How Much Do You Know About Randomness?

All Draw Curiosity videos are fully subtitled in English and Spanish. The blog post builds on the concepts touched upon in the video.

I hope you enjoyed this video. This was my presentation for the FameLab Oxford Finals back in March, and whilst it didn’t get me into the Nationals, I am very satisfied with my performance. You can watch the live version here:

Thank you to Colin Silvester for filming and editing the footage, and ScienceOxford for organising the event.

Like every video, here is a bit more information on the topics covered.

Is 7 really the number you are most likely to choose between 1 and 10?

Apparently yes, followed closely by 3. The line of reasoning typically used is the following:

• 1, 9 and 10 are discarded because they are too extreme, being close to the edges
• 5 is also discarded because it is right in the middle
• All even numbers (2,4,6,8) are also discarded because their evenness makes them easier to conceptualise
• This leaves us with 3 and 7, and most people choose 7

Likewise, if you were to ask people to pick a number between 1 and 100, they often choose 37 or 73. I additionally expect that stating ‘7’ at the start of my video is likely to prime people to think of 7 and make them more likely to choose it, regardless of whether they are consciously aware of this bias or not.

Tim Blaise (AcapellaScience on YouTube) recently showed on twitter that the same principle applies to a random choice between 1 and 4:

Which one?

— Tim Blais (@acapellascience) 4 de junio de 2016

‘3’ feels like the most random choice, as it is neither close to the edges and is not an even number – but is it really if nearly 40% of voters chose it?

Can I generate true random numbers on my computer?

Hopefully finding out that we can’t generate random numbers due to a lack of radioactive elements on your computer hasn’t disappointed you too much. However, it is possible to acquire radioactive sources and wire your computer to a Geiger-Müller counter, which detects radioactive electrons being released. With the adequate software, you could count the number of electrons being released and measure the time interval in between consecutive ones.

If that sounds like too much effort, there are also several websites where you can obtain random numbers generated by hardware that does have access to radioactive materials. My personal favourite is HotBits – who uses a Geiger-Müller counter to count the number of electrons released from a source of Caesium-137, generating approximately 100 random numbers per second. You can place a request on their website, and receive truly random numbers – hot off their radioactive server.

In addition to using radioactivity, there are other ways of generating random numbers considered truly, or close to truly random, such as using thermal noise. Radioactivity can be picked up in the background, but at a much lower rate than from a strong radioactive source such as those described above. Some computers therefore are capable of generating ‘true’ random numbers from these sources, but they are more limited.

Are pseudorandom number generators really random?

Not really – you can find patterns if you generate enough of them, but in small amounts they are indistinguishable from a random distribution. You also have to bear in mind that you are using the remainders of a division, which necessarily has a finite number of possible values – so as soon as one is repeated, you will cycle through the numbers you already generated in the exact same order. This is why varying the seed, the number you insert into the formula (as well as the different parameters themselves) is important.

The primes found in these formulas tend to be Mersenne primes, which are ones generated by the formula 2ⁿ – 1. The standard value of ‘n’ used in random number generators is 19937.

Let’s play with some Mersenne Twisters

Illustrated by Caro Waro

This section is unfortunately still under construction. I’m coding a small widget where you can play around with generating random numbers. It is almost done, I just need to embed it, test it works (and also go on holiday first and catch up on other stuff…) so feel free to check back in the future. If you’re signed up to the mailing list, you will be notified when new posts are made and when I add fun, interactive sections to older posts.

I hope you enjoyed and learned something new today! Let me know what you think in the comments – I would love to know! If you enjoyed this blog and would like to be notified of new entries, consider signing up to the mailing list here and subscribing to the YouTube channel!