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

[@angelac5628]

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

[@inkonmyhands]

Yess, gettin high on knowledge. I feel him in each one of these episodes, hahaha

[@michaelccopelandsr7120]

Neil and Chuck for 2024

[@Bowie_E]

I'd vote for that party

[@padude_]

omgggg can u imagine!!! that would be awesome

[@dunderwood4444]

Dr. Tyson & Lord Nice 2024

[@leeFbeatz]

Presidents! The first 2 together for America!

[@ericthompson3982]

I'd work on that campaign.

[@My123Tutorials]

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

[@sammo7877]

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

[@FMFvideos]

It's like a teacher randomly picking a student but there is only one student. There must be a lot of pressure.

[@NojotroBand]

​@@FMFvideos 😂😂😂😂

[@RustyStringz]

​ I used to be that student who was picked in math class and put on the spot, and it wasn't fun being an introverted, awkward adolescent.

[@Bowie_E]

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

[@user-pq7jj3vs3e]

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

[@onceagain6184]

No it isnt!

[@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.

[@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.

[@richmorin424]

Wikipedia is your friend: en.wikipedia.org/wiki/Benford%27s_law#History

[@HarnessedGnat]

Whenever I move $ between accounts it is some number of dollars and 11 cents. This helps me, I think, but now I’m wondering if that’s “fraudulent” 😂

[@jevinday]

I was wondering what the real world application of this was. Fascinating! Makes sense

[@abrahambounty1949]

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.

[@chrome9455]

yes but what you are describing is a pattern an algorithm which can be use to narrow it down, it wont be completely random which is the point.

[@ahmadsyakirin9430]

Bro.The title is INITIAL DIGIT. Its the first digit that will appear. And 1 will have a higher percentage to be the first digit.

[@nickdsp8089]

​@@ahmadsyakirin9430 You can always reverse or rotate one place the number and then pick the FIRST digit. Problem solved. But humans always like to drown themselves on a drop of water.

[@Danceofmasks]

I did this with a geiger counter back in 1982. Discard the first couple of digits AND the last digit. These days, you can attach a geiger counter to your PC, call for a readout, and do the same thing. Not as easy to replace all your seed algorithms with this process, but hey ... if we'd just built geiger counters into all our motherboards over the last 20 years, random numbers wouldn't seem so un-random.

[@readjordan2257]

Theres plenty of randomization techniques that produce statistically random outcomes. Using the squaring method is my personal favorite on a moments notice. Otherwise...shuffle a deck of cards 7 times ideally, and you get a random arrangement of cards. From there, you can assign a number scheme to identify the arrangement back to a number... preferably mod something, or else thats wholly impractical as 52! Is an inhuman number. Theres no shortage of ways to generate something random. The issue is the trade-offs with each method. The atom decay one Neil himself mentioned is rarely used, because theres no repeatable results. Once it occurs youll never have it again and youll have to have a whole system for logging as much of the information as you can. Its probably the heaviest duty form or random seeking, but also usually the most impractical and unnecessary.

[@emark8928]

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.

[@geraldplayle803]

This. His comment about picking numbers from civilization, and almost 1/3 starting with the digit of 1, this is based on the tendencies of humans. Pick a number from a book, well most of the books we have are within 300 pages or less. Look at anything, and we tend to limit things to certain amounts. This accounts for that issue. Him using it as an example to reference the problem with generating a purely random number is a disingenuous connection.

[@shexec32]

Computer PRNG algorithms are still subject to Benford’s law. It’s just that the PRNG throws away the leading digits before returning that you don’t see an initial digit problem.

[@patocat.3141]

@@geraldplayle803 In fairness, he didn't actually present it as an issue with generating a purely random number. His intro was basically "Generating random numbers is hard. So why don't we just randomly pick numbers from civilisation instead? Here's why that wouldn't be random." Not his fault if you misinterpret that

[@hlizzle]

​@Hamish McAlley I saw the title and caption, "Does true randomness exist?" and presumed this was going to be about entropy sources for applications in science and technology. Also bit of a disappointment to get to the end of 12 minutes without much of a conclusion. Mildly interesting observation, but this was a pointlessly verbose way of explaining it!

[@jpdemer5]

Not true: look up Benford's law (Wikipedia has a good introduction.)

[@light487]

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. :)

[@luciogutierrez997]

That's so cool. It's my intuition that you could use similar methods to generate seeds from nature at the macroscopic level, without diving so deep to measure sub-atomic particles as Neil mentioned... But I'm no physicist, so...

[@jawstrock2215]

@@luciogutierrez997 that assumes that nature is random...

[@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".

[@mrtienphysics666]

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

[@0-by-1_Publishing_LLC]

(3:20) *"Zero is one of the more important numbers ever conceived!"* ... Second only to the number 1. In fact, both are so important that I wrote a book about them.

[@jasonyoung7705]

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$"":)

[@RussellSubedi]

QBASIC?

[@jasonyoung7705]

@@RussellSubedi Started with the Basic that came with the Spectrum, then went to GWBasic, then QBasic, and then learned Turbo Pascal. This was 30+ years ago, so its all blended together in my alcohol fueled brain at this point.

