Does Randomness Exist?

[997GT3]

Even random, or pseudo-random rather, numbers generated by computers are calculated by an equation. Is there a such thing as randomness?

Aren't all things connected?

Wouldn't it be possible for an event on the other side of the world some 20 years ago and everything else (how we were raised; our past; our genes; our immunities; our environment; even the little molecules invisible to the naked eye; etc.) to affect our next actions and the way we see the world?

Does God know what we're going to do next by knowing all the variables to a huge equation and plugging them in? God even knows when we'll pray.

Is Free Will truly Free Will?

Free will is essential to Christianity in that we have to choose to accept Jesus Christ. Is it really "choosing"? Are some people pre-destined to accept Him on Earth and some later?

Please discuss.

[QED]

So may I assume that there *is* no credible evidence for random phenomena, as no one has provided me with any?

I wouldn't assume as much on this basis. I don't think we've really captured the essence of the intrinsic indeterminacy of the world. It seems that you are persuaded by the Laplace's vision of a fully deterministic universe

An intellect which at any given moment knew all the forces that animate Nature and the mutual positions of the beings that comprise it, if this intellect were vast enough to submit its data to analysis, could condense into a single formula the movement of the greatest bodies of the universe and that of the lightest atom: for such an intellect nothing could be uncertain; and the future just like the past would be present before our eyes.

But now physicists and mathematicians understand that order can give rise to deterministic chaos. Isn't indeterminacy in principle the element that you believe to be absent? There was once a battle between two giants of mathematics: David Hilbert once declared in an early radio broadcast "We must know, we shall know." but Kurt Gödel knew better; there are some things we cannot know.

[The Persnickety Platypus]

I wouldn't assume as much on this basis.

I was more asking for evidence than drawing any conclusion.

Based on my knowledge, the mechanics of nature are perfect, patterned, and strictly deterministic. I would be willing to change this perspective for something more accurate. But so far, no one has given me any reason to do so.

The question for debate is "does randomness exist".

Well, does it? Don't just tell me. Show me.

I don't think we've really captured the essence of the intrinsic indeterminacy of the world.

And what is stopping you from catching it right now?

But now physicists and mathematicians understand that order can give rise to deterministic chaos.

Do they?

but Kurt Gödel knew better; there are some things we cannot know.

Like what?


Just curious. Not trying to be belligerent.

[QED]

I think an example of what you are essentially asking for is given by Turing's halting problem

The determination of whether a Turing machine will come to a halt given a particular input program. The halting problem is solvable for machines with less than four states. However, the four-state case is open, and the five-state case is almost certainly unsolvable due to the fact that it includes machines iterating Collatz-like congruential functions, and such specific problems are currently open. The problem of whether a general Turing machine halts is undecidable, as first proved by Turing

Ian Stewart summarizes Turing's proof as a card with different messages printed on each side:

Code: Select all

THIS MACHINE HALTS IF AND ONLY IF THE MACHINE ON THE OTHER SIDE HALTS

Code: Select all

THIS MACHINE HALTS IF AND ONLY IF THE MACHINE ON THE OTHER SIDE DOES NOT HALT

No end of specific processes may be abstracted from this generalised form leading to the existence of undecidable in principle outcomes.

[Curious]

I was more asking for evidence than drawing any conclusion.

Based on my knowledge, the mechanics of nature are perfect, patterned, and strictly deterministic. I would be willing to change this perspective for something more accurate. But so far, no one has given me any reason to do so.

The question for debate is "does randomness exist".

...Just curious. Not trying to be belligerent.

