Is There a Common-Denominator Temporal Interval? The Gelug Prasangika Position
We were speaking about the issue of a common denominator in terms of: Is there an actual temporal interval, somehow like this blank screen, that’s the basis for labeling by different persons with many different labels? And we saw that in Chittamatra according to Tsongkhapa’s earlier interpretation, conventionally there is, but on the deepest level, or ultimately, there isn’t. And in his later interpretation of Chittamatra, Tsongkhapa said that both on the conventional and ultimately, or deepest level, there is no such thing as a common denominator.
What about Prasangika? Prasangika, the Gelug Prasangika, agrees with Tsongkhapa’s later interpretation of Chittamatra – that there’s no common-denominator clay pot or year 2006, either from the viewpoint of conventional truth or deepest truth, experienced by two different persons either at different locations or travelling at different speeds. But the Prasangika understanding of this is quite different from the Chittamatra one.
From the point of view of appearances, Prasangika agrees with Chittamatra – that the appearance of something like the clay pot or the year 2006 depends on the mind that cognizes the appearance. There’s not some sort of set, fixed appearance that everybody is seeing together from the side of the object. But the reason for this, from the Prasangika point of view, is that there is no findable referent thing on the side of a validly knowable object that corresponds to the names or labels for it. This was the understanding of the absence of truly established existence from the point of view of Prasangika.
As you recall, what establishes the existence of something? Well, it is merely what the name refers to, or concept of it refers to, on the basis for labeling. But – and this is the point here – although the word or concept refers to something (btags-chos), there’s no referent thing (btags-don) itself sitting on the side of the object that can be found there, with defining characteristics and stuff like that, that corresponds to the word. The word refers to something, but there’s nothing that corresponds exactly to the word.
I’m just doing this briefly here because this isn’t a course on voidness. But when we think of words and concepts, these are like entries in a dictionary in which something falls within, categories of an entry in a dictionary, like table or orange or red or good or bad, or something like that. And what does that imply? That implies that there are actually things out there that exist in a box of red or orange or green or blue and so on, these type of things. And so although we can use these concepts and categories and words to refer to things (“Okay, what color is that?” “That shirt is red”), it’s not that there is such a thing as red there on the color spectrum – that somehow on the color spectrum there are two bars which say, “This side is red. The other side is orange,” or things like that.
And of course the same thing in terms of time. Somebody brought up the example of a new year. Well, this is totally arbitrary. But then again this gets into a weird viewpoint. But let’s say if we take an interval of a lifetime, it isn’t that there are set boundaries in it that say: one year, two years, three years, things like that. We have these words that are a convenient way of referring to it. “How old are you?” “Well, I am five years old,” or fifty years old, whatever it is. Well, what kind of year are we measuring it in to start with? Is that on the side of the… Well, where is it? We have a mental continuum. Does that mental continuum have little bars on it, and on one side it is this year, and on the other side it’s that year?
Tibetans count birthdays and age very differently: it’s how many calendar years you’re alive in. So if you’re born in December of our calendar, the last month of the year, let’s say – well, you may only be alive for one month of that year, but that’s your first year. And then as soon as it turns the next month, which is the first month of the next year, you’re two years old, because you’ve been alive in two calendar years. It may only be that you’re alive for three weeks, but you’re two years old.
So this indicates the arbitrariness of how you actually measure things. It’s not referring to something set and fixed – these words and concepts, year and so on – on the side of the object. Nevertheless, they refer to something. Well, there is a year – you’ve lived for a year, however it might be defined – but that is established purely from the mind by mental labeling. Okay? So, like that, there is no common-denominator year which is somehow a referent of the word year. We all use the word year, and it refers to a year, and we all understand it, those of us who follow the same convention, but it’s not a referent thing existing somewhere, like in a time line or whatever. So that’s the Prasangika point of view.
Thus the year 2006 experienced by the person traveling at a faster speed and the year 2006 experienced by the slower speed person are neither the same nor different. They’re neither one nor many. Then you get into the whole Prasangika analysis: My 2006 and your 2006 in the starship, are they the same year 2006, or are they two different years 2006? Actually they’re neither of those. Because that type of discussion is: Is there a truly existent findable year 2006? And are they the same findable year 2006? Or are they two totally different findable years 2006? So that’s not the case – it’s neither of them – because there’s no such thing as a truly existent findable year 2006.
But, unlike Chittamatra, Prasangika does assert that there are external objects, which means validly knowable objects, such as a clay pot and the year 2006, that have a different natal source and a different essential nature from those of the cognitions of them. So the year 2006 does have its own natal source in terms of the events that have happened since… What is it? Is it from the birth of Christ or the death of Christ that it’s measured?
From the birth. Plus the calendar has changed.
And they had solar days in that time, and the hours were counted differently. But aside from all of that, it’s 2006 years from that event (and now we’re in the 2007th or whatever). But it has its external source – it’s not just coming from a seed of karma – in terms of my being aware of what year it is. So Prasangika says that, but nothing findable.
And also Gelug Prasangika asserts that the existence of a clay pot or the year 2006 can’t be established from the side of a common-denominator defining characteristic on the side of the clay pot or the year 2006. Remember that was what Chittamatra was saying, that there is some findable defining characteristic on the side of the object that would make a common denominator, even if it’s in everybody’s cognition. Prasangika says no – and we’ve discussed this before – defining characteristics, after all, are made up by concepts in a dictionary, by people who decide what is a table, what is a year, and so on. It’s certainly not on the side of the object.
An easy example is a color. Somebody just decides that from this point in the spectrum to that point in the spectrum, we’re going to give it a name, and we’ll call that red. And we’ll call it orange if it’s one little wavelength less, or more, whatever it is. So defining characteristics likewise are just mentally labeled. They’re not findable on the side of the object, so you couldn’t have a common denominator established by a common defining characteristic findable on the side of the object.
So the existence of an interval of time, such as the year 2006, is established only in terms of what a valid mental label for it refers to, whether there’s just one valid mental label or many valid labels, and whether the many valid labels are labeled by one individual or many different individuals. And remember a valid label, like a clock day, is established by a convention. So for it to be a valid label, there just has to be:
- A convention that is agreed. So we all have this convention of a clock day of twenty-four hours.
- And it’s not contradicted by others validly measuring and labeling the same label in terms of conventional truth. So everybody else who is looking at a clock and working in this convention of twenty-four times that the hand goes around the clock – or some quartz crystal vibrates, or something like that – that we’re going to have the convention of calling that a day. So it’s not contradicted by other people who look at their clock.