[@djdedan]

@@destructodisk9074 there are no random numbers in computers but they produce a random sequence, what we usually do is pick a random starting point in the sequence (usually by using the current time which is random)

[@thereallostprince6251]

so in a nutshell it’s a bigger list😭

[@gnarthdarkanen7464]

@@destructodisk9074 It's my understanding that they used an algorithmic generator and started it with a "seed" usually from some input of the Player... What makes it so damnably unpredictable (so cheaply) is that the particular inputs quantified to a "seed valu" to start the algorithm off could be from anything, anywhere, and at almost any time... I've not only experimented with the old cartridge games, but grew up playing them... AND it's amazing how easily one can find all the patterns in the game if you pay attention. They might get timed a little different from one play-through to the next, but the patterns are distinctly there in every single one... What I have also noticed is that when you first get on an old console for the cartridges, it's a responsible ritual to "test the controls" over the character on the screen... It's as simple as move left and right, jump and shoot (since many controllers only had two buttons and a directional pad or stick)... AND it's entirely possible that an internal timer initiated at the start of play would run out and wherever the character-sprite was on the screen would be taken by X,Y ordinals and used for seed values, depending on how many randomizing threads might be desired... I have no good idea of where and how to prove it... at least, not without devoting a LOT more time than I have for replaying retro-games on a cartidge console than I can justify.

[@djohanson99]

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.

[@davemottern4196]

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.

[@robadkerson]

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

[@utetopia1620]

Thank you "Big Bang Theory"!

[@richardfellows5041]

In my town there is only one First Street, every other in the original grid was either E or W 'nth' St.

[@CamMcGinn1981]

I love the way that Neil chortles with delight. So.... wholesome.

[@TheLOLWHATTTTTTT]

Yet another awesome explainer. Good job guys!

[@julianb1550]

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?

[@joekenorer]

Your bias would then be to 9.

[@scrappymark]

Seems legit to me! It’s amazing how many problems we have solved, but generating random numbers is the problem we struggle with!

[@charliew9515]

0-9 (ten sided) die will give true randomness to the extent the die is perfect and the throwing method is no biased. So, a pretty good random number generator.

[@billdodson207]

I like that it is simple enough for a kid to do, and can be tested without a computer. Tedious perhaps, but practical.

[@klausgehle8494]

If you use a Python script for the dice rolls, the dice rolls are not really random. It should work with real dice imho.

[@supernovaw39]

I'm a computer scientist and I have a little rant. I love StarTalk and Neil very much, but this one just frustrated me. 😔 The most obvious thing for me, if you were to use the approach of pulling numbers from random sources (which, of course, have different ranges, and often not strictly defined - some are mostly 1900-2020, some are 1-12, some are 1-31, some are mostly 10000-1000000), would be to take either the last digit, or, even more reliable and "random" - take the last binary digit. In other words, if the number you came across is even, remember that as 0, if it's odd, as 1. This way the natural range from which it was taken mostly does not matter (if you take months, 1 through 12, half of them are odd, on the other hand, days of the week have a bias because 7 is not divisible by 2 so you'd want to ignore such cases). Then, it depends on what number you want to generate. It is the easiest if it is a power of 2, say 64 - you will need to pull out 6 digits, ones or zeros, and make a binary number in range of 1 through 64 (more precisely that'd be 0-63 and you add 1 to make it 1-64). I really don't understand who would want to use numbers that have an indefinite range as explained in the video. If one time you could get a year of some publication, within 2000, then some random page number, within 500, then someone's day of birth, within 31, then the number of stars in the observable universe, an astronomically large number. Who would want that? The most sensible thing to do is take the last digit (which will have a lot less bias), or, even more clever - use binary digits so you take small pieces of entropy from each number and mix them to make up a number. For me it is as obvious as it can be that taking raw numbers from random sources would have a bias towards a leading 1 (part of the reason, we never include leading zeros, of which there could be an infinite amount). But if the range is arbitrary, again, why care about the whole number and not its last and the least predictable digit? The first digit of a number from a random source is the least unpredictable and useful digit and they spend the whole video talking about it alone ignoring the rest of them which actually could be used as a source of randomness... I was genuinely frustrated when Chuck and Neil said it's freaky, when it's so obvious on one hand and so easily avoidable on the other, it seems like they missed the whole point. By the way, unpredictable (not inherently random but sufficiently obscure) numbers can be generated from noise, when out-of-control factors influence the number, such as when you focus a camera on a lava lamp and take the pixel color values from some spot (again, you take the LAST digits, enough of them, over a long enough period, to make up a long cryptographically-strong random number). There is a million factors that can determine the pixel value, the more the better, such as the position of bubbles, sunlight, clouds, electromagnetic noise in the circuitry of the camera that it picks up, someone walking in the room, reflecting light rays at different angles that end up in the camera, making the result completely unpredictable and good enough for practically any applications.

[@miakiceh]

Great episode! Got me thinking about random functions just for fun... Thanks for awakening the geek in me! Blessings

[@davidevans3227]

the visuals make me chuckle.. glad i'm watching 🙂 x number one is cool

[@DaellusKnights]

I wish I could find the reference, but some engineer back in the 70's tried making a radio-decay number generator (someone even used the concept in a Writers of the Future short story) and the numbers STILL eventually generated a pattern. The math is light years beyond me, but it came down to the frequency of the electricity powering the detector and, of course, the initial digit problem. That was how I first learned of the concept.

