Are true random numbers possible?

Question

The idea of randomness is abstract but has important applications in statistics, probability, numerical analysis, physics, and all the natural sciences. Quantum-mechanical descriptions involve probability distributions necessitating the idea of randomness; radioactive decay may be understood to occur in a predictable macroscopic way, but with an element of randomness in terms of an individual particle's timing of decay. Is it possible to generate a "true" random number, or are existing random number generators or algorithms always "pseudo-random"? Has anyone thought of using naturalistic observation to generate "true" random numbers; i.e. assuming the moment of decay for a particle is truly random, and monitoring decay rates systematically so as to generate a set of random numbers.
Maybe the terminology could be paradoxical, for example maybe the sequence of digits in a decimal expansion of an irrational number is "truly random" but is also precisely determinable.

Answer 1

Pseudo Random Numbers:
Computer engineers chose to introduce randomness into computers in the form of pseudo-random number generators. As the name suggests, pseudo-random numbers are not truly random. Rather, they are computed from a mathematical formula or simply taken from a precalculated list. A lot of research has gone into pseudo-random number theory and modern algorithms for generating them are so good that the numbers look exactly like they were really random. Pseudo-random numbers have the characteristic that they are predictable, meaning they can be predicted if you know where in the sequence the first number is taken from. For some purposes, predictability is a good characteristic, for others it is not. Strong cryptography, for example, would be compromised by keys that were generated using a pseudo random algorithm.

True Random Numbers
True random numbers are typically generated by sampling and processing a source of entropy outside the computer. A source of entropy can be very simple, like the little variations in somebody's mouse movements or in the amount of time between keystrokes. In practice, however, it can be tricky to use user input as a source of entropy. Keystrokes, for example, are often buffered by the computer's operating system, meaning that several keystrokes are collected before they are sent to the program waiting for them. To the program, it will seem as though the keys were pressed almost simultaneously.

A really good source of entropy is a radioactive source. The points in time at which a radioactive source decays are completely unpredictable, and can be sampled and fed into a computer, avoiding any buffering mechanisms in the operating system. In fact, this is what the HotBits people at Fourmilab in Switzerland are doing. Another source of entropy could be atmospheric noise from a radio, like that used at random.org, or even just background noise from an office or laboratory. The lavarand people at Silicon Graphics have been clever enough to use lava lamps to generate random numbers, so their entropy source not only gives them entropy, it also looks good! The latest random number generator to come online (both lavarand and HotBits precede random.org) is Damon Hart-Davis' Java EntropyPool which gathers random bits from a variety of sources including HotBits and random.org, but also from web page hits received by the EntropyPool's web server.

Answer 2

Random number subroutines intrinsic to languages such as FORTRAN-90 and C++ use algoithms to produce a series of seemingly random numbers from 0 to 1. However the algorithm requires a seed number. You can imagine designing a subroutine to calculate pi out to an arbitrary number of digits, it could also pick a certain section of digits after the decimal based on a seed number you provide. Random, in the sense that you couldn't find a pattern within that series, but not random in the sense that you still get the same series if you give it the same seed. If you need an indefinitely long list of 'random' numbers you could run a program that continually calculates the position of a number of 'planets' moving within the gravitational field of a system of three 'stars'. But, again, if you restart the program with the same numbers you'll get the same series. To remove the human element of repeatability, you could seed a random number subroutine or the initial conditions of a complex physical system (one without an analytic solutions) with numbers determined by variables we can observe but not control...for example, the the latest air temperature reading in Clovis, New Mexico, the sum of the magnitudes of the last 10 earthquakes reported by the US Geological Survey...etc. Thats about the best you can do I think. I think the computer programs used to pick lottery numbers use a system similar to this - a regular random number generator seeded by a set of observables independent of human control.

Answer 3

When your computer or calculator calls up a random number, it is actually referencing a standard table of random variables. If you take two TI-83s and reset them entirely (you have to do this even if you buy them fresh from the factory) and call up a random integer, they will both give you the same number. If you continue to ask for random integers in the same format, you will continue to get the same number on both calculators every time.

Thoeretically, quantum computers, which utilize not just the "on / off" states of semi-conductors, but upto 32 quantum states of individual atoms, could generate trully random numbers, since the various quantum properties of the atoms fluctuate in a truly random fashion. A quantum computer with only eight bits of power would match current PC computing power. If it could manipulate 16 bits, it would be more powerful than our best super-computers.

Answer 4

your example wouldn't be truely random because you'd be sampling from some distribution over the space of decay times where certain outcomes are more likely than others. Even though the deay is random, its still governed by a distribution where we can assign probabilities to certain regions of time (because any instantaneous value has probability 0).

Perhaps the real question is : Can you think of a situation where pseudorandom isn't good enough?

Answer 5

yes.. truly random numbers are possible... but most applications that people want random numbers for.. actually need "repeatable" random numbers.. or pseudo-random numbers so that they can reproduce the process later in exactly the same way (or know how to reverse it)

for gambling situations.. where you might want truly random numbers.. how much you would need to pay to acquire a source of truly random numbers is too high.. so they use pseudo-random numbers too.

pseudo-random combinations of random counts of radioactive decay from multiple sources is one way of producing non-reproducible random numbers.

Answer 6

Wow! Lot's of Blah Blah Balh for a simple question with a simple answer. Yes! Of course! Just roll the dice...

Answer 7

Possibly yes.

Answer 8

"Anyone who considers arithmetic methods of producing random digits is, of course, in a state of sin."

Answer 9

You almost answered that yourself.