Thank you for citing my work from the early and mid 1990s at 51:30 :) On my KZread channel (Mark Nigrini) I have a Benford's Law playlist that includes a video with free Excel software (the link is in the Description) as well as a video that shows how to do the analysis in R without using any packages, again with a link to the code and other files in the Description.

This is wonderful. The explanation of WHY it works (at 15:26) was the first truly satisfying one for me.

long, but well worth the listen! thanks for the upload.

Heavier than air flying machines are an impossibility? Had he never seen a bird or an insect or a bat?

This is a really fascinating lecture with a most surprising outcome. I think the missing question, though, is: 'Why should this be so?' We have the 'How' type solution; but not the 'Why'. It seems to be bordering on the metaphysical!

The reason it is scale invariant is that scaling creates more number of 1 than 2, and more number of 2 than 3 and so on. So Benford's law is due to 2 factors, factor 1 as I mention previously and factor 2 as scaling also creates this frequency distribution of more 1s than 9s. e.g. Scale 1,2,3,4,5,6,7,8,9 by 2 = 2,4,6,8,10,12,14,16,18 see that because anything above 5 becomes 2 digit with a 1, frequency of 1 is higher.

xp’(kx) = -p(x)/k^2 is the correct differential equation in the slide at 20:00. This is given in the transcript.

Hello 2020 election KZread algorithm

@georgemckenzie2525

3 жыл бұрын

This is why we are all learning how easy to spot fraud can be.

I wonder if the distribution would also follow the law if the data are A: The money people spend in a supermarket. B: The money the cashier gives to the customers as change.

Human heights measured in cm's don't satisfy the critera (39:39) no built-in min/max values, more observations of small values than large values or data spans several whole numbers on the log scale. If, however, you measured height in angstroms, would the distribution of the first digit be Benford? How about the second digit, would it follow the second digit distribution? What about abs(average human height) - measured heights)? On a second track, what is the distribution around 31% for 1 as the first digit (e.g. measuring stock market results for many individual days)? Would that be a normal distribution, or would there be strange artifacts from the underlying Benford distribution? Considering the lottery example as a game, does the equilibrium for the game just flatten out the distribution?

Every street has houses starting with 1. Not every street has houses starting with 9.

That isn't the reason, because when Benford's law applies to a set of numbers, it applies no matter what units you use.

How did he derive the formula for probabilities? He seems to have considered it obvious.

The reason is simple if you know that numbers are interchangable, it is the units behind that matters e.g. 1 inch = 2.54 cm, see that 1 becomes 2.54 if the unit changes. People who develop units usually starts with 1 for the most common size, e.g if sweets comes in 3 pieces most of the time, the developer will say "1" pack (1p) = 3 sweets therefore probability of 1 unit "1p" is higher than "2p" or 3p as determined before, 3 pieces of sweets = 1p is most common as choosen by developer of the unit

@voidisyinyangvoidisyinyang885

3 жыл бұрын

makes sense! thanks

hi /pol/, Trust me there shorter videos that explain it all better out there. But if you are going for a deep dive, this will do great. Numberphile does a pretty good job

Did you just disprove infinity, and zero?

I tested the law with all the numbers on my screen at the exact time, and 30.5% my answer. nice.

So I have an idea for why this is the case. It is because there are more things in the real world that are small rather than big. For instance, there are more galaxies with relatively small numbers of stars than there are galaxies with relatively big numbers of stars. So those galaxies with fewer stars will more likely have a number of stars beginning with 1 because the probability of a number starting with 1 is highest at the smaller relative size.

This Wintersville High School in Wintersville, Ohio is now INDIAN CREEK High School-the very same Building where former President BILL CLINTON spoke at a Rally there before 2012's Presidential Election.(see U Tube Video on it...)

It only makes sense because you can’t reach 2 without 1 and so forth ; you can’t reach 3 without first reaching 1 and 2, and so forth

9 out of 36 for me.... 1/4 LOL that is WEIRD 25%!

It's an artefact of the base 10 number system. Try doing it with all the numbers in binary and the probability of 0 or 1 occurring will be 1/2.

@ecpgieicg

3 жыл бұрын

You are missing the point. The video is about the frequency of *leading* digit. Not any digit. The probability of 0 occurring as a leading digit in any number system is 0. Getting that wrong also shows how you misunderstood the whole premise.

why no "0"?

@automaticreply

9 жыл бұрын

I hypothesize that like infinity it is unusable in it's "value" this is making numbers our of numbers. zero and infinity doesn't come into to play. like the apples when you need to be counting oranges as it were. lol

@haronaillibush

9 жыл бұрын

and nobody hit .090?

@woopseyesharted1499

9 жыл бұрын

Lots of people bat .090. But lots of people also bat .000. Me, for example. I didn't get an at-bat all year. Most people, in fact.

@automaticreply

9 жыл бұрын

Numbers are illusions

@shodaddydrunk

9 жыл бұрын

woopseye sharted when they say '1st digit' they mean the 1st significant figure, meaning not a zero. for your BA(.090), for example, it would be 9

Seems to me that because we live in a finite environment there's going to be more small sets of things, small sets will probably start with a one.

