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Elaboration of the Buddhist and the Scientific Understandings of the Nature of Time

Alexander Berzin
Berlin, Germany, September 2007

Session One: The Nature of Time as a Temporal Interval

Unedited Transcript
Listen to the audio version of this page (0:52 hours)

The Relevance of the Topic of Time

Time (dus, Skt. kala) and such topics within the category of time like the past, the present, and the future are very important topics to study when we are on the Buddhist path. They’re not just metaphysically interesting, but they are actually quite relevant. That’s because one of the things that we’re aiming to do in the Buddhist path, one of the most important things, is to purify away the various types of tendencies and aftermath that have come from our various karmic impulses and actions when we’ve actually enacted these impulses and so on, so that we don’t have to experience their results. And so that of course brings up the topic of, well, what type of existence do these no-longer-happening karmic actions have and what type of existence do these future results that might happen from them have. And how do we actually purify them? If we don’t know how they exist, then it’s a little bit difficult to be precise about that. Also if we’re aiming with bodhichitta on the Mahayana path to reach our enlightenment, and that’s something in the future – it hasn’t yet happened – then how does that exist? Are we aiming for something that doesn’t exist at all? How can we know what it is? How can we actually focus on it? What are we focusing on?

So these topics concerning time – although they are highly philosophical and metaphysical, nevertheless they’re very important. Also in order to reach enlightenment, we need to build up positive force over a period that’s called three countless, or zillion, eons. So that’s a period of time. Well, what is time? And how does that time actually exist? If we were going in a rocket ship at nearly the speed of light, would it take much less time in order to reach enlightenment? Etc. So these are the aspects of the relevance of this topic.

The Definition of Time

Now, Buddhism doesn’t regard time as an absolute container in which events occur and which exists somehow independently of these events. It’s not that space and time are some sort of background grid that provides the space-time coordinates of objects located in it and the objects can just move from one place to another as if they were on some sort of grand four-dimensional chessboard. And it’s also not something that is sort of there and passing, as if time were an entity that is moving and passing by (although that might be the way that we experience it). But the definition of time in Buddhism: it’s a nonstatic phenomenon that is neither a form of physical phenomenon nor a way of being aware of something, so it’s in this category that sometimes we’ve been describing as a nonstatic abstract phenomenon (ldan-min ’du-byed, noncongruent affecting variable) – nonstatic means that it changes from moment to moment – and it is something which is conceptually imputable on a nonstatic continuum.

So we have a continuum, and it’s something that can be imputed or inferred or labeled on that continuum. And a little bit more specifically, it’s an interval which is imputed or measured in the continuum of the occurrence of a sequence of cause and effect. That’s very important actually. There’s a sequence of cause and effect that occurs. And what is time? It’s the interval that can be measured between the cause and the effect. Do you follow that? So it’s very integrally associated with phenomena that are happening. It’s not something which exists independently of that. So it’s this type of interval. And since time is conceptually imputable, time is a function of, and therefore relative to, the mind that conceptually imputes it. It’s something that can be imputed, so therefore it’s related to a mind that could impute it. Therefore it is relative to the mind that imputes it on this continuum of cause and effect.

I think it’s important to go a little bit slowly because these are not easy ideas. So if you understand, sort of nod your head, and if you don’t, please ask a question, or if you need a few moments to digest that, that is necessary.

Participant: What does impute mean?

Alex: That’s a difficult word. How do you translate it usually?

Participant: Zuschreiben.

Alex: So to explain a little bit further, impute means “to give a name to something,” and that is based on inference from certain characteristics that are there. So from certain characteristics of this object, we can impute or label it as a table. And from certain characteristics that are happening – let’s say when the glass changes position and reaches the floor, we can impute on that falling, for example. So it’s something which the mind ascribes to something, to a basis. Zuschreiben I think is a very good German word for that. That’s imputation. It’s very important in the Buddhist way of understanding reality.

