6 ms·

This reminds me of a confusion I have with theoretical physics and mathematically describing a universe without time. I don’t understand how you could use mathe

by dotsam 5y ago

This reminds me of a confusion I have with theoretical physics and mathematically describing a universe without time. I don’t understand how you could use mathematics - numbers and operations on numbers - to specify a timeless universe, given that mathematics has time as a precondition (how can you perform an operation like 1+1 without time?).

deleted 5y ago
[deleted]
madsbuch 5y ago
It's the difference between the domain of reasoning and complexity of reasoning.
k1t 5y ago
Presumably the issue is that you have defined 1+1 as an operation, rather than just an alternative representation (of 2).
- GlobalFrog 5y ago
  That's interesting actually : isn't that more a philosophical question or just an interpretation ? That is, if 1+1 is just an alternatative representation of '2', you can postulate that the universe is fixed, predefined and timeless. But if you consider that '1 + 1' is not just a representation of '2' but has more information in it, that information could be the dynamic and evolution that we call time. Isn't that linked also to the usual question of the link to reality of Mathematics ?
  - slibhb 5y ago
    It's a philosophical question. Whether 1 + 1 = 2 is a tautology (analytic) or if it "has more information in it" (synthetic) is an open question. This dispute is associated with the analytic-synthetic distinction which has existed since at least Kant.
nl 5y ago
> how can you perform an operation like 1+1 without time? 1+1 is a dimensionless operation. Do you mean how it would physically happen without time? It's possible time is just an illusion that emerges from our perception of the universe. See https://www.nature.com/articles/d41586-018-04558-7 https://www.nature.com/articles/d41586-018-04558-7 and https://www.quantamagazine.org/does-time-really-flow-new-clues-come-from-a-century-old-approach-to-math-20200407/ https://www.quantamagazine.org/does-time-really-flow-new-clu... or https://www.npr.org/2013/05/17/184775924/resetting-the-theory-of-time https://www.npr.org/2013/05/17/184775924/resetting-the-theor... for a counter argument.
- dotsam 5y ago
  My confusion is around the feeling that space and time must be preconditions for numbers and operations. How can you differentiate one number or symbol (or anything) from another without dimensions? It seems to me that you wouldn't be able to have the notion of "1" and "2" unless they can be separated, and to separate them you need dimensions. So for a number to be intelligible at all, it requires dimensions; but how do you get dimensionality in the first place, if your equation is specifying the universe?
  - bourgwaletariat 5y ago
    You need time to differentiate, but the universe does not. The one and the one and the two of them are always here in the universe. You just need time to speak it. You need time to observe the difference between the neuronal pattern between an awareness of one and the other one and the two of them. But they are all at once.
    - dotsam 5y ago
      To have the one and the two in the first place grants spatial dimensions, to separate them. Otherwise you end up with a single point, or maybe not even that. I can't get my head around how anyone can generate time (whether an illusion or not) just from spatial dimensions. If I have to assume spatial dimensions to get anywhere, can I also assume time?
jl6 5y ago
Addition is just a function and functions are just sets of pairs and sets can just sit there merrily existing in the abstract without any need for time or flow or movement or such.
- sharkbot 5y ago
  That is true, but that would be the definition of +. The OP is referring to the application of that operator to its arguments, which (depending on semantics) could also be a set of sets, or it could be a rewriting (ie, time based) process.
  - mannykannot 5y ago
    Anything you can do as a sequence of operations on symbols can be written out, and then there you have it, on the page, all at once! Time does not appear in formal logic or number theory, even though it is convenient to think of a derivation or a calculation as as sequence of steps performed one at a time. it is also very convenient to use mathematics to model a temporal process, but we can, and often do, then show what happened (or will happen) as tables, graphs or other static representations. I know that last sentence presupposes time, but I am not even going to attempt to rewrite it in a way that avoids doing so!
meroes 5y ago
Does a triangle have a duration? Does a line? An equation of a line is very close to 1+1=2. X=2 and y=2 are lines. Nothing in math has time or duration. 1+1 = 2 = area of a triangle with base and height 2 = 362/181 = -2(-1). These are timeless relations. If 2 has no duration, none of the others do. They are just statements of relations. In fact ontic structural realism (some versions) says there is only these abstract relations and everything can be reduced to mathematical relations. Spacetime, consciousness, subjecive experience - all of it are just timeless relations like numbers in a table.
- dotsam 5y ago
  My brain sputters out when I try to go from timeless relations (which assume spatial dimensionality as a given) to a timeless universe within which I sit with the illusion of time! I can't get my mind around anything that doesn't also assume time as a given -- all I end up with is a load of geometry sitting around doing nothing.
  - meroes 5y ago
    No one actually has a working model of consciousness so that programme has a long way to go. But if the only evidence for time is change as Barbour likes to say, and change basically boils down the relative motion of particles, why not describe the whole thing as a timeless table of coordinates essentially? And let psychologists build sensation and a perception of a flow of time from that. It's a tempting view due to its simplicity and the importance of math. But it is extreme, but so is every other theory or metaphysics trying to explain the same stuff!
    - fpoling 5y ago
      This is a circular argument since motion is a change in position. So a change is a motion and a motion is a change. This implicitly refers to personal experience of perception of time flow, but nobody has figured out how to describe it with equations or model without references to that perception. It can be that this is even impossible since as with equations the words of language are static and can only refer to the perception of time without capacity to describe it.