[@charlesbrightman4237]

NUMBERS: (copy and paste from my files): 'IF' my latest TOE idea is really true, (and I fully acknowledge the 'if' at this time, my gravity test has to be done which will help prove or disprove the TOE idea), that the pulsating, swirling 'gem' photon is the energy unit of this universe that makes up everything in existence in this universe (including 'space' which is energy itself, 'time' being the flow of energy), and what is called 'gravity' is a part of what is currently recognized as the 'em' photon, the 'gravity' modality acting 90 degrees from the 'em' modalities, which act 90 degrees to each other, then the oscillation of these 3 interacting modalities of the energy unit would be as follows: Gravity: Maximum in one direction, Neutral, Maximum in the other direction; Electrical: Maximum in one direction, Neutral, Maximum in the other direction; Magnetic: Maximum in one direction, Neutral, Maximum in the other direction. Then: 1 singular energy unit, with 3 different modalities, with 6 maximum most reactive positions, with 9 total basic reactive positions (neutrals included). Hence 1, 3, 6, 9 being very prominent numbers in this universe and why mathematics even works in this universe. (And possibly '0', zero, as possibly neutrals are against other neutrals, even if only briefly, for no flow of energy, hence the number system that we currently have. This would also be the maximum potential energy point or as some might call it, the 'zero point energy point'.). And also how possibly mathematical constants exist in this universe as well. * While in bed one morning after a restful nights sleep, and assuming the above is correct, I mentally went 'inside' the 1 (the singular pulsating, swirling 'gem' photon itself). I still saw with my mind the 3 different interacting modalities, the 6 maximum modality points, the '9' including and being the neutral points in the middle which faded into a 6 (as each maximum modality point came towards zero), that 6 fading into a 3 (as each modality came together), which turned into a 1 (which was the '0' point), but '0' wasn't zero. So, '0' is not really '0' but is something, not nothing. '0' is a relative '0'. But then here again, the zero point energy point is the maximum potential energy point for any and all modalities of the 'gem' photon. '0' is '1' and '1' is '0', this is the '1' inside the '1'. Now I just have to come up with some tests to test this idea of the zero point energy point being '1', a maximum potential energy point of the singular pulsating, swirling 'gem' photon itself. The maximum potential energy point not really being potential energy per se, but the neutral point of kinetic energy. Tapping into here would be tapping into the 'zero' point energy point of eternally existent ever flowing energy. But then again, tapping into here, 'if' distorted what makes up space and time itself (assuming that 'space' is energy itself [the 'gem' photon] and that 'time' is the flow of energy), could it alter or even destroy the very fabric of space itself? What would occur if even only a single pulsating, swirling 'gem' photon were to explode? What potential ripple effects could occur with the rest of space and time? Hence also why I try to think some things all the way through so as to try to identify potential issues before the test. Unexpected, unintended, potentially dangerous or even deadly consequences. If nothing else, it keeps my mind active. The mind, use it or lose it, but using it could also lose it, permanently. (My own and other's). Putting the 'zero point energy point' into actual practice could be deadly. Warning: Proceed with Caution. The last words of human existence on this Earth might be, 'Hey it worked, ooooppppppsssssss.............'. * Note also: Nobody as of yet has been able to show me how numbers and mathematical constants can exist and do what they do in this universe from the Standard Model of Particle Physics (SMPP). While the SMPP has it's place, I believe we need to move beyond the SMPP to get closer to real reality.

[@MattIsntYoung]

​@@charlesbrightman4237 Tl;DR: ... idk, tl;dr

[@DreamScene1st]

​@Charles Brightman I truly tried to follow...man I wish I was back in school...why is it I had to be intellectually active in my 20s

[@charlesbrightman4237]

@@MattIsntYoung Remaining ignorant is a choice. You have chosen unwisely.

[@charlesbrightman4237]

