For a biological timekeeping
Scarborough, April 15th, 2006
This short essay has been written for the “festschrift” to honour
Prof. Dr. Don Bradshaw
Time Wisdom bits
There is surely nothing other than the single purpose of the present moment.
A man’s whole life is a succession of moment after moment. If one fully understands the present moment, there will be nothing else to do, and nothing else to pursue.”
-Yamamoto Tsunetomo, Hagakure-
Time is not a line, but a series of now-points.
Time has no division to mark its passage, there is never a thunderstorm or blare of trumpets to announce the beginning of a new month or year. Even when a new century begins it is only we mortals who ring bells and fire pistols.
-Thomas Mann, The Magic Mountain-
Time is money, but money is not time. (WA anonymous)
Ticking up the moments that make a dull day
You fritter and waste the hours in an offhand way.
…You are young and life is long and there is time to kill today
and then one day you find ten years have gone behind you.
Every year is getting shorter; never seem to find the time…
“Time” from The Darker Side of the Moon
Men have always been curious about “time”. Our fore fathers felt the changes in nature, saw the movement of the stars and of the sun, seasonal changes, night and day and wisely attributed them to the Gods in charge of each specific environment.
The doubt about the essence of time as something that “moves” or “flows” or as something that “stays” while we stroll through has been obscure for millennia. Even today the definition of time does not supply an answer to the question. The matter became even more complex with Hermann Minkowski’s space (four dimensional space-time as presented in his book “Space and Time” 1907) and the subsequent special theory of relativity by Albert Einstein and its various interpretations does not explain the essence of time. The idea of a curved space-time is fascinating but difficult to grasp. As for the relationship of the curved space-time with gravity that is not an easy concept either, at least for me.
The master of Christianity’s philosopher Augustine who thought a lot about time, gave up and said: “I know what it is, but I cannot explain it!”
It’s interesting to notice that also electricity is known as a phenomenon, but mysterious in its essence. But I am not qualified to elaborate any further about that.
For centuries. the measurement of time was in fact the recording of the movement of the sun during the day and of the stars during the night. In relatively recent human history (300-400 B.C.) tools different from sundials were devised as water clocks and clepsydrae. The first mechanical clocks were built around 1400. The first ones were based on the isochronous pendulum then on the double pendulum and around 1700 by a spring-operated motor connected to an oscillating escapement.
When the Roman Consul Messalla brought the first sundial to Rome from Catania (Sicily) and placed it in the centre of the Forum without any adaptation to negotiate the different latitude, the Romans used it for a whole century, unaware of or disregarding the structural error. Plinius the Elder commented with sarcasm, but disregard for the exact time is still today a peculiar trait of the Roman culture, where it is a current habit, if not an institution, to be at least half an hour late. Romans have been smart to stamp punctuality as a somewhat negative habit, of more concern to plebeian society.
One peculiarity of Roman timekeeping is that the subdivision of the daylight time into twelve periods implied the subdivision of the night into twelve periods. Night “hours” were longer or shorter than day “hours” according to the season. Only on the equinox would the night and the day “hours” be of the same duration.
The great Roman timekeeper after the year 10 BC was the obelix in Campo Marzio erected by Octavian Augustus. Recent archaeological excavations brought to light the marble slabs with the hour signs traced into them, marking the time of the day as the shadow of the tip of the obelix would reach them. A monumental and celebratory sun dial: on September 23rd (the Emperor’s birthday) the shadow reached the Ara Pacis which was the Giulia Family Mausoleum.
In the late Imperial period in Rome, to own an “horologium” was an important status symbol. Lucretius tells of a great water clock in the palace of the rich Trimalchio: a slave with a golden trumpet was standing by signalling every hour that passed so that his lord would know about the passing of life. The slave and the big water clock have long gone, but the idea of the clock as a status symbol is still strong, as evidenced by the likes of Girard Perregaux advertisements
Eventually, mechanical clocks became more sophisticated and accurate: the pendulum, the double pendulum, Harrison’s marine chronometer (H4 the model that won the Board of Longitude prize was presented in 1759 could be accurate to less than 6/100 seconds per day.