- And it’s not contradicted by others validly measuring and labeling the same label in terms of deepest truth. Somebody says, “It’s a truly existent day: the day,” and then “This was an inauspicious day,” “This was a terrible day” – which we can get if we become superstitious with astrology and so on (“This is going to be a bad day: a black cat crossed my path,” this type of stuff) – then it’s contradicted by somebody that sees validly the deepest truth, that things don’t exist that way.
So the validity of a label is established by these three criteria and not by there being some findable defining characteristic, common to everybody who perceives it, on the side of the object. So again validity is established from the side of the mind, not from the side of the object. Okay?
So that’s a very quick summary of the Prasangika position, something that in other courses we’ve spent years on, just to touch a little bit on this topic of: Is there a common denominator in terms of “Well, is there really a year? And does everybody experience the same thing? Or what do we experience?” And are there any questions on that?
So the Chittamatra school says there’s a common denominator, and the Madhyamaka school says no?
It’s not quite that simple. The Chittamatra – as we saw, there are two views of it. Both views of Chittamatra say that ultimately, from the deepest point of view, there isn’t a common denominator that’s coming from some external source. So there isn’t that. But one view says there is conventionally a common denominator, and one view says that there isn’t. One says there’s a common denominator because in everybody’s cognition of a year, or of something, there’s the same findable defining characteristic on the side of the object. The other one says that that doesn’t mean that it’s a common denominator, because it’s in different cognitions. So one view will accept that there’s a common denominator on a conventional level, and one won’t, but both say on the deepest level there isn’t a common denominator. That’s Chittamatra.
And the Gelugpa Prasangika (which is different from non-Gelugpa Prasangika) within Madhyamaka will agree with the second Chittamatra view – that from those two points of view, conventional and deepest point of view, there isn’t a common denominator – but their reason for it is different.
Right. There are many, many different opinions, depending on the school of Buddhist philosophical positions. Vaibhashika says there are common denominators, for example, and then they explain them in their four different assertions. So a lot of different possible explanations. And it makes one think, as I explained before, to analyze: Could this be true? Could this not be true? Can one be a way of starting to understand something? What’s the relationship between milk that changes into yogurt and the yogurt changes into cheese? Is there something that maintains the identity of the substance? Are they totally the same? They can’t be totally the same. Are there two completely different things? Then how can they be related? How does a cause-and-effect relationship hold? And this is a very important issue in Buddhist understanding and Buddhist philosophy – how is the relationship between cause and effect maintained? Which is not an easy question to answer.
Why is a causal event leading to a result? And what connects them if there’s nothing solid connecting the two? Remember in the Indian Nyaya system, the non-Buddhist system, that they had truly existent connectors, like little sticks connecting two balls. Well, Buddhism doesn’t say that. So is there something that connects them? And how are they connected? Why should this result come from that cause? So we speak about time as explaining the interval between them, sort of involved with the issue.
And this is of course extremely relevant to our path to liberation and enlightenment. I’m doing various actions now as a cause to somehow bring about liberation and enlightenment. Well, how can that work? Or even just in terms of avoiding destructive actions bringing about happiness. What’s the connection? How is the connection there? And what is this time interval? Do I have to wait a million eons before any happiness comes from this? Will I accrue interest? Will it get bigger the longer I wait? That time interval – is it fixed? Is it shorter? What is that time interval? So these are relevant questions to the spiritual path, not just irrelevant philosophical speculations.
Time According to Western Science
Now, let's invite Dr. Jorge Numata to give the scientific discussion of time.
Dr. Numata: I want to talk to you a little bit about the scientific views on time, like the different theories and the relevant models that exist in science where time has come up as an important variable and what we can learn from it.
First of all, it’s always hidden assumptions that hinder our progress, at least in science. There are a lot of little assumptions and unconscious biases that we have that can impede our progress and understanding. And this is, I think, also the case with spiritual progress; either doctrinally based or automatically arising biases and wrong assumptions are hindering our progress on the path.
For example, this is a very popular picture from Stephen Hawking – he loves to use this picture in talks – about how some people might view the world as being flat and being placed upon millions and millions of successive turtles. And what’s holding the next turtle? Another turtle under it. So this is probably a wrong assumption about the way the world exists. But you wouldn’t automatically think this. You would have to be taught that turtles hold the world.
The relevant fields that can say something to us about the nature of time in science are:
- Relativity theory. This is probably the most important one. It tells us there is no such thing as simultaneity or a universal present time or a now.
- The mechanical laws of science, including quantum mechanics and Newtonian mechanics, and so on.
Basically the mechanical laws are time-symmetric. This means that they’re applicable in both time directions. The basic laws of interaction, energy, and forces are not time-asymmetric: they do not give an arrow of time; they do not tell us in which direction time goes forward. However, entropy and thermodynamics do have an arrow of time or provide a directionality to time. I’ll also be talking about entropy.
And lastly just a brief mention about circadian rhythms or biological clocks. How do our bodies – also plants, bacteria, animal bodies, and human bodies – how do they keep time? How do they keep track of time?
Dr. Berzin: Please give an example of a mechanical law that would work in both directions of time.
For example, Newton’s third law: Any action causes a reaction of the same magnitude. It’s time-reversible. It works if you’re going from the past into the future or on the way back. It’s exactly equivalent. And so is most of quantum mechanics and Maxwell’s laws of electricity and electromagnetism. All of them are time-symmetric, which is interesting, because they don’t really tell you in which direction time goes.
Time is the Rate of Change of Something
So does time flow? Because we always intuitively, probably even automatically arising, have this idea that time flows – this feeling that we’re standing still, and there’s this river of time flowing. However, time within science is defined as the rate of change of something.
I’ll give you an example – this is probably the only equation I’m using in this talk, so don’t get scared – the definition of velocity, which is just the derivative of the position of a particle with respect to time (this means the rate of change). So, in this case, time is not going anywhere. Time is not moving; it’s simply a variable that helps us define the rate of change.
So if you wanted to ask how fast does time flow, you would get a nonsensical answer. How many seconds per second? That doesn’t make any sense. So you can’t really say that time flows. There is no speed of flow of time. Time is what you define the rate of change with.
Throughout history there have been several standards of time used. First we used the celestial motions. And right now what we tend to use are atomic vibrations because they’re more reliable than the motions of planets. They are not absolute – that’s not the point (there is no such thing as absolute time) – but they are quite reliable within their frame of reference. So within their frame of reference, they are a good source of time. I’ll be explaining a bit more what frame of reference means.
