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Author Topic:   Randomness - What is it?
SuperNintendo Chalmers
Member (Idle past 5834 days)
Posts: 772
From: Bartlett, IL, USA
Joined: 12-27-2005


Message 1 of 13 (287881)
02-17-2006 7:22 PM


Since the information addition thread got completely hijacked by arguing over Randomness I figured it was time for a thread dealing with the issue.
I think this piece of the Wikipedia entry is a good start:
Randomness should not be confused with practical unpredictability, which is a related idea in ordinary usage. Some mathematical systems, for example, could be seen as random; however they are actually unpredictable. This is due to sensitive dependence on initial conditions (see chaos theory). Many random phenomena may exhibit organized features at some levels. For example, while the average rate of increase in the human population is quite predictable, in the short term, the actual timing of individual births and deaths cannot be predicted. This small-scale randomness is found in almost all real-world systems. Ohm's law and the kinetic theory of gases are statistically reliable descriptions of the 'sum' (i.e. the net result or integration) of vast numbers of individual micro events, each of which are random, and none of which are individually predictable. (Theoretically the micro-events of gases, for example, could be predicted if the exact position, velocity, atomic composition, angular momentum, and so on of each particle were known.) All we directly perceive is circuit noise and some bulk gas behaviors.
It is important to note that chaotic systems are only unpredictable in practice due to their extreme dependence on initial conditions. Whether or not they are unpredictable in terms of computability theory is a subject of current research. At least in some disciplines computability theory the notion of randomness turns out to be identified with computational unpredictability.
Unpredictability is required in some applications, such as the many uses of random numbers in cryptography. In other applications (e.g. modeling or simulation) statistical randomness is essential, but predictability is also required (for instance, when repeatedly running simulations or acceptance tests, it can be useful to be able to rerun the model with the exact same random input several times).
Sensibly dealing with randomness is a hard problem in modern science, mathematics, psychology and philosophy. Merely defining it adequately, for the purposes of one discipline has proven quite difficult. Distinguishing between apparent randomness and actual randomness has been no easier. In addition, assuring unpredictability, especially against a well-motivated party (in cryptographic parlance, the "adversary"), has been harder still.
Some philosophers have argued that there is no randomness in the universe, only unpredictability. Others find the distinction meaningless (see determinism for more information).
Randomness - Wikipedia
I think as part of the discussion we can discuss evolution and random mutation.
From my perspective it may be possible that mutation is like predicting the weather (but even harder). When forecasting the weather it is impossible to know all the starting conditions, so the probability that the forecast is correct is always less than 1 and more than zero. This makes weather effectivly random, because we can not predict it with 100% accuracy.
It seems that if mutation is effectively random that should be sufficient for the puposes of evolution. (If there were a creator and his actions were indistinguisable from a random outcome we can ignore this creator using occam's razor. Of course it's impossible to prove that anything is random 100%, but mutation seems to be mathetically random).
I'm interested in other thoughts on the subject of randomness.

Replies to this message:
 Message 3 by randman, posted 02-17-2006 7:40 PM SuperNintendo Chalmers has replied
 Message 5 by mick, posted 02-17-2006 7:50 PM SuperNintendo Chalmers has replied
 Message 12 by nwr, posted 02-18-2006 11:59 AM SuperNintendo Chalmers has not replied

  
AdminNosy
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Message 2 of 13 (287886)
02-17-2006 7:29 PM


Thread moved here from the Proposed New Topics forum.

  
randman 
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Posts: 6367
Joined: 05-26-2005


Message 3 of 13 (287891)
02-17-2006 7:40 PM
Reply to: Message 1 by SuperNintendo Chalmers
02-17-2006 7:22 PM


randomness is an illusion
I suspect this is the case.
Some philosophers have argued that there is no randomness in the universe

This message is a reply to:
 Message 1 by SuperNintendo Chalmers, posted 02-17-2006 7:22 PM SuperNintendo Chalmers has replied

Replies to this message:
 Message 4 by SuperNintendo Chalmers, posted 02-17-2006 7:42 PM randman has replied

  
SuperNintendo Chalmers
Member (Idle past 5834 days)
Posts: 772
From: Bartlett, IL, USA
Joined: 12-27-2005


Message 4 of 13 (287893)
02-17-2006 7:42 PM
Reply to: Message 3 by randman
02-17-2006 7:40 PM


Re: randomness is an illusion
Some philosophers have argued that there is no randomness in the universe
It's certainly possible. What would be required?
1. A grand unifying theory of physics exists and can be understood and applied.
2. It becomes possible to know the exact initial conditions for a situation. (keep in mind this means we learn how to get around the heisenberg uncertainty principle)
Does that sound reasonable?