I think you make some really good points here. It is amazing how readily people ascribe to the idea of randomness. Maybe it's because we don't like to admit that we don't know. Take, as an example, a friend rings you up who you have'nt spoken to for years ( minutes after you have thought about them for the first time in years ). There are those who say it is ESP and there are those who try to say it is coincidence. On closer examination of the facts though it is often found that an event precipitated both the call and the remembrance of the friend. One such factor could be a particularly bad thunderstorm which, in their youths, both friends had experienced together. Or perhaps a high pollen count had previously caused one friend to have a particularly bad attack of hayfever and the present high pollen count caused a subsequent attack in one and the other friend might have witnessed an attack or merely witnessed the TV weather report. There are countless ways in which people, especially with today's mass media, can simultaneously experience memory cues.
Sorry if I am rambling a bit here but my point is that everything in isolation appears random or coincidental. When scrutinised though, everything appears to be ordered and effect is always found to have cause. Even the decay of radioactive elements does not appear to be random. If it was random, then why would different radioactive elements have vastly different half-life's and the same elements have the same?
I have just made myself a cup of tea and decided that I should not waste my time simply waiting for the kettle to boil. I therefore attempted to predict which molecule of water would be the first to evaporate. After several minutes struggling with the safety cap of my medication bottle I discovered that this was impossible. I know that several factors are involved and that the molecule that achieves energy above a certain limit will evaporate, but I can't for the hell of me work out which molecule will reach this state first. I therefore come to the conclusion that water boiling is a random event and should save myself a considerable sum of money in gas and look forward to many an inpromtu cup of tea to boot.

[QED]

It is amazing how readily people ascribe to the idea of randomness. Maybe it's because we don't like to admit that we don't know. Take, as an example, a friend rings you up who you have'nt spoken to for years...

That was a good read Curious You've touched on some very interesting issues like entanglement and coincidence. Humans can easily be shown to be poor judges of mathematical probabilities and consequently end up misunderstanding coincidences. But many subtler entanglements exist like the ones you mention. Add to this the non-linear processing and pre-processing that our minds and sensory organs perform and you've got quite a lot getting in the way of a "clear perception" of the world.

I personally think this frequently bends our thinking into seeing convergences where there are none in much the same way as things like natural selection and fractal decompression shape randomness into products that are independent in principle upon the content of the random element. I think this very effectively eliminates any question of there being a deterministic pathway that can be navigated by some ultra precise process (one capable even of surmounting the perils of chaotic systems -- which are at heart deterministic but infinitely susceptable to infinitesimal error). Another way of stating this is that statistically, the shaping processes swamp any bias in the raw ingredients.

[The Persnickety Platypus]

No end of specific processes may be abstracted from this generalised form leading to the existence of undecidable in principle outcomes.

So niether of the machines will ever hault.

Wouldn't that be a decidable outcome?

I'm afraid I still don't see the randomness in this equation.

[QED]

So niether of the machines will ever hault.

Wouldn't that be a decidable outcome?

I'm afraid I still don't see the randomness in this equation.

I think you're confusing the proof that there is a halting problem with the problem itself. The halting problem shows that some things are undecidable despite complete knowledge of initial conditions.

[Curious]

I think you're confusing the proof that there is a halting problem with the problem itself. The halting problem shows that some things are undecidable despite complete knowledge of initial conditions.

Please elucidate. I don't see how you come to this conclusion. How exactly does this show that "some things are indecidable"?

[The Persnickety Platypus]

I think you're confusing the proof that there is a halting problem with the problem itself. The halting problem shows that some things are undecidable despite complete knowledge of initial conditions.

But I can easily decide the outcome of this situation. Niether machine will hault.

So how is randomness demonstrated?

Perhaps it would be more helpful (and relatable) if you explained a random process found in nature, such as the previously mentioned radioactive decay.

[Curious]

Perhaps it would be more helpful (and relatable) if you explained a random process found in nature, such as the previously mentioned radioactive decay.

Radioactive decay is not proven to be random. Radioactive decay seems to be not random at all. Even apparent "quantum randomness" cannot be said to be proven to be random. The insistence that an occurrence is random requires the absolute understanding of everything that could theoretically contribute to the occurrence. Do humans believe they know this much?
The uncertainty principle is bandied about quite a lot. What has this to do with randomness exactly?