“Is there time before the Big Bang?” is a common question. Stephen Hawking also always answers that it doesn’t make sense to ask this. The reason is simply that time and space are very intricately interwoven; you can’t separate time from space. And at the moment of the creation of this universe, the time of this universe, of the processes going on in this universe, was also born. It doesn’t mean that there was nothing before the Big Bang. It just means that the time of that matter and energy was born also at the time of the Big Bang, in a way of speaking. It’s completely interwoven with it. It cannot be separated.
Time and Relativity
The first version of relativity was basically given by Galileo. He proposed a thought experiment (which you could nevertheless actually do in practice). I’m just going to read it out loud: He proposed you shut yourself up with some friend in the main cabin below the decks on some large ship, and have with you some flies, butterflies, and other small flying animals. Also hang up a bowl that empties drop by drop into a wide vessel beneath it. And have the ship proceed with any speed you like, so long as the motion is uniform (meaning no acceleration) and not fluctuating this way and that (meaning no acceleration also in either side). So just constant speed. The droplets will fall into the vessel beneath without dropping toward the stern – so the water will not seem like it’s going backwards – although while the drops are in the air, the ship runs many spans. The butterflies and flies will continue their flights indifferently toward every side; nor will it ever happen that they’re concentrated toward the stern (meaning the back of the ship), as if tired out from keeping up with the course of the ship. This is a quote from Galileo which was reproduced in a book from Roger Penrose called The Road to Reality from 2005.
This is one of the first versions of relativity. Of course it doesn’t include the relativity of time, but it’s already the relativity of frames of reference. So there is no privilege to the velocity frame of reference. If you have nothing to indicate what velocity you’re going at (for example, being over the crust of the earth and moving at a constant speed), you cannot tell that the earth is moving at a certain velocity.
Just one more picture from a book from Stephen Hawking, where you can see two people playing ping-pong. And first you cannot see that they’re inside a train. So from the point of view of an observer inside that’s just looking at the people playing ping-pong and moving at the same speed as them – this observer could say that the ball is moving at ten miles per hour. However, an observer outside the train who sees these people playing ping-pong are actually moving with the train at 90 miles per hour – this observer outside the train will see that the ping pong ball is moving at 100 miles per hour. So this is another form of the relativity of speed.
Just one comment, going back to Galileo. When Galileo first heard of this idea that the earth is rotating around the sun, because he understood exactly this relativity of movement, he had no problem with it. He thought it’s perfectly normal that we don’t feel this velocity.
There is a certain difference of speed of the observer that’s there. And so of course you can have different frames of reference from which you view it, how you interpret it, for example. You view the ball as moving relative to the moving train, or you view the ball as moving relative to the ground, but still the relative velocities are there. But is there a common denominator, the ping-pong ball traveling at 10 miles an hour which is seen by both the people in the train and the person outside (who, to their point of view, it’s moving at 100 miles an hour).
In this case, in this level of physics, you would say yes. But you also would have to say that all the observers are correct; none of them is wrong. Each one, from their own frame of reference, is correct in saying that the ball is either going at 10 or at 100 miles an hour. From the point of view of the ball...
Would you say that the ball is going at 10, and so the person outside the train has to add to that basic 10 another 90 of the train?
You could say that. But the ball – from its own point of view, inside the ball – can also say, “I’m going at 0 miles per hour, and these people inside the train are moving at 10 miles per hour, and the people outside are moving at 100.” All of those are correct. So the point is that none of the points of view is privileged; none of them is better than the other ones.
There is yet another frame of reference, which is the whole earth, or a spaceship outside the earth looking at this train and the little ping-pong ball. And that would also not be a privileged frame of reference. There is no privileged frame of reference that’s really absolute. All of them are right.
It's not the case that the basis for the movement is there, but then you have different points of view about the same thing. This is not the case. If you’re running towards me, I’m running towards you, and she’s watching us, each one of us is going to see different velocities of the whole situation, I’m going to see that she’s standing still and that you’re running to me at twice the speed of what I think my speed is. Am I more right than you? And you would see that my speed is different from what I think, because you’re also running towards me. So there is not like one basic movement which is correct and then it’s watched by different observers and interpreted differently. It’s not like that.
So, it’s not that there is a large chessboard of space-time that is the absolute measure of position and speed, and things like that, and everybody on that board that’s moving at a different speed observes something different, but what the chessboard says is true, is more true, is privileged. And that gets into the whole Chittamatra thing, because how would you know what the chessboard says? There would have to be somebody looking at it.
Another way of calling this chessboard would be that it’s like a screen. It’s not that the reality is like a projection screen which has very definite points and then things move on it. It’s not like that. If you ask, “Is this point in space the same as this point in space at the next second?” You cannot really say this. Because, for example, while we were speaking, this point of the earth has moved a few kilometers since we last mentioned this point. And also the whole solar system as such is also moving. These movements in space do not occur within a fixed grid or within a fixed projection screen that you could use as an absolute reference.
Does that means that these miles per hour, 10 or 100, are only created by the mind, and there’s no reference point to it?
I would say no, because it’s not only by the mind; it’s also dependent on your relative relationship to that object, your relative speed to that object. And you can’t even say that the ball is moving, because if you were sitting on the ball, the ball isn’t moving; it’s everything else that’s moving. And all of these statements are all equal about it. That’s the point. But it gets more complicated now with the twin paradox.
Also when we use the units miles per hour, an hour isn’t passing, and the ball isn’t moving ten miles. We’re only talking about a short period of time. So that’s also a projection – that if it were to move like that for an hour, it would go ten miles. I mean, you have to define hour, and you have to define miles.
Yeah. So also in that sense it’s relative.
The Special Theory of Relativity
Okay, so now I’m going on to a deeper level of relativity. This is basically the level that Einstein discovered with his special theory of relativity (which is not really a deepest point of view, but it’s deeper than what Galileo and Newton understood). One of the consequences of Einstein’s special theory of relativity is the so-called twin paradox, which is not really a paradox but actually something that would happen if you were to try this experiment.
The experiment is: You have two twin brothers, and one of them goes into a spaceship, and this spaceship is able to travel at, let’s say, 80% of the speed of light. And if this astronaut twin brother spent some years, measured in his time, let’s say two years in his time – in his internal clock and his mechanical clock, he saw that two years passed, traveling at 80% of the speed of light – and then he were to come back to the earth, he would see that his twin brother is a lot older. So the space traveler is younger than his twin brother.
