enough to produce a universe like the one we observe. The problem with this idea comes from the fact that small drops in entropy are vastly more common than big ones. So instead of getting a whole big universe like the one we see, we're much more likely to get just a single galaxy. We're even more likely to get a single solar system. This makes a prediction that is flatly contradicted by reality: the universe we observe should be minimal.

The general idea, that our universe might be some random fluctuation, might still be correct, but the true answer has to be quite a bit more complicated than simply saying there's a random fluctuation.

 

[Morphsnorkle]

Thanks Chalnoth,

This makes a prediction that is flatly contradicted by reality: the universe we observe should be minimal.

That's pretty much what I'm getting at.

The general idea, that our universe might be some random fluctuation, might still be correct, but the true answer has to be quite a bit more complicated than simply saying there's a random fluctuation.

Could there be a way to calculate the frequency (if any) of the fluctuation?

 

[Chalnoth]

Could there be a way to calculate the frequency (if any) of the fluctuation?

You'd first have to have a specific model for the result of the fluctuation. In general the probability will be proportional to ##e^{\Delta S}## where ##\Delta S## is the entropy difference of the fluctuation. If this is a fluctuation from equilibrium, ##\Delta S## will always be negative (equilibrium is the state of maximum entropy, so any change in the entropy would have to be a reduction). So if you have a way to calculate the entropy of whatever kind of fluctuation you're talking about, you can calculate its probability.