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Author Topic: Random Stuff Part III  (Read 349797 times)

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sudgy

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Re: Random Stuff Part III
« Reply #2950 on: November 06, 2017, 09:03:24 pm »
+1

I was thinking about quantum physics and my very very limited knowledge of it. How at the very core of it all, it's entirely random. There's no pattern. But what if there was? What if quantum mechanics at its very core was a highly complex chain that was so incredibly long that it might as well be random? They probably have math to prove it's actually random, again I don't have a lot of knowledge on quantum mechanics.

Quantum mechanics is not "entirely random".  We have a set of observations, and several theories that explain those observations.  Parts of those theories say that particles have a probability to be in certain places, to have certain momenta, etc.  The theories are probabilistic, yes, but not entirely random.  Quantum mechanics is a theory, so there can't be more stuff going on than we've given it, so there can't be some hidden part of the theory that we haven't determined (okay, maybe we haven't figured out some distant consequence, but nothing could change the probabilistic aspect of quantum mechanics).

Of course, there isn't any proof that these theories are reality.  Maybe objects are always in certain places and have certain momenta and we just can't measure them (this is called a hidden variable theory).  Maybe every possibility is another universe and we're just in one of them.  Maybe objects do inherently have probabilistic positions and momenta.  There's no scientific evidence for any of these theories so we're just left to speculate.
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   Quote from: sudgy on June 31, 2011, 11:47:46 pm

Seprix

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Re: Random Stuff Part III
« Reply #2951 on: November 06, 2017, 09:04:47 pm »
0

Random is not the same as without pattern.

Is that true? Randomness necessitates a lack of a pattern. If there was no pattern, it would truly be random. Maybe if there was a guy picking random numbers off the back of his head, but there would be some sort of mental pattern, since humans tend to gravitate towards numbers.
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ConMan

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Re: Random Stuff Part III
« Reply #2952 on: November 06, 2017, 09:45:36 pm »
+3

Random is not the same as without pattern.

Is that true? Randomness necessitates a lack of a pattern. If there was no pattern, it would truly be random. Maybe if there was a guy picking random numbers off the back of his head, but there would be some sort of mental pattern, since humans tend to gravitate towards numbers.
Things with random components can still have patterns. Two random variables may be correlated, meaning that when one varies the other tends to as well. A series of random numbers may be autocorrelated, meaning that its value tends to depend on its previous values in some fashion (for example, a random walk, where I flip a coin that tells me whether to take a step forwards or backwards, is strongly autocorrelated because if I'm 5 steps forward my next position can only be 4 or 6 steps forward).

Even the existence of probability distributions is a form of patterns within randomness - the number of red cars that goes past an intersection each hour will have a different distribution to the number of times I have to roll a d20 until I see a 1.

A lot of work in probability theory and statistics is about trying to see what patterns drive otherwise random processes.
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Witherweaver

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Re: Random Stuff Part III
« Reply #2953 on: November 06, 2017, 10:57:43 pm »
+4

Well try this.  Roll 2d6 and add the sum, record it.  Do this 5000 times and plot the results.  I bet you'll see a pattern.
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Donald X.

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Re: Random Stuff Part III
« Reply #2954 on: November 07, 2017, 03:33:00 am »
+1

Well try this.  Roll 2d6 and add the sum, record it.  Do this 5000 times and plot the results.  I bet you'll see a pattern.
Take the same set of die rolls. Instead of adding the dice, take six times the first die, plus the second die. Huh, now the pattern is a flat line. What happened?

It sounds like you're giving an example of a pattern found in randomness. What you're actually giving an example of is a pattern found in a pattern. The randomness is superimposed, and you have enough samples that it averages out to not disturbing the pattern you provided. Which was, "how often does each sum occur when adding two numbers from 1 to 6."
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Witherweaver

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Re: Random Stuff Part III
« Reply #2955 on: November 07, 2017, 08:51:59 am »
+1

Well try this.  Roll 2d6 and add the sum, record it.  Do this 5000 times and plot the results.  I bet you'll see a pattern.
Take the same set of die rolls. Instead of adding the dice, take six times the first die, plus the second die. Huh, now the pattern is a flat line. What happened?

It sounds like you're giving an example of a pattern found in randomness. What you're actually giving an example of is a pattern found in a pattern. The randomness is superimposed, and you have enough samples that it averages out to not disturbing the pattern you provided. Which was, "how often does each sum occur when adding two numbers from 1 to 6."

The flat line would be a pattern, too, inasmuch as the sum distribution was. I considered using the 1d6 example.

So the distribution itself is not random. Random variables obey one, though. It seems a bit arbitrary whether we call that pattern in randomness or randomness superimposed on a pattern. I consider it the former (like ConMan).
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Witherweaver

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Re: Random Stuff Part III
« Reply #2956 on: November 07, 2017, 09:04:27 am »
+1

So here's a thought.. you want to put a design on your wall, so you make a grid of squares (say odd number of columns), and alternate coloring in one square (the same color for all) and skipping the next, starting at the top left and returning to below the first one for the second row, and so on. So we have a pattern (checkered).

