{"id":514,"date":"2020-08-01T00:41:56","date_gmt":"2020-08-01T00:41:56","guid":{"rendered":"http:\/\/region12.herbzinser07.com\/dir\/science03\/?p=514"},"modified":"2020-08-01T00:41:56","modified_gmt":"2020-08-01T00:41:56","slug":"dirac-4-x-4-math-dna-matrices","status":"publish","type":"post","link":"https:\/\/region12.herbzinser07.com\/dir\/science03-optics\/2020\/08\/01\/dirac-4-x-4-math-dna-matrices\/","title":{"rendered":"Dirac 4 x 4 math DNA matrices"},"content":{"rendered":"
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RD-blog-number-2717 by Herb Zinser<\/span><\/p>\n

Dirac 4 x 4<\/span> math DNA matrices<\/span><\/strong><\/span><\/h1>\n

The 4 DNA nucleotides are composed of atoms \u00a0and existence in a EARTH LAB \u00a0mathematical-physics space\/time \u00a0continuum.<\/span><\/p>\n

Thus…the primordial atomic of source DNA.<\/span><\/p>\n

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Nature’s atomic bio-physics engineers designed and built<\/span><\/p>\n

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A key feature of DNA are the 4 nucleotides.<\/span><\/p>\n

DNA<\/a><\/span>\u00a0– Wikipedia, the free encyclopedia<\/a><\/span><\/h3>\n

en.wikipedia.org\/wiki\/<\/span>DNA<\/span><\/p>\n

Deoxyribonucleic acid<\/span>\u00a0(<\/span>DNA<\/span>) is a molecule encoding the genetic instructions\u00a0<\/span>…<\/span>\u00a0Genetic information is encoded as a sequence of\u00a0<\/span>nucleotides<\/span>\u00a0(guanine,\u00a0<\/span>…..<\/span>\u00a0<\/span>Since there are\u00a0<\/span>4<\/span>\u00a0bases in 3-letter combinations, there are 64 possible codons (\u00a0<\/span>4 math exponent 3 = 64)<\/span>\u00a0<\/a><\/span>\u00a0<\/a><\/span><\/p>\n

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Nucleic acid – Wikipedia, the free encyclopedia<\/a><\/span>\u00a0<\/span><\/p>\n

en.wikipedia.org\/wiki\/Nucleic_acid<\/span><\/p>\n

They include DNA (deoxyribonucleic acid) and RNA (ribonucleic acid).\u00a0<\/span>…<\/span>\u00a0and forensic science, as well as the biotechnology and pharmaceutical industries.\u00a0<\/span>…<\/span>\u00a0The basic component of biological nucleic acids is the nucleotide, each of which\u00a0<\/span>…<\/span><\/p>\n

What are the\u00a0<\/a><\/span>four<\/a><\/span>\u00a0types of\u00a0<\/a><\/span>nucleotides<\/a><\/span>\u00a0of\u00a0<\/a><\/span>DNA<\/a><\/span><\/h3>\n

wiki.answers.com \u203a<\/span>\u00a0<\/a><\/span>Wiki Answers<\/a><\/span>\u00a0\u203a<\/span>\u00a0<\/a><\/span>Categories<\/a><\/span>\u00a0\u203a<\/span>\u00a0<\/a><\/span>Science<\/a><\/span>\u00a0\u203a<\/span>\u00a0<\/a><\/span>Biology<\/a><\/span><\/p>\n

Why are there four types of nucleotides in\u00a0<\/span>DNA<\/span>? Over eons of evolutionary history, nature decided that\u00a0<\/span>four nucleotides<\/span>\u00a0provides the right balance. What are the\u00a0<\/span>…<\/span><\/p>\n

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Introduction to\u00a0<\/a><\/span>DNA<\/a><\/span>\u00a0Structure<\/a><\/span><\/h3>\n

www.blc.arizona.edu\/molecular_graphics\/<\/span>dna<\/span>…\/<\/span>dna<\/span>_tutorial.html<\/span><\/p>\n

