Medical Hypotheses I
Mebid
i?)pdwu (1992) 29.291-294 oLqmmnG7ulpuKlAd1992
Ageing, Information and the Magical Number Seven J. A. MORRIS Department
of Pathology,
Lancaster
Moor Hospital, Lancaster
LA 1 3JR,
UK
Abstract-Concepts from information theory are applied to human ageing. An equation is derived, based on the general properties of information systems, which closely predicts the mortality rate in old age. The same equation predicts that infection will be increasingly severe when first exposure to micro-organisms is delayed leading to diseases which peak in early and middle age. A parameter of the equation is the level of redundancy in human information processing. Observed mortality rates show that this is sevenfold and it is suggested that seven is a fundamental dimensionless biological constant.
Introduction The concept that information theory or statistical decision theory (1) can be applied to an analysis of the age incidence of human disease has been examined in a number of recent articles (2, 3, 4). The idea is that the interaction between a biological system and the environment can be analysed in terms of infon-nation flow. The biological system must make correct decisions on the basis of the information presented in order to maintain its integrity. Incorrect decisions, and inappropriate responses based on those decisions, will compromise integrity and contribute to disease. There are certain features which are common to all information processing systems: 1. Information systems have a finite capacity. 2. All information systems operate in noise so that there is a finite chance of error even with an optimal decision strategy. 3. The components of an information system are subject to the laws of entropy so that perforDate received 4 June 1992 Date accepted 10 July 1992
mance will deteriorate with time and the error rate will rise. 4. Most information systems are highly redundant. This reduces the error rate and influences the way in which the error rate changes with time. These features can be applied directly to the study of human disease and give some insight into the way disease incidence changes with age. The decision theory model A complex biological system needs to make many, perhaps thousands, of decisions per minute. These will vary from setting appropriate immune responses to potentially lethal micro-organisms to minor adjustments to the internal mileu. All these decisions are subject to error and thus damage will accumulate. If a mistake is sufficiently serious death could occur.
291
292 Consider any single independent decision system faced with a potentially lethal challenge: The chance of a fatal mistake = 1 - R, where R = probability of a correct decision. If the components of the decision system decay at random with time then, the chance of a fatal mistake at time t = 1 - Re-h where k = decay constant If there are n identical but independent decision systems the chance of a fatal mistake at time t = (1 Re-kt)“. the probability of death in any year = c(1 Re-kt)” where c = number of potentially fatal events per Year. The equation allows for the intrinsic performance of the decision process (R), the laws of entropy (k) and redundancy (n). In practice the components of a biological system are complex and interdependent not identical and independent as assumed above. The equation, however, is a mathematical absuaction and the value of n can be regarded as a measure of redundancy in the system. It does not equate to the number of components in the system. The equation relates the probability of serious disease or death to age. It predicts that the incidence of disease will rise with age and a plot of log incidence against log age will be approximately linear with a maximum slope of n. In other words the maximum slope of the curve relating log incidence to log age is a measure of the redundancy in the system.
MEDICAL HYPDTHESE.3
the function c (1 - Re-kt)n to these curves. In which case n takes a value of seven.
l
MALES -----*
THEORETlRALCURVE
-
FEMALES
Diseases in late life The integrity of human beings is maintained by the efficient functioning of many body systems. Information theory indicates that these systems are fallible and their performance will deteriorate with time. It can be assumed, however, that evolution will lead to an optimal distribution of information processing capacity so that potentially lethal errors in different systems are reduced to a comparable extent. In other words the chance of error in different systems will rise at similar rates and this explains the observations made by Burch (5, 6, 7), amongst others, that the age incidence of the common killing diseases of old age are similar. A plot of incidence against age for ischaemic heart disease, the common cancers and overall mortality all show an exponential increase. In Figures 1 and 2 the mortality rate by age is shown for men and women in England and Wales in 1988. In Figure 2 a plot of log of mortality rate against log of age is approximately linear for both men and women with a maximum slope close to seven. Similar relationships have been shown for ischaemic heart disease (6) and cancer (7). It is straight forwards to fit
30
40
60
60
70
60
AGE (YEARS) -
1 The mortality rate by age for men and women in England andWalesin 1988 together with a theoretical curve generated by the function (1 - Re-hy where R = 0.999, n = 7, k = 0.00174 per Fig.
year, and c = l@ per year.
