Benford's Law - How mathematics can detect fraud!
Вставка
- Опубліковано 8 кві 2011
- UPDATE 11-11-2020
Hi all, this video is currently being shared in relation to the 2020 USA election.
Benford's Law applies when the dataset is a form of geometic growth over several orders of magnitude, such as the lengths of rivers. So would Benford's Law apply to an election?
Here is a great video by Matt Parker explaining why we would not expect the first digit of election returns to follow Benford's Law • Why do Biden's votes n...
Some are currently citing the work of Walter Mebane as an example of Benford's law being applied to elections. Mebane's method is a test based on the second digits of election results. (Rather than the first digits). If you have heard of Benford's law being applied to elections, that is probably referring to Mebane's work.
Mebane's own analysis of the 2020 election is now here www-personal.umich.edu/~wmeban... and does not support evidence of fraud in the 2020 election.
Note that Mebane says "The first-digit distribution has nothing whatsoever to do with any kind of election fraud."
Mebane's test on the second digits of elections is not universally accepted. One paper that disagrees (or at least advises caution) is this paper (core.ac.uk/download/pdf/20642...) from the California Institute of Technology.
The paper simulated an election and found the test to be unreliable: "labeling a free and fair vote as fraudulent 34% of the time and... labeling a fraudulent election as free and fair 60% of the time."
Their conclusion was that, since Benford's Law proved to be unreliable in a simple simulation, you should be extra cautious about applying it to a complicated, real, election.
For completeness, Mebane's rebuttal to the above paper is here pdfs.semanticscholar.org/e667...
However, both papers agree that more research needs to be done to verify if Benford's law applies to elections.
----------
Benford's Law is a truly surprising fact about the frequency of numbers when studying data such as prices, populations, rivers, even street addresses. And if someone's accounts do not follow Benford's Law then they may be committing fraud!
-----------
Here's a good article by Ted Hill: web.williams.edu/go/math/sjmil...
Hill, TP. The First-Digit Phenomenon. American Scientist 86 (4), 358-363. (1998)
Here's a list of papers www.benfordonline.net/list/chr...
-----------
This law was first notice in 1881 by the astronomer Simon Newcomb, then again in 1938 by the physicist Frank Benford. They both noticed that the starting digits of a lot of real world statistics do not appear evenly but follow a logarithmic distribution, for example this would mean numbers that start with a 1 appear over 30% of the time.
A quick appeal to intuition will show this is true for data that grows exponentially (geometrically). If something grows by some multiplication factor, you will soon see that the distribution is logarithmic, i.e. that numbers starting with a 1 appear 30% of the time. This explains the law for a lot of things that grow in this way, like prices and populations. Yet this law also appears in other types of growth, including factorials and Fibonacci numbers.
However, remarkably, this law also describes what happens when you take data randomly from a variety of sources, such as you might do if you took numbers from a newspaper. Although this data comes from a variety of distributions, not just from exponential growth but many other distributions, yet still follows Benford's Law. Although Benford observed this fact in his original paper, it was not proven until 1995 by Ted Hill.
However, you can still prove Benford's Law without knowing this. If we can assume Benford's Law exists, then it must be scale invariant, i.e. it would not matter which units we choose to make our measurements in - kilometres, miles, feet, centimetres or whatever. As I prove in this video, the only distribution that is scale invariant must be the logarithmic distribution. Hence Benford's Law is logarithmic. This proof was first put forward by Roger Pinkham in 1961.
In 1992, Mark Nigrini wrote his PhD thesis on the detection of income tax invasion using Bedford's Law, and his ideas are applied in the detection of fraud.
We see Benford's Law in observational data because real data can be a complex mix of many distributions and because it is the distribution achieved when data is repeatedly multiplied, divided, or raised to integer powers. And, once achieved, the distribution persists under further multiplication, division, and raising to integer powers.
Raise your hand if this appeared in your feed due to the American Election.
More due to the whiny Trumpists desperately sharing it like it were relevant when even the guy that uploaded it says it isn't.
@@gavsmith1980 But what if it is relevant?
I'm American and 👍
Algorithm played itself 😆
@@gavsmith1980 Trump owns you
The 2020 election is about to make this video popular again
Yep
Maybe not, depends on coverage
Biden somehow broke benfords law when all of his down ballot dems followed it in the same counties.....interesting lol
Here!! Lol Gooooooo TRUMP!!
I just wondering to myself how many other people are searching for explanations of Benford's law on YT right now because of the election, & out of them how many chose this young man to explain it to them? Let's hope it's enough
this guy doesn’t even realise the danger he is in 9 years later
Does anyone know if this poor guy committed "suicide" in the last few weeks by any chance?
@@tombergins8215 Obviously not. The description was edited just a few days ago explaining how this does not or is unlikely to apply to elections.
Twitter has already Canceled this poor guy lol
😂
@@SgvSth he had to say that or he was dead you moron. Smh
I'm surprised there isn't a "the AP has called the election" thingie yet
That’s the only reason I clicked on this video. Just to see. Honestly, I’m very surprised.
Just wait for YT to catch up.
Lmao YT is hilarious with the actions they take sometimes. No one believes in your viewpoint, guys. Thanks for the free videos tho
This video isn't about the election.
@@anticorncob6 indirectly, it is about the election.
