What is Randomness and does relative randomness make sense?

2005-02-04, 22:10

I was just wondering whether Randomness has meaning and can there be any real test (through there are many tests) for randomness.

What are the properties of Randomness? As if we do not know that, we cannot test a string of numbers of Randomness.

So some would say obvious qualities is (for instance all your string letters come from a set {1,2,3,4,5,6}) that in the string the number of 1s or 2s .. all should have a frequency of 1/6 to guarantee uniform distribution and the string is not skewed to any specific number or a set of numbers and thus increasing Shannon's uncertainity or entropy.

So based on above reasoning one would say 111111 is not as random as 123456.

I would say I am not sure. Why are people so sure of this is what I am not able to understand?

If I look in another way the sequences of both are defined as :

a(n) = 1
a(n) = n

Both seem non random and definable and why do we ascribe relative randomness to both series?

Let us take the series:

1342346456432

Is there a way to write the n th term of this series like the previous two. I do not know. But the fact that I do not know shouldnt make it more random than the previous two series. This is the heart of my doubt.

At present I believe non cognizance of a rule which define a sequence, makes that sequence more random than the sequence for which we are cognizant of the rule. This non cognizance might make it random for us in a very subjective manner, but definitely not objective.

So I feel when we havent understood what is truly random, we should just say that the letters of sequence A is more uniformly distributed than the letters of the sequence B and not corrupt our terminologies of confusing uniformity with randomness.

If randomness is unpredictability,

then predict the seventh number of the sequence

111111

I have a sequence in mind, please predict the next number.

Is it 1 or 2 or 3 or 4 or 5 or 6?

I feel randomness has no mathematical basis other than human inability to figure out sequences. Measuring randomness is just a contradiction or a paradox.

Please comment.

Uncwilly · 2005-02-04, 23:29

Randomness is easy to test when one has a random item generator.

Let us generate values from 1 to 26 and then assign that to a letter A to Z.

After generating 1000 items, we should have about 38 of each.
After 1,000,000 items, we should have about 38460 of each, also if we count in pairs (like AA, AB,..AZ,BA, BB,...ZZ) we should have about 1480 of each of those.
If we were to ramp this up to 1,000,000,000,000 items, we should have about 3240 of every 6 character unit.

As out sample size becomes large, it is easier to see how random something is.

The other main element, is that to be random, it must not have any predictablity. That is to say that there is nothing that allows you to improve your odds at guessing what the next 1, 5 or 10 characters may be. If A hasn't come up in the past 52 times, it shouldn't be 'due'.

The human mind is designed (yes that is what I mean) to detect patterns and thus true randomness is hard for people to deal with.

2005-02-04, 22:10	#1
sakreha 3942₁₀ Posts	What is Randomness and does relative randomness make sense? I was just wondering whether Randomness has meaning and can there be any real test (through there are many tests) for randomness. What are the properties of Randomness? As if we do not know that, we cannot test a string of numbers of Randomness. So some would say obvious qualities is (for instance all your string letters come from a set {1,2,3,4,5,6}) that in the string the number of 1s or 2s .. all should have a frequency of 1/6 to guarantee uniform distribution and the string is not skewed to any specific number or a set of numbers and thus increasing Shannon's uncertainity or entropy. So based on above reasoning one would say 111111 is not as random as 123456. I would say I am not sure. Why are people so sure of this is what I am not able to understand? If I look in another way the sequences of both are defined as : a(n) = 1 a(n) = n Both seem non random and definable and why do we ascribe relative randomness to both series? Let us take the series: 1342346456432 Is there a way to write the n th term of this series like the previous two. I do not know. But the fact that I do not know shouldnt make it more random than the previous two series. This is the heart of my doubt. At present I believe non cognizance of a rule which define a sequence, makes that sequence more random than the sequence for which we are cognizant of the rule. This non cognizance might make it random for us in a very subjective manner, but definitely not objective. So I feel when we havent understood what is truly random, we should just say that the letters of sequence A is more uniformly distributed than the letters of the sequence B and not corrupt our terminologies of confusing uniformity with randomness. If randomness is unpredictability, then predict the seventh number of the sequence 111111 I have a sequence in mind, please predict the next number. Is it 1 or 2 or 3 or 4 or 5 or 6? I feel randomness has no mathematical basis other than human inability to figure out sequences. Measuring randomness is just a contradiction or a paradox. Please comment.

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2005-02-04, 23:29	#2
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 2²·3·11·71 Posts	Randomness is easy to test when one has a random item generator. Let us generate values from 1 to 26 and then assign that to a letter A to Z. After generating 1000 items, we should have about 38 of each. After 1,000,000 items, we should have about 38460 of each, also if we count in pairs (like AA, AB,..AZ,BA, BB,...ZZ) we should have about 1480 of each of those. If we were to ramp this up to 1,000,000,000,000 items, we should have about 3240 of every 6 character unit. As out sample size becomes large, it is easier to see how random something is. The other main element, is that to be random, it must not have any predictablity. That is to say that there is nothing that allows you to improve your odds at guessing what the next 1, 5 or 10 characters may be. If A hasn't come up in the past 52 times, it shouldn't be 'due'. The human mind is designed (yes that is what I mean) to detect patterns and thus true randomness is hard for people to deal with.