So since time is conceptually imputable, time is a function of, and therefore relative to, the mind that conceptually imputes it. Okay? So it’s relative to the mind. The mind could have different concepts of time and would impute that on an interval. So this doesn’t mean that if you stop conceptually imputing time and enter into a totally nonconceptual state, time no longer exists, either objectively or subjectively. Just because it’s conceptually imputable with names and concepts doesn’t mean that it’s just conceptual. Time is conceptually imputable, but that doesn’t mean that it exists only when somebody imputes it, nor does it mean that time or a temporal interval can only be cognized conceptually.

From a Gelug point of view, we certainly do cognize time nonconceptually. It’s a nonstatic phenomenon. It’s neither a way of being aware or a form of physical phenomenon, but it can be known nonconceptually. Conceptually means “through a category.” It doesn’t have to be known through some sort of category or a name necessarily. When we see a glass fall from the table and break on the floor, we don’t just see a sequence of still frames, do we, like a strip of a movie film, and then conceptually synthesize them into an event (although there are some Buddhist schools that say that, the non-Gelugpa schools). But according to the Gelug explanation, simultaneously with seeing the glass in all these different locations, we’d have to say that we also see the falling of the glass, and we also see the impermanence of the glass, and we also see the moment of its falling or the interval of its falling, so time.

Now, the Gelug explanation is one that fits more in terms of common sense: We do see a falling. We do see somebody running. We don’t just see still frames, do we? Now, how that fits in with brain physiology, I don’t know. Do you have any idea, Jorge? Isn’t it that it takes a certain duration of very tiny moments for the brain to actually build up a picture of what’s happening, a duration?

Participant: The absolute minimum would be – like in Francisco Varela’s work, this kind of stuff – the minimum time would be the time of processing of a neuron, which is less than a millisecond.

Alex: So the minimum time would be, according to Francisco Varela, the time for a neuron to process something, and that is a very small millisecond. Buddhism would say something similar. They explain that in terms of one sixty-fifth of a finger snap. But it doesn’t matter what the measurement of it is. The point is that from this Gelug point of view, we do actually see the falling of the glass. And we actually see that it is impermanent; we don’t just conceptualize that through the category of impermanence. You don’t have to give it the name impermanent, you don’t have to say in your head falling, but you can see it. So time is something that although it can be imputed, something that’s imputable on an interval between a cause and an effect – the glass leaves here, and the effect is that it reaches the ground and breaks – it can be seen nonconceptually.

Participant: One thing that I also read from studies that Francisco Varela did is that it seems there’s a limited temporal resolution that the brain can really process, so things that happen in very close proximity to each other are perceived as happening simultaneously. So that would be more like putting things into steel frames on a very, very low nonconceptual basis. I don’t know. But also we’re not like a movie camera that has only one piece of hardware that’s capturing everything. The brain processes the signals in many different parts. For example, shapes are processed in one place; colors are processed in another place. So this movement wouldn’t be processed just in one central place, let’s say. This processing could also have different time scales and resolutions, but we perceive it as happening smoothly.

Alex: So in the end we perceive it as movement. And you wouldn’t really say that it is – well, it’s hard to say if it’s conceptual or nonconceptual from a Western physiological point of view. Conceptual has to do with categories. Like for instance when you give a name to this object as a table. Well, it is an item that fits in the category of table. There are a lot of other items that can also fit into the category of table. So it’s seeing it in terms of a category; that’s conceptual.

Okay, so we can see the time; we can know it nonconceptually or think of time nonconceptually. Impermanence, nonstaticness, or change implies cause and effect – if something changes, it implies cause and effect – and cause and effect implies time (as the measurement of an interval between the occurrence of a cause and an effect). Right? So although voidness is a static phenomenon, and it’s the deepest truth about everything (it’s the fact that nothing exists in impossible ways, so it’s the absence of impossible ways of existing), and that’s not subject to cause and effect (it’s just a fact that is always true, that’s always the case), that doesn’t mean that the deepest truth about everything is that everything actually exists independently of time.

