User talk:Ramon Roca
- Please, contact directly: ramonrocabcn@gmail.com
http://openwetware.org/wiki/Molecular_computing
http://openwetware.org/wiki/User_talk:Ramon_Roca
http://openwetware.org/wiki/Talk:Molecular_computing
http://www.youtube.com/user/rmnDeliriaLegitur
A SET THEORY OF INFORMATION: MODES OF VIBRATION
bibliography: http://openwetware.org/wiki/Talk:Molecular_computing
|
E. Lubkin; Keeping the entropy of measurement: Szilard revisited. |
Reality is not subdivided
|
|
R. Landauer; |
There really is no software, in the strict sense of disembodied information, but only inactive and relatively static hardware. Thus, the handling of information is inevitably tied to the physical universe. Evolution and the origin of life can be viewed as an optimization process, in which fluctuations (e.g., mutations) take us from one metastable ecology, to a new one. We might, with equal justice, refer to the revolution of an electron around a hydrogen nucleus, or the rotation of a water wheel, as self organization. |
|
Erbium (Er) n=68 -integer- (atomic number -protons-) p=331 -prime- (atomic information quanta) Fourier phase analysis: (inverse sine waveform)
 |
[1972: Hugh Montgomery has just been introduced to Freeman Dyson] Montgomery: [the distribution of the zeros of the Riemann zeta function] It seems the two-point correlations go as.... (turning to write on a nearby blackboard):
Dyson: Extraordinary! Do you realize that's the pair-correlation function for the eigenvalues of a random Hermitian matrix? It's also a model of the energy levels in a heavy nucleus [erbium-166 (protons neutrons)].
|
|---|
NUMBER THEORETICS AND INFORMATION LEVELS
Levin and Chaitin definition of algorithmic entropy: A program is self-delimiting it if needs no special symbol, other than the digits 0 and 1 of which it is composed, to marks its end; discrete objects other than binary strings, e.g., integers, or coarse-grained cells in a continous phase space, may be defined by indexing them by binary strings in a standard way (as Monte Carlo program describes distributions of macrostates).
Fundamental Theorem of Arithmetic: Every natural number is uniquely decomposable into a product of prime powers. Primes are the building blocks (factors) of the positive integers: The prime integers of an integer determine its properties.
Euler's function [cos θ + j sen θ = ejθ] describes vibrations (waves) connecting geometry (trigonometric functions -the integer values n, in real space-) and algebra (exponential function -the prime factors p, in reciprocal space-) -consider: n + n' = p -.
Any arbitrary shape can be regarded as a locus of intersecting surfaces of nth order (generated in terms of Fourier descriptors). The total amount of information embodied in simple shapes is determined by the shape category, the number of surfaces and the form or order of the surfaces-defining equations (e.g., quadratic, cubic, etc) [tesis/biblio.html#Ayers (Ayers, 1994)] - [tesis/fig3_4.html see table] -:
| symmetry information embodied in simple shapes |
Hsym (bits) |
| rectangle | 1 |
| square | 2 |
| cone | 10 |
| sphere |
30 |
Badii utilized the idea that chaos is made up of combinations of the periodic orbits. A 'primitive' is defined by two conditions: it is periodic (i.e., in the infinity sequence there are arbitrarily long repetitions of it) and it cannot be broken down to other primitives. The [hierarchical] tree [structure] is constituted by the primitives and their admissible combinations (the first level, the primitive combination; 2nd level, pairwise combination; n-th level, n-ary combinations, and so on). [tesis/biblio.html#Kampis (Kampis, 1991)].
With Gödel numbering (by instance, using the original symbols as exponents of a prime factorization) it becomes possible to encode and decode state transformations to and from states directly. This procedure, which is itself algorithmic, ensures the existence of a dynamics without the use of any further information. All we need is a component-system which produces them by complexity-increasing procedures. [tesis/biblio.html#Kampis (Kampis, 1991)].
Golay codes are based upon prime numbers: Golay codes G23 (binary, [23,12,7]2, 3-correcting) and G11 (ternary, [11,6,5]3, 2-correcting) are perfect, systematic and linear. Theorem of Best: All perfects codes over any alphabet, with p≥3 and p≠6,8 are equivalent to Rep2(n) or G23. [tesis/biblio.html#Brunat (Brunat, 2001)]
This theorem implies two basic levels of information (2 and 23). Similarly, in music, it is possible to observe these same levels: first one, ternary, it would be formed by values 0, 1 and 2 and they correspond to silence, semitone and tone; second level depends on "musical temperament", so, considering temperated scale, it is formed by 12 notes. Another example results from comparing binary (2 elements, first level) and decimal (10 elements, second level) systems; in this case, adding a third level (20, 100, 1000), although related to logarithmic scales, it is usually done on an arbitrary and subjective manner.
