# The Naked Scientists Forum

### Author Topic: Randomness -- can it be measured?  (Read 3163 times)

#### Herman Melville

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##### Randomness -- can it be measured?
« on: 09/07/2009 11:34:57 »
Can you measure how random something is, or is it either random or non-random?

Is it a contradiction in terms for something to be said to be slightly random?

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« Last Edit: 09/07/2009 11:36:28 by Herman Melville »

#### Chemistry4me

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##### Randomness -- can it be measured?
« Reply #1 on: 09/07/2009 12:01:50 »
I don't know, but it was interesting reading this:

http://mathforum.org/library/drmath/view/65666.html

#### JP

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##### Randomness -- can it be measured?
« Reply #2 on: 09/07/2009 14:18:19 »
The Shannon entropy kind of does this.

http://en.wikipedia.org/wiki/Entropy_%28information_theory%29

#### RD

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##### Randomness -- can it be measured?
« Reply #3 on: 10/07/2009 09:07:03 »

#### lyner

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##### Randomness -- can it be measured?
« Reply #4 on: 10/07/2009 12:21:01 »
If you statistically analyse a set of figures / values / voltage waveform, etc you can give it a measure  of its randomness. The Autocorellation Function takes the set of values and, basically, sees how well the function correlates (what it has in common/how closely it resembles) with time shifted versions of  itself. Any set of values correlate perfectly with itself when non-time shifted - obviously, because each value is identical to what it is being compared with.
If you take an endless sine wave (very non-random), it will correlate perfectly with a version of itself that has been shifted by one cycle, two cycles ad infinitum - so the autocorellation function will have an infinite series of peaks every time the original sine wave sits on top of the shifted version of itself.  Stay with me, here.
The autocorellation function just shows you the way this corellation changes as you shift the waveform against itself.
Take a slightly more complicated waveform (still extremely/ infinitely long). As you compare it with shifted versions of itself, then there may be certain regular aspects of the pattern which correlate for sertain values of time shift.  Its autocorellation function will consist of a main peak and a whole family of other smaller peaks.
A totally random waveform will ONLY have a peak when it actually coincides with itself. A 'slightly' random waveform will show a high peak of corellation and some smaller peaks of corellation with its shifted self. A very structured, repeated pattern will show autocorellation peaks all over the place.
So you can tell how random a set of data is  by seeing how close its autocorellation function is to just one peak.

The SETI project has to subject its received data to this sort of scrutiny before ringing bells and saying they have found a genuine Extra Terrestrial source of signals.

Randomness is counter-intuitive. If you try to make up a long string of random  numbers using the digits 0 to 9, it is very likely that they will fail this test because you would 'never' bring yourself to insert a row of 222222 in the set. However, this is just as likely as a row of 1426437.

#### lyner

• Guest
##### Randomness -- can it be measured?
« Reply #5 on: 16/07/2009 10:44:31 »
I would take issue with that.
Standard deviation is a crude measure of spread, not randomness. A Gaussian distribution about a single value  (due to a totally random process) and just two numbers (non-random) may easily have the same standard deviation.
The CV, is the same - it is a measure of the variance, not the randomness.
The ANOVA compares the means of two distributions and determines whether the difference is significant or not.
R2, similarly, can be the same for two sets of results - one which is random and one which is not.

The statistical functions, above, all were derived from a random distribution and are applied to all sorts of data.  They actually assume randomness. If the data is very non random then the conclusions of those analyses can be misleading as they actually give no indication about the randomness of the data.

#### lightarrow

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##### Randomness -- can it be measured?
« Reply #6 on: 17/07/2009 19:40:35 »
All distributions (and concepts as standard deviation ecc.) don't require randomness: I could find a well determined mathematical law which reproduces the values, with the correct probabilities, and of course those values wouldn't be random at all...

#### The Naked Scientists Forum

##### Randomness -- can it be measured?
« Reply #6 on: 17/07/2009 19:40:35 »