A measure of evolution. Diffusion equation of natural selection and elections.

Thomas Huxley

To freely know is to know freedom.

Despite philosophical differences with the physicists of sub-atomic uncertainty, Einstein's natural philosophy is akin to theirs, in a theory of relativity that is also a method of creativity, in the technique of infering each other's observations ( rather like an election result ) called "changing the co-ordinates".

The idea that we exist in a finite universe is the logical outcome of a finite method, creative of a universe manifestly conditional upon observation. Relating observations is creative of more adaptive observation, which transformation may be considered an evolutionary development of observation. The observer measures from a transferable choice of co-ordinates. The theory of relativity is a scientific method of elections or "choosing-out".

Sub-atomic physicists accepted that their experimental observations may be to selective effect rather than completely determinate. And political voters select the things that are important to them to elect candidates.
I would rather make the terms of my own choices from among many candidates than have the terms of my choices made for me between a few candidates.

( On another web page, Ive described what appears to be a statistical basis to relativity, thus more akin to quantum mechanics than previously thought. Chance is more consistent than a completely determinist theory with a method of choosing observations. )

Electron Transfer

The philosophy, of matter made-up of atoms, eventually led to the knowledge of nuclear fusion between lighter atoms to form heavier atoms, in the stars. This was a chemical evolution of the elements, starting from hydrogen, of atomic number one, transformed into helium, number two...

The helium nucleus has less mass than its constituent four hydrogen nuclei, the lost mass being converted into solar energy. The chemical table of elements follows the four main scales ( classifying, order, interval and ratio scales ) of measurement. Each element is classified by name and ordered, by relative weight, with an atomic number, which turned-out to be the number of electrons in an atom.

Mendeleev's periodic table of the elements derived the regular intervals for the elements with similar properties. Bohr related these chemical regularities to the physical types of orbits in an atom's outer electrons. In the meantime, Einstein's equation of ( atomic) mass to energy amounts to a ratio scale of measurement. It was used to calculate the rate of energy release for the sun's mass. This agreed with the measured amount of the sun's radiation, verifying the equivalence of the conservation laws of mass and energy.

The periodic table co-ordinates the elemental order to a sub-order of stable "shells", containing full "quotas" of electrons. Taking the elements in order of their increasing number of electrons, after hydrogen and helium, a group of eight elements follows. Each has a first full shell or stable quota of two electrons. They also have an incomplete second shell of from one to eight electrons more. The next eight elements have complete first and second shells of two and eight electrons each, respectively, as well as the makings of a third shell in from one to eight electrons more...

It was known that some elements more readily combined, like friends who choose each other's company. Such elements were said to have 'elective affinities'. Goethe used the term as a title for a literary work. Preferential bonding takes place between an element, with an easily transferable surplus of electrons over a quota, and another element, with a corresponding deficit, so that their respective outer shell complements are at stable quota strength.

Carbon has a strong nuclear attraction, surrounded by only a first shell of two electrons, plus four more electrons, which are half-way to making up a second shell quota of eight electrons. So, carbon most readily combines with itself and other elements, especially to evolve life's complexity.

Electrons in transition, from outer to inner energy orbits, requiring lower energy levels, emit quotas of surplus energy, in light-quanta or photons. The 'quantum' is a minimum energy quota. Planck's quantum concept was required when calculations based on an assumption, that radiation is continous down to the smallest measurable quantities, conflicted with observation.

Compare the mensural structure of atomic physics with that of electoral system in the single transferable vote. The Droop quota is an elective minimum of votes. We distinguish between the normal electoral procedure of transfering a surplus over a quota and the extent this involves transfering quotas themselves as surpluses.

For example, 50 votes out of 100 are treated as one transferable quota, from the voters to the one majority candidate.
( If there are only two candidates with 50 votes each, they both have the minimum votes needed for election, and the winner is selected by chance, such as drawing lots. )

100 votes out of 150, that might be won as first preferences by the most popular candidate, may amount to two transferable quotas. As such, 150 out of 200 are three transferable quotas.

The classifying scale simply counts the votes: 1,2,3, etc. This is followed by the ordinal scale's 1,2,3,.. order of choice, the preference vote. The interval scale dimension is of 1,2,3,.. transferable quotas. The ratio scale is a rational series of 1,2,3,.. member majorities, in multi-member constituencies. This makes up the set of all four scales of measurement, expressed in terms of the natural numbers.

