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
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/
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!"
When the TH-cam algorithm is feeling suicidal. It also recommended me 'America First with Seb Gorka' featuring Steve Bannon on massive election fraud. Thanks TH-cam
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.
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.
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.
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.
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.
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.
@@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.
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.
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.
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.
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)
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.
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.
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!
@@Uwrath 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.
@@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.
I believe this is the most intuitive explanation of how this works I have ever found on TH-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.
I would venture the guess that (2:45) indeed the results for "meters", "kilometers", and "centimeters" would be very similar when counting starting numbers.
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!
@@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.
Well TH-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.
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 🙏
@@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. 🙇
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.
@@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.
@@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
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
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.
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
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!"
@@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.
singingbanana Have you ever wondered what the world would be like if our everyday counting system wasn't base 10, but was something else such as base 12? 12 for example is so much more divisible than 10, which might make our lives practically different. The imperial measurement system perhaps tried to leverage this property but using different number bases to our natural counting perhaps created more problems than the benefit it provided.
Nick Hill Well alot of old tech is Base 2 , with more modern tech being base 8 i believe. Base 20 is the form of some ancient counting systems, and there are other examples of Base 16 (I think thats asia). The maths stays the same, and really it depends what your brought up with. Im at Uni atm, and i find Imperial counting stupidly confusing to the point i use a computer to calculate it - yet it would be a basic O-Level question in 1960. If you force the French to speak English their children eventually will (though they themselves maybe not), so itll be the same with number systems. If you learn it a certain way from birth, it becomes your Native Base (in the same way you have a native tongue) and it would sound simple to those children.
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/
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.
Would this work to check lottery fraud as the outcomes should be random? If it was being tampered with then we should see a pattern similar to Benford’s law.
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.
So, when you count from 1 up to anything, the digit 1 starts ahead before any of the other digits catch up. For example, after going from 1 to 9, all the digits are tied as far as leading digit, until you get into the tens range, where 1 gets to start ahead again while all the other digits need to catch up. Now, if you are to consider all the digits from 1 to a very large number, the range in which 1 has the lead before other numbers catch up to it gets bigger and bigger, by powers of ten. Additionally, if you start at any random number and start counting up then after passing some orders of magnitude, it will start showing the same advantage for the leading digit being 1. I think this is intuitive because regardless of what useable base you take this by, the first digit after the digit 0 will always be 1, and since we dont consider leading zeros here, its only natural that Benford's Law works with leading digits.
What is it about rivers that means their lengths are distributed this way? When can I expect something to follow this law? For example I might expect length of leaves or cells to follow a normal distribution. Why are there more shorter rivers so that the probability of having a river between 1 and 2 units length is the same as the probability of having a river between 10 and 20 units, rather than the same as the probability of a river between 10 and 11 units which I might expect if there was a uniform distribution? What other things can I expect to be distributed like this, and why does it work for numbers in a newspaper?
Does the fact that stores commonly charge $4,999 rather than $5,000 skew the results? Or that many stores charge $X.99 rather than $(X+1).00 skew the results?
Stores charge $999.99 instead of $1000 because it has a psychological effect on the customers. It makes customers think that it is a lot less and tempts the customer to buy the product.
The ratio seems to be about 1/10, so it's 10 %. It is presumed that Pi is a normal number, meaning that no digit, or combination of digits, occurs more frequently than any other. The proof for this has yet to be discovered. I was interested in this question myself, so I've just done a quick frequency distribution of Pi for the first 10.000 digits. Here is the result: 0: 968 1: 1026 2: 1021 3: 975 4: 1012 5: 1046 6: 1021 7: 969 8: 948 9: 1014
Gryphon1984 I did the same test for a million digits. Here are the results. 0: 99959 1: 99758 2: 100026 3: 100230 4: 100230 5: 100359 6: 99548 7: 99800 8: 99985 9: 100106 Yeah, pi is a "normal" number. I've once done a test for even more and they turn out even closer.
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.