This phenomenon occurs because when traveling at speeds very close to the speed of light, time slows down, so time passes slower. Does that mean that the person inside the ship feels that everything is slowed down? It’s not like that. It has nothing to do with that. For the person inside the ship, he looks at his watch and everything goes on as usual. It’s just when you talk about the relative perception of the person traveling at the very low speed on earth and the person traveling at the speed of light – when you look at the relationship between them, this is when relativity comes in. Relative to the brother who stayed on earth, the clock and all the biological processes of the traveling twin brother were slowed down.
One important point is that the velocity of the earth is actually very low. I mean, one tends to think that the earth is moving very, very quickly in space. But in relationship to the speed of light, it’s very slow. Relativistic effects do not become so important at that speed. So you could say that the speed of the earth traveling in space is a very low speed compared to the speed of light.
The Dalai Lama in his book The Universe in a Single Atom – which I definitely recommend – when he mentions the twin paradox, he says that it reminds him a lot of Asanga and how he went to Maitreya’s pure land to receive some of the most important Mahayana teachings. Asanga’s perception was that the time that passed was the time needed to have tea, but when he came back to earth to share the teachings, actually fifty years had passed. So the Dalai Lama says it reminds him a lot of this twin paradox that results from Einstein’s special relativity theory.
This is not only a thought experiment; this kind of lengthening or slowing down of time can be carried out experimentally. In the CERN particle accelerator in Switzerland, you can achieve speeds very close to the speed of light, but you cannot really accelerate an astronaut at that speed but only very small particles. However, there are some subatomic particles which have very, very small lives or half-lives. That means that whenever they’re generated, they disintegrate very quickly. Let’s say if you have a subatomic particle whose life is one millisecond. When you accelerate it very close to the speed of light, observing as an experimenter on the floor of CERN, moving at a very low speed relative to that particle, you will see that that particle has a very much longer lifetime. So this is a consequence of relativity theory. If you were sitting inside that little particle, you would see that the lifetime of the particle is still one millisecond. But from the point of view of the slow-moving experimentalist, it’ll have a very long lifetime. It’s kind of like an experimental validation of the theory of relativity.
Always relativity theory implies two frames of reference. Relativity theory says nothing about the speed of clocks within one single frame of reference. If both of us are moving at the same speed, relativity theory doesn’t tell us what time it is or how fast time moves. It does nothing like that. It’s only in relation to two observers moving at different speeds.
Another consequence of relativity theory is that all observers measure the same speed of light – you could say this is a constant – which is close to 300,000 kilometers per second.
Is it exactly 300,000?
No, it’s two hundred and ninety-nine blahblahblah thousand kilometers per second. It actually has no decimal points because the meter was defined in a way that the speed of light would be a number without decimal points. It was actually defined to be that. The definition of the meter is no longer a piece of wood, but it’s defined to make the speed of light a special number.
Which did they know first, the speed of light or the length of a meter?
The speed of light. They redefined the length of a meter so that it would be close to what was used as a meter before. So there are old meters and new meters. It’s an example of mental labeling and conventions. It's like redefining an hour, a minute, a seeond and stuff like that by using atomic vibrations. That’s the same thing.
So traveling at speeds close to the speed of light, time slows down and also space contracts.
There's a quote from Einstein, from 1949, that “Today everyone knows that all attempts to clarify this paradox satisfactorily” – the paradox of the twins, or the paradox of simultaneity – “were condemned to failure as long as the axiom of the absolute character of time, or of simultaneity, was rooted unrecognized in the unconscious. To recognize clearly this axiom and its arbitrary character already implies the essentials of the solution of the problem.” So basically he’s saying that our automatically arising feeling that there is simultaneity and that you can define absolute simultaneity – this unconscious assumption turned out to be a block to progress.
So I’m just going to give an example with three observers of what this would look like numerically. In this example:
- You have people at a mission-control center on Earth.
- And you have an astronaut on Mars, in a space station, and he has agreed to eat lunch exactly at 12 p.m. and then send a signal to Earth saying, “I ate lunch,” and then the folks back on Earth will say, “Oh, he ate lunch.” So they want to know exactly at what time he did it. The radio signal will take 20 minutes to get to Earth because the distance between the Earth and Mars is 20 light-minutes.
- Additionally there is a spaceship traveling at 80% of the speed of light which is moving from the left of the Earth, it’s going to pass Earth, and it’s going to go all the way to Mars. And it’s also going to watch the sequence of events.
Let’s first only look at what’s happening on Earth (Earth and Mars are moving at different speeds, but compared to the speed of light, their speed difference doesn’t play a role in this).
- The first event that happens before noon is that the people on Earth and Mars exchange light signals, and they measure the distance between them, they determine it to be 20 light-minutes, and they synchronize their clocks.
- So at 12 p.m. the people at mission control on Earth think, “Okay, surely the astronaut on Mars has begun to eat lunch,” and then they prepare to wait 20 minutes to receive the radio signal.
- The spaceship is traveling from the Earth towards Mars. The people on Earth know what velocity the spaceship is traveling, so the people on Earth deduce that at 12:11, so eleven minutes afterwards, the ship surely must have encountered the signal that they will receive a few moments later.
- So at 12:20 effectively the signal from Mars arrives at Earth, and the people on Earth know that the astronaut has eaten lunch at 12:00 (because the signal arrived at 12:20). So now they know that noon on Mars is the same as noon on Earth.
- And at 12:25 the ship arrives at Mars.
So the whole point in this analysis is that because these two planets are moving at almost the same speed, they can actually synchronize their clocks, and they can actually recognize events in a similar time frame.
But, however, if this whole situation is seen from the ship traveling at 80% of the speed of light:
- The first effect that this has is a contraction of space. So the ship measures the distance between Earth and Mars and determines it to be 12 light-minutes. So not 20 light-minutes but 12. Space is contracting because the ship is traveling at such a high speed.
- So at 12 p.m. exactly, the ship passes the Earth. And the person in the spaceship thinks, “Oh, because I synchronized my clock with the Earth, the Martian must be eating lunch right now.”
- So at 12:07 the signal arrives in the ship, and the person in the ship says, “Okay, the person on Mars must have eaten lunch early.” It’s only 12:07, according to the time on the spaceship, so that means that he must have eaten lunch before noon.
- So at 12:15 Mars arrives at the ship – the ship arrives at Mars, or Mars arrives at the ship (it’s actually equivalent) – and the rocketman and the Martian notice that their two clocks are out of synch, and they disagree about who is right. Actually both are right.
- And at 12:33 (the spaceship’s time) the signal arrives at Earth.
