Paradoxes Newsgroup Article

Malcolm McMahon wrote:

>[I'm attempting to merge three sub-threads here since they are becoming
>redundant]

Good idea. :)

=== Potential, Hypothetical, Possible, Actual ===

>>Would this be a wide field of potential timelines occupying a single
>instance
>>of hypertime, and then all collapsing away in the next instance of
>hypertime?
>
>Yes. That's the one. I see no reason when the various potential
>time-lines would be arranged in any kind of sequence.

>>So there's just the two hyperstates? The "pre" state, with every imaginable
>>timeline, and the "post" state consisting of just those that don't contain
>>paradoxes?
>
>No, the "post" state contains only on time line, "What really happened",
>just as, in the normal movement of "now", the future contains large
>numbers of potential states but when it becomes the past it is single
>valued.
>
>
>> But then what about the example we went through earlier where the
>>single timeline went through multiple versions (states) until it finally
>>arrived at one that was internally consistent? Are you saying now that those
>>intermediate timelines wouldn't occur? That it would just go from the
>>paradoxical one to the final acceptable one in a single "pass"?
>
>Not exactly, or not in any kind of sequential manner. From many
>time-lines direct to one.

>>As I asked in another post, if these diagrams don't adequately match your
>own
>>"picture" of your own views, then I'd appreciate it if you could try and
>>produce similar diagrams that do capture your meaning.
>
>
>Aha! I see where we are somewhat at cross purposes. I think this relates
>to my reluctance to treat hypertime as a continuum rather than some kind
>of real ordering.
>
>I'm not assuming that it's meaningful to compare the position of the
>"now" in different potential timelines or that the movement of "now" in
>one of those timelines is some kind of substep in the process of
>selecting "what really happened". Indeed I'm not sure if my
>"constructive now" ever moves down the non-viable timelines. They have
>tentative kind of existence, in order to be rejected, but I don't think
>anyone ever _experiences_ them.
>
>This, perhaps, highlights the nature of my conception of "now" which is
>not so much constructive as selective. You could regard it as
>consciousness groping it's way through a branching tree of
>possibilities, moment by moment. Each observation or decision takes us a
>step forwards. My notion of what you might like to call "chronological
>protection" is that it prunes the tree of possibilities before the
>choice is made. "What really happened" would be the only path down which
>the "now" actually moved.
>
>

>>What would an occupant of that paradoxical timeline experience during that
>>timeline's tentative temporary existence within hypertime? Will the events
>>within a paradoxical timeline appear any different to someone living inside
>>that timeline? How will those events be different?
>>
>>Could we ourselves be living in such a paradoxical timeline?
>>
>
>As above, I don't think anyone actually experiences these "failed"
>time-lines. They never exist as more than potential time-lines to be
>avoided.
>
>

After looking at all these related statements, I think maybe we've just been
arguing over semantics (as often happens). I have in the past made a
distinction timelines that are "possible" and timelines that are merely
"hypothetical" or "imaginable". Meanwhile you're using the term "potential". I
think it might help if we decide just what we each mean by those terms. Maybe
that'll help clear up some of this semantic confusion. And just possibly, we
might find we agree with each more than we thought. ;)

As I use the terms, "hypothetical" or "imaginable" is used to refer to /any/
timeline that can be described, without any concern whether such a timeline
makes sense or not. So a timeline containing a physical rendition of an Escher
staircase would (in my terms) be considered "imaginable". So would a timeline
with a Grandfather's Paradox. When talking about a particular timeline, the set
of "imaginable" timelines that could be involved would be all those consistent
with whatever conditions have been placed upon the nature of the timeline being
discussed.

In my mind, a timeline goes from being merely "hypothetical" to "possible" once
we look at the set of conditions being assumed for that timeline, and find that
they are internally consistent. Any timeline containing a paradox, which means
an internal inconsistency of one sort or another, fails to meet this test. So a
paradoxical timeline cannot be "possible", even though it is "imaginable".
Timelines containing an Escher staircase or Grandfather's Paradox include an
internal inconsistency, so any such timelines would not be "possible". And, if
we are talking about a particular timeline, the "possible" timelines would be
those timelines which are internally consistent /and/ consistent with the
conditions established to identify the timeline in question.

I could also see making a reference to /the/ "actual timeline". This would be
the one timeline out of all the "possible" timelines which turns out to be the
one that actually exists. Of course, this kind of assumes that we are looking
for only one timeline. A multi-timeline construction would include several
"actual" timelines. The other "possible" timelines would in effect be
discarded, not because there's anything wrong with them (unlike the paradoxical
ones), but simply because they just don't happen to be the ones that exist.
Saying that they aren't actual doesn't necessarily mean they /can't/ exist. It
just means that for purposes of the current context, whether they exist or not
doesn't matter. All that matters is the timeline(s) that /does/ actually exist.


I think that the "potential" timelines you refer to sound something like what I
call the "possible" timelines. Timelines that /can/ exist, but which then
collapse down into the one that actually does exist. However, I also think that
your "potential" timelines are also supposed to include what I'm calling
"imaginable" timelines. If so, this could be because you believe that all
"imaginable" timelines are "possible". That a paradox only means a timeline
can't /actually/ exist. If this is in fact what you have in mind, then this
could be a point of disagreement we could discuss. 

Does the presence of a paradox in a hypothetical timeline mean that timeline
can't be possible, or just that it can't actual (but can still be possible)?


=== What is NOW ===

>>You're assuming a "building NOW" for realtime here, right? Where the state
>of a
>>moment in realtime before NOW passes is different from its state after NOW
>>passes? And since this collapse of potential timelines is like that,
>hypertime
>>has a "building NOW" as well? 
>
>That's a good way of describing it.
>
>But (I'm making this up as I go along now) we may need to rethink the
>constructive (or, in my picture, selecitive) "Now" a bit.
>
>Consider the sheaf of time lines emerging from the earliest point of the
>time travel incident. Suppose we consider some kind of influence from
>the future. A signal, if you like, from the end of the universe that
>says this thread is connected.
>
>It would be rather like one of those "lightning disc" toys. The arc can
>go many ways but only along a path where the potential from the target
>electrode has found it's way through the pins to the next link in the
>chain.
>
>That way the "now" will always be drawn along a viable time-line. It's
>this reverse signal that checks for viability.
>
>To the person whose "now" is actually tracing the path this appears as a
>kind of limited free-will. He appears to be chosing as normal but
>certain choices just don't occur to him.
>
>If we do it that way maybe we can dump some of this hypertime stuff.
>Though we still need to explain the motion of "now" at least we have
>only one "now" to explain.
>
>

>>Since hypertime is used to separate the different
>>states of the timelines before and after you deal with time travel, I think
>>you'd have to assume a supertime through which the realtime "building NOW"
>is
>>ordered. Would you say that this supertime has an "arbitrary NOW", or one of
>>the other kinds?
>>
>
>I think, if we must have one, it had better be a constructive now
>otherwise we're back to a somewhat more complex block universe and the
>problems of a block universe remain essentially untouched.
>
>

>just as, in the normal movement of "now", the future contains large
>numbers of potential states but when it becomes the past it is single
>valued.

>>If we start by assuming that realtime has an "arbitrary NOW", we can then
>look
>>at the entirety of a hypothetical timeline, and judge whether it contains a
>>paradox or not. If it does, then that entire timeline could never actually
>>exist. If it doesn't, then that timeline could possibly exist. There's no
>need
>>for supertime and hypertime to run through the possibilities. There's just a
>>superspace containing all of the actual timelines which do in fact exist.
>And
>>that's all that exists.
>>
>
>True, but then we're back in the block universe and "now" becomes
>extremely hard to characterise.
>
>
>

>This, perhaps, highlights the nature of my conception of "now" which is
>not so much constructive as selective. You could regard it as
>consciousness groping it's way through a branching tree of
>possibilities, moment by moment. Each observation or decision takes us a
>step forwards. My notion of what you might like to call "chronological
>protection" is that it prunes the tree of possibilities before the
>choice is made. "What really happened" would be the only path down which
>the "now" actually moved.
>
>

>>>One of the problems that arrises is the natural expectation that the
>>>"now" belonging to a time traveller gets out of step with the "now" of
>>>non-travellers (including granddad). (Which would require an extra
>>>symbol in your notation). If "now" is a function of the interface
>>>between consciousness and the world then is there any reason why there
>>>should be a common "now"? But if not how does that work with free will.
>>
>>If we want to assume that NOW is like you describe here, then that would
>>correspond to what I was calling the "arbitrary NOW". And in that case, NOW
>is
>>not actually a specific unique aspect of the timeline itself, but a mere
>>referential description like "here". 
>
>That just doesn't work for me. "Here" implies "here at this moment in
>time." What, exactly, is it that's "at this moment in time"? In the
>block universe every object, including human beings, has a long
>extension in time. They define a _range_ of absolute time, not a moment.
>
>

>>I think we either have a choice of no unique now at all (an "arbitrary
>NOW"),
>>or a specific unique NOW of one type or another. I guess you could try to
>>concoct a theory where the time traveller may get his own personal NOW which
>is
>>just as valid as the primary NOW. But I suspect any such attempt will most
>>likely lead to difficulties. 
>
>Yes it leeds to difficulties but, if you imagine a time travel
>experience, that's really the way it's got to be. You step into the time
>machine and your "now" moves "forward" to a previous moment of absolute
>time. Consciousness experiences first a later point in time, then an
>earlier point. To me "now" can have no meaning outside of conscious
>experience.
>
>

>>Especially if the "building NOW" or "disposing
>>NOW" are being assumed. Since both of those have NOW actually affecting what
>>exists in the physical universe, I think it'd be hard to reconcile having
>two
>>such NOWs in the same timeline. You might be able to get away with having
>>multiple "moving NOWs" in a timeline, but that would then seem to lead to
>>changing over to an "arbitrary NOW". Unless you can properly justify why the
>>/time traveller/ gets his own personal NOW, while /nobody else/ gets their
>own.
>>
>
>Nope, I think if time travel is possible then everyone gets their own
>"now". I don't begin to understand what it means to say that one
>person's "now" is ahead of, or behind, someone else's. Would the one who
>went first restrict the possibility space available to those that came
>later?
>
>

I'm having a hard time reconciling all that you are saying here. You say you
want a "building NOW", presumably because of the concerns over free will raised
by an "arbitrary NOW". And yet you also say "everyone gets their own 'now'". So
that (presumably) when a time traveller goes back ten years, he has a now which
is just as valid as the people he left behind. Maybe you can explain how the
two concepts can actually fit together. I can't quite grasp it myself yet.

Seems to me, if we assume a "building NOW" which collapses potentialities into
actualities, then the moments left behind by the NOW as it moves are devoid of
potentiality. They've already had those potentials collapsed. So any moment
earlier than the NOW must be completely actualized. Which should mean that when
the time traveller goes back to the past, he ought to arrive in a timeline that
only has one actual line for him to follow, and no other potential lines. And
yet, if he has his own personal now, I would expect from that that there
/should/ be potential lines for the time traveller to follow. If the moments to
follow from his time of arrival do become mere potentials again, doesn't that
imply a resetting of the NOW back to where the time traveller appeared? 

I personally think the "arbitary NOW" and "building NOW" are mutually exclusive
for realtime (and any other individual time dimension). Either there is no
unique NOW, which means no physical collapsing of potentials to actuals as
described; or there /is/ a unique NOW, so not all "nows" actually count for
anything.

But, I can't rule out the possibility that you may have come up with a viable
way of combining the two. I don't as yet understand how, though, so I'd
appreciate it if you wouldn't mind trying to explain in further detail. I think
this is an important topic within this discussion, and thus worth pursuing
further.


=== Where is NOW ===

>>If we want to assume that NOW is like you describe here, then that would
>>correspond to what I was calling the "arbitrary NOW". And in that case, NOW
>is
>>not actually a specific unique aspect of the timeline itself, but a mere
>>referential description like "here". 
>
>That just doesn't work for me. "Here" implies "here at this moment in
>time." What, exactly, is it that's "at this moment in time"? In the
>block universe every object, including human beings, has a long
>extension in time. They define a _range_ of absolute time, not a moment.