| Atomic periodicity (n protons of noble gases): |
| |||||||
| Number of elements per period (Mendeleiev table): |
| |||||||
| Types of electronic orbitals or (sub)shells: |
| |||||||
|
Reinterpreting theorem of Best, i.e., if G23 is a prototypical perfect code, it could be stablished the next periods for prime numbers:
| period I: | 1 | 2 |
2 elements; n=2 | ||||||
| period II: | 3 |
5 |
7 |
11 |
13 |
17 |
19 |
23 |
8 elements; n=10 |
| period III: | 29 |
31 |
37 |
41 |
43 |
47 |
53 |
59 |
8 elements; n=18 |
(because of "technical" reasons, it is considered 1 as the "first" prime, i.e., n=1)
First period (elements 1 and 2) defines the even-odd concepts, equivalent in signal transmition, to renormalized [-1, 0, 1], or in musical terms to semitone and tone. Second period (8 elements, primes from 3 to 23: increment=20) defines -consolidates- the primity concept and is equivalent, for instance, to 2 musical scales, or to binary Golay code G23. Third period (8 elements, primes from 29 to 59: increment=30) determines the self-organizing character of the progression of the prime numbers: 29 is (almost 30) a "prime multiple" of 3.
With only 18 elements, it is incremented the "informative value" from a signal type 2 to another signal type 59 (almost 60). In music, considering equal-tempered scales, it is possible to divide the octave into 59 intervals to approximate the frequency ratios from just intonation; so, it is also a good choice the standard division of the octave in 12 intervals, as 5 octaves of 12 notes (i.e., 60 notes is quite near of 59: just a semitone) permit to "construct a quasiperfect code" (as extended Golay codes G24 and G12 can be generators of perfect codes G23 and G11).
From an "evolutionary" point of view (as increment of information complexity), it must be considered the three first elements as critical (and concentrical):
1 defines unity and appears as "opposition" to 0 (algebraically, a "trivial" vectorial subspace);
2 defines pair/even, as first distinctive of symmetry (1 1);
3 defines "primity" concept in its orthodox sense, considered as another distinctive of (a/self)symmetry (2 1), conditioning asymmetrical interactions.
The most important detail is just the increase of complexity: as the number of elements grows, "the growing itself becomes faster". Essentially, this increasing is due to main basic relationships of the three first elements (2 1, 3 2), that, altogether with the fourth element (5, just a consequence of the previous relationships), conform the first "extended period". Another approach is to consider "3 2" interaction as the combination of ternary and binary systems, a basic subset of complexity in terms of information.
| prime (p) |
1 |
2 |
3 |
5 |
7 |
11 |
13 |
17 |
19 |
23 |
29 |
31 |
37 |
41 |
43 |
47 |
53 |
59 |
| integer (n) | 1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
Analogous to Golay code G11, parameters [11,6] (respectively, dimension and length) could be extended to other concrete/discrete pairs [p,n], being p prime and n its integer (the number of protons); the third parameter of Golay codes, related to error correction, is named "Hamming minimum distance" [could be equivalent to the number of neutrons?]. Then, Carbon is represented as a "ternary code" with parameters C [11,6]; first fourth elements are defined as the next pairs (vectors, matrices, codes): Hydrogen, H [1,1]; Helium, He [2,2]; Lithium, Li [3,3]; and Beryllium, Be [5,4].
'
From these premises:
a.- It is represented, by FFT phases of generated inverse sine waves, "p orbitals" (p spheres of information) of the first 118 elements and others, so some elements, like Er (atomic number: n=68; p= 331), Rn (86,439) and predicted Ac' (121,659), "reorganize their orbitals into N beams".
b.- Simple arithmetical rules are used for different molecules (from water to ATP; resp., p=19 and p=541). My initial question was if hydrogen and ATP could be compared "quantitatively" at entropy and information levels; within "primity scale", H and ATP information values differe in a "logarithmic order 1:101".
My proposal implies that different levels of information are organized in a complex system within the basis of prime numbers, as a result from considering as "Golay codes" the atomic elements, and then, distributed by "Medeleiev periods ".
COMPLEX SYSTEMS: MOLECULAR COMPUTATION
In biology, different molecules interact by means of their composing elements and determine diverse informative values by their respective surfaces and volumes. For example, H and Ca2 are two types of signals at the subcellular level; at protein level, 20 aminoacids are classified depending on their characteristics (analysable through Markov models or equivalence matrices). So, it seems logical to consider each atom as a characteristic signal type, quantizable, normalized by "Gödel numbers". Evolutionary, increment of complexity appears because of the periodical progression (Mendeleiev) of prime numbers, and because of interactions that appear due to increasing possibilities and elements.
