## Arguments for discrete time

• 891
I have a couple of arguments for time being discrete rather than continuous (actually similar arguments can be used for discrete space too). Thanks in advance for any feedback.

1. A point in space cannot have size=0 because it would only exist in our minds and not reality (no width; insubstantial)
2. Similarly, the point in time ’now’ cannot have length=0 (if it exists for 0 seconds, it does not exist)
3. Or if a ‘now’ had length=0, then a second would contain 1/0=UNDEFINED ‘nows’
4. So ‘now’ has length >0
5. Can’t be length = 1/∞ because ∞ does not exist (∞ + 1 > ∞ making a nonsense of ∞. Or if you define ∞ + 1 = ∞, implies 1 = 0)
6. So a ‘now’ has a finite, non-zero length. Time is composed of a chain of ’nows’ so time must be discrete

Or

a) Imagine a second and a year
b) By the definition of continuous, both time period are graduated identically (to infinite precision).
c) So there must be the same information content in both (same number of time frames: ∞)
d) But a year should contain more information than a second
e) Reductio ad absurdum, time must be discrete
• 891
Or

Let length of now = L, then:

L/second > L/year
->
L x year > L x second

Equality not satisfied with L=0 or L=1/∞

L must be finite and > 0

IE time is discrete
• 7.7k
I have a couple of arguments for time being discrete rather than continuous (actually similar arguments can be used for discrete space too). Thanks in advance for any feedback.

1. A point in space cannot have size=0 because it would only exist in our minds and not reality (no width; insubstantial)
2. Similarly, the point in time ’now’ cannot have length=0 (if it exists for 0 seconds, it does not exist)
3. Or if a ‘now’ had length=0, then a second would contain 1/0=UNDEFINED ‘nows’
4. So ‘now’ has length >0
5. Can’t be length = 1/∞ because ∞ does not exist (∞ + 1 > ∞ making a nonsense of ∞. Or if you define ∞ + 1 = ∞, implies 1 = 0)
6. So a ‘now’ has a finite, non-zero length. Time is composed of a chain of ’nows’ so time must be discrete

Or

a) Imagine a second and a year
b) By the definition of continuous, both time period are graduated identically (to infinite precision).
c) So there must be the same information content in both (same number of time frames: ∞)
d) But a year should contain more information than a second
e) Reductio ad absurdum, time must be discrete

Alternatively, one can realize that mathematics doesn't actually occur per se in the external world, that time is just change/motion, and that change/motion only makes sense relatively (to something changing at a different relative rate/in a different way), so the question of whether it's discrete or continuous is kind of a category error.
• 891
time is just change/motion

If time is just change/motion, why does it run slower when an object travels near the speed of light or is near an intense gravity field?

If time is just change/motion, what mechanism enforces the speed of light speed limit?
• 7.7k
If time is just change/motion, why does it run slower when an object travels near the speed of light or is near an intense gravity field?

The effects on mass (basically a kind of "pulling" on the mass in both cases) is a counteracting force that make changes/motions relatively slower.

Think if you were moving a bunch of helium-filled balloons around. If something were pulling on the balloons, it would be harder to move them around. Near light-speed and intense gravitational fields are how much of a "pulling" difference we need to notice a significant difference in how things are relatively moving/changing.
• 891
The effects on mass (basically a kind of "pulling" on the mass in both cases) is a counteracting force that make changes/motions relatively slower.

But the force of gravity is attractive, why should it slow motion?

Anyhow, there are no massive objects involved in the case of an object is travelling near the speed of light. Speed = distance / time so the universe must be time-aware to enforce the speed limit.
• 7.7k

Pulling is attractive, right? Pulling is towards something. Imagine you have a simple electron orbiting a proton. If the electron is being pulled on gravitationally, it's more difficult to keep moving in the orbiting motion. Hence a relative slow-down of motion.

Speed increases mass. That's the reason that exceeding light speed isn't possible.
• 891

I need to read up on relativity. Thanks.

