>If so, where would that occur?
If reality is spatial then it is meaningful to ask that question but
if it is not then it isn’t. Currently it is spatial but as I have
stated in the future it might not be. Whether it is spatial or not is
a property of it. It is not the fact that it is – it is the fact that
it is spatial. The question “where” is answered by specifying the
coordinates of one place relative to another. The number of vectors
required to span the space is the dimension and defines the number of
coordinates required to specify the answer. However, there are many
sets that are not spatial and will not allow you to specify an answer
to the question “Where?” If I give you the set {Green, Red, Blue} what
is the answer to the question “Where is Red? Remember the set is not
ordered so you can't say "In the middle". Mathematically this means
that the set of vector spaces is a subset of the set of sets and that
there are non-spatial sets. In particular I gave you an example of a
single sound. If the universe were reduced to that single sound the
question of where that sound was would be meaningless.
>I cannot envisage an event that can occur at a
given time and, yet, occurs nowhere, as that is what MUST happen if a
purely spatial event occurs.
Yes as you say “if” a purely spatial event occurs....but what if the
event is not spatial? It can still occur.
> Boil it down, though. Where would a non-spatial existence take
place? Equally, WHEN would a non-temporal event occur?
“When” is a much more difficult question than where. I did not say
that existence wasn’t temporal. I might argue that but it is much
harder. Spatial to me is easy but time has a much more profound
relationship with existence. In a sense all existence occurs now and
in order to temporalize it some difference must be had. Now the
difference could be conceived of as being “subjective”. So, in the
example of the note, I would experience that the note had a duration
even though “it” was “unchanging”. “I” would change from initial
recognition of it to an experience of having listened for a while.
Some might say that that note is and that my experience of duration is
“purely subjective”. There are other concepts of time that are very
profound. In any case it is not my argument. My argument was solely
about space – not time.
>These
questions appear koan-like because space and time are intrinsically
joined to one another in a space-time continuum. There is no way to
separate them and have non-temporal or non-spatial events as, by
definition, an event must occur at some place at some time. And, I'm
afraid, THAT'S the governing logic here.
No it isn’t. The unity of space and time that Einstein (actually
Minkowski) achieved has to do with the fact that spatio-temporal
coordinate transformations are such that a spacetime interval can be
conceived of as an object in 4-space and, due to the Lorentz metric,
the transformation equations between frames of reference result in a
rotation of the space time vector relative to the new frame so that
more of it is “in space” for one observer and more of it is “in time”
for another. There in fact are pure time intervals relative to each
coordinate system. They correspond to spacetime vectors that occur at
a single location relative to a frame of reference. Likewise spacetime
vectors that go from one point in the present relative to a given
coordinate system to another point in that same present are purely
spatial. However when transformed to another coordinate system in
motion relative to the first the purely spatial coordinate interval
would no longer be purely spatial, nor would the temporal be purely
temporal. Therefore the notion of some interval being purely spatial
or purely temporal is a relative concept. Still there are no frames
that don’t have separable time and space coordinates (Mathematically,
if it were true that time and space were the same thing then the
determinant of the metric of space time would be degenerate (=0) and
Riemanian geometry, explicitly assumes that the space-time metric is
not degenerate)
All of this is based on the science of physics which is grounded in
reality through experiment. If you look at that process you will see
that it does not allow one to make predictions with absolute
certainty. Basically the whole process is based on an assumption of
the homogeneity of time. That assumption cannot be tested in a way
that will allow you to confirm it absolutely for the future. We exist
in a permanent possibility that future scientific experiments might
result in a contradiction with past experiments. Not a refinement –a
contradiction. My assertion is just that one path the universe could
take would be to become non-spatial. I am not asserting that it will
only that it is logically possible and that the notion of existence is
compatible with a non-spatial reality.
>Nope. You hear because air is being compressed at different rates.
The sound waves move through the air (this takes both time and space,
the time it takes for the wave to leave its source, travel through a
medium and land on your ear).
Actually the causal connection between my hearing and the physics of
my neurology and its environment is scientifically factual but not
logically necessary. It is logically possible that the particular
state that you describe could change in the future and change in a way
where there is no air, no neurology, no body and yet still sound. That
is logically possible. It is scientifically undemonstrated but
logically possible to be demonstrated in the future. We may conclude
that it is not possible physically, but that would not be a logical
conclusion it would be a physical one – one based on empirical
physical science and therefore open to future disproof. You can see
that the entire subject of physics cannot be derived logically. It
requires something in addition to mathematics to make a physics and
that something is dependent on what we observe. Your assertion was
that it was logically necessary for existence to be spatial. I am just
challenging your definition.
>The air exists within space-time. Smells are also received by chemicals that
>are passed past one's olfactory bulbs when one breathes. This takes time, and
>space is
involved, again, as the medium through which the chemicals pass.
Again that is just the way things happen to be right now.
> I'm intrigued by but unsure what you mean by 'the spatial
nature of the universe', as, since Einstein, we've come to understand
the universe as not spatial and temporal but spatio-temporal.
As I have already stated above there are purely spatial intervals
relative to any coordinate system. Also there are purely temporal
intervals relative to any coordinate system (and relative to any point
in any coordinate system). If you look at the Lorentz metric it
contains both time and space terms.
But to answer directly: By spatial I mean the fact that the set of
events with a given time coordinate relative to any frame of reference
can be put locally into a one to one correspondence with an open ball
of R^n where n >0.
In the current universe we believe that three vectors of space and one
of time are needed so an open ball of R^3 is needed for space and R^1
for time in any given coordinate patch.
Visually this means that I can provide overlapping maps from sets of
three real numbers to the set of points that exist at one point in
time relative to any coordinate system.
I understand that this is scientific fact. I am just stating that 1)
there is a difference scientific fact and logical possibility. 2) The
spatial nature of reality (including its current number of dimensions)
is not derivable logically from the fact of existence. It is an
observation – not a necessary conclusion based solely on the fact of
existence.
>That is, our universe is a space-time continuum with NO missing (spatio-
temporal) points.
I have no idea of what you mean by “missing points”. The topology of
the universe is a matter of current investigation. In some ways
singularities are “missing points” In some ways, topologically
speaking, a plane is a sphere with a point missing. The famous “point
at infinity”. I am just not sure what you mean.
>... all events within said continuum are within a cause- and-effect framework,
>that is, no uncaused events can occur.
Einstein’s theory does not say that at all. Causal relationships do
obtain in time and space but, for example, there is spontaneous decay
of radioactive particles. What do you think “causes” spontaneous
decay. Events can occur that are not caused. There is nothing in
relativity theory that would contradict that. The meaning of causality
is very difficult. My point is simply that it is not logically
necessary to be spatial in order to be.
>This
understanding, in a sense, does away with the medieval understanding
of 'accident' by demonstrating that everything that exists MUST have
a
cause (or many causes) and, therefore, could NOT have been changed,
as
the event was already a part of the space-time continuum anyway. I
hope that helps clarify what I meant, but, I expect it may also clash
with your paradigm (especially if you believe in free will).
The notion of accident does not mean something that does not have a
cause. If I take a green cup and note that what it is, its essence is
“a cup” and then I change its color from green to red then it is still
“a cup”. That means that the real property “green” is not essential
but accidental. If however I change the cup into a baseball then it is
no longer a cup but a baseball. Its essence has changed. What remains
the same is only its material. I just used that idea to illustrate
that to be does not mean to be spatial. It is possible to have non-
spatial existence and, indeed, if our scientific theories turn out to
be wrong and the universe heads that way then it can in fact happen.
Einstein was once in a German government office and was asked to give
his religion and he wrote “Jewish”. His friend said something like
“Better not, might cause problems” so Einstein crossed it out. The
German bureaucrat said something like “You can’t do that!” and
Einstein responded something like ‘Young man, on whose authority did
you accept the fact that I was Jewish” and the bureaucrat responded
“On yours” to which Einstein replied “Very well, I withdraw my
authority!”.
A similar situation exists for science. If one asks on whose authority
we base our claim that scientific theories are true one must answer –
“On the basis of experiment.” Therefore science is continually
dependent on that basis changing its story. At some point the universe
might say to us "Young man on whose authority did you base your
theories." We will have to answer "On yours" and the universe may
answer "I withdraw my authority". My only point is that it can change
it in a way where the universe would no longer have spatial
dimensions.
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