Growth (was Re: so what would be wrong with sayingwhatyou think?)

[Phil Henshaw-2]

Robert,

Just curious, I was very delighted to get your question, and thought I
gave a meaty answer, but it apparently didn't connect.   Rereading your
question, though, maybe it seemed I was off on a tangent, since I didn't
directly answer what you actually asked.   Let me try again, and let me
know if I'm still off the mark.

You asked about the term 'scale violations' and 'attributes whose
derivatives are all positive' when things are born.  

By 'scale violations' I mean places in tracing the origins of things
where you have to change your model of description because it's changes
in kind violate your model.  That happens at least four times for an
individual: 1)starting from tracing your growth back from a youth to a
fetus it's mostly the maturation of an established system, 2)before that
the model has to change to describe the differentiation of the cells,
and 3)before that has to change to describe the undifferentiated
doubling of the single cell and 4)before that to describe fertilization,
which also has precedents, but 5)they get lost in the complexity of the
egg's inner world it seems to me.   In the birth of a corporation it's
similar, as the seed you can trace it all back to evolves through a
succession of growth stages in which it becomes a whole different kind
of organization and you need different models to describe it.

I don't think 'attributes' actually ever change so that all derivatives
are positive.  I have a careful way of using that idea.   In this case I
had qualified it by saying 'have periods of' and 'implied derivatives'.
Things that begin and end only have any property for finite periods, and
strings of dots, as you know, don't have any level of derivatives unless
you imagine some connection between them.  

Where the implication that things beginning from scratch have to display
implied derivatives of the same sign comes from is a corollary of the
conservation laws.  Combining energy and momentum conservation and the
limiting speed of light implies that infinite accelerations can't occur,
consequently any beginning must develop.   That is indeed what you
observe in nature.   What we can observe beginning does almost always do
so with clear exponential-like growth curves, and things you can observe
ending do so with clear exponential-like decays.  That includes
organisms and organizations.  

A smooth curve following those shapes will have all derivatives of the
same sign.   The actual rule I use is a topological interpretation of
the corollary, that attributes of things that begin or end will have
periods that trace a path between upper and lower bound exponentials.
It seems like a loose requirement, but it works very well as a default
assumption for identifying emerging systems with time series data.

That's kind of technical, but I'm trying to give it a real bottom.   You
see any gaps?


Phil Henshaw                       ????.?? ? `?.????
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
680 Ft. Washington Ave
NY NY 10040                      
tel: [phone]                
e-mail: pfh at synapse9.com          
explorations: www.synapse9.com    

 

