1. The Nature of Time. Now that we've reviewed some of the ways that humans measure time, we might say that we have defined it. However many find that kind of definition unsatisfactory and circular. What IS it that we are measuring? Here we first explore the issues by a look at what one of the early people to think about them said. He is known as Augustine of Hippo, and lived from 354 AD to 430 AD in what is now Algeria, which was then a province of the Roman Empire. He was not the first to be concerned with some of these issues. I will mention various early Greek thinkers who wrote and taught nearly 1000 years earlier. But I think he summarizes the puzzles better than most people of the prescientific and even the present era.

2. Augustine's mother was a Christian but he did not convert to Christianity until 386 when he was 32. Before that he had attended several schools and had been appointed to a prestigious position as professor of rhetoric in Milan, Italy. When he converted, he abandoned that career and became a priest, and was posthumously declared a saint, in the Christian church. But book XI of his famous 'Confessions', though containing frequent references to religious entities, is not mainly about religion but is a philosophical and scientific inquiry into the nature of time.

3. As noted in the exercise statement Augustine was concerned with at least the following questions: Does time have a beginning? What is the nature of the past, present and future? Are the past and future 'real' and, if so, in what sense? How should and do humans measure time? What are they measuring? To get you started on your essays, we will have a brief discussion of each of these.

4. Does time have a beginning? Augustine was trying to reconcile his philosophical confusions with the Christian writings which declared that God created everything at what could be interpreted as a particular time. However Augustine rejects that interpretation because he wants to believe that his God is not subject to the passage of time. So he states that, at the creation, time itself, along with everything else, was created. This was a way of dealing with the question, which he apparently heard frequently: 'What was God doing before he created everything?'. To paraphrase Augustine's answer: The question is meaningless because there is no 'time before' the creation, because time did not exist before the creation. Notice that a somewhat related issue arises in the Big Bang cosmological model of the universe. We will return to this.

5. Does this seem to you like a satisfactory resolution of the issue of whether time has a beginning? Do you think the question has a scientific meaning? That is, might there be a way in which it could be addressed by observation or measurement?

6. What is the present? Is it real? Augustine confronts the issue of the duration of the present quite directly and comes very close to describing the limiting process by which physics would describe the point of infinitesimal extent on a line of real numbers denoting time which it denotes as the present. (See if you can find this in the reading.) When you consider that Augustine was writing 1300 years before the invention of calculus, this is really remarkable.

7. Augustine seems to contend that only the present is real (this is called 'presentism' in modern philosopy) but that, on the other hand, the present is infinitesimally short. Is this a contradiction? Or does it imply that hardly anything is real? See if you can figure out how Augustine resolves the apparent contradiction, if he does, in Chapter XI.

8. Turning to the past Augustine discusses the issue of the reality of past events. He expresses a lot of confusion about it but finally comes up with the idea that only the traces of past events, mainly in human memory, are real. As you read it, you should find the relevant passages in Augustine and decide whether you agree with that interpretation. Assuming that it is the right interpretation, how does that idea compare with modern scientific and subjective (not necessarily the same) ideas of time?

9. Augustine on the future: Reading this part, you should bear in mind that in Augustine's lifetime, a lot of people believed that some people could foretell the future. However, assuming that to be true, I interpret that Augustine did not believe such foretold future events to be 'real' until they 'passed through the present' and became real. However he finds that process quite mysterious. Be sure to find the relevant passages and see if you agree with that interpretation. What do we believe these days about the power to foretell future events? In reading Augustine and writing your essay, try to understand what he meant by 'real' in this context. What do people mean by it in our historical period? Does everyone mean the same thing by 'real' these days?

10. Augustine on the measurement of time: He rejects the use of the motion of astronomical bodies in the sky, particularly discussing the sun, as a valid way to measure time. As we have discussed, that is the way clocks were calibrated from the dawn of the scientific era in the 17th century until quite recently (when we have turned mainly to atomic standards.) Try to understand Augustine's argument against using the motion of astronomical bodies to measure time and discuss it briefly in your essay. Is he complaining about the use of astronomy to measure time or to define it or does he mix and confuse the two uses? In our era, are we using our calibration standards, like atomic clocks to measure time or to define it? If the former, then how do we define it?