In the case of ischaemic heart disease there are many processes involved. These include endothelial cell ulceration and repair, systems controlling the inflow and removal of lipid from the intima, the proliferative response to intimal lipid and systems controlling blood coagulation and lysis. All these processes require intricate control. As these controls deteriorate with time the chance of significant ischaemic heart
disease rises. In the case of cancer the mechanisms involved are quite different but the concept of progressive damage to information systems leading to a rapid rise in incidence with age still applies. The information con-
293
AGEING. INFORMATION AND THE MAGICAL NUMBER SEVEN
eases rise in incidence at comparable rates. The theory also makes it clear that there is no single cause of ageing other than the laws of entropy which will become manifest in every facet of bodily function. Diseases of early life
so
m
79
II)
AGE YEARS(LCIQSCALE) Fig. 2 The mortality rate by age for men and women in England and Wales in 1988 plotted on a log-log scale. The maximum slope is 6.8 for males and 7.04 for females.
trolling cell function is coded in DNA. With each cell division there is a finite change of mutation leading to damage to part of the DNA. The system is redundant, however, in that several specific mutations are required in a single cell before a malignant clone arises. Thus the age incidence is determined by progressive damage to an information system which is highly redundant. In addition there are other information processes involved. These include error prone systems of DNA repair and possibly error prone systems concerned with eliminating or suppressing malignant clones. Their function will also deteriorate with time. Similar arguments can be applied to infections, such as bronchopneumonia, caused by common organisms and to diseases leading to progressive impairment of cerebral or pulmonary function. In each case the mechanisms are different but the central principle of deterioration in handling information applies. The information theory helps one to understand why disease increases in incidence with age. In fact it goes further and shows that such an increase is inevitable. It also shows why completely different dis-
The information theory predicts that disease will become more common with advancing age. There are, however, a number of specific conditions which have their peak incidence in early or middle life. These diseases can also be explained in terms of this model. More importantly age incidence curves which deviate from a steady increase with age gives clues to the pathogenic mechanisms involved. The best examples are diseases caused by first exposure to specific micro-organisms. If the chance of encountering a specific organism is constant from year to year then the percentage of the population who have not encountered the organism and are susceptible to it will fall exponentially with age. According to the information model the chance of serious disease occurring on first exposure will rise with age according to the function (I - Re-ki)“. The age incidence curve will be the resultant of these two processes and it has been shown elsewhere that this leads to a curve which rises to a peak and then falls (2,4). For common organisms the exponential curve of susceptibility will fall rapidly and the peak will be in early life. For less common organisms the peak will be delayed till later life. First exposure to micro-organisms can lead to infectious diseases such as infectious mononucleosis and poliomyelitis. In addition first exposure could trigger autoimmune disease, perhaps by molecular mimicry, and this might be important in multiple sclerosis (4) diabetes mellitus (8) and psoriasis (3). All these conditions have distinctive age incidence curves which peak in early or middle life (9, 10, 11). It has been shown elsewhere that the mathematical functions from information theory can be used to closely match the general form of the age incidence of these conditions (2, 3,4). A special and interesting case is the age incidence of childhood acute lymphoblastic leukaemia (ALL). In this case the incidence rises to a peak at 3-4 years and then falls rapidly (12). This can also be explained as the resultant of two processes. 1) Lymphocyte proliferation, driven by first exposure to micro-organisms, leads to the generation of malignant clones. The rate of exposure to new antigens will be maximal at birth and lymphocyte proliferation rate will decrease steadily thereafter. 2) Impaired rejection of malignant
294 clones governed by the ageing function-(1 - Re-kt)n. This has been explored in detail elsewhere (13, 14). In general terms if the number of decisions to be made falls progressively from birth but the chance of error rises then the incidence will peak in early or middle life. The magical number seven Miller wrote a classical article on human information processing entitled ‘the magical number seven’ (15). In it he noted that when human performance is analysed in terms of information theory the number seven has a prominent role. There are seven items in short term memory and seven categories of absolute judgement. Thus when subjects are asked to estimate along a visual or auditory continuum they seem to be able to use seven categories but no more. This is illustrated by the convention of using seven notes on a musical scale and more fundamentally by the fact that our brains recognise seven colours in the rainbow in spite of the fact that it is a continuum of electromagnetic radiation. Miller also noted that seven has been regarded as a magical number throughout human history. There are seven wonders of the ancient world, seven seas, seven deadly sins, seven daughters of Atlas in the Pleiades, seven ages of man, seven levels of hell and seven days in the week. It is therefore of considerable interest that when human disease and mortality is analysed in terms of information theory that the number seven reappears as the level of redundancy in DNA. Is this just coincidence? It could be. However if there is sevenfold redundancy in human information processing then seven is a fundamental biological constant and it will appear in all aspects of
MEDICAL HYKYIIESES
human behaviour, human disease and human mythology. References 1. Green D M. Swets J A. Signal detection theory and psychophysics. London: John Wiley and Sons, 1%6. 2. Morris J A. Autoimmunity: a decision theory model. J Clin 3. 4. 5. 6. I. 8.