If mass increases with speed, then the universe must be speed-aware? In some sense the universe must know how fast an object is going to allocate the appropriate mass.

Speed = distance / time so the universe must be time-aware?
• 7.7k

What increases is the inertial mass, or in other words, the amount of resistance it has to any change in its motion.

It's just a fact about how relative motion works.
• 891

Maybe I'm getting confused, but:

E = mc² ∕ √ (1 - v² ∕ c²)
So
m = E × √ (1 - v² ∕ c²) / c²

So time (in the v term) determines mass. So something in the universe must be aware of time else it could not assign a mass. That suggests time is real?
• 7.7k
So time (in the v term) determines mass. So something in the universe must be aware of time else it could not assign a mass. That suggests time is real?

My view of time isn't the standard physics view of time . . . well, and that's especially the case since physics still leaves time unanalyzed ontologically and just treats it as an instrumental quantity that doesn't need to be pegged otherwise.

Time is definitely real on my view. Only creatures with minds are aware of anything, though, and that's a very small subset of what we find in the universe.
• 198
I have a couple of arguments for time being discrete rather than continuous (actually similar arguments can be used for discrete space too). Thanks in advance for any feedback.

1. A point in space cannot have size=0 because it would only exist in our minds and not reality (no width; insubstantial)
2. Similarly, the point in time ’now’ cannot have length=0 (if it exists for 0 seconds, it does not exist)
3. Or if a ‘now’ had length=0, then a second would contain 1/0=UNDEFINED ‘nows’
4. So ‘now’ has length >0
5. Can’t be length = 1/∞ because ∞ does not exist (∞ + 1 > ∞ making a nonsense of ∞. Or if you define ∞ + 1 = ∞, implies 1 = 0)
6. So a ‘now’ has a finite, non-zero length. Time is composed of a chain of ’nows’ so time must be discrete

Or

a) Imagine a second and a year
b) By the definition of continuous, both time period are graduated identically (to infinite precision).
c) So there must be the same information content in both (same number of time frames: ∞)
d) But a year should contain more information than a second
e) Reductio ad absurdum, time must be discrete

Who says the temporal continuum needs to contain instants? Likewise who says that the spatial continuum needs to be pointy? Perhaps the continuum has no fundamental level at all, no unit with which all other quantities are multiples of.

If that is the case, then the idea of "now" as a snapshot moment in time is mistaken and the passage of time as a succession of said moments (not unlike a succession of strips on a piece of film) is also confused. This is what you seem to implicitly assume in the your argument. Just as objects may be distant from one another without any fundamental length, events simply come and go continuously without any fundamental duration.
• 46
Who says the temporal continuum needs to contain instants? Likewise who says that the spatial continuum needs to be pointy? Perhaps the continuum has no fundamental level at all, no unit with which all other quantities are multiples of.

If that is the case, then the idea of "now" as a snapshot moment in time is mistaken and the passage of time as a succession of said moments (not unlike a succession of strips on a piece of film) is also confused. This is what you seem to implicitly assume in the your argument. Just as objects may be distant from one another without any fundamental length, events simply come and go continuously without any fundamental duration.

I agree. The concept of 'now' presupposes that time exists; and now separates the past from the future - two more meaningless concepts without that of time itself.

Einstein said that space-time is one 'thing' I think and that the 2 cannot be separated. So, since we don't doubt space exists, can we doubt time does too? One thing that fascinates me is that time only flows one way (so far as we know) - whereas movement in space can go back and forth. I considered once whether time could flow just as well backwards, but concluded it couldn't, because the laws of cause and effect wouldn't work in reverse. So surely time must exist, but what it's made of must be similar to what space is made of. And I think space must have some physical form because it is warped by mass so that passing light beams are curved by it. How does the light beam know to travel in a curve?
• 891
Who says the temporal continuum needs to contain instants? Likewise who says that the spatial continuum needs to be pointy? Perhaps the continuum has no fundamental level at all, no unit with which all other quantities are multiples of

What structure does time have if it's not a series of instants?

events simply come and go continuously without any fundamental duration.