11. More on measuring time in Augustine: Some commentators state that Augustine determines that time is best measured by use of the duration of, presumably standard, sounds, such as the length of syllables in spoken language. Such measurements are definitely discussed in the reading. See if you agree that Augustine advocates their use as the best way to measure time and discuss your interpretation of those passages in your essay. What are the advantages and disadvantages of using spoken language as a way to measure time? Is that method related to any of the clocks that we have discussed?

12. Augustine on the nature of time: You will see, I think, that Augustine is quite tentative in his conclusions about the nature of time. However some conclusions, or at least hypotheses, seem to me to emerge: Time is held to have a beginning. This conclusion seems to be made on theological grounds but it is associated in the discussion with the logical inconsistencies which arise in trying to conceive of a period of time which contains no events. Since Christian theology insisted that all events began at a fixed time, the question of whether there was any meaning to talking about time before that arose, as it did not in the Greek and Roman 'pagan' notion of time and events stretching without limit into the past and future. Is this question settled these days? If any events before the big bang are unobservable, is it meaningful to discuss them and attribute a time to them?

13. Augustine on the nature of time II: Regarding the past and the future Augustine seems to come to fairly definite conclusions concerning the reality of past and future events. I interpret (check me on this and cite relevant passages) that such events are only real in as far as they are present in human memory (for the past) or conception (for the future). How does this compare to attitudes toward past and future events in our era? Does this conclusion, if accepted, settle anything about the nature of time itself? Can you find anything in Augustine about time 'flowing' or somehow 'proceeding' 'smoothly' or 'uniformly'? We will see that that latter notion was an important part of Newton's conception of time.

14. Nature of time part II. Newtonian time. Let's start with a translation of a famous passage early in Newton's book The Principia, which set out the foundations of physics for nearly three hundred years and which are still used to describe many aspects of nature: “ Absolute, true, and mathematical time, from its own nature, passes equably without relation to anything external, and thus without reference to any change or way of measuring of time (e.g., the hour, day, month, or year).” Some questions: Does this suggest that time has a beginning? What does it mean to say 'time passes'? With respect to what? What does it say with respect to whether clocks measure or define time? What does it say about whether the future comes toward us or we move into it??

15. Newtonian time 2. To get a more concrete notion of how Newton thought about time we have to look in some more detail at his theory, which entails some mathematics. As I have emphasized, Newton described time mathematically as a a set of real numbers in a line, with the present somewhere in the middle and stretching without limit to negative values (the past) and positive values (the future). He thought of the present as an infinitesimally short instant, but it is important to understand that by use of the ideas of limit which you may have learned in a precalculus course, he was able to to assign more properties to that instant than might be immediately apparent.

16. The Newtonian present. Within Newtonian physics, everything is described by the positions of material particles at each instant in time. That doesn't present any serious conceptual problems, though atoms were unknown in Newton's day so the identity of the particles was not specified. What was conceptually more challenging was that, at each instant of time (eg at the present) a complete description of the Newtonian world also required the specification of the velocities of all the particles. If you think of speed as the magnitude of the velocity and define speed as speed =(distance gone)/(time elapsed) then there is a puzzle because the present is thought to be infinitesimally short in time so no time can have elapsed during it.

17. Instantaneous velocity. Newton resolved the issue by defining a quantity called instantaneous velocity, which we will discuss, However to illustrate the nature of the problem further and illustrate that it had been troubling for a long time let's briefly consider one of Zeno's paradoxes: Zeno was a philosopher who lived in Italy about 2500 years ago. One of his paradoxes concerned an arrow in flight. In modern terms, it is easiest to describe in terms of photography, though of course Zeno had no cameras. If you look at a still photograph of the arrow, which presumably is representative of the state of the arrow at the instant that the photo was taken, you generally CANNOT TELL IF THE ARROW IS MOVING OR NOT. (For example it could be hanging by a very fine thread not visible in the picture. In fact this is a common way to fake pictures of flying saucers.)

18. The picture is only telling us the position of the arrow, and the example illustrates why Newton could not be content to describe the state of a system in his theory by only specifying postions of things at each instant. To understand the way out, think about how you would find out whether the arrow in the picture is moving. Ideally, the picture might be one still (or frame) from a movie. Then you could look at a few frames just before the instant in question and a few frames just after that instant. If the arrow is in different positions in those neighboring frames you are confident that it was moving at the instant of the original picture. But those other frames are characteristic of the past and the future, not of the present. How do we get quantities which only involve the present and which tell us if the arrow (or anything else) is moving?

