Old man from story: Probability is omnipotent and omnipresent. It influences every coin at any time in any place, instantly. It cannot be shielded or altered. We might see randomness in the outcome of an individual coin toss, but as the number of tosses increases, probability has firm control of the outcome. And probability is not limited to coins and dice and slot machines. Probability is the guiding force of everything in the universe, living or nonliving, near or far, big or small, now or anytime.
Probability is a function of perspective. We frame “events” and “outcomes”. The universe doesn’t do it for us. There is nothing universal about probability.
A coin flip is framed as begining with the force being applied to the coin so that it shoots up tumbling into the air, and ending when it falls back to the ground. The outcome is framed as which side is facing up. These are artificial distinctions, though from the human perspective they seem very natural. To an ant walking across the floor the outcome will be whether the coin lands on him or not. And the start of the event won’t have to be the coin being “flipped”, it can be any instance of the coin entering free fall in the area above it.
Probability never controls any particular outcome. Probability, in fact, can’t control any finite number of outcomes. Probability is just a way of filling in gaps in our knowledge. In theory ( under classical mechanics ) we could know once any coin was in the air during a flip whether it would land heads or tails. The “probability” is only 50-50 because of our ignorance. If we knew more it would be 100 percent for one result or another.
It's nonsense to call probability a guiding force, I think. What does that mean? Probability is a tool that we can use to predict the cumulative outcomes of a large number of events. These predictions are "usually" accurate. But probability isn't what causes the outcomes! Known probabilities let us guess at certain features of the outcomes. Calling probablity a force is like calling multiplication a force because it's used in the equations that describe classical gravity.
edit: The point of this isn't to prove that probablity isn't a force. The point is to maybe understand more about probablity ( which is really hard to understand ) by figuring out why it can't be a force even though it seems sort of plausible that it might be one.
God's Debris
I need to get that book I mentioned about the flow of time in front of me before I can say much more about this reversibility stuff.
Yeah, I'm interested in what it says!
Um ... a film of subatomic particles would be a film of a series of events all of which already happened. I'm not sure that's the same thing as being able to predict from the equation what's going to happen next. You can't, for example, take different slices of a time-series sample (in the normal sized world) and predict forwards or backwards from any set of events. You would never get the same prediction twice.
But things are different at the subatomic level!
Jn
Yeah, I'm interested in what it says!
Um ... a film of subatomic particles would be a film of a series of events all of which already happened. I'm not sure that's the same thing as being able to predict from the equation what's going to happen next. You can't, for example, take different slices of a time-series sample (in the normal sized world) and predict forwards or backwards from any set of events. You would never get the same prediction twice.
But things are different at the subatomic level!
Jn
A fool's paradise is a wise man's hell.
Faramond, for some reason I only saw your last post at the bottom of the previous page and not your first post at the top of this page. Yes, I agree that probability is represented inaccurately.
Calling probablity a force is like calling multiplication a force because it's used in the equations that describe classical gravity.
Great analogy!
I found this by googling. It has two minor errors which I'll note and there was a bunch of blah-dee-blah-blah in the middle which I cut out.
http://www.bookrags.com/sciences/physic ... e-wop.html
Here's why subatomic particles do not appear to have a time arrow (assuming this is correct) - because they've been unable to measure differences in entropy between events, except for the one experiment mentioned at the end.
Jn
eta: Here's a lucid explanation of the impact of entropy on path equations: http://www.christianhubert.com/hypertex ... aw_of.html
Would you like to hear my crackpot theory based on Von Neumann's definition of entropy? (my underlines below)
Calling probablity a force is like calling multiplication a force because it's used in the equations that describe classical gravity.
Great analogy!
I found this by googling. It has two minor errors which I'll note and there was a bunch of blah-dee-blah-blah in the middle which I cut out.
http://www.bookrags.com/sciences/physic ... e-wop.htmlThat last sentence is not phrased properly, but I understand the point to be that physicists sequence events by measuring the entropy.The second law of thermodynamics, or the law of entropy, states that the universe and all of its energy systems will increase in disorder as time moves forward. In physics, disorder means the breakdown of energy into useless heat, from which no work can be done.
This is the experiment that Einstein suggested. It does not demonstrate the reversability of time. What it demonstrates is that the speed of time is not constant, as it must be for Newtonian equations to be accurate. [The speed of time, dt is the constant in Celestial Mechanics; the speed of light, c, is the constant in relativity theory.] Or, if you squint at it a different way, it proves that space is curved. The ambiguity generated by this experiment arises from the fact that bent space and accelerating time are mathematically equivalent and we can't tell one from the other based on results. We have to pick a perspective and run with it. (Heisenberg's uncertainty principle.)A phenomenon illustrating reversibility of time is the barely perceptible lag of atomic clocks transported on jets traveling at high speeds. The people on such flights are a microproportion of time behind the people at the flight's origin and the people at the flight's destination. Is this discrepancy in the measure of time truly a lag or actually a slight reversal of time?