@@DreamScene1st Never stop learning. KZbin, internet, libraries, used book stores. Find a topic that interests you and study it. Find some entity to do my gravity test, and 'if' true, and 'if' it does not literally wipe out this entire Earth, all on it, and maybe more, potentially have the literal theory of everything for this universe. WARNING: (CONTAINS EXISTENTIAL MATTERS): GRAVITY: (copy and paste from my files): Here is the test for the 'gravity' portion of my TOE idea. I do not have the necessary resources to do the test but maybe you or someone else reading this does, will do the test, then tell the world what is found out either way. a. Imagine a 12 hour clock. b. Put a magnetic field across from the 3 to 9 o'clock positions. c. Put an electric field across from the 6 to 12 o'clock positions. (The magnetic field and electric field would be 90 degrees to each other and should be polarized so as to complement each other.) d. Direct a high powered laser through the center of the clock at 90 degrees to the em fields. e. Do this with the em fields on and off. (The em fields could be varied in size, strength, density and depth. The intent would be to energy frequency match the laser and em fields for optimal results, cancelling out the em modalities of the laser, thereby leaving behind the gravity modality.) f. Look for any gravitational / anti-gravitational effects. (Including the utilization of ferro cells so as to be able to actually see the energy field movements.) (And note: if done right, it's possible a mini gravitational black hole might form. Be ready for it. In addition, it's possible a neutrino might be formed before the black hole stage, the neutrino being a substance with a very high gravitational modality with very low 'em' modalities.) (An alternative to the above would be to direct 3 high powered lasers, or a single high powered laser split into 3 beams, each adjustable to achieve the above set up, all focused upon a single point in space.) 'If' effects are noted, 'then' further research could be done. 'If' effects are not noted, 'then' my latest TOE idea is wrong. But still, we would know what 'gravity' was not, which is still something in the scientific world. This test can speak for itself. It will either be true, partly true, or not true at all. It will either show what gravity truly is, might be, or is not. Science still wins either way and moves forward. * And note: Whether my gravity test or another's, a gravitational black hole would have to be formed to prove the concept as being really true. A gravitational black hole that 'if' self fed itself, could literally wipe out this Earth and all on it, possibly this solar system, possibly put a black hole in this section of our galaxy, and potentially even causing a ripple effect in this galaxy and surrounding universe. But hey, if it does, no worries. Nobody would be left to prosecute those who did so. (Possibly famous last words: "Hey, it worked. Ooooppppssss.................) But as NASA has already proven that low gravity conditions over a prolonged period of time is harmful to the human species, and large rotating space ships won't really work for space bases on planets and moons, those space bases probably being needed somewhere along the way out of this solar system and galaxy, we need to figure out what gravity truly is and see if we can generate artificial gravity so as to have smaller space ships and proper gravity conditions for space bases on planets and moons. Otherwise, at least all human life will most probably die and go extinct one day. Currently, no exceptions. * Added note: Just trying to save at least 1 single species from this Earth to exist beyond this Earth so that life itself from this Earth has continued meaning and purpose to. Gives me something to do while I exist, otherwise, what is it all and everything for? Even if my TOE idea were correct, but if it did not help species survive beyond this Earth, what good would it ultimately be? So, are you feeling lucky? Doing nothing and at least the entire human species eventually dies and goes extinct with a high degree of certainty. Doing a gravity test, (mine and/or another's), and there is at least a slim chance of literally wiping out this entire Earth and all on it, and possibly more. Do you and other's truly want me to prove my TOE idea as being really true? But also: Questions: Are at least some black holes in this universe due to a species who were trying to discern what 'gravity' truly was, came up with a test to do so, were successful, but the black hole generated (to prove what gravity truly was) self fed itself and wiped them and at least their entire planet out? What species might have existed where a black hole now resides? (Since all of life itself is ultimately meaningless in the grand of scheme of things anyway, do the gravity test and see what occurs?) * Added note: Suggestion: 'IF' society did not want to do the gravity test, one suggestion might be to at least create a model as if it were true, then see how that model matches with observations and predictions. It might be possible to discern the theory of everything without actually generating a gravitational black hole (which would definitely prove the TOE idea as being really true).

[@karlgoebeler1500]

Mine was a unstable oscillator, Clip the filter caps on the crystal and will have uncontrolled oscillation. Gated counters count the freq. from the oscillator. Temp sensitive. using that as baseline reference in an encryption equation for broadcast. Receiver would use that # as a reference gate for its own unstable oscillator. Receiver would rebroadcast new # Back and forth. Mutating encryption in real time. Go figure Talking about that with my brother back in 1987.

[@sandeebrooke5623]

I had to watch this Explainer 6 times before I got it. Math is not an easy thing for me. But I got it. Sandee Brooke from Tucson Arizona.♥️

[@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.

[@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.

[@paulveldhuizen-lj8dc]

As an engineer I’ve worn out two calculators and the #1 key always goes first. A physical manifestation of Benford’s law?

[@doctorgyrus]

“How often do you count things and end ar exactly one hundred?” “When there’s one hundred things to count” LOOOL

[@isatousarr7044]

The initial digit problem presents an intriguing perspective when applied to the cosmos, random numbers, and binary codes in astrophysics. As we analyze cosmic phenomena and encode them in binary form, we often find that certain numbers appear more frequently as leading digits, a pattern that Benford's Law can help explain. This apparent order in what we perceive as randomness challenges our understanding of the universe's structure. Could this tendency for certain digits to appear more frequently as initial digits in binary codes offer insights into the fundamental laws of the cosmos?

[@jeffkaylin892]

Actually, it is more like 11.11% getting up to 999, as NONE of them start with zero.

[@Cabriellopez]

Appreciate you guys. Thanks for all the knowledge you provide for us. Best channel!

[@kerryemberlyhamby6213]

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. 🤷‍♀

[@pablonarducci]

If you pick numbers like that, they are still going to be random, the thing they are not going to be is uniformly distributed, right? It's a random distribution that favors the lower numbers.

[@stephanienirenberg7426]

This show makes me so happy

[@hrgwea]

This is just an artifact of notation. If you represent numbers using binary notation, then ALL numbers start with the digit 1. There's no bias.

