Benford\'s Law AGAIN...

[Fred Bloggs]

The Scientific American article is one of the better writeups. An otherwise useless result that can be used to detect accounting and election fraud.

\"The message is clear: organic processes generate numbers that favor small leading digits, whereas naive methods of falsifying data do not. \"

https://www.scientificamerican.com/article/what-is-benfords-law-why-this-unexpected-pattern-of-numbers-is-everywhere/

 

[John Larkin]

On Mon, 8 May 2023 10:34:15 -0700 (PDT), Fred Bloggs
<bloggs.fredbloggs.fred@gmail.com> wrote:

The Scientific American article is one of the better writeups. An otherwise useless result that can be used to detect accounting and election fraud.

\"The message is clear: organic processes generate numbers that favor small leading digits, whereas naive methods of falsifying data do not. \"

https://www.scientificamerican.com/article/what-is-benfords-law-why-this-unexpected-pattern-of-numbers-is-everywhere/

Citing \"This bizarre overrepresentation of 1s and 2s\" is crazy. Of
course there are more small clusters of things than big clusters.

How many cars do you own? How many kids do you have?

 

[RichD]

On May 8, John Larkin wrote:

The Scientific American article is one of the better writeups. An otherwise useless result that can be
used to detect accounting and election fraud.
\"The message is clear: organic processes generate numbers that favor small leading digits,
whereas naive methods of falsifying data do not. \"

https://www.scientificamerican.com/article/what-is-benfords-law-why-this-unexpected-pattern-of-numbers-is-everywhere/

Citing \"This bizarre overrepresentation of 1s and 2s\" is crazy. Of
course there are more small clusters of things than big clusters.

It\'s easily explained by the fact that things accumulate upward, not
downward. We count up from zero, not down from one million.

If data were generated by subtraction instead of addition, what
would be the analogous statistical result?

--
Rich

 

[Wandere]

He gives a probality distribution argument that he doesn\'t explain but the simplest explanation has to do with logarithms.

Here is the old trick for converting linear graph paper into log paper knowing:
3db is almost 2 (10log2 = 3.01...) and
The square root of 10 is almost Pi.
Multiplying by 2 is adding 3.
Dividing by 2 is subtracting 3.

Let see if my table gets screwed up
starting with 1,2,pi and 10 I can fill in the rest of the values.

lin log calc
0 1
1 1.25 10-9 is 10/8
2 pi/2 5-3 is pi/2
3 2
4 2.5 10-6 is 10/4
5 pi
6 4 3+3 is 2*2
7 5 10-3 is 10/2
8 2pi 5+3 is 2*pi
9 8 3+6 is 2*4
10 10

Quote the article \"An astonishing 30.1% begin with 1\" aka 100%*log2.
Resistor values follow this pattern.

 

[Fred Bloggs]

On Monday, May 8, 2023 at 4:15:41 PM UTC-4, RichD wrote:

On May 8, John Larkin wrote:
The Scientific American article is one of the better writeups. An otherwise useless result that can be
used to detect accounting and election fraud.
\"The message is clear: organic processes generate numbers that favor small leading digits,
whereas naive methods of falsifying data do not. \"

https://www.scientificamerican.com/article/what-is-benfords-law-why-this-unexpected-pattern-of-numbers-is-everywhere/

Citing \"This bizarre overrepresentation of 1s and 2s\" is crazy. Of
course there are more small clusters of things than big clusters.
It\'s easily explained by the fact that things accumulate upward, not
downward. We count up from zero, not down from one million.

That\'s not even close. The distribution is independent of scale of measurement, and numbers extracted from from varied, independent ( unrelated) datasets more closely approach the ideal Benford distribution.

If data were generated by subtraction instead of addition, what
would be the analogous statistical result?

It\'s a multiplicative distribution idempotence. And, no, I\'m not going to explain that to you.

--
Rich

 

[Fred Bloggs]

On Monday, May 8, 2023 at 3:28:21 PM UTC-4, John Larkin wrote:

On Mon, 8 May 2023 10:34:15 -0700 (PDT), Fred Bloggs
bloggs.fred...@gmail.com> wrote:

The Scientific American article is one of the better writeups. An otherwise useless result that can be used to detect accounting and election fraud..

