Memory retrieval as a p-adic dynamical system.

We propose a mathematical model of the memory retrieval process based on dynamical systems over a metric space of p-adic numbers representing a configuration 'space of ideas' in which two ideas are close if they have a sufficiently long common root. Our aim is to suggest a new way of conceptualizing human memory retrieval that might be useful for simulation purposes or for the construction of artificial intelligence devices, as well as for a deeper understanding of the process itself. The dynamical system is assumed to be located in a blackbox processing unit (the 'subconscious') and controlled by an interface control unit (the 'conscious') that fixes parameters in the dynamical system and starts its iteration by sending an initial generating idea to it. We show that even simple p-adic dynamical systems admit behavioral scenarios that could explain some of the essential features of the human memory retrieval process.

Slower aging in women: a proposed evolutionary explanation.

Differential female longevity is so far unexplained in evolutionary terms. The theory of evolutionarily necessary aging which goes back to Wallace appears to be up to the task. In this theory, aging minimizes competition between forebear and offspring. The aging equation which is implicit contains the well-known empirical Gompertz law as a special case. Moreover, its parameters are automatically sex-specific. It is shown that the slower aging of the female members of two species of mammals, humans and sperm whales, can be 'predicted' on the basis of this equation. A prediction of effective human monogamy under archaic conditions is obtained as a corollary. The analogous if opposite prediction for sperm whales (strong promiscuity) is empirically testable.

Artificial life extension. The epigenetic approach.

An epigenetic approach starts out from the direct (rather than the underlying genetic) causes. An epigenetic approach to aging has little chance of succeeding before a minimum amount of knowledge has been accumulated on the "genetic programming" that is currently believed to underlie aging. Two recent advances, one empirical and one theoretical, jointly brighten the prospect. The empirical one is the discovery that melatonin functions as an aging-controlling hormone in mammals. In 1979, Dilman and co-workers isolated a biologically active pineal extract (epithalamin) in rats which, as they later showed, stimulates melatonin production. Pierpaoli and co-workers in 1987 directly administered melatonin to mice. Both groups observed a surprising 25-percent increase of life span in conjunction with a postponed senescence. A similar effect was also achieved with an engraftment of young pineal tissue into the thymus of old mice by Pierpaoli's group. Beneficial effects of epithalamin in humans were reported by Dilman's group. The second advance is a deductive evolution-theoretical approach to aging discovered in 1988. In populations living in a niche with a fixed carrying capacity, any individual is in the long run replaced by a single successor. It follows that, as the expected cumulative number of adult progeny of the same sex approaches unity as a function of life time of the progenitor, the latter's survivability must approach zero if the sum is to remain unity. A physiological prediction follows: a centralized physicochemical clock--like a sedimentation process--must exist somewhere in the organism controlling a secreted substance that reaches all cells. In this way, the pineal coacervates and the pineal's hormonal product melatonin were arrived at on an independent route again. While melatonin as a drug has been used on human volunteers for decades, its anti-aging effect has yet to be proved. Detailed hormone profiles in different age groups and under different life styles have to be performed. A modified Hayflick in vitro experiment is also needed to elucidate the mechanism by which melatonin works in cells.

Timekeeping in genetically programmed aging.

Genetically programmed aging, with its cellular genetic switching implied by the in vitro Hayflick limit, requires additional timing devices to coordinate the switching processes within the different cells of a highly complex life form. Evolutionary arguments have been presented elsewhere to support the need for a centralized timing mechanism as against a localized mean-field alternative. Extensive evidence is now available for the role of the pineal gland and its secreted melatonin in the aging process. The nightly melatonin peak changes with age, thus providing a potential signal to inform all of the cells in the organism of its age. Here it is hypothesized that the decoding of this "durational signal" at the cellular level is carried out with the aid of the sleep induced pCO2 changes in the blood. To test this hypothesis, modifications of the in vitro Hayflick experiment and of the in vivo Pierpaoli longevity experiment involving rhythmic addition of melatonin and pH manipulations are proposed.

Does a centralized clock for ageing exist?

It is proposed that a centralized clock controlling ageing is located in the pineal gland with the calcification process occurring there providing a highly accurate bio-inorganic timing mechanism and the secreted melatonin carrying a signal to all cells in the organism. An explicit programme of data gathering and experiments suitable for the falsification of the proposal, which is consistent with presently known anatomical and physiological facts, is presented. The underlying motivation comes from evolutionary biology and the invariance, that is the allometry, of life expectancy curves.

A predictive model for life expectancy curves.

Life expectancy curves have a characteristic ominous shape that has fascinated scientists for centuries. Medawar was the first to explain this shape, specifically the steeply rising proneness of an average individual to die as a function of age, in evolutionary terms. The idea was that the "selective value" of the individual decreases as it has triggered other individuals taking its place (and carrying its genes) into existence. We demonstrate that this idea can be turned into a quantitative model. The resulting 4-parameter function reproduces well two well-known life expectancy curves from the first half of this century. Moreover, the easily interpretable parameters (3 of the 4) seem intuitively reasonable.