[@tiberiupaslaru3830]

Lol, quite correct 😂😂😂

[@Nefville]

I remember in high school programming on the Ti-83 and there was a random integer function when programming in Basic ("randInt(X,Y)") and I never could figure out how it worked. I thought about ways to program a random number generator from scratch but no matter what you do you're always just kicking the ball down the road. Yes that class was BORING 😂

[@johnlarro6872]

For me, it was HyperCard in 1992. I needed a random number. Used the built-in "Random" feature. Great - gave me a random number. BUT if you tried to generate another random number within 60 seconds, you got the SAME "random" number... It just used the time to generate, and not even down to the seconds LOL

[@jawstrock2215]

Did you find out? It's just a mathematical formula, dependent on a starting seed number. same seed = same string of numbers. Best we got is using the current time for the seed everytime, so the random is hidden with the call timing and speed of the pc. It's a formula that always return between 0 and 1(with lots of decimals). Then more simpler math is done to set actual range.

[@Nefville]

@@jawstrock2215 That's interesting! That makes total sense. I remember I got so deep into it I made a program that would generate a number between say 0 and 10 which would loop with a total counter and then keep track of how many times each was picked to see if there was a pattern. I'd let it run for an entire school day and get tens of thousands of random numbers but they were actually pretty random. I would think you could generate a truly random number with a quantum computer but I'm curious to see the best they can do with a traditional supercomputer.

[@jawstrock2215]

@@Nefville For any method we use, it implies using something from nature/physics. The real kicker is, is there anything truly random in nature/physics? Doesn't seem like it so far.

[@jeremiahlethoba8254]

​@@jawstrock2215I think quantum states can help us tap into the world of true randomness. For example a free electron, say at the very edge of the universe far from fields and heat can have an infinite number of states, and when you observe any particular state then all other state probabilities collapse to zero. So it's like you're guaranteed to find something in a pool of intinite options from exactly the same place. That sounds pretty random

[@Samuel101]

Hello Sir Neil, I am a big fan of your explainer and interview videos. Your content is really thought provoking and interesting to me as a newbie in the field of science( who have just passed out high school diploma choosing Physics, chemistry, Mathematics and computer science ). I am here to ask you to make a video on how do researchers and scientists write and publish research papers and how you do it. I am from Nepal and I thank you very much for your videos😊.

[@Mudiwamufaro]

Thanks Neil and Chuck from Zimbabwe 😎

[@bellaa8663]

it took a minute for his explanation to make sense to me but once again, hes taught me

[@itsd0nk]

Been missing a classic Neil and Chuck sesh!

[@sameer26121980]

I tried in excel, randbetween() function and I do not see any bias towards 1. I used pivot table to see percentage of first digit between 1 to 99 and used Data -> Refresh multiple times to generate numbers. It is not biased towards 1.

[@kumarraj2012]

This reminds me of my boss, always putting me on spot and I would always answer like Chuck “well, I would say MOST..” 😂😂

[@TCN8202]

So, in terms of Hindu-Arabic numerals we have been spamming ourselves with 1's since adoption, i.e for about 1000 years . Several questions come to mind: A. How about Roman numerals ? Is the first digit distribution a bit more skewed towards the X's - or is it still the I's that win ? B. What about cumulatively ? If we add the digits of any written number - will the first digit of the sum still be perdominantly 1 ? And still once out of three on average ? C. What about letters ? Latin alphabet translated as 1 = a, 2 = b is skewed for sure, but how about Chinese characters ? Can we use machine learning (self-taught) to find a geometrical feature that is evenly distributed within the letters ?

[@Amprobiuss]

Chucks eyes deliver his comedy...love these dudes

[@JohnDlugosz]

3:00 "random" does not mean "uniform distribution". The numbers are indeed random, just a different distribution. You can transform it into the desired distribution.

[@Milesco]

I heard about this law a long time ago, but I've never seen it explained as well as Neil just did.

[@nickblondeel5556]

@startalk I am curious what the math would be if you reversed the number (first digit last, ....) or starting from 4 digit numbers swap the first and tirth number? How random are we then?

[@WilliamOrtiz-i7w]

Wow that is cool but I already have a headache just processing this ha thanks for the video.

[@kartaltoker2378]

Here is a random digit generator: start a chronometer with 0.01sec precision, wait for a while (look around, chat with your friend, sing a song, whatever, at least several seconds), stop the chronometer, the 1/100s (i.e. last) digit is purely random.

[@giangvu7902]

This explainer was quite fascinating

[@J2TMFA]

I said “Elm” with Chuck immediately also😂😂😂 My second guess was “1st st” right as Neil said it. That was funny for me😊 🤙💞🤙

[@oldcrow6990]

Thanks for making my day so many times!

[@planethedgehog2427]

6:20 "90 percent." No! Not even if you're rounding. The number of integers from 10 to 20, inclusive, is 11, not 10. 10/11 is .9090 repeating. It's 90.9 percent, or 90 10/11 percent. To try to get random digits, I would suggest choosing the rightmost digit from pages in the middle of a book.

[@anthonylogan381]

When your dad tells a joke and you feel obligated to laugh 10:11

[@AlphaSTAR.]