> Robert,
> > On 10/15/06, Phil Henshaw <sy at synapse9.com> wrote:
> > <snip>
> >
> >> It's very hard to tell when or if anything begins or ends,
> >> because if so
> >> it's at times and in ways that are too small to observe.  
> >> Another way
> >> to say that is that beginning and ending always seem to
> >> violate their
> >> scales.   That theorem I mentioned says that energy conservation
> >> requires that if things are to begin or end they must do so
> >> at invisible scales and have periods of development during
> >> which all implied derivatives are of the same sign.  The
> >> testable part of that seems to
> >> match observation.
> >
> > I need a couple of concrete example to understand this. Could
> > you please tell me (i) the scale violations that occur and
> > (ii)  the attributes whose derivatives are all positive when:
> >
> > a human (me, for example) is born; and
> > a company (Coca-Cola, for example) is born
> > Robert
>
> Let me try,
>
> Not having any data for either event makes it harder to make
> statements about how to interpret the data.  Without data
> everything is quite invisible, so let's talk about
> hypothetical data.  What might you choose?, the curvature of
> your mom's belly, perhaps, and for Coke the documented assets
> of the legal entity?   You can quickly see that both might
> make reasonably interesting measures of the early phases of
> the development of either new entity, but are going to be
> useless in locating "the beginning".  
>
> Pregnancy develops a very noticeable curvature in a belly,
> but tiny changes might be quite hard to measure accurately,
> and a single cell, or probably even a million, won't produce
> a noticeable change.  The assets of a corporation are
> problematic since it's beginning certainly comes before it's
> a legally recognized entity.  The formal signing of the
> incorporation documents comes after lots of other organizing steps.  
>
> One can work backward from the evidence you have, of course,
> but it's all guess work and peters out.   We can hypothesize
> that fertilization is the beginning of a human, though it's
> generally not observable, and then you can quibble about
> whether it's the penetration of the cell wall or the
> molecular joining that hypothetically divides before and
> after, or another point.  For Coke there might be a
> particular handshake between two people to signify their
> common commitment to form a corporation.  It might even be
> recorded at a particular time and place, but invariably it
> will be the culmination of a process of idea sharing and
> planning which is complex and perfectly untraceable as to its
> beginning.
>
> You might try another tack.  For each one try to find a time
> prior to any evidence of their beginnings and work forward.  
> What you get is another fuzzy horizon, an greatest lower
> bound to pair with your leas upper bound.   If you liked you
> could call the space between the forward and backward
> approaches the definite period of beginning, but that's just
> a window of probability, not the beginning.  If it were just
> a matter of always dividing time up finer and finer to make
> it unclear when events that require a duration occur you
> could agree to use some inflection point of a definitive
> beginning moment or triggering event.   That might be the
> moment of the firmest pressure in the handshake or the signal
> which the unfertilized egg sends to select which of the
> pressing sperms is to be invited in.  Events that fit that
> convention might be found meaningful and useful in some
> circumstances, but it's a convention to stop a search at a
> satisfying point, not the result of finding their own
> beginnings and ends.
>
> If you consider a single time-series data set, rather than a
> ranging 'forensic' type investigation as implied above,
> finding where the beginning of growth occurs is where the
> horizontal line turns into a lasting upward curve.  That's
> inherently imprecise because the change one wishes to
> identify is always smaller than the irregularity of the data.
>
> There's also the important question of whether anything
> begins at all, or whether all things are unchanging and
> ever-present in a universal continuum, and just emerging and
> vanishing like the composite shapes produced by a Fourier
> series.  That seems plausible perhaps from a view that all
> form follows mathematical functions.  That's not anyone's
> current view, I don't think, and becomes untenable when
> watching how natural systems operate through resource pools.  
> Cells would need extra sensory perception to coordinate what
> they deposit in the blood stream with what other cells
> independently sweep up from the blood stream and make use of.
>  The weaker of two hypotheses is not a good candidate for
> being one's automatic assumption and requires some
> demonstration of feasibility to entertain.  For things
> existing in perpetuity there does not seem to be any.  
> Still, some things do definitely seem to happen, so they must
> begin and end.
>
> I use the term "scale violation" to make it seem like there's
> something remarkable about a trail of evidence vanishing into
> the confusion of other contexts.   Science has mainly focused
> on questions where causation seems to be more definite.  The
> 'violation' is really of the common expectation that
> definitive causes and evidence exist for everything and we
> can potentially find them.  I think when you carefully  look
> at beginnings and endings it looks like the opposite is the
> case, at least for the point to point model of causation.  
>
> As to finding periods of change having all higher derivative
> rates of the same sign, that's the common feature of growth.  
>  To treat data curves as having derivatives at all you need
> the same thing you have for functions, a rule for finding
> points along the curve that does not conflict with the
> continuity of the underlying structure (physical or
> mathematical).  One slippery point is that you sometimes
> can't demonstrate that the data at hand may be treated that
> way (as having continuity).   You might choose to first
> assume it to be true, and then need to confirm that
> assumption by being led to more substantial evidence from the
> shapes you find.  - This is basically about an investigative
> tool, that leads to better descriptions, not a descriptive
> tool itself. -   Most times, though, any evidence of change
> that begins and ends is enough to trigger the presumption
> that there had to be a growth process of some kind to then go
> look for, and treat the data accordingly...  
>
> Of course, sometimes you just don't have the data.  You could
> say that not having evidence of a progression of change is
> evidence of change without a progression, but you can usually
> find more evidence of connecting progressions in proportion
> to the effort you put in.   Concluding that such evidence
> does not exist would violate the conservation laws anyway and
> call for confirming evidence of an absence.  That amounts to
> a proof by speculation based on a lack of evidence, and
> that's usually unreliable.
>
> I would agree it may all seem a little sneaky, but it also
> seems to work, so I don't mind.
>
> Phil
>
>
>

