On Jul 22, 12:57=A0am, Alexm <amcwill...@[EMAIL PROTECTED]
> wrote:
> On Jul 20, 11:16=A0pm, Alexm <amcwill...@[EMAIL PROTECTED]
> wrote:
>
> > On Jul 19, 4:04=A0pm, mcja...@[EMAIL PROTECTED]
wrote:
>
> > > On Jul 19, 4:54=A0pm, mcja...@[EMAIL PROTECTED]
wrote:
>
> > > > On Jul 18, 11:55=A0am, Alexm <amcwill...@[EMAIL PROTECTED]
> wrote:
>
> > > > > On Jul 18, 2:24=A0am, mcja...@[EMAIL PROTECTED]
wrote:
>
> > > > > > > > I saw something interesting about a grid pair puzzle
proble=
m that
> > > > > > > > might be interesting.
> > > > > > > > it's the problem where in a grid any size you say so many
t=
hat are
> > > > > > > > pairs.
> > > > > > > > |1a|2a|3a|
> > > > > > > > |2b|1a|3b|
> > > > > > > > |4a|4b|5a|
> > > > > > > > |6a|5b|6b|
> > > > > > > > to make one move is to make the other of the pair move at
t=
he same
> > > > > > > > time, but to solve where it can move first is to figure
out=
every way
> > > > > > > > it can be solved until you know the last one to move where
=
the first
> > > > > > > > one chosen to move comes from. a recursive problem said
usu=
allly. the
> > > > > > > > pairs switch each move.
> > > > > > > > if I figure each to be able to move with all involved in
mo=
ving, and
> > > > > > > > for each they overlap the involved pieces that have to
move=
.. so if
> > > > > > > > you
> > > > > > > > draw somehow how each can be solved with all that have to
m=
ove
> > > > > > > > together where you say together with how you can solve the
=
other ones
> > > > > > > > the way where each that solves a way is together but all
th=
at solve
> > > > > > > > are together with how they solve it makes what looks like
a=
machine
> > > > > > > > that can move.
> > > > > > > > so if I pick one to move how it can be solved to move and
d=
raw how it
> > > > > > > > looks now by seeing how they solve now, it looks like if
th=
is were a
> > > > > > > > machine the entire machine has been rearranged where if
you=
pick one
> > > > > > > > to move as the part of the machine to move, the whole
machi=
ne is
> > > > > > > > moved
> > > > > > > > to where that part of the machine moved. that's to draw
how=
they
> > > > > > > > solve
> > > > > > > > again.
> > > > > > > > it seems to be able to make a whole machine said with
pairs=
on a
> > > > > > > > board
> > > > > > > > move to any position the whole machine can be in for any
pa=
rt of the
> > > > > > > > machine moved. like, it seems to solve a whole machine .
> > > > > > > > so figure a machine out of these pairs to be a machine
that=
works,
> > > > > > > > see
> > > > > > > > it in how the ones that solve overlap the other ones that
s=
olve to
> > > > > > > > use
> > > > > > > > the same involved in how any can move.
> > > > > > > > see it in how it draws again, it's the whole machine moved
=
if one is
> > > > > > > > moved where it would be for that part of the machine
moved.
> > > > > > > > like, it seems to make the whole machine say it's been
runn=
ing for a
> > > > > > > > while.
> > > > > > > > it looks like pairs in a grid can say any machine the way
t=
hey can be
> > > > > > > > arranged, like each one that solves a way uses the same
pie=
ces as the
> > > > > > > > others that solve a way, so it looks togther as how they
so=
lve as
> > > > > > > > pieces together and other pieces together, together with
ea=
chother.
> > > > > > > > and to move one that solves any way that it does is to see
=
all over
> > > > > > > > again how they solve together a new way, and it looks like
=
the whole
> > > > > > > > machine has moved the way it is to move where only the
part=
of the
> > > > > > > > machine you want moves.
> > > > > > > > it seems like any machine that can express a problem to
sol=
ve can be
> > > > > > > > said with pairs, where the machine hasn't moved yet but is
=
in
> > > > > > > > original
> > > > > > > > position, but then in a completely different position it
ca=
n be in,
> > > > > > > > just be moving one that solves. sticking with how they
rear=
ranged and
> > > > > > > > moving them again always is the same part of the machine,
f=
or the
> > > > > > > > rest
> > > > > > > > to be different the way they solve but as the rest of the
m=
achine the
> > > > > > > > way it's moved connected the part moved.
