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| Fig. 1 Benford's Law Applied To Human Chromsomal DNA |
I have a hypothesis that Benford's Law reveals a type of containment entity (On The Origin of The Containment Entity - 10).
Like the ubiquitous yet unseen gravity that shapes planets and galaxies, there are unseen containment entity forces at work having some degree of widespread impact on the universe.
The entire realm of biology is impacted by the concept of containment entities in the sense of "morphology", which is a branch of biology that is not at all as straight forward as many would have it (Disparities in the analysis of morphological disparity).
As an example for argument's sake, notice the graph at Fig. 1 and the data associated with it at Fig. 2 and Fig. 3.
The graph depicts how close to alignment with Benford's Law the locations of codons are within human chromosomal DNA.
| First Digit | 1st Digit Count | 1st Digit Percent | Benford Percent | Difference |
| 1 | 632,812 | 32.15 | 30.10 | 2.05 |
| 2 | 296,393 | 15.06 | 17.60 | 2.54 |
| 3 | 225,648 | 11.46 | 12.50 | 1.04 |
| 4 | 189,417 | 9.62 | 9.70 | 0.08 |
| 5 | 162,860 | 8.27 | 7.90 | 0.37 |
| 6 | 146,807 | 7.46 | 6.70 | 0.76 |
| 7 | 118,476 | 6.02 | 5.80 | 0.22 |
| 8 | 104,731 | 5.32 | 5.10 | 0.22 |
| 9 | 91,272 | 4.64 | 4.60 | 0.04 |
The data from which Fig. 1 and Fig. 2 were generated is listed below in Fig. 3
The "version" portion of the detail is a link to the Genetic data in a government database where the chromosomal DNA can be viewed (use the FASTA option to view the large genome).
Fig. 3
Codon = 'AAA'
Codon = 'GCT'
version: CM000671.2, DNA source: Homo sapiens chromosome 9
version: CM000665.2, DNA source: Homo sapiens chromosome 3
version: CM000666.2, DNA source: Homo sapiens chromosome 4
version: CM000682.2, DNA source: Homo sapiens chromosome 20
version: CM000678.2, DNA source: Homo sapiens chromosome 16
version: CM000679.2, DNA source: Homo sapiens chromosome 17
version: CM000683.2, DNA source: Homo sapiens chromosome 21Codon = 'AAC'
version: CM000677.2, DNA source: Homo sapiens chromosome 15
version: CM000676.2, DNA source: Homo sapiens chromosome 14
version: CM000675.2, DNA source: Homo sapiens chromosome 13
version: CM000681.2, DNA source: Homo sapiens chromosome 19
version: CM000683.2, DNA source: Homo sapiens chromosome 21Codon = 'AAG'
version: CM000667.2, DNA source: Homo sapiens chromosome 5
version: CM000674.2, DNA source: Homo sapiens chromosome 12
version: CM000684.2, DNA source: Homo sapiens chromosome 22
version: CM000676.2, DNA source: Homo sapiens chromosome 14
version: CM000663.2, DNA source: Homo sapiens chromosome 1
version: CM000678.2, DNA source: Homo sapiens chromosome 16
version: CM000668.2, DNA source: Homo sapiens chromosome 6
version: CM000675.2, DNA source: Homo sapiens chromosome 13
version: CM000669.2, DNA source: Homo sapiens chromosome 7Codon = 'AAT'
version: CM000680.2, DNA source: Homo sapiens chromosome 18
version: CM000666.2, DNA source: Homo sapiens chromosome 4
version: CM000672.2, DNA source: Homo sapiens chromosome 10
version: CM000674.2, DNA source: Homo sapiens chromosome 12
version: CM000682.2, DNA source: Homo sapiens chromosome 20
version: CM000663.2, DNA source: Homo sapiens chromosome 1
version: CM000678.2, DNA source: Homo sapiens chromosome 16
version: CM000668.2, DNA source: Homo sapiens chromosome 6
version: CM000679.2, DNA source: Homo sapiens chromosome 17
version: CM000675.2, DNA source: Homo sapiens chromosome 13
version: CM000681.2, DNA source: Homo sapiens chromosome 19
version: CM000669.2, DNA source: Homo sapiens chromosome 7Codon = 'ACA'
version: CM000667.2, DNA source: Homo sapiens chromosome 5
version: CM000670.2, DNA source: Homo sapiens chromosome 8
version: CM000663.2, DNA source: Homo sapiens chromosome 1
version: CM000679.2, DNA source: Homo sapiens chromosome 17Codon = 'ACC'