I have learned so much from both of you, I have also loved all your special guest also, all of you geeks are the best.. Thank all of you for changing the way i explore and adore science.. Also Mr. Neil Tyson, you have been such a inspiration in my life that i named my newborn Tyson!! The whole team will inspire his generation and I love seeing his face light up when he hears Neil explain the universe and laughs along with Chuck every time he chuckles!! So my son's name fits him well❤️ Thank everyone for every bit of knowledge and laughs. The Colors of the Science , can be so inspiring 🔭🌎🌝⭐🌌♾️🙏

[@rileychadwell5635]

These are a lot more fun than I thought it would be

[@EdwardHowton]

Try this experiment with friends and/or family. Something I've noticed. Ask them (or you can do it right now!) to pick a number between 1 and 10. Then ask if it's a seven. Or ask them to pick any number at random and see if a 7 shows up in the selection. The longer the number they pick the more likely there is to have a seven, of course, but it's likely to be a 70 or 700. The reason for it, I think, is that nobody wants to pick obvious numbers. 1? Obvious. Same for 2, 3, and 4. 5 is right in the middle, it's basically a bullseye, so it's too obvious. 9? Too close to 10 so it's in the same boat as 1, and both 6 and 8 are too close to "obvious" choices. But seven hits that imaginary sweet spot. I noticed _myself_ doing exactly that before I ever heard about this tendency. So you're asking people to randomly pick a number with no strings attached, but invisibly there's a TON of non-random considerations taking place. The same happens with all attempts at Random in a ton of little ways. The initial digit problem's the same kind of invisible selection weight that makes things non-random. It's pretty widely known, but some people might not be aware that a lot of casinos and lotteries have been exploited through people examining their results over years and years to figure out exactly what "random" results the computers will spit out next. An algorithm in use might not repeat for 20 years, but imagine waiting for the right moment and knowing how to bet every single time when you recognize which list of numbers the computers are using today!

[@jpdemer5]

That's why I always pick "2".

[@pbarnrob]

'Steve Wozniak tackled 'Random Number Generator' with a Random Number Seed captured somewhat like fission timing. One sixteen (or however many-) -bit free-running counter chip would be read to get that number, which seeds the calculation. That will in time, bring us to more complexities, but first principles are still flavorful!

[@DuhIdiot1]

7:50 1's dominate the initial digits of the years, but they damn near _monopolize_ the digits of the counts of the years by initial digit: ID - Count - Percentage 1 - 1,111 - 54.9 2 - 135 - 6.7 3 - 111 - 5.5 4 - 111 - 5.5 5 - 111 - 5.5 6 - 111 - 5.5 7 - 111 - 5.5 8 - 111 - 5.5 9 - 111 - 5.5 In 1999, it was a true monopoly.

[@vincentforbes7622]

On the computer I work with, it gives me time to 6 decimal points & I use that to create my random #. Since time gets slower the closer you get to a black hole... Would time be faster in the voids between galaxies? If time is faster in the voids, would that help explain why it is expanding faster than in/near galaxies? Is the speed of light affected by the differences in time? i.e. Would light move slower (travel a shorter distance) near a black hole? Also, would light travel a longer distance in the voids?

[@tiberiupaslaru3830]

“They” would say to you that light moves with the same speed everywhere, but time itself is stretched near black holes, so light takes longer to cover “the same distance” as in the void 😊 But I credit you with the best thought jump, from benfords law to black holes 🤣

[@MrKingdomhearts2010]

My love of science has always clashed with my hate for math and I want to be upset with Chuck and Neil for now inspiring an interest in the field I used to hate so much but the video was so good I can't be mad 😩😩

[@dube7729]

This was a good one!

[@dynad00d15]

I don't know if it truely worked, but i needed random numbers for some work and in my research, i came across an article saying that true natural randomness was only found in the chaos of the universe, at it's most raw form, like in space. So i thought that i would simply use the raw format of an infrared heat sensor snapshot as a seed for the RND function. Then i realized what Mr. Tyson mentioned, early in the clip : after numerous rounds, a pattern started to show, that was seemingly caused by the algorythm of the RND function. So i decided to discard it and instead, read the raw image data as binary, convert it into it's octal value and divide it until i reach a value that satisfy the conditions that i needed. (i kept the processed value within N scope by simply discarding the decimals, no rounding up or down) I didnt tested it thoroughly (which i regret) but it seemed to work for my needs at the time. My thought process was to reduce data manipulation to a minimum to avoid a logic pattern footprint appear in the end results. I need to revisit this, one day. I'm open to ideas / criticism / counterpoint / ridiculism (please don't) etc.. :D

[@azhwanhaghiri6336]

7:51 Fun Fact ever since the birth of Jesus (in gregorian calendar) there have been 1111 years that start with number 1

[@nowandrew4442]

This is only a problem if you use the 1st digit as your selector. Yes the same principle applies for the following digits also but then just toss a coin/throw a die for which digit you take in any number, and you will get much much closer to almost-ideal randomness.

[@RogaineForEwoks]

I always heard it was 2nd Street that was the most, because of Main Street and maybe to a lesser degree "Town Name" Street, that throws off 1st's dominance.