On another wall, do the same thing but at each square, flip a coin to decide whether or not it should be colored.

Do we consider the second case to be without a pattern? There is also one case where the two walls are identical, so does the pattern lie in the end result or in the design?
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pingpongsam

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Re: Random Stuff Part III
« Reply #2957 on: November 07, 2017, 09:10:33 am »
+1

Random does not mean without pattern, in fact, it means any pattern is possible.
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Awaclus

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Re: Random Stuff Part III
« Reply #2958 on: November 07, 2017, 03:31:02 pm »
+1

I just came up with a life hack that makes me sit in a much healthier position when I'm on the computer (i.e. almost all the time).

I placed the keyboard further away, so that I have to sit pretty straight to reach it comfortably.
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Donald X.

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Re: Random Stuff Part III
« Reply #2959 on: November 07, 2017, 07:24:26 pm »
0

Well try this.  Roll 2d6 and add the sum, record it.  Do this 5000 times and plot the results.  I bet you'll see a pattern.
Take the same set of die rolls. Instead of adding the dice, take six times the first die, plus the second die. Huh, now the pattern is a flat line. What happened?

It sounds like you're giving an example of a pattern found in randomness. What you're actually giving an example of is a pattern found in a pattern. The randomness is superimposed, and you have enough samples that it averages out to not disturbing the pattern you provided. Which was, "how often does each sum occur when adding two numbers from 1 to 6."

The flat line would be a pattern, too, inasmuch as the sum distribution was. I considered using the 1d6 example.

So the distribution itself is not random. Random variables obey one, though. It seems a bit arbitrary whether we call that pattern in randomness or randomness superimposed on a pattern. I consider it the former (like ConMan).
The flat line is again a pattern that we have provided - the randomness has nothing to do with it.

By rolling lots of dice, you subtract out the randomness, leaving you with just whatever pattern you initially offered up. Randomness has zero to do with your result. Zero. There's no question of "is it a pattern in randomness or randomness on a pattern." You pretended to add randomness and then took it back out. There's whatever tiny bit of noise on top of a pattern that you provided.
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Witherweaver

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Re: Random Stuff Part III
« Reply #2960 on: November 07, 2017, 08:07:32 pm »
0

Then I guess with that point of view, I don't know what "random" means.
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Witherweaver

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Re: Random Stuff Part III
« Reply #2961 on: November 07, 2017, 08:16:36 pm »
0

The flat line is again a pattern that we have provided - the randomness has nothing to do with it.

I mean this doesn't seem right. The flat line is fundamentally a property of the die roll. We define it by taking expectations,, but it's still a property of the variable itself.

Edit: I guess 'define by taking expectations' is not correct. I should say define through an integral with respect to the probability measure.
« Last Edit: November 07, 2017, 08:30:57 pm by Witherweaver »
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Donald X.

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Re: Random Stuff Part III
« Reply #2962 on: November 07, 2017, 08:33:53 pm »
0

Then I guess with that point of view, I don't know what "random" means.
It means unpredictable.

If you roll a die, you get some number from 1 to 6. You don't know what it will be until you roll it. It's random.

If you add up the numbers from 1 to 6 and divide the total by 6, you get 3.5. There's nothing random about that. It's always the same answer.

If you roll a zillion dice, add up the results and divide the total by a zillion, you will get something very close to 3.5. By rolling so many dice we average out the randomness and are left with the original pattern.

It's the same with the bell curve, just harder to see.
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Witherweaver

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Re: Random Stuff Part III
« Reply #2963 on: November 07, 2017, 08:41:47 pm »
0

Then I guess with that point of view, I don't know what "random" means.
It means unpredictable.

If you roll a die, you get some number from 1 to 6. You don't know what it will be until you roll it. It's random.

If you add up the numbers from 1 to 6 and divide the total by 6, you get 3.5. There's nothing random about that. It's always the same answer.

If you roll a zillion dice, add up the results and divide the total by a zillion, you will get something very close to 3.5. By rolling so many dice we average out the randomness and are left with the original pattern.

It's the same with the bell curve, just harder to see.

But you can make predictions; they just have uncertainty.  You know how likely you are to get each value. If you roll a weighted d6, those probabilities change. Taking averages is one way to get an idea of what those probabilities are.
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Donald X.

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Re: Random Stuff Part III
« Reply #2964 on: November 07, 2017, 11:52:58 pm »
0

Then I guess with that point of view, I don't know what "random" means.
It means unpredictable.

If you roll a die, you get some number from 1 to 6. You don't know what it will be until you roll it. It's random.

If you add up the numbers from 1 to 6 and divide the total by 6, you get 3.5. There's nothing random about that. It's always the same answer.

