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(The Study of Threes)
http://threesology.org
By studying genetics on an elementary level, we learn that there are three basic components of life sometimes referred to as the triad of the biosphere. These three are RNA (Ribose-Nucleic-Acid), which is predominantly single stranded; DNA (Deoxyribo-Nucleic-Acid), which is predominantly double stranded, and Proteins, which may have a (1) primary ~ (2) secondary ~ or (3) tertiary structure, with a quaternary form referring to a composite of these first three. Hence, for the present discussion, it is necessary that this arrangement be viewed as a 3 to 1 formula, where the "3" refers to RNA~ DNA~ and the simple 1-2-3 structured proteins, and the "1" refers to the quaternary form of proteins that arise from a composite of the first three.
(Other examples could be offered such as the notion of 3 spatial dimensions and 1 time dimension, and the idea of 3 basic "gaseous" elements of life (hydrogen- oxygen- nitrogen) and 1 "solid" form called carbon, which is sometimes referred to with the acronym CHON.)
The building blocks of proteins are called Amino acids. RNA has four amino acids known as Adenine, Cytosine, Guanine, and Uracil. DNA has the same amino acids with the exception of Thymine substituted for Uracil. Hence, I refer to this distinction as a 3 to 1 ratio, because there are 3 (the same) amino acids in both RNA & DNA, and 1 different amino acid.
A simple table may be of some value:
| RNA | DNA | 3 to 1 comparison |
| Adenine | Adenine | Three the Same |
| Cytosine | Cytosine | |
| Guanine | Guanine | |
| Uracil | Thymine | One is Different |
In humanity's early attempts to unravel the genetic code, it was determined that in order for us to account for the 20 amino acids used in the synthesis of most proteins, there would have to be a code that would, at its very minimal, contain at least 20. As can be seen in the following chart, a singlet code would only provide us with 4 amino acid "words," and a doublet code would only provide us with 16 "words." It is obvious that both of these code formulas fall short of the minimum requirement of 20, but that a triplet code satisfies this need quite easily by having a 64 "word vocabulary":
| Singlet code (4 "words")
|
Doublet code (16 "words")
|
Triplet code (64 "words")
|
| AAAAAGAACAAT | ||
| AGAAGGAGCAGT | ||
| ACAACGACCACT | ||
| ATAATGATCATT | ||
| GAAGAGGACGAT | ||
| GGAGGGGGCGGT | ||
| A | AAAGACAT | GCAGCGGCCGCT |
| G | GAGGGCGT | GTAGTGGTCGTT |
| C | CACGCCCT | CAACAGCACCAT |
| T | TATGTCTT | CGACGGCGCCGT |
| CCACCGCCCCCT | ||
| CTACTGCTCCTT | ||
| TAATAGTACTAT | ||
| TGATGGTGCTGT | ||
| TCATCGTCCTCT | ||
| TTATTGTTCTTT |
With the understanding that it takes three nucleotides to make up one "word" (called a codon), it is interesting to find that a sequence of codons (that we might refer to as a sentence), uses three "punctuation marks" called "stop codons," to end the sentence. There are 3 "stop" codons in RNA and 3 "stop" codons in DNA, along with 1 start codon for each, as is indicated in the following two tables. (We are thus presented with a 3 to 1 ratio formula that has cropped up in other areas:
http://www.threesology.org/321-a.php
Note that for each table, the left-hand column gives the first nucleotide of the codon, the 4 middle columns give the second nucleotide, and the last column gives the third nucleotide.
The RNA Codons:
| U | C | A | G | ||
| U | UUU Phenylalanine (Phe) | UCU Serine (Ser) | UAU Tyrosine (Tyr) | UGU Cysteine (Cys) | U |
| UUC Phe | UCC Ser | UAC Tyr | UGC Cys | C | |
| UUA Leucine (Leu) | UCA Ser | UAA STOP | UGA STOP | A | |
| UUG Leu | UCG Ser | UAG STOP | UGG Tryptophan (Trp) | G | |
| C | CUU Leucine (Leu) | CCU Proline (Pro) | CAU Histidine (His) | CGU Arginine (Arg) | U |
| CUC Leu | CCU Pro | CAC His | CGC Arg | C | |
| CUA Leu | CCA Pro | CAA Glutamine (Gln) | CGA Arg | A | |
| CUG Leu | CCG Pro | CAG Gln | CGG Arg | G | |
| A | AUU Isoleucine (Ile) | ACU Threonine (Thr) | AAU Asparagine (Asn) | AGU Serine (Ser) | U |
| AUC Ile | ACC Thr | AAC Asn | AGC Ser | C | |
| AUA Ile | ACA Thr | AAA Lysine (Lys) | AGA Arginine (Arg) | A | |
| AUG Methionine (Met) or START |
ACG Thr | AAG Lys | AGG Arg | G | |
| G | GUU Valine Val | GCU Alanine (Ala) | GAU Aspartic acid (Asp) | GGU Glycine (Gly) | U |
| GUC (Val) | GCC Ala | GAC Asp | GGC Gly | C | |
| GUA Val | GCA Ala | GAA Glutamic acid (Glu) | GGA Gly | A | |
| GUG Val | GCG Ala | GAG Glu | GGG Gly | G |
The Genetic Code (DNA):
These are the codons as they are read on the (5' to 3') strand of DNA. Except that the nucleotide thymidine (T) is found in place of uridine (U), they read the same as RNA codons. However, mRNA is actually synthesized using the (3' to 5') as the template.