Here's why subatomic particles do not appear to have a time arrow (assuming this is correct) - because they've been unable to measure differences in entropy between events, except for the one experiment mentioned at the end.
I'll google around some more and try to find Markov's argument for irreversibility. The reason that one intrigues me is because (iirc) I believe it only holds for a one-dimensional universe.In studying subatomic particles, there are few means of detecting time as a systematic sequence of events. Particles continuously come together to form new particles only to separate to form particles identical to the original particles, which again interact to form new particles. The laws of physics allow that the incidence of new particles reverting back to the original particles may occur as easily as the incidence of original particles interacting to create new particles. Viewing the steps in this process, one has little clue which event came before which. A common standard for measuring time, observing entropy, is very difficult at the subatomic level.
In the late twentieth century, an arrow of time may have been discovered at the subatomic level. The important characteristic of the reversibility of time is the concept of charge-parity symmetry. This concept implies that there is no breakdown in the order of the subatomic particles at the different phases of interaction and separation. In 1998, the Fermilab in Illinois and the CERN (European Organization for Nuclear Research) in Switzerland reported independent results from work with subatomic particles. Both laboratories found significant differences associated with time in the activity of neutral particles called kaons. Therefore, as one becomes aware of what to look for, even at the subatomic level, one will find an arrow of time.
Jn
eta: Here's a lucid explanation of the impact of entropy on path equations: http://www.christianhubert.com/hypertex ... aw_of.html
Would you like to hear my crackpot theory based on Von Neumann's definition of entropy? (my underlines below)
Btw, remember when Sid asked us to go look at that Christian website that gave alternative interpretations to recent scientific advances, and she wanted us to explain the stuff about Information Theory? (the thread was on B77) This theory, summarized in one sentence above, was the one they were talking about at that site.Claude Shannon, on the advice of John von Neumann, called transmission loss entropy. For Shannon, its inverse is information. Norbert Wiener: Just as the amount of information in a system is a measure of its degree of organization, so the entropy of a system is a measure of its degree of disorganization. Metric entropy is information production rate. It can be measured, for example, in bits per second (see Crutchfield)
A fool's paradise is a wise man's hell.
Quickly ... the name of the book is
Time's Arrow and Archimedes' Point
by Huw Price
Here is a quote that sort of shows what the book is about:
Huw Price: I want to show that if we want to understand the assymetry of time then we need to be able to understand, and quarantine, the various ways in which our patterns of thought reflect the peculiarities of our own temporal perspective. We need to acquaint ourselves with what might aptly be called the view from nowhen.
Time's Arrow and Archimedes' Point
by Huw Price
Here is a quote that sort of shows what the book is about:
Huw Price: I want to show that if we want to understand the assymetry of time then we need to be able to understand, and quarantine, the various ways in which our patterns of thought reflect the peculiarities of our own temporal perspective. We need to acquaint ourselves with what might aptly be called the view from nowhen.
Faramond, Ah! Very good.
I'm going to take that as permission to post my own crackpot theory of nowhen.
Going back to one of the excerpts above:
So, if you send the signal: ABCDEFGHIJ
and what comes through at the other end is: ABCDEFGHIx
then 10% of the information has been lost.
If order matters, it is also possible to measure the conditional probabilities: p(B)|A, p(C)|B, .... etc.
so that if you send the signal: ABCDEFGHIJ
and what comes through at the other end is: ABCDEGFHIJ
you can also calculate the loss of correlation between the two sets. So loss of correlation is evidence of irrreversibility - you can't predict perfectly from the second set backwards to the first set. You'll get something different for the first set.
If it's a Markov chain, where the conditional probabilities are (e.g.):
p(G)|F and not p(G)|{A,B,C,D,E,F} then the correlation between the conditional probabilities of F and G goes to zero and F -> G cannot be calculated at all from G -> F, i.e. they are irreversible.
Now ... picture a Mobius strip ...
If it is truly two-dimensional, i.e. it has no thickness, then as you 'walk' along the Mobius strip, you cross each spatially-defined point twice, once going in one direction and once going in the other direction. The correlation between spatial information in {-> G ->} and {<- G <-} is perfect. The only difference is the directionality of the 'walker.' One trip around the entire strip produces two perfectly correlated sets of spatial information, i.e. zero entropy. If one's position on the stip is determined stochastically, it does not matter as long as every point occurs once. If it is stochastic and order matters (e.g. even a Markov chain) it still does not matter as long as every point occurs once. There will always be two sets of perfectly correlated spatial information as long as every point occurs once.
One could conceivably take any system of 2n-dimensions and place it inside a larger system of 2n+1 dimensions and if it had this property of generating two perfectly correlated sets of data it would be a zero entropy system.