This 9 year old video has a chance to go viral once this mathematical law hits the news cycle regarding the 2020 USA presidential election.
Regarding the news cycle, they may try to avoid it deliberately. Just talking about it encourages independent inquiry.
These clowns won't comment on the glitch nor the PROVEN dead that voted in Michigan, you think they're going to comment on an esoteric mathematical theory?
I found an article in the washington post of all places where they use it TO PROVE PUTIN CHEATED IN HIS LAST ELECTION HAHAHAHA www.washingtonpost.com/news/monkey-cage/wp/2017/01/11/when-the-russians-fake-their-election-results-they-may-be-giving-us-the-statistical-finger/
SPREAD THIS everywhere
The mainstream media would never do it. They are too biased for that!
Never thought I would be learning a complex statistics law because of an election.
Same here 😂
Now imagine if you actually understood it.
Now imagine winning at three card monte.
.
Democratic Party likes keeping people educated...
It’s basic statistics and probability if you get in to it
2011: "Benfords law is a great way to detect fraud."
2020: "Benfords law is COMPLETELY unreliable!!!"
Funny how even mathematics have a political twist, isn't it? Just how many propaganda is fed to people in the name of science?
@@YC-ls4yx the "trust the science" narrative doesn't include math scientists ig lol
@@YC-ls4yx look at Global Warming and weep!
@blbrd30 You do realize there is a show called "keeping up with libtards" that is already running 24/7 on your TVs, right?
There’s more than one type of fraud, and in some mathematic paper about Benford’s law, it says that it is inaccurate for detecting fraud in a vote between 2 things. Also, where did you read that Benford’s law is completely unreliable? Benford’s law definitely has certain applications, but not in elections between 2 people.
In 2020- “warning, this math is disputed”
Fact checked : Benfords law is Mostly false or lacking context. -Pravda squad (pravda is russian for truth and only the state speaks it)
It's been deboonked
@@sadfasdf74 Ooohhh I'm debooooonkiiiiing!
2+2=5
deboonked
Math guy: no one will ever watch this 😔
2020: Hello there!
Ha! I was saying the same thing just a minute ago!! 9 years this video is up and titled "how math can detect fraud", all of a sudden 2020 hits and everyone's like "no, benford's law can't detect THAT kind of fraud!"
Read the description
@@ferrumitzal4584 read the description
I'm watching, and I hate math!!!
@@rubenvanderaa8420 True. He's already in damage control mode. Suddenly Benford's Law doesn't apply anymore. ;-)
when the presidential election sends me to a video from 9 years ago
When the UA-cam algorithm is feeling suicidal. It also recommended me 'America First with Seb Gorka' featuring Steve Bannon on massive election fraud. Thanks UA-cam
@@Sam-go3mb
Maybe some of them are good guys. I think we have little more freedom here.
Sam I BET you UA-cam is going to “fix” its algo soon.
Lucille yup, you’re def lost
Read the description
9 years later and this is more relevant than ever
With the exception of it not being relevant to the election, as the author of the video notes.
Only if you didn't understand it
God bless you all folks.
The UA-cam algorithm has horrific humour.
It's learning from reality.
I just watched an old CNN video on how Dominion voting stations are easily hacked. Quite humorous indeed.
Biden's campaign forgot to watch this before hitting the upload button.
Gender Studies majors won't understand it.
Communists are much better @ subtracting than adding (unless it's "adding useless rules to govern your life")
Im not sure they'd follow (I didnt, on the 2nd part)
@@-ColorMehJewish- I don’t know, looks like there’re pretty good at adding fictitious votes!
@@-ColorMehJewish- According to Americans, everyone is communist.
Because they are commies
2020 election is gonna blow this video up
I hope so.
It just popped up in my recommended feed.
Yeah! This video just organically was recommended in my feed. I already know about it now but it is sort of poetic.
@@wasblocked6133 makes ya is someone at youtube pointing us in this direction?
Come on man!
I really appreciate that you added some context to this video in the description. It's a shame that so many people either don't bother to read it or presume to know more than experts in the field.
Here is an explanation of how Benford's Law is applied to the Quran:
The Quran is divided into chapters of unequal length, each of which is called a sura.
Quran consists of 114 suras. Each sura is composed of a certain number of verses, for example, sura 1 has 7 verses and sura 96 (the first sura revealed to Prophet Muhammad) has 19 verses. So we have a set of 114 data to which we can apply Benford's law. There are 30 surahs that have the number of verses starting with the number 1. For example, surah 4 has 178 verses, and Sura 5 has 120 verses. There are 17 suras that have the number of verses starting with the number 2. For example, sura 2 has 286 verses and sura 3 has 200 verses. You can see that both of these numbers start with the number 2. There are 12 suras that have the number of verses starting with the number 3. For example, sura 31 has 34 verses and sura 32 has 30 verses. If you keep doing this for the whole Quran you will find that there are 30 suras that start with 1, 17 suras start with 2, 12 suras start with 3, 11 suras start with 4, 14 suras start with 5, 7 suras start with 6, 8 suras start with 7, 10 suras start with 8, and 5 suras start with 9. Now take 30/114; 17/114; 12/114, 11/114; 14/114; 7/114; 8/114; 10/114; 5/114. For example, 11/114=9.6% which matches Benford’s Law for 4, which uses Logarithm base 10: Log(1+1/4) =9.6% If you do this to all numbers, you will find there is a match between the Quran arrangement of numbers and Benford’s Law. This shows that humans didn’t interfere with Quran. In the same way, when you do your taxes and you don’t change the numbers, your tax numbers will fit Benford’s Law curve. The US government crackdown on people who cheat using this method. If the US government uses this method on the Quran they will know that nobody messed up its numbers.
lol. Funny I'm getting recommended this 9 year old clip now... good to see UA-cam's algorithm hasn't buried it yet
Little did he know that his video would one day save Western civilization.