And the clock discrepancies demonstrate that there is no universal present moment.
So you cannot say that there is a universal present moment. What for some seems to be a present, for others it’s either the past or the future. So this is one of the consequences. My present can be someone else’s past and a third person’s future if all three are moving relative to each other. So all moments are equally valid. There is no privileged present moment as such. However, one has to say that, according to these laws and according to the limits of how fast information can travel (which is the speed of light), causality has to be maintained. No matter how weird these time discrepancies and clock differences look, causality, the activity of cause and effect, is maintained.
However, some scientists conclude from this picture of time that, because there is no privileged present moment, you can talk about a “block time” or a fixed timescape that you’re simply sliding in – that everything is already determined back into the past and forward into the future; everything’s already completely set.
Before you get into this discussion of block time: If time is integrally related to the speed of light, and causality is integrally related to the speed of light, what about causality and dark matter (which doesn’t reflect light, and so there’s no information going on)? Dark matter and dark energy supposedly makes up ninety-something percent of the universe. So we’re not talking about black holes, where causality doesn’t seem to work, but what about most of the universe? Does that mean there’s no causality if there’s no light or speed of light with which you would reckon time?
Well, first of all, speed of light is like an upper limit to the speed that anything can travel, any kind of information transfer, any kind of interaction. Speed of light is not limited to light. For example, electrons also cannot travel faster than the speed of light. Any kind of particle or any kind of interaction. Dark matter, even though it cannot be directly seen, it still interacts with the rest of matter – interacts, for example, through gravity. The fact that it still interacts means that it’s still bound by the laws of causality, and the speed of interaction would still apply.
I think the problem that I’m having here is that there seems to be not a very clear differentiation between time and information about time.
That’s actually how time is defined in physics, because you have these problems with relative reference frames. Heisenberg writes that the future is everything that you could possibly know about but haven’t known about; the past is everything that you can know about, where the laws of physics wouldn’t prevent you from knowing that; and the present is anything in between, which might be a timespan.
So in fact time – past, present, and future – is very much integrally related with mind and knowing, as Buddhism would say.
However, material processes also experience the same kind of time dilation. Also that’s why when you accelerate a subatomic particle, it also perceives the same kind of time dilation.
The problem is that also causality itself cannot be faster than the speed of light. Why? That’s the way it is. And this is an important point, because you cannot exchange information faster than the speed of light. This is why there is this connection between time and information.
But take the example of two photons which were previously entangled, but are sent in opposite polarizations when one is observed – or in the case of electrons, when you measure the spin of one, the spin of the other particle is completely determined. This happens at a speed that is larger than the speed of light. However, you cannot transmit information through this medium. It would be great, but you can’t.
So how do we talk about time in that context?
The thing is that this collapse of the wave function or this collapse of superimposed states – of up-and-down spin, for example, when you just get up or down – this automatically causes the other particle to also collapse at the same time.
In no time?
In no time, it just collapses. But you cannot use this to transmit information.
What if you have two spaceships moving in opposite directions, and you have entangled photons which are entangled with each other. Why couldn’t they use the states of these entangled photons to send a signal (for example, to tell the other spaceship to turn back when they see the signal)?
The problem is that in order to even read the signal, you have to make the wave function collapse. First you have both photons coexisting in two states at the same time. If we’re talking about photons, then we have to talk about polarization, not spin. So we’re talking about the polarization. There are two states of polarization, say zero and one, for photons, and while the particles are entangled, they coexist. And it’s also the case if they’re entangled, no matter how far apart they are, if you make one of them collapse by measuring it – you measure, you ask the particle, “Are you in a zero or in a one state?” – if you ask that, then it will immediately collapse either to one or zero with 50% probability. And automatically, when you do that, the other entangled photon will collapse to the opposite state (if this was one, the other will be zero). The problem is that if you measure it, you make it collapse, and you make it acquire the opposite state. What information can you transmit with this?
Can you somehow choose the states that you want to collapse it in?
There’s the problem. You cannot choose the state. It doesn’t have to be 50 % likely which one will be chosen. It can be other probabilities. However, you cannot choose this. This is one part of quantum mechanics; it’s stochastic, which means there is a random probability distribution or pattern that may be analyzed statistically, but may not be predicted precisely.
What about an experiment where you have two of these particles, one of them is in a zero state, the other is in a one state. And the way to send a signal from afar is to change the state of the first particle, and then the other one will change automatically, and so then you’ll have a signal.
The problem is that you cannot do this unless they’re entangled, and they stop being entangled once you measure them for the first time, so you only get one chance to change them at the same time. You said one of them was in a zero state. You can’t know this unless you already measured it, and if you already measured it, you collapse the wave function, which means that they are not entangled anymore and they will not do this nice trick anymore.
So what it comes down to is how is there a connection between the two when they must have traveled miles and miles. When one wave function collapses, how does the wave function light-years away know that it should collapse in this way or another?
Nobody knows what this connection is. Nobody understands this. It’s not known how these particles know about each other, why they collapse simultaneously and into opposite states.
One of the wildest interpretations is the so-called many-worlds interpretation, or Everett interpretation, of quantum mechanics, which basically says that when you have a situation like this, the universe splits into all possibilities. A universe is generated automatically (a world leaf I think it’s called) where the first particle collapses to zero and the other to one, and another universe leaf is formed where the opposite happens. The thing is that this interpretation agrees very nicely with a lot of the properties of quantum mechanics – in some cases better than the Copenhagen interpretation, which is like the old-school interpretation.
Basically that the active act of measuring something, whether by a consciousness or by an unconscious interacting particle, causes the wave function to collapse. It’s a causal thing. However, there is no known mechanism why it should cause it to collapse. This has never been explained.
This is very interesting if we correlate this now with Buddhist theory, let’s say in a Chittamatra sense, which is that observing something establishes that it exists; it doesn’t cause it to exist. The same thing as we were saying in terms of mental labeling in Prasangika. Mental labeling doesn’t create it, but it establishes its existence as this or that.
Also what is interesting is when you say that two things occur simultaneously, that’s time because simultaneous is also from a point of view of time.
In the Buddhist teachings, we were talking about how time is the interval between the experience of a cause and the experience of an effect, and so we’re talking about experience here. Whereas from the Western point of view, you’re talking about information that is transmitted which would allow you to have an experience at two different… well, you can’t say it’s at two different times, but which would allow you to experience a cause and experience an effect.
