Randomness in formal Mathematical functions?

[bill harris]

The branch of math called 'statistics' reduces randomness to 'probability'. 

 

BH

[Harrison Danneskjold]

Is there a proper way to define randomness in a formal mathematical function?

Define "random".  Then you'll be able to do that. . .  If you can define it.

[bill harris]

Define "random".  Then you'll be able to do that. . .  If you can define it.

In math, the definition is simple: a non-predictable outcome.

[dream_weaver]

In math, the definition is simple: a non-predictable outcome.

That might have been predictable. Genus; differentia; please? Edited March 26, 2014 by JASKN
Quote fix

[bill harris]

That might have been predictable. Genus; differentia; please?

To the extent that i understand your cryptic response, i disagree. Statistics don't replace replace a certainty as much as describing real situations in which randomness and variance naturally occurs.

 

For example, while you can say that the results of any particular coin flip is random, the boundary conditions are set by sidedness (2) and long-term evenness of outcome based upon the equal weights of the two sides.

 

What frustrates many people is the extension of this into QM. Elementary particles really do behave in sort of a random manner.

 

BH

[dream_weaver]

BH, if you're unclear on the question, it would behoove you to ask for clarification. It might save you time trying answering a question that isn't being asked depending on what you conjure up in your mind of what you might think the question might be.

 

Can you provide the genus and differentia for the concept "random"?

 

edit:

For example, if you take "random" to be of the genus "order" where the differentia is "yet unidentified" - that can provide a handier framework for assessing it by.

Edited March 26, 2014 by dream_weaver

[StrictlyLogical]

Define "random".  Then you'll be able to do that. . .  If you can define it.

 

Arbitrary would have been a better term to use in the context of mathematical abstraction.

 

e.g.  building an abstract class of function as follows

 

For any member A1 in set X do dfghfj, for any member A2 in set X (and not A1) do skfhdhj, for any member A3 in set X (and not A1 and not A2) do gkjkrjk... 

[Harrison Danneskjold]

For any member A1 in set X do dfghfj, for any member A2 in set X (and not A1) do skfhdhj, for any member A3 in set X (and not A1 and not A2) do gkjkrjk...

The point being to prohibit any sort of coherent pattern; right?

If so then, in devising a truly random function, what you're attempting to do is to create an algorithm that eliminates patterns.

 

Some areas of cryptography might help you make a function for apparent randomness but I'm not sure actual randomness can be procedurally generated; hence the definition.

Because if you can mathematically define your goal then you can make a function for it.  I just don't think it can be defined, except as the absence of other concepts.

---

 

Edit:  Although, if it is possible, you'd have to embrace that 'absence of a pattern' like:

 

For any Ai in set X, do a or b or c UNLESS i-1 did a or b or c. . .

Edited March 27, 2014 by Harrison Danneskjold

[frank harley]

The point being to prohibit any sort of coherent pattern; right?

If so then, in devising a truly random function, what you're attempting to do is to create an algorithm that eliminates patterns.

 

Some areas of cryptography might help you make a function for apparent randomness but I'm not sure actual randomness can be procedurally generated; hence the definition.

Because if you can mathematically define your goal then you can make a function for it.  I just don't think it can be defined, except as the absence of other concepts.

---

 

Edit:  Although, if it is possible, you'd have to embrace that 'absence of a pattern' like:

 

For any Ai in set X, do a or b or c UNLESS i-1 did a or b or c. . .

Yes, indeed, there are real arguments as to whether generated randomness is really 'random'. Again, from a mathematician's pov, the issue of predictability.

 

So yes, to 'Dream Weaver': 'non-predictibility' stands as a sufficient definition without genus classification and yes, perhaps, Harrison that 'arbitrary might easily stand for 'random', It's just that the later has always been in current use.