Obviously here because of the election... liked and subscribed because you enjoy explaining maths, and I enjoy learning. Keep being awesome, regardless of your personal political beliefs.
Also, can we all admit the election needs further scrutiny until doubts by rational people are resolved fully and fairly? Every legal vote should count.
you make a whole video talking about how this mathematical law can detect fraud but change the description years later to counter act the video. Weak sauce dude.
Can you do an update video showing how Biden's law worked in closing that gap to end up with the blue more than the red? Seemed non probable to me.......
+Gustav Mårdby Interesting... There are 78 498 primes less than 1 million. A quick and perhaps not entirely accurate count finds that 8648 of these primes start with the number 1. This is slightly more than 11%, which is as near to 1/9 as you would care to go. However, I don't think it casts doubt on Benford's Law because the selection of primes is not what I would regard as observational data. I would argue that the selection of primes is "experimental" - the environment in which these numbers are selected is highly controlled and restricted to some quality of the numbers themselves. "Observational" data requires a mix of "real world" influences on the selection of the numbers in the data set in that the numbers themselves are not selected on the basis of some inherent quality. I COULD BE WRONG. The sample (primes
+JMan LOL! What did we do without the Web? I'm 54 and remember visiting Central Library in Manchester aged 13 to help with my homework. Anyhoo, I've done the same now and discovered disagreement among brains bigger than mine. For example, from phys.org/news/2009-05-pattern-prime.html I found: "Since the late ‘70s, researchers have known that prime numbers themselves, when taken in very large data sets, are not distributed according to Benford’s law. Instead, the first digit distribution of primes seems to be approximately uniform. However, as Luque and Lacasa point out, smaller data sets (intervals) of primes exhibit a clear bias in first digit distribution." So... Don't know, is the answer.
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.
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.
my intuitive 10s answer was. numbers from 100-200 cover a 50% range while nimbers from 300-400 cover a 25% range and so on. Its a pretty similar idea but much less elaborated. tank you for the detail!
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.
@@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
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.
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.
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.
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
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
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
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
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.
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!!!
@@MCSTINKYWEINER 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 TH-cam algorithm is feeling suicidal. It also recommended me 'America First with Seb Gorka' featuring Steve Bannon on massive election fraud. Thanks TH-cam
@@Sam-go3mb
Maybe some of them are good guys. I think we have little more freedom here.
Sam I BET you TH-cam is going to “fix” its algo soon.
Lucille yup, you’re def lost
Read the description
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.
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
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
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
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!
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.
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.
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
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.
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.
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.
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.
The TH-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.
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, TH-cam dramatically increased its meddling with the algorithm, so you've essentially just discovered fraud.
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
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.
That whipping away of the newspaper and loud "HELLO" startled me.
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.
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!
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.
@@Uwrath 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.
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
I believe this is the most intuitive explanation of how this works I have ever found on TH-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.
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
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
Now's probably a good time to tell everyone you aren't feeling suicidal and don't plan on disappearing anywhere.
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).
I wonder why this video could possibly be in my recommended.
Well TH-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.
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. 🙇
Fascinating! Thanks for sharing this James...
Indeed... very very interesting 🧐
we found a 9 year old comment wow
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
if it can be used to detect fraud, can't it be used to perpetrate fraud?
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.
so if an election doesn't follow bedfords law all of a sudden why do previous elections follow the law?
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
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.
lol. Funny I'm getting recommended this 9 year old clip now... good to see TH-cam's algorithm hasn't buried it yet
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.
this looks like zipfs law, but with numbers
#VSauce
Michael here
Or does it...?
_Vsauce music starts playing_
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
Does this apply if you use a different base? E.g. base 12, should it be log12(n+1)-log12(n) ?
+TheDaftySage Yes.
In base two/binary every number starts with a 1.
The formula would still work though: Log2(2) - Log2(1) = 1 - 0 = 1.
Except for 0.
"oh no math doesn't line up with my politics, better change the description" xDDDDDDd
My thoughts exactly:)
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
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!"