USA election 2020 was defrauded. Biden and his ilk have seen the near death of Western Civilization. It is remarkable to me that people can witness that death at the hands of the cabal and think that cabal members like Biden are saviors. Just shows that sentience is optional for humans.
Born too late to explore the world
Born too early to explore space
Born just in time to save the west!!
🙏🙏🙏🙏🙏
No, it won't, because Benford's law cannot be used to detect fraud in elections. Read the description.
"Save western civilization" LMFAOOOOO. Nice cope attempt.. there was no election fraud.
Imagine asking your brilliant friend what he’s doing with his spare time and he says he’s circling all the numbers in the newspapers to look for patterns.
Lol
🤣 wait I think I watched a movie about this kind of content
And that friend looks a lot like Russel Crow for some funny reason :-P
schizophrenia
They called me schizophrenic cause of that
I believe this is the most intuitive explanation of how this works I have ever found on UA-cam. I think there are other prettier productions, but this was the most concise. Suggestions of other better one's would be great. Thanks for this masterpiece!
Here is an explanation of how Benford's Law is applied to the Quran:
The Quran is divided into chapters of unequal length, each of which is called a sura.
Quran consists of 114 suras. Each sura is composed of a certain number of verses, for example, sura 1 has 7 verses and sura 96 (the first sura revealed to Prophet Muhammad) has 19 verses. So we have a set of 114 data to which we can apply Benford's law. There are 30 surahs that have the number of verses starting with the number 1. For example, surah 4 has 178 verses, and Sura 5 has 120 verses. There are 17 suras that have the number of verses starting with the number 2. For example, sura 2 has 286 verses and sura 3 has 200 verses. You can see that both of these numbers start with the number 2. There are 12 suras that have the number of verses starting with the number 3. For example, sura 31 has 34 verses and sura 32 has 30 verses. If you keep doing this for the whole Quran you will find that there are 30 suras that start with 1, 17 suras start with 2, 12 suras start with 3, 11 suras start with 4, 14 suras start with 5, 7 suras start with 6, 8 suras start with 7, 10 suras start with 8, and 5 suras start with 9. Now take 30/114; 17/114; 12/114, 11/114; 14/114; 7/114; 8/114; 10/114; 5/114. For example, 11/114=9.6% which matches Benford’s Law for 4, which uses Logarithm base 10: Log(1+1/4) =9.6% If you do this to all numbers, you will find there is a match between the Quran arrangement of numbers and Benford’s Law. This shows that humans didn’t interfere with Quran. In the same way, when you do your taxes and you don’t change the numbers, your tax numbers will fit Benford’s Law curve. The US government crackdown on people who cheat using this method. If the US government uses this method on the Quran they will know that nobody messed up its numbers.
@@hamzamohamed1872 This is quite a cool application of Benford’s law. However, there is a problem with your claim that the fact that Benford’s law approximately holds for the numbers of verses in the suras of the Quran demonstrates that humans didn’t interfere with the Quran. Your claim assumes that humans are incapable of choosing numbers randomly offer a wide range of magnitudes. While it is true that humans tend to struggle to be random (we have a tendency to adhere to patterns), we are capable of forcing ourselves to be random enough to create a set of data for which Benford’s applies as well as it does for the Quran. Other than randomness, we also require the set of data to be spread across a wide range of magnitudes in order for Benford’s law to hold. If the Quran was created by humans, then there are reasons why there could be a wide range of magnitudes of verse numbers in the suras. For instance, suras could have been written independently over a wide range of time spans, as is the case with the bible, which even Christians accept was written by humans. This would mean that the authors could have different ideas about what an appropriate number of suras for a verse might be. None of this suggests that the Quran was interfered with by humans, but you will have to look elsewhere if you want to find evidence that the Quran wasn’t interfered with by humans.
UA-cam's algorithm is trying to tell us something, hmmm.
Smith Rockford that post show how much you need to go back to grammar school
@@mooltipass5635 you must not have a grad degree in a hard or natural science. Legitimate statisticians definitely do disagree
@Smith Rockford dont speak it
@@willjones6400 - I hate to break you, but Trump betrayed his White voters.
If only he had done what he had promised with millions of White working class non-voters, the voter fraud itself would be in vain.
@@willjones6400 - Remember that he said he would be giving half of trillion dollars to the "N" people, you know he capitulated to the enemy of the West/World.
This guy hasn't aged whatsoever in nearly 10 years lol.
10 starts with a 1 lol
Hasn't been outside in 10 years
Lol
Wikipedia updated the Benford's law entry. It is now deemed "problematic". I wonder why...
Its “problematic” to liberals in that it points to fraud
FIGURES !!!
Use wayback machine for earlier version of article!
Well halfwit users get on there and begin editing/vandalizing until the semi-protection lock must be engaged. So far there have been over 70 edits since the polls closed 3 November. Only one incidence where the word "problematic" occurred and has since been removed from the published article text.