After Harrison H4 the spring-loaded escapement chronometer became more and more accurate, mechanically sophisticated and smaller. The mechanical watch era was superseded in 1975 with the advent of commercial quartz watches.
Our post-Galilean culture privileges “measurement”. Everything must have a quantitative dimension; every dimension a consistent size. This has been the basic mandate for scientific research, certainly after Galileo, and quite possibly even long before his time.
Measurement was mainly related to the human body. The name of some of the early units is revealing: arm, foot, inch, palm, “passus” … History of science is the history of the measure of reality as the crucial tool for its knowledge. In some fields knowledge and measure of reality conceptually overlap: to measure reality is to know reality and vice versa. To measure means to be able to know and to know means to be able to measure.
Thus scientific culture privileges “quantification” as a peculiar specific element to the understanding of any physical phenomenon.
Transfer of this concept to problems which do not belong to the domain of physics has been a consequence.
To be qualitative is a frequent comment that American researchers whip out to European peers – a well known comment in the international scientific community. A quantitative attitude is in fact mandatory in the American scientific culture: if you do not have the “numbers” your paper is dismissed as irrelevant, not supported by evidence…amateurish and thus usually disregarded. This was the situation as I remember it in the seventies and eighties when I was active in research and in close contact with many US Institutions. I do not know if this is still the case today.
The need to have “numbers” often induces manipulation of data or to “shoehorn” the interpretation of statistics to fit/support the pre assumed result. Sometimes the analytical method and field procedures are moulded by the need to achieve quantitative results beyond the scope of the research. The quantitative drive can sometimes betray the fundamental goal to obtain reliable, solid data for the scientific account of the reality object of the study. Numbers can be solid evidence, but they can also subtly be bent to support an assumed result.
An interesting example of how numbers can be tricky is illustrated by the works and book by the Danish Statistician Björn Lomborg (The Sceptical Environmentalist). With the same “numbers” of other researchers, through subtle manipulations or murky mathematical processing of data, he reaches utterly different conclusions on the environmental reality. Lomborg’s work has been challenged by many authors who disclosed the mistakes and the manipulations, often well within the field of fraud.
For centuries, quantitative measurement of phenomena has been rewarded with considerable success, thus strengthening the concept that “to measure means to know” and that a physical phenomenon which cannot be measured or which has not been measured is, in fact, unknown. Strong doubt remains on what could have been achieved with holistic-intuitive methods, a question strongly supported by the intuition of the atomic structure of matter which the Greek philosopher Democritus reached with an inductive mind-process 400 years B.C., an intuition that has been dismissed as “fantasy” for 20 centuries. The scientific method embraced after the Renaissance revolutionized research, the holistic intuitive way of thinking was abandoned, but nobody knows what we could have achieved if that had not happened.
A specific peculiarity of measurement and of measurement criteria is “conventionality”. All measurement units are “conventional” and “relative”: the meter (a word that in Greek means “measure”) until a few decades ago was the 40 millionth part of the Earth Meridian (according to Napoleon’s scientists) and the definition was re-established in 1983. The meter is the distance that light covers in vacuum in 1/299.752.458 of a second, one degree Centigrade is 1/100 of the thermal difference between water’s freezing point and water’s boiling point, the kilogram is the weight of one cubic decimetre of water at 4 °C, where weight is the force applied to a body immersed into a gravitational field (on Earth is the result of gravitation and centrifugal force due to terrestrial rotation: thus weight varies with latitude and distance from the Earth’s centre).
As for time, the natural frequency of the Caesium atom has been conventionally assumed as the new international time unit in 1967: the “second” is the time needed to complete 9.192.631.770 cycles of the caesium atom resonance. This assumption supersedes the previous “rotational” convention by which one second was the 86.400th part of the time needed for the earth to complete one rotation around its axis.