You have this in some of the non-Buddhist Indian systems, that time and space and these things are just an illusion, and when you gain liberation, the atman, or the soul, just exists outside of time and outside of space. So if you saw the deepest truth (that space and time are just an illusion), then you would be freed from the constrictions of it. That’s not Buddhism. When you see the deepest truth about things, it’s not that you are then liberated from time and space; not that at all. If everything existed independently of time and space in the deepest truth about it, then there’d be no cause and effect, and so then there would be no liberation, because liberation couldn’t occur through a causal process of a spiritual path. So that doesn’t make any sense: that somehow we can get out of space and time.

Likewise, if we approach the deepest truth in terms of it being beyond the categories of truly existent, truly nonexistent, both, or neither (that it’s inexpressible), that still doesn’t make time totally nonexistent. Right? It’s not that the deepest truth is beyond all these things.

But time, like all validly knowable phenomena, exists devoid of impossible ways of existing. That’s the deepest truth about it. Which means it doesn’t exist as some absolute thing independently of everything else. It exists, it actually does exist, but how do we establish it exists? We establish that it exists only by the words or concepts for it. This is the way that we’ve been explaining voidness for a long time here. In other words: What is time? What establishes that it exists is just the words for it. It’s the referent object of the words or concepts for it that are imputable on a sequence of cause and effect.

In other words: What is time? Its existence isn’t established from the side of that sequence of cause and effect. So where is it then? Is the time in the cause? Is the time in the effect? Is the time somewhere in between? You can’t establish its existence by that way – that’s impossible – as if there were an absolute thing, like a background. But what establishes that it exists? When we have the word or concept time, what is it? It’s what the word refers to, but you can’t actually point at it or find it. For those who are not familiar with all the voidness discussion, this is really, really difficult to understand, admittedly. But for those of you who have a little bit of familiarity, it exists in the same way as everything else that’s validly knowable exists.

So time does conventionally exist. The deepest truth about it is that it doesn’t exist in impossible ways. Impossible ways would be as an absolute container somewhere in the background or as something that we could exist independently from. These are all impossible. It’s not some absolute. It’s not something that’s merely an illusion. So what is it? Well, you can’t actually find it anywhere – although you can know it validly – you can’t point to it. So all that you can say is that it’s imputable on a sequence of cause and effect and it’s what the word time refers to on the basis of that, whether we talk about a year or a month or a moment or whatever. That’s the only thing that we can say can establish or prove that it exists. But it doesn’t make it exist. Labeling it doesn’t make it exist.

Now, there are several views about time in the different Indo-Tibetan traditions of Buddhism. In all the Buddhist systems, however, time is a nonstatic phenomenon – that means that it’s changing from moment to moment – and it’s conceptually imputable on a mental continuum. Everybody says that it’s imputable on a mental continuum. In other words, time is a mentally constructed measurement of changes that are occurring in the mental continuum of an individual being’s experience. More specifically, time is defined as an amount or length of an interval measured along an individual mental continuum between the occurrence of a causal action that’s committed by that individual and the experience of its result by the same individual. That’s much more specifically what time is.

So it’s a measurement of the interval that can be imputed on somebody’s mental continuum, or mind-stream, between the occurrence of when they have a karmic impulse to do something (or to say something or to think something) and the occurrence of a karmic result from that. So in a sense it’s like a distance, measured in the dimension of time, between two points on a specific individual’s mental continuum. Do you follow that? Here we can conceptualize it a little bit that way.

Temporal Intervals

So it’s not speaking about time as a thing that passes, but rather we can think of time in terms of a temporal interval. Right? Temporal intervals, like a year, are nonstatic since we can experience them from moment to moment and each moment that we experience the year is different, isn’t it? Think about that. Right? We don’t experience the whole year at once, although we can think about the whole year, and obviously we can think about it conceptually and sort of in a sense summarize the whole year through a category of the year, and many things happened during the year. But we experience the year moment to moment. It changes from moment to moment. But keep in mind it’s not a form of physical phenomenon, and it’s not a way of being aware of something. It’s a little bit more abstract, isn’t it?