OK, my Lotto numbers are now 1, 10, 11,12,13,14,15. Where do I go to collect?
As stated in the video, it doesn't work with random numbers.
TH-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.
Time for this Video to EXPLODE!
If we change the number base from base 10 to say log 16, does the same formula apply but the log base needs to be changed?
Nick Hill Exactly.
singingbanana Have you ever wondered what the world would be like if our everyday counting system wasn't base 10, but was something else such as base 12? 12 for example is so much more divisible than 10, which might make our lives practically different. The imperial measurement system perhaps tried to leverage this property but using different number bases to our natural counting perhaps created more problems than the benefit it provided.
Nick Hill Yes, I've talked about it before Base 12 - Numberphile Although I'm sure others have done better videos.
singingbanana
I thought I was alone!
Nick Hill Well alot of old tech is Base 2 , with more modern tech being base 8 i believe. Base 20 is the form of some ancient counting systems, and there are other examples of Base 16 (I think thats asia).
The maths stays the same, and really it depends what your brought up with. Im at Uni atm, and i find Imperial counting stupidly confusing to the point i use a computer to calculate it - yet it would be a basic O-Level question in 1960.
If you force the French to speak English their children eventually will (though they themselves maybe not), so itll be the same with number systems. If you learn it a certain way from birth, it becomes your Native Base (in the same way you have a native tongue) and it would sound simple to those children.
Supreme Court: “what’s ur evidence Trump?”
Trump: “u seen this TH-cam vid?”
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/
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.
Would this work to check lottery fraud as the outcomes should be random? If it was being tampered with then we should see a pattern similar to Benford’s law.
Move along nothing to see here, video will soon be memory holed just like they changed the wiki article on this topic.
This was just recommended. Interesting timing!
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.
TH-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.
I'm amazed I don't see a "The Associated Press has called the election for Joe Biden" under this video
So, when you count from 1 up to anything, the digit 1 starts ahead before any of the other digits catch up. For example, after going from 1 to 9, all the digits are tied as far as leading digit, until you get into the tens range, where 1 gets to start ahead again while all the other digits need to catch up. Now, if you are to consider all the digits from 1 to a very large number, the range in which 1 has the lead before other numbers catch up to it gets bigger and bigger, by powers of ten. Additionally, if you start at any random number and start counting up then after passing some orders of magnitude, it will start showing the same advantage for the leading digit being 1. I think this is intuitive because regardless of what useable base you take this by, the first digit after the digit 0 will always be 1, and since we dont consider leading zeros here, its only natural that Benford's Law works with leading digits.
He seemed so happy explaining this while still leaving most just as confused 😂
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.
What is it about rivers that means their lengths are distributed this way? When can I expect something to follow this law? For example I might expect length of leaves or cells to follow a normal distribution. Why are there more shorter rivers so that the probability of having a river between 1 and 2 units length is the same as the probability of having a river between 10 and 20 units, rather than the same as the probability of a river between 10 and 11 units which I might expect if there was a uniform distribution? What other things can I expect to be distributed like this, and why does it work for numbers in a newspaper?
Does the fact that stores commonly charge $4,999 rather than $5,000 skew the results? Or that many stores charge $X.99 rather than $(X+1).00 skew the results?
It shouldn't, as these are still invariant under conversion to different currencies.
Stores charge $999.99 instead of $1000 because it has a psychological effect on the customers. It makes customers think that it is a lot less and tempts the customer to buy the product.
all active binary begins with a 1.
that's a lot of 1's to add to the list...
could these types of proofs/were these types of proofs ever used to audit financial frauds like the Madoff scandal?
2020 election results brought me here
how many times does the number 1 turn up in pi? the ratio i mean.
The ratio seems to be about 1/10, so it's 10 %. It is presumed that Pi is a normal number, meaning that no digit, or combination of digits, occurs more frequently than any other. The proof for this has yet to be discovered. I was interested in this question myself, so I've just done a quick frequency distribution of Pi for the first 10.000 digits. Here is the result:
0: 968
1: 1026
2: 1021
3: 975
4: 1012
5: 1046
6: 1021
7: 969
8: 948
9: 1014
Gryphon1984
I did the same test for a million digits. Here are the results.
