PUZZLaTOMictM Part 2

*State Logic*

page 1

Paul Davies wrote in 9-02 Scientific American that time could be viewed as a
series of states like the frames of a film. I think this idea has been around
since Greek times but his article was very illustrative of current ideas about
time.

If time is like this sequence of frames in a film you could play it in either
direction and in fact physics of the small can not show any direction of time.
Of course some might not agree and might believe that wave collapse is
irreversible as well as uncertainty since you might get a different result every
time you play the uncertainly film experiment, assuming that the film is an
exact reproduction of reality.

In the frame system time is seen as a frozen series of states with no arrow of
time inherent in the states. We know that time paradoxes cana be resolved by the
many-worlds idea of quantum mechanics first proposed by Hugh Everett. The
many-worlds interpreted as time states fits the film idea easily. All time
paradoxes then become easy to resolve and are no longer paradoxes. Here below is
one way to see how this works.

Of course the real situation would be much more complicated than this. Where the
films intersect time travel has occured from one world to another world. Where
the film branches either time travel is beginning or a quantum decision is
invoked causing one world to branch off from another world. This example would
be interpreted more as time travel than as quantum branching. We see that no
pardoxes occur when states can intersect. Where they intersect you would have
the time traveler meeting himself or herself but then any event change would
cause branching avoiding any paradox. This is a very simplistic approach to some
subtle ideas but it gets the basic idea accross that you can see everything as a
series of states. Each frame represents a universe at an instant of time or in a
specific state.

Above we illustrate one way that the state idea can be expanded by viewing a finite time sequences as another more complex set of frames. Many other state structures can exist only limited by our imaginations. The idea is very plastic and seems to be even more versatile than the main mathematical idea of sets and set theory but this is only a speculation at present. We will list a few of the possibilities.

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1. The State of All States

This is similar to the concept of the set of all sets except that it forms an
infinite number of sets of all sets as the film always advances to the next
state of all states frame shot. If you try to freeze this and put it all into a
single frame then that over all frame can advance to the next big overall frame
to form sets of all sets of all sets and so on in infinite progress. In this
sense the state of all states seems to be simpler than the set of all sets
concept since it makes no attempt to form a final state of everything. It is
just states as needed for the discussion or investigation at hand.

2. The State of Repeating the Same State

If a state contemplates itself would an infinity of states result as in the
paradox of self reference? Any computer programmer knows the defeat of a program
paradox such as an infinite loop. The computer freezes up and does nothing until
it is unplugged and rebooted. Of course modern processors have a means of
warning that an application is not responding and allows the user to end the
program. An insane assylum probably has some patients who have too many infinite
mental loops in their heads leaving not enough normal brain matter left over to
have normal control of their mental states.

3. The State Where the Future is Forbidden

This is probably a state that will never be seen since it cannot advance into
the future. Perhaps it only exists once as a frame shot and therefore you cannot
prove it ever existed in the first place. Would a single vision of a ghost
qualify?

4. The P State

P State is so named because when translated to set theory it is a paradox set.
The idea is that state logic can include paradoxical stuff that loses the
paradox feel when contemplated as a state system. For instance in electrical
circuit logic a relay race is an infinite loop where a set of relays
continuously turn on an off in a sequence similar to a simple pair of paradox
statements. Here is an example "The next sentence is false. The previous
sentence is true" Obviously wired electrically or in a program this would give
an infinite loop of activity that requires at lest two repeating time states to
operate continuously. In state logic it is just a two state system repeating
forever. In that sense it is no longer a paradox. We have many mechanical
systems that perform by cyclical repetition. Factories are modeled on this kind
of system but they always build in stop switches. If there is no stop switch or
means of stopping then we have a more natural system like an orbiting planet. In
set theory this time element is usually missing but in state systems it is the
main subject. Thus adding the P set to set theory simply emulates state theory.
It would require a time variable to be added to mathematical theorems about P
sets. In that case state theory might be seen as one step above set theory and
set theory.

A Turing machine uses a state table and an infinite tape with square frames.
Each frame contains blank or a symbol and the state table instructs the machine
what to do based on what symbol it reads. It can erase and write a new symbol or
just erase then move right or left. This a crude definition but the simplicity
of the idea makes it possible to characterize the essence of a computer. We
would like to compare this to natural state frames. In nature the state table is
now the laws of physics and the frames of the tape are the states of the
universe. Of course such a simple definition immediately seems inadequate to
define nature or reality. What about quantum properties which are not explianed
in a completely local manner? Would any kind of state machine be adequate to
explain all the mysteries of quantum theory? Even so it is fun to speculate
about state logic since it is so simple to understand the basic idea and seems
to fit well with how our minds organize and store information.