version: CM000667.2, DNA source: Homo sapiens chromosome 5
version: CM000666.2, DNA source: Homo sapiens chromosome 4
version: CM000676.2, DNA source: Homo sapiens chromosome 14
version: CM000668.2, DNA source: Homo sapiens chromosome 6
version: CM000679.2, DNA source: Homo sapiens chromosome 17
version: CM000681.2, DNA source: Homo sapiens chromosome 19Codon = 'ACG'
version: CM000666.2, DNA source: Homo sapiens chromosome 4
version: CM000678.2, DNA source: Homo sapiens chromosome 16
version: CM000681.2, DNA source: Homo sapiens chromosome 19Codon = 'ACT'
version: CM000667.2, DNA source: Homo sapiens chromosome 5
version: CM000672.2, DNA source: Homo sapiens chromosome 10
version: CM000674.2, DNA source: Homo sapiens chromosome 12
version: CM000676.2, DNA source: Homo sapiens chromosome 14
version: CM000679.2, DNA source: Homo sapiens chromosome 17
version: CM000669.2, DNA source: Homo sapiens chromosome 7Codon = 'AGA'
version: CM000682.2, DNA source: Homo sapiens chromosome 20
version: CM000684.2, DNA source: Homo sapiens chromosome 22Codon = 'AGC'
version: CM000664.2, DNA source: Homo sapiens chromosome 2Codon = 'AGG'
version: CM000672.2, DNA source: Homo sapiens chromosome 10
version: CM000682.2, DNA source: Homo sapiens chromosome 20
version: CM000668.2, DNA source: Homo sapiens chromosome 6Codon = 'AGT'
version: CM000671.2, DNA source: Homo sapiens chromosome 9
version: CM000670.2, DNA source: Homo sapiens chromosome 8
version: CM000673.2, DNA source: Homo sapiens chromosome 11
version: CM000674.2, DNA source: Homo sapiens chromosome 12
version: CM000663.2, DNA source: Homo sapiens chromosome 1Codon = 'ATA'
version: CM000680.2, DNA source: Homo sapiens chromosome 18
version: CM000671.2, DNA source: Homo sapiens chromosome 9
version: CM000665.2, DNA source: Homo sapiens chromosome 3
version: CM000670.2, DNA source: Homo sapiens chromosome 8
version: CM000672.2, DNA source: Homo sapiens chromosome 10
version: CM000674.2, DNA source: Homo sapiens chromosome 12
version: CM000678.2, DNA source: Homo sapiens chromosome 16
version: CM000669.2, DNA source: Homo sapiens chromosome 7
version: CM000664.2, DNA source: Homo sapiens chromosome 2
version: CM000683.2, DNA source: Homo sapiens chromosome 21Codon = 'ATC'
version: CM000667.2, DNA source: Homo sapiens chromosome 5
version: CM000673.2, DNA source: Homo sapiens chromosome 11
version: CM000677.2, DNA source: Homo sapiens chromosome 15
version: CM000684.2, DNA source: Homo sapiens chromosome 22
version: CM000676.2, DNA source: Homo sapiens chromosome 14
version: CM000663.2, DNA source: Homo sapiens chromosome 1
version: CM000668.2, DNA source: Homo sapiens chromosome 6
version: CM000675.2, DNA source: Homo sapiens chromosome 13
version: CM000669.2, DNA source: Homo sapiens chromosome 7
version: CM000683.2, DNA source: Homo sapiens chromosome 21Codon = 'ATG'
version: CM000665.2, DNA source: Homo sapiens chromosome 3
version: CM000670.2, DNA source: Homo sapiens chromosome 8
version: CM000673.2, DNA source: Homo sapiens chromosome 11
version: CM000678.2, DNA source: Homo sapiens chromosome 16
version: CM000668.2, DNA source: Homo sapiens chromosome 6
version: CM000669.2, DNA source: Homo sapiens chromosome 7
version: CM000664.2, DNA source: Homo sapiens chromosome 2Codon = 'ATT'
version: CM000667.2, DNA source: Homo sapiens chromosome 5
version: CM000665.2, DNA source: Homo sapiens chromosome 3
version: CM000670.2, DNA source: Homo sapiens chromosome 8
version: CM000666.2, DNA source: Homo sapiens chromosome 4
version: CM000682.2, DNA source: Homo sapiens chromosome 20
version: CM000677.2, DNA source: Homo sapiens chromosome 15
version: CM000684.2, DNA source: Homo sapiens chromosome 22
version: CM000663.2, DNA source: Homo sapiens chromosome 1
version: CM000679.2, DNA source: Homo sapiens chromosome 17
version: CM000669.2, DNA source: Homo sapiens chromosome 7
version: CM000664.2, DNA source: Homo sapiens chromosome 2Codon = 'CAA'