There are four different types of nucleotides found in\u00a0<\/span>DNA<\/span>, differing only in the nitrogenous base. The\u00a0<\/span>four nucleotides<\/span>\u00a0are given one letter abbreviations as\u00a0<\/span>…<\/span><\/p>\n

Scientists Just Added Four New Letters to the Genetic Code<\/span><\/h1>\n

By\u00a0<\/span>Edd Gent<\/a><\/span>\u00a0-Feb 24, 201925,692<\/span><\/p>\n

A four-letter alphabet might seem limited, but it\u2019s all nature needed to write the instructions for all life on the planet. News that researchers have added four letters to the genetic alphabet opens the door to new possibilities in synthetic biology, data storage, and even the search for life beyond our planet.<\/span><\/p>\n

The genetic code at the heart of all living things is elegantly simple. Each half of the famous double helix structure is built from four small molecules called bases: adenine, thymine, cytosine and guanine (ATCG). The order in which they appear determines what the DNA codes for, just like series of zeros and ones at the hearts of computers do.<\/span><\/p>\n

But now scientists at the Foundation for Applied Molecular Evolution in Florida have successfully<\/span><\/p>\n

added four new bases<\/a><\/span>\u00a0to create what they are calling \u201chachi-moji DNA\u201d\u00a0<\/span>(eight-letter DNA<\/span>\u00a0in Japanese), doubling the potential information density of genetic code.<\/span><\/p>\n

This isn\u2019t the first attempt at expanding the genetic code. In 2014, scientists at the Scripps Research Institute in California unveiled DNA with two extra bases, and in 2017 they showed that they could get\u00a0<\/span>bacteria to use this code<\/a><\/span>\u00a0to build proteins that don\u2019t exist in nature. But the new work not only adds an extra two bases, it also sticks more closely to the blueprint used by nature.<\/span><\/p>\n

The double helix of DNA is held together by hydrogen bonds between complementary bases\u2014A pairs with T and C pairs with G.<\/span><\/p>\n

The Scripps research used\u00a0<\/span>water-repelling molecules<\/span>\u00a0that stick together but repel the other bases. These bases need to be sandwiched between natural bases, so it\u2019s not possible to have extended stretches of unnatural bases limiting what they can code for.<\/span><\/p>\n

Hachi-moji DNA, however, uses hydrogen bonds just like natural DNA to link its two new pairs\u2014<\/span>S with B and P with Z\u2014<\/span>and the bases are also capable of appearing next to each other. Because DNA is read in triplets of bases called codons, each of which codes for a particular amino acid, this significantly increases the number of potential codons compared to the previous approach: 512 compared to conventional DNA\u2019s 64.<\/span><\/p>\n

The experiments also suggest hachi-moji DNA preserves all the key characteristics required to support Darwinian evolution, crucial for supporting life. The bases pair reliably, the structure remains\u00a0<\/span>stable regardless of the sequence<\/a><\/span>\u00a0of bases, and they\u2019ve demonstrated that it can be copied into RNA.<\/span><\/p>\n

That\u2019s crucial, because while DNA holds the blueprints for an organism, in order for cells to do anything with that information it has to be converted into the mobile, single-stranded molecule RNA, which can act as instructions for protein factories called ribosomes or can help regulate genes.<\/span><\/p>\n

In terms of potential uses for the new letters, the possibilities are broad. All of nature\u2019s complexity has been created from the 20 amino acids conventional DNA can produce (multiple codons code for the same amino acid). New codons make it possible to code for\u00a0<\/span>new amino acids\u00a0<\/a><\/span>with novel properties, which could enable everything from more powerful medicines and industrial catalysts to more outlandish ideas, like electrically-conducting proteins.<\/span><\/p>\n

Scientists Just Added Four New Letters to the Genetic Code<\/a><\/span><\/p>\n

singularityhub.com<\/a><\/span>\u00a0\u203a 2019\/02\/24 \u203a scientists-just-added…<\/a><\/span><\/p>\n

Feb 24, 2019 –\u00a0<\/span>Eight-<\/span>letter DNA<\/span>\u00a0uses hydrogen bonds just like natural\u00a0<\/span>DNA<\/span>\u00a0to link its … But now scientists at the Foundation\u00a0<\/span>for<\/span>\u00a0App<\/span>lied\u00a0<\/span>Molecular<\/span>\u00a0Evolution<\/span>\u00a0in …<\/span><\/p>\n