9.
10. 11. 12.
13. 14. 15.
Pathol 40: 210-215, 1987. Morris J A. The age incidence of psoriasis. Clin Exp Dermatol 14: 92-93, 1989. Morris J A. The age incidence of multiple sclerosis: a decision theory model. Medical Hypotheses 32: 125-135. 1990. Burch P R J. Mutation, autoimmunity and ageing. Lancet ii: 299-300, 1963. Burch P R J. Cardiovascular diseases: new aetiological considerations. Am Heart J 67: 139-40, 1%4. Burch P R J. The biology of cancer: a new approach. Lancaster M T P Press, 1976. Morris J A. A possible role for bacteria in the pathogenesis of insulin dependent diabetes mellitus. Medical Hypotheses 29: 231-236, 1989. Acheson E D. The epidemiology of multiple sclerosis. In: McAlpine’s multiple sclerosis (Matthews W B. Acheson E D, Batchelor J R, Weller R 0, eds) Edinburgh: Churchill Livingstone, 346, 1985. Bloom A, Hayes T M, Gamble D R. Register of newly diagnosed diabetic children. BMJ 3: 580-583. 1975. Farber E M. NaU M L. The natural history of psoriasis in 5.600 patients. Dermatologica 148: l-18, 1974. Greaves M F, Pegram S M. Chan L C. Collaborative group study of the epidemiology of acute lymphoblastic leukaemia subtypes: background and first repott. Leuk Res 9: 715-33. 1985. Morris J A. A mutational model of leukaemogenesis. J Clin Pathol 42: 337-340. 1989. Morris J A. The age incidence of childhood scum lymphoblastic leukaemia. Medical Hvuotheses 35: 4-10. 1991. _. Miller G A. The magical number seven, plus or minus two: scsne limits on our capacity for processing information. In: The psychology of communciation. Penguin Press, London, 1968.
Mebid
i?)pdwu (1992) 29.291-294 oLqmmnG7ulpuKlAd1992
Ageing, Information and the Magical Number Seven J. A. MORRIS Department
of Pathology,
Lancaster
Moor Hospital, Lancaster
LA 1 3JR,
UK
Abstract-Concepts from information theory are applied to human ageing. An equation is derived, based on the general properties of information systems, which closely predicts the mortality rate in old age. The same equation predicts that infection will be increasingly severe when first exposure to micro-organisms is delayed leading to diseases which peak in early and middle age. A parameter of the equation is the level of redundancy in human information processing. Observed mortality rates show that this is sevenfold and it is suggested that seven is a fundamental dimensionless biological constant.
Introduction The concept that information theory or statistical decision theory (1) can be applied to an analysis of the age incidence of human disease has been examined in a number of recent articles (2, 3, 4). The idea is that the interaction between a biological system and the environment can be analysed in terms of infon-nation flow. The biological system must make correct decisions on the basis of the information presented in order to maintain its integrity. Incorrect decisions, and inappropriate responses based on those decisions, will compromise integrity and contribute to disease. There are certain features which are common to all information processing systems: 1. Information systems have a finite capacity. 2. All information systems operate in noise so that there is a finite chance of error even with an optimal decision strategy. 3. The components of an information system are subject to the laws of entropy so that perforDate received 4 June 1992 Date accepted 10 July 1992
mance will deteriorate with time and the error rate will rise. 4. Most information systems are highly redundant. This reduces the error rate and influences the way in which the error rate changes with time. These features can be applied directly to the study of human disease and give some insight into the way disease incidence changes with age. The decision theory model A complex biological system needs to make many, perhaps thousands, of decisions per minute. These will vary from setting appropriate immune responses to potentially lethal micro-organisms to minor adjustments to the internal mileu. All these decisions are subject to error and thus damage will accumulate. If a mistake is sufficiently serious death could occur.
