Dear colleagues,
the term string as mentioned by Joseph triggers a comment.
We can use the term string like any of the terms sqrt(), sin(),route
between(), etc. The term string does have a solid concept behind it, but,
alas, it needs more arguments. A string is to be observed to connect
fragmentational states and spatial coordinates. HOW MANY spatial coordinates
(and fragmentational states) a string connects is one of the properties of
the string, as are properties of a string WHICH fragmentational states cum
spatial coordinates the string connects.
The idea of a string comes from observing elements of a set being
resequenced. If one reorders a set, the elements move in a way that is very
precisely given. Those elements that move together during a rearrangements
constitute a sequenced group. The movements of members of this sequenced
group are called a string.
To visualise the concept, it helps to write up the first 136 additions and
then rearrange this collection. Let me quote from one of my papers: (here we
discuss the sequential place of an addition a+b=c among other additions.
Writing up 1+1, 1+2, 1+3, 1+4,..., 16+16 gives us the 136 cases we sort -
order, sequence - around. We then resort from sorting order ab - what we see
now in 1+1,1+2,1+3,...- into order ba, which runs like
1+1,1+2,2+2,1+3,2+4,3+3,1+4,...)
quote
Place As Such, Place of Each Case
The order implicates a place for each case. If the order changes, the place
of the case may or will change. E.g. in order AB the sequence of the cases
is (1,1),(1,2),(1,3),... In order BA this modifies into
(1,1),(1,2),(2,2),(1,3) Place 3 in an ordered sequence is (1,3) if the
order is AB and (2,2) if the order is BA. The place* of* (1,3) – the place
now as an attribute of the specific pair of *(a,b)* – is 3 if the order is
AB and 4 if the order is BA.
Threads
The term *thread* can be demonstrated on the place changes that follow from
the change in order from AB to BA. The thread that involves (1,3) moving
from place 3 to place 4 concurrently causes successive place changes of
elements {3, 4, 7, 22, 23, 30, 107, 114, 115, 130, 133, 134, 120, 116, 66,
71, 21, 17}.
endquote
So, if one talks of strings, one has a clear definition of the term, but the
sentence gains on precision if one adds, which reorder one means. Like
pointing out the meaning of the min() function is one thing, and pointing
out which element we mean, it is helpful to provide the arguments, too.
The case is similar with the term structure for which there exists also a
clean definition. The idea behind the term vacuum can be demonstrated and
receive a definition by observing the spatial points to which no strings are
attached.
The idea of Strings is an implication of the idea of Order which is an
implication of the term Number of Summands.
Karl
2010/11/14 Srinandan Dasmahapatra s...@ecs.soton.ac.uk
Hi,
I've been meaning to send a note on Kevin Kirby's brief outline of
Conrad's fluction framework, but haven't had the time to compose my
thoughts coherently. I realised that I wouldn't really have the time
to do so, so I had better send something half-baked along anyway to
contribute to the discussion. Kevin concludes his piece with the
following remark: quoteOverall, within fluctuon theory the
interaction between the manifest organism and its unmanifest vacuum
sea image abets the evolution, persistence, and maintenance of this
unique complexity [of life]. This is a fascinating and rich notion.
What can we unfold from this notion now in 2010?/quote
The way I see it, organisms are organisational units, and we tend to
view genomic content as informational units. However, genomic
identifiers are merely one way of providing information tags. Apart
from the presence/absence of sequence, there is also the notion of the
multiple/collective (to borrow Alain Badiou's language) -- collections
of molecules that bear that signature. It is these collectives that
comprise the dynamical state of cells and organisms, and the
cardinalities of these sets may often be used as a proxy for snapshots
of organismal state. This tells us that organisational units such as
tissues may be characterised via such cardinalities -- liver cells and
heart cells have different protein number distributions within the
same organism yet protein distributions in liver cells are more
similar across taxa. Hence the fluctuon concept may be viewed in this
concept as the creation and annihilation of molecules following gene
expression, or the transition into and out of active or inert
molecular state, around the vacuum -- the steady state of an open
dynamical network. The response characteristics of this proteomic or
messenger RNA cloud and the entropy production (as measured in terms
of fluctuating numbers around the steady state) offer dynamical
proxies of the organism, extending the static snapshot. This becomes
conceptually and mathematically accessible to perturbative ideas