Wiki isn’t credible
Well UA-cam has handed me this video, and I clicked on it for some reason. But I wasn't disappointed, you've got a truly incredible way of making something complex seem simple and understandable. I can walk away from this video feeling confident I understand Benford's law and it's applications as well as limitations well enough that I could explain it to someone else and they'd be able to understand it too.
That's not a simple feat, and it's absolutely worthy of admiration, respect, and praise.
Can you imagine discovering this? “Crazy grandpa circling all the numbers on the front page again. I think it’s time we put him in a home, dear.”
love this concept
Joe Biden: "I will listen to the scientists"
Also Joe Biden: Wait that's illegal
Yeah. Sounds like Joe. Something's up. It's as if they don't like investigations anymore...
The Descripttion of the video says that Benford's law, when applied to the 2020 US Election, does not indicate that there was fraud.
I was hoping for a Trump victory, too. The Supreme Court, and respective states still have to finalize who actually won the election.
I think there was fraud in the election, but Benford's law is not a peice of evidence you could use to support that argument. Please don't spread this around without researching Bedford's law 🙏
@@onpoint2292 Video description is nonsense. Benford's law has been used to detect know fraudulent elections.
@@Prolute reread the description. It says if you go by Benford's Law, there was not fraud in the 2020 US election. 🤦
Researchers do dispute whether Bedford's law could be used to accurately predict fraud or not. The description also says that even when you use Bedford's law, it does not support evidence of fraud IN THIS ELECTION.
@Kunth Thank you for the information, kind stranger.
I was just being abundantly cautious of my right-wing bias. I have seen too many times when people would cite something, anything, even if they barely understood the peice of evidence, to support their argument. I thought that's what Trump supporters were doing in this case.
I'm glad that you proved me wrong. 🙇
Views: 100,973
Likes: 1,937
Dislikes: 11
Huh. They all start with one.
Blargzargo Hlaaluington if my calculation is correct, that means 100% of numbers naturally generated start with a 1!
not anymore
@@lonewalker5446 but this comment and the ones responding to it do
124 likes 🧐
125 likes on the comment
9:30 "imagine I threw a dart at this" - you utterly nailed this explanation and twelve seconds later I understand exactly both how Benford's law comes about and how to calculate its probabilities.
Here's why Biden's Chicago data doesn't follow Benford's law, for anyone who actually wants to know.
The famous chart shows how many Chicago precincts there are where a certain number is the leading digit of the number of votes given to Biden. So if Biden got 372 votes in one precinct, then that makes the 3rd bar that much taller.
So here's the thing
98.7% of the precincts in Chicago had a vote total which was exactly 3 digits long. This means that in most cases, the first digit simply means how many times 100 votes Biden received. The precincts had a vote total concentrated around 500, and Biden received a percentage of them concentrated around 70%. Which means that the largest share of precincts had around 350 Biden votes, or to put it differently, a number starting with 3. This is why the graph is skewed towards 3 rather than 1.
This phenomenon is actually mentioned in this very video, when James explains that Benford's law doesn't apply to people's height since it doesn't cover enough orders of magnitude.
Stand up maths did a video on this
Which you are probably referencing
@@curiouschris3032 Indeed I am
Hello from the 2020 election
How long before this gets censored?
@@jasonransdell7055 Check the description edit. The video maker covered himself.
@@jasonransdell7055 not before the Dunning Kruger conservatives and trump bootlickers try to use it and make a fool of themselves.
@@benshapiroismysexsiave2028 funny coming from someone with your user name and post history.
You have let him get so far in your brain that you have drastically altered your behavior.
@@goolabbolshevish1t651 doesn’t matter, trump lost anyway chud.
UH OH, CHECK THOSE SWING STATE PRECINCTS
and only swing states. oh and only votes for the new president. how odd that DNC voters forgot to tick any other ballot...
Read the description.
@@antoniosoares9273 the masters got to this weak pathetic man and had him come out in defense and obfuscation of their failed defrauding of the US election 2020.
@@TheBelrick still beat your strong man.
dakota640540 There has literally been found zero evidence of any of it lmao. Blind sheep following a desperate mans lies.
It's almost like deep down in the algorithms running youtube, there's still that old rabbit hole from the early 10's just dying to come out -despite all they've done to mutilate it
Reminds me of Wisconsin's voter turnout- 50 year average of 67%, yet this year it was magically 89%.
If only there was some global event requiring urgent political action going on that could explain why people feel the need to vote...
@@jabronijackpot ...
Sorry, did you have anything else to say after those smug three dots or should I reply now
@@jabronijackpot theres nothing special about this year
I’ll bet this video is suddenly very popular with the recent election madness
@Joe Sniffs Childen's Hair Biden read the description
U mean election fraud?
@@Cba409 this video is about fraud *in general* . If you want something specific to election fraud, check out the video description. It has a link to matt parker's video.
You mispelled 'fraud' ;)
Too bad nobody will read the description which clearly shows a video showing why bentfords law is not applicable to elections
Is it a coincidence that this video showed up in my recommended feed after the 2020 election?
And the presenter clearly had a gun to his head by the cabal demanding that he aid in covering up the election fraud.