coldtea 5y ago
>given that mathematics has time as a precondition Citation needed :-) >(how can you perform an operation like 1+1 without time?). As a long tautology -- all steps exist in advance. There is no "movement" in mathematics. 1+1 is already 2. Same way in e.g. a holographic universe could have all developments present at the "same time" (or rather, in a timeless state). Where time is just the perception of focusing on one or the other pre-existing point (with no actual process of change from one to the other).
User23 5y ago
You don’t perform anything it’s just a statement. You’re conflating mathematics and computation.
- dotsam 5y ago
  That's a good distinction, thank you. But how would we have mathematics at all, if we could not compute? How can a statement have any meaning if you cannot 'read' it? Both require time to be intelligible. That is the problem I am wrestling with: it is only from within time that we can make sense of something existing timelessly.
  - User23 5y ago
    This is one of those philosophy if mathematics things that people have been debating for a very long time[1]. I don’t have much interest in philosophy of mathematics, so that link isn’t much more than a starting point, but there is plenty to read if you do. [1] https://en.m.wikipedia.org/wiki/Constructivism_(philosophy_of_mathematics) https://en.m.wikipedia.org/wiki/Constructivism_(philosophy_o...
  - jerf 5y ago
    The fact that we can only understand timeless concepts with time is a property of our existence, not a property of the timeless facts. In 0 seconds I can "do" nothing, but that's a property of my existence, not necessarily a universal absolute across the entire Tegmark-ian multiverse.
  - hnjst 5y ago
    I'd say that an important part of mathematics aims at understanding structures and relations between entities in order to avoid inefficient computations. Maybe a trivial example would be multiplication algorithms that allow to bypass costly iterated sums while preserving confidence in the result. Complexity (and entropy) have surely a crucial importance and can't be totally avoided but I think that mathematics precisely work at minimizing their impact.
fsloth 5y ago
Mathematics does not have time as a precondition. I think you have confused something somewhere, but I'm not sure what. 1+1 is a dimensionless computation and hence has no notion of time. To use time, we need to add it explicitly as a dimension to the numbers used. We generally use SI units to abbreviate the dimensions. I.e. s = seconds, m = meters. Now 1s + 1s = 2s. There we have used second as the dimension of the unit. We can do the same thing for lengths. 1m + 1m = 2m. Speed is generally expressed as a dimension, that when multiplied by time, gives us the length travelled. speed * time = distance or speed = distance/time If we set time = 1 s, distance 1=m, we can deduce the unit of speed as. speed = 1 m / 1 s = 1 m/s Hence we get the dimension of speed, m/s ,or meters per second. We can now ask time related questions like "How long - how many seconds - does it take to travel 6 meters with speed 3 m/s". We can just observed the dimensions to get the correct calculation: 6m / (3m/s) = (2/1s^-1) = 2s So that is how mathematics and time generally interact. Time is used like a dimension, just like distance or weight. I'm not sure if this is what you meant or something else.
- dotsam 5y ago
  Performing your dimensionless computations took time -- that's what I mean. And if you don't perform any computations, how can you derive mathematics?
  - fsloth 5y ago
    One way to view this is that while the "act of performing" mathematics happens in a physical world, the results as such are unrelated to time. Below is written from a specific pedestrian view of mathematics, and is partly arm-chair philosophy. Similarly to one playing a specific piece from sheet music, the sheet music is an invariant of time, while the act of performance, is, yes, very much time related. I think what you mean is the act of performing the computation 1+1 always takes some time, what mathematically is generally understood as relevant is the relationship 1+1 itself, which does not really change. We can change the numbers so we don't know the result beforehand, but that does not mean the end result would change - it does not, as long as the rules don't change. The relationship of the diameter of a circle and the the circumference is always pi. We can take any number of of circumferences and diameters, and given one or another is unknown, we may need to do some computations to know for example the circumference of a wheel with a diameter of 2. While we need to perform the computation pi * 2, the result itself actually never changes, and is irrelevant of time -an eternal truth so to speak, crystallized forever in the fundamental logical nature of our reality. Or, another example, if we take a right triangle, say with the Egyptian famous example with side lengths of 3,4, and 5, it gives us many more invariants that don't change no matter how many times you perform any computation. Given a right triangle with non-hypotenuse sides 3 and 4, the hypotenuse is always a length of 5. No matter how many times we perform the computation, for example, sqrt(3*3 + 4*4) - the end result is something timeless. Pythagorean theorem holds for all planar right triangles, for all eternity, and everywhere, Acapulco or for example on a some desolate rock circling a star in Magellanic Clouds 2 million years ago. While "Pythagorean theorem" is just a name given to a specific logical relationship, the logical relationships described by the theorem do not change. They are eternal. Discovering Pythagorean theorem certainly took time. One view of mathematics is that it's just a way to navigate a vast logical landscape of logical relations that are invariant of time or space. That the act of "performing" mathematics is navigating a static landscape crystallized beyond space and time, into a fundament. Others view mathematics as just a logical game. Never the less, even there with fixed rules, specific input will always result in specific output.
tsimionescu 5y ago
You are confusing computation, which is a branch of mathematics, with all of mathematics. In general in mathematics, the thinking is equational: equality is absolute. In computation you generally do follow a process which follows from one step to the next. However, this doesn't necessarily imply time in any meaningful way, I think having a countable base like the natural numbers is enough (such that you can meaningfully say 'this is step 1, this is step 2, step 2 comes after step 1 in our ordering').

