What Is The Initial Digit Problem? | Neil deGrasse Tyson Explains...

What is Benford’s Law? Neil deGrasse Tyson and comedian Chuck Nice explore the initial digit problem and whether we can find truly random numbers in human society.

Why do most numbers in society start with one? We pick apart the numbers that humans come up with and the patten that emerges. Is pure randomness achievable? We learn yet again that mathematicians have too much time on their hands…

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Science meets pop culture on StarTalk! Astrophysicist & Hayden Planetarium director Neil deGrasse Tyson, his comic co-hosts, guest celebrities & scientists discuss astronomy, physics, and everything else about life in the universe. Keep Looking Up!

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00:00 - Can we generate random numbers?
03:44 - Initial Digit Problem
07:58 - Numbers in Society

[angelac]

It’s really cool to see Chuck feeling the wonder of learning.

[pqjjvse]

Chuck’s aptitude for quickly catching on to complex topic is next level.

[sammo]

Always funny when Neil puts Chuck on the spot with maths - rather him than me 😅 👍

[MyTutorials]

Neil and Chuck are an entertainment and knowledge gold mine. I'm so happy that I stumbled upon this channel. 😂

[Bowie_E]

I love when Neil records from this room. It's my favorite of his rooms 😂

[formulabrian]

Thanks for covering this topic, Neil and Chuck. I am in infosec and getting true randomness is very very difficult. Commonly used random bit generators are completely deterministic, and requires you to feed it entropy (randomness). And random bits are required everywhere for cryptography and security protocols.

[abrahambounty]

This can be mitigated (not solved, just mitigated) by picking one digit at a time and choosing the least significant digit, almost always the unit's digit if you're going with real life numbers (so if you got page 237 in a text book, the number you picked is 7). And if you need three digits, do it three times. Definitely slower than just grabbing the entire number at once, but way closer to random. Still not an even 10% chance per digit, but way better than the examples Neil chose.

[WickidestTing]

It''s called Benford's law, what Neil and Chuck explained is used to detect fraud in finance and also in social media following.

[jasonyoung]

I remember programming on the spectrum (decades ago), and the problem of generating random numbers. You could do "x=RND", and get a 'random' number, but it wasnt really. the computer ran through a set list of random numbers, so when you turned on your spectrum, it would be the same results every time.
There was a way around this. create a 'start screen', a screen that gave the logo and options and basic info about your program, and at the bottom there would be an instruction "press any key to continue". In the program, the program was running a loop. Something like (I'm paraphrasing for the non-programmers here) : "start loop. Get random number. Repeat loop until any key press". The computer would then fly though the loop thousands of times per second, each time moving through the list of random numbers. Theres no way of knowing where in the list of random numbers you had gotten to..
(this would be different in different languages, along the lines of "Do: x=rnd: loop until inkey$<>"":)

[davemottern]

This is also known as Benford's law. Wikipedia has a good entry about it. It's used in detecting accounting fraud.
You should also look at the entry about Zipf's law, which is even weirder.

[emark]

The initial digit problem is a problem only for the case you present of a human picking from human-generated numbers. It has little to do with computerized random number generators, which are hard for other reasons.

[light]

What a great topic for us mathematically inclined thinkers.

The most interesting method I've seen is to use lava lamps in an array that a camera monitors for pixel changes and then uses snapshots to generate random number seeds. :)

[julianb]

What about this?

Die A is a 10 sided die numbered 0-9. Die B is a 9 sided die numbers 1-9.

Die B's single roll informs how many times you roll Die A. It is implied that the dice have been made without bias, and each side has equal chance of landing.

Every time you roll Die A, mark down the value. You will roll die A between 1 and 9 times in a row. That row of values is your first sequence of random numbers.

Repeat the process for longer sequences.

I ran this through ChatGPT, it agrees with the randomness and I had it write the script in Python.

The "rolling dice" method probably wouldn't be practical for generating a sequence of values a mile long, but it is a way of generating a sequence of numbers randomly.

Thoughts?

[mrtienphysics]

I love it. This is how teaching is supposed to be done.

[mrgreatbigmoose]

11:02 I'm going to call you out on this, the most common street is often 2nd. Because most cities call their first street "Main". But for everything else you're absolutely right there is a bias toward "1".

[kerryemberlyhamby]

I used to be a nurse, but I still don't know if heart rates are too regular for this idea to work, but if there were an instrument that could time each heartbeat to the millisecond, maybe the final digit of the length of each heartbeat would have equal chances of being any single-digit whole number. If you dig into how fast the heart decides to beat at the smallest level, it technically isn't random, but I think that final digit should be pretty evenly distributed. I don't have the means to test it, but I can write a tiny program that's constantly counting from 0 to 9 as fast as my processor can handle it and have it return the number it's currently counting each time a user presses a key. Sometimes that isn't practical though when you need random digits in programming things like games and especially non-interactive simulations. 🤷‍♀

[IroAppe]

That sentence cleared it up for me: Since we are always counting from one, there is a bias towards the lower numbers. And you can even see that bias if you go further: 2 is the second-likeliest initial digit. 3 the third-likeliest and so on.

[djohanson]

Very well said. I remember programing my Commadore 64 and dealing with the same thing. Even had a random number generator. I think this philosophy discussion.

[Ecclesia_]

Good way to explain it is like this: going from a number starting with a 1 to a number with a 2 is the same absolute size as all the numbers before that (i.e. going from 100 to 200 is same as going from 1 to 99). But going from a 2 to a 3 is already less in size (200 to 300 is less than 1 to 200).
It is about selection pools. In any full random pool size most numbers will begin with a 1.

[robadkerson]

I think the most common street name was actually 2nd Street. Because many of the first streets turned into Main Streets