Calculus How To

Random Sequence

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A random sequence is a sequence of numbers with zero correlation. In other words, given one number in a sequence {r1, r1, r1, …) there’s no way to predict the second number.

Mathematicians have never been able to agree what is “random” and what isn’t. Many authors have tried (and failed) to pin down a formal definition. Others doubt if such a definition is possible [1]. Every sequence is going to show some kind of pattern or regularity [2].

A Random Sequence Isn’t Really Random

coin toss random sequenceSome sequence that you think are random actually aren’t at all. For example, if you toss a coin three times, you might think that getting a HHT or TTT or THT is completely random. But that’s not the case, because tossing a coin (assuming it’s a fair one) actually follows the laws of probability: your odds of getting a heads are ½ and your odds of getting a tails are ½.

Computerized “Random Sequence Generators” aren’t truly random either: someone programmed it with a set of deterministic rules that govern what sequence is spat out. Generating a sequence of random number is impossible [3].

What about a human generated random sequence? Off the top of my head, I’m going to type a sequence of random numbers from my laptop keypad (I’ll even keep my eyes closed):

{4578656846879}.


Is this an example of a random sequence? Perhaps surprisingly, the answer is no. Even if you were asked to generate a random sequence of 300 digits between 0 to 9, the result wouldn’t be random either. These types number sequences are not mathematically random; the internal random number generator in your brain is subject to bias, always producing certain patterns [4].

References

[1] Church, A. On the Concept of Random Sequences. Retrieved 4/9/2021 from: http://www.socsci.uci.edu/~bskyrms/bio/readings/church_randomness.pdf
[2] Random sequences. Retrieved 4/9/2021 from: https://web.northeastern.edu/afeiguin/phys5870/phys5870/node57.html
[3] Volchan, S. What is a Random Sequence? Retrieved 4/9/2021 from: https://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/Volchan46-63.pdf
[4] Schulz, M. et al. (2012) Analysing Humanly Generated Random Number Sequences: A Pattern-Based Approach. Retrieved 4/9/2021 from: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0041531

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Stephanie Glen. "Random Sequence" From CalculusHowTo.com: Calculus for the rest of us! https://www.calculushowto.com/random-sequence/
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