So then of course the question is (and this came up in our discussion of the existence of external phenomena or not): Is the information coming from an external causal event, like a person eating on Mars, and then we know the result of that later on (so there’s a time interval)? Or is the information coming from our own mental continuum? Or where is this information coming from? But it’s this whole idea of information. And whatever that information is, the information is encoded in light? Or what is the information? What is information? That’s a difficult question, and perhaps you can answer that from informatics. Science is also dealing with the question of: What’s the connection between cause and effect? Is it an information connection? What is it?
Information is whatever allows you to reduce the uncertainty, to refine your guess, whatever allows you to refine your understanding.
What type of phenomenon is it? Is it a form of physical matter? Is it a way of being aware of something? Is it neither? Is it a static fact? Is it affected by things? Where would you put it in the Buddhist classification scheme of knowable phenomena?
It would probably be a nonstatic phenomenon. No, it would probably be static.
I don’t know. I’m asking you.
I’m not sure. I never thought about it.
If it’s static, how can it move at the speed of light? How does information come from an object to us? Before you know the information, how could you say that the information has left its source? A star a billion light years away – that information left that star, we receive it now, and you somehow infer that it left there a billion years ago. Well, did it really leave there a billion years ago? Was it information then?
Well, information is an abstract term. I mean, even if you use it just conventionally and say, “I’ve received information,” or something like that, or you have “essential information,” then information is an abstraction that might be made on the basis of different carriers. For example, I could have a CD, or an old-fashioned record or whatever, as the carrier that carries information about music, and I can reproduce it.
But you need a physical basis for the information, don't you?
So the physical basis is not the same as the information, which would be an abstraction imputable on that, I think. If you think about it, also the information received depends on whether you know how to decode it. So it not only depends on the message; it also depends on how you decode it. There can be more information than you know how to decode.
So when a Buddha teaches and everybody hears it in their own language, is it that the Buddha’s giving common-denominator information, and everybody then decodes it according to their own conceptual framework?
Difficult. I don’t know. Can we say that ultimately information is a cognitive category, like a fact, so it doesn’t make sense independently of a cognitive reference for it.
But if it’s a category, it's static and so can’t be heard. But isn't the static information a cause for hearing it? If information is a static fact, is it created?
Well, you have to differentiate here. The mental event that’s cognizing the category – that would be created, but not the contents, the cognitive content, which would be a category, which would be static.
So the information doesn’t get changed? Can information get distorted?
I must say, information is a very difficult concept to fit within the Buddhist framework, this concept of information.
However, it’s gaining a lot of preponderance in the scientific view (in a way, even more than matter and energy). So it’s something to consider.
But in any case, time seems to be, from a Western point of view, very much tied up with information, and information implies relationship with a mind – inform. If there were no minds, could there be information?
A plant, for example, gives its genetic information through seeds to the next generation. From the Buddhist point of view, that’s not a mind there.
Well, the molecular structure of a crystal or a snowflake or stuff like that, that’s information?
It’s a form, a form of information. It’s both the carrier and the message, in a way.
So now we are confusing a pattern with information. Is it information if it’s never known?
No, because information is what reduces uncertainty. And it has to be transmitted. There has to be a source, and there has to be a receptor, and the receptor’s uncertainty is reduced.
Take the example of a crystal. You can have a bowl full of water below zero degrees, and if it’s very still, it doesn’t freeze. However, if you add just a drop of ice, just a small piece of crystal of ice, it will immediately crystallize. It’s a kind of information about the structure that ice should have.
So information doesn’t have to inform a mind.
Right. Western science is concerned mostly with external objects, and Buddhism concerns itself mostly with sentient beings and with the mind. However, there is definitely a relationship and a transfer of information from one external object to another.
But relativity all has to do with observers, doesn’t it?
They don’t have to be minds, though. They can be two cesium atoms.
They can be two cesium atoms, but it would be irrelevant unless somebody looked at the so-called information from the cesium atoms. How would you know?
Physics speaks about the vanishing of uncertainty when it speaks of quantum leaps. You have an interaction, and that interaction allows you to know more, and so it changes your view of the thing, and only that can be described in the formulas. Physics describes what could be known about something in a certain setting, not the thing independently of that, because you can know more than you know, if there is more to the thing that you could know.
What about these entangled particles? Isn’t it that when you observe it, then it’s one or the other – it’s either zero or one?
Until you observe them, they are superimposed.
So where’s the information? Where’s the information that it’s zero or one?
It still has not been decided.
So there is uncertain information? Your observing it makes it certain, so it makes it information?
So then is there time?
It’s also a difficult issue because it’s not possible to unite quantum mechanics and relativity. I mean, a moment ago we were criticizing the idea of simultaneity, and right now we have no problem with the simultaneity of two particles collapsing at the same time, no? This problem also arises because there is no theory of quantum gravity.
What if those particles were traveling at different speeds? What makes two particles entangled?
Two particles become entangled in the physical process of them being created, them being generated.
And will they always be traveling at the same speed?
Not necessarily. You could even contain one and make it stationary, and the other one could travel in a fiber optic for miles and miles. And it’s been done actually.
So then really simultaneity wouldn’t work.
The problem is that normal processes that can’t be explained without quantum mechanics really can’t perpetuate themselves through space at a speed faster than light, and here you have some sort of strange connection which is not limited by the speed of light.
It's "spooky action" at a distance. Einstein was very much put off by quantum mechanics, because this exactly undermines the thing that he found in relativity. And in a way it undermines causality because then you don’t have this neat chain of causation where one thing will trigger the next, and that triggers the next. However, you cannot transmit information through this. But it points to a connectedness that is not limited to the normal causality which is limited by the speed of light. So you get two different partial theories which unto now haven’t been combined, because nobody has been able to completely remove the contradictions.
Anyway, let’s go on.
Okay. So we made a little jump to quantum mechanics now, and this is actually good because I had not really devoted much time to it here. I’ll tell you in a second why I didn’t devote so much.
Past, Present, and Future in Western Science
Dr. Berzin: What’s next in the Buddhist presentation is: Past, present, and future – are they simultaneous or what?
Some scientists conclude from this fact that there is no privileged present moment that you have past, present, and future which are just as real or as fantasy as each other. So if you have no privileged present moment, then you could conclude that time is a kind of timescape – in the way that you could speak about a landscape – in which you can move forwards or backwards. And experience is only movement in these four dimensions, but it’s actually that everything is already preset, in a way, and you’re only moving forward in this direction. I think this interpretation is not very good if you take causality into consideration, but some scientists hold this view.