19. Well, you (and Newton) do it like this. Look at a bunch of frames in the past of the arrow picture and a bunch of frames in the future. Let's just focus on the position in the horizontal direction, call it x. Then from each frame we get an arrow position, and we can make a table: time in frames position of arrow -4 x(-4) -3 x(-3) -2 (past) x(-2) -1 x(-1) 0 (present) 0 1 x(1) 2 (future) x(2) 3 x(3) 4 x(4)

20. Now make a series of estimates of velocity at frame 0 (the present) time interval estimate 1: (x(5)-x(-5))/10 10 estimate 2: (x(4)-x(-4))/8 8 estimate 3: (x(3)-x(-3))/6 6 estimate 4: (x(2)-x(-2))/4 4 estimate 5: (x(1)-x(-1))/2 2 If the arrow is behaving in a Newtonian way, then if you graph this up and your measurements are sufficiently good they will look like this: 2 4 6 8 10 x x x x x estimated instantaneous velocity interval estimate

21. Thus you can use data from the past and the future to get a quantity, the instantaneous velocity, which is characteristic of the present instant. Those instantaneous velocities are absolutely central to making Newton's theory work. He must characterize each instantaneous moment in time by postions AND instantaneous velocities. I hope you see that the latter implicitly contain information about the past and/or the future through the limiting process I have described. (You could go through a similar process using only data from the past.) So in a sense, one can say that Newton regards the present as an infinitesimally short instant, but the description of that instant depends on use of information about the immediate past (or future).

22. To be sure you got it, you will carry out this process of estimating instantaneous velocities using some (rather crude) data in this week's exercise.

23. Newton on the past and the future: How the future is fixed in Newtonian physics: We now see, I hope, how Newton describes an instantaneous state of the world. It is a list of the instantaneous positions and the instantaneous velocities of all the particles in it. But Newton went farther and found a way to predict the future from the instantaneous present with arbitrarily good precision.

24. The Newtonian future. Newton's dynamical theory. So far, we've described how Newton conceived and characterized the present: It is an infinitesimally thin slice of time characterized by the positions and instantaneous velocities of all the particles (in general) in the universe. I emphasized that determining instantaneous velocities involved using some information about the past though. Now what about the future? Newton found that at least in many cases, he could PREDICT the future of at least part of the universe given the information he required to characterize the present. This could be done if he had a correct mathematical model of the forces on all the particles in the present and he knew their masses.

25. So what's a Newtonian force? It is related to, but not necessarily the same as, one's intuitive idea of force. To understand it, first one has to understand the idea of instantaneous ACCELERATION in the present instant. It is related to the instantaneous velocity in the same way that instantaneous velocity is related to position, by a limiting process. You are working through that process in the exercise this week. Call the instantaneous acceleration of some particle at the present time t a(t). Then the formula that makes prediction possible is Ma(t) =F(t) where M is the mass of the particle and F(t) is the force on the particle at the present instant.

26. How to make predictions: Let's suppose you know the force at the present instant t. Let's write an approximate expression for the acceleration, using the method you are using in the exercise. Let Δt be a short time interval like 1/30 sec in the exercise. The instantaneous velocity at t- Δt/2 (just a little before the present) is approximately v(t- Δt/2)=(x(t)-x(t- Δt))/( Δt) and at t+Δt/2 (just a little into the future) is v(t+ Δt/2)=(x(t)-x(t+ Δt))/( Δt) and an approximation for the acceleration is at the present is a(t)=( v(t+ Δt/2)-v(t- Δt/2))/( Δt)

27. We have past present past v(t- Δt/2)=(x(t) -x(t- Δt))/( Δt) future future present v(t+ Δt/2)=(x(t+ Δt)- x(t))/( Δt) future past present Ma(t)=M( v(t+ Δt/2)-v(t- Δt/2))/( Δt) =F If we know about the present and the immediate past we can SOLVE these equations for the quantities x(t+ Δt) and v(t+Δt/2) which tell us about the future. You can do it (ordinary algebra) but I will give the answer here: future past present v(t+Δt/2) =v(t-Δt/2)+(F/M)Δt future past present x(t+Δt) =v(t-Δt/2)Δt+ x(t) + (F/M)Δt 2