So a temporal interval on a mental continuum can be in terms of karmic sequences, such as the interval between somebody acting destructively and the same person’s experiencing unhappiness and suffering as a result that ripens from it. Or a temporal interval can be in terms of cognitive sequences, such as the interval between somebody seeing a leaf falling from a tree and then the same person seeing the leaf on the ground. That’s also a type of causal sequence that occurs on a mental continuum. And in most Buddhist systems, but not all, time is also a nonstatic phenomenon imputed on a continuum of a nonstatic external object that’s undergoing change according to the laws of cause and effect, like the continuum of the leaf that we were just talking about that’s falling from a tree, or on the continuum of a pot of milk transforming into a pot of yoghurt and that transforming into a pot of cheese.

Actually those are quite different examples, the leaf falling from the tree and the milk changing into yoghurt and that into cheese, but we won’t go into that. That’s a very large topic that is discussed in terms of transformation. Is it one thing that is transforming? In the case of the leaf, it might seem fairly obvious that the leaf is just transforming from being here to being there. But what about when the milk transforms into yoghurt and the yoghurt into the cheese? Is there a something that has transformed and just changed its nature or its function or its form in three different phases? That’s a very complicated and full topic. We won’t go into that, not here. Actually there are four different positions that you get in the Vaibhashika school of Buddhism, but we won’t go into that. Actually I discussed that in the lecture that I gave about time that’s on my website, if you’re interested.

[See: The Nature of Time as a Temporal Interval.]

So if we speak of time simply in terms of a measurement of an interval between events on the mental continuum of an individual – let’s restrict ourselves to that discussion, not in terms of a measurement of external events but just in terms of being on the mind-stream of an individual (that actually is the most relevant to the Buddhist path of gaining liberation from karma, the results of karma, and so on) – it’s clear that time is relative to and dependent on the observer, both from the point of view of the observer’s experience of two events (a cause and an effect) and an observer’s mentally labeling both the events and the interval between them.

If it is an interval between events on somebody’s mental continuum, then it’s relevant to, and dependent on, the observer – how they experience it and label it. Do they notice it? Do they not notice it? Do you even have to notice it? Do you even have to make the connection between a cause and an effect in order to experience the interval between the two? Well, no, you don’t. So that’s why I was saying that you don’t have to actually mentally label it – but it could be mentally labeled – and you still experience it. So again you have to keep in mind that time is a nonstatic phenomenon. It’s neither a form of physical phenomenon nor a way of being aware of something. That means that a period of time, that interval, is not the same as a person’s subjective perception and conceptualization of a period of time. That’s a way of being aware of something. Your experience of time is different from time. How you regard time is different from time itself. For most people the interval of a year, for instance, seems much shorter as they grow older. A year seems to pass more quickly at age four than it does at age forty. Why?

Participant: It’s the other way around.

Alex: Right. I’m sorry. The other way around – that time appears to pass more slowly at the age of four than at the age of forty. Why is that? Anybody? I mean, it is true, isn’t it? A year seems much longer when you’re four years old than when you’re forty or when you’re sixty.

Well, the reason for that, I think – it’s not explained in the texts – is because one year is 25% of the life of a four-year-old and it’s only 2.5% of the life of a forty-year-old. So because it’s a much larger percentage of your life, it seems to take much longer to pass. But then again is it still a year? So being a year has nothing to do with – not that it has nothing to do with it, but it’s a separate issue from our perception of a year. Perception is a way of being aware of it. A year is not a way of being aware of something. Okay? Do you need a moment to digest all of this? Maybe that would be useful.