version: CM000671.2, DNA source: Homo sapiens chromosome 9
version: CM000672.2, DNA source: Homo sapiens chromosome 10
version: CM000663.2, DNA source: Homo sapiens chromosome 1
version: CM000678.2, DNA source: Homo sapiens chromosome 16Codon = 'CAC'
version: CM000673.2, DNA source: Homo sapiens chromosome 11
version: CM000672.2, DNA source: Homo sapiens chromosome 10
version: CM000668.2, DNA source: Homo sapiens chromosome 6
version: CM000664.2, DNA source: Homo sapiens chromosome 2Codon = 'CAG'
version: CM000670.2, DNA source: Homo sapiens chromosome 8
version: CM000674.2, DNA source: Homo sapiens chromosome 12
version: CM000682.2, DNA source: Homo sapiens chromosome 20
version: CM000677.2, DNA source: Homo sapiens chromosome 15
version: CM000676.2, DNA source: Homo sapiens chromosome 14
version: CM000663.2, DNA source: Homo sapiens chromosome 1
version: CM000668.2, DNA source: Homo sapiens chromosome 6
version: CM000675.2, DNA source: Homo sapiens chromosome 13
version: CM000683.2, DNA source: Homo sapiens chromosome 21Codon = 'CAT'
version: CM000680.2, DNA source: Homo sapiens chromosome 18
version: CM000673.2, DNA source: Homo sapiens chromosome 11
version: CM000666.2, DNA source: Homo sapiens chromosome 4Codon = 'CCA'
version: CM000684.2, DNA source: Homo sapiens chromosome 22
version: CM000675.2, DNA source: Homo sapiens chromosome 13
version: CM000681.2, DNA source: Homo sapiens chromosome 19Codon = 'CCC'
version: CM000666.2, DNA source: Homo sapiens chromosome 4Codon = 'CCT'
version: CM000676.2, DNA source: Homo sapiens chromosome 14Codon = 'CTA'
version: CM000665.2, DNA source: Homo sapiens chromosome 3
version: CM000677.2, DNA source: Homo sapiens chromosome 15
version: CM000676.2, DNA source: Homo sapiens chromosome 14
version: CM000668.2, DNA source: Homo sapiens chromosome 6
version: CM000675.2, DNA source: Homo sapiens chromosome 13Codon = 'CTC'
version: CM000667.2, DNA source: Homo sapiens chromosome 5
version: CM000680.2, DNA source: Homo sapiens chromosome 18
version: CM000671.2, DNA source: Homo sapiens chromosome 9Codon = 'CTG'
version: CM000667.2, DNA source: Homo sapiens chromosome 5
version: CM000674.2, DNA source: Homo sapiens chromosome 12Codon = 'CTT'
version: CM000665.2, DNA source: Homo sapiens chromosome 3
version: CM000670.2, DNA source: Homo sapiens chromosome 8
version: CM000674.2, DNA source: Homo sapiens chromosome 12
version: CM000684.2, DNA source: Homo sapiens chromosome 22
version: CM000683.2, DNA source: Homo sapiens chromosome 21Codon = 'GAA'
version: CM000667.2, DNA source: Homo sapiens chromosome 5
version: CM000670.2, DNA source: Homo sapiens chromosome 8
version: CM000672.2, DNA source: Homo sapiens chromosome 10
version: CM000674.2, DNA source: Homo sapiens chromosome 12
version: CM000677.2, DNA source: Homo sapiens chromosome 15
version: CM000676.2, DNA source: Homo sapiens chromosome 14Codon = 'GAC'
version: CM000665.2, DNA source: Homo sapiens chromosome 3
version: CM000677.2, DNA source: Homo sapiens chromosome 15
version: CM000668.2, DNA source: Homo sapiens chromosome 6Codon = 'GAG'
version: CM000670.2, DNA source: Homo sapiens chromosome 8
version: CM000674.2, DNA source: Homo sapiens chromosome 12
version: CM000675.2, DNA source: Homo sapiens chromosome 13
version: CM000669.2, DNA source: Homo sapiens chromosome 7Codon = 'GAT'
version: CM000667.2, DNA source: Homo sapiens chromosome 5
version: CM000680.2, DNA source: Homo sapiens chromosome 18
version: CM000672.2, DNA source: Homo sapiens chromosome 10
version: CM000682.2, DNA source: Homo sapiens chromosome 20
version: CM000663.2, DNA source: Homo sapiens chromosome 1
version: CM000669.2, DNA source: Homo sapiens chromosome 7Codon = 'GCA'
version: CM000680.2, DNA source: Homo sapiens chromosome 18
version: CM000664.2, DNA source: Homo sapiens chromosome 2Codon = 'GCC'
version: CM000667.2, DNA source: Homo sapiens chromosome 5