28. future past present x(t+Δt) =v(t-Δt/2)Δt+ x(t) + (F/M)Δt 2 future past present v(t+Δt/2) =v(t-Δt/2) + (F/M)Δt This is the essence of the way Newton predicts the future. You will use Excel next week to see how it works in a simple case. Essential features The present is characterized by positions and instantaneous velocities We must know the forces in the present and the masses. With that, people regularly solve Newton's equations for billions of interacting particles and predict the behavior of solids, liquids, galaxies and much else

29. Further features of Newtonian prediction: One must know the forces and masses, However, even if we don't, if we believe that SOME forces and masses would give correct predictions using Newton's equations, then the future will be fixed, though we can't predict it. The process works just as well BACKWARDS: That is, if you knew the future you could postdict the past. Further more the backward postdiction would look EXACTlY like the past to future prediction in reverse order: All the positions would appear in reverse order and the velocities would have exactly the same magnitudes and exactly opposite directions. We say that the Newtonian theory is TIME REVERSIBLE.

30. Should we believe that this Newtonian picture describes the real world? Maybe yes because It has a tremendous track record. And not only in astronomy. Many properties of solids and liquids and gases are correctly predicted by Newtonian physics.

31. But we should be cautious because There are issues There turn out to be practical limits on Newtonian prediction (chaos). Thermal physics appears to be time irreversible Quantum physics reduces to Newtonian physics on large scales but,in it, it is not clear that future is fixed. The theory of relativity reduces to Newtonian physics when velocities are low, but does not have a well defined and universal present. We will discuss all of these later.

32. Meanwhile let's contrast the Newtonian past present and future with ordinary human perceptions of time (Human Time) The present is not perceived as an infinitesimal instant by most humans. Our neurological equipment has a response time limit of the order of 10 -5 seconds, but actual perceptions of the interval regarded as the present are much longer. The past is often regarded by humans as fixed, That is qualitatively consistent with the Newtonian view. But in practise, human knowledge of the past is constrained by the limits of human personal and collective memory and what can be learned from the geological, astronomical and paleontological record. Further the records, both between human memories and in the geological and other data, are not always consistent. The uncertainties get larger deeper into the past.

33. Personal Human Memory: Though human memory does not all occur in the brain (think dancers, athletes) I will mainly refer to conscious memory thought to reside in the brain. At the phenomenological level, psychologists find two types of memory, short and long term and possibly a third, unconscious retention of all or most experience. Short term memory permits retention of small amounts (a few words for example) of detailed information for a very short time (eg 30 seconds) as when one remembers a phone number long enough to dial it and then forgets it.

34. Long term memory lasts, as the name implies, much longer, has a much larger capacity, and takes longer to form. Experiments at the macroscopic level suggest that, unlike short term memory, information in long term memory is reorganized and stored in some kind of hierarchical form, which presumably makes items easier to retrieve. See sections 2.9 and 2.10 of Whitrow's longer book (The Natural Philosopy of Time) for a review of what had been learned about human memory from the macroscopic point of view up to around 1980. One interesting feature which connects to our earlier reading from Augustine is that experiments indicate that aural (sound) based long term memory seems to dominate visual memory and to be more reliable.

35. I will return to this but first review a little of what is known about human (and other animal) memory at the physiological level. All the activity in the brain is based on circuit elements called neurons which are cells with the same basic structure as other cells in the body (cell wall made of lipids, nucleus containing DNA, proteins) but with a particular structure. They are very long (up to meters!) though the structure in the other two dimensions is much smaller, on the scale of 10's of microns (1 hundred thousandth of a meter). An electron microscope image of a human brain neuron is shown in the next slide.

36. The fat part of the cell is called the soma The long skinny part is called the axon. Electrical signals propagate along the axon from the soma to the ends of the axon where it branches and makes contact with dendrites through synapses. dendrites receive signals from axons of other neurons through synapses synapsebar is 4 x 10 -5 m long

37. Activity in the brain occurs through the passage of electrical currents which result in a peak in sodium ion concentraton down the axon from the soma to the synapses. The signals are then passed across the gap to the next neuron through the passage of small molecules called neurotransmitters. These include amino acids but also other molecules such as dopamine. The molecular processes at the synapse are complex and are still being sorted out. However it is evident that long term memories are formed by changing the structure of the synapses. This is known as synaptic plasticity and the molecular details by which it occurs are being sorted out, using, for example experiments on the brain tissue of rodent brains. Here is a recent reference: Science 334, 623 (2011)

38. We can get some insight from the numbers of these elements in the brain: There are about a trillion neurons (10 12 ) There are about a quadrillion (10 15 ) synapses. (This means about 1000 synapses per neuron) How then, does the information storage capacity of the human brain compare with that of a computer? To understand this a little better, we should say a little about how we quantify the notion of information storage.