291
292 Consider any single independent decision system faced with a potentially lethal challenge: The chance of a fatal mistake = 1 - R, where R = probability of a correct decision. If the components of the decision system decay at random with time then, the chance of a fatal mistake at time t = 1 - Re-h where k = decay constant If there are n identical but independent decision systems the chance of a fatal mistake at time t = (1 Re-kt)“. the probability of death in any year = c(1 Re-kt)” where c = number of potentially fatal events per Year. The equation allows for the intrinsic performance of the decision process (R), the laws of entropy (k) and redundancy (n). In practice the components of a biological system are complex and interdependent not identical and independent as assumed above. The equation, however, is a mathematical absuaction and the value of n can be regarded as a measure of redundancy in the system. It does not equate to the number of components in the system. The equation relates the probability of serious disease or death to age. It predicts that the incidence of disease will rise with age and a plot of log incidence against log age will be approximately linear with a maximum slope of n. In other words the maximum slope of the curve relating log incidence to log age is a measure of the redundancy in the system.
MEDICAL HYPDTHESE.3
the function c (1 - Re-kt)n to these curves. In which case n takes a value of seven.
l
MALES -----*
THEORETlRALCURVE
-
FEMALES
Diseases in late life The integrity of human beings is maintained by the efficient functioning of many body systems. Information theory indicates that these systems are fallible and their performance will deteriorate with time. It can be assumed, however, that evolution will lead to an optimal distribution of information processing capacity so that potentially lethal errors in different systems are reduced to a comparable extent. In other words the chance of error in different systems will rise at similar rates and this explains the observations made by Burch (5, 6, 7), amongst others, that the age incidence of the common killing diseases of old age are similar. A plot of incidence against age for ischaemic heart disease, the common cancers and overall mortality all show an exponential increase. In Figures 1 and 2 the mortality rate by age is shown for men and women in England and Wales in 1988. In Figure 2 a plot of log of mortality rate against log of age is approximately linear for both men and women with a maximum slope close to seven. Similar relationships have been shown for ischaemic heart disease (6) and cancer (7). It is straight forwards to fit
30
40
60
60
70
60
AGE (YEARS) -
1 The mortality rate by age for men and women in England andWalesin 1988 together with a theoretical curve generated by the function (1 - Re-hy where R = 0.999, n = 7, k = 0.00174 per Fig.
year, and c = l@ per year.
In the case of ischaemic heart disease there are many processes involved. These include endothelial cell ulceration and repair, systems controlling the inflow and removal of lipid from the intima, the proliferative response to intimal lipid and systems controlling blood coagulation and lysis. All these processes require intricate control. As these controls deteriorate with time the chance of significant ischaemic heart
disease rises. In the case of cancer the mechanisms involved are quite different but the concept of progressive damage to information systems leading to a rapid rise in incidence with age still applies. The information con-
293
AGEING. INFORMATION AND THE MAGICAL NUMBER SEVEN
eases rise in incidence at comparable rates. The theory also makes it clear that there is no single cause of ageing other than the laws of entropy which will become manifest in every facet of bodily function. Diseases of early life
so
m
79
II)
AGE YEARS(LCIQSCALE) Fig. 2 The mortality rate by age for men and women in England and Wales in 1988 plotted on a log-log scale. The maximum slope is 6.8 for males and 7.04 for females.
trolling cell function is coded in DNA. With each cell division there is a finite change of mutation leading to damage to part of the DNA. The system is redundant, however, in that several specific mutations are required in a single cell before a malignant clone arises. Thus the age incidence is determined by progressive damage to an information system which is highly redundant. In addition there are other information processes involved. These include error prone systems of DNA repair and possibly error prone systems concerned with eliminating or suppressing malignant clones. Their function will also deteriorate with time. Similar arguments can be applied to infections, such as bronchopneumonia, caused by common organisms and to diseases leading to progressive impairment of cerebral or pulmonary function. In each case the mechanisms are different but the central principle of deterioration in handling information applies. The information theory helps one to understand why disease increases in incidence with age. In fact it goes further and shows that such an increase is inevitable. It also shows why completely different dis-
The information theory predicts that disease will become more common with advancing age. There are, however, a number of specific conditions which have their peak incidence in early or middle life. These diseases can also be explained in terms of this model. More importantly age incidence curves which deviate from a steady increase with age gives clues to the pathogenic mechanisms involved. The best examples are diseases caused by first exposure to specific micro-organisms. If the chance of encountering a specific organism is constant from year to year then the percentage of the population who have not encountered the organism and are susceptible to it will fall exponentially with age. According to the information model the chance of serious disease occurring on first exposure will rise with age according to the function (I - Re-ki)“. The age incidence curve will be the resultant of these two processes and it has been shown elsewhere that this leads to a curve which rises to a peak and then falls (2,4). For common organisms the exponential curve of susceptibility will fall rapidly and the peak will be in early life. For less common organisms the peak will be delayed till later life. First exposure to micro-organisms can lead to infectious diseases such as infectious mononucleosis and poliomyelitis. In addition first exposure could trigger autoimmune disease, perhaps by molecular mimicry, and this might be important in multiple sclerosis (4) diabetes mellitus (8) and psoriasis (3). All these conditions have distinctive age incidence curves which peak in early or middle life (9, 10, 11). It has been shown elsewhere that the mathematical functions from information theory can be used to closely match the general form of the age incidence of these conditions (2, 3,4). A special and interesting case is the age incidence of childhood acute lymphoblastic leukaemia (ALL). In this case the incidence rises to a peak at 3-4 years and then falls rapidly (12). This can also be explained as the resultant of two processes. 1) Lymphocyte proliferation, driven by first exposure to micro-organisms, leads to the generation of malignant clones. The rate of exposure to new antigens will be maximal at birth and lymphocyte proliferation rate will decrease steadily thereafter. 2) Impaired rejection of malignant
294 clones governed by the ageing function-(1 - Re-kt)n. This has been explored in detail elsewhere (13, 14). In general terms if the number of decisions to be made falls progressively from birth but the chance of error rises then the incidence will peak in early or middle life. The magical number seven Miller wrote a classical article on human information processing entitled ‘the magical number seven’ (15). In it he noted that when human performance is analysed in terms of information theory the number seven has a prominent role. There are seven items in short term memory and seven categories of absolute judgement. Thus when subjects are asked to estimate along a visual or auditory continuum they seem to be able to use seven categories but no more. This is illustrated by the convention of using seven notes on a musical scale and more fundamentally by the fact that our brains recognise seven colours in the rainbow in spite of the fact that it is a continuum of electromagnetic radiation. Miller also noted that seven has been regarded as a magical number throughout human history. There are seven wonders of the ancient world, seven seas, seven deadly sins, seven daughters of Atlas in the Pleiades, seven ages of man, seven levels of hell and seven days in the week. It is therefore of considerable interest that when human disease and mortality is analysed in terms of information theory that the number seven reappears as the level of redundancy in DNA. Is this just coincidence? It could be. However if there is sevenfold redundancy in human information processing then seven is a fundamental biological constant and it will appear in all aspects of
MEDICAL HYKYIIESES
human behaviour, human disease and human mythology. References 1. Green D M. Swets J A. Signal detection theory and psychophysics. London: John Wiley and Sons, 1%6. 2. Morris J A. Autoimmunity: a decision theory model. J Clin 3. 4. 5. 6. I. 8.
9.
10. 11. 12.
13. 14. 15.
Pathol 40: 210-215, 1987. Morris J A. The age incidence of psoriasis. Clin Exp Dermatol 14: 92-93, 1989. Morris J A. The age incidence of multiple sclerosis: a decision theory model. Medical Hypotheses 32: 125-135. 1990. Burch P R J. Mutation, autoimmunity and ageing. Lancet ii: 299-300, 1963. Burch P R J. Cardiovascular diseases: new aetiological considerations. Am Heart J 67: 139-40, 1%4. Burch P R J. The biology of cancer: a new approach. Lancaster M T P Press, 1976. Morris J A. A possible role for bacteria in the pathogenesis of insulin dependent diabetes mellitus. Medical Hypotheses 29: 231-236, 1989. Acheson E D. The epidemiology of multiple sclerosis. In: McAlpine’s multiple sclerosis (Matthews W B. Acheson E D, Batchelor J R, Weller R 0, eds) Edinburgh: Churchill Livingstone, 346, 1985. Bloom A, Hayes T M, Gamble D R. Register of newly diagnosed diabetic children. BMJ 3: 580-583. 1975. Farber E M. NaU M L. The natural history of psoriasis in 5.600 patients. Dermatologica 148: l-18, 1974. Greaves M F, Pegram S M. Chan L C. Collaborative group study of the epidemiology of acute lymphoblastic leukaemia subtypes: background and first repott. Leuk Res 9: 715-33. 1985. Morris J A. A mutational model of leukaemogenesis. J Clin Pathol 42: 337-340. 1989. Morris J A. The age incidence of childhood scum lymphoblastic leukaemia. Medical Hvuotheses 35: 4-10. 1991. _. Miller G A. The magical number seven, plus or minus two: scsne limits on our capacity for processing information. In: The psychology of communciation. Penguin Press, London, 1968.