by dotsam 5y ago

deleted 5y ago

[deleted]

madsbuch 5y ago

It's the difference between the domain of reasoning and complexity of reasoning.

k1t 5y ago

Presumably the issue is that you have defined 1+1 as an operation, rather than just an alternative representation (of 2).

GlobalFrog 5y ago
That's interesting actually : isn't that more a philosophical question or just an interpretation ? That is, if 1+1 is just an alternatative representation of '2', you can postulate that the universe is fixed, predefined and timeless. But if you consider that '1 + 1' is not just a representation of '2' but has more information in it, that information could be the dynamic and evolution that we call time. Isn't that linked also to the usual question of the link to reality of Mathematics ?
- slibhb 5y ago
  It's a philosophical question. Whether 1 + 1 = 2 is a tautology (analytic) or if it "has more information in it" (synthetic) is an open question. This dispute is associated with the analytic-synthetic distinction which has existed since at least Kant.

nl 5y ago

> how can you perform an operation like 1+1 without time? 1+1 is a dimensionless operation. Do you mean how it would physically happen without time? It's possible time is just an illusion that emerges from our perception of the universe. See https://www.nature.com/articles/d41586-018-04558-7 https://www.nature.com/articles/d41586-018-04558-7 and https://www.quantamagazine.org/does-time-really-flow-new-clues-come-from-a-century-old-approach-to-math-20200407/ https://www.quantamagazine.org/does-time-really-flow-new-clu... or https://www.npr.org/2013/05/17/184775924/resetting-the-theory-of-time https://www.npr.org/2013/05/17/184775924/resetting-the-theor... for a counter argument.