But if an event has no duration it would not exist. 'Now' could not exist if it had zero duration. Think about filming someone for zero seconds - you'd have no film right?

How many zero duration 'nows' in a second? 1/0=UNDEFINED. Thats not right.

The concept of 'now' presupposes that time exists; and now separates the past from the future - two more meaningless concepts without that of time itself.

Because time has a start (see for example https://thephilosophyforum.com/discussion/4702/argument-from-first-motion), it must be real.

We can also tell the difference between past, present and future so there must be something special about 'now' so the concepts of past and future have meaning. Some sort of positional cursor that regular eternalism/relativity does not incorporate must exist.

So surely time must exist, but what it's made of must be similar to what space is made of.

Yes as I mentioned the same arguments work for space too.

One more argument. Consider actual infinity. Aristotle who defined it did not believe in actual infinity. It's a mad concept so I don't believe in it either. Consider a second in the past. The definition of continuous time implies that a second must contain an actual completed infinity of ‘nows’. So all those 'nows' actually existed; thats a funny money number of 'nows' (the cardinality of the set of natural numbers).
• 198
What structure does time have if it's not a series of instants?

Just a series of events without any smallest units. Similarly space without points would simply be space without any fundamental composition. There is no need for time to be a series of instants or fundamental units any more than there is a need for space to be composed of fundamental units or points.

But if an event has no duration it would not exist. 'Now' could not exist if it had zero duration. Think about filming someone for zero seconds - you'd have no film right?

I never said that there are events that are instantaneous nor that time is composed of them. Quite the opposite really.
• 891
Just a series of events without any smallest units

Problem is that means a second and a year would have the same information content which does not seem right. Clearly more information in a year - the continuum seems paradoxical. Maybe it's one of those concepts that we can conceive of in our minds but never occurs in reality? Reality seems deeply logical and free of paradoxes.
• 198
Problem is that means a second and a year would have the same information content which does not seem right. Clearly more information in a year - the continuum seems paradoxical. Maybe it's one of those concepts that we can conceive of in our minds but never occurs in reality? Reality seems deeply logical and free of paradoxes.

Thing is, you're arguing against the opposite of my position. I never advocated for the point continuum where everything is made up of an infinite number of points (which would lead to your criticism), but instead a gunky continuum that doesn't contain any such fundamental units at all. Personally, I find the point continuum to be a useful tool that doesn't describe reality, but that does not mean I take reality to be discrete, which is a concept I also consider to be problematic in other ways.
• 46
We can also tell the difference between past, present and future so there must be something special about 'now' so the concepts of past and future have meaning. Some sort of positional cursor that regular eternalism/relativity does not incorporate must exist.

I think this again is a circular argument. The past and the future may exist as concepts within that of time in our minds, but they have no concrete reality outside our minds - and that's even if time does exist.

An interesting idea is that of the man with no memory. For him the past does not exist. he simply experiences a continual present. So if none of us had any memories, would the past exist at all? Likewise the future, assuming we had no imagination to picture what it might hold? It seems to me hard to argue that the past exists outside our minds when it is not perceivable in the world or available for us to 'travel' to.
• 984
What structure does time have if it's not a series of instants?

It is a true continuum, such that an instant with no duration, or even a very small finite duration, is a strictly hypothetical discontinuity. Rather than being sharply separated, the past and future meet and overlap in the infinitesimal "now."

The analogy is with a mathematical line, which does not consist of individual dimensionless points or tiny finite segments, but instead can always be divided infinitely into shorter and shorter lines. We arbitrarily mark instants of time and measure the intervals between them, just as we arbitrarily mark points on a line and measure the distances between them.

Because space-time is a true continuum, motion/velocity is a more fundamental reality than either position or duration. Incidentally, recognizing this is the key to dissolving Zeno's famous paradoxes.
• 245
Who says the temporal continuum needs to contain instants? Likewise who says that the spatial continuum needs to be pointy? Perhaps the continuum has no fundamental level at all, no unit with which all other quantities are multiples of.