So now I’m going to jump to this factor – I think it’s not very well known – that laws of physics are actually time-reversible. The laws of quantum mechanics, which is this last one – which are basically Schrödinger’s equations – are time-reversible mostly, except for the phenomenon of collapsing wave functions. But the classical simplifications of Schrödinger’s equations – which are both Newton’s laws of motion and Maxwell’s equations which described electromagnetism – all of them are time-reversible, meaning that if you played a tape of any of these laws in action in the forward direction and the reverse direction, you really couldn’t tell which one is a correct direction.
Could you please give a more specific example? Those of us who don’t have a scientific background don’t really know what you’re referring to.
Yes, it’s coming. The example is a water molecule and what water looks like at a microscopic scale. Water’s a good example because you have the action of all these laws together:
- You have the laws of electromagnetism because water has a positive and a negative partial charge, meaning that it has positively charged hydrogens and slightly negatively charged oxygen.
- Newton’s laws of motion also play a role because water molecules are continuously crashing into one another. Think of liquid water and how that looks at the microscopic level. They are constantly undergoing crashes against each other, and so the laws of motion apply.
- Schrödinger’s equations (meaning quantum mechanics) also apply because you have electrons surrounding this molecule. And if you want to know about the behavior of the electrons around it, you would have to solve Newton’s equations of motion.
So I’m going to show you a little movie of so-called molecular dynamic simulation of water to demonstrate how it’s really hard to tell if these laws are going in the forward or the backward direction. In the case that if you have an equilibrium – meaning that the water is at a fixed temperature, say 25 degrees Celsius, and if the water is not undergoing any phase changes, meaning that it’s not evaporating and it’s not freezing – if the water is left alone in this equilibrium of 25 degrees, if you look at the microscopic structure of it, which is dynamic, you can’t really tell if it’s going in the forward or the backward direction.
So the big part is the oxygen, and the two smaller parts are hydrogens. And the waters are interacting with each other following, in this case, the classical Newton’s laws of motion. These yellow things that you’re seeing there are interactions between positive and negative parts, also called hydrogen bonds. And think about it. If I played this in the reverse direction, could you really tell that I’m playing it in the reverse direction? All the little clashes would be played back in the reverse direction, but could you really tell? Sadly this computer format doesn’t let me play this video backwards, which is what I wanted to do, but I cannot do it, but try to imagine what this looks like when you play it backwards.
So time reversibility means that at a very, very microscopic scale within the equilibrium regime, all of these laws of physics are time-reversible.
To help those who are just reading or listening to this: If you imagine a container filled with ping-pong balls, and you shake it up, and you take a movie of the balls and their interactions as they bounce against each other, and you play that forward and you play it backwards, you wouldn’t be able to tell which one is the forward one and which one is the backwards one.
So, for example, Newton’s third law of motion, their action and reaction, which is definitely active in this computer simulation, is time-reversible.
So what makes nature have an arrow of time? What makes us definitely distinguish what is the direction of time? The answer has to do with irreversibility and with a quantity called entropy, which was discovered by a guy called Rudolf Clausius in 1865. He lived here in Berlin. Actually it’s very likely that the concept of entropy was invented in this city. Entropy can be defined for any kind of random event or for any kind of event that occurs that can have several possible outcomes.
What is entropy?
Entropy is the amount of disorder in a system. For example, ice (frozen water) has a much lower entropy than molten water, because in the molten water – in the glass of water – you would have many more possibilities for the water to arrange. In the ice, in the crystal ice, the ice is very, very tightly packed in a very regular shape, so the entropy of that shape would be a lot lower because it’s a lot more ordered.
Is it measured with numbers and a unit?
It’s measured with numbers and a unit. In thermodynamics, calories per degree kelvin are the units of entropy. However, entropy has these units only so that they cancel out in a formula called free energy. The main point here is that entropy is only a measure of the multiplicity or the amount of possibilities available to a substance. So water has available a lot more possibilities than ice, in that sense.
So that would be very relevant to karma and the discussion of karmic tendencies. Does it have a large entropy (it could ripen into many possible forms) or a very low entropy (it could only ripen into one possible result)? You could apply entropy to karma in our Buddhist discussion. So that’s very interesting.
Matthieu Ricard suggests that entropy is very similar to the concept of subtle impermanence because the entropy of the universe is raising, is always going up. The universe’s entropy is always increasing. The disorder of the universe is always increasing. So entropy is similar to this subtle impermanence. Do you know what I mean?
Well, if things are going to a more disordered state, a bigger multiplicity of states, that change is happening moment to moment. Subtle impermanence means that each moment something is going closer to its end, and the cause for the disintegration of something is its creation.
Exactly. That would be another statement for the second law of thermodynamics, in a way. Being made of parts means that they are arranged in a very special way with a very low entropy, and because entropy’s always increasing, these parts are becoming disordered and disintegrating, thereby destroying what had been constructed. So it’s not entropy that’s similar to subtle impermanence. Rather, it’s the second law of thermodynamics – that entropy is always increasing. That’s the one that’s actually similar to subtle impermanence.
But what about in terms of the ripening of karma? You do a certain action, and there are many, many possibilities of what it could ripen into. And as you progress in terms of your lifespan, or many lifespans, you could do various things which would make it stronger or weaker, etc. But when it ripens, then it can only be in one state that it ripens. It’s going from many possibilities to less possibilities, so that’s negative entropy.
Yeah. But that would also be, in a way, similar to the collapse of a wave function. It has many ways to ripen but just ripens into one.
So how does that fit with entropy, the laws of entropy, that the universe is going to increase the entropy? When things happen, that means decreased entropy.
Yes, but the entropy of the matter and energy is always increasing [which means their order is always decreasing]. I have not given thought to the mind-stream’s karma and how you could define entropy for it. It would be very interesting.
Well, it would be a very good topic for you to analyze and report back.
Okay. Now in this next movie, you can certainly see that something is wrong. First you have a liquid with mixed colors, and suddenly this liquid starts unmelting into ice, and it forms ice of different colors [which means it has more order]. The colors of the water unmix and they form ice, which is definitely something that we would never see.
The water looked as though it was just one color, mixed together to make a blur.
Yes, that's because all the colors in the beginning of the movie were mixed together as a blur, and the color started separating, the ice started reforming, and we definitely recognize this is something that’s impossible.
So what is this an example of, increased or decreased entropy?
It's playing backwards from what would actually happen. So it would be an example of decreasing entropy, which would be against the second law of thermodynamics. So this would never happen.
I see. If that were to happen, it would be a decrease of entropy because it goes to a higher state of being fixed in structure.