Heat Transfer

Molecules are the smallest physical particles of substances made up from proportions of atoms of the same or different elements. Heat is molecular motion. Heat is transfered in proportion to the concentration of molecules, because the greater the concentration, the more probable are collisions between molecules, and the greater is their resulting dispersion or diffusion.

Likewise in elections, the probability, of how many votes are transfered, is in proportion to the "concentration" or "conservation" of votes, in terms of the size of the quota required to elect representatives and the number of seats to elect them to. Candidates, with votes in a transferable surplus or in deficit of a quota, may be said to have a positive or negative dispersion of votes about the quota. Statistics can estimate the probability that the size of the dispersion shows a significant preference or corresponding lack of preference for those candidates.

Molecular motion tends to zero at the extrapolated absolute zero of temperature ( -273C ), beyond observable reality -- reality being observed in relative terms. Electorally, something close to an absolute zero of choice, between one candidate or none, is no real choice, because unrelated to any other candidate as an observable alternative.

Lyell and Malthus.

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Charles Lyell's Principles of Geology explained the appearance of the landscape by small cumulative changes, wrought mainly by aqueous and igneous agents, on the earth's crust. Lyell's theory moved away from the importance of catastrophic natural changes. True to the natural history of the planet, the Bible contains examples of devastating ordeals by flood and fire and probably asteroid impact. Hence the Bible doctrine of 'catastrophism.' Modern science has largely moved back to an emfasis on drastic, as well as gradual, transformations.

The Bible was taken as authority on life, in terms of sacrosanct special creations. John Milton envisaged such a spontaneous outburst, of the animals ready-made from the Earth, in Paradise Lost. Darwin's love, of these books, was a great and painful mental bloc to his conceiving an evolution of life forms, thru small cumulative changes, as Lyell conceived geological change.

Darwin knew that clerical authority would oppose this idea and planned only to publish after his death, as was the case with Copernicus' heliocentric hypothesis. But Alfred Wallace independently came up with Darwin's theory, actually trying out his ideas on Darwin, without knowing Darwin had long held the same opinion. This forced Darwin's hand. And Thomas Huxley relished defending the new theory in public debate with the clergy. Religious fundamentalists have continued to oppose 'Darwinism'.

The Bible had set man above the general run of creation. Hence, the religious reluctance to claim man's heritage as relatives in the family of life.This is reflected in Darwin's publications. The Origin Of Species only intimates that man, too, might be just another product of the evolution of life forms. He didnt really tackle this question till his later work, The Descent Of Man.

The Scholastic philosophy of 'Realism' had used the term to mean the reality of logical classes. Their opponents, the Nominalists had insisted that classifying was but the naming of things to identify them and become more familiar with one's surroundings. Nominalism implied testing one's knowledge against experience. The scientific attitude is based on this.

Linnaeus had conceived a general and special classification of species that broadly stands to this day. Linnaeus stands in relation to Darwin rather as Euclid's geometry stands to Einstein: Variations on straight-line geometry and variations on distinct species were long unquestioned, because resting on classical Greek and biblical authorities.

But taxonomists disagreed with each other's judgments, so one had to admit of 'doubtful forms'. Darwin said:

I was much struck how entirely vague and arbitrary is the distinction between species and varieties...
there is no infallible criterion by which to distinguish species and well-marked varieties...

I look at the term species, as one arbitrarily given for the sake of convenience to a set of individuals closely resembling each other, and that it does not essentially differ from the term variety, which is given to less distinct and more fluctuating forms.

The classification of species was a convenient way of bringing ordered understanding to the diversity of creatures. It didnt correspond absolutely to observation. Darwin was arguing like those descendants of the nominalists, his contemporaries, the American philosophers of 'pragmatism', from Charles Pierce onwards. Classification works as a useful approximation to reality rather than its complete determination.

Darwin pointed out that creatures have individuality that can cut across hard and fast distinctions between species. An underlying unity could be found to the divisions between life forms. For long, Darwin wondered on the mode or mechanism or means of growth to evolution as a tree of life branching out into different species.