I think this is quite important, to overcome or dismiss the misconceptions that we might have about time. When we think of time passing as something that passes, and it can pass more quickly or more slowly for us, what is the misconception behind that? The misconception behind that is that time, like space, is a background grid and that just as you can move from one point in space to another more quickly and the location passes or changes in terms of our perception of it, similarly the same thing is happening with time. That there’s time sitting somewhere over there, and we’re running past it, or we’re staying stationary and it’s moving past us, and so therefore it seems as though time is something in the background that’s passing, and it passes more quickly or less quickly depending on your age. But that’s a misconception; that’s not the way it is, but it might feel like that.

That’s why when we speak about voidness in Buddhism, we’re talking about identifying what’s impossible and saying that there is no such thing. That’s what voidness is saying: There’s no such thing; it doesn’t exist like that. And remember the main reason why it doesn’t exist like that is because then there couldn’t be cause and effect, because what we do would be something separate from that background – we could be separated from that background (it would be there whether we’re there or not). So it can’t be like that, that time and space are some absolute, like a grid in the background, and that it moves, or we’re moving through it, so that it passes.

Units of Time

Since time is a mentally labeled measurement on a nonstatic continuum, whether an internal or an external one, the units with which it’s measured are relative and merely convention – how do you measure it? what are the units? – so a specific interval can be labeled by one individual in many different ways, depending on the conventions he follows.

Years

Take for example the label a year. What is a year? A year is usually measured in terms of the spatial movement and position either of heavenly bodies or of the persons measuring a year. So that raises the topic of the relation of time and space, doesn’t it?

Participant: The starting of a new year is a good example of this.

Alex: Well, the start of a new year – that’s totally arbitrary, totally, totally arbitrary. There are so many different calendar systems that have the new year starting at a different time. But what about the interval of a year itself? This is what I’m speaking of. And it’s usually measured in terms of the motion of something, which is very interesting in terms of showing us the relation between space and time (of course physics would say there’s a very integral relationship).

So usually there are two types of years:

  • There’s a solar year. A solar year is the temporal interval measured according to one revolution of the earth around the sun. And traditionally this was measured from the perspective of the earth according to the passage of the sun through either twelve signs of the zodiac or, in Indian and Chinese systems, twenty-seven stations of the moon (where the moon is in successive parts of its phases). These signs of the zodiac or stations of the moon are actually galaxies other than our own Milky Way. So there’s something in the background, as it were, from our perspective of our earth and sun. The sun orbits around the center of the Milky Way galaxy, and the other galaxies are moving in different ways, and they appear stationary from our point of view, but because of that the interval between successive times a certain galaxy appears in the background behind the rising sun will differ each year. It’s because of that that we have things like leap days and leap years and these sort of things. The interval of a year isn’t constant in terms of the solar year.

  • Then we have a lunar year. A lunar year is measured according to twelve cycles of the phases of the moon. In other words, from new moon to new moon, or full moon to full moon. Twelve of those are counted a year. But that interval also varies from year to year since new and full moons depend on the position of the sun relative to the position of the moon. When the moon is between the earth and the sun, it’s the new moon. When the moon’s on the other side of the earth, it’s the full moon. The interval of the new moon will occur when the sun and the moon are, from our perspective on the earth, together at the beginning of one constellation (let’s say Aries), and then it has to go all the way around from our perspective on the earth to the next galaxy (Taurus), when the next new moon will occur. But of course that’s going to vary over many, many years – each month will be slightly different, and each year will be slightly different.

Also one person can label twelve cycles of phases of the moon a year, but the same person or somebody else could label it less than a year if the same period is measured with solar years. A lunar year is not the same as a solar year. So you have a period of time, and you can measure it by lunar years, or you can measure it, the same period of time, with solar years; and in one case it will be a year, and in another case it will be less than a year or more than a year.