Scientists create an<\/a><\/span>
\n<\/a><\/span>expanded 8-letter<\/a><\/span>\u00a0DNA<\/a><\/span>\u00a0genetic code …<\/a><\/span><\/p>\n

sitn.hms.harvard.edu<\/a><\/span>\u00a0\u203a flash \u203a scientists-create-expande…<\/a><\/span><\/p>\n

Feb 27, 2019 –\u00a0<\/span>Life as we know it uses 4 bases called A, C, T, and G. Recently, scientists expanded this alphabet to include\u00a0<\/span>8<\/span>\u00a0bases \u2013 4 natural and\u00a0<\/span>4 artificial ..with David Letter Letterman television comedy bases.<\/span><\/p>\n

letter<\/a><\/span>\u00a0DNA<\/a><\/span><\/p>\n

letter<\/a><\/span>\u00a0D \u00a0NA<\/a><\/span><\/p>\n

Letterman David North America<\/a><\/span><\/p>\n

What are the\u00a0<\/a><\/span>four<\/a><\/span>\u00a0types of\u00a0<\/a><\/span>nucleotides<\/a><\/span>\u00a0of\u00a0<\/a><\/span>Dirac North America<\/a><\/span><\/h3>\n

wiki.answers.com \u203a<\/span>\u00a0<\/a><\/span>Wiki Answers<\/a><\/span>\u00a0\u203a<\/span>\u00a0<\/a><\/span>Categories<\/a><\/span>\u00a0\u203a<\/span>\u00a0<\/a><\/span>Science<\/a><\/span>\u00a0\u203a<\/span>\u00a0<\/a><\/span>Biology<\/a><\/span><\/p>\n

Why are there four types of nucleotides in\u00a0<\/span>DNA<\/span>?<\/span><\/p>\n

ver eons of evolutionary history, nature decided that<\/span><\/p>\n

four nucleotides<\/span>\u00a0provides the right balance. What are the\u00a0<\/span>…<\/span><\/p>\n

Introduction to\u00a0<\/a><\/span>DNA<\/a><\/span>\u00a0Structure<\/a><\/span><\/h3>\n

www.blc.arizona.edu\/molecular_graphics\/<\/span>dna<\/span>…\/<\/span>dna<\/span>_tutorial.html<\/span><\/p>\n

There are four different types of nucleotides found in\u00a0<\/span>DNA<\/span>, differing only in the nitrogenous base. The\u00a0<\/span>four nucleotides<\/span>\u00a0are given one letter abbreviations as\u00a0<\/span>…<\/span><\/p>\n

Image for\u00a0<\/a><\/span>dna 4 nucleotides<\/a><\/span><\/h3>\n

<\/a><\/a><\/p>\n\n\n\n\n\n\n\n\n\n\n\n
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Paul Dirac<\/span><\/p>\n<\/td>\n<\/tr>\n

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\"\"<\/p>\n<\/td>\n<\/tr>\n

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Born<\/span><\/p>\n<\/td>\n

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Paul Adrien Maurice Dirac<\/span><\/p>\n

8 August 1902<\/span><\/p>\n

Bristol<\/a><\/span>, England<\/span><\/p>\n<\/td>\n<\/tr>\n

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Died<\/span><\/p>\n<\/td>\n

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20 October 1984 (aged 82)<\/span><\/p>\n

Tallahassee, Florida<\/a><\/span>, USA<\/span><\/p>\n<\/td>\n<\/tr>\n

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Residence<\/span><\/p>\n<\/td>\n

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United Kingdom<\/span><\/p>\n<\/td>\n<\/tr>\n

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Nationality<\/span><\/p>\n<\/td>\n

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Switzerland<\/a><\/span>\u00a0(1902\u201319)<\/span><\/p>\n

United Kingdom<\/a><\/span>\u00a0(1919\u201384)<\/span><\/p>\n<\/td>\n<\/tr>\n

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Fields<\/span><\/p>\n<\/td>\n