Prime integers are hierarchical strange attractors (characteristic or typical tones) of complex self-organized (harmonized) systems.
Results and other conjectures
Atom prime chart:
| n=19 |
n=36 | ||||||||||||||||
| n=37 |
n=54 |
| n=55 |
n=86 | ||||||||||||||||||||||||||||||
| n=87 |
n=118 |
| n=119 |
n=172 | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| n=173 |
n=226 |
| n=227 |
n=306 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| n=307 |
n=386 |
Digital signal processing
Phase analysis (Lissajous Plot graphs ***) of prime generated tones:
- Inverse sine (pure tone: fundamental, no harmonics);
- Audio signals in Hz.
Non prime: Control data and Dynamics
Prime phases of atomic elements (p orbitals): [original size] & [reduced view]
"Nobles":
|
2 |
23 |
59 |
149 |
241 |
439 |
"Erbium-like":
|
37 |
73 |
109 |
223 |
331 |
439 |
More prime phases: part I (661 to 1427); part II (1429 to 7919); part III (7927 to 21059).
|
661 |
769 |
881 |
991 |
1103 |
1213 |
Dynamics, transitions and polarization
|
Realtime data:
Gibbs Energy = Enthalpy Entropy (or Information)  (Phase modulation and primes kaleidoscope: supernovae, crystals, viruses) |
wav files (5 seconds each prime wave)
|
|
Slow motion rendering (only phases): [Unregistered] Screen Movie Studio (MandSoft) (download FrontPlayer: simple viewer for avi files)
 |
avi files (1000 frames per second)
|
"Erbium-like" series (local strong attractors: the Riemann series)
| erbium-like prime |
nearby note |
|
| 1429 |
F#6 | |
| 1321 |
E6 | |
| 1213 |
D#6 | |
| 1103 |
G#6 | |
| 991 |
B5 | |
| 881 |
A5 | |
| 769 |
G5 | |
| 661 |
E5 | |
| 547 |
C#5 | |
| 439 |
A4 | |
| 331 |
E4 | |
| 223 |
A3 | |
| 109 |
A2 | |
| 73 |
D2 | |
| 37 |
D1 | |
| erbiumlike.avi | 1'22'' (97.4Mb) |
Uncoupled and coupled terms are related to even and odd (1/2 or N/N 1), determining the L (levo) or R (dextro) character {anti-matter/matter, to be or not?}.
Volume is a function of distribution of mass-energy quanta
Integers: Atomic numbers (electrons and protons) represent mass/energy quanta. Primes: Every prime is associated to its integer, and represents a standarization of atomic volume/surface relationship, defining atomic information quanta.
Atomic typology (prime vs. integer):
Prime series of atomic elements
Periods K to Z20 [n/p (log p - log n)]
| p=prime H 1 |
Medeleev period (n =atomic number) |
additional protons= 1 [1 0] (n'=1) |
zz=n/p | log p
|
log n | log p - log n | zz Δlog |
zz Δln |
| He 2 |
K (2) 1s2 |
= 2 (n'=2) [1 1<==>2] |
1 | 0.30 |
0.30 |
0 |
0 |
0 |
| Ne 23 |
L (10) 1s22s22p6 |
= 8 (n'3, n'=2 Σ2p) |
0.435 | 1.36 |
1 |
0.36 |
0.157273 |
0.362134 |
| Ar 59 |
M(18) | = 8 |
0.305 | 1.77 |
1.26 |
0.52 |
0.157295 |
0.362186 |
| Kr 149 |
N (36) d10 | = 18 [2 (3x2) (5x2)] |
0.242 | 2.17 |
1.56 |
0.62 |
0.1490 |
0.3432 |
| Xe 241 |
O (54) | = 18 |
0.224 | 2.38 |
1.73 |
0.65 |
0.1456 |
0.3352 |
| Rn 439 |
P (86) f14 | = 32 [2 (3x2) (5x2) (7x2)] |
0.196 | 2.64 |
1.93 |
0.71 |
0.1387 |
0.3193 |
| Uuo 643 |
Q (118) | = 32 |
0.184 | 2.81 |
2.07 |
0.74 |
0.1351 |
0.3111 |
| etz1 1019 | R (172) | = 54 [2 (3x2) (5x2) (7x2) (11x2)] |
0.169 | 3.01 |
2.24 |
0.77 |
0.1304 |
0.3003 |
| etz2 1427 | S (226) | = 54 |
0.158 | 3.15 |
2.35 |
0.80 |
0.1267 |
0.2919 |
| etz3 2011 | T (306) | = 80 [2 (3x2) (5x2) (7x2) (11x2) (13x2)] |
0.152 |
3.30 |
2.49 |
0.82 |
0.1244 |
0.2865 |
| etz4 2659 | U (386) | = 80 |
0.145 |
3.42 |
2.59 |
0.84 |
0.1217 |
0.2802 |
| 3559 4517 5827 7177 8969 10781 13183 15647 18787 21961 |
V (500) 'W (614) X (766) Y (918) Z1 (1116) Z2 (1314) Z3(1570) Z4 (1826) Z5 (2144) Z6 (2462) |
80 34= 114 80 34= 114 114 38= 152 114 38= 152 152 46= 198 198 58= 256 256 62= 318 |
0.140 0.136 0.131 0.127 |
|||||
| 25933 29989 34843 39877 45887 51929 59023 66383 74857 83401 93377 103573 |
2854 3246 3720 4194 4754 5314 5968 6622 7382 8142 9020 9898 |
318 74= 392 392 82= 474 474 86= 560 560 94= 654 654 106= 760 760 118= 878 |
0.0956 |
5.02 |
4.00 |
1.097 |
0.0974 |
0.2244 |
| 115303 126943 |
10898 11898 |
878 122= 1000 |
0.0945 0.0937 |
5.06 5.10 |
4.04 4.08 |
1.025 1.024 |
0.0968 0.0964 |
0.2230 0.2219 |
| p = Σ n | n = Π p |  a pictorial view of Theorem of Best for Golay codes |
e= Σ (1+1/n)1/n [e**=Σ(1+1/p)1/p] |
"Prime interactions"
| molecule | fract[ion]al
interaction |
enharmonic number (prime)
|
|
H2 |
1:1 |
2 |
|
CH4 |
11:1 |
15 |
|
NH3 |
13:1 |
16 |
|
NH4 |
13:1 |
17* |
|
H2O |
1:17 |
19 |
|
N2 |
13:13 |
26 |
|
CO |
11:17 |
28 |
|
CH5N |
11:1:13 |
29 |
|
O2 |
17:17 |
34 |
|
C3H8 |
11:1 |
41 |
|
N2O , C2H4O |
|
43 |
|
CO2 |
11:17 |
45 |
|
NaOH |
29:17:1 |
47 |
|
Acetic (C2H4O2) |
11:1:17 |
60 |
|
ClOH |
53:17:1 |
71 |
|
C3H6O2 |
|
73 |
|
Gly |
|
74 |
|
SO2H2 |
47:17:1 |
83 |
|
Ala |
|
87 |
|
C6H6O , CaC2 |
|
89 |
|
PO3H3 |
43:17:1 |
97 |
|
Ca(OH)2 |
67:17:1 |
103 |
|
Ser |
|
104 |
|
Guanine (C5H5N5O) |
|
105 |
|
Pro |
|
111 |
|
Val |
|
113 |
|
Thr |
|
117 |
|
Thymine (C5H6N2O2) |
11:1:13:17 |
121 |
|
Adenine (C5H5N5) |
11:1:13 |
125 |
|
Leu |
|
126 |
|
Orn |
|
127 |
|
Asn |
|
129 |
|
Asp |
|
132 |
|
Cys |
|
134 |
|
Lys |
|
140 |
|
Gln |
|
142 |
|
Arg |
|
143 |
|
Glu |
|
145 |
|
His |
|
148 |
|
C5H10O5 |
|
150 |
|
Phe |
|
157 |
|
Met |
|
160 |
|
olivine (Mg2SiO4) |
31:41:17 |
171 |
|
Cl2Ca |
53:67 |
173 |
|
Tyr |
|
174 |
|
Glucose (C6H12O6) |
|
180 |
|
Trp |
|
193 |
|
Adenosine (C10H13N5O4) |
|
256 |
|
olivine (Fe2SiO4) |
97:41:17 |
303 |
|
chromite (Cr2O4Fe) |
83:17:97 |
331 |
|
Fe3O4 |
97:17 |
359 |
| 3Fe 4H2O = Fe3O4 4H2 |
[97]3::[19]4 == [359]::[2]4 |
367 |
|
2Fe 3Cr |
[97]2::[83]3 |
443 |
|
3Fe 2Cr |
[97]3::[83]2 |
457 |
| mFe nNi | ||
|
serpentine (Mg3Si2O5 - 2H2O Fe Ni) |
[253]::[19]2:: [97]::[103] |
491 |
|
Porphyirine (C34H34N4O4) |
|
528 |
|
ATP (C10H16N5O13P3) |
11:1:13:17:43 |
541 |
|
(CrO4)3Fe2 |
|
647 |
|
Lecitine (C42H82NPO8) |
|
736 |
Atoms vs. molecules
|
|
NOTES
Lissajous figure
[from wims]
[from "Collins English Dictionary", 1984]
CODING THEORY
Ternary Golay code G11.