(Some might refer to this table as the Rosetta Stone of life.)
| TTT | Phe | TCT | Ser | TAT | Tyr | TGT | Cys | |||
| TTC | Phe | TCC | Ser | TAC | Tyr | TGC | Cys | |||
| TTA | Leu | TCA | Ser | TAA | STOP | TGA | STOP | |||
| TTG | Leu | TCG | Ser | TAG | STOP | TGG | Trp | |||
| CTT | Leu | CCT | Pro | CAT | His | CGT | Arg | |||
| CTC | Leu | CCC | Pro | CAC | His | CGC | Arg | |||
| CTA | Leu | CCA | Pro | CAA | Gln | CGA | Arg | |||
| CTG | Leu | CCG | Pro | CAG | Gln | CGG | Arg | |||
| ATT | Ile | ACT | Thr | AAT | Asn | AGT | Ser | |||
| ATC | Ile | ACC | Thr | AAC | Asn | AGC | Ser | |||
| ATA | Ile | ACA | Thr | AAA | Lys | AGA | Arg | |||
| ATG | Met*** (START) | ACG | Thr | AAG | Lys | AGG | Arg | |||
| GTT | Val | GCT | Ala | GAT | Asp | GGT | Gly | |||
| GTC | Val | GCC | Ala | GAC | Asp | GGC | Gly | |||
| GTA | Val | GCA | Ala | GAA | Glu | GGA | Gly | |||
| GTG | Val | GCG | Ala | GAG | Glu | GGG | Gly | |||
| ***When within gene; at beginning of gene, ATG signals start of translation. | ||||||||||
The genetic code is almost universal. The same codons are assigned to the same amino acids and to the same START and STOP signals in the vast majority of genes in animals, plants, and microorganisms. However, some exceptions have been found. Most of these involve assigning one or two of the three STOP codons to an amino acid instead.
Mitochondrial genes: When mitochondrial mRNA from animals or microorganisms (but not from plants) is placed in a test tube with the cytosolic protein-synthesizing machinery (amino acids, enzymes, tRNAs, ribosomes) it fails to be translated into a protein. The reason for this is that these mitochondria use UGA to encode Tryptophan (Trp) rather than as a chain terminator. When translated by cytosolic machinery, synthesis stops where Trp should have been inserted.
In addition, most:
- Animal mitochondria use AUA for methionine not isoleucine and
- All vertebrate mitochondria use AGA and AGG as chain terminators.
- Yeast mitochondria assign all codons beginning with CU to threonine instead of leucine (which is still encoded by UUA and UUG as it is in cytosolic mRNA).
Plant mitochondria use the universal code, and this has permitted angiosperms to transfer mitochondrial genes to their nucleus with great ease.
The above table information and accompanying comments are adapted from:
http://www.ultranet.com/~jkimball/BiologyPages/C/Codons.html
As a correlation to the "64" representation in genetics, we find another occurrence in logic. Taken by itself, the presence of a "64" seems rather superficial and more in tune with a mystical excursion into numerology, but when we look at the underlying formula used to arrive at such, we identify a recurrence of a three-patterned structure (Major premise- Minor premise- Conclusion), that may have an underlying parallel to triplet coding pattern found in DNA, and triads found in Music. If such a case can be made, it must be ascertained whether or not this recurrence is due to an underlying pattern in the human brain that is exhibited by those humans who represent a particular type of brain development consistent with an evolutionary change.
Note: We can cite a 3 to 1 ratio of references to the "64":
1 of 3- 64 "word" vocabulary in genetics.
2 of 3- 64 "moods" in logic (to be mentioned below).
3 of 3- 64 "Trigrams" in I Ching Philosophy
1 of 1- "64 dollar question" (a recurring colloquial expression denoting an unanswered question.)
As with a four base triplet codon system, we can find another arrangement of this 4/3 formula in western (Indo-European) music, philosophy, and some out-dated ideas as well, such as the notion of a Triumvirate list of courses (Grammar, Rhetoric, Logic) coupled with a Quadrumvirate list of academic courses (Arithmetic, Music, Geometry, Astronomy) as was once practiced by Midieval Universities. What needs to be acknowledged is that the number 7 has a special significance as a symbolic reference to a sequential numerical placement, in that it is arrived at through addition of the two numbers 3 and 4, irrespective of what mythological, scientific, theological, metaphysical, etc., connotations are applied to these numbers as referential attributes with personal meaning.
