page 2
(The Study of Threes)
http://threesology.org
| p | q | ~p | p . q | p v q | p + q | p É q | p º q |
| a statement | a statement | not p denial | p and q conjunction | p or q (inclusive)inclusive disjunction | p or q (exclusive)exclusive disjunction | if p then q conditional | p if and only if q biconditional |
| T | T | F | T | T | F | T | T |
| T | F | F | T | T | F | F | |
| F | T | T | F | T | T | T | F |
| F | F | F | F | F | F | T |
| Truth Table for One simple statement |
| A |
| True |
| False |
| Truth Table for Two simple statements | |
| P | Q |
| True | True |
| True | False |
| False | True |
| False | False |
| Truth Table for Three simple statements | ||
| P | Q | R |
| True | True | True |
| True | True | False |
| True | False | T |
| True | False | False |
| False | True | True |
| False | T | False |
| False | False | True |
| False | False | False |
| Truth Table for Conjunctions | ||
| 1st Conjunction | 2nd Conjunction | Statement |
| A | B | A and B |
| True | True | True |
| True | False | False |
| False | True | False |
| False | False | False |
| Truth Table for Disjunctions | ||
| 1st Disjunction | 2nd Disjunction | Statement |
| A | B | A or B |
| True | True | True |
| True | False | True |
| False | True | True |
| False | False | False |
| Truth Table for Conditionals | ||
| Antecedent | Consequent | Statement |
| A | B | A > B |
| True | True | True |
| True | False | False |
| False | True | True |
| False | False | True |
Above truth tables from:
http://www.kcmetro.cc.mo.us/longview/ctac/ttable.htm
In the most general terms a computer is a device that calculates a result ("output") from one or more initial items of information ("input"). Inputs and outputs are usually represented in (two-patterned) binary terms---i.e., in strings of 0s and 1s--- and the values of 0 and 1 are realized in the machine by the presence or absence of a current (of electricity, or water, or light, etc.,). When the output is a completely determined function of the input, the connection between a computer and the two-valued logic of propositions is immediate, for a valid argument can be constructed as a partial function of the truth values of the premises such that when the premises each have the value true, so does the conclusion.
One of the simplest computers has one input, either 0 or 1 (i.e., a current of some type that is either off or on), and one output, namely, the reverse of the input. That is, when 0 is input, 1 is output, and, conversely, when 1 is input, 0 is output. This is also the behavior of the truth function negation (~p) when applied to the truth values true and false. Thus a circuit element that behaves in such a way is called a NOT gate. When no current is input from the left, a current flows out on the right, and, conversely, when a current flows in from the left, none is output to the right:
| The NOT operation truth table: | |
| A | !A |
| True | False |
| False | True |
http://mathworld.wolfram.com/NOT.html
Similarly, devices with two inputs and one out put correspond in behavior to the truth functions conjunction (p · q) and disjunction (p V q). Specifically, in an AND gate, current flows out to the right only when current is present in both inputs; otherwise there is no output:
| The binary AND operator truth table: | ||
| A | B | A Ù B |
| True | True | True |
| True | False | False |
| False | True | False |
| False | False | False |
http://mathworld.wolfram.com/AND.html
In an OR gate, current is output when a current is present in either or both of the inputs are on the left:
| The binary OR operator truth table: | ||
| A | B | A Ú B |
| True | True | True |
| True | False | True |
| False | True | True |
| False | False | False |
http://mathworld.wolfram.com/OR.html
Other truth functional connectives are easily constructed using combinations of these gates. In other words, just as we find in the construction of proteins, a larger more complex formula can be designed by using the first three primary types. For example, the conditional, p É q is represented by the symbol in the following image. There is no output if there is input from p ("p" is true) and none from q ("q" is false):
Let us look at some other forms of combinations such as...
The NAND-gate:
| The binary NAND operator truth table: | ||
| A | B |  |
| True | True | False |
| True | False | True |
| False | True | True |
| False | False | True |
http://mathworld.wolfram.com/NAND.html
The XOR-gate:
| The binary XOR operator has the following truth table: | ||
| A | B |  |
| True | True | False> |
| True | False | True |
| False | True | True |
| False | False | False |
http://mathworld.wolfram.com/XOR.html
The XNOR-gate:
| The XNOR "two argument" truth table: | ||
| A | B | A XNOR B |
| True | True | True |
| True | False | False |
| False | True | False |
| False | False | True |
http://mathworld.wolfram.com/XNOR.html
*** Mendelian inheritance is usually described as the process by which one of two alternate alleles of a gene is inherited from each parent so that the offspring has one of the following combinations: two dominant alleles, two recessive alleles, or one of each. If both parents are heterozygous, that is, have one of each allele, the three genotypes will occur among the offspring with the following probabilities: one homozygous dominant, two heterozygotes, and one homozygous recessive. Phenotypically the two heterozygotes will be indistinguishable from the homozygous dominant. This results in the famous 3:1 ratio. (James C. King, The Biology of Race, 1981, page 28)
In music: we have a "2" with respect to minor/major; a "3" with respect to the triadic structure; a "4" with respect to major/minor~ diminished/augmented. (a "7" value is garnered from a combination.)
In genetics: (RNA/DNA) or Purines= {2 fused rings: Adenine, Guanine} or Pyrimidines= {1 ring: Cytosine, Thymine} 4 varieties of nitrogenous bases: adenine, guanine, thymine, cytosine. (A "7" value is garnered from a combination.)
In addition, for the simple sake of inclusion:
Adenine + Thymine = 2 hydrogen bonds
Guanine + Cytosine = 3 hydrogen bonds
(???) + (???) = 1 hydrogen bond???