Interestingly, the international prototype of the kilogram (kept at the International Bureau of Weights and Measures in Paris) seems to have lost 50 micrograms in the last 100 years and the reason for the loss is unknown. The observed variation of the prototype has intensified the search for a new definition of the kilogram. It is accurate to state that any object in the Universe that had a mass of 1 kilogram 100 years ago, now has a mass of 1.000 050 kg. This perspective is very disturbing (or pleasantly suggestive according to the point of view: destabilizing such a monument of certainty) and defeats the purpose of a standard unit of mass, since the standard should not change arbitrarily over time. The alternative is that we should accept the change and consistently negotiate the subsequent changed reality.
The effort of international Institutions responsible for the definition of “measures” is, wherever possible, to bring all the units to absolute values based on “astronomical” references (the speed of light in vacuum, Earth rotation, gravity) or to physical invariants (like the natural resonance vibration of atoms). An effort that does reduce the conventional fickleness, but does not solve conflicts between our subjectivity and its relationship with the historical and environmental context.
As for timekeeping standards its measure is today entrusted to the relative constant resonance vibrations of a quartz crystal used as a capacitor interfering with an inductor.
This technology reached the market with commercial quartz watches in 1975 with the catastrophically famous Black Watch by Sinclair. The product was a total failure.
The chip could be ruined by static from your nylon shirt, nylon carpets or an air-conditioned room. This problem also affected the production facility, leading to a large number of failures before the watches even left the factory. The result was that the display would freeze on one very bright digit, causing the batteries to overload (and occasionally explode).
The accuracy of the quartz timing crystal was highly temperature-sensitive: the watch ran at different speeds in winter and summer.
The batteries had a life of just ten days which meant that customers often received a Black Watch with dead batteries inside. The design of the circuitry and case made them very difficult to replace.
The control panels frequently malfunctioned, making it impossible to turn the display on or, alternatively, impossible to turn it off – which again led to exploding batteries.
The kit was almost impossible for hobbyists to construct (and barely any easier for Sinclair’s hard-pressed workforce). Practical Wireless advised readers to use two wooden clothes pegs, two drawing pins and a piece of insulated wire to work the batteries into position. You then had to spend another four days adjusting the trimmer to ensure that the watch was running at the right speed.
The casing was impossible to keep in one piece. It was made from a plastic which turned out to be unglueable, so the parts were designed to clip together. The clips didn’t work either and the problem was turned over to a subcontractor. Sinclair later (much later) received a small box on which was written, “We’ve solved the problem of the Black Watch!”. Inside was a Black Watch with a half-inch bolt driven though it.
From that horrible experience, present day quartz watches have come a long way. They are very inexpensive and incredibly accurate (some of the commercial makes boast an accuracy within 1 second per year). All the original problems have been solved by design and technological innovations.
An “absolute” accuracy (an audacious qualifier in the science of measurements) is granted by atomic clocks based on the vibration resonance of Caesium atoms interfering with proper electromagnetic frequencies. The cesium atom’s natural frequency was formally recognized as the new international unit of time in 1967: the second was defined as exactly 9,192,631,770 oscillations or cycles of the cesium atom’s resonant frequency, replacing the old second that was defined with reference to the Earth’s rotation.
This kind of accuracy responds to the needs of scientific measurements and is a vital tool for providing evidence to the theories of quantum physics and post-Einstein relativity positions, but it does not fill the gap between the measurement of time and the anthropological, cultural and biological perception that we have of it. The psycho chronometry or chronobiology has yet to find its measurement means. The time we “live” in fact and the perception we have of it, is only vaguely related to the data available through timekeeping technologies. We can detect and assess sound, noise, weight, heat, textures, light with our senses, but a sense for “time” is still a secret securely kept in our organism. It is a reasonable assumption that, since we have all the other senses, we also have an organic, built-in, sense of time.
It is not by chance that in our colloquial language time is qualified in a subjective, qualitative way: long, short, hard. slow, tormented, terrible, happy, far, close… In our everyday talk we seem to think about time as about something that “moves”: time goes by, runs, lags, doesn’t pass, stands still ………
This may be the consequence of the simple fact that timekeeping tools “move” or have moving components: clepsydras, sun dials, the hours and minutes hands, the vibrations of Quartz or Caesium. It could also be that the ”movement” of time is a logical consequence of the “changes” through which we perceive it.