39. To consider information storage it is useful to have a somewhat more definite definition of information. The quantitative definition of the information stored in any kind of message is defined to be I = log 2 (number of possible messages) The definition means that there is more information in a message if there is a larger number of possible messages that could have been stored in the same medium. For example, for DNA of length N, each monomer could have 4 values so the number of possible genetic messages is 4 N and the amount of information stored is Nlog 2 4=Nlog 2 2 2 = 2Nlog 2 2=2N

40. In a computer, the information is stored as 'on' or 'off' states in various media, for example in tiny magnets or in transistors. Each such magnet or transistor has two possible states so the total number of messages possible with N magnets or transistors is 2 N and the information stored by a message is Nlog 2 2=N 'bits'. In the brain, the information is stored in synapses, which are also on or off so the amount of information that can be stored is of the order of 10 15. For computers, memory specification is usually stated in terms of 8 bit bytes, so with 10 gigabyte memories (typical for small computers) there are about 10 11 bits. That is about 10000 times less than the brain. On the other hand, the computer is faster: It performs operations about every nanosecond, while brains do so every millisecond, about a million times slower. 2

41. Is total retention possible? These numbers can establish whether there is any possibility of the total retention which has been speculated on the basis of anecdotal evidence to exist. Supposing that a 216x216 pixel (8bit) picture was stored each second for 1/3 of the time one estimates, in a 90 yr life that 216x216x30yrx8x3x10 7 sec/yr ≈ 4x10 13 bits. which is about 1/24 times the estimated storage capacitance of the brain. Thus the reported almost total retention might be possible in a long life, but it would be pushing the available capacity.

42. A few details about what is known about the operation of the brain with particular emphasis on memory. It should be emphasized that the subject is under intense study and that complete understanding of how memory works does not exist at the present. Studies include investigations at these levels: Cellular/molecular level: Investigations of 'synaptic plasticity' in which the chemical manner in which synapses are changed during the formation of long term memory are studied. Neural network studies: Investigations of how neurons linked together lead to memory and memory recall. This is particularly difficult because the entire network has not been mapped, though there is progress in that direction using new tools.

44. Some neurotransmitters glutamate dopamine serotonin gamma-Aminobutyric acid

45. 4-isoxazolepropionic acid receptor AMPAR= glutamate receptor

46. An aspect of memory formation is the increase in the number of these AMPAR receptors for the neurotransmitter glutamate. It is believed that long term memory formation requires changes in the expression of genes which code the information about such proteins, and this requires that whatever signals in the synapse are causing the memory to form must be transmitted back to the nucleus where the genetic material (DNA) resides. How this takes place seems to still be under study.

47. The operation of the brain at the circuit level: neural networks Working up from the microscopic picture just described, neuroscientists are making models of how the network of neurons works to encode and retrieve information. The resulting mathematical models are then compared with experiments at several levels: Electrodes are placed at the soma and along the axon to detect how electrical signals propagate. The following has been determined: 1.The signals propagate in pulses, originating from flow of ions in and out of the axon membrane. They all have the same strength and the information in the pulse is encoded in the number and frequency of pulses. This is known as frequency modulation.

48. In human radio communication we use a ‘carrier frequency’. This is what you tune the dial of a radio to. Then we impose a signal varying more slowly than the carrier frequency on top of the carrier sine wave. Signal can be imposed on the carrier sine wave by varying the amplitude (AM or amplitude modulation) or by varying the frequency (FM frequency modulation). The neural network system in terrestrial organisms including humans is using frequency modulation: The pulses all have the same amplitude but vary in frequency. This has advantages in getting a weak signal through a lot of noise.

49. Operation of the brain 2: There are two dominant modes of information processing Parallel processing: in which several signals are processed at the same time and Serial processing, in which one signal is processed after another.. There are computers of both types. Your laptop is primarily a serial processor. The advantage of serial processing is that the result of one computation can affect the input to the next one and serial processing deals well with that: You need to look for oncoming traffic before you decide to cross the street, not at the same time. On the other hand, serial processing is slower.

