Re: Mathematics and Analogy

[John M <***>]

Judith, something must be wrong: this is another time
within a very short period that I praise your post.
(ha ha). You had the right conclusions to RR's right
quote - well evaluated and commented. 
Now let me add my tuppence and paraphrasing to the
topic and my question whether RR went into such
considerations in his writings?
*
True: math is a complex on its own, using its own
language and mindset. Pure, theoretical math, that is.
I find it a bit simpler than the 'regular'
complexity-talk, as seen in your RR-quote, for numbers
vs burning-floating-etc. aspects of the sticks. One
plane logic, as I like to say. Mathematicians get
along with that OK. Alas, many other can learn it who
work in reductionist topical sciences and APPLY their
math knowledge to their model-views. This constitutes
"Applied Mathematics" in physix, biol, econ, gen, geo,
etc. etc. models. Limited, cut values within the
topical boundaries are included in equational math,
applying all the complexity-deducted 'rules' math
could come up with. The equations between the cut
model-values do not fit in a simple way which requires
constants, modifiers, a convoluted treatment to make
it stick. Inadvertently also paradoxes occur. -"High
sci".-
Mathematicians who prostitute themselves into the
model-based math application, make good money in
successful technology development. (Analogy: a gifted
musician who 'rockify' a Bach or Beethoven tune to
make a good buck from the teen-crowd). 
Make no mistake: applied math is successful and
contributes very much to humanity's advancement. I am
talking theoretical aspects. 
One cannot draw a trajectory of a million-body system,
or build a machine or software on unlimited
(~infinite?) variable functions.

I would paraphrase your sentence: 
">...Robert Rosen argued that the system had been 
> changed from one that was complex to one that is
simple....< 
into: 
> Application of the 'natural' math system to the
reductionist model-sciences made it into a 'mental
machine'. <

This is my prejudice and I do not expect a general
approval. Tim?

John M
--- Judith Rosen <***> wrote:

> The recent discussion comparing
> quantitation/digitization/mathematics 
> with qualitation/analogy/modeling got me to thinking
> about what exactly 
> mathematics is used to accomplish, in science, and
> WHY... Which leads 
> me into wondering if it would be possible to come up
> with a set of 
> rules about when it is productive and when it can be
> counterproductive 
> to the point of being dangerous-- particularly where
> biological systems 
> are concerned. This includes the fields of medicine
> and 
> ecology/ecosystems science plus all of the
> human-created, interactive 
> social systems (political, recreational, or
> otherwise). Mathematics is 
> a complex system in its own right, a language
> created to communicate 
> certain truths about human perception of aspects of
> the universe. It 
> has its own set of entailment rules, which can often
> be used to model 
> or illustrate entailment patterns of natural
> phenomena (because 
> entailment patterns are exportable, a fact which RR
> said he regarded as 
> one of the Laws of Nature.) Mathematics is often
> considered to be 
> incapable of lying, beyond politics, and utterly
> rock solid in its 
> capacity for representing truth. I think it might be
> useful to analyze 
> why mathematics has that reputation and what,
> exactly, mathematics IS.
> 
> On page 4 of "Life, Itself," Robert Rosen wrote:
> 
> Let me begin with a few words about the relations
> existing  between the 
> mathematical universe and the perceptual one. It is
> a fact of 
> experience, for instance, that 2 sticks + 3 sticks =
> 5 sticks. On its 
> face, this is a proposition about sticks. But it is
> not the same kind 
> of proposition as, say "sticks burn" or "sticks
> float". It differs from 
> them in that it is also about something else besides
> sticks, and that 
> "something else" takes us into the world of
> mathematics.
> 
> The mathematical world is embodied in percepts but
> exists independent 
> of them. "Truth" in the mathematical world is
> likewise manifested in, 
> but independent of, any material embodiment and is
> thus outside of 
> conventional perceptual categories like space and
> time. These facts  
> have, indeed, from the time of Pythagorus on,
> spawned another profound 
> dualism, a dualism between idealism (which at root
> is an attempt to 
> extend the reality of number to the rest of the
> perceptual universe) 
> and materialism (which is an attempt to include
> "mathematical reality" 
> inside conventional perceptual realms).
> 
> But of this I need not speak. To motivate our
> discussion, it is enough 
> to observe that both science, the study of
> phenomena, and mathematics 
> are in their different ways concerned with systems
> of entailment, 
> causal entailment in the phenomenal world,
> inferential entailment in 
> the mathematical. Where [qualitative and
> quantitative advocates] differ 
> is precisely in their views about entailment, about
> what is entailed 
> from a datum and about how that datum is itself
> entailed. Hence, at a 
> sufficiently deep level, the controversy between
> them, and the dualism 
> they represent, pertains to entailment itself,
> entailment in the 
> abstract, free of any qualifying adjectives like
> "causal" or 
> "inferential".
> 
> It is in this sense that I turn to the mathematical
> world in order to 
> illuminate what it tells us about entailment. That
> is, I will be 
> talking about entailment, rather than about
> mathematics, just as, in 
> the example above, I could talk about number while
> apparently talking 
> about sticks."
> 
> There is a lot to talk about, just in this section
> of the book. It 
> seems to me that mathematics, as a system, is just
> as relational and 
> interactive as the natural world is. If numbers
> represent the 
> equivalent of material particles, or "things", then
> it's just as true 
> that nothing happens until those numbers interact
> with one another via 
> various entailment relations and according to
> specific organizational 
> matters. In other words, there are semantic aspects
> which cannot be 
> dispensed with, in the system called Mathematics. My
> father argued that 
> all attempts to try divorcing mathematics from all
> semantic aspects 
> (reducing mathematics to syