Re: [math-fun] The moving now (was: Messages in pi)
Thoughts about what Mike wrote below: 1. I don't know about this arrow of time. I haven't kept up to date, but isn't there a theorem that if you reverse charge, parity, and time, any movie of something physically possible would still be possible if run backward? (And if charge and parity are not involved, then you can just run the same movie backward without change.) Of course, in our neighborhood of spacetime, we are living in a part of the universe where stars radiate energy in the positive direction of time (t+). Given that fact, things like eggs breaking in t+ but seemingly never reassembling follow from the existence of evolution. But in principle if we could imagine where the recent past of [all spacetime that could affect our present] is being copied — in a CPT-reversed way, at least T — presumably the same past would unfold just like our own future. But Mike himself pointed out that "entropy increases" isn't by itself a fully adequate explanation. 2. Mike asks "More carefully, how could you distinguish the experience of living the events out of order from living them in order, or from living them simultaneously?" My first answer is, It sure *feels* as if the recent past is something that I lived very recently. And the recenter the past, the recenter it feels. It's enough to make one want to locate one's focus in a new place, to recenter oneself. *Maybe* it's just a coincidence that all these moments fit together into a continuous narrative. It feels much more likely that something crucial about how the moments came into being is real-numbery, i.e., somehow 1-dimensional. I think the real numbers R can be characterized as the only connected topological space such that the removal of any point leaves just two connected components. But there may be another condition like, y'know, Hausdorffness or local compactness or homogeneity, that I'd rather not mention, necessary for this uniqueness. But: Would we indeed feel as we in fact do, if all phases of our lives were being lived, kind of, "at the same time" ? Who is feeling all those other moments that we lived or will live? (Not 100% serious, but still.) —Dan "All you have is the state of your brain at that given point in time." I think. —Dan ----- On Wed, Nov 28, 2018 at 1:47 PM Dan Asimov <dasimov@earthlink.net> wrote:
That's probably my preferred view, but there are problems reconciling it with everyday experience. It would mean that all ages t of (say) me are living their lives equally, in some sense of equally.
But how does that explain the experience we have of living our lives in the order of the real numbers, and the fact that it keeps getting later?
A too-cute answer is, "Because the arrow of time points in the direction of increasing entropy." More carefully, how could you distinguish the experience of living the events out of order from living them in order, or from living them simultaneously? All you have is the state of your brain at that given point in time. -----
I think the real numbers R can be characterized as the only connected topological space such that the removal of any point leaves just two connected components. But there may be another condition like, y'know, Hausdorffness or local compactness or homogeneity, that I'd rather not mention, necessary for this uniqueness.
It feels like the missing condition is second-countability, to remove counterexamples such as the Alexandroff line. -- APG.
My own take is that while it’s possible to model “time” as a Dimension, it isn’t actually a Dimension, it’s merely the experience of change of state in a system. My reason for this is AFAIK nowhere in (known) existence is something shown to “rotate” a spatial dimension into time, sure physical effects modify the local rate of change of state, but that’s the closest I can think of…... As to 1 below, if a change of state involves the equivalent of roots or non-commutative math being done a particular way then it’s possible you get a hyperverse and going backwards becomes problematic since there’d not necessarily be any way of knowing which path got you there in a particular Universe.
On 29 Nov 2018, at 01:12, Dan Asimov <dasimov@earthlink.net> wrote:
Thoughts about what Mike wrote below:
1. I don't know about this arrow of time. I haven't kept up to date, but isn't there a theorem that if you reverse charge, parity, and time, any movie of something physically possible would still be possible if run backward? (And if charge and parity are not involved, then you can just run the same movie backward without change.) <snip>
Here’s my highly speculative and almost certainly wrong idea on time:
On Nov 29, 2018, at 5:15 AM, D J Makin via math-fun <math-fun@mailman.xmission.com> wrote:
My own take is that while it’s possible to model “time” as a Dimension, it isn’t actually a Dimension, it’s merely the experience of change of state in a system. My reason for this is AFAIK nowhere in (known) existence is something shown to “rotate” a spatial dimension into time, sure physical effects modify the local rate of change of state, but that’s the closest I can think of…...
As to 1 below, if a change of state involves the equivalent of roots or non-commutative math being done a particular way then it’s possible you get a hyperverse and going backwards becomes problematic since there’d not necessarily be any way of knowing which path got you there in a particular Universe.
On 29 Nov 2018, at 01:12, Dan Asimov <dasimov@earthlink.net> wrote:
Thoughts about what Mike wrote below:
1. I don't know about this arrow of time. I haven't kept up to date, but isn't there a theorem that if you reverse charge, parity, and time, any movie of something physically possible would still be possible if run backward? (And if charge and parity are not involved, then you can just run the same movie backward without change.) <snip>
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I think it's a mistake to think of "the state of your brain at a given time" as corresponding to a conscious thought. A biologist or chemist may think of the state at your at a given time in the sense of at a real numbered point on a time coordinate. But a thought takes time and is a process spread over different parts of the brain. And of course a physicist will note that the concept "at a given time" is not an invariant concept and depends on how you slice spacetime. Brent On 11/28/2018 5:12 PM, Dan Asimov wrote:
Thoughts about what Mike wrote below:
1. I don't know about this arrow of time. I haven't kept up to date, but isn't there a theorem that if you reverse charge, parity, and time, any movie of something physically possible would still be possible if run backward? (And if charge and parity are not involved, then you can just run the same movie backward without change.)