A unique mind or logic transfer makes us think that “time” flows, drifts away, goes by, as if it were a fluid moving around us in the midst of which we stand still. Time would be better thought of as a huge, perfectly still ocean, in which we sail.
We sail: we move, we change, things around us change, move, grow, mature, season, lighten up or get dark, are born, live and die. We are born, live and die. Time is.
Its not easy to think about a measure of time that “is”: the measure of time is the measure of the changes that we see or perceive. Changes can happen in the most diverse fields: physics, physiology, biology, biochemistry, astronomy, gravity, heat, culture, anthropology, society, politics, economy, geography, history, meteorology…Clearly each field is dominated by subjectivity, hence the reason for the many “qualitative” adjectives, which qualify “time” for us and the perceptive assessment of it, more than its measure.
This is the important boundary: chronological measurement of time is different from its assessment through subjective perception. The search to supply subjective perception of time with quantitative parameters has not gone far and does not seem to be very popular in the present general field of human speculation. Bio-chronology and psycho-chronology are very specialized fields between psychology and biology, but they do not seem to have great communication channels with other interested disciplines.
The perception of time is still consigned to “qualitative” criteria. Can anything be done to get out of this segregation?
The fact that our perception of time and the current conventions for its measurement have marginal common ground is quite clear in all the literature. Some authors have also tried to explore a logarithmic time perception scale (Logtime) after the early attempts of Paul Janet (1823 -1899) a professor of philosophy at the Sorbonne, whose specific works on time are lost but they are quoted by William James (1842-1910) often referred to as “the father of American Psychology” in his monumental and ground breaking work “The Principles of Psychology”. (Chapter XV The perception of time.) William James’s book has been placed online in its entirety (http://psychclassics.yorku.ca/James/Principles/index.htm)
The accepted observation that our time perception shrinks with our age suggests that time perception should be scaled as a logarithmic function: time appears to us to be slow (long) when we are young, and shorter as we grow older. We seem to assess and judge periods of time relating them in some way to our age. One year for a ten year old boy is 10% of his life but only 5% of the life of a twenty year old man. So one more year in the life of the ten year old is felt like 10% of his life added to the experience where as the twenty year old young man will feel to have added only 5% to his lived life.
As we get older the faster we seem to age and years seem shorter.
“The Logtime assumption is consistent with the widely accepted description of the perception of physical stimuli commonly referred to as the Weber-Fechner law. For time perception, clock time (calendar age) is the “stimulus”. Weber-Fechner has been found to be only an approximation over a limited stimulus range, and this would probably be the case for aging perception if objective measurements were possible.” (James Main Kenney “Logtime: the subjective Scale of Life”)
Jaqmes.M. Kenney in his essay available at:
Kenney elaborates on the concept and supplies tables to scale one’s life according to the Logtime scale of life.
The literature on “time” is vast and of the philosophical debate is lively and demonstrates the difficulties of the cognitive problem.
Basic definitions of “past”, “future” and “present” are far from settled. William James in 1890 chose a “virtual” category to define “present” after the first use of the term by E.R. Clay: that of “specious present”. (he says: “the prototype of all conceived times is the specious present, the short duration of which we are immediately and incessantly sensible”).
Starting from the classic Greek philosophers to Augustine and to the monuments of modern philosophical speculation, the efforts to understand what time is exactly have been incessant, but the results are still vague. Time sequences, simultaneity, time order, time perception, memory are still open issues.
Philosophy and logics developed a conceptual line of inquiry, neuro-biology and bio-chronometry achieved some results, but there seems to be no connection or communication between the various disciplines, as often happens on account of the segregation of domains and of the academic barriers which are so typical of the organization of science and knowledge in our universities and scientific Institutions.
The field of chrono-biology should be explored by psychology and philosophy researchers working on the concept of time. It would also be useful for general medical practitioners to have an interest in the field.