version: CM000682.2, DNA source: Homo sapiens chromosome 20
version: CM000663.2, DNA source: Homo sapiens chromosome 1Codon = 'GCG'
Codon = 'GCT'
version: CM000664.2, DNA source: Homo sapiens chromosome 2Codon = 'GGA'
version: CM000665.2, DNA source: Homo sapiens chromosome 3
version: CM000673.2, DNA source: Homo sapiens chromosome 11
version: CM000663.2, DNA source: Homo sapiens chromosome 1
version: CM000678.2, DNA source: Homo sapiens chromosome 16
version: CM000668.2, DNA source: Homo sapiens chromosome 6
version: CM000679.2, DNA source: Homo sapiens chromosome 17Codon = 'GGC'
version: CM000666.2, DNA source: Homo sapiens chromosome 4
version: CM000675.2, DNA source: Homo sapiens chromosome 13Codon = 'GGG'
version: CM000669.2, DNA source: Homo sapiens chromosome 7Codon = 'GGT'
version: CM000673.2, DNA source: Homo sapiens chromosome 11Codon = 'GTA'
version: CM000670.2, DNA source: Homo sapiens chromosome 8
version: CM000666.2, DNA source: Homo sapiens chromosome 4
version: CM000672.2, DNA source: Homo sapiens chromosome 10
version: CM000676.2, DNA source: Homo sapiens chromosome 14
version: CM000681.2, DNA source: Homo sapiens chromosome 19Codon = 'GTG'
version: CM000674.2, DNA source: Homo sapiens chromosome 12
version: CM000682.2, DNA source: Homo sapiens chromosome 20
version: CM000684.2, DNA source: Homo sapiens chromosome 22
version: CM000681.2, DNA source: Homo sapiens chromosome 19
version: CM000683.2, DNA source: Homo sapiens chromosome 21Codon = 'GTT'
version: CM000665.2, DNA source: Homo sapiens chromosome 3
version: CM000682.2, DNA source: Homo sapiens chromosome 20Codon = 'TAA'
version: CM000673.2, DNA source: Homo sapiens chromosome 11
version: CM000666.2, DNA source: Homo sapiens chromosome 4
version: CM000677.2, DNA source: Homo sapiens chromosome 15
version: CM000676.2, DNA source: Homo sapiens chromosome 14
version: CM000663.2, DNA source: Homo sapiens chromosome 1
version: CM000679.2, DNA source: Homo sapiens chromosome 17
version: CM000675.2, DNA source: Homo sapiens chromosome 13Codon = 'TAC'
version: CM000671.2, DNA source: Homo sapiens chromosome 9
version: CM000674.2, DNA source: Homo sapiens chromosome 12
version: CM000663.2, DNA source: Homo sapiens chromosome 1
version: CM000679.2, DNA source: Homo sapiens chromosome 17
version: CM000681.2, DNA source: Homo sapiens chromosome 19Codon = 'TAG'
version: CM000673.2, DNA source: Homo sapiens chromosome 11
version: CM000668.2, DNA source: Homo sapiens chromosome 6
version: CM000681.2, DNA source: Homo sapiens chromosome 19Codon = 'TAT'
version: CM000667.2, DNA source: Homo sapiens chromosome 5
version: CM000680.2, DNA source: Homo sapiens chromosome 18
version: CM000673.2, DNA source: Homo sapiens chromosome 11
version: CM000666.2, DNA source: Homo sapiens chromosome 4
version: CM000674.2, DNA source: Homo sapiens chromosome 12
version: CM000676.2, DNA source: Homo sapiens chromosome 14
version: CM000678.2, DNA source: Homo sapiens chromosome 16
version: CM000668.2, DNA source: Homo sapiens chromosome 6
version: CM000681.2, DNA source: Homo sapiens chromosome 19
version: CM000669.2, DNA source: Homo sapiens chromosome 7Codon = 'TCA'
version: CM000667.2, DNA source: Homo sapiens chromosome 5
version: CM000670.2, DNA source: Homo sapiens chromosome 8
version: CM000666.2, DNA source: Homo sapiens chromosome 4
version: CM000682.2, DNA source: Homo sapiens chromosome 20
version: CM000684.2, DNA source: Homo sapiens chromosome 22
version: CM000676.2, DNA source: Homo sapiens chromosome 14
version: CM000675.2, DNA source: Homo sapiens chromosome 13
version: CM000664.2, DNA source: Homo sapiens chromosome 2
version: CM000683.2, DNA source: Homo sapiens chromosome 21Codon = 'TCC'
version: CM000679.2, DNA source: Homo sapiens chromosome 17Codon = 'TCT'
version: CM000680.2, DNA source: Homo sapiens chromosome 18
version: CM000665.2, DNA source: Homo sapiens chromosome 3