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The human brain is a very complex state machine, if it can be called that. When
we remember things we can remember in many different ways either as a verbal
recollection of what happened or as a visual sequence with just a few still
frames of the experience. When we try harder or take time to recollect the mind
can often reproduce the memory as if it were being relived in reality. In fact a
few people have been identified with almost perfect autobiographical memory,
covering every awake moment back to about 8 or 10 years old. It is as though the
brain's memory capacity is many terabytes or many times larger than a one
terabyte computer hard drive. The brain may not need such a large capacity by
having compression techniques that far surpass anything presently known. Very
little is known at present about how so much detail can be accessed by a single
mind. Yet when tested these special people can recite exact dates, names, time
of day and even what was said for important events they lived through, as well
as trivial events such as riding in a car and seeing the number on a licence
plate on the car ahead the cars color, the weather at the time the conversation
if any or what was being said on the radio. Such an incredible amount of detail
stored over many years is hard to comprehend. However with the present advance
of technology this will soon become an ordinary feat for electronic devices.

The idea that our brain stores all this stuff in a sort of state stream that can
be accessed at will is not difficult to imagine since we are all familiar with
film and with pages of a book, writing in notebooks and so forth. So to refer to
state logic to try to emulate nature is not a big stretch and fits naturally
with the way we organize and form memories and think about things. It is much
easier to separate things into distinct pictures where each picture shows a kind
world of the instant it records even though it is restricted in both time and
space. Without such a simplifying system it would be harder to cubbyhole things
and make them availble for future access.

The brain is marvelous in being able to replay reality when desired or when
daydreaming, almost as if it contains within it a multiverse of state films
available for dreaming or imagining at will.

We want to emphasize that we think that state logic should contain a natural P
state system which is the paradox states when time is removed. The simplest P
state being states that turn on and off, on and off continuously, like a
miswired or 'pardoxica'l relay race, or like truth telling false to turn on and
false telling truth to turn off. These on off systems or repetitive systems
being the main way that factories or any repetitive cyclical system operates.
Nature by being mostly composed of cyclical actiions is then produced mainly by
the actions of the Paradox state system.

The P state is a generalized idea that what is paradoxical when time is not
included may not always be so paradoxical when time is included. Here is an
example where perhaps time can include a paradox but can still accomodate it as
a recurrance of the same circuit as already mentioned.

The following statement is false

The previous and following statements are true

The previous statement is false

repeat

It represents a continuous stream of repeating states where things turn on and
off as the film plays forward in time. Does it play exactly the same when played
backwards?

Note that in quantlum theory playing a film backwards is no longer adequate.
This is because you need to reverse not just time but parity and charge
conjugation due to an assymetry of the weak force interactions. To apply this to
film you would need mirror image words and perhaps some reversed forces so the
film would no longer look like time can be sensibly reversed in the traditional
sense.

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To conclude then we want to emphasize that we think that state logic should
contain a natural P state system which is the paradox states. The simplest P
state being states that turn on and off, on and off continuously, like a
pardoxical relay race, or like truth telling false to turn on and false telling
truth to turn off. These on off systems or repetitive systems being the main way
that factories or any repetitive cyclical system operates. Nature by being
mostly composed of cyclical actiions is then produced mainly by the actions of
the Paradox state system.

Finally we want to make a bunch odd statements about states to get the effect of
state system thinking that the brain seems to have a natural feel for. This is a
speculative and somewhat recreational or entertaining conclusion to this old
idea. You can view the singular word state as sometimes meaning a series of
states or an infinite series of states.

1. The state of entertainment. 2. A state of illness. 3. A state ment about
states. 4. A state of mind. 5. Alice in state land. 6. The state where futures
are forbidden. 7. The state where states all play backwards except the present
state. 8. The state where forces are reversed except gravity. 9. The state of
happyness 10. A state of infinite lists. 11. The null states or the set of all
states where nothing exists. 12. The states where Godel's theorems can't exist.
13. States of no motion. 14. The state where gravity repels. The many states of
mathematics.

As you can see the word and the concept can mix together in confusing ways yet
individual statements seem to cohere as being about states or a state. State
logic as we use it is just a convenient way of compartmentalizing the passage of
time.

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Mathematics as States

page 6

Why is a time variable seldom seen in a mathematical equation? This is because
time is assumed as automatic and unnecessary. We postulate some items to show
this.

1. The number 1 written on a piece of paper continuously cycles thru time. If
you see it again tomorrow it has cycled thru one day of time. The paper exists
in a time line therefore the symbol on it exists in repeating units of time. The
same is true of any equation.

2. The mind also cycles the number 1 in a re-circulating mental circuit when it
contemplates or uses it. In this way time is automatic in mathematics. A time
variable only comes into play explicitly when needed such as a velocity.

3. To become more aware of how time is ingrained in mathematics we propose a way
of looking at an equation or a number as a system of states. The number 1 would
be a repeating set of film frames showing the number 1. You then see it as
existing only by the action of time.

Every mathematical manipulation has a state number S = s+1 = number of steps
plus 1.

The list of manipulations is the state list which is the frames of the film or
the list of states.

Sometimes given just parts of a state list it is possible to reconstruct the
whole list, or play a state game. We can then list some of the things used in a
mathematical manipulation, at least involving solving an equation. For an
equation such as y=4+5*3-6*2 we have a state number, Sn = 5. To this we can add
a State list of operators Sop = +,*,-,*. In addition we have the elements Se =
y,4,5,3,6,2. In a crude but interesting analogy with physics Sn is like sn
energy level, Sop are like forces, and Se are like particles. The equal sign may
or may not be included as an op. Continuing the analogy we can see
mathematicians brains as colliders of equation particles.

We can create a game of mathematical bread crumbs by only listing parts of the
Sn, Sop, Se at each state. Object: find the original expression. For instance
given a list 4,8,17 what simplest expression produced it? One answer might
4*2+9. Another answer is 4+4+9. The second answer might be preferable as being
simpler. You could also be given 4,,17,*. Thus 4*2+9 or 4*3+5 would work. Given
4,2,*,+ we could have 4-3*16+1. This is not preferred since it includes a
negative sign and we want to get as close to the given state list as possible so
4*2+7 seems to be best as it includes only 1 extra list number n=7.

We see that to arrive at a # such as 6 and infinity of different ways is
possible. This is not like a qubit where the qubit is both a 0 and a 1. It is
never 1/2 or 1/3 or some real number in between. It is 0 and 1, only two
possibilities while math can get to 6 in an infinity of ways. There is a
similarity with entanglement in that we would like to limit our bread crumb game
to very few and very simple elements. For instance one expression for 6 is
6=1/6*6*6*1/30*30. We have Sn=5, and Sl=1/6,6,6,1/30,30, if we treat simple
fractions as single numbers, and 4 Sop=*,*,*,*. The main idea of such a game is
to develop a feeling for the time aspect of mathematics. It can only exist as
moving circuitry, it is never just ink on paper which alone contains zero
meaning and has zero effect on anything. The game could continue to develop
eventually incorporating more and more of mathematics, geometry and topology.

All this state logic brings up the subject of times arrow or the non-reversible
nature of time in mathematics. For instance once you have a result if you do not
know how the result was gotten you probably and usually cannot reproduce exactly
the manipulations that produced the result. The result is like a wave collapse
and uncertainty in quantum mechanics as a very crude but illustrative analogy.
You do not get to fully reverse things that have slipped away. Mathematicians
and logicians would object strenuously saying that different ways of obtaining
the same result are equivalent. And I do not object, I only want to point out
how much we take for granted when we make our powerful generalizations. In fact
by investigating these processes in detail we might reveal new knowledge about
logic an math not previously obvious.

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We can point out other simple uncertainties in any result. For instance given Sr=1(Sr
is the result) and Sop=*, two equally simple answers are possible -1*-1=1 and
1*1=1. If square root is the op and 1 the list then you could also have the same
two possible manipulations in reverse as equally valid answers showing that
uncertainty is built into mathematical information. Another very deep
uncertainty is the inability to get absolute exactness when using real numbers
applied to the real world. Nature seems to exploit this powerful continuity or
quantum non ability to not always round off to the nearest quantum metric in
producing her chaos, which is at work pretty much everywhere we look and even in
our own thoughts and heartbeats.

Temporal or non time reversible operations are defined by quaternions and
Octonions. For instance ij=k and ji=-k. Since we always tend to work equations
and operations in a left to right manner we see time moving left to right
predominantly as we think mathematically. To alert our minds to this when using
ijk operators we propose to invent a substitute for equals such as >>> and <<<.
Then ij>>>k and ji>>>-k. Reversing time we can go right to left and write

k<<<ji and -k<<<ij.

These anti expressions then annihilate as

( ij>>>k)+(-k<<<ij)=0

The new signs for equals could always be used in place of = to remind us that
time is an important element in our every detail of thinking and might give
humans an edge in expanding our understanding of the great power of mathematics.
Writing a simple expression like 1>>>1 or if a>>>b and b>>>c the a>>>c and
reversing c<<<a because c<<<b and b<<<a. You can see how difficult it is to
reverse our time line of thinking for fairly simple ideas without going all the
way and writing in mirror image and reading from right to left and Leonardo
seemed to be fond of doing.