All the activities directly or indirectly related to the human body and mind are interested in “lived time perception”: sports, recreation, work, education, communication, artistic expression, creative activities, food, social and public relations, sociology, management techniques, decision-making processes and methods, long term planning, financial strategies…
Architectural and industrial design, urban design and town planning are all activities which interfere with “lived time”. Cities and houses contain and constrain time activities which interfere with our biological time.
Knowledge of biological time could be extremely useful while making financial decisions or strategic investments.
Inter-generational and intercultural understanding can be greatly assisted by the knowledge of biological time.
Quite clearly, timekeeping machines based on astronomical references (rotational time) or on atomic resonance (quartz, caesium) cannot be abandoned because they are a fundamental structure for an organised society and because they are essential tools for research.
Log time is more related to humans and can be useful in many fields, but it is a hypothetical assumption supported by intuitive deductions, quite strong for its logical consistency with the Weber-Fechner theory.
Our personal daily matters and life choices, food, health, sport, social and family relationships could be better informed by our own “bio-time”, but we do not know anything yet about our inner, organic clock for the subjective time perception of each individual.
The big question has not been answered yet. Which specific elements of our complex metabolic processes or endocrinal system change on an hourly or daily rate to supply the perception of our time to our brain?
«Future history will no longer produce ruins. It doesn’t have the time» (Augè, 2004). While for many other environmental physical phenomena we have “sensors” and organs capable of recording them, for time we do not have an organ that records, fҽҽls, translates it into an image or into a physical provocation. If it exists, we do not know it. The eyes see light, colours, distances, depths. The question remains whether what I see is exactly the same as what others see, but there are good reasons to suspect so. Ears hear sounds, noises, rҽgіstҽr the direction from which vibrations and acoustical energy arrive and recognize frequencies within certain limits. They probably also record many other characteristics of sound energy according to categories that are unnoticeable, unquantifiable or incomprehensible to most of us. The thermal sensors of our body tiѕѕuҽs fҽҽl the heat and react to it in different ways: increasing or decreasing their temperature, secreting sweat, dilating or contracting their pores to grant the organic balances necessary for our well-being, comfort and safety. We also have sensors that react to pain caused by environmental, “social”, accidental and mechanical situations. These sensors can react to trauma by cancelling the sensation of pain to allow rational control behavioural patterns to handle the emergency/life threatening situation, an assumption I make because it is contradicted and confirmed by many different stories. We do not know “organs” in our body that “fҽҽl”, “record”, “evaluate”, “quantify” or “qualify”, time as a physical dimension of the environmental context. Perhaps it is our whole physical and organic system that “fҽҽls” and “records” time: in fact, the system “ages”, changes physical, dimensional, organic, biological, chemical, mechanical, neuro-vegetative qualities and sensitivities of various kinds and nature. Overall, for this reason, it is correct to say that it is by living that we measure time. A few decades ago, in a short essay pυblisһed by the UWA (University of Western Australia), I wrote that «time is like an immense motionless ocean that we cross while changing» (Matteoli, 2002). It is a literary and suggestive image, but in reality only useful to contradict the other “figures” of “time”, which “passes”, “rolls”, “unfolds”, “runs away”, while it is we who “pass”, “roll”, “run away”, pursued by a strange, benevolent or evil demon or genius. For us, the “dimension/fҽҽling” of time is even more relative and is lіnκed to the time we have lived, to the activities we carry out or that we would like to carry out, to the pleasure or boredom or discomfort of the present. A year of life for a ten year old is 10% of the life he has lived. For a 50-year-old adult, it is only 2 percent of the life he has lived: the same 365 days are worth less for the adult by a factor of 5 (500%). This is why the summers of our childhood seemed very long and those of our later years seem very short.
Augustine, St. (1961) Confessions, ed. R.S. Pinecoffin, Harmondsworth: Penguin
Andrewes, William J.H., editor, The Quest for Longitude, Cambridge, Massachusetts: Harvard University, 1996.
Audoin, Claude, and Bernard Guinot, The Measurement of Time: Time, Frequency, and the Atomic Clock, Cambridge: Cambridge University Press, 2001.