Darwin's classical theory of natural selection combined the ideas of the reverend Malthus and Lyell. Malthus noted that population growth out-paced food production, rather as a geometric rate of increase exceeds an arithmetic rate of increase. The reverend advised 'moral restraint' in one's number of off-spring.
( Warning against over-population, Isaac Asimov was aware his readers would be wondering how many children he had. So, he gave the number in a foot-note. )

Independently taking their cue from Malthus, Darwin and Wallace realised there must be a competition between too many mouths chasing too little food. Those individuals with slight advantages over their fellows, in finding sustenance, would be more likely to survive and have their advantages passed on. Thus there was a prospect of advantages accumulating, till descendants became so differentiated that they became whole new species.

In one of his popular series of books on ethology, Robert Ardrey cites the case of animals doing sentry duty. This puts them in danger from delaying flight, while thumping a warning to the herd, being ambushed by predators coming up to full speed. He suggests that there may not only be a hereditary selfishness to promote individual survival but also a hereditary altruism to promote collective survival. Compare Kurt Vonnegut's remark: I believe in original sin. I also believe in original virtue.


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Gregor Mendel's breeding experiments on plants showed a statistical re-distribution of genes in reproduction. This provided a mechanism for the appearance of individual differences in species. Their natural selection would take place according to which differences confered a survival advantage.

The gene is a simple hereditary characteristic, such as eye color. Dominant and recessive genes may be likened to governing and opposition hereditary preferences for variations in that characteristic, such as brown or blue eyes. There are four logical possibilities of combination between dominant and recessive genes: one pure dominant, one pure recessive, one dominant-recessive and one recessive-dominant. The latter two count as two hybrids.

On grounds of chance, the combinations will appear in approximately these proportions of 1:2:1, which is known in statistics as an example of a binomial distribution. Mendel's ratio is an apparent three-to-one ratio, because the recessive gene, say the blue eye color, only shows up when two blue recessive genes combine.

I'm told that, in early infancy, I had blue eyes, before they turned brown. I assume that means a hybrid of dominant brown and recessive blue eye color.

Genetics was one of the earliest and most important refinements on Darwin's and Wallace's theory, which has under-gone much qualification -- 'evolved' -- ever since.

Genetic Information Transfer

Obviously modeled on the suffrage of one man one vote, "one gene, one enzyme" means a gene, which is a DNA ( deoxyribonucleic acid ) molecule, from a body cell nucleus, governs a protein catalyst of the chemical construction of life. A one-to-one relationship distinguishes classification, as measurement. On the ordinal scale of measurement, the genetic code is one of preference permutations in the four bases, found in living organisms in different proportions, for combining ( by electron sharing from bases to acids ) with the twenty amino acids found in proteins.

Prof. Bronowski said: "It is the number of amino acid differences which is the measure of the evolutionary distance between me and the other mammals". This suggests, on the interval scale, a "periodic table" for biological species comparable to that for chemical elements. The difference in the number of electrons of elements may be analgous to the number of amino acid differences in species. The mammals could be one of the periods in the biological table. Man, perhaps, begins a new period, if not merely ends an old one.

( My web page, on Scientific theories and methods of natural selection, mentions an inorganic natural selection of molecular structures, as preceding Darwin's natural selection of organic structures. )

The living cell nucleus divides in the form of chromosomes. Each species chromosomes have a specific "quota" of DNA, the double helix molecule, modeled on spiral steps of two pairs of bases. But the respective sums of the base partners exist from organism to organism in a variable proportion, called the "base ratio", our ratio scale of measurement. This was found to signify any order of base along the spiral strand.

The double helix splits with each side actIng as a mould or template. Such is the means of genetic information transfer, from nucleic acid to nucleic acid, when cells divide or when the genetic message is copied from the nucleus into the cell at large, and from nucleic acid to "body-building" protein. But not vice versa. The latter case would mean, in chemical effect, the Lamarckist inheritance of environmental adaptation, going against Francis Crick's "central dogma" of molecular biology.

The territorial surplus.

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Malthus advised the prudence of populations reproducing within the limits of subsistence afforded by their territories. Ethologists showed some species achieve this thru territorial mating rituals. But the territorial portions, to which reproduction is limited, still furnish quotas of survival, within which nature selects slight individual advantages to accumulate by heredity.

Wynne-Edwards said:

...evolution has favoured conventional modes of competition which limit numbers well below the carrying capacity of the habitat. Maybe animals do not compete for such direct rewards as food or females. They compete for symbols, like territory or high rank in a hierarchy which in turn present them with first access to food or females.