Read the description
Some right-wing propagandist probably cried and whiend about Bendord's law and all the sheep believed it unthinkingly. So yeah, not a coincidence. Right-wingers are easily manipulated.
im here
@@DrZaius3141 lol leftwingers ever project. why? because they are sociopathic cvnts.
The issue, the real issue. is that you were allowed to live among decent people. banishment for humanities sake is the answer.
I am not a mathematician. Math is probably my worst and least liked subject ever. But I found this video fascinating. Your passion pulled me right in. If you are not a teacher or a professor, please consider it!
Fellow UA-camrs,
Please read and consider the description before commenting. We should do this for EVERY video, and it's especially important this time.
Thank you.
In base 2, numbers starting with 1 occur 100% of the time.
Wowmaxy uh, no? you mean base 2 as in binary, 1 and 0? or base two as in 1 and 2? because base two would be 0 1 2 , which is three numbers, so it would be half of the time basically, the logarithmic area of the scale of a third.
base 2 is binary, since each place value is a power of two, and 012 is base 3 (note that base 10 has 10 digits 1-9)
E N-M 0-9*
Wowmaxy What about 0?
WeAreGRID I like how you tried to redeem your complete fail by correcting his minor mistake.
That whipping away of the newspaper and loud "HELLO" startled me.
UA-cam be like: The claims in this videos are disputed.
The comment section with all the misinformed, angry Trump voters is what should be marked as disputed
@Fabian Sosa Don't bother to learn anything and change your mind. Just keep calling people rats without knowing anything about them.
Read the description.
Now's probably a good time to tell everyone you aren't feeling suicidal and don't plan on disappearing anywhere.
Regardless of this, the anomalies seen in the recent 2020 US presidential election should be investigated and the ballots audited. Even if it only confirms the result, I don't want to have to spend the next 4 years listening to people claiming the election was invalid.
"I don't want to have to spend the next 4 years listening to people claiming the election was invalid"
Yeah the last 4 years of hearing this was bad enough
@@morganfreeman1906 Oh they did a lot more than just claim it was invalid. They tried everything they could think of to stop him. democrats are often horrible people. No wonder there is so many walk away videos.
Why are they horrible people? That mindset is so bad.
@@cor3598 Not all, just the low information ones that didnt even look into Bidens policies. Check his website, its not going to be fun im telling you.
Yes. It has been super annoying for the last 4 years.
Time for this Video to EXPLODE!
Looks like very few people actually clicked the SHOW MORE tab and read what is there.
He seemed so happy explaining this while still leaving most just as confused 😂
There are 12 recommended videos that appear by this video and 7 of them have number of views that starts with 1.
lmao true
i got 5/17 = 29.4 omg
The first 100 results when I search for Numberphile on YT; 1=32%, 2=18%, 3=16%, 4=7%, 5=8%, 6=9%, 7=5%, 8=3%, 9=2%, nice curve
yeah I know it's 2 years..., math is eternal
I have 18 videos with views and only 1 starts with a 1.
I kinda dislike Dr Grimes' explanation of this phenomenon. Numberphile's own video explanation with lottery ticket numbers made a lot more immediate sense of the thing. I'm not saying he's wrong, obviously, but it feels like reserve logic, even when (or maybe *because* of) having seen the other video. "We need data to have 30% to start with a 1".
On a side note, I think that rounding also influences the numbers in a paper. Those large numbers are probably more often rounded to be more easily read/understood. "about 1 million cases of flu" or whatever. For the general public it isn't necessary to always know the exact number.
Well, it's three years later, UA-cam dramatically increased its meddling with the algorithm, so you've essentially just discovered fraud.
I wonder why this video could possibly be in my recommended.
How long before an explanation of Benford’s Law violates youtube’s terms of service? 😆
This is very surprising, and even more so - surprisingly useful! Thank you for posting this!
this is ridiculous... i just looked up the dollar amount associated with the last 100 transactions in my bank account, and indeed, 32% of numbers started with a 1...
nachos Well, it's actually very natural. Unless we concentrate otherwise, our brains work with logaritmic scales. That's why when you check discounts, you compare percentages, or when comparing performances, you use ratios (something is twice as fast or some burger has 10% more meat than another). Money comes in logarithimic scale as well (1 dollar, 2 dollar, 5 dollar, 10 dollar) because it's the easiest way of using them and because of that also older numeric systems are logarithmic (eg. Roman or Greek). Arabic numerals are actually what is ridiculous and strange.
Most of mine started with a "-"...
+TheMasonX lol :)
My balance is $100,000 but it's surrounded in parenthesis for some reason
And ~33% of numbers in your comment are 32. And 25% of numbers in this comment ARE 1.
Thanks this has helped me cook the books for my business :)
Will be caught by this law: Digit Analysis.
Too Bad Biden didn't see this Video for his Election, maybe they would have followed the LAW.
@@VtreyusV3 His son Hunter got a job (thanks to his dad) working in the industry that makes extensive use of this technique. If he had taken more interest in his son's career and business activities he might have learned something useful. Lol
@@sharonjuniorchess Beijing Biden was too busy sniffing
As an exercise for the reader: Tally the first digit of each comment's likes ☝️🤠
What a great idea. I tallied the likes of first 55 comments, which were all the comments I read till I got tired and decided to stop. I counted 16 out of 55 = 29.09%. Incredible exercise!!!