\"The message is clear: organic processes generate numbers that favor small leading digits, whereas naive methods of falsifying data do not. \"

https://www.scientificamerican.com/article/what-is-benfords-law-why-this-unexpected-pattern-of-numbers-is-everywhere/
Citing \"This bizarre overrepresentation of 1s and 2s\" is crazy. Of
course there are more small clusters of things than big clusters.

How many cars do you own? How many kids do you have?

It\'s not about the size of anything. It\'s about the most significant digit of the size, or the multiplier of the highest power of 10 used in the representation of the size as a number. It\'s totally mysterious. And it does have a use.

 

[Fred Bloggs]

On Monday, May 8, 2023 at 4:30:07 PM UTC-4, Wanderer wrote:

He gives a probality distribution argument that he doesn\'t explain but the simplest explanation has to do with logarithms.

Here is the old trick for converting linear graph paper into log paper knowing:
3db is almost 2 (10log2 = 3.01...) and
The square root of 10 is almost Pi.
Multiplying by 2 is adding 3.
Dividing by 2 is subtracting 3.

Let see if my table gets screwed up
starting with 1,2,pi and 10 I can fill in the rest of the values.

lin log calc
0 1
1 1.25 10-9 is 10/8
2 pi/2 5-3 is pi/2
3 2
4 2.5 10-6 is 10/4
5 pi
6 4 3+3 is 2*2
7 5 10-3 is 10/2
8 2pi 5+3 is 2*pi
9 8 3+6 is 2*4
10 10

Quote the article \"An astonishing 30.1% begin with 1\" aka 100%*log2.
Resistor values follow this pattern.

Maybe it\'s me, but I don\'t see where that\'s going.

 

[Wandere]

Mon, 08 May 2023 13:47:39 -0700 (PDT), Fred Bloggs
>Maybe it\'s me, but I don\'t see where that\'s going.

When you look at the first digit of a number you are reducing the numbers
to scientific notation which tends to be logarithmic. Look at resistor values. You use about the same number of values between 1k and 10k as you use between 10k and 100k. You don\'t have 10 times more values between 10k and 100k as you do between 1k and 10k. Look at log paper 30% of the space falls between 1 and 2. 50% of the space falls between 1 and the square root of 10.

 

[Martin Brown]

On 08/05/2023 18:34, Fred Bloggs wrote:

The Scientific American article is one of the better writeups. An otherwise useless result that can be used to detect accounting and election fraud.

\"The message is clear: organic processes generate numbers that favor small leading digits, whereas naive methods of falsifying data do not.\"

https://www.scientificamerican.com/article/what-is-benfords-law-why-this-unexpected-pattern-of-numbers-is-everywhere/

It seems a bit unfair that it is called Benford\'s Law when poor old
Newcomb discovered it in 1881 by looking at wear and tear of log tables
at the Nautical Almanac computors was mostly in the early pages.

https://en.wikipedia.org/wiki/Simon_Newcomb#Benford\'s_law

Newcomb had priority on noticing this nearly 60 years earlier!

--
Martin Brown

 

[Fred Bloggs]

On Monday, May 8, 2023 at 5:14:33 PM UTC-4, Wanderer wrote:

Mon, 08 May 2023 13:47:39 -0700 (PDT), Fred Bloggs
Maybe it\'s me, but I don\'t see where that\'s going.
When you look at the first digit of a number you are reducing the numbers
to scientific notation which tends to be logarithmic. Look at resistor values. You use about the same number of values between 1k and 10k as you use between 10k and 100k. You don\'t have 10 times more values between 10k and 100k as you do between 1k and 10k. Look at log paper 30% of the space falls between 1 and 2. 50% of the space falls between 1 and the square root of 10.

You may be onto something with that approach. A Monte Carlo on that log scale should produce a Benford. That\'s the most sensible observation I\'ve seen yet about it.