I have encountered numerous pseudo-scientists who seem to latch onto any terminology scientists actually use with 'pseudo' in the name, such as pseudo-tensor, or pseudo-random number generator and try to leverage the terminology to insinuate the methodology is unreliable.
Since pseudo-random number generators are routinely used by scientists in generating test datasets and testing their algorithms (and I will start using them in the next post), I felt the need to do a pre-emptive strike.
Why Do Scientists Need Random Number Generators?
As mentioned above, often times scientists need to develop software for data analysis to test their algorithms. Sometimes they might add a little random noise to a simulation run to determine how these changes influence their results. Sometimes they just want to create datasets of random noise to determine how such data might be distinguished from a real signal.
Why Are they Called PSEUDO-Random Number Generators (PRNG)?
- While the sequences are not truly random, they do pass many of the tests for randomness
- Initializing a PRNG with the same 'seed' makes the PRNG generate the same sequences of random numbers. This is valuable for the development of reproducible test processes.
- After a certain number of numbers are drawn from the generator with a given seed, the sequence will repeat. The length of this sequence is called its period. Ideally, you want a PRNG with a LONG period.
How Good are Pseudo-Random Number Generators?
- Modern PRNGs are very good, suitable for a wide variety of problem-solving and simulation applications.
- The primary application for which PRNGs are NOT suitable is cryptography. This is because the underlying engine of PRNGs is deterministic and it is, in principle, possible for a cracker to determine the underlying PRNG sequence with enough samples of cypher-text.
The Random module in Numpy uses the Mersenne Twister (Wikipedia) as its underlying engine for generating random numbers (Python Documentation, Statistics in Numpy & Scipy). This is also the generator used in the standard Python library. At one time, these PRNGs were different and this can generate some confusion in online searches.
How many random numbers are in the period used by the Mersenne Twister algorithm?
2**19937-1
>>> 2**19937-1 >>> 4315424797388162648055235516337919839053935043226711505165250541403330680137658 0911304513629318584665545269938257648835317902217334584413909528269154609168019007 8753437413962968019201144864809026614143184432769803000667281049840954515881760771 3296984376213462179039639134128520562761960051310664637664861599423667548653748024 1964350295935168662363909047948347692313978301377820785712419054474332844529183172 9732423108882650813216264694510777078122828294447750226804880578200287646593991647 6626520090056149580034405435369038986289406179287201112083361480844748291354732836 7277879565648307846909116945866230169702401260240187028746650033445774570315431292 9960251877807901193759028631710841496424733789862675033089613749057663409052895722 9001603800057163087519137397955504746815433325347499104624813250451634179655147057 5481459200859472614836213875557116864445789750886277996487304308450484223420629266 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69786916734625618430175454903864111585429504569920905636741539030968041471L
(Wow! Isn't Python's long integer type cool?)
That's 6002 digits, in case you were wondering, far more than a googol (Wikipedia), but smaller than a googolplex(Wikipedia).
If you called this generator one billion times per second (10^9 /second), you could run the program for a year and you would have only used about 3.1x10^7 seconds * 10^9 seconds = 3.1 x 10^16 of the numbers in the cycle. There is no concern of repetition of a cycle when using this PRNG.
A Simple Sample
To illustrate the use of the numpy random number generator, here's a simple python program that generates and plots 1500 random x,y pairs with values between zero and one.
import numpy as np from numpy import random import matplotlib.pyplot as plt points=random.uniform(0.0,1.0,size = (1500,2)) ax = plt.subplot(111,aspect='equal') ax.scatter(points[:,0], points[:,1],color='r',marker='o',s=2,label='random') plt.show()
For those who will still want to complain...
If you want to complain about PRNGs, then you must demonstrate that a true random number generator (TRNG) will generate significantly different results than a PRNG in the particular application. This is the standard of evidence for anyone wishing to complain about the use of pseudo-random number generators.
Additional References
- Pseudorandom number generator
- Introduction to Randomness and Random Numbers. Service which generates sequences of true random numbers.
- Paul E. Black, "pseudo-random number generator", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology. 22 June 2010. (accessed 2011-March-03) Available from: http://xlinux.nist.gov/dads/HTML/pseudorandomNumberGen.html
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