Incidentally, I only watched this because it was 9 years old, so I knew that the content of the video would actually be an explanation of the law by someone unaware of the fact he would have to deny its applicability later to avoid uncomfortable implications, and not something like Matt Parker's handwaving "nothing to see here" explanation for why math doesn't work on anything with political consequences.
Read old books people, old encyclopedias. Archive articles and webpages, download videos, all that stuff. Buy print books, and try not to do so in traceable ways. Get things that they cannot take from you or rewrite, and consume media from before the Ministry of Truth gets its hands on it to make it congruent with tomorrow's subjective political reality.
If you think this video supports the voter fraud arguments, maybe you should send this to Trump's elite strike force legal team so they can show it in court and actually win something rather than being tossed out by federalist society judges?
00:22 He literally states within the first 30 seconds of the video that the law DOES NOT apply to certain situations. In the case of his newspaper, circling page numbers would be a bad application. So go back and actually watch this 9 year old video properly this time, without ignoring things which are inconvenient for you.
Also you sound like a tinfoil hat wearing paranoid lunatic.
@@ag-bf3ty Actually newspapers are a great example of benfords law because newspapers usually dont have hundreds of pages so the pages in tenths and twentieths (starting with 1 and 2) are a larger share than bigger digits, which is what the law predicts
This is the first time I've ever heard somebody speak and thought "this guy is genuinely a genius". I have an M.Sc. in engineering so I've spent many years of my life with bright technical people (professors from both the mathematics and the engineering fields) but you have a particular passion and quick fluent way of juggling numbers and explaining concepts that I find very impressive. Especially given that that your speech is unscripted (I assume) and the annotations are only added to the video later so you must be following those in your head.
I'll admit, what convinced me to subscribe was how you tackled the shortest-path problem using a rig with soap bubbles and pegs. I've always had a fondness for genetic algorithms, but that setup was just brilliant. Keep up the great work man!
Indeed
Agreed. But as I've explored Numberphile, a channel where James makes frequent appearances, I keep saying this for every new presenter I see.
@@FlyingSavannahs What's with Matt Parker?
@@tsunghan_yu I know the topic but I don't remember this video. Yes, James Grime is brilliant, explains concepts flawlessly, and is never dull. The quip I was trying to make seems hard to root out now. My comment about Matt sure seems harsh, not humorous. Matt gets a lot of teasing because of a career defining video on Numberphile. Search for "Parker Square" if you're not aware of his landmark work. Thanks for the heads up. I'll edit out the rude bits.
@@FlyingSavannahs Thanks for the reply. I didn't know the video (a really funny one indeed).
Whos here in 2020
Me
After so many videos, when I think of math I think of this guy
Supreme Court: “what’s ur evidence Trump?”
Trump: “u seen this UA-cam vid?”
2020 election results brought me here
"oh no math doesn't line up with my politics, better change the description" xDDDDDDd
My thoughts exactly:)
Thank you for this video, your wonderful channel and all of the lovely details you added to the description of this very video.
Thank you friend.
Great presentation and analysis mate! 💯👍🏼👏🏼🙏🏼
I would venture the guess that (2:45) indeed the results for "meters", "kilometers", and "centimeters" would be very similar when counting starting numbers.
"Huh?"
--- Americans
lol
Here because 2020 elections
I'm amazed I don't see a "The Associated Press has called the election for Joe Biden" under this video
Very interesting, great job presenting it in a visual manner that even a layman can understand.
Here is an explanation of how Benford's Law is applied to the Quran:
The Quran is divided into chapters of unequal length, each of which is called a sura.
Quran consists of 114 suras. Each sura is composed of a certain number of verses, for example, sura 1 has 7 verses and sura 96 (the first sura revealed to Prophet Muhammad) has 19 verses. So we have a set of 114 data to which we can apply Benford's law. There are 30 surahs that have the number of verses starting with the number 1. For example, surah 4 has 178 verses, and Sura 5 has 120 verses. There are 17 suras that have the number of verses starting with the number 2. For example, sura 2 has 286 verses and sura 3 has 200 verses. You can see that both of these numbers start with the number 2. There are 12 suras that have the number of verses starting with the number 3. For example, sura 31 has 34 verses and sura 32 has 30 verses. If you keep doing this for the whole Quran you will find that there are 30 suras that start with 1, 17 suras start with 2, 12 suras start with 3, 11 suras start with 4, 14 suras start with 5, 7 suras start with 6, 8 suras start with 7, 10 suras start with 8, and 5 suras start with 9. Now take 30/114; 17/114; 12/114, 11/114; 14/114; 7/114; 8/114; 10/114; 5/114. For example, 11/114=9.6% which matches Benford’s Law for 4, which uses Logarithm base 10: Log(1+1/4) =9.6% If you do this to all numbers, you will find there is a match between the Quran arrangement of numbers and Benford’s Law. This shows that humans didn’t interfere with Quran. In the same way, when you do your taxes and you don’t change the numbers, your tax numbers will fit Benford’s Law curve. The US government crackdown on people who cheat using this method. If the US government uses this method on the Quran they will know that nobody messed up its numbers.
Anyone else here because of the stolen election attempt? Great vid by the way. I really like this guy's enthusiasm for the maths.
He is a very good teacher.
I cant believe im looking up Benfords Law right now. I used to be one of those kids in school who would ask how am I going to apply math in the real world. Well now I know.
LOL! I needed that!