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Physics<\/a><\/span>\u00a0(<\/span>theoretical<\/a><\/span>)<\/span><\/p>\n<\/td>\n<\/tr>\n

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Institutions<\/span><\/p>\n<\/td>\n

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University of Cambridge<\/a><\/span><\/p>\n

University of Miami<\/a><\/span><\/p>\n

Florida State University<\/a><\/span><\/p>\n<\/td>\n<\/tr>\n

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Alma mater<\/a><\/span><\/p>\n<\/td>\n

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University of Bristol<\/a><\/span><\/p>\n

University of Cambridge<\/a><\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Images for\u00a0<\/a><\/span>dna 4 nucleotides<\/a><\/span><\/h3>\n

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Dirac Matrices<\/span><\/h1>\n

\"DOWNLOAD<\/p>\n

The Dirac matrices are a class of\u00a0<\/span>\"4\u00d74\"\u00a0matrices which arise in quantum electrodynamics. There are a variety of different symbols used, and Dirac matrices are also known as gamma matrices or Dirac gamma matrices.<\/span><\/p>\n

The Dirac matrices\u00a0<\/span>\"alpha_n\"\u00a0may be implemented in a future version of<\/span>\u00a0<\/a><\/span>Mathematica<\/a><\/span>\u00a0as DiracGammaMatrix[<\/span>n<\/span>], where\u00a0<\/span>\"n=1\", 2, 3, 4, or 5.<\/span><\/p>\n

The Dirac matrices are defined as the\u00a0<\/span>\"4\u00d74\"\u00a0matrices<\/span><\/p>\n

<\/a><\/a><\/p>\n\n\n\n\n
\n

\"sigma_i\"<\/p>\n<\/td>\n

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\"=\"<\/p>\n<\/td>\n

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\"I_2<\/p>\n<\/td>\n

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(1)<\/span><\/p>\n<\/td>\n<\/tr>\n

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\"rho_i\"<\/p>\n<\/td>\n

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\"=\"<\/p>\n<\/td>\n

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\"sigma_i^((P))<\/p>\n<\/td>\n

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(2)<\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

where\u00a0<\/span>\"sigma_i^((P))\"\u00a0are the (<\/span>\"2\u00d72\")<\/span>\u00a0<\/a><\/span>Pauli matrices<\/a><\/span>,\u00a0<\/span>\"I_2\"\u00a0is the\u00a0<\/span>\"2\u00d72\"\u00a0<\/a><\/span>identity matrix<\/a><\/span>,\u00a0<\/span>\"i=1\", 2, 3, and\u00a0<\/span>\"A\u00a0is the<\/span>\u00a0<\/a><\/span>Kronecker product<\/a><\/span>. Explicitly, this set of Dirac matrices is then given by<\/span><\/p>\n

<\/a><\/a><\/p>\n\n\n\n\n\n
\n

\"I\"<\/p>\n<\/td>\n

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\"=\"<\/p>\n<\/td>\n

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\"[1<\/p>\n<\/td>\n

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(3)<\/span><\/p>\n<\/td>\n<\/tr>\n

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\"sigma_1\"<\/p>\n<\/td>\n

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\"=\"<\/p>\n<\/td>\n

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\"[0<\/p>\n<\/td>\n

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(4)<\/span><\/p>\n<\/td>\n<\/tr>\n

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\"sigma_2\"<\/p>\n<\/td>\n

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\"=\"<\/p>\n<\/td>\n

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\"[0<\/p>\n<\/td>\n

<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Dirac Matrices<\/a><\/span>\u00a0and Feynman’s Rest of the Universe<\/a><\/span><\/h3>\n

arxiv.org \u203a<\/span>\u00a0<\/a><\/span>quant-ph<\/a><\/span><\/p>\n

by YS Kim – 2012<\/span><\/p>\n

Oct 23, 2012 \u2013 Abstract: There are\u00a0<\/span>two sets of four-by-four\u00a0<\/span>matrices<\/span>\u00a0introduced by\u00a0<\/span>Dirac<\/span>. The first set consists of fifteen Majorana\u00a0<\/span>matrices<\/span>\u00a0derivable from his\u00a0<\/span>…<\/span><\/p>\n

two sets of four-by-four\u00a0<\/span>matrices\u00a0<\/span>—> two (Double helix) \u00a0….. four (4 nitrogenous bases)<\/span><\/p>\n