Another example of the 3/4 model representation can be found in particle physics:
--- Standard Model of Particle Physics ---
http://www-sldnt.slac.stanford.edu/alr/standard_model.htm
|
While some readers may attribute each number as harboring some especial independent significance such as the number 3 represents the male form, the number 4 represents the female form, and the number 7 represents the union of the two, it is necessary to strip away such precontrived notions in order to perceive the possibility that the significance to the presence of the number 7 in and of itself, may represent nothing more than being the 3rd symbol in a sequence of three. In other words, it is not the individual numbers 3, 4, and 7 that have the greatest merit for further comparisons in other disciplines, but that these three numbers are but another example of a pattern-of-three sequence that is related to an underlying cognitive characteristic that is measurably different amongst the different human races, and is related to a developmental trend of human consciousness in response to changing environmental conditions. In other words, there are individuals in particular races who are experiencing (on an individualized level) more cognitive growth towards a three-patterned perspective than are other individuals in their own or other races. No less, it appears as if the 3rd born Indo-European race of peoples has a larger proportion of individuals experiencing this growth than are others in other races as is indicated by the overall usage of patterns-of-three in the race-respective cultures. The 3rd born race of humans (after Africans being 1st born and Asians being 2nd born according to some interpretations of the Out-of-Africa Hypothesis), gives us the impression that the 3rd born group is the baby of the human race, so to speak, and like any child, are more susceptible (and thereby adaptable) to environmental changes than are the "older" races, which can be viewed to be set in their ways in many respects of relying on traditions for many characteristics of survival. The repeated and intermittently growing usage of such a pattern over the centuries may refer to an environmentally-influenced genetically-predisposed evolutionary specific attribute that is transferred from one generation to the next in a few individuals whose physiology is maturing in a different direction than most. And that this maturational process is taking place more so with Indo-Europeans than with Asians or Africans, as is suggested by the obvious differences in quantity and quality of "threes" when comparing religious, socio-economic structures, philosophies, music, language, etc... We can substitute the numbers 1~ 2~ 3 with 32 + 42 = 52, or x- y- z, or a- b- c, or sounds, or colors, or gestures, or feelings, or dreams, or types of food, types of clothing, etc..., but the underlying pattern-of-three recurs again and again. |
A categorical syllogism infers a conclusion from two premises. (Major premise ~ Minor premise ~ Conclusion). It is defined by the following four attributes. Each of the three propositions is an A, E, I, or O proposition:
| Major premise | Minor premise | Conclusion | |
| A | |||
| E | |||
| I | |||
| O | |||
The subject of the conclusion (called the minor term) also occurs in one of the premises (the minor premise). The predicate of the conclusion (called the major term) also occurs in the other premise (the major premise). The two remaining term positions in the premises are filled by the same term (the middle term). Since each of the three propositions in a syllogism can take one of four combinations of quality and quantity, the categorical syllogism may exhibit any of 64 moods. (43) | |||
Each mood may occur in any of four figures---patterns of terms within the propositions--- thus yielding 256 possible forms. One of the important tasks of syllogistic logic has been to reduce this plurality to just the valid forms.
Aristotle recognized these 19 valid forms, (seen here in their medieval mnemonic names) while others recognized 5 others called subalternate moods:
First figure:
Barbara, Celarent, Darii, Ferio
Subalternates: Barbari, Celaront
Second figure:
Cesare, Camestres, Festino, Baroco
Subalternates: Cesaro, Camestrop
Third figure:
Darapti, Disamis, Datisi, Felapton, Bocardo, Ferison
Fourth figure:
Bramantip, Camenes, Dimaris, Fesapo, Fresison
Subalternate: Camenop
Let us now briefly compare the above philosophical truth formula to a truth formula that can be generated from genetics by substituting the word "true" for "yes" and the word "false" for "no":
| RNA | DNA | Proteins | |
| Adenine | Yes (true) | Yes (true) | Yes (true) |
| Cytosine | Yes (true) | Yes (true) | Yes (true) |
| Guanine | Yes (true) | Yes (true) | Yes (true) |
| Thymine or Uracil |
False (Thymine) True (Uracil) |
True (Thymine) False (Uracil) |
True |
Major/Minor Triadic Harmony:
The structure of all music can ultimately be traced back to the overtone series and its mirror undertone series. It is the great principle of the many contained within the one. This series is not only the basis of musical tones; it is also to be seen in the structure of plants, crystals and the periodic table of chemical elements. As the materials of music are increasingly reduced in the future, the major and minor triad, as the fundamental progeny of the series and its mirror image, will become the primal harmonic forces in NCM (New Consciousness Music). This phenomenon has been an important part of the NCM of Philip Glass. Beyond this a single tone would evolve so richly and profoundly produced that it could be experienced as a melody.
http://www.planettree.org/2000/caqumus.html
Links that may be of interest:
http://www.tortuga.com/science/dna/5.html
--- Basic Circuits for Computing ---
http://turing.cs.camosun.bc.ca/comp112/notes/chapter4.html
Herb O. Buckland
herbobuckland@hotmail.com