dotsam 5y ago
My confusion is around the feeling that space and time must be preconditions for numbers and operations. How can you differentiate one number or symbol (or anything) from another without dimensions? It seems to me that you wouldn't be able to have the notion of "1" and "2" unless they can be separated, and to separate them you need dimensions. So for a number to be intelligible at all, it requires dimensions; but how do you get dimensionality in the first place, if your equation is specifying the universe?
- bourgwaletariat 5y ago
  You need time to differentiate, but the universe does not. The one and the one and the two of them are always here in the universe. You just need time to speak it. You need time to observe the difference between the neuronal pattern between an awareness of one and the other one and the two of them. But they are all at once.
  - dotsam 5y ago
    To have the one and the two in the first place grants spatial dimensions, to separate them. Otherwise you end up with a single point, or maybe not even that. I can't get my head around how anyone can generate time (whether an illusion or not) just from spatial dimensions. If I have to assume spatial dimensions to get anywhere, can I also assume time?

jl6 5y ago

Addition is just a function and functions are just sets of pairs and sets can just sit there merrily existing in the abstract without any need for time or flow or movement or such.

sharkbot 5y ago
That is true, but that would be the definition of +. The OP is referring to the application of that operator to its arguments, which (depending on semantics) could also be a set of sets, or it could be a rewriting (ie, time based) process.
- mannykannot 5y ago
  Anything you can do as a sequence of operations on symbols can be written out, and then there you have it, on the page, all at once! Time does not appear in formal logic or number theory, even though it is convenient to think of a derivation or a calculation as as sequence of steps performed one at a time. it is also very convenient to use mathematics to model a temporal process, but we can, and often do, then show what happened (or will happen) as tables, graphs or other static representations. I know that last sentence presupposes time, but I am not even going to attempt to rewrite it in a way that avoids doing so!

meroes 5y ago

Does a triangle have a duration? Does a line? An equation of a line is very close to 1+1=2. X=2 and y=2 are lines. Nothing in math has time or duration. 1+1 = 2 = area of a triangle with base and height 2 = 362/181 = -2(-1). These are timeless relations. If 2 has no duration, none of the others do. They are just statements of relations. In fact ontic structural realism (some versions) says there is only these abstract relations and everything can be reduced to mathematical relations. Spacetime, consciousness, subjecive experience - all of it are just timeless relations like numbers in a table.

dotsam 5y ago
My brain sputters out when I try to go from timeless relations (which assume spatial dimensionality as a given) to a timeless universe within which I sit with the illusion of time! I can't get my mind around anything that doesn't also assume time as a given -- all I end up with is a load of geometry sitting around doing nothing.
- meroes 5y ago
  No one actually has a working model of consciousness so that programme has a long way to go. But if the only evidence for time is change as Barbour likes to say, and change basically boils down the relative motion of particles, why not describe the whole thing as a timeless table of coordinates essentially? And let psychologists build sensation and a perception of a flow of time from that. It's a tempting view due to its simplicity and the importance of math. But it is extreme, but so is every other theory or metaphysics trying to explain the same stuff!
  - fpoling 5y ago
    This is a circular argument since motion is a change in position. So a change is a motion and a motion is a change. This implicitly refers to personal experience of perception of time flow, but nobody has figured out how to describe it with equations or model without references to that perception. It can be that this is even impossible since as with equations the words of language are static and can only refer to the perception of time without capacity to describe it.

coldtea 5y ago

>given that mathematics has time as a precondition Citation needed :-) >(how can you perform an operation like 1+1 without time?). As a long tautology -- all steps exist in advance. There is no "movement" in mathematics. 1+1 is already 2. Same way in e.g. a holographic universe could have all developments present at the "same time" (or rather, in a timeless state). Where time is just the perception of focusing on one or the other pre-existing point (with no actual process of change from one to the other).

User23 5y ago

You don’t perform anything it’s just a statement. You’re conflating mathematics and computation.

dotsam 5y ago
That's a good distinction, thank you. But how would we have mathematics at all, if we could not compute? How can a statement have any meaning if you cannot 'read' it? Both require time to be intelligible. That is the problem I am wrestling with: it is only from within time that we can make sense of something existing timelessly.
- User23 5y ago
  This is one of those philosophy if mathematics things that people have been debating for a very long time[1]. I don’t have much interest in philosophy of mathematics, so that link isn’t much more than a starting point, but there is plenty to read if you do. [1] https://en.m.wikipedia.org/wiki/Constructivism_(philosophy_of_mathematics) https://en.m.wikipedia.org/wiki/Constructivism_(philosophy_o...
- jerf 5y ago
  The fact that we can only understand timeless concepts with time is a property of our existence, not a property of the timeless facts. In 0 seconds I can "do" nothing, but that's a property of my existence, not necessarily a universal absolute across the entire Tegmark-ian multiverse.
- hnjst 5y ago
  I'd say that an important part of mathematics aims at understanding structures and relations between entities in order to avoid inefficient computations. Maybe a trivial example would be multiplication algorithms that allow to bypass costly iterated sums while preserving confidence in the result. Complexity (and entropy) have surely a crucial importance and can't be totally avoided but I think that mathematics precisely work at minimizing their impact.