Extended ternary Golay code G12.
"Perfect e-error correcting code" Theorem (Tietäväinen and Van Lint, 1971)
and proof tools (sphere packing condition & Lloyd's theorem). From "Ten milestones in the history of source coding theory":
Discovery of Lempel-Ziv codes. The well-known universal noiseless source coding technique due to Jacob Ziv and Abraham Lempel was announced in 1977 [26], although the method is based upon a notion of string complexity that had been proposed by these two authors in a paper the year before. With probability one, a stationary ergodic finite-alphabet source generates a sequence which, when encoded using the Lempel-Ziv algorithm, yields a compression rate equal to the entropy rate, asymptotically as the number of source samples goes to infinity. The Lempel-Ziv algorithm is the most important noiseless source coding technique in the entire history of source coding. A spate of papers has been devoted to the theoretical and practical aspects of Lempel-Ziv coding. On the theoretical side, perhaps the most significant of these is the recent paper by Ornstein and Weiss [18].
Digital Signal Processing: LWZ Compression
The spectrum of Riemannium
Brian Hayes (American Scientist July-August, 2003; vol. 91 (4), 296:300)
Prime numbers not so random? (Phillip Ball, 2003).
Surprising connections between number theory and physics (M. Watkins, 2004).
M. Wolf, "1/f noise in the distribution of prime numbers", Physica A 241 (1997), 493-499.
Data
(audible spectrum: 16.4 - 21096 Hz; ~ 10 scales)
|
Standard La (A4) is usually tuned at 438-440 Hz   Dynamics: Unstable/Instable & Hyperstable
|
|
FREQUENCIES AND WAVELENGTHS FOR EQUAL-TEMPERED SCALE
|
from C0 to D#8 / Eb8  |
|
|
| Major constituents (and fraction of total mass) of a heavy star, at the end of its evolution, just prior to a supernova explosion |
(from The Natural Selection of the Chemical Elements: ''''The Environment and Life's Chemistry, by R. J. P. Williams & J. R. R. Frausto Da Silva): |
| ~40% |
H He |
| ~20% |
He |
| ~20% |
C O Ne Mg |
| ~10% |
Si S Cl Ar K Ca |
| ~10% |
Ti V Cr Mn Fe Co Ni |
| Rare elements in Nature | Li Rb Cs Sr Ba Ra Ga In Tl Ge Sn Se Te |
| Stable nuclear forms (protons neutrons) |
He(4), C(12), Mg(24), Si(32), Fe(56) |
| ******************** |
******************** |
| Comet "Wild2" | olivine: (Mg,Fe)2SiO4 Al Ca Ti |
| (from La historia de la Tierra. Un estudio global de la materia, M.J. Mediavilla-Pérez; McGrawHill 1999) |
|
Stable nuclides(neutrons minus protons vs. atomic number) |
Euler: La naturaleza de la radiación que nos permite ver un objeto [...] depende del movimiento vibratorio de los átomos de su superficie, como cuerdas tensadas afinadas con cierta frecuencia, con la radiación incidente, emitiendo sus propias ondas. [Oliver Sacks; El Tío Tungsteno (Recuerdos de un químico precoz). Anagrama, 2003] | |
|
Wittgenstein: Logic when already stablished may be used for describing formal implications, but the rules themselves do not follow any logic. [from Kampis] |
|
|
Bernhard Riemann {1826-1866}: Zeta function (1859).
|
En Milán, Eckermann recapacita taciturno sobre el efímero valor de escrutar vidas ajenas y la importancia de contemplar las propias manos vacÃas. "Cuál debe ser la naturaleza de mi existencia?", se pregunta. Y escribe a Goethe, de retorno: "Vuestra excelencia dice en broma que viajar serÃa gran cosa si no hubiera que volver. Yo vuelvo ya". En Weimar, lo recibe Goethe y halla la repuesta a sus tres necesidades: "Aumentar mis conocimientos, mejorar mi existencia y sobre todo hacer algo". En esta sencilla fórmula, se encierra el secreto de las Conversaciones: la trama de complicidades entre el narrador y su oyente. [from an undocumented newspaper clipping] |
{{las Álgebras del ritmo}}