If you roll a zillion dice, add up the results and divide the total by a zillion, you will get something very close to 3.5. By rolling so many dice we average out the randomness and are left with the original pattern.

It's the same with the bell curve, just harder to see.

But you can make predictions; they just have uncertainty.  You know how likely you are to get each value. If you roll a weighted d6, those probabilities change. Taking averages is one way to get an idea of what those probabilities are.
Describing the properties of the die, that it has 6 faces equally likely to appear, is not making a prediction.
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pacovf

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Re: Random Stuff Part III
« Reply #2965 on: November 08, 2017, 12:12:12 am »
+2

Oh boy a probability discussion.

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Awaclus

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Re: Random Stuff Part III
« Reply #2966 on: November 08, 2017, 12:18:18 am »
+1

Is probability ambiguous?
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sudgy

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Re: Random Stuff Part III
« Reply #2967 on: November 08, 2017, 12:45:56 am »
+3

Is probability ambiguous?

I would give it a 90-93% chance.
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   Quote from: sudgy on June 31, 2011, 11:47:46 pm

ConMan

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Re: Random Stuff Part III
« Reply #2968 on: November 08, 2017, 12:52:31 am »
+1

Is the problem with the word "pattern" rather than, say, "structure"? Something which is random can have an underlying structure which you can use to make predictions. I roll a d6, I'm not going to predict that the roll is 13. I draw my opening hand in Dominion, I know that on a typical board there are only 4 different hands I might see and two of them are more likely than the other two. I look at the stock market today, I can take a guess at where it will be tomorrow. I can never be 100% certain about the outcome of any of those events, but I know *something* about them that lets me make predictions, and if I observe such events a lot of times then, on average, I know what those observations will look like.
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blueblimp

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Re: Random Stuff Part III
« Reply #2969 on: November 08, 2017, 01:28:40 am »
+2

Oh boy a probability discussion.


More like a definitions-of-English-words discussion disguised as a probability discussion...
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Witherweaver

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Re: Random Stuff Part III
« Reply #2970 on: November 08, 2017, 08:23:42 am »
0

Is the problem with the word "pattern" rather than, say, "structure"? Something which is random can have an underlying structure which you can use to make predictions. I roll a d6, I'm not going to predict that the roll is 13. I draw my opening hand in Dominion, I know that on a typical board there are only 4 different hands I might see and two of them are more likely than the other two. I look at the stock market today, I can take a guess at where it will be tomorrow. I can never be 100% certain about the outcome of any of those events, but I know *something* about them that lets me make predictions, and if I observe such events a lot of times then, on average, I know what those observations will look like.

I'm with your thinking on this. I'm not sure I'm following Donald's point.
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Kuildeous

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Re: Random Stuff Part III
« Reply #2971 on: November 08, 2017, 09:00:43 am »
0

*there
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Donald X.

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Re: Random Stuff Part III
« Reply #2972 on: November 08, 2017, 04:24:07 pm »
+1

Is the problem with the word "pattern" rather than, say, "structure"? Something which is random can have an underlying structure which you can use to make predictions. I roll a d6, I'm not going to predict that the roll is 13. I draw my opening hand in Dominion, I know that on a typical board there are only 4 different hands I might see and two of them are more likely than the other two. I look at the stock market today, I can take a guess at where it will be tomorrow. I can never be 100% certain about the outcome of any of those events, but I know *something* about them that lets me make predictions, and if I observe such events a lot of times then, on average, I know what those observations will look like.

I'm with your thinking on this. I'm not sure I'm following Donald's point.
You gave an example of randomness having a pattern, but were actually providing the pattern and just adding noise to it that didn't eliminate it. It wasn't a pattern in randomness at all.
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Witherweaver

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Re: Random Stuff Part III
« Reply #2973 on: November 08, 2017, 05:04:56 pm »
0

Is the problem with the word "pattern" rather than, say, "structure"? Something which is random can have an underlying structure which you can use to make predictions. I roll a d6, I'm not going to predict that the roll is 13. I draw my opening hand in Dominion, I know that on a typical board there are only 4 different hands I might see and two of them are more likely than the other two. I look at the stock market today, I can take a guess at where it will be tomorrow. I can never be 100% certain about the outcome of any of those events, but I know *something* about them that lets me make predictions, and if I observe such events a lot of times then, on average, I know what those observations will look like.

I'm with your thinking on this. I'm not sure I'm following Donald's point.
You gave an example of randomness having a pattern, but were actually providing the pattern and just adding noise to it that didn't eliminate it. It wasn't a pattern in randomness at all.

But the random variable has a probability distribution function, which is what I'm considering as the pattern. Taking a bunch of samples was just a way to visualize it.
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Witherweaver

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Re: Random Stuff Part III
« Reply #2974 on: November 08, 2017, 05:09:24 pm »
+10

Notably, this conversation is on topic.
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