From the point of view of 'God' ... 'God' does not have to be 'nowhen', that is, completely outside the 2n+1 dimensional system in order to see the whole system as if it were happening 'at once.' He/she can be inside the 2n+1 dimension system as long as he/she is not 'inside' the Mobius strip, where only 2n dimensions can be perceived.
You can think of the strip as a kind of flypaper .... anything stuck on the strip can only look forward, and therefore thinks it is always moving in the same direction - forward - even though it is actually moving in a potentially infinite number of directionalities (every point in the 2n dimension system has a potentially unique eigenvalue in the 2n+1 dimension system) which could be seen (and calculated) by a being able to inhabit the 2n+1 dimensions.
'God' does not have to be infinite, therefore, at least not in the sense defined by Windy in her Tol Eressëa discussion Which Starts Here. He/she does not even have to be outside Time, if we are defining time as the 2n+1st dimension. He/she can be inside Time as long as he/she is not stuck to the Mobius strip where the 2n+1st dimension in which the system is embedded cannot be perceived.
Clear as mud?
Jn
eta: This presumes, of course, that vN's definition of entropy can be extrapolated from information theory to physical reality
I'm going to take that as permission to post my own crackpot theory of nowhen.
Going back to one of the excerpts above:
The way von Neumann suggested that transmission loss be measured for purposes of information theory was the loss of correlation between the original information set and the information set after transmission.Claude Shannon, on the advice of John von Neumann, called transmission loss entropy. For Shannon, its inverse is information. Norbert Wiener: Just as the amount of information in a system is a measure of its degree of organization, so the entropy of a system is a measure of its degree of disorganization. Metric entropy is information production rate. It can be measured, for example, in bits per second (see Crutchfield)
So, if you send the signal: ABCDEFGHIJ
and what comes through at the other end is: ABCDEFGHIx
then 10% of the information has been lost.
If order matters, it is also possible to measure the conditional probabilities: p(B)|A, p(C)|B, .... etc.
so that if you send the signal: ABCDEFGHIJ
and what comes through at the other end is: ABCDEGFHIJ
you can also calculate the loss of correlation between the two sets. So loss of correlation is evidence of irrreversibility - you can't predict perfectly from the second set backwards to the first set. You'll get something different for the first set.
If it's a Markov chain, where the conditional probabilities are (e.g.):
p(G)|F and not p(G)|{A,B,C,D,E,F} then the correlation between the conditional probabilities of F and G goes to zero and F -> G cannot be calculated at all from G -> F, i.e. they are irreversible.
Now ... picture a Mobius strip ...
If it is truly two-dimensional, i.e. it has no thickness, then as you 'walk' along the Mobius strip, you cross each spatially-defined point twice, once going in one direction and once going in the other direction. The correlation between spatial information in {-> G ->} and {<- G <-} is perfect. The only difference is the directionality of the 'walker.' One trip around the entire strip produces two perfectly correlated sets of spatial information, i.e. zero entropy. If one's position on the stip is determined stochastically, it does not matter as long as every point occurs once. If it is stochastic and order matters (e.g. even a Markov chain) it still does not matter as long as every point occurs once. There will always be two sets of perfectly correlated spatial information as long as every point occurs once.
One could conceivably take any system of 2n-dimensions and place it inside a larger system of 2n+1 dimensions and if it had this property of generating two perfectly correlated sets of data it would be a zero entropy system.
From the point of view of 'God' ... 'God' does not have to be 'nowhen', that is, completely outside the 2n+1 dimensional system in order to see the whole system as if it were happening 'at once.' He/she can be inside the 2n+1 dimension system as long as he/she is not 'inside' the Mobius strip, where only 2n dimensions can be perceived.
You can think of the strip as a kind of flypaper
.... anything stuck on the strip can only look forward, and therefore thinks it is always moving in the same direction - forward - even though it is actually moving in a potentially infinite number of directionalities (every point in the 2n dimension system has a potentially unique eigenvalue in the 2n+1 dimension system) which could be seen (and calculated) by a being able to inhabit the 2n+1 dimensions.'God' does not have to be infinite, therefore, at least not in the sense defined by Windy in her Tol Eressëa discussion Which Starts Here. He/she does not even have to be outside Time, if we are defining time as the 2n+1st dimension. He/she can be inside Time as long as he/she is not stuck to the Mobius strip where the 2n+1st dimension in which the system is embedded cannot be perceived.
Clear as mud?
Jn
eta: This presumes, of course, that vN's definition of entropy can be extrapolated from information theory to physical reality
A fool's paradise is a wise man's hell.
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Voronwë the Faithful
- At the intersection of here and now
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Brain hurts! Jn: I'm going to take that as permission to post my own crackpot theory of nowhen.
Why did you need permission?
The way von Neumann suggested that transmission loss be measured for purposes of information theory was the loss of correlation between the original information set and the information set after transmission.