Super-symmetry physics … mirrors and parallels suggest<\/span><\/p>\n

Gamma matrices<\/span><\/h1>\n

From Wikipedia, the free encyclopedia<\/span><\/p>\n

Jump to:<\/span>\u00a0<\/a><\/span>navigation<\/a><\/span>,<\/span>\u00a0<\/a><\/span>search<\/a><\/span><\/p>\n

In<\/span>\u00a0<\/a><\/span>mathematical physics<\/a><\/span>, the\u00a0<\/span>gamma<\/span>\u00a0<\/a><\/span>matrices<\/a><\/span>,\u00a0<\/span>\", also known as the<\/span>\u00a0<\/a><\/span>Dirac<\/a><\/span>\u00a0matrices<\/span>, are a set of conventional matrices with specific<\/span>\u00a0<\/a><\/span>anticommutation<\/a><\/span>\u00a0relations that ensure they<\/span>\u00a0<\/a><\/span>generate<\/a><\/span>\u00a0a matrix representation of the<\/span>\u00a0<\/a><\/span>Clifford algebra<\/a><\/span>\u00a0<\/span>C<\/span>\u2113<\/span>1,3<\/span>(<\/span>R<\/span>). It is also possible to define<\/span>\u00a0<\/a><\/span>higher-dimensional gamma matrices<\/a><\/span>. When interpreted as the matrices of the action of a set of<\/span>\u00a0<\/a><\/span>orthogonal<\/a><\/span>\u00a0<\/a><\/span>basis vectors<\/a><\/span>\u00a0for<\/span>\u00a0<\/a><\/span>contravariant<\/a><\/span>\u00a0<\/a><\/span>vectors<\/a><\/span>\u00a0in<\/span>\u00a0<\/a><\/span>Minkowski space<\/a><\/span>, the column vectors on which the matrices act become a space of<\/span>\u00a0<\/a><\/span>spinors<\/a><\/span>, on which the<\/span>\u00a0<\/a><\/span>Clifford algebra<\/a><\/span>\u00a0of<\/span>\u00a0<\/a><\/span>spacetime<\/a><\/span>\u00a0acts. This in turn makes it possible to represent infinitesimal<\/span>\u00a0<\/a><\/span>spatial rotations<\/a><\/span>\u00a0and<\/span>\u00a0<\/a><\/span>Lorentz boosts<\/a><\/span>. Spinors facilitate spacetime computations in general, and in particular are fundamental to the<\/span>\u00a0<\/a><\/span>Dirac equation<\/a><\/span>\u00a0for relativistic<\/span>\u00a0<\/a><\/span>spin-\u00bd<\/a><\/span>\u00a0particles.<\/span><\/p>\n

In<\/span>\u00a0<\/a><\/span>Dirac representation<\/a><\/span>, the four<\/span>\u00a0<\/a><\/span>contravariant<\/a><\/span>\u00a0gamma matrices are<\/span><\/p>\n

\"<\/p>\n

\"\\gamma^2<\/p>\n

Could the above 4 math matrices \u00a0be the precursor to the existence of the 4 nucleotides?<\/span><\/p>\n

Did Nature have mathematical-physics engineering diagram \u00a0(an archtitectural drawing) \u00a0that it used \u00a0….. to build the similar configured 4 molecular structures<\/span><\/p>\n

.<\/span><\/p>\n

.<\/span><\/p>\n

.<\/span><\/p>\n

So that was the scientific introduction, now lets start with the basics. Nucleotides are molecules that, when joined, make up the individual structural units of the nucleic acids RNA and DNA. We have<\/span><\/p>\n

four different nucleotides<\/span>;<\/span><\/p>\n

adenine (A),<\/span><\/p>\n

thymine (T),<\/span><\/p>\n

cytosine (C) and<\/span><\/p>\n

guanine (G). To serve some chemistry with this, here are the chemical formulas:<\/span><\/p>\n

\"\"<\/p>\n