0: 99959
1: 99758
2: 100026
3: 100230
4: 100230
5: 100359
6: 99548
7: 99800
8: 99985
9: 100106
Yeah, pi is a "normal" number. I've once done a test for even more and they turn out even closer.
I use binary. Can you tell me how to apply Benford's law to 0 and 1?
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
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.
Apparently no one reads the text in the description of this video and jumps to wild conclusions.
Whos here in 2020
Me
2020 election brought me here
and me
The Supreme Court need to watch this video now or America is done for.
Shocking that YT didn't put the "Election has been called by the AP" warning....yet.
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
Obviously here because of the election... liked and subscribed because you enjoy explaining maths, and I enjoy learning.
Keep being awesome, regardless of your personal political beliefs.
Also, can we all admit the election needs further scrutiny until doubts by rational people are resolved fully and fairly?
Every legal vote should count.
how often does the number "33" appear?
I suspect this video will be removed very soon.
you make a whole video talking about how this mathematical law can detect fraud but change the description years later to counter act the video. Weak sauce dude.
Either he's letting his own politics get in the way of rationality, or I wonder how much they paid him off.
@@FelixNothus The former. As a university graduate, I can tell you that's what universities are for. Rationality goes right out the window.
@@FelixNothus it’s probably because Dunning Kruger conservatives keep ignorantly misusing it when they have absolutely no understanding of it.
@2ManyLayersOfIrony ok chud
Can you do an update video showing how Biden's law worked in closing that gap to end up with the blue more than the red? Seemed non probable to me.......
Does the primes numbers follow benfords law?
+Gustav Mårdby
Interesting... There are 78 498 primes less than 1 million. A quick and perhaps not entirely accurate count finds that 8648 of these primes start with the number 1. This is slightly more than 11%, which is as near to 1/9 as you would care to go.
However, I don't think it casts doubt on Benford's Law because the selection of primes is not what I would regard as observational data. I would argue that the selection of primes is "experimental" - the environment in which these numbers are selected is highly controlled and restricted to some quality of the numbers themselves. "Observational" data requires a mix of "real world" influences on the selection of the numbers in the data set in that the numbers themselves are not selected on the basis of some inherent quality.
I COULD BE WRONG. The sample (primes
+JMan
Can you enlarge on this?
+JMan
LOL! What did we do without the Web? I'm 54 and remember visiting Central Library in Manchester aged 13 to help with my homework.
Anyhoo, I've done the same now and discovered disagreement among brains bigger than mine. For example, from phys.org/news/2009-05-pattern-prime.html I found:
"Since the late ‘70s, researchers have known that prime numbers themselves, when taken in very large data sets, are not distributed according to Benford’s law. Instead, the first digit distribution of primes seems to be approximately uniform. However, as Luque and Lacasa point out, smaller data sets (intervals) of primes exhibit a clear bias in first digit distribution."
So... Don't know, is the answer.
+Gustav Mårdby primes.utm.edu/notes/faq/BenfordsLaw.html
+Gustav Mårdby hmm, a connection with the Riemann hypothesis ?
How long before an explanation of Benford’s Law violates youtube’s terms of service? 😆
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)
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.
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!
my intuitive 10s answer was. numbers from 100-200 cover a 50% range while nimbers from 300-400 cover a 25% range and so on. Its a pretty similar idea but much less elaborated. tank you for the detail!
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
Nice change of the description lmao.
2011: Benford's law can be used to detect election fraud
One week after election: We changed our mind
Does this law apply to different base number systems or does base 10 have something to do with 1 occurring more frequently?
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.
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.
I had some difficulty following this logic. I wonder how the same principles apply to numbers expressed in binary, base-12, hexadecimal and base-60.
Here because 2020 elections