So, if you send the signal: ABCDEFGHIJ
and what comes through at the other end is: ABCDEFGHIx
then 10% of the information has been lost.
What if we look at this from a time direction neutral perspective? We have ABCDEFGHI at one end, and ABCDEFGHIJ at the other end, and a transmission in between. If it's seen as ABCDEFGHIJ --> ABCDEFGHI, then it's information loss as you described. If it's seen as ABCDEFGHI --> ABCDEFGHIJ, then it's what? Maybe information loss because the "real" information has been lost amidst some extraneous information. Or ... it's evolution, and the J is 'valuable' new information ... a beneficial mutation. Similarly, we could say that the transmission ABCDEFGHIJ to ABCDEFGHI was actually a gain of information because the J was really extraneous.
I guess I'm not ready to just accept that the transmission between ABCDEFGHIJ and ABCDEFGHI is necessarily an information loss. It only becomes one when we deliberately choose one direction of time as more important.
so that if you send the signal: ABCDEFGHIJ
and what comes through at the other end is: ABCDEGFHIJ
you can also calculate the loss of correlation between the two sets. So loss of correlation is evidence of irrreversibility - you can't predict perfectly from the second set backwards to the first set. You'll get something different for the first set.
But can you predict accurately from the first set what the second set will be? It seems to me that you could just as accurately predict forward what you'll get for the second set from the first than it would be to predict backward from the second set to the first set.
Now ... picture a Mobius strip ...
If it is truly two-dimensional, i.e. it has no thickness, then as you 'walk' along the Mobius strip, you cross each spatially-defined point twice, once going in one direction and once going in the other direction.
I'm not sure I understand this. If I imagine a little man walking along the center of the strip you showed, he starts a X and will walk all the way around and then have his head pointing in the opposite direction as it was when he started at X ... but I don't understand how he's going in a different direction. I see orientation flipping, but not direction flipping.
Until I understand this first bit I can't really get into the rest of it!
Why did you need permission?
The way von Neumann suggested that transmission loss be measured for purposes of information theory was the loss of correlation between the original information set and the information set after transmission.
So, if you send the signal: ABCDEFGHIJ
and what comes through at the other end is: ABCDEFGHIx
then 10% of the information has been lost.
What if we look at this from a time direction neutral perspective? We have ABCDEFGHI at one end, and ABCDEFGHIJ at the other end, and a transmission in between. If it's seen as ABCDEFGHIJ --> ABCDEFGHI, then it's information loss as you described. If it's seen as ABCDEFGHI --> ABCDEFGHIJ, then it's what? Maybe information loss because the "real" information has been lost amidst some extraneous information. Or ... it's evolution, and the J is 'valuable' new information ... a beneficial mutation. Similarly, we could say that the transmission ABCDEFGHIJ to ABCDEFGHI was actually a gain of information because the J was really extraneous.
I guess I'm not ready to just accept that the transmission between ABCDEFGHIJ and ABCDEFGHI is necessarily an information loss. It only becomes one when we deliberately choose one direction of time as more important.
so that if you send the signal: ABCDEFGHIJ
and what comes through at the other end is: ABCDEGFHIJ
you can also calculate the loss of correlation between the two sets. So loss of correlation is evidence of irrreversibility - you can't predict perfectly from the second set backwards to the first set. You'll get something different for the first set.
But can you predict accurately from the first set what the second set will be? It seems to me that you could just as accurately predict forward what you'll get for the second set from the first than it would be to predict backward from the second set to the first set.
Now ... picture a Mobius strip ...
If it is truly two-dimensional, i.e. it has no thickness, then as you 'walk' along the Mobius strip, you cross each spatially-defined point twice, once going in one direction and once going in the other direction.
I'm not sure I understand this. If I imagine a little man walking along the center of the strip you showed, he starts a X and will walk all the way around and then have his head pointing in the opposite direction as it was when he started at X ... but I don't understand how he's going in a different direction. I see orientation flipping, but not direction flipping.
Until I understand this first bit I can't really get into the rest of it!
Faramond: I guess I'm not ready to just accept that the transmission between ABCDEFGHIJ and ABCDEFGHI is necessarily an information loss. It only becomes one when we deliberately choose one direction of time as more important.
Yes, that's exactly right. We have chosen the direction of information loss as the direction in which the time arrow is moving.
You can also look at it from the opposite direction and say that information has been gained (or entropy lost), but human time perception is such that what we perceive to be 'past' was a time when entropy was lower than it is now.
(Hawking says that if time were reversible, we could remember the future. The proper empirical counter-argument is that there are people who can remember the future (see thread about scary dreams) but this is not an everyday experience and not repeatable in ways that allow theory-building.)
von Neumann's definition does not overturn the second law or say that human perception can go in either direction, it simply says that where information is concerned, correlations are a viable measure of entropy.
I see orientation flipping, but not direction flipping.
