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Credit: "Szilard's Theory of Aging". Source: Wellcome Collection.
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![Writing 2m' (5) we may write In - = m[£ + pfil - (£ + p)], (6) J provided r <C .c 2m (i.e., p £ — 1) jt- In 1 = my 2 (I - ,), r 1 (7) 1 S Jt where r¡ = £ + p. Tn place of equation (7) we may write, in our approximation, / — [1 — (1 — ; Uj U, / 4 * rnA < (8) We may also write inversely ^ CM- ^ /A ^ rc . 1 V = In : . /■ .1^, / (9) i _ Vi - f 1/m ' V-'' or, expanding, V = 4/ ' In -. + In ~ ~ (10) m j 2m J According to the assumption of the crude theory, /, the surviving fraction of the somatic cells, reaches the critical value /* at the age of death, which we designate by t r . Further, we designate by x T the average number of aging hits suffered in toto, up to the age of death, by the m pairs of homologous chromosomes of the somatic cells. Thus we have, at the age of death, X, = tr = 2 m£ (11) r and X ' + r /io\ V = — —• 2m Accordingly, we may write at the age of death, where we have f = f*, from equation (8), ln \_u-rrr ■ r\ J * 4m \ 2m J Similarly, we may write at the age of death, from equation (10), X, + r = -4/4m In A + In A (14) or tr + r = 4/4 m ln A + In A. (15) For the genetically perfect female, for whom we have r = 0, we shall designate the age at death by t 0 . We shall call t 0 the life-span of the species. From equation (15) we may write for, the life-span, / 0 , (16) or t T = ¿o — TV (17) Ol io - tr r = (18) As may be seen from equation (17), the addition of one fault to the genetic makeup of an individual shortens the life of that individual by At = r, so that we may write Ai per fault = r. (19) This expresses one of the basic results of our theory. According to equation (19), an individual whose genetic makeup contains one fault more than another individual has a life-expectancy which is shorter by r, the basic time interval of the aging proc ess. This holds true within the crude theory for individuals who have inherited a small number of faults. Concerning the life-span, to, we may write, from equations (11), (13), and (16), In A = — (-)Yl - l ta \ (20) /* 4 m\T/\ 2m r and, from equations (15) and (16), we may write ío = J4m ln A + In A. (21) The Distribution of the Ages at Death. —The above equations hold within the framework of the crude form of the theory. In this form of the theory, members of one cohort would die only in certain years—at the critical ages, t r —and thus the years in which death occurs within one cohort would be separated from each other by time intervals of r years; no deaths would occur in the intervening years. Further, if the distribution of the faults in the population is random, then the number of deaths, P r , occurring at each age, is given by the Poisson distribution: 71 r 6 )l Pr = ~ (22) ri f ¿ where, according to equation (18), we have r = r and where n stands for the r average number of faults per individual.](https://iiif.wellcomecollection.org/image/b18184078_PP_CRI_H_2_29_0004.jp2/full/800%2C/0/default.jpg)