50. Our brains are wired in a highly parallel manner but operate serially for certain tasks. At the macroscopic level, this is related to the issue of attention. See M. Cohen, Science 338, 58 (2012), who mentions the case of a baseball pitcher: The pitcher monitors the positions of the runners on the bases in parallel with his attention to the batter, the catcher and the pitch. This is a highly parallel operation. Cohen deduced from experiments with monkeys that attention to a single feature of visual images can be processed in parallel at many locations (eg looking at the color of uniforms on 3 bases at once) but attention to several details at a location can only be done at one location at a time.(eg paying attention to the batter, the catcher and the details of the pitch). This might contain hints on doing homework.

51. Operation of the brain 3. Current understanding of neural networks. The detailed circuitry of the brain has not been mapped, though, in principle that is possible and will probably be done in the next few decades. Mapping the circuitry will not immediately tell scientists how it works, and that will require further effort, but it is also possible in principle. Definite conclusions regarding how it works are likely to take longer, on the scale of several more decades. Here I summarize current theoretical ideas on how the neural network works, based on the microscopic knowledge of neurons and the pulses they carry and transmit and on experimental data on the resulting behavior of organisms including humans.

52. MRI derived picture of the brain. Colors represent orientation of white matter fibers.

53. Starting with the microscopic picture of how synapses work (inasfar as it is known) and the number (particularly the connectivity) of the network, theorists build hypothetical models of how the brain might be wired. The models can be given mathematical form and solved either by computer or using approximate mathematical techniques on paper to give predictions of how the brain might store and retrieve memories, recognise things and make decisions. These predictions can then be compared with experiments on people and animals performing these tasks to determine how well the models predict the observations. Some of this process is outlined on the next slides from Science 338, 60 (2012). The whole procedure is typical of how science is done. In the case of the study of memory, it s a work in progess.

56. In summary, human memories are encoded by chemical modification of synapses in the nerve cells, mostly in the brain, and are recalled by a process involving a kind of cooling of the currents in the resulting circuits. A good lot, but not a complete understanding, has also been learned about the physical locations of different kinds of information in the brain. It appears that some kinds of information are localised and others are not. I will not discuss that aspect further. Another aspect concerns lifetime. Obviously, personal human memory is limited by human lifetime. Current life expectancies in wealthy countries are around 70 years and memory starts to decay for the early parts of that period as an individual life gets longer, though that decay is far from uniform.

57. Collective human memory: Collective human memory resides in data bases and libraries in its most organised and intentional forms. Starting with the bulk magnitude of these resources, we have estimates that the current amount of digital storage world wide is about 2.4 x 10 19 bits (300 exabytes. An exabyte is 10 18 bytes.) That's about 10,000 times the number of synapses in an individual human brain. The lifetime of most of these resources is extremely short. Magnetic storage has to be rewritten every year or two, tape storage at least every 10 years and CD/DVD storage every 40 years. Longevity of microfilm (not much used for digital storage) is 100's of years.

60. Print storage, now less than 6% of the total, also has a limited lifetime. Books printed from the 1920's to quite recentlywere printed on acidified paper which deteriorates very rapidly. Millions of volumes are being lost yearly and very little is being done about it in the US. The natural record of the past includes geological data providing information to 4.5 billion years ago and astronomical data to 13.8 billion years ago. For human consciousness, it has to be interpreted. Information on events farther back in time have also deteriorated in this record.

61. Collective human future: In quite sharp contrast to the Newtonian picture and even the personal human perspective, collectively there is very little accurate projection of the human future. However collective attempts at sharpening our predictions of aspects of the human future are ongoing. Important examples include climatology and the study of earthquakes. The underlying assumption in both cases is that the phenomena are Newtonian and the computational efforts, based on that assumption, suffer from the chaotic nature of the underlying (deterministic) equations as mentioned earlier. I will discuss the example of climate a little more in the section on thermal physics.

62. Regarding the definition of time: Despite the assertions of Newton and Augustine it appears that, in practise, personal as well as scientific, events perceived as proceeding in a regular and reproducible fashion are used to measure, and thus implicitly define, time. Without such events humans would be unable To measure time, and thus to define what it is. Whether something called time would still exist without such events for use in making a clock then becomes an observationally meaningless question.