[@CarterFrank-r9o]

Hey Neil, really enjoyed your explanation of this topic. More importantly, I've been following along for a while and you seem like a smart guy. As a friend, do you think you could help me out with my physics test? I'm struggling with the class and would enjoy some help. I know you'll come through like always. Thanks.

[@dat_boah]

When Neil gets excited explaining things it amplifies my excitement 😂

[@dennysschmid3078]

Funny video but seriously now, how do we know it's pure randomness? Maybe we just don't understand the pattern. That's what I always think about random mutations, too. Are they really random? Aren't they caused by something we don't know yet? I don't get the probability-based quantum theory universe yet. Is probability really probability or is there something, that seems to be magical now, that defines that spin somehow, in a way we can't imagine?

[@brianmcbride3847]

Excellent logic... I wish more people thought this way.

[@MattIsntYoung]

Good thought. I think random can exist versus purely random the way Einsteins theory works up until juuust thaaat poooint where us brains just say.... aweh crap

[@m.r.keeper]

There are lots of mathematical and experimental proofs that probability randomness of particles is their integral fundamental characteristic. Non-intuitive, our brain doesn't like that, but that is how it works. There is no "hidden" mechanism behind this probability.

[@tiberiupaslaru3830]

Denny’s in short, there are mathematical test suites that you can feed a seemingly random sequence and they tell you just how good it is (check Marsaglia’s Diehard, and L’ecuyer+ Simard TestU01). On the other issue you’ve raised, the randomness of a quantum process seems to be proved by contradiction by Bell’s inequality theorem. Although in practice “quantum randomness” just means “no one in this world can predict the next output” and there are plenty of physical processes that can be harvested for this purpose 😊

[@larrypriest5789]

brought tears to my eyes

[@gwolf7716]

So don’t use items to count where there is a growing set. Why not randomize each digit? For a ten digit number… first digit is the total number of digits second is the rolling position to start assigning values to digits then assign values to each digit. A ten would obviously be recorded as a zero. Is my thinking flawed? The random number must be within a defined set otherwise we get stuck picking from an infinite set of numbers.

[@AugustoFeyh]

I work at a place where the sections are called with numbers. In my city, we have 6 sections, 1st to 6th. Some cities have only 1 section and the largest one has 26. But every city has a 1st section and, as I work at the 1st of mine, I always get misaddressed emails that should have been sent to other cities' 1st sections. I have to tell my bosses to create sections with real random numbers instead.

[@erichbaumeister4648]

Two comments: 1) We often start counting things in Germany with zero, not one. The first issue of a new newspaper or magazine is called the "zeroth" issue. When you walk into a tall building you're on the zeroth floor. 2) One can evaid (or is it "avoid"?) the "initial one" problem by selecting the _second_ of the two digits you select. Your proportion is then 10% ten times. You're welcome.

[@walterhitchins64]

I got it. 1. Run PI out to 1 million + digits. 2. Randomly choose from that list (or set) Does this work? Can I be extended? 1. Run Pi out to 1 million + digits. 2. Randomly choose 1 million + digits from that list. 3. Randomly choose from the number 2nd list?

[@baddoodle6876]

I always feel for Chuck. Every question sounds like a trick question to me too. Neil is like "what percentage!?" And I'm in the back going 🙋 purple? Just one of those days..

[@roberthutchison8197]

I have an idea about that, and it's very easy to do, print out the value of Pi, and pick out the numbers you need and add a letter...

[@jcmn02]

Startalk = #1

[@longlostkryptonian5797]

What a mind blowing fact, that has been staring us all in our faces our whole lives!

[@KateSuhrgirlPlays]

What if you rolled a D10 or a 10 sided die and whatever number you get you use that to make a random number with the number 10 being 0 when it lands on it. Would that make it random since then all numbers have a ten percent chance?

[@datblauebrz7167]

Did you add a sound when the animations come to screen or has it been there in all your videos before? I’ve never noticed it as much as in this video. Or is it just louder than usual? (Quite irritating to me, once I had noticed it. 😅)

[@scott32714keiser]

Use a 10 sided dice and use a Arduino to automatically shake and use yolo to see the number and store the number in a text file and repeat and you can make a truly random number of any length

[@jpdemer5]

Way (way) back when, I used the computer's clock to provide random numbers. Threw out the first several digits (hours/minutes/seconds) and the last, and used the rest, if I recall correctly. It might not have been perfect (could have been some correlation between the cycle count and the moment the calculation would call for it) but it worked well enough for the task at hand. You could always multiply two of them to get a longer number if needed.

[@netgnostic1627]

I would suggest appending the two numbers together to get a larger number if one is needed. If you multiply them together, the product will never be a prime number. So your randomness would be less, because you're pulling from a pool of numbers where none are prime.

[@jpdemer5]

@@netgnostic1627 You'd want to toss the last digit of the product in any event . . . the distribution of the last digit is going to be uneven (for the reason you give.) Here's a method that I think approaches true randomness: Grab a time from the clock, take the nth digit (call it m), grab another time, take the mth digit, grab another time . . . and repeat until you have as many digits as you need. (Maybe toss out the first 2 or 3, just to be sure.)

