Re: Eternity

On May 11, 11:04 am, "Thomas" <some...@xxxxxxxxxxxxx> wrote:

[...]
" Do you have some reason to think it's impossible? "

Yes.
Quantum field theory provides an amazingly successful framework for
describing the material world - QED for example predicts a value for the
magnetic moment of the electron which is in staggering agreement with the
measured value. Our best model of the quantum vacuum (the fabric of reality
if you like) is based on gauge symmetry groups in which the electrical force
corresponds to the circle. Other particles and forces are based on higher
level symmetries (the group of spherical rotations for example) - the whole
framework hints at a beautiful underlying simplicity.

Yes, the model is known to be incomplete (most notably wrt gravity), but
its current accuracy suggests it must be in very close harmony with nature.
But in any case biology is just a branch of chemistry and chemistry is
almost totally controlled by the electrical (or electromagnetic) force. The
periodic table of elements that essentially defines the world in which we
live, necessaily follows from the symmetry of the electrical force - iow
this is the way chemistry (at least at these temperatures) has to be.

The fact that people's bodies decay follows not from just chemistry
but also the environment we find ourselves in - in particular the lack
of a source of replacement parts to the body. In principle such a
source could exist, even in our universe. It probably couldn't keep
the body going eternally - eventually you'd run up against problems
with the second law of thermodynamics, at least if our cosmology is as
we currently understand it to be. However if the laws of physics were
altered a bit it's by no means clear this would be a problem. (Think
of steady state cosmology for example - utterly ruled out by
observations yes, as far as our universe goes, but quite internally
valid as a model.)

Besides, I never imagined that heaven would run according to laws of
physics - at least ones that are at all similar to what we're used to.
Heaven might be a purely spiritual realm.

<.....>

In any event, infinity must be used with great care in mathematics and
logic
and is generally used in the sense of a limit to which some well defined
sequence tends. For example, in the limit, the sum of the series 1, 1/2,
1/4, 1/8 etc is 2, however any particular evaluation of this series will
always be less than 2.

" Both limits and "actual infinities" are frequently used in
mathematics. "

Interesting, my experience is prinicpally in the physical and computer*
sciences, maybe you could give an example of an actual infinity of finite
objects being used in mathematics.

You gave an example yourself: infinite sets.

Eternality is most easily modelled by letting the time co-ordinate
range over the real number line. (Or perhaps the positive real number
line, if time is meant to have a beginning.) In fact all of the
purported paradoxes you mentioned would, if they actually were
paradoxes, prove that the real number line does not exist.

There are also infinite cardinals, infinite ordinals and points at
infinity in projective geometries.

*The use if the term computer science does not imply any agreement with the
idea that computing is a branch of science!

If we try to transfer the idea of infinity to any physical world then we
have to be at least as cautious. So in the real world, Zeno's paradox is
easily resolved but Hilbert's Hotel is not.

"There is no paradox that I know of concerning Hilbert's Hotel. (Nor
Zeno for that matter.)"

I assume you're being disingenuous and what you really mean is that you
believe that both paradoxes have accepted resolutions. Perhaps you could
exhibit your favoured resolution of Hilbert's Hotel.

I am using the word paradox in the sense of a derivation of an actual
contradiction rather than just a conclusion that seems counter-
intuitive, since the former notion is what is relevant if one wants to
argue that something is logically unsound.

I do not know of anything that even purports to being a paradox, in
this sense, when it comes to Hilbert's Hotel. AFAIK, HH is a nice
illustration of a particular way in which infinite sets are counter-
intuitive, at least by naive everyday standards. But counter-intuitive
is not the same as logically contradictory.

In other words we can have a
countable infinity of objects which tend to zero but not a countable
infinity of objects which each have a finite extent - at least not without
running into a real paradox.

In the context of heaven for example, we might imagine the big boss
welcoming a recently deceased (or should that be re-born) 'elect' and
giving
him the standard intro'; "welcome home, enjoy yourself but remember I
can't
abide idleness, be sure to work as much as you play". Now, an elect who
was
well versed in Cantor could simply work for one day and then party for the
next million years and so on. When the big fella demands to know what's
going on he points out that in the limit, the number of days in which we
works is exactly the same as the number on which he parties. Don't believe
me? look they can be paired off against each other, (.....see any standard
work on infinite sets to see how this is done).

"Assuming that "work as much as you play" means "make sure that the
cardinality of the set of days you work is at least equal to the
cardinalilty of the set of days you play". I can think of much more
plausible things it might mean.

Anyway is there supposed to be a paradox here? If so what?"

Yes, the paradox is that on the one hand the cardinality of the days spent
working is the same as the cardinality of the days spent playing and on the
other hand, on any particular day N the elect will have spent millions of
more days partying than working.

Those two statements are not negations of each other and don't appear
to contradict each other in any way that I can see. If you think they
do then you need to explain why. If you manage then in addition to
having disproved eternal life you will also have shown that the set of
natural numbers does not exist.

But let me try to strengthen this a little and hopefully bring out the
paradox a little more clearly.

Suppose the recently reborn elect is greeted by god who gives him a list
showing him a suggested schedule for his time in ever-ever land. "I've just
printed out the first trillion years but I have the full list on my
hard-drive" (god might use the sequence of digits in an irrational number to
do this ... or whatever). "Now, I know you humans are quite keen on choice
so if you want me to rejig the list just say"

The elect studies the list and to his horror he sees that cauliflower-cheese
appears on the menu every so often - and he really really hates cauliflower
cheese. "Hmmm he says, do you think it might be possible to move the entries
for the days with cauliflower-cheese back to the end of the schedule, by
that time I should have acquired sufficient wisdom to see the beauty of even
cauliflowr cheese?" God frowns.

There is no such thing as the "end of the schedule" if the schedule is
eternal so what you're talking about would be not rejigging but
elimination. This is no more contradictory than if, in a finite
schedule, I try to "move" some task I don't like to the sqrt(-1)th day
or to the 30th of February.

So, will the elect ever have to sample the delights of heavenly
cauliflower-cheese?

Now, the list is a real list and the days to which each entry relates are
real days (supposedly). We can exhibt the entry for any day and there are
mechanisms for generating an inexhaustable supply of entries. So why should
it not be possible to rearrange the entries, and if it is possible to
rearrange the days then will our elect get to eat the c-c and if not then
what is the ontological status of those days in which he is scheduled to
eact the c-c?

Ok, it's just off the top of my head and maybe it's not the cleverest
example, but I think it helps to illustrate the problems that arise when you
make the category error of trying to move a concept from the platonic realm
into the physical realm.

Actually, purported paradoxes can never do that, as any object or
concept that lives in the Platonic realm must be just as free from
contradictions as one that exists physically.

Michael


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