There will soon be a warning from yt saying that this math is “DIsputed”
It's just another one of those "glitches"
It is disputed, because it is not applicable to votes.
Acording to "What does/doesn’t follow Benford’s law" it's a great fit for "valid" votes. Thanks for helping me prove that votes that don't follow Benfor's Law are statistically invalid.
Why does this video remind me of the lesson on percentages from the original film Willy Wonka. "I can't do 2!"
@@jimk5145 see ‘stand up maths’ video on benfords law.
I've been waiting for this to show up in my recommended.
Fascinating! Thanks for sharing this James...
Indeed... very very interesting 🧐
we found a 9 year old comment wow
2020 election brought me here
and me
The Supreme Court need to watch this video now or America is done for.
so if an election doesn't follow bedfords law all of a sudden why do previous elections follow the law?
2011: This is how we can detect election fraud in 3rd world
2020: This is how we can detect election fraud in Detroit
They're the same statement.
Exactly, part of the 3rd world.
Only that it can't detect election fraud. It only works if you have a data set with numbers spanning multiple magnitudes, while election districts are roughly equally sized, almost all being in the 100s.
This was just recommended. Interesting timing!
Feels like a good time to watch..
It is 2023 and I got this recommended and it helped me aplly pricing for my business. Wild!
Hey James, I would encourage you to post the update in your description as a pinned comment to make it more visible for folks.
(Edit: typo)
Move along nothing to see here, video will soon be memory holed just like they changed the wiki article on this topic.
I just realized this even though I've seen this many times. When pumping down a vacuum chamber, about 1/3 of the time is spent on a pressure that starts with 1 regardless of the power of ten following it.
Thanks, you just declared me old. Not only do I know what a log table is; I still have my old slide rule.
Interesting that this shows up in my recommended, after 9 years.
wow did you just learn what an algorithm was after 9 years too?
I remember learning about this in my accounting classes, but not my math classes. It's kind of interesting where you come across certain things.
benfords law:
Here is an explanation of how Benford's Law is applied to the Quran:
The Quran is divided into chapters of unequal length, each of which is called a sura.
Quran consists of 114 suras. Each sura is composed of a certain number of verses, for example, sura 1 has 7 verses and sura 96 (the first sura revealed to Prophet Muhammad) has 19 verses. So we have a set of 114 data to which we can apply Benford's law. There are 30 surahs that have the number of verses starting with the number 1. For example, surah 4 has 178 verses, and Sura 5 has 120 verses. There are 17 suras that have the number of verses starting with the number 2. For example, sura 2 has 286 verses and sura 3 has 200 verses. You can see that both of these numbers start with the number 2. There are 12 suras that have the number of verses starting with the number 3. For example, sura 31 has 34 verses and sura 32 has 30 verses. If you keep doing this for the whole Quran you will find that there are 30 suras that start with 1, 17 suras start with 2, 12 suras start with 3, 11 suras start with 4, 14 suras start with 5, 7 suras start with 6, 8 suras start with 7, 10 suras start with 8, and 5 suras start with 9. Now take 30/114; 17/114; 12/114, 11/114; 14/114; 7/114; 8/114; 10/114; 5/114. For example, 11/114=9.6% which matches Benford’s Law for 4, which uses Logarithm base 10: Log(1+1/4) =9.6% If you do this to all numbers, you will find there is a match between the Quran arrangement of numbers and Benford’s Law. This shows that humans didn’t interfere with Quran. In the same way, when you do your taxes and you don’t change the numbers, your tax numbers will fit Benford’s Law curve. The US government crackdown on people who cheat using this method. If the US government uses this method on the Quran they will know that nobody messed up its numbers.
Oh, so that's why I'm seeing this being in my recommended
What a timely video!
Another statistical anomaly is Wisconsins 89% turnout of registered voters.
89% is about 5 standard deviations over the average turnout in Wisconsin since 1960. Probably greater than 2000 to 1 odds.
Debunked by Fact Check. Wisconsin went from 69.34% in 2016 to an actual 72% in 2020. Rework your standard deviations. It's probably a good idea to stop and reconsider when your own figures scream 2000 to 1 odds against its happening. It didn't!
@@deucebollards
Fact check may have debunked it but you should fact check Fact Check.
According to the Wisconsin Election Commission as of 11-1-2020 there were 3,684,726 registered voters in the state of Wisconsin.
Alleged results were
1,630,716 Biden
1,610,151 Trump
38,493 Jorgenson
10,409 two other candidates
3,289,769 total
That is 89.23% of registered voters in Wisconsin. If you have different numbers please post them.
Now I know why Trump has been so certain!
You don't need mathematics to say something is fishy about more people voting than were registered to vote, not to mention all of the other problems.
@@remyllebeau77 some people just need the math to believe
@Harvey Weinstein And dead people, and people that have moved to another state, etc etc.
Look at the description
@@ViridiVulpis Look at the numbers of the election. Trump's votes in WI, MI, and PA follow Biden's law pretty well but the biden votes dont. Biden's law, formerly Benford's law, has been used historically to prove voter fraud. They added that so the video would not get taken down. Same reason you can only post evidence of voter fraud on IG or Twitter with a "Fact Checkers say this is wrong please please don't believe this and please don't retweet it" tag on it.