[@seth7745]

I figured this out a long time ago. Have a computer take a measurement of the ambient temperature with as many bits as possible. Take the least significant (smallest) bits and use those. These digits will change so erratically and rapidly that no human based technology would be able to find a pattern.

[@smeglor1]

From what I understand this is close to what computers do for random seeds. It uses the voltage on the cpu but starting at a very low digit.

[@Arexack999]

Nice. In programming I just took the seconds digit from clocktime, because I am lazy. But doesnt removing the first (several) digits from a generated number, circumvent the first digit problem rather than solve it? Not that it should be solvable. Even if based on something theoreticaly random such as isotope decay, the sample rate of the method of observing/ recording this number would superimpose a pattern in the random data.

[@tiberiupaslaru3830]

Arnoud the method of extracting randomness from quantum processes must be clever indeed, in order to not introduce human patterns into it. Now think of grouping all the decaying events into groups of 3 consecutive events and measuring the 2 intervals of time between those 3 events. Now take a binary “1” in case the first interval was longer and a “0” in case the second interval was longer (and discard in case of equality:) This way you can generate good random bit sequences out of “pure random” quantum events.

[@1999fxdx]

In my college days, stat textbooks had random tables in the index area. You could close your eyes and poke one. It would suffice for most techniques.

[@jessicaheger1880]

But then at 10:25 we see a solution to the problem without acknowledgement or discussion: lotto balls, each with a unique digit, can be randomly picked with reasonable expectations that each number will be represented 1/10 of the time (assuming we only use ten balls numbered 0-9).

[@KindHappyLove]

Why wouldn’t you just randomize with any available option that didn’t begin with one? So you turn to a page or whatever and it’s a 1… you pick again. I mean we could try that or look to space and try to find something completely random. Idk whichever is easier I guess.

[@Danielle-zq7kb]

I love Neil’s vest!

[@tomthibodeau6576]

Right, when counting we start from 1, so we see more 1's, but more generally this is a result of our number system having a base of 10, a small base in relation to the range of number we deal with in many situations. If we used a larger base say 10^100 this effect would be seen less often.

[@Fister_of_Muppets]

"Zero was the most important number ever conceived." When I was 20 years old, my bank account was zero quite often.

[@michaelmcchesney6645]

I went to Bronx Science as well, but I don't recall learning Benford's law as a high school student. I don't think I learned about it until I started watching KZbin videos. Does that means it's better to watch KZbin videos than to go to high school?

[@tiberiupaslaru3830]

Lolz…it means Benford law is not that important after all, despite some KZbin videos who try to make it so. There are thousands of interesting mathematical quirks presented on KZbin, and you would need hundreds of school years to learn about all of them😊

[@GarrettOtt-ls2ml]

I found the title quite intriguing 🧐

[@njdevilsforlifewoohoo5533]

The city I live in, Elizabeth New Jersey actually has 2 streets that have a 1, 1st Avenue and 1st street. Nothing above 7 though. As a kicker. There is no Main Street.

[@thejoshbtv]

This is explanation is conflating randomness and probability. Just because we have to start counting somewhere, which is 1, that doesn't mean that a randomly chosen number is not in fact random. It just means the probability of that number starting with 1 is substantially higher than the random number starting with any number other than one.

[@sabinrawr]

This is a great explainer for Benford's Law. For me, the idea of choosing a "random" number from a book made me flinch. Humans are pattern-based creatures. Those numbers will be no more random than the humans that created them!

[@sabinrawr]

I do think, however, that looking at the LAST number is better, if imperfect. There will still be a slight bias toward smaller digits, but much less extreme.

[@tiberiupaslaru3830]

No Sabin… Taking the last digit only will completely avoid benford’s law

[@sabinrawr]

@@tiberiupaslaru3830 It will avoid Benford's Law, yes. But it's still not sufficiently random because there is still a slight bias.

[@iwannaseenow1]

5:08 Chuck nails it.

[@kevoatway2348]

I heard that 2nd street was the most common street name, as in lots of cities 1st street has been renamed after a local famous person

[@AceSpadeThePikachu]

I don't know if I sound dumb asking this but...why don't random number generators use physical dice? Being physical objects, they're analogue, so as long as they're manufactured well enough that their center of mass is exactly in the center of their volume (not weighted more or less on one side), the numbers you get from them should;d be about as random as possible, right?

[@luciogutierrez997]

I think the same way: maybe it's difficult with something like dice, where you'd have to build an unrealistically perfect die to generate truly random numbers, but you could use other physical, macroscopic things, like temperature, the position of clouds, etc.

[@shexec32]

Dice only give you numbers 1 to 6. How do you get your dice to generate the numbers 7-9 and 0, uniformly? (There are answers to this, and some of those answers do give you the basis for the simpler PRNG algorithms used in computers)

[@AceSpadeThePikachu]

@@shexec32 Have you never heard of dodecahedral dice?

[@shexec32]

​@@AceSpadeThePikachu I like your thinking. Dodecahedral dice does point you in the right direction for one of the solutions. With dodecahedral (& icosahedral) dice, you run into the problem that they bias toward 1 in the leading digit. How do you sort that out?

[@AceSpadeThePikachu]

@@shexec32 Easy. For dodecahedral dice, you make the "10" a "0".