Of course, in our neighborhood of spacetime, we are living in a part of the universe where stars radiate energy in the positive direction of time (t+). Given that fact, things like eggs breaking in t+ but seemingly never reassembling follow from the existence of evolution. But in principle if we could imagine where the recent past of [all spacetime that could affect our present] is being copied — in a CPT-reversed way, at least T — presumably the same past would unfold just like our own future.
But Mike himself pointed out that "entropy increases" isn't by itself a fully adequate explanation.
2. Mike asks "More carefully, how could you distinguish the experience of living the events out of order from living them in order, or from living them simultaneously?"
My first answer is, It sure *feels* as if the recent past is something that I lived very recently. And the recenter the past, the recenter it feels. It's enough to make one want to locate one's focus in a new place, to recenter oneself. *Maybe* it's just a coincidence that all these moments fit together into a continuous narrative. It feels much more likely that something crucial about how the moments came into being is real-numbery, i.e., somehow 1-dimensional.
I think the real numbers R can be characterized as the only connected topological space such that the removal of any point leaves just two connected components. But there may be another condition like, y'know, Hausdorffness or local compactness or homogeneity, that I'd rather not mention, necessary for this uniqueness.
But: Would we indeed feel as we in fact do, if all phases of our lives were being lived, kind of, "at the same time" ? Who is feeling all those other moments that we lived or will live? (Not 100% serious, but still.)
—Dan
"All you have is the state of your brain at that given point in time."
I think.
—Dan
----- On Wed, Nov 28, 2018 at 1:47 PM Dan Asimov <dasimov@earthlink.net> wrote:
That's probably my preferred view, but there are problems reconciling it with everyday experience. It would mean that all ages t of (say) me are living their lives equally, in some sense of equally.
But how does that explain the experience we have of living our lives in the order of the real numbers, and the fact that it keeps getting later? A too-cute answer is, "Because the arrow of time points in the direction of increasing entropy." More carefully, how could you distinguish the experience of living the events out of order from living them in order, or from living them simultaneously? All you have is the state of your brain at that given point in time.
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A couple of points in connection with previous remarks on this braid ... There are apparently species on Earth with which communication is problematic, specifically on account of vastly different time-scales: https://www.theguardian.com/science/2018/dec/10/tread-softly-because-you-tre... Communication with very ancient groves of trees is another intriguing possibility. It is not necessary to go looking for LGM's on distant planets in order to explore these questions; thought we might need no expand our notion of "intelligence". Regarding malleability of time with space: as I understand general relativity (which is not a lot, to be honest), in the neighbourhood of the event horizon of a black hole, time and radial space axes are progressively interchanged with respect to the frame of a distant observer; with the result that an infalling object appears paradoxically to come to rest at the horizon. GR folk apparently refer to such hyperbolic rotations as "boosts". WFL On 11/29/18, Brent Meeker <meekerdb@verizon.net> wrote:
I think it's a mistake to think of "the state of your brain at a given time" as corresponding to a conscious thought. A biologist or chemist may think of the state at your at a given time in the sense of at a real numbered point on a time coordinate. But a thought takes time and is a process spread over different parts of the brain. And of course a physicist will note that the concept "at a given time" is not an invariant concept and depends on how you slice spacetime.
Brent
On 11/28/2018 5:12 PM, Dan Asimov wrote:
Thoughts about what Mike wrote below:
1. I don't know about this arrow of time. I haven't kept up to date, but isn't there a theorem that if you reverse charge, parity, and time, any movie of something physically possible would still be possible if run backward? (And if charge and parity are not involved, then you can just run the same movie backward without change.)
Of course, in our neighborhood of spacetime, we are living in a part of the universe where stars radiate energy in the positive direction of time (t+). Given that fact, things like eggs breaking in t+ but seemingly never reassembling follow from the existence of evolution. But in principle if we could imagine where the recent past of [all spacetime that could affect our present] is being copied — in a CPT-reversed way, at least T — presumably the same past would unfold just like our own future.
But Mike himself pointed out that "entropy increases" isn't by itself a fully adequate explanation.
2. Mike asks "More carefully, how could you distinguish the experience of living the events out of order from living them in order, or from living them simultaneously?"
My first answer is, It sure *feels* as if the recent past is something that I lived very recently. And the recenter the past, the recenter it feels. It's enough to make one want to locate one's focus in a new place, to recenter oneself. *Maybe* it's just a coincidence that all these moments fit together into a continuous narrative. It feels much more likely that something crucial about how the moments came into being is real-numbery, i.e., somehow 1-dimensional.
I think the real numbers R can be characterized as the only connected topological space such that the removal of any point leaves just two connected components. But there may be another condition like, y'know, Hausdorffness or local compactness or homogeneity, that I'd rather not mention, necessary for this uniqueness.
But: Would we indeed feel as we in fact do, if all phases of our lives were being lived, kind of, "at the same time" ? Who is feeling all those other moments that we lived or will live? (Not 100% serious, but still.)
—Dan
"All you have is the state of your brain at that given point in time."
I think.
—Dan
----- On Wed, Nov 28, 2018 at 1:47 PM Dan Asimov <dasimov@earthlink.net> wrote:
That's probably my preferred view, but there are problems reconciling it with everyday experience. It would mean that all ages t of (say) me are living their lives equally, in some sense of equally.
But how does that explain the experience we have of living our lives in the order of the real numbers, and the fact that it keeps getting later? A too-cute answer is, "Because the arrow of time points in the direction of increasing entropy." More carefully, how could you distinguish the experience of living the events out of order from living them in order, or from living them simultaneously? All you have is the state of your brain at that given point in time.
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participants (6)
-
Adam P. Goucher -
Brent Meeker -
D J Makin -
Dan Asimov -
Fred Lunnon -
Tom Knight