You have to picture the 'walker' abstractly, not as a person with a head 'on top' and feet 'on the bottom' but as something abstract which occupies successive points along the strip, where each point could be defined by two spatial coordinates, x and y. Meanwhile the walker does not perceive its own value in dimension z.
But if the strip is constructed so that it is curvilinear throughout, you could draw a tangent to the strip at any point (x,y). If the walker could perceive z, it could walk off into z, so to speak, along the tangent, and the direction in which it walked along the tangent would depend on the direction from which it approached the (x,y) point. The tangent in z is hypothetically linear and reversible. (You can also have plane tangents to the strip but then the interpretation of physical reality gets fuzzy - what would it mean for me to have constant height and width but variable time and thickness? The n-values have to remain constant when you move into z for it to make physical sense - for starters, at least, it is easier to imagine it this way, though anything might be possible.)
In this hypothesis, instead of mass being something that bends space or accelerates time, it is what makes an n-dimensional subset 'sticky' such that the walker inside that subset cannot move into the extra dimension at will, even though the dimension is there and the walker occupies it and, theoretically at least, from the perspective of that extra dimension the sequence of events within the subset would be reversible.
Jn
Yes, that's exactly right. We have chosen the direction of information loss as the direction in which the time arrow is moving.
You can also look at it from the opposite direction and say that information has been gained (or entropy lost), but human time perception is such that what we perceive to be 'past' was a time when entropy was lower than it is now.
(Hawking says that if time were reversible, we could remember the future. The proper empirical counter-argument is that there are people who can remember the future (see thread about scary dreams) but this is not an everyday experience and not repeatable in ways that allow theory-building.)
von Neumann's definition does not overturn the second law or say that human perception can go in either direction, it simply says that where information is concerned, correlations are a viable measure of entropy.
I see orientation flipping, but not direction flipping.
You have to picture the 'walker' abstractly, not as a person with a head 'on top' and feet 'on the bottom' but as something abstract which occupies successive points along the strip, where each point could be defined by two spatial coordinates, x and y. Meanwhile the walker does not perceive its own value in dimension z.
But if the strip is constructed so that it is curvilinear throughout, you could draw a tangent to the strip at any point (x,y). If the walker could perceive z, it could walk off into z, so to speak, along the tangent, and the direction in which it walked along the tangent would depend on the direction from which it approached the (x,y) point. The tangent in z is hypothetically linear and reversible. (You can also have plane tangents to the strip but then the interpretation of physical reality gets fuzzy - what would it mean for me to have constant height and width but variable time and thickness? The n-values have to remain constant when you move into z for it to make physical sense - for starters, at least, it is easier to imagine it this way, though anything might be possible.)
In this hypothesis, instead of mass being something that bends space or accelerates time, it is what makes an n-dimensional subset 'sticky' such that the walker inside that subset cannot move into the extra dimension at will, even though the dimension is there and the walker occupies it and, theoretically at least, from the perspective of that extra dimension the sequence of events within the subset would be reversible.
Jn
A fool's paradise is a wise man's hell.
Here ya' go, Yov.
A Mobius strip is a two-dimensional object embedded in three-dimensional space and twisted in such a way that if you start from some point on the strip and skim along the surface of the strip until you return to your starting point, you actually cross every point on the strip twice, once going in one direction and once going in the opposite direction. But from your perspective, you are always going 'forward.' You have to be able to get off the strip and view it from above to see that your directionality has changed.
Pretend that the curve in the figure below is a short section of a Mobius strip.
Does that help or make it worse?
A Mobius strip is a two-dimensional object embedded in three-dimensional space and twisted in such a way that if you start from some point on the strip and skim along the surface of the strip until you return to your starting point, you actually cross every point on the strip twice, once going in one direction and once going in the opposite direction. But from your perspective, you are always going 'forward.' You have to be able to get off the strip and view it from above to see that your directionality has changed.
Pretend that the curve in the figure below is a short section of a Mobius strip.
Does that help or make it worse?
A fool's paradise is a wise man's hell.
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Voronwë the Faithful
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Oh, I know what a mobius strip is. I used to make 'em as a kid out of strips of paper cuz I thought the concept was so cool. But I can barely make it three sentences into the rest of ya'lls posts before my eyes start to glaze over. 
I wanna love somebody but I don't know how
I wanna throw my body in the river and drown
-The Decemberists
I wanna throw my body in the river and drown
-The Decemberists
I still don't see where direction is changing. Certainly not direction of travel! All I see is orientation flipping. I see the apparent direction of left and right switching.
I made a Moebius strip. I cut a long strip of paper and twisted it once and taped it the ends together, and traced out a path along the center, and the direction never changes, but the apparent orientation of left and right to the little traveller in the strip does change. When the little dot reaches the point of origin left and right from its perspective are reversed from what they were when it started. But it's still going in the same direction!
I must be missing something in your scenario here.
I made a Moebius strip. I cut a long strip of paper and twisted it once and taped it the ends together, and traced out a path along the center, and the direction never changes, but the apparent orientation of left and right to the little traveller in the strip does change. When the little dot reaches the point of origin left and right from its perspective are reversed from what they were when it started. But it's still going in the same direction!
I must be missing something in your scenario here.
but the apparent orientation of left and right to the little traveller in the strip does change.
That is direction from the point of view of someone standing outside of the strip. Orientation and direction imply an independent object against which one's position can be compared. Go to the image of the Mobius strip posted above and trace a path with your finger or a pencil point. As you move around the strip, your hand moves from left to right and then from right to left (or vice versa) across the screen. You are the independent object and it is with respect to you that both orientation and direction change.
It is not a change of direction from the point of view of the person walking along the strip. For him it's not even a change of orientation because 'left' and 'right' are always where they are relative to his own body. If there were some object outside the strip that remained stationary while he moved, and he could perceive it, then he could talk about his own direction and orientation relative to that object, but there is no such object available to his experience.
He experiences the extra dimension horizonally ... it is the space that opens up before him as he moves into it. From his point of view he is always going in the same direction - forward. He does not even realize that the 'surface' he is walking on is twisted because what is under his feet is also always the same direction - 'down.'
That's how we experience time. And gravity.
This is not so different from relativity theory except that in relativity theory 'forward' and 'down' are just two different ways of saying the same thing. In the mobius strip analogy they are different - forward turns into backwards but down is always down. Gravity is the 'stickness' of the strip and 'ever forward' is the way that the stickiness affects our perception of the direction in which we move through time.
Jn
That is direction from the point of view of someone standing outside of the strip. Orientation and direction imply an independent object against which one's position can be compared. Go to the image of the Mobius strip posted above and trace a path with your finger or a pencil point. As you move around the strip, your hand moves from left to right and then from right to left (or vice versa) across the screen. You are the independent object and it is with respect to you that both orientation and direction change.
It is not a change of direction from the point of view of the person walking along the strip. For him it's not even a change of orientation because 'left' and 'right' are always where they are relative to his own body. If there were some object outside the strip that remained stationary while he moved, and he could perceive it, then he could talk about his own direction and orientation relative to that object, but there is no such object available to his experience.
He experiences the extra dimension horizonally ... it is the space that opens up before him as he moves into it. From his point of view he is always going in the same direction - forward. He does not even realize that the 'surface' he is walking on is twisted because what is under his feet is also always the same direction - 'down.'
That's how we experience time. And gravity.
This is not so different from relativity theory except that in relativity theory 'forward' and 'down' are just two different ways of saying the same thing. In the mobius strip analogy they are different - forward turns into backwards but down is always down. Gravity is the 'stickness' of the strip and 'ever forward' is the way that the stickiness affects our perception of the direction in which we move through time.
Jn
A fool's paradise is a wise man's hell.
Well, there seems to be a gap here. I just can't figure out how the direction of travel changes from any perspective
I maintain that from the perspective of the little walker inside the strip, orientation does change, and that from the perspective of me outside of the strip, the direction of travel around the strip ( either clockwise or counterclockwise ) never in fact flips.
I'll try to explain this all as I understand it.
A moebius strip can be represented in two dimensions ... sort of, as long as we allow for an identification of separate points to each other.
A regular looped strip would be like this:
The ends are glued together by the scheme represented by the numbers, so 1 goes to 1, 2 goes to 2, and so on. This is just a regular loop, or bracelet, if you will.
A Moebius strip is the same, except that there is a single twist in it when we glue the ends together.
The numbers down the right side go the opposite way, so when like numbers are glued there is a twist in the looped strip, and this makes it a moebius strip. If you cut out a strip of paper and glue the ends together according to the numbers above you will get a picture the same as the image Jn provided.
On the moebius strip below the little walker starts the journey on X. The walker perceives the directions left and right, indicated by the L and R above and below the X. The fixed point A is to the his left and the fixed point B is on his right. The little walker starts walking down the strip, following the arrows.
Left and Right from his perspective remain constant from his perspective as he moves along. They never flip. When the walker reaches the point labeled 4, his left is associated with the point labeled 5, and right with 3. This will not change when he crosses this gluing point to the other side of the strip. ( In fact the walker does not perceive anything special at this place where we put the twist in the strip. ) Left for him will stay associated
with 5 and right with 3. So now when the walker gets back to point X where he started, A is on the right and B is on the left! Left and right have flipped for the walker, and yet he is still going in the same direction as he was when he started his walk. If he goes all the way around the loop again, left and right will flip back to where they started for him.
I maintain that from the perspective of the little walker inside the strip, orientation does change, and that from the perspective of me outside of the strip, the direction of travel around the strip ( either clockwise or counterclockwise ) never in fact flips.
I'll try to explain this all as I understand it.
A moebius strip can be represented in two dimensions ... sort of, as long as we allow for an identification of separate points to each other.
A regular looped strip would be like this:
Code: Select all
1-----------------------------------------------------1
2-----------------------------------------------------2
3-----------------------------------------------------3
4-----------------------------------------------------4
5-----------------------------------------------------5
6-----------------------------------------------------6
7-----------------------------------------------------7A Moebius strip is the same, except that there is a single twist in it when we glue the ends together.
Code: Select all
1-----------------------------------------------------7
2-----------------------------------------------------6
3-----------------------------------------------------5
4-----------------------------------------------------4
5-----------------------------------------------------3
6-----------------------------------------------------2
7-----------------------------------------------------1On the moebius strip below the little walker starts the journey on X. The walker perceives the directions left and right, indicated by the L and R above and below the X. The fixed point A is to the his left and the fixed point B is on his right. The little walker starts walking down the strip, following the arrows.
Code: Select all
1-----------------------------------------------------7
2-------------------------A---------------------------6
3--R---------R------R------L--------L-----------L-----5
4-->-------->------>------X-->---->------------>------4
5--L----------L------L-----R--------R-----------R-----3
6-------------------------B---------------------------2
7-----------------------------------------------------1with 5 and right with 3. So now when the walker gets back to point X where he started, A is on the right and B is on the left! Left and right have flipped for the walker, and yet he is still going in the same direction as he was when he started his walk. If he goes all the way around the loop again, left and right will flip back to where they started for him.
Faramond, we're talking about the same thing ... and yeah, there's a gap.
From the walker's perspective, direction never changes.
When you say that it does not change from your perspective, you mean that his perspective of his direction does not change from your perspective. That's right, his perspective of his direction does not change from my perspective either.
But look at point X on your strip. In line 3.....5 he approaches that point moving from right to left. In line 5....3 he approaches that point moving from left to right. He approaches the point from two opposite directions.
edit: No wait, this is wrong. My mistake. He does not approach the point from different directions. See below
You have to stand outside the strip to see that the point can be approached from two opposite directions and that it is the same point in both cases. The person on the strip cannot see that. [/edit]
Maybe we're getting confused over what this is supposed to demonstrate?
Jn
eta: it is because the walker is always moving in the same direction (from his perspective) that he perceives z (time) to be linear and irreversible. But for us, looking down at this little cubic system, we can see that as he moves from point to point along the strip the value of z is sometimes going up and sometimes going down. (The sum of all changes in the value of z is in fact zero.) Z is not irreversible. And his path through z is not linear. When all three dimensions are shown, his space - the surface of the strip - is bent even though it feels flat and straight to him.
Edit: Wait, I see what you mean now. It is because an arrow representing his movement is always going in the same direction and does approach every point from the same direction that you are saying the direction does not change. That is also why that value of z appears to him to be always increasing.
But if you are standing outside the strip and can see the extra-dimension of space in which it is nested, and you look at the directional arrows on the strip, sometimes they point from right to left and sometimes they point from left to right. The value of z can either increase or decrease, and the net of all changes is zero.
So that if each positive change in z were associated with increasing entropy, and each negative change in z were associated with decreasing entropy, the net entropy of the system would be zero.
From the walker's perspective, direction never changes.
When you say that it does not change from your perspective, you mean that his perspective of his direction does not change from your perspective. That's right, his perspective of his direction does not change from my perspective either.
But look at point X on your strip. In line 3.....5 he approaches that point moving from right to left. In line 5....3 he approaches that point moving from left to right. He approaches the point from two opposite directions.
edit: No wait, this is wrong. My mistake. He does not approach the point from different directions. See below
You have to stand outside the strip to see that the point can be approached from two opposite directions and that it is the same point in both cases. The person on the strip cannot see that. [/edit]
Maybe we're getting confused over what this is supposed to demonstrate?
Jn
eta: it is because the walker is always moving in the same direction (from his perspective) that he perceives z (time) to be linear and irreversible. But for us, looking down at this little cubic system, we can see that as he moves from point to point along the strip the value of z is sometimes going up and sometimes going down. (The sum of all changes in the value of z is in fact zero.) Z is not irreversible. And his path through z is not linear. When all three dimensions are shown, his space - the surface of the strip - is bent even though it feels flat and straight to him.
Edit: Wait, I see what you mean now. It is because an arrow representing his movement is always going in the same direction and does approach every point from the same direction that you are saying the direction does not change. That is also why that value of z appears to him to be always increasing.
But if you are standing outside the strip and can see the extra-dimension of space in which it is nested, and you look at the directional arrows on the strip, sometimes they point from right to left and sometimes they point from left to right. The value of z can either increase or decrease, and the net of all changes is zero.
