Saturday, July 15, 2006


How to destinguish a "true" random number from something else is often difficult to decide, since the concept of randomness is itself somewhat difficult to define. What is universally agreed is that any "random number generator" based solely on deterministic computation cannot be regarded as a "true" random number generator, since its output is inherently predictable. John von Neumann once famously said "Anyone who uses arithmetic methods to produce random numbers is in a state of sin", thus neatly summarizing the situation.
- Wikipedia (Random number Generator)

For eg., if you use a single random number generation algorithm and initialize it with the same seed twice, it generates the same sequence of random(??) numbers.
Yes, there are random number generators which use chaotic sources to generate "high quality" random numbers. But in the end, all they seem to use is the inherent randomness in the universe to generate random numbers.

This is in fact pointing to something quite fundamental.
Is there anything thats actually random in this universe?
Look at this now:
What exactly is chaos? The name "chaos theory" comes from the fact that the systems that the theory describes are apparently disordered, but chaos theory is really about finding the underlying order in apparently random data (see here).

To look at an example,
The flapping of a single butterfly's wing today produces a tiny change in the state of the atmosphere. Over a period of time, what the atmosphere actually does diverges from what it would have done. So, in a month's time, a tornado that would have devastated the Indonesian coast doesn't happen. Or maybe one that wasn't going to happen, does. (Ian Stewart, Does God Play Dice? The Mathematics of Chaos, pg. 141)

David Deutsch, in The Fabric of reality, goes on to conclude that given enough computational resources, it is possible to build a virtual reality generator whose repertoire includes every physically possible environment (The Turing principle).That is what makes reality comprehensible. Which kind of says that the universe in itself is completely deterministic.


Aparna said...

hey, a really nice post..
thought provoking.. will discuss more with ya offline.. :)

Karthik said...

Blimey, I wont be surprised if this post ends up being a 'reading comprehension passage' in CAT 2006!

About the bit on 'random generators using the inherent randomness of the universe', dont you think the argument you employ is one of formal fallacy?

What a post though! Good work!

Karthik said...

@Karthik - Thanks a lot!
It would be nice if you can elaborate on what you mean by formal fallacy.

@Aparna - Thanks, and sure.. will talk with you sometime:-)

Karthik said...

Formal fallacy takes into question the manner of the argument, rather than the truthness or falsity of the argument itself.

So I was just wondering, how random number generators had the inherent randomness as one of the premises. :)

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