There is a hint of "the territorial imperative" in Darwin's first publication, Voyage Of The Beagle. This is his most enjoyable book of adventure round the world as ship's naturalist, gathering the evidence on which his theory would be based. In a foot-note, he says he was puzzled why horses never left the east end of the East Falkland Island. On a simple Malthusian notion, they should cover all the grazable land available till no further population could be fed.
Gauchos said the male possession of mares forced them to follow for their life, leaving foals to their death.

Territorial creatures resemble the medieval farmer who left some land fallow to recover its fertility. Having a territorial surplus of land, to that being used for sustenance, affords a safety margin of survival. Such practise follows the precept of Mr Micawber. Live just within your means, result: happiness. Live just outside your means, result: misery.

Measures of nature.

David Attenborough said: Life can be measured in the order of different species capacity to inhabit the most limited environment over the longest time to the most diverse environment in the shortest time. Evolution is then defined as this capacity of life on earth to "change the space-time co-ordinates", as it were, from the most simple to the most complex motor-sensory forms of "observers".

Time was believed to be a dislocated dimension of space, on which life is borne in a deterministic stream of events, issuing from a Prime Mover or God outside Nature, who is the only agent of free-will, setting in motion the machine of creation. Newton's mechanics implied such a theology. But a relativist space-time, in nature's transferable selection of life's motor-sensory co-ordinates, rather implies an evolutionary god of free-will growing out of nature.

The time taken for this evolutionary transformation follows a logarithmic interval scale. At first, the intervals of change are very far apart but each succeeding interval follows closer than the last. Evolution is measured on a logarithmic scale, as decreasing intervals represent accelerating stages of life's adaptation from the most limited to more diverse environments.

Natural selection and elections.

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Like Darwin's 'pragmatism' in biological classification of species, pragmatism in politics also requires parties to be considered no more than as broad classifications of continuous degrees of policy difference between individual politicians. And we may remember our political community, by voting for an individual order of preference, that can transcend party lines.

A partisan error is that all voters vote solely for a party. The product of this error is partisan voting systems that dont allow voters to prefer candidates, whether or not of the same party. This partisan fallacy is as if a biological variety, that can inter-breed, within a species was confused with a separate species that cannot inter-breed.

Cross party fertilizations of ideas would help parties to adapt and politics to evolve or transform itself thru the agency of transferable voting.

As Enid Lakeman concluded, in the standard work, How Democracies Vote:

A co-operative spirit is fostered, and its application is in the hands of those men and women most trusted by their electors; with the single transferable vote sharp divisions into mutually hostile factions are discouraged. Sweeping changes resulting from trifling causes are prevented, and gradual evolution in any direction desired by the bulk of the voters is facilitated.

Lyell's theory of slight cumulative changes on the earth's crust, led Darwin to search for such an agent on heredity. Like the gradations of choice in preference voting, it was easily ignored by dogmatism but vital to the understanding. This is an analogy of natural selection with STV elections by preference voting for individual variations, in or across rigid party classes, and quota counting the prefered individuals' political survival as representatives.

By analogy, the more natural selection ( or seats to elect to ) and the more survival quotas ( or vote quotas for differingly adaptable opinion patterns) the more variety of life ( or voters represented in their true variety of choice ).The more specialized species become, the more interdependent they become as an eco-system. A species relying too heavily on one vulnerable food source or a one-product economy is unstable because it is so dependent on fluctuations in its one product's fortunes.

The more competitive diversity in an ecology or an economy, the more possibilities for adaptation to adverse circumstances and therefore the more stability. But the more division of labor, the more interdependence of services and the more of a premium put on co-operation.

An ecological electoral system would have to combine these functions of competition in adaptive diversity and co-operation in stable interdependence. The unity in diversity that we've seen in transferable voting qualifies it for electoral democracy, or the rule of the people, considered ecologicly, as "biocracy" or the rule of life.

Diffusion equation of natural selection and elections.

On my web page about the diffusion equation, an electoral interpretation is given. It is possible to do the same for Darwinian biology with an analogy between elections by transferable voting and evolution by natural selection.

Darwin's theory appeared in 1859. The original version of STV appeared in 1857, as Hare's system ( independent of Andrae in Denmark in 1855 ). Darwin's work had been unpublished for many years. I dont know whether Wallace could have been at all influenced, at least unconsciously, by Thomas Hare's proposals. It seems unlikely.