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mick
Member (Idle past 4987 days)
Posts: 913
Joined: 02-17-2005


Message 5 of 13 (287900)
02-17-2006 7:50 PM
Reply to: Message 1 by SuperNintendo Chalmers
02-17-2006 7:22 PM


randomness is a statistical property
Just to start you guys off -
Randomness does not mean unpredictability.
If you have a six-sided dice, which you toss, you can predict quite confidently that your score will range from 1 to 6, with an expected value of 3.5. The expected value is just from (1+2+3+4+5+6)/6. Toss that dice as much as you want, and these parameters will not be betrayed.
However, say you have a ten-sided dice. These are common in role playing games and things like that. When you toss this dice, your score will range from 1 to 10, and your expected score is 5.5.
So these are two random systems, which are completely predictable, and give reliably different results every time.
Randomness is predictable.
Chaos is something altogether different. It ain't predictable. But that doesn't make chaos "more random" than the boring old dice. In fact, chaotic activity is entirely non-random. It's unpredictability arises from its determination by nonlinear equations which are not comprehensible by your average ape.
Mick
This message has been edited by mick, 02-17-2006 07:52 PM

This message is a reply to:
 Message 1 by SuperNintendo Chalmers, posted 02-17-2006 7:22 PM SuperNintendo Chalmers has replied

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randman 
Suspended Member (Idle past 4899 days)
Posts: 6367
Joined: 05-26-2005


Message 6 of 13 (287916)
02-17-2006 8:13 PM
Reply to: Message 4 by SuperNintendo Chalmers
02-17-2006 7:42 PM


Re: randomness is an illusion
Those are not necessary really to consider randomness an illusion since they deal with increasing man's perspective. If you want to say something is random from our perspective, and define randomness in a relative way, then fine, but that's what I mean by illusory.

This message is a reply to:
 Message 4 by SuperNintendo Chalmers, posted 02-17-2006 7:42 PM SuperNintendo Chalmers has replied

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 Message 9 by SuperNintendo Chalmers, posted 02-17-2006 8:28 PM randman has replied

  
randman 
Suspended Member (Idle past 4899 days)
Posts: 6367
Joined: 05-26-2005


Message 7 of 13 (287918)
02-17-2006 8:16 PM
Reply to: Message 5 by mick
02-17-2006 7:50 PM


Re: randomness is a statistical property
Mick, then randomness refers to a limited aspect in a system since non-random factors are in the system as well?
In other words, the parameters are non-random, but the individual choice or events within those parameters are?

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SuperNintendo Chalmers
Member (Idle past 5834 days)
Posts: 772
From: Bartlett, IL, USA
Joined: 12-27-2005


Message 8 of 13 (287926)
02-17-2006 8:26 PM
Reply to: Message 5 by mick
02-17-2006 7:50 PM


Re: randomness is a statistical property
I'm with you Mick. I understand that mathetical definition of probability quite well.
Think of this situation (and this may be more of a philosophical question than anything). If we could know the exact starting conditions for rolling a die, in theory we might be able to predict the outcome. Of course this is more of a physics question than a math question I think.
Although, now that I think about it... I guess this all gets back to the question of whether or not there is inherent randomness in the universe.
From a practical mathematical perspective that does not seem to matter.
I like the definitions you gave.
Here's a question for biologists: Is there a range of possible mutations that can occur (for example we know the range of possible mutations will be in this set.... at least at a low level).... I'm guessing the answer is no.. butI'll leave it to an expert to weigh in and also google it myself.

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SuperNintendo Chalmers
Member (Idle past 5834 days)
Posts: 772
From: Bartlett, IL, USA
Joined: 12-27-2005


Message 9 of 13 (287927)
02-17-2006 8:28 PM
Reply to: Message 6 by randman
02-17-2006 8:13 PM


Re: randomness is an illusion
Randman,
I am only dealing from the human perspective because that is the only perspective we can experience.
What I was trying to come up with was the conditions that would have to be satisfied in order for humans to predict the outcome to ANY event.

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 Message 6 by randman, posted 02-17-2006 8:13 PM randman has replied

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randman 
Suspended Member (Idle past 4899 days)
Posts: 6367
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Message 10 of 13 (287969)
02-17-2006 11:04 PM
Reply to: Message 9 by SuperNintendo Chalmers
02-17-2006 8:28 PM