This article is a rebuttal to the article the channel provided in the bio:
t.co/crK9HChfnW
The paper doesn't conclude that Benford's law DOES apply to elections, just that the article supposedly discrediting such an idea is deeply flawed and unreliable at best.
It raises questions which warrant further investigation. Such as this article which points to Milwaukee www.thegatewaypundit.com/2020/11/using-audit-statistical-technique-known-benford-analysis-wisconsin-precincts-milwaukee-absolutely-investigate-fraud/
That video dosen't have to be appealling. When you have trouble, don't give up. You are still on ones. Keep going.
He’s currently being questioned by the FBI...
this looks like zipfs law, but with numbers
#VSauce
Michael here
Or does it...?
_Vsauce music starts playing_
Make Benfords Law Great Again!
benfords law:
Here is an explanation of how Benford's Law is applied to the Quran:
The Quran is divided into chapters of unequal length, each of which is called a sura.
Quran consists of 114 suras. Each sura is composed of a certain number of verses, for example, sura 1 has 7 verses and sura 96 (the first sura revealed to Prophet Muhammad) has 19 verses. So we have a set of 114 data to which we can apply Benford's law. There are 30 surahs that have the number of verses starting with the number 1. For example, surah 4 has 178 verses, and Sura 5 has 120 verses. There are 17 suras that have the number of verses starting with the number 2. For example, sura 2 has 286 verses and sura 3 has 200 verses. You can see that both of these numbers start with the number 2. There are 12 suras that have the number of verses starting with the number 3. For example, sura 31 has 34 verses and sura 32 has 30 verses. If you keep doing this for the whole Quran you will find that there are 30 suras that start with 1, 17 suras start with 2, 12 suras start with 3, 11 suras start with 4, 14 suras start with 5, 7 suras start with 6, 8 suras start with 7, 10 suras start with 8, and 5 suras start with 9. Now take 30/114; 17/114; 12/114, 11/114; 14/114; 7/114; 8/114; 10/114; 5/114. For example, 11/114=9.6% which matches Benford’s Law for 4, which uses Logarithm base 10: Log(1+1/4) =9.6% If you do this to all numbers, you will find there is a match between the Quran arrangement of numbers and Benford’s Law. This shows that humans didn’t interfere with Quran. In the same way, when you do your taxes and you don’t change the numbers, your tax numbers will fit Benford’s Law curve. The US government crackdown on people who cheat using this method. If the US government uses this method on the Quran they will know that nobody messed up its numbers.
This was really interesting to watch. I will test this law myself in a newspaper.
It's been almost 10 years since you posted this video - but I hope you realize how excellent your explanations are, here. far too often statistics are taught by statisticians for statisticians.... designed either to make themselves feel good in front of their peers, or because they really can't grasp what a beginner level looks like.... my university "beginner" statistics was so atrocious that I stopped going after the 3rd week... and because the grades were curved, I still got a D+! I've gotten much more competent in the subject since then - in no small part because of creators like you - so.... long way of saying "thanks!"
All of a sudden this became even more relevant... Trump2020
Dude already admitted to fraud, I dont know why tf anyone is talking about this. If it was one of us, we'd be locked up already. Its time to make the politicians who think they're above us, below us by 6ft. If the courts don't get justice then the people need to get justice on the injustices and executioners.
@@lukesutton4135 Yeah, what Thomas Jefferson said about the thirsty tree of liberty.
Read the description
@@lukesutton4135 read the description
If you want this to prove US election fraud, you also need to accept everything else mathematics can detect. Let's start with climate change and vaccines, and we can go from there ya stupid Trumpists.
Got to love your enthusiasm mate.
I wonder if there's a law that states that for any mathematical phenomenon that becomes popular, the probability of misuse of it exponentially increases with the increase of popularity. Because that seems to happen every time some mathematical object becomes popular.
I am DELIGHTED by these segments. Thank you! Thank you SingingBanana!
Here the Singing Banana describes why numbers have a much higher probability of beginning with 1 than (for instance) 7. I noticed it years ago in financial data.
Calvin, thanks for the tip! A great series of very interesting math stuff.
Can you please apply this to counties in WI, PA, MI and other contested states in the US?
Yes, here you go imgur.com/rR8WBt2
The numbers are from here election-county-reports-prod112020.s3.amazonaws.com/4539283c-3f09-4fdf-ad93-0bfd82d32be1/c64f9ade-9049-43ef-ab73-3feebc7ef5f0/Results%20per%20Precinct%20Data%20report.pdf
@@CocoXLarge Thanks!
@@JC-gb2en NP, I'm not a big fan of Trump but people need to hang for this.
@@CocoXLarge Thanks for having an open mind about things. Wish we had more people like that from both sides.
One side agreed to the idea that Trump had that mail-in votes were fraudulent, and so didn't vote as much by mail. The other side took the virus seriously, and so voted by mail more frequently. With these conditions, there would be a different result comparing the mail-in votes as opposed to the votes done in person.
Wow, love the explaination and your enthusiasm! You are a great facilitator of learning as I don't like the term teacher since it does not imply student responsibility for their learning.
Even this video... Singingbanana - 179 videos, 76534 subscribers, 117,756 views, 2213 likes, 14 dislikes... 10:46 long... published 2011... 542 comments - that's 4 out of 8 starting with 1 :o
Albert Renshaw ILLUMINATI !!!!!
1LLUM1NAT1