> > > > > > > > can anyone back up how this seems to work?
> > > > > > > it looks like a machine when you find each that work out the
=
way it
> > > > > > > does and say with all the others that work out the way they
d=
o
> > > > > > > together overlapping common pieces but say connected each
wor=
king out
> > > > > > > as connected, but together as connected it's connected with
t=
he others
> > > > > > > connected. a whole machine where connected together is a
cond=
ition of
> > > > > > > the machine together as complimentary of what is said for
wha=
t is said
> > > > > > > about where the machine is at. the way where a loop in the
ma=
chine is
> > > > > > > what won't loop on it's own unless the whole machine's set
po=
sition is
> > > > > > > where that loop can move on it's own. a set of pairs that
wor=
k out
> > > > > > > together as sets in different sizes say conditioned together
=
like
> > > > > > > where for what matters is for what matters together as what
m=
atters
> > > > > > > for eachother. it's hard to recognize it as a machine unless
=
you see
> > > > > > > that. what's together as pairs that work out together are
lik=
e the
> > > > > > > idea of for what matters is for what matters as where the
mac=
hine is
> > > > > > > at. so machine input is what matters for machine output.
alwa=
ys
> > > > > > > machine input that makes difference of output is pairs that
w=
ork out
> > > > > > > together. machine beginning and machine ending. to see as
mac=
hine is
> > > > > > > a machine to turns back around to beginning if it were to
ope=
rate as a
> > > > > > > machine. very im****tant is trying to recognize it as a
machin=
e,
> > > > > > > because it's hard to see. so if you move pairs that work out
=
together
> > > > > > > as any way they can move, see all over again the way they
wor=
k out and
> > > > > > > how they share pairs that work out another way too. how to
se=
e it as
> > > > > > > the same machine again will be flipped around but try in
diff=
erent
> > > > > > > ways. any machine can be said with pairs. because with pairs
=
you can
> > > > > > > also say this, given how they can be setup, a way for them
to=
be where
> > > > > > > any much of them saying they work out a way can say
different=
in any
> > > > > > > way for how other pairs work out, and how other pairs are
arr=
anged.
> > > > > > > any machine always has it so the bigger part of the machine
t=
hat moves
> > > > > > > any way it can p***** all the movment it can have to a
smalle=
r part.
> > > > > > > so the smaller part moved any way makes the bigger part move
=
ways.
> > > > > > > because of what any condition can be.
> > > > > > > the moving pairs problem i can't find a webpage for. it's
whe=
re on a
> > > > > > > board you setup pairs in any way (but saying a machine that
w=
orks)
> > > > > > > like where
> > > > > > > |1|1|2|2|
> > > > > > > |3|4|3|4|
> > > > > > > |5|5|6|6|
> > > > > > > |7|8|8|7|
> > > > > > > and each number the same is a pair, now see pair move, each
n=
umber
> > > > > > > moves together at the same time with the other. there's one
a=
nswer
> > > > > > > there can be, but a recursive problem usually to find it.
it'=
s where
> > > > > > > that pair can move where it can, but it can because the
outco=
me known
> > > > > > > for where the last pair moves to where the first pair left.
b=
ut the
> > > > > > > pairs switch each move with where they go, to be not the
same=
pair but
> > > > > > > a different pair as paired with where each can go to be
pairs=
with
> > > > > > > what left where it can go.
> > > > > > > so
> > > > > > > |1|1|
> > > > > > > |2|2| -> 2 and 2 is 2 and 1, and 1 and 1 is 2 and 1 the
other=
way.
> > > > > > > pick any and the same but another way. make moved and try
aga=
in, it
> > > > > > > turns around. the machine idea of it is at beginning then
end=
ing, then
> > > > > > > beginning again. because that's all this machine does.
> > > > > > > make me look better about this?
> > > > > > > it is a machine. see how. see how setup bigger they figure
to=
work out
> > > > > > > one way for each pair, and each other pair, they do. so see
h=
ow each
> > > > > > > pair you figure can work out has the same pairs as how
others=
work
> > > > > > > out. they do.