[Robert Holmes]

On 10/29/06, Phil Henshaw <sy at synapse9.com> wrote:
>
> Robert,
> <snip>
>
Where the implication that things beginning from scratch have to display
> implied derivatives of the same sign comes from is a corollary of the
> conservation laws.

  <snip>

Consider these 3 attributes of a company: revenue R, cost C, profit P. My
simple model of a company's finances say that P = R - C. Differentiate with
respect to time and get dP/dt = dR/dt - dC/dt. Assume that dR/dt at t=0 and
dC/dt at t=0 are both positive. Does this imply that dP/dt >0? No; not if
dR/dt < dC/dt at t=0.

So the first derivatives of the attributes of a system do not necessarily
have the same sign.

Robert
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[Phil Henshaw-2]

Yes of course.   You're comparing different attributes of something, not
different time periods of the same attribute.   It's also important that
you're substituting a model for a physical system, but the main reason
your comparison of doesn't follow my principle is that you're comparing
they're different things, not different times.   Think about it this
way.   For a continuous process to have an increase it needs time and a
rate of change.   To achieve that rate of change it first needs a finite
period of acceleration.   To achieve that acceleration it first needs a
finite period of jerk (3rd deriv), and so on, etc, etc.,  with all
higher derivatives of the same sign for some finite period.
 
It may be the general case that during the growth of a physical system
you can find many measures that change in similar ways, but you will
also also find many measures that don't.    Of course any physical thing
has many kinds of measures and frequently science can only make sense of
a few, or sometimes none at all.   Without searching the range of
measures available It's more or less a matter of luck whether you pick
one that reflects what's happening broadly.  Energy flow is a good bet
in almost circumstances, for example, and temperature may not show any
evidence of change at all in a dramatically reorganizing complex system.
 
The theorem is about the beginning and ending of energy flows, and my
observation that the same principle also broadly applies to any kind of
measure that reflects change that begins or ends.    The statement is
that you can reliably expect to find periods of time during which that
measure will imply change that is exponential-like.   Models as far as I
can tell (like P = R - C) don't ever describe their own emergence and
project only virtual worlds consuming no energy,... so my machinations
about the physical world don't seem to apply to them or any of the
abstract measures they contain.    I'm only talking about real stuff.
 
 

Phil Henshaw                       ????.?? ? `?.????
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
680 Ft. Washington Ave
NY NY 10040                      
tel: [phone]                
e-mail: pfh at synapse9.com          
explorations: www.synapse9.com <http://www.synapse9.com/>    

-----Original Message-----
From: [hidden email] [mailto:[hidden email]] On
Behalf Of Robert Holmes
Sent: Monday, October 30, 2006 5:02 PM
To: FRIAM
Subject: Re: [FRIAM] Growth (was Re: so what would be wrong
withsayingwhatyou think?)




On 10/29/06, Phil Henshaw <sy at synapse9.com> wrote:

Robert,
<snip>


Where the implication that things beginning from scratch have to display

implied derivatives of the same sign comes from is a corollary of the
conservation laws.

  <snip>


Consider these 3 attributes of a company: revenue R, cost C, profit P.
My simple model of a company's finances say that P = R - C.
Differentiate with respect to time and get dP/dt = dR/dt - dC/dt. Assume
that dR/dt at t=0 and dC/dt at t=0 are both positive. Does this imply
that dP/dt >0? No; not if dR/dt < dC/dt at t=0.

So the first derivatives of the attributes of a system do not
necessarily have the same sign.

Robert




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