Then now we bring in science in terms of a year. From a relativistic point of view, the interval of a year is relative not only to the counting system that somebody uses for measuring it, but the interval of a year is also relative to the speed at which the person is traveling on whose mental continuum it’s measured and the speed at which the person measuring it is traveling, isn’t it? There’s a year in terms of the motion of the speed of somebody and also in terms of the speed of somebody else measuring it. I mean, you can measure your own time, but something else could measure your time.

So what’s a year? The closer the person travels to the speed of light, the longer the duration between the person’s twenty-ninth and thirtieth birthdays would be when measured by the observation of somebody traveling at a slower speed. All right? But recall we’re not talking here about the experiencing of the two birthdays by the two people traveling at different speeds. That’s a way of being aware of a year. We’re talking about the actual interval between the two birthdays itself, which could be labeled a year. One interval, from the point of view of the person who’s traveling near the speed of light, will be a year between the twenty-ninth and thirtieth birthday. When measured from the point of view of somebody moving slower, it will be much longer than a year.

Days

So this brings the question: If we consider one interval being called a year, is there an objective interval that’s being labeled differently here by one person or by two different persons even if they are at the same location and traveling at the same speed relative to each other? This really gets to the heart of the matter. Is there actually a year that is happening and different people measure it differently, or different people experience it differently, or it’s actually different to different people? Is there some objective year?

Now, if there were such an objective interval of time, it would have to be something labeled on parts, wouldn’t it, such as a certain number of days. But then the labeled days, however, could have different definitions, depending on how it’s measured. For example, there are three types of days discussed in Hindu and Tibetan astrology, depending on how you define it:

  • A day can be a solar day (nyin-zhag). This is the temporal interval from one dawn to the next dawn. That’s a solar day. This interval, though, is relative to the person’s position on the planet and will vary over the course of the year, as a dawn occurs later each day after the summer solstice and earlier each day after the winter solstice. So each solar day is actually a different interval, although it’s called a day. And then you have a year being a certain number of those. Well, is a year different for a certain number when measured at a different location etc.? It becomes a very interesting question.

  • Then a zodiac day (khyim-zhag). A zodiac day is the temporal interval between the sun being located, from the perspective of the earth, at one degree and then the next degree in the course of its movement around the three hundred and sixty degrees of the zodiac. This was used very much in ancient times in terms of astrology and so on. So you divide the heavens, the course that the sun goes through, into 360 degrees, and a day is the time it takes for the sun to go from one degree to the next degree over the course of a year, right, at a certain time. But these intervals also vary over the course of a year since the orbit of the earth around the sun is an ellipse and so the speed of the earth varies as it orbits the sun. So in the Tibetan astrological calculations, you have to correct for different speeds. So that becomes a variable thing, what a zodiac day is, how long it is. Is there some definite length, though, that is behind all of this? That’s the interesting question.

  • Then you have a lunar-date day (tshes-zhag), which is correlated with the phases of the moon. So if we divide into thirty equal portions the distance, relative to the zodiac, between the position of the moon at one new moon and the next new moon – right? with these different phases of the moon, what’s going to be in the background is going to be a different constellation – then a lunar-date day is the temporal interval between the moon being located at one thirtieth the portion of that distance and the next (that’s how you get months, by the way). So these too vary over the course of a month and a year, again because the moon’s orbit around the earth is also an ellipse and the earth’s orbit around the sun is an ellipse (so the speeds are going to be different at different times of that orbit), so that also changes everything and makes it a variable.

So these are very varying types of days with which you would measure what a year is, because a year has to be imputed on these parts.

And then in the West we have a clock day, which is the temporal interval from the halfway point between one sunset and sunrise to the halfway point between the next sunset and sunrise, isn’t it? But sunrise and sunset of course are labeled in terms of the position of the sun relative to the east and west horizons of the person observing them. The halfway points don’t vary over the course of a year, but they’re relative to one’s location. So what happens when you’re at the North Pole and the sun doesn’t set? This becomes a problem, how you would actually calculate the start of a day. So these are our Western clock days.