What do you think about using Benford's Law to look for problems with Covid-19 data?

10 out of 15 of the side videos on this page have seconds starting with 1, ignoring zeroes.

@hxhdfjifzirstc894

3 жыл бұрын

Time doesn't use a linear counting system... e.g. 1-59, 2

The U Tube Video is "Former President Bill Clinton In Wintersville, Ohio"!

Lol... if you take all the numbers on this page right here, you will get the same variations. Crazy!

Roman numera, hahaha! :)) What you can do is to represent irrational numbers as continous fractions. That works fine for roman numbers as well.

43:43 How to win lottery.

Lmfao! "what of benfords law in roman numerals?"

The audio is way too low.....Need to hire a better technician ....

So... The closer a number is to zero, the more frequently it is employed. I mean, it sounds really anomalous at first, but what if you ask the question this way-- How many times have you smoked meth today? One would hope that in most cases the answer would be zero, but there is reason to believe that if you are being asked that question in the first place, the number "zero" might not be accurately represented, and there just might be some rounding involved in some of those instances, so let's just deal with one through nine. Its still not a matter of random probability whether a given person will have smoked meth one or four or nine times today. The guy who says "nine" also said "one" this morning, and "four" about ten minutes after that. The guy who says "one," on the other hand... Well, he's full of shit. Don't ever trust a meth freak or a math freak. They're a bunch of deceivers, man... Here's another one-- how many shits have you taken today? Better yet, how many turds can you precisely recall dropping last time around? I'll bet you its not a number that ends in nine. There are zero examples of a practically infinite number of specific things that might be cited in any given record-- there are zero Godzillas destroying Tokyo, there are zero mermaids in my shoes, there are zero ice cubes on the sun, there are zero Godzillas destroying Kyoto, there are zero mecha-godzillas destroying either Tokyo or kyoto, etc-- endless examples of things that exist in the quantity of zero. In a finite universe, there are zero examples of things that exist in infinite quantity. At one end of the spectrum between, you have small numbers of many specific things, and at the other end, you have large numbers of a few broad categories-- there is one "planet earth", some enormous number of "planets". But really there's just one each of a whole bunch of things that have features in common. There aren't two of anything. There is (or is not) a singular infinity, any subdivisions of which are singular infinities in themselves. There is a jerry Seinfeld and there is a Hillary Clinton. To say that they are two " people" is nothing more than a descriptive convention for two unique events in the universe-- in absolute terms, it says more about the speaker and the means of communication than it does about the objects it describes. If we wanted to, we could invent a category called "bleople" that includes all "people" except jerry Seinfeld and Hillary Clinton. "Gleople"-- all " bleople", minus "glee" viewers, plus any apes who can sign at least fourteen words. "Jeeple" -- all gleople minus those who've been run over by a jeep. Now, three stones sitting in a row are, of course, more practically thought of as a "set" than the collection of people I have just rhetorically stripped of their jersonhood, but, strictly speaking, their assignment to the descriptive realm of "three of a thing" is similarly arbitrary. They are distinct items with distinct spatial coordinates and characteristics, which are disregarded and lost in the entropy of set membership, increasingly as the scope of the set is expanded. Accuracy and relevance of information is lost when "jerry Seinfeld" is designated a "TV star named jerry." Every time. The value of the information is less. It is less true. If we refer to the set "TV stars," it gets even fuzzier. And if I say " I saw 'a guy with a pretty cool job' walking down the street in Manhattan... Well, I haven't really said anything, have I? Point being, things are more relevant in smaller number. Things are more true when talked about in specific categories of description, and we don't have the benefit of an infinite vocabulary. It starts at one, and recedes from there. I didn't CREATE the concept of bleople just now. It has been there all along, unnamed, uncounted, and just as extant a set as "people"-- that's where all those missing eights and nines are. In unnamed sets of nineteen things we chose not to lump into a set of nineteen. We like small numbers of things. Things that occur with less frequency are by definition more noteworthy. If you write down the first word each person says to you throughout the week, you get "hello" like, NINE TIMES more than "submarine"! Spooky!!!!! ....the answer to your question is girl scout cookies. Pretty good stuff.

@morbidmanatee5550

8 жыл бұрын

+woopseye sharted The distribution has to spread over several orders of magnitude for it to become evident. You are using single digit examples which will not follow this law. Nice try though!

Why am I getting fact checked over this?

Much ado about nothing

@FlockOfHawks

5 жыл бұрын

Statistics can prove just about anything

@FlockOfHawks

5 жыл бұрын

Either the lecture was given or conceived on april fools day

@FlockOfHawks

5 жыл бұрын

But whatever the content : it's always a delight to visit a lecture by prof Barrow

Rubbish, that's this is all about....

@JuusoAlasuutari

9 жыл бұрын

Hugo Ise Care to explain what sort of deep wisdom led you to conclude that?

This video is sponsered by the very corporations that I hate and need to be put out of bisiness...taken down.!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!