> > > > > > > so draw, draw it so they work out together and others that
wo=
rk out
> > > > > > > together are showing how any pair works out the way it does
a=
s
> > > > > > > together, togther with other pairs that work out together,
as=
one
> > > > > > > thing together. one thing together where any pair that works
=
out with
> > > > > > > other pairs the way it can move is together with other pairs
=
that can
> > > > > > > work out together as together itself, but together with the
o=
ther
> > > > > > > pairs overlapping the same pairs that work out the other
way.
> > > > > > > altogether though.
> > > > > > > now see as a machine. a machine that can work, like any
machi=
ne. a
> > > > > > > machine that starts and begins again where it started. it is
=
a
> > > > > > > machine. it's any machine you want depending on how you
setup=
the
> > > > > > > pairs. find a pair that can move and move it, see how it's a
=
machine
> > > > > > > again another way. it is. see what it is? it's the whole
mach=
ine
> > > > > > > another way. where a part of the machine moved, the whole
mac=
hine
> > > > > > > moved like where that part moved the way it did. it does.
> > > > > > > a machine like this shows connected conditions, conditions
th=
at
> > > > > > > compliment machine position together. not like seeing a loop
=
inside a
> > > > > > > loop be it's own, but together.
> > > > > > > it's a whole machine, any machine. where a machine is said
li=
ke it can
> > > > > > > be any other way it can be. it's a machine that looks like a
=
machine
> > > > > > > when you see how for what matters is for what matters,
becaus=
e it's
> > > > > > > like beginning matters for end as pairs that work out
togethe=
r, not
> > > > > > > like next machine position is with next machine position,
tha=
t's not a
> > > > > > > machine you see that way.
> > > > > > > try making a machine where you see pairs work out together
an=
d others
> > > > > > > that do, the pairs that work out together are there like
loop=
that
> > > > > > > begins is together with where the loop ends because it's a
wh=
ole
> > > > > > > machine. a whole machine that altogether has one position to
=
be in,
> > > > > > > one position altogether. a machine like any. it's true.
> > > > > > > draw pairs as a machine, but see it be a machine. because
it'=
s a
> > > > > > > machine like it is. see it all over again when you move
pairs=
together
> > > > > > > and see it all again, but now see it as whole machine in a
di=
fferent
> > > > > > > position, all of it is, because that's the part of the
machin=
e that
> > > > > > > makes the rest of the machine where it can be for that part
o=
f the
> > > > > > > machine. it's not like moving the machine one step, it's
like=
moving
> > > > > > > it altogether in one place, so try an easy place to move
pair=
s where
> > > > > > > it's at the part of the machine that shows easy how the rest
=
of the
> > > > > > > machine should be. it's the whole machine when you move that
=
part
> > > > > > > where that part is moved that looks different, it's the
whole=
machine
> > > > > > > set position. set position inbetween where it works, for the
=
rest to
> > > > > > > be in position different to how that position is set.
> > > > > > > see so carefully as whole machine again, the same machine,
bu=
t
> > > > > > > different altogether, because it's altogether set in a
differ=
ent
> > > > > > > position. like a machine that's been operated until it gets
t=
here, the
> > > > > > > position it's in now.
> > > > > > > it is, but careful to see as the same machine. because it's
a=
ll
> > > > > > > different. pairs together are connected conditions, togther
a=
s all
> > > > > > > pairs together is all connected conditions together with
conn=
ected
> > > > > > > conditions that are connected. you see beginning and ending
c=
onnected,
> > > > > > > and inbetweens the way they are. pairs say any machine, they
=
do.
> > > > > > > try
> > > > > > > make pairs visible as a machine, you see, any way pairs are
i=
s for the
> > > > > > > way the machine works. a real machine though, a machine that
=
can be
> > > > > > > any machine, so see pairs together as how they work with
pair=
s
> > > > > > > together as how they work together as what looks like what a
=
machine
> > > > > > > can be. a machine can stop in the middle and go back to the
b=
eginning,
> > > > > > > see it like that. but sometimes not with where it gets to.
so=
see
> > > > > > > machine that anywhere can say go backwards, or anywhere
befor=
e can be
> > > > > > > read more =BB- Hide quoted text -
> > > > > > > - Show quoted text -...
>
> > > > > > so say this as a test:
>
> > > > > > setup a board of moving pairs, find for each pair how it works
=
out to
> > > > > > be how it can move. say those togther, and the others together
> > > > > > connected as what would take a 3 dimentional diagram to see.