If that is the case, then the idea of "now" as a snapshot moment in time is mistaken and the passage of time as a succession of said moments (not unlike a succession of strips on a piece of film) is also confused.

Hi. I like this questioning of the 'now.' It seems to be a kind of default metaphysical assumption, and yet I argue that it does not square with experience. I think our very experience of reading complicates this now. Here's an example:

The end of this sentence specifies its beginning.

What we have read is held in suspense and anticipation. The past is determined by the future as the future is determined by the past, at least it seems within the flow of meaning. And given that 'clock time' and its mathematical 'now' exist within this 'meaning time,' we have a fascinating situation.
• 891
The analogy is with a mathematical line, which does not consist of individual dimensionless points or tiny finite segments, but instead can always be divided infinitely into shorter and shorter lines.

That's paradoxical. It works ok in the mind but not in reality: If I have a real line length 1 mile, it contains more information than a real line length 1 centimetre. But if they are both continuums then they both contain the same amount of information. Which is impossible. Which is proof by contradiction that continuums do not exist in the real world.
• 7.7k
That's paradoxical. It works ok in the mind but not in reality: If I have a real line length 1 mile, it contains more information than a real line length 1 centimetre. But if they are both continuums then they both contain the same amount of information. Which is impossible. Which is proof by contradiction that continuums do not exist in the real world.

Just curious what definition of "information" you're using.
• 891
Just curious what definition of "information" you're using.

My own I admit. If you imagine a particle in an interval, the position of the particle relative to the beginning of the interval can be regarded as information. In a continuum, that piece of information (particle position) has infinite precision so infinity many bits of information.

That leads to the paradox of the continuum; all sizes of continuum contain the same amount of information.

Obviously discreteness is the only way out of the paradox.
• 984
If I have a real line length 1 mile, it contains more information than a real line length 1 centimetre. But if they are both continuums then they both contain the same amount of information. Which is impossible.
Why? It begs the question to presuppose discrete units of "information" (i.e., points or finite segments) that comprise a "real line." Again, the "parts" of a true continuum are also true continua.

If you imagine a particle in an interval, the position of the particle relative to the beginning of the interval can be regarded as information. In a continuum, that piece of information (particle position) has infinite precision so infinity many bits of information.
I repeat: Because space-time is a true continuum, motion/velocity is a more fundamental reality than either position or duration. Marking and measuring the position of a particle at any particular instant imposes an arbitrary discontinuity, like a point on a line.
• 891
Because space-time is a true continuum,

Your continuum is just magic - how can 1 light year be structurally the same as 1 millimetre? I don't believe in magic so I have to take a different view - no continuums in nature; they are logically unsound and nature does not do unsound.

Also it can't be a continuum because actual infinity does not exist.
• 984
Your continuum is just magic - how can 1 light year be structurally the same as 1 millimetre?
An argument from incredulity is not persuasive, and alleging "magic" suggests a lack of interest in engaging in serious philosophical discussion. What exactly do you mean by "structurally the same" in this context?

I don't believe in magic so I have to take a different view - no continuums in nature; they are logically unsound and nature does not do unsound.
In what specific sense do you hold that the hypothesis of a real continuum is "logically unsound"? Are you claiming that it is somehow logically impossible, or merely not actual? Either way, why do we nevertheless routinely refer to "the space-time continuum"?

Also it can't be a continuum because actual infinity does not exist.
A bare assertion is also not persuasive. Even if I grant the premise, the discontinuity of actuality/existence does not, by itself, rule out the reality of true continua.
• 802
1. A point in space cannot have size=0 because it would only exist in our minds and not reality (no width; insubstantial)
2. Similarly, the point in time ’now’ cannot have length=0 (if it exists for 0 seconds, it does not exist)
3. Or if a ‘now’ had length=0, then a second would contain 1/0=UNDEFINED ‘nows’
4. So ‘now’ has length >0
5. Can’t be length = 1/∞ because ∞ does not exist (∞ + 1 > ∞ making a nonsense of ∞. Or if you define ∞ + 1 = ∞, implies 1 = 0)
6. So a ‘now’ has a finite, non-zero length. Time is composed of a chain of ’nows’ so time must be discrete

I think all this depends on your concept of time. What is time, to you? What do you want to do with it? Before you decide it's quantised, perhaps you should wonder whether it is quantisable (if that's a word)?