version: CM000672.2, DNA source: Homo sapiens chromosome 10
version: CM000674.2, DNA source: Homo sapiens chromosome 12
version: CM000668.2, DNA source: Homo sapiens chromosome 6
version: CM000669.2, DNA source: Homo sapiens chromosome 7
version: CM000664.2, DNA source: Homo sapiens chromosome 2Codon = 'TGA'
version: CM000680.2, DNA source: Homo sapiens chromosome 18
version: CM000671.2, DNA source: Homo sapiens chromosome 9
version: CM000670.2, DNA source: Homo sapiens chromosome 8
version: CM000673.2, DNA source: Homo sapiens chromosome 11
version: CM000677.2, DNA source: Homo sapiens chromosome 15
version: CM000669.2, DNA source: Homo sapiens chromosome 7
version: CM000683.2, DNA source: Homo sapiens chromosome 21Codon = 'TGC'
version: CM000684.2, DNA source: Homo sapiens chromosome 22
version: CM000664.2, DNA source: Homo sapiens chromosome 2Codon = 'TGG'
version: CM000681.2, DNA source: Homo sapiens chromosome 19Codon = 'TGT'
version: CM000671.2, DNA source: Homo sapiens chromosome 9
version: CM000682.2, DNA source: Homo sapiens chromosome 20
version: CM000664.2, DNA source: Homo sapiens chromosome 2Codon = 'TTA'
version: CM000680.2, DNA source: Homo sapiens chromosome 18
version: CM000671.2, DNA source: Homo sapiens chromosome 9
version: CM000665.2, DNA source: Homo sapiens chromosome 3
version: CM000673.2, DNA source: Homo sapiens chromosome 11
version: CM000666.2, DNA source: Homo sapiens chromosome 4
version: CM000672.2, DNA source: Homo sapiens chromosome 10
version: CM000663.2, DNA source: Homo sapiens chromosome 1
version: CM000679.2, DNA source: Homo sapiens chromosome 17
version: CM000664.2, DNA source: Homo sapiens chromosome 2Codon = 'TTC'
version: CM000673.2, DNA source: Homo sapiens chromosome 11
version: CM000679.2, DNA source: Homo sapiens chromosome 17
version: CM000681.2, DNA source: Homo sapiens chromosome 19Codon = 'TTG'
version: CM000671.2, DNA source: Homo sapiens chromosome 9
version: CM000665.2, DNA source: Homo sapiens chromosome 3
version: CM000673.2, DNA source: Homo sapiens chromosome 11
version: CM000674.2, DNA source: Homo sapiens chromosome 12
version: CM000684.2, DNA source: Homo sapiens chromosome 22
version: CM000663.2, DNA source: Homo sapiens chromosome 1
version: CM000664.2, DNA source: Homo sapiens chromosome 2Codon = 'TTT'
version: CM000680.2, DNA source: Homo sapiens chromosome 18
version: CM000671.2, DNA source: Homo sapiens chromosome 9
version: CM000670.2, DNA source: Homo sapiens chromosome 8
version: CM000666.2, DNA source: Homo sapiens chromosome 4
version: CM000672.2, DNA source: Homo sapiens chromosome 10
version: CM000682.2, DNA source: Homo sapiens chromosome 20
version: CM000678.2, DNA source: Homo sapiens chromosome 16
version: CM000668.2, DNA source: Homo sapiens chromosome 6
version: CM000683.2, DNA source: Homo sapiens chromosome 21
You may recall that there hasn’t yet been a complete answer to the question of why Benford's Law "works":
"The law is hard to prove mathematically, as it’s more akin to a theory that works (sort of like the multiplication rule). Many attempts have been made to explain the phenomenon, ranging from Benford’s initial thoughts about the logarithmic nature of data to Hill’s probability framework which used mixtures from different probability distributions to partially explain it. At the time of writing, there hasn’t yet been a complete answer to the question of why it works.
But work it does — kind of. Diaconis and Freedman (1979) suggest
Benford was rather liberal with how he rounded off numbers, to make the
data better fit the equation."
(Statistics, emphasis in original). Why human chromosomal DNA codon locations would follow the Benford's Law pattern is just another thing to ponder when hypothetically discussing containment entities.
Have fun.
The next post in this series is here, the previous post in this series is here.
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