Yet it is curious that coming up to mid nineteenth century Britain and nearby Denmark, two pairs of thinkers should independently make two first-rate discoveries, both following the logic of measurement.

The single transferable vote, STV consists of a preference vote for a proportional ( or quota ) count. Darwin's theory of natural selection was made-up of Lyell's principle of small cumulative changes applied to animals evolving ultimately into new species thru the accumulation of small hereditary advantages. Thus, nature wields a 'preference vote' in the form of genes with a survival order of value.

The reverse is also true. Many genetic mutations have an adverse survival value, which effect a reverse 'preference vote' for individual 'candidates' in the contest to survive. ( In fact, Ive suggested a Reversible STV for elections. )

Besides the Lyell factor, Darwin's theory consists of a Malthus factor based on the limits of sustenance, which only supports a given quota of a species. Natural selection is nature's genetic preference vote for a survival quota, that is evolution's 'transferable vote'.

The naturally selected individual 'candidates' become hereditary 'representatives' of the next generation's genetic make-up or 'votes'. Biologists consider 'the gene pool' typically as a normal distribution of all the genes of a given species.

Elsewhere, in discussing the diffusion equation, the distribution of votes was treated as a dependent variable on the number of candidates prefered per voter. By analogy, this could become the distribution of advantagous genes, dependant on the number of individuals nature prefers with an advantagous gene.

The diffusion equation is of a distribution spreading over time, as well as in space. A ( geometric ) growth in the number of voters may correspond to ( arithmetic ) growth in the number of candidates prefered per voter. A ( geometric ) growth of the advantagous gene pool may come with ( arithmetic ) growth in the number of individuals prefered by an advantagous gene.

STV elections are a multi-member system that often allows different numbers of representatives ( or 'seats' ) per constituency. Densely populated cities have more seats than sparsely populated rural areas. This keeps constituency boundaries true to natural communities. This forms another statistical distribution: The distribution of constituencies depends on the number of seats per constituency. If most communities have an average of, say, 4 or 5 seats per constituency, then there will be few single or double member constituencies for the sparsest areas and few 8 or 9 member constituencies for the densest areas.

Constituencies can be thought-of as made up of communities which contain randomly mixed proportions of rural and urban districts. The population extremes are those few areas made up solely of sparse districts or solely of dense districts. On theoretical grounds of chance, most communities will be more or less a mixture of sparse and dense districts, the average being half and half.

This situation readily carries over into an ecology of fertile and barren habitats, supporting greater or lesser proportions of population. Constituencies as 'environments' ( say ) combine more or less districts as 'habitats' ( say ). Such environments carry different numbers of hereditary 'representatives' of a species.

The diffusion equation or heat conduction equation has a constant as well as variable factors. When habitats are classed into sparse and dense, the simplest assumption is a constant ( of probability ) of a half of each kind of habitat. The resulting distribution gives the dependent variable in terms of the binomial distribution.
( Another of my web pages takes into account skewed distributions, also, in field-like distributions of two dimensions. )

The constant of probability can be increasingly refined. The constant could be set at probability a third, for each of three kinds of habitat, say: forest, grass-land and scrub. This would solve the dependent variable in terms of the trinomial distribution. In general, a multinomial distribution is arrived-at, depending on how the constant is adjusted to measure the lie of a land.

Voters and candidates, or genes and individuals, have a geometric to arithmetic relation in time-dependence of the diffusion equation. The same applies to constituencies and representatives, or environments and survivors. On the assumption of randomly distributed fertile and barren habitats within environments, geometric increase in environments only sees an arithmetic increase in survivors.

In physics, the diffusion equation only works as a simple closed system, wherein the same amount of heat is conserved in the whole, even as it gradually disperses thru the system. Whereas, in ecology, the inter-relations between species can be too complex to be experimentally reproduced in a conservation zone.

But economics' adoption, of an open system of unlimited economic growth, chasing 'insatiable' consumption, using-up non-renewable resources, is rapidly destroying life on earth. Life is sustained on the feed-backs of an eco-system, even with some continual input, such as the sun's energy.

Further sources:

Krauskopf and Beiser, Fundamentals of Physical Science. 1969.
C D Darlington, Genetics and Man. 1966.
J M Smith, The Theory of Evolution. 1966.
O Gillie, The Living Cell. 1971.
Wells, Huxley and Wells, The Science of Life. 1938.

Richard Lung.
1981; 28 March 2004.

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