So that if each positive change in z were associated with increasing entropy, and each negative change in z were associated with decreasing entropy, the net entropy of the system would be zero.
A fool's paradise is a wise man's hell.
Ii y'all
First I'd like to thank my friend who invited me her (you know who you are).
Second, I have a lot of thoughts about this little book and since I came in leat in this thread I hope none of this is redundant.
First of all, the "mistake" in the book may be different dependending on one's point of view. Nothing I have seen in it is logically implausable (I am on my second read now, my first about six months ago).
The biggest problem I see with the major idea of the book is about the nature of God. How ever ideas about God may differ, a few generally agreed upon premises make Avatar's idea about the origen of the universe and its relationship to god problematic.
First. God is a being who necessarily exists. That is to say, IF God exists, his/her/its (the article is problematic) existence isn't something that could just as well not be.
2. Because of the first premise, God is generally understood to be the source of all being or, put another way, God is what being is. This is usually called the ontological argument for the existence of God.
Therefore if God were to cease to exist everything would cease to exist. There would be no "debris" because debris exists, has being and therefore God would have to continue to exist.
Another problem here is that God, being all knowing, would already know everything just said and would therefore not even attempt the sort of self immolation that Avatar suggests.
Unless....
God's action didn't have the meaning which Avatar ascribes to it. While God might already know that he/she has no choice about whether he/she exists (this could start a whole other set of questions but I'll just assume that this is the only effective limit to the freedom of God) there could be another reason why God would do something like Avatar suggests.
God has many qualities, necessary existence being only the most basic. Some of the other qualities that are generally agreed upon are essential oneness (integrity) and absolute benevolence. If god wanted to create a universe and there was nothing there to work with but his/her own "body" then he/she would sacrifice one of his/her most basic features (and we can assume joys) which is the integrity of his/her own being. This is where the generosity of God comes in.
In this view, god did not "create" the world out of some idle curiosity about whether he/she could die (he/she would already know the answer to that question) but rather as the only means of sharing the absolute joy of being. A god that sacrifices his/her own body so that the whole world might live, this might sound a familiar theme to some.
Well there is more to say here but I am interested in what others think of these thoughts.
One more thing. Particles do not pop in and out of existence. There is no "frame rate" to the universe. It only seems this way because all things exist in a kind of vibratory flux. So what appears to be a "quantum leap" is realy a phase shift between the observer (or parts thereof) and what is being observed. his is a conjecture which I have no real proof of but I feel it intuitively to be true.
First I'd like to thank my friend who invited me her (you know who you are).
Second, I have a lot of thoughts about this little book and since I came in leat in this thread I hope none of this is redundant.
First of all, the "mistake" in the book may be different dependending on one's point of view. Nothing I have seen in it is logically implausable (I am on my second read now, my first about six months ago).
The biggest problem I see with the major idea of the book is about the nature of God. How ever ideas about God may differ, a few generally agreed upon premises make Avatar's idea about the origen of the universe and its relationship to god problematic.
First. God is a being who necessarily exists. That is to say, IF God exists, his/her/its (the article is problematic) existence isn't something that could just as well not be.
2. Because of the first premise, God is generally understood to be the source of all being or, put another way, God is what being is. This is usually called the ontological argument for the existence of God.
Therefore if God were to cease to exist everything would cease to exist. There would be no "debris" because debris exists, has being and therefore God would have to continue to exist.
Another problem here is that God, being all knowing, would already know everything just said and would therefore not even attempt the sort of self immolation that Avatar suggests.
Unless....
God's action didn't have the meaning which Avatar ascribes to it. While God might already know that he/she has no choice about whether he/she exists (this could start a whole other set of questions but I'll just assume that this is the only effective limit to the freedom of God) there could be another reason why God would do something like Avatar suggests.
God has many qualities, necessary existence being only the most basic. Some of the other qualities that are generally agreed upon are essential oneness (integrity) and absolute benevolence. If god wanted to create a universe and there was nothing there to work with but his/her own "body" then he/she would sacrifice one of his/her most basic features (and we can assume joys) which is the integrity of his/her own being. This is where the generosity of God comes in.
In this view, god did not "create" the world out of some idle curiosity about whether he/she could die (he/she would already know the answer to that question) but rather as the only means of sharing the absolute joy of being. A god that sacrifices his/her own body so that the whole world might live, this might sound a familiar theme to some.
Well there is more to say here but I am interested in what others think of these thoughts.
One more thing. Particles do not pop in and out of existence. There is no "frame rate" to the universe. It only seems this way because all things exist in a kind of vibratory flux. So what appears to be a "quantum leap" is realy a phase shift between the observer (or parts thereof) and what is being observed. his is a conjecture which I have no real proof of but I feel it intuitively to be true.
----------------------------------------------------
Our idea of God tells us more about ourselves than about him.
-Thomas Merton
Our idea of God tells us more about ourselves than about him.
-Thomas Merton