Is randomness real or the inability to perceive hyper complex order?

[blazh femur]

How did you find PF?: random Brownian motion

Is randomness real or is it simply defined as such due to our inability to perceive hyper complex order? Randomness is a troublesome word. I'd feel better if I knew it was an objective phenomenon and not merely a placeholder description of something beyond our comprehension.

 

[bobob]

Randomness is not really a troubling word and although defining it precisely in mathematical terms is a little nuanced, it is not that difficult to have a good picture of what it means. Loosely speaking, if you are given a sequence of events, can you create an algorithm to predict the next event with a probability of better than 1/2? You don't need to be able to correctly describe the process (long live models of heavy nuclei). You just need to have _some_ algorithm that does better than p=1/2 because no algorithm can produce a random sequence. If you want to have the above expanded upon (in several chapters), see "An Introduction to Kolmogorov Complexity and Its Applications," Vitanyi and Li. That should clear up any notion that randomness is not simply non-random, but beyond something our comprehension.

I'm not sure what perception has to do with anything. We make measurements and try to find ways to describe those measurements mathematically so that we can predict the results of future experiments. You have to observe some physical process before you have anything to explain.

 

[blazh femur]

I'm thinking about something like Brownian motion, or the trajectories of every chunk of material in Saturn's rings. There are so many interactions in the rings of Saturn it's impossible to follow them all, so we call the motion "random" - or some people do - even though, from a distance, the "system" appears very stable. If the system isn't actually random but is better described as "so complex we can't decipher it", does it have a name other than random?

 

[DaveC426913]

Events such as the decay of individual atoms are thought to be truly random. Note that this event involves the decay of a mere one atom - not an aggregate of an unfathomably large number of them.

 

[blazh femur]

And yet, if we have a million carbon 14 atoms we know in 5,730 years half of them will decay very predictably, though it's impossible to know which ones will decay. So, using my own term here, the "system" of a million carbon 14 atoms does NOT behave randomly, but each atom individually behaves randomly.

Can something similar be said of all the chunks of material in the rings of Saturn? As a whole the rings behave predictably, but as individual chunks, randomly?

 

[DaveC426913]

Can something similar be said of all the chunks of material in the rings of Saturn? As a whole the rings behave predictably, but as individual chunks, randomly?

No. The individual chunks are each behaving deterministically, as per orbital mechanics.

 

[blazh femur]

Okay, so even though it would take a supercomputer millions of years to calculate, the future trajectories of each chunk of material in the rings of Saturn is theoretically possible, unlike decaying carbon 14 atoms which are subject to the random behavior dictated by quantum mechanics. Correct? But there is a bit of a paradox with the million carbon 14 atoms, isn't there? I mean, an individual atom's behavior is not predictable - it's random - but the behavior of the whole mass of a million carbon 14 atoms is predictable in its aggregate decay rate - it's NOT random. Correct? It can't be random or we wouldn't use it to date fossils.

To my mind this is similar to rolling two die. Roll the die thousands of times and your odds of rolling a 7 are 16.6667%, and of rolling snake eyes, 2.7778%. But if your sample is not in the thousands but is only one - one chance to roll anything from 2 to 12 - YOUR ODDS ARE EVEN ACROSS THE BOARD. (I'd still bet on the 7, in case I'm wrong.) It's another paradox: You really can't prove the odds of only one roll of the die unless you roll again and again, which defeats the premise of only a single roll, just as you can't predict a single carbon 14 atom will decay in 5,730 years, 4 million years, or tomorrow.

Okay, that last part about the single roll of the die may be off (more of a philosophical question perhaps). Final question: Outside the realm of quantum mechanics, what other examples, if any, of true randomness are there?

 

[HomogenousCow]

The kind of randomness that you're talking about is encoded in the density matrix of states, and does not explain the probabilistic nature of pure states.

 

[Vanadium 50]

YOUR ODDS ARE EVEN ACROSS THE BOARD

Not true. (Also NOT TRUE)

It sounds like you are no longer asking us, but are trying to tell us.

 

[Nugatory]

Correct? But there is a bit of a paradox with the million carbon 14 atoms, isn't there? I mean, an individual atom's behavior is not predictable - it's random - but the behavior of the whole mass of a million carbon 14 atoms is predictable in its aggregate decay rate - it's NOT random. Correct? It can't be random or we wouldn't use it to date fossils.

It's random, but random in a useful way. Although any given atom might randomly decay a bit "too soon" or "too late", that is itself random so the fluctuations one way cancel out the fluctuations the other way. When we're considering numbers like $10^{20}$ atoms, the probability that we'll get enough more of one than the other to affect the result is near as no never mind zero. Something similar is going on with Boyle's apparently non-random gas law $PV=C$; the motion of each individual molecule is random so it could happen that they are all moving towards the center of your tank of compressed air at the same time and the pressure would drop to zero. It could happen, but it never does (and it would be a good exercise to calculate the probability of getting a noticeable pressure fluctuation assuming each molecule is equally likely to be moving in or out) and the randomness disappears.

 

[DrChinese]

And yet, if we have a million carbon 14 atoms we know in 5,730 years half of them will decay very predictably, though it's impossible to know which ones will decay. So, using my own term here, the "system" of a million carbon 14 atoms does NOT behave randomly, ...

That's incorrect. There are plenty of things that show patterns when building up from individual events to a large number. That in NO WAY means the large collection is deterministic ("does not behave randomly") in any way.

Ask 10 people to flip a coin and tally the results. Then ask 1 million to do the same. The results will approach 1:1 ratio. And yet each person's toss is uniquely random, and cannot be predicted in advance, as each person flips a coin differently.

A rock that appears at rest is made up of atoms that have individually possesses momentum. Their momenta is random even though it sums to 0.

I would reject the concept you pushing. By any measure, the next click on a Geiger counter or the next flip of a coin is random.

 

[PeroK]

Outside the realm of quantum mechanics, what other examples, if any, of true randomness are there?

There is nothing outside the realm of QM.

 

[EPR]

Some things are truly(possibly fundamentally) unpredictable.

This is the only statement you can make and be on the safe side. If i were to spaculate, the world is likely neither random nor deterministic. It's likely emergent. This would make randomness and determinism apparent/approximate in nature.

 

[Souma]

There is nothing outside the realm of QM.

That is a bold statement, sir. I like it.

 

[DaveC426913]

Gravity.

 

[Jarvis323]

How did you find PF?: random Brownian motion

Is randomness real or is it simply defined as such due to our inability to perceive hyper complex order? Randomness is a troublesome word. I'd feel better if I knew it was an objective phenomenon and not merely a placeholder description of something beyond our comprehension.

There is another thing called deterministic chaos, which can be indistinguishable from randomness.

 

[hilbert2]

Mathematically, you'd need an infinite set of "completely random" numbers before no imaginable statistical test could find any non-random looking pattern in them.