Exactly. So the normal course of things is of course for things to decay and to go into a state of higher entropy.
We naturally recognize an arrow of time, so when we see a process like that, of ice unmelting, we recognize it as wrong. And it’s not because of the laws of mechanics – it’s not because of the laws of quantum mechanics – it’s rather because of entropy, which creates a kind of arrow of time, because everything is going into a state where the possibilities are greater. For example, the water on its own goes from this state of very ordered ice into a state of molten water.
What happens when it’s winter and the water turns to ice?
Well, that’s because the general temperature allows for it, but energy is also released into the system, so it’s an equilibrium.
When you put water in an ice cube tray into the freezer, the freezer has to extract energy from the water in order to generate ice. So it has to take energy or heat away. However, you have to plug in your freezer in order for it to do that, right? And this is because you need more energy to generate that ice than the energy that you get from the ice itself. Because you want to reduce the entropy of that system, you need to put a lot more energy than the little energy that comes out of the ice when it becomes ice. A demonstration that ice actually releases energy when it freezes is that – the reverse operation – when you put it into your drink, it absorbs energy in the process of melting.
The heat convection belt of the whole earth would make some regions colder than others, but that still doesn’t violate the second law of thermodynamics. At certain times of the year, certain regions will be colder.
So can we say that time is a measurement of different states of entropy? I’m trying to stay relevant to our topic.
I think you can say that entropy gives us a natural feeling of which direction time goes forward, nothing more. It doesn’t tell us the rate of change, because there is no such thing as a rate of change of time; there is no “one second per second.”
There’s only one little topic left. Just as a last topic, I wanted to briefly mention that there is such a thing as a biological clock which works inside all ourselves. All living beings, from bacteria all the way to plants and animals, humans, we all have actually more than one biological clock. I’m not talking about aging. I’m talking about the 24-hour cycles of ourselves and all the things that are coupled to it, like release of hormones and the substances that keep us awake, and so on, states of the brain – all of these are coupled to internal clocks.
Is it a function of there being light?
No, it’s a chemical function by itself. It can become entrained by light, meaning that if you have access to light, your biological clock will synchronize with this light. But if you’re locked in a room with no light, your cycles will continue to be more or less 24 hours; once you see light again, they will synchronize, so to speak, again with these cycles. But they are not controlled by light.
What about a blind person who doesn’t see light?
Interesting. I don’t know about this. Their biological clocks probably have other cues. I think I have heard that if some part of the optical nerve is damaged – or I don’t know what should be damaged – so that you can’t see visual images, then still in some cases it seems to be possible that the information of it being bright or not being bright still affects you through the eyes, although not in a way that is processed as seeing. And that also seems to affect people’s feeling of time in some way. But if your eyes are plucked out, then of course that doesn't happen.
What about the industrial raising of chickens for eggs? They keep chickens in this house with 24 hours of light, and as a result they give more eggs. But the eggs are not so good as when there was darkness for the chickens to enjoy.
You are forcing the biological cycles when you keep a chicken 24 hours with light in order for them to produce more eggs. Certainly you are making these biochemical functions run much faster.
One big development two years ago: It was possible for the first time to make a biological clock in a test tube, using just three proteins, and without light, without the influence of light, have them perform a 24-hour cycle. And these are the three proteins that do this, just like a representation we use in molecular biology of the shape of these proteins. And you basically need three different proteins and an energy source, which is ATP, and you put those in a test tube and they perform a 24-hour cycle.
ATP is adenosine triphosphate. It’s like the energy source – it’s the major energy currency of plants, animals, and humans (well, we are animals). It’s a chemical, and it’s the major energy currency of the body, the most easily tapped energy source. Of the food that we use for gaining energy, a lot of it gets transformed directly into ATP, which is stored in the cells and is ready to be used in any process needed. You just have to break a little chemical bond and use the energy that’s released, with no residue. So it’s very clean, so to speak. All the dirty stuff is done in other parts of the metabolism.
So you just need three proteins and ATP, and you can reproduce a bacterial biological clock like this.
Why is it 24 hours?
It just works like that. You can change the temperature, you can change the pH – you can change a lot of conditions – and it’s very resilient and keeps to 24-hour cycles.
Also, as I mentioned, we don’t have just one biological clock; as humans, we have more than one biological clock. Different functions are controlled by different biological clocks, but this is not really well understood. The ones that I’ve read about are actually 24-hour clocks which can be entrained, but I don't know if all of them are 24-hour cycles.
Give us an example of things that run according to biological clocks. Sleep I guess would be an obvious one. What else?
Mood. Hunger. Going to the toilet. It depends on the person. But what happens when you get jetlag is a good example of how this biological clock needs a reset and needs to be entrained again.
Why is it some people have horrible jetlag and some don’t? I’ve never really experienced jetlag. I travel all the time.
It probably has to do with the biochemical flexibility of that biological clock. It’s probably that different people have evolved different proteins and mechanisms to deal with it. Some of them are easier to reset. But, in a way, a biological clock or a bacterial clock is not really that different from a mechanical clock in the sense that it’s subject to the same laws of physics; it would be subject to the same kinds of effects from relativity. It’s no different from a cesium atom being measured. It’s just time, in that sense.
Dr. Numata: Just a brief take-home message: We measure change, but we don’t measure time itself.
Dr. Berzin: Well, Buddhism would agree with that.
Like relativity theory would say that there is no universal present.
Buddhism would agree with that too.
Mechanical laws are time-reversible.
As we said, that has to do basically with the observation of events and not with time itself.
However, through entropy – which is just the tendency towards decay or disorder – we perceive an arrow of time, that time flows in one direction and not in the other one.
How does entropy fit together with cause and effect?
I don’t know. I really don’t know. So this is homework.
Right. Think about that. Because this is saying that entropy, the tendency towards decay, gives an arrow of time. But Buddhism would say there is a certain arrow of time. It isn’t that something that’s already happened is going to happen in the future; it’s not yet happening. So it has to do with cause and effect. So there must be a relationship. So that we’d have to think about.
And I would think, as you said, there are the various causes, and there are many possibilities of what could be the result, and when it actually reaches the result, that’s the most ordered state. And this is a very important principle in terms of cause and effect in Buddhism, particularly cause and effect in Buddhism, and particularly in terms of what a Buddha knows when a Buddha knows the future.
But we’ll get to that. Does a Buddha just know all the possibilities that could happen? Does a Buddha know the final, lowest entropy state of what actually will happen? These are questions that we have to think about. Does a Buddha know what could happen or what will happen, what will definitely happen?