Fo=
r each
> > > > > > way you can move a pair, hold the idea of the same pairs
togeth=
er and
> > > > > > try every position they can be in. Doesn't this look like a
mac=
hine
> > > > > > not makine one move, but showing how it's in a completely
diffe=
rent
> > > > > > position like after having been operating for a while?
>
> > > > > > it seems to cheat how a machine can work.- Hide quoted text -
>
> > > > > > - Show quoted text -
>
> > > > > Moving pairs of what? =A0For example, pairs of physical objects
w=
hich
> > > > > cannot overlap or, at the other extreme, pairs of mathematical
> > > > > points? =A0Or is the board itself divided into parts which can
be=
called
> > > > > pairs?
>
> > > > > AlexM
>
> > > > pairs where you can say are setup like this (too I guess):
>
> > > > a pair, just said to be, where to move one of them you have to
move
> > > > the other of the pair too.
> > > > so a pair, to move, each of the pair moves to each of another
pair,=
a
> > > > same pair together.
> > > > the pair moves to the other pair, at the same time the pair it
move=
s
> > > > to moves to another pair.
> > > > so the pair moves to another pair, and the first pair is no longer
=
a
> > > > pair together, and the pair moved to is no longer a pair together,
> > > > they became not pairs anymore but two new pairs. with each of the
p=
air
> > > > being a new pair with where it moved to. the other of the pair
with
> > > > where it moved to is having the same happen at the same time, so
it=
's
> > > > with a new pair to.
>
> > > > so to say what it looks like... given lots setup, a group of pairs
> > > > that reorganize how they are paired for each move they can make.
th=
ey
> > > > go around as the pairs many ways but can get back to pairs the
same
> > > > way at first.
>
> > > > so pairs are said to be on a board, but to say pairs and where
they
> > > > move to is like working out already the problem they are with
figur=
ing
> > > > out how they move.
>
> > > so the pairs are like where they can move past each other to where
> > > they're getting to, but just said so as pairs are what has to move
at
> > > the same time where they move to, to another pair together as the
onl=
y
> > > way it works to move back around. so each of the pair goes to each
in
> > > another pair. now each pair is not a pair together anymore but are
tw=
o
> > > new pairs, like if one in the pair went it's pair with what leaves
> > > where it goes, same as the other. to leave is to go where that pair
i=
s
> > > going to another pair. so if you think any time when it's moving
> > > around there can never be where a pair is not moving to become
anothe=
r
> > > pair, or when a pair is staying and nothing is coming. so it's like
a
> > > circuit of pairs that move to reoganize have to all the way for any
> > > one move.
>
> > I will have to study all the above again.
>
> > AlexM
>
> Well, I tried to study your discussion with not very much
> understanding. =A0Perhaps if you would use more diagrams with very much
> less in the way of words your ideas would become clearer. =A0I.e., show
> some simple examples with a few words to explian what is going on with
> the examples. =A0So, for example, start with
> |1|1|2|2|
> |3|4|3|4|
> |5|5|6|6|
> |7|8|8|7|
> where each number the same is called a pair. I guess that numbers are
> "conserved" so that, for example, the total number of 3's (which is
> two) never changes. =A0So one outome can be:
> |1|1|2|2|
> |3|5|3|4|
> |4|5|6|6|
> |7|8|8|7|
> where the pairs 55 and 44 become 45 and 54, although there seems to
> remain a question of ordering. By "machine" do you mean "array" or a
> succession of arrays - like the two arrays above?
>
> AlexM
thanks for answering.
if all the pairs together are considered with the way they move a
machine.. say it's a machine in the way you can assort them the way
that if you move a pair, then the way it moves is for the pairs to
arrange another way. so given how they are arranged to begin with,
they arrange again another way...
so for how pairs are setup, you can say that the way they're setup
makes it so a pair moved is for another pair moved somewher else, so
there's a way to set them up I suppose where you can say for any pairs
moved, is for any other pairs moved.. the way it works out that one
can move.
so works like a machine then I guess? like, they specify an induction
capability.
What do you think of what happens when this is tried... say for a pair
if you draw a line from one piece to another that has to move the
same, then it looks like a machine diagram right? like, a diagram the
way a machine would work.
what do you think of how the diagram would look after a pair is moved?
because all the pairs work differently now to be able to move.
|