Hours

And then a day is imputed on hours. So is there a certain absolute number of hours that are being measured by the different labels of a day? No. The twenty-four-hour day, for example, was invented by the ancient Egyptians, and it went from the Egyptians into the Hebrew calendar and the Greek calendar and the Roman calendar. But for all of them a day was the division of a solar day; the twenty-four hours was a division of a solar day (if you remember, a solar day is from dawn to dawn). So the day and night were each divided into twelve hours, from dawn to dusk and dusk to dawn, so the length of an hour, being one twelfth of the day or night, varied according to the season and the length of daylight, and whether it was an hour of the day or the night, and also according to your position on the planet. So if the day was much, much longer than the night, one hour of the day was much longer than an hour of the night. And what would be the hour if you were further north would also change. That makes it very difficult to coordinate military movements, doesn’t it, if you say we’re going to have the invasion at a certain time.

Hindu and Buddhist astrology divides the day and night, from dawn to dusk and dusk to dawn, each into six hours, not twelve hours. A standard-length hour with twenty-four such hours in a day was not adopted in Western Europe until the end of the thirteenth century with the invention of mechanical clocks. It was only at that point that you got a standard-length hour. But of course if you travel at different speeds, what is the standard-length hour?

So that’s solar days. And if you talk about these zodiac and lunar days in Hindu and Buddhist astrology, they divide them into sixty hours. So how many hours are in a day? Twelve hours, twenty-four hours, sixty hours? What’s an hour?

So then you could apply the same type of analysis for minutes and seconds. Then we get into this whole discussion of the relation of the whole and the parts. Is there an ultimately smallest part? And if all these parts are variable, what in the world is going on here? Is there some sort of absolute interval of time that can be called a year or a day or an hour or a minute or a second? What about atomic clocks? They use as a standard of measurement the intervals on the atomic resonance frequency of cesium. Is that absolute, or doesn’t that also vary depending on the speed the cesium atom is moving (for instance, if you had a cesium atom on a starship going near the speed of light)? So even that will vary, won’t it?

Participant: Also gravity has an influence. If you have this atomic clock in an airplane, where gravity is slightly less than down on earth at sea level, then there’s already a measureable effect, a measureable difference in the amount of cycles that you have here on earth and up there in an airplane.

Participant: You’re further away from the earth, and so gravity is less strong.

Alex: Right. So gravity also affects time, an interval of time in the vibration of the radio frequency of a cesium atom. I think I remember reading about an experiment at Harvard where they measured this thing at the top of a tower and at the bottom of the tower, and there was a micro-micro-microsecond difference. But then again, what were they measuring it based on? Is there a standard?

Participant: You’re just counting it at the top of the tower and then bringing it back down. Or I don’t know. Yeah, of course, that’s the problem. You don’t have an absolute time.

Alex: That’s the problem. That is exactly what we’re talking about here, that there is no absolute time. Anyway, let’s think…

Participant: You’re comparing one thing to another. You’re comparing one length of time to another length of time. There’s no absolute.

Alex: Well, we’re comparing one length of time to another length of time when you’re talking about measuring? Or is there an actual interval between a cause and an effect? Yes, there is an interval. Well, how long is that interval (we’re not talking about your experience of the interval)? This is the question. So then that brings up the whole topic of a common-denominator (gzhi-mthun) temporal interval that serves as the basis for labeling by different persons and with many different labels of temporal units. And that gets into the whole discussion of external phenomena and the Chittamatra-Prasangika difference here, but that I think, that can wait till after the break.

Participant: What is a common denominator?

Alex: A common denominator is something that is common to many different things or many different systems, so it’s shared. But let’s just take a moment to digest what we’ve discussed so far, and then we’ll have our coffee and tea break, and then we’ll get into this whole discussion of common denominators. And that brings in the topic of external phenomena, which of course brings in the topic of the Chittamatra versus the Prasangika difference. Is there an actual externally happening year 2006 that different people are experiencing differently or not?