Now can indeed be of zero length. Now is a bookmark, not a duration (which would require a start and an end).
• 891
In what specific sense do you hold that the hypothesis of a real continuum is "logically unsound"

How on earth could you construct a continuum? It requires us to construct an actual infinity of possible positions for particles to occupy. Thats impossible. So the fact we could never construct a continuum goes a long way to arguing against its existence.

A bare assertion is also not persuasive

Actual infinity, if it existed, would be a quantity greater than all other quantities, but:

There is no quantity X such that X > all other quantities because X +1 > X

Now you could define:

∞ + 1 = ∞
But that implies:
1 = 0
• 984
How on earth could you construct a continuum? It requires us to construct an actual infinity of possible positions for particles to occupy. Thats impossible.
Yet again: Because space-time is a true continuum, motion/velocity is a more fundamental reality than either position or duration. We can construct a continuum as the path that a particle traces (or would trace) over an interval of time--which is not a collection (infinite or otherwise) of discrete positions. Besides, how could merely possible positions constitute an actual infinity?

Actual infinity, if it existed, would be a quantity greater than all other quantities ...
That definition is incorrect, according to the standard mathematics of infinity; mainly because it begs the question by presupposing the discreteness of quantity. In any case, I am advocating the reality of continua, not the actuality of infinity.
• 891
That definition is incorrect, according to the standard mathematics of infinity; mainly because it begs the question by presupposing the discreteness of quantity

How I am 'presupposing the discreteness of quantity'?

X in my proof could be real or natural; I made no assumptions. That is a fair proof that actual infinity is not a quantity IMO.

In any case, I am advocating the reality of continua, not the actuality of infinity

But a continuum requires actual infinity. If you look at the mathematical models for continua, they use actual infinity (gunky or otherwise). Think about a real-life line segment, say the distance between your eyes and the screen; that HAS to be an actual infinity of points/line segments by the very definition of continuous.

Think about the second that just past; by the definition of continuous; its has to include an actually infinite number of moments/periods of time. They just all happened. All 'cardinality of the set of natural numbers' moments just happened if you can make sense of that.
• 984
X in my proof could be real or natural; I made no assumptions. That is a fair proof that actual infinity is not a quantity IMO.
All I can suggest at this point is looking into the standard mathematics of infinity. I side with Peirce, rather than Cantor, in denying that the real numbers constitute a true continuum.

Think about a real-life line segment, say the distance between your eyes and the screen; that HAS to be an actual infinity of points/line segments by the very definition of continuous.
No, it does not. That is only one way to model it, which I consider incorrect. Another is that the line is a true continuum that does not consist of discrete points or line segments at all. You can arbitrarily mark any such point or segment, but by doing so you introduce a discontinuity into that which is really continuous in itself.

Think about the second that just past; by the definition of continuous; its has to include an actually infinite number of moments/periods of time. They just all happened.
No, they did not. That is only one way to model it, which I consider incorrect. Another is that any finite interval of time is a true continuum that does not consist of discrete instants at all. You can arbitrarily mark any such instant, but by doing so you introduce a discontinuity into that which is really continuous in itself.

All 'cardinality of the set of natural numbers' moments just happened if you can make sense of that.
I can make sense of that, but it is not the case. A true continuum has a cardinality exceeding that of any infinite set. In Peirce's terminology, a true continuum has a multitude exceeding that of any infinite collection. Between any two points that we mark on a line, there is an inexhaustible continuum of other potential points; between any two instants that we mark in time, there is an inexhaustible continuum of other potential instants.
bold
italic
underline
strike
code
quote
ulist
image
url
mention
reveal
youtube
tweet

#### Welcome to The Philosophy Forum!

Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.