In physics we find the "2" in matter/anti-matter; the "3" in the three families of fundamental particles, three basic particles, three quarks, etc...; the "4" in the out-dated concept of four fundamental forces of nature, though there are some who still prefer to hold on to a "four" concept, and a "7" can be garnered by combination.
| Names for hydrogen species | General | 1H | 2H | 3H |
| Atom (H) | hydrogen | protium | deuterium | tritium |
| Cation (H+) | hydron | proton | deuteron | triton |
| Anion (H-) | hydride | protide | deuteride | tritide |
| Group (-H) | hydro | protio | deuterio | tritio |
| Transfer of cation to substrate | hydronation | protonation | deuteronation | tritonation |
| Replacement of hydrogen by a specific isotope | protiation | deuteriation (or deuteration) |
tritiation |
http://www.chem.qmw.ac.uk/iubmb/newsletter/misc/proton.html
3-patterned formulas used by humanity in different disciplines with varying symbols may be an expression of an evolutionary developmental change taking place with some humans. When we expand our application of this pattern to include nuclear formulas for energy production, we find the following "3-patterned" (D~T~He4) formula which would produce the most energy output per energy input with respect to Hydrogen power:
(Notice that there is no supplemental letter used for the He4, but that the 2H and 3H have the letters D and T, respectively, just like there are separate words for the three sizes of small~medium~large, but beyond large, there is not a separately designated label...only a re-usage of the word "large" in the sense of X-large~ XX-large~ XXX-large.)
It is clear that a 2, 3, 4 and "seven"-teen is being expressed. (And a "9" value is gained from a combination of 2 + 3 + 4 = 9. (For those who wish to add the n + 1.70 to this numerological excursion equation, we get (using a shorthand method): 2 + 3 + 4 + 1 + 1.70 = 18 = 1 + 8 = 9.)
Note: I arrived at n = 1 arbitrarily. If we associate the letter with a strict numerological association, the letter n = 14 because of its placement in the alphabet. By adding the 1 + 4 of the "14" we can arrive at 5, but by leaving it intact for use in a long-hand method of equation: 2 + 3 + 4 + 14 + 1.70 = 24.70 = 2 + 4 + 7 + 0 = 13 = 1 + 3 = 4. It is clear that by including or excluding various letters in the equation, we can arrive at different "answers" to suit any preconceived inclination.
8:21 AM 10/1/2013: The "n" should have the value of "1".
Let us now look at the "3-patterned" (Carbon~Hydrogen~Oxygen) equation for photosynthesis:
By adopting a parallel exchange of symbols amongst the different academic disciplines with respect to the triadic structures, there may be a possible derivative defined that gives an expression to an underlying representation of inclusiveness for generating a formulaic model that can be applied to such things as computer design. In effect, we will move away from the binary operational model now being used and progress into a trinary model which may be more beneficial for creating the basis of an artificial consciousness. In our own modern sense, we will have developed our own "music of the spheres" philosophy that has a much broader application.
Are amino acids the notes of a key board specific only to Earth, or notes to a key board applicably resonate throughout the Universe, as is presently conceived? Is the human genome project merely 1 type of musical manuscript? In parallel, all the above tables, in their own way, may be extremely superficial examples of scrambled representations of underlying sequences that, if unraveled, will help to produce a type of musical notation that could be used to construct a type of "keyboard" from which could be "sprouted" the renditions of different forms of life? Different forms of basic chemicals? Different forms of atomic energy? Different forms of mass destruction weapons?
And by parallel equivalent, what is the "music" of the human genome if the triplet sequences of amino acids could be translated into musical triad configurations? Is it this "song" that is pervasive throughout the Universe, or is it a unique composition specific to this time and place, (cosmologically speaking) which must be used as a "message" to sent out into space using the Very Large Array (VLA) of radio antennas as speakers? Can the VLA antennas be used as speakers to blast the "song" of humanity into space, or must a different form of "speaker system" be designed to transmit the "musical triads" of the human genome? Perhaps it is some other Earth-based life form's "genetic musical composition" that will be tuned into by some extra-terrestrial species, because they will recognize it as the very basis of their own from which they evolved into a conscious species?
Will any Earth-based life form's "genetic musical composition" be appealing to any Extra-terrestrial that may exist elsewhere? Do other beings talk, hear, see, feel, think, etc., in triadic formulas that are more expressive than any form of vocal expression existing on Earth? So what is the song of the human genome? Who will be the first musician to unravel the notes of the human genome sequence and play the song of human identity... all the while being cognizant that such a song may be an old refrain not sung elsewhere in the Universe anymore? Is the "song" of the human genome nothing more than a short witless ditty sporadically made-up like some drunken sailor's murmurings in a dark alley? Or a drunken sailor who is puking their guts out due to being sea sick on a white-capped ocean?
Or is the human genome "song" the equivalent of some rebellious rock and roll tune? Or is it the one and only song that has ever been and will ever be written in the Universe because it is a serendipitously occurring mutation that required certain conditions to produce the results, and those conditions will never arise again because human memory does not and will never last long enough to know otherwise?
However, if humanity is able to create some form of musical composition from the amino acid sequences in the human genome and blast the song into space, those Extra-terrestrial creatures that hear the "music to our ears," may not find it appealing, and in fact may feel threatened by it to the extent of sending out a inter-galactic police car to issue a complaint. And the complaint may be that we humans have broken some Inter-galactic law of disturbing the peace, which is punishable by extermination. If we humans apologize and claim we were not aware of such a law, we might very well be met with the response: "Ignorance of the law is no defense," just before the verdict of extinction is carried out.
One reference to logic can be found at:
http://www.tcdsb.org/external/schools/chaminade/oac-philosophy/public_html/logicnotes.htm
Herb O. Buckland
herbobuckland@hotmail.com