Re: randomness is an illusion
It's certainly possible. What would be required?
1. A grand unifying theory of physics exists and can be understood and applied.
2. It becomes possible to know the exact initial conditions for a situation. (keep in mind this means we learn how to get around the heisenberg uncertainty principle)
Let me try again being more specific. It doesn't matter if we can ever understand and apply a grand unifying theory. All that would change is our knowledge. It would not make things more or less random. I suppose we could discuss whether a grand, unifying theory exists or could exist as relevant, but even there I am not so sure it matters.
On the 2nd point, it doesn't matter ever if we know the exact conditions or not. Something is random or not random regardless. In fact, if knowing the exact conditions means that something is not random, then nothing is random because exact conditions do exist presumably, and the act of knowing doesn't change those conditions....well except maybe with observer/participancy.
Now, on the Heisenberg uncertainty principle, awhile back I wondered if entanglement has not lessened that somewhat, but we are getting into some sticky areas with QM. Perhaps there is a random element in the universe, but even there rules still apply. My sense is that what will occur can actually be known (for example if we could manipulate time) but that there could well be a random aspect to a degree within a system though that is predominantly non-random. But on the other hand, I would not rule out that there are governing factors deciding the seeming random event, even at the quantum level.
The reason this is important, or one reason, is the seeming random "autonomy" as Watson put it has been used to argue that science is incompatible with God and especially a personal God, but the fact is if randomness merely describes our perspective and not an absolute one, then randomness being used to argue against a Being that does not the exact conditions is a major logical fallacy.
Let's posit whether randomness exists in an absolute sense. In theology, we consider ideas not just from our perspective but from the perspective of God to the extent of our imagination, sometimes balanced by intution, revelation and reason.
And even if one rejects God, if knowing the exact conditions and causes changes something from being random to non-random, then randmoness is an illusory and relative quality and not an absolute one.
This message has been edited by randman, 02-17-2006 11:09 PM

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Modulous
Member
Posts: 7801
From: Manchester, UK
Joined: 05-01-2005


Message 11 of 13 (287995)
02-18-2006 2:42 AM


No order
Randomness, in context of random mutations, is akin to 'no particular order'. Any one of the base pairs could mutate during replication (as far as I am aware), and over time the mutations may follow a frequency pattern. However, the order of the mutations is not able to be predicted, and the order is very important.
If mutations are purely deterministic (I don't think they are for a moment), they can still be described as random. In a deterministic universe true randomness doesn't exist so the word random is meaningless unless it is meant by 'having the appearance of or behaving similar to a random function'.
Random mutation seems to be a system that has chaotic properties (highly sensitive to initial conditions), and it occurs at a molecular level so quantum effects can mean the initial conditions can not be fully known.

  
nwr
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Posts: 6408
From: Geneva, Illinois
Joined: 08-08-2005
Member Rating: 5.1


Message 12 of 13 (288076)
02-18-2006 11:59 AM
Reply to: Message 1 by SuperNintendo Chalmers
02-17-2006 7:22 PM


"Random" is a mathematical term
It is best to think of "random" as a technical term in mathematics (from probability theory). We apply that mathematics to real world phenomena where we find that appropriate. We find it natural, in such circumstances, to apply the word "random" to what is modelled.
There is also some colloquial use of the word "random". One common instance of this is in the local port used for a network connection. If you look at the output of "netstat -n" on your computer, you might see something like this:

1.2.3.4:1179 207.36.231.74:80 ESTABLISHED

where the "1.2.3.4" is your local IP address, and "207.36.231.74" happens to be the IP address of evcforum. The "80" is the port you are connecting to. The "1179" is the local port you are using for this connection. The local port is often called a "random port". On a window box, the first connection ever made will use 1024 for a random port, 1025 for the next random port, 1026 for the next, etc. That is, these are usually assigned sequentially. Sequential is pretty neat for something called "random.". The term "random" is used here to mean that there is no significance to the particular choice. It could be anything. It happens to be done sequentially, because thats the easiest thing for software to do.
For the term "random" as used in "random mutation", you should simply take that as saying that there is no rhyme or reason for this particular mutation rather than a different one. Or, at least, there is no known reason or mechanism that preferred this mutation over a different one, and all the evidence suggests that there could not be a mechanism behind the choice.

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 Message 1 by SuperNintendo Chalmers, posted 02-17-2006 7:22 PM SuperNintendo Chalmers has not replied

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randman 
Suspended Member (Idle past 4899 days)
Posts: 6367
Joined: 05-26-2005


Message 13 of 13 (288173)
02-18-2006 5:56 PM
Reply to: Message 12 by nwr
02-18-2006 11:59 AM


a far-fetched claim?
For the term "random" as used in "random mutation", you should simply take that as saying that there is no rhyme or reason for this particular mutation rather than a different one. Or, at least, there is no known reason or mechanism that preferred this mutation over a different one, and all the evidence suggests that there could not be a mechanism behind the choice.
Can you offer some evidence or substantiation for your claim here? From the little I have learned on the subject, there appears to be rhyme and reason since there are indeed determining factors to at least some aspects of mutations. For example, there is some evidence of convergent DNA, and I believe some other factors which some have pointed out here.
Maybe wk or someone can add some links. So saying all the evidence, without detailing that evidence and in light of there being at least some evidence to the contrary suggests your comment is more what you think must be rather than what is based on evidence.
But I could be wrong.....can you elaborate?

This message is a reply to:
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