Each can convert to one of the next two, ie A =>B or C, B => C or D,
... D => A or B.
Now, each of these transformations is a Feynman interaction, and
allowing
one at a time, we get:
ABCD => BBCD
ABCD => CBCD
...
ABCD => ABCA
ABCD => ABCB
So, ABCD branches out to 8 USS's, and has 8 incoming USS's, but in no
case do we have:
AAAA => DDDD
which can be done, but not in one step.
> Again there are lines, plural. But is this necessary?
It depends. Some states may have no predecessors. For example, in
Conway's Life, the set of all cells being filled has no predecessor.
> Imagine a grid of dots, some red, some "off". The red ones represent
> possible states of the universe, the others represent impossible states.
I can imagine a large set of connected subsets which are themselves not
connected. If you start within one of these you may not enter one of the
others. Sources (no predecessors) and sinks (no successors) are also
possible.
> Does the concept "Feynman interaction" still apply to it?
As I recall Feynman diagrams are time invariant, so all interactions
therin
are reversible. However the sense of time requires memory / event
histories
whose consistency supports the arrow of time. I don't know if this means
anything.
> Does it too have lines leading to other points?
See above.
> If so, do all its lines lead to other "off" points, or could some of them
> lead to red points?
> In other words, could you have a situation where each red point
> has more than one line leading into it, but only one of those
> incoming lines comes from another red point?
You can only traverse the USS's connected by allowed transitions.
> Suppose each red point does have more than one line leading out,
> toward other points. Does it follow that each red point has more than
> one line leading into it? No! Consider:
>
> Let the integers be represented by points on a line. Suppose numbers
> divisible by three are red: 3, 6, 9, 12, etc. All other numbers are "off."
> Suppose each point n has two lines leading out, one going to 3n + 1,
> the other going to 3n + 2.
> Each point has two outgoing lines.
> Each point has at most one incoming line.
> Red points have no incoming lines.
>
I am presuming a finite universe, ie, the total number of particles is
finite. Ergo the total number of USS's is also finite, though hugely
larger.
> > One point to notice here is that every state of the Universe
> > comes from a large and finite number of possible past states,
> > that there is NO single past.
>
> is far from obvious, at least to me. Maybe I'm missing something.
I wasn't speaking in terms of mathematical rigor, but from my knowledge
of physics.
> I hope so, because
>
> > Miracles require absolute forgetfulness.
>
> is too beautiful not to be true.
>
To echo another thread here, I nearly had an orgasm when I understood
this. BTW, I've had a few personal experiences which though certainly
not scientifically rigorous, fit well with this idea. Also, it is easy
to demonstrate than once there is a miracle, it always has a plausible
causal explanation.
> [PS Nadia, are you with us on this thread? Imagining grids of points,
> and having them light up in various patterns and colors, is the
> connection between art and mathematics. Mathematics, when you learn
> to see it as it is, is like a laser show in a cathedral full of mirrors.]
>
Your appreciation is sweet to behold. Beauty! = an Extropian
Principle...
PS - I've done laser light shows for years....
O---------------------------------O
| Hara Ra <harara@shamanics.com> |
| Box 8334 Santa Cruz, CA 95061 |
O---------------------------------O