Well, one way to define it would be to say that a particular utterence of
"here-and-now" is a specific event located in space-time. Given a common set of
coordinates, observers located at specific points in space-time could then
describe the relative position of that particular utterance of "here-and-now"
with respect to their own positions. If those observers are relatively local to
that utterance in spacetime, they can then interpret the sub-utterance "now" as
referring to the temporal location of that utterance and themselves within
their common reference frame. Likewise, if those observers are relatively local
to that utterance in spacetime, they can interpret the sub-utterance "here" as
referring to the spatial location of that utterance and themselves within their
common reference frame.

To put it more simply, I would say that "here" is shorthand for "here at this
/place in space/" (not "moment in time". And "now" is shorthand for "now at
this /point in time/".

Given your interpretation, we'd rephrase the comment "I've been here before" as
"I've been [here at this moment in time] before". The interpretation I just
offered would rephrase it as "I've been [here at this place in space] before".
I think the latter rephrasing is more appropriate, but that may just be me.


=== On Free Will ===

I'd like to temporarily table any actual discussion on the nature of free will,
if you don't mind. It's an interesting an important topic, but I feel to do it
justice would require going off on a fairly divergent tangent. I realize that
concerns over free will may play an important part in why you may choose to
reject the possibility of an "arbitrary NOW". However, I'd rather look at any
other arguments we can come up with related to what kind of NOW realtime has
before bringing in free will. Once we've dispensed with the others, I think we
could then move on to look at free will with a clearer picture of what we are
looking for.

That sound OK to you?


=== "Sliding" to Other Timelines ===

>>>>(We could probably eliminate the logical conditionals and draw something
>>>like:
>>>>>-_g1--[ ]_-_a1--{a2=A2}-->
>>>>>-_{g1,A2,~g2}--[ ]-_-~a1--->
>>>
>>>Still paradoxical. 
>>
>>How so?
>>
>>The first timeline has a living grandfather, and a living time traveller.
>The
>>time traveller then leaves that timeline.
>>
>>The second timeline has a living grandfather, and a time traveller arriving
>>from the previous timeline. The time traveller then kills the grandfather,
>so
>>the analogue of that time traveller in the second timeline is never born.
>>
>
>But you're left with A2 without an origin. This kind of think is better
>than an actual paradox but still doesn't seem self-consistent to me.
>
>You're right though, "paradoxical" isn't the word.

A2 does have an origin - it just happens that here his origin is located in the
future of a different timeline than the one in which he arrived.

Would the problem here be that the diagram above incorporates /two/ timelines,
when you were perhaps wanting to assume only one? If the scenario conditions
stipulate only one timeline, but then lead to two, then that would imply some
internal inconsistency within that scenario.

If we allowed for the possibility of two actual parallel timelines, would you
still have a problem with the events as diagrammed above? Is there a reason why
a time traveller couldn't "slide" from one timeline to the other during his
trip? Are you perhaps making a global assumption that /all/ time travellers
must arrive at a point in time within the specific timeline they departed from?



BTW, if we make the assumption that realtime has a "building NOW", and also
make the assumption that time travellers can only go to other moments in their
own timeline, then I think we would have to reach the conclusion that time
travel to the past (under those assumptions) is in fact not possible. The
(assumed) "building NOW" would produce past histories that don't contain time
travellers, meaning no time travellers did/will/can appear there. And the
would-be time travellers couldn't go to an earlier time in some other timeline
because they would be constrained (by those assumptions) to their own timeline.

This doesn't prove though that time travel to the past isn't possible. Merely
that time travel to the past isn't possible /under those conditions/. We could
still adopt other assumptions that do allow for time travel to the past. To
argue that time travel to the past is completely impossible, it would be
necessary to prove that those conditions (or similar ones) are the only ones
that can actually hold. If all possible timelines exist under those conditions,
then no possible timeline would contain time travel to the past, so time travel
to the past would not be possible.
Alan Hench