fsloth 5y ago

Mathematics does not have time as a precondition. I think you have confused something somewhere, but I'm not sure what. 1+1 is a dimensionless computation and hence has no notion of time. To use time, we need to add it explicitly as a dimension to the numbers used. We generally use SI units to abbreviate the dimensions. I.e. s = seconds, m = meters. Now 1s + 1s = 2s. There we have used second as the dimension of the unit. We can do the same thing for lengths. 1m + 1m = 2m. Speed is generally expressed as a dimension, that when multiplied by time, gives us the length travelled. speed * time = distance or speed = distance/time If we set time = 1 s, distance 1=m, we can deduce the unit of speed as. speed = 1 m / 1 s = 1 m/s Hence we get the dimension of speed, m/s ,or meters per second. We can now ask time related questions like "How long - how many seconds - does it take to travel 6 meters with speed 3 m/s". We can just observed the dimensions to get the correct calculation: 6m / (3m/s) = (2/1s^-1) = 2s So that is how mathematics and time generally interact. Time is used like a dimension, just like distance or weight. I'm not sure if this is what you meant or something else.

dotsam 5y ago
Performing your dimensionless computations took time -- that's what I mean. And if you don't perform any computations, how can you derive mathematics?
- fsloth 5y ago
  One way to view this is that while the "act of performing" mathematics happens in a physical world, the results as such are unrelated to time. Below is written from a specific pedestrian view of mathematics, and is partly arm-chair philosophy. Similarly to one playing a specific piece from sheet music, the sheet music is an invariant of time, while the act of performance, is, yes, very much time related. I think what you mean is the act of performing the computation 1+1 always takes some time, what mathematically is generally understood as relevant is the relationship 1+1 itself, which does not really change. We can change the numbers so we don't know the result beforehand, but that does not mean the end result would change - it does not, as long as the rules don't change. The relationship of the diameter of a circle and the the circumference is always pi. We can take any number of of circumferences and diameters, and given one or another is unknown, we may need to do some computations to know for example the circumference of a wheel with a diameter of 2. While we need to perform the computation pi * 2, the result itself actually never changes, and is irrelevant of time -an eternal truth so to speak, crystallized forever in the fundamental logical nature of our reality. Or, another example, if we take a right triangle, say with the Egyptian famous example with side lengths of 3,4, and 5, it gives us many more invariants that don't change no matter how many times you perform any computation. Given a right triangle with non-hypotenuse sides 3 and 4, the hypotenuse is always a length of 5. No matter how many times we perform the computation, for example, sqrt(3*3 + 4*4) - the end result is something timeless. Pythagorean theorem holds for all planar right triangles, for all eternity, and everywhere, Acapulco or for example on a some desolate rock circling a star in Magellanic Clouds 2 million years ago. While "Pythagorean theorem" is just a name given to a specific logical relationship, the logical relationships described by the theorem do not change. They are eternal. Discovering Pythagorean theorem certainly took time. One view of mathematics is that it's just a way to navigate a vast logical landscape of logical relations that are invariant of time or space. That the act of "performing" mathematics is navigating a static landscape crystallized beyond space and time, into a fundament. Others view mathematics as just a logical game. Never the less, even there with fixed rules, specific input will always result in specific output.

tsimionescu 5y ago

You are confusing computation, which is a branch of mathematics, with all of mathematics. In general in mathematics, the thinking is equational: equality is absolute. In computation you generally do follow a process which follows from one step to the next. However, this doesn't necessarily imply time in any meaningful way, I think having a countable base like the natural numbers is enough (such that you can meaningfully say 'this is step 1, this is step 2, step 2 comes after step 1 in our ordering').