Broad, C.D. (1923) Scientific Thought, London;
Butterfield, Jeremy (1984) ‘Seeing the Present’, Mind 93, 161-76; reprinted with corrections in R. Le Poidevin (ed.) Questions of Time and Tense, Oxford: Clarendon Press, 61-75
Bartky, Ian R., “The Adoption of Standard Time,” Technology and Culture, Vol. 30 (Jan. 1989), pp. 25-56.
Breasted, James H., “The Beginnings of Time Measurement and the Origins of Our Calendar,” in Time and its Mysteries, a series of lectures presented by the James Arthur Foundation, New York University, New York: New York University Press, 1936, pp. 59-96.
Campbell, John (1994) Past, Space and Self, Cambridge, Mass.: MIT Press
Cowan, Harrison J., Time and Its Measurements, Cleveland: World Publishing Company, 1958.
Crosby, Alfred W. “The measure of reality, quantification and the Western Society, 1250-1600”, Cambridge university Press, 1997, Cambridge, UK.
Dainton, Barry (2001) Time and Space, Chesham: Acumen
Dennett, Daniel (1991) Consciousness Explained, London: Allen Lane
Dohrn-Van Rossum, Gerhard, History of the Hour: Clocks and Modern Temporal Orders, Chicago: University of Chicago Press, 1998.
Fotheringham, Heather (1999) ‘How Long is the Present?’, Stoa 1, No. 2, 56-65
Friedman, William J. (1990) About Time: Inventing the Fourth Dimension, Cambridge, Mass.: MIT Press
Garver, Thomas H., “Keeping Time,” American Heritage of Invention & Technology, Vol. 8, No. 2 (Fall 1992), pp. 8-17.
Gombrich, Ernst (1964) ‘Moment and Movement in Art’, Journal of the Warburg and Courtauld Institutes XXVII, 293-306
Goudsmit, Samuel A., Robert Claiborne, Robert A. Millikan, et al. Time, New York: Time Inc., 1966.
Hawkins, Gerald S., Stonehenge Decoded, Garden City, N.Y.: Doubleday, 1966.
Hellwig, Helmut, Kenneth M. Evenson, and David J. Wineland, “Time, Frequency and Physical Measurement,” Physics Today, Vol. 23 (December 1978), pp. 23-30.
Hestevold, H. Scott (1990) ‘Passage and the Presence of Experience’, Philosophy and Phenomenological Research 50, 537-52; reprinted in Oaklander and Smith (1994), 328-43
Hirsh, I.J. and Sherrick, J.E. (1961) ‘Perceived Order in Different Sense Modalities’, Journal of Experimental Psychology 62, 423-32
Hoerl, Christoph (1998) ‘The Perception of Time and the Notion of a Point of View’, European Journal of Philosophy 6, 156-71
Hood, Peter, How Time Is Measured, London: Oxford University Press, 1955.
Howse, Derek, Greenwich Time and the Discovery of the Longitude, London: Philip Wilson Publishers, Ltd, 1997.
Itano, Wayne M., and Norman F. Ramsey, “Accurate Measurement of Time,” Scientific American, Vol. 269 (July 1993), pp. 56-65.
James, William (1890) The Principles of Psychology, New York: Henry Holt
Paul, Janet Théorie de la morale, Paris (approximately 1845)
Jespersen, James and D. Wayne Hanson, eds., “Special Issue on Time and Frequency,” Proceedings of the IEEE, Vol. 74, No. 7 (July 1991).
Jespersen, James and Jane Fitz-Randolph, From Sundials to Atomic Clocks: Understanding Time and Frequency, ( 26 MB, 306 pages) 2nd (revised) edition, Mineola, New York: Dover Publications, 1999.
Jones, Tony, Splitting the Second, Bristol, UK: Institute of Physics Publishing, 2000.
Landes, Davis S., A Revolution in Time: Clocks and the Making of the Modern World, Cambridge, Massachusetts: Harvard University Press, 1985.
Le Poidevin, Robin (1997) ‘Time and the Static Image’, Philosophy 72, 175-88
Le Poidevin, Robin (1999) ‘Egocentric and Objective Time’, Proceedings of the Aristotelian Society XCIX, 19-36
Le Poidevin, Robin (2004) ‘ A Puzzle Concerning Time Perception ’, Synthese (forthcoming)
Lombardi, Michael A., NIST Time and Frequency Services, NIST Special Publication 432*, revised 2002. ( 2.83 MB).
Mabbott, J.D. (1951) ‘Our Direct Experience of Time’, Mind 60, 153-67
Mackintosh, N.J. (1983) Conditioning and Associative Learning, Oxford: Clarendon Press
Mayo, Bernard (1950) ‘Is There a Sense of Duration?’, Mind 59, 71-8
Mayr, Otto, “The Origins of Feedback Control,” Scientific American, Vol. 223, No. 10 (October 1970), pp. 110-118.
Mellor, D.H. (1998) Real Time II, London: Routledge
Mundle, C.W.K. (1966) ‘Augustine’s Pervasive Error Concerning Time’, Philosophy41, 165-8
Merriam, John C., “Time and Change in History,” Time and Its Mysteries, (see Breasted above), pp. 23-38.
Millikan, Robert A., “Time,” Time and Its Mysteries, (see Breasted above) pp. 3-22.
Morris, Richard, Time’s Arrows, New York: Simon and Schuster, 1985.
Myers, Gerald (1971) ‘James on Time Perception’, Philosophy of Science 38, 353-60
Needham, Joseph, Wang Ling, and Derek J. deSolla Price, Heavenly Clockwork: The Great Astronomical Clocks of Medieval China, Cambridge: Cambridge University Press, 1986.
Oaklander, L. Nathan (1993) ‘On the Experience of Tenseless Time’, Journal of Philosophical Research 18, 159-66; reprinted in Oaklander and Smith (1994), 344-50
Oaklander, L. Nathan, and Smith, Quentin (1994), eds., The New Theory of Time, New Haven: Yale University Press
Odegard, D. (1978) ‘Phenomenal Time’, Ratio 20, 116-22
Ornstein, R.E. (1969) On the Experience of Time, Harmondsworth: Penguin
Parker, R.A., The Calendars of Ancient Egypt, University of Chicago, 1950.
Plumer, Gilbert (1985) ‘The Myth of the Specious Present’, Mind
Plumer, Gilbert (1987) ‘Detecting Temporalities’, Philosophy and Phenomenological Research 47, 451-60
Pöppel, Ernst (1978) ‘Time Perception’, in Richard Held et al., eds., Handbook of Sensory Physiology, Vol. VIII: Perception, Berlin: Springer-Verlag
Price, Huw (1996) Time’s Arrow and Archimedes’ Point: New Directions in the Physics of Time, Oxford: Oxford University Press
Priestley, J. B., Man and Time, Garden City, New York: Doubleday, 1964.
Roache, Rebecca (1999) ‘Mellor and Dennett on the Perception of Temporal Order’, Philosophical Quarterly 49, 231-38
Russell, Bertrand (1915) ‘On the Experience of Time’, Monist 25, 212-33
Russell, Bertrand (1921) The Analysis of Mind, London: George Allen and Unwin
Seidelmann, P. Kenneth, ed., Explanatory Supplement to the Astronomical Almanac, Sausalito, Calif.: University Science Books, 1992.
Shallis, Michael, On Time, New York: Schocken Books, 1983.
Smith, Quentin (1988) ‘The Phenomenology of A-Time’, Diálogos 52, 143-53; reprinted in Oaklander and Smith (1994), 351-9
Snyder, Wilbert F. and Charles A. Bragaw, “In the Domains of Time and Frequency” (Chapter 8), Achievement in Radio, NIST Special Publication 555*, 1986.
Sobel, Dava, Longitude, New York: Penguin Books, 1995.
Walsh, W.H. (1967) ‘Kant on the Perception of Time’, Monist 51, 376-96
Williams, Clifford (1992) ‘The Phenomenology of B-Time’, Southern Journal of Philosophy 30,
James Main Kenney
Logtime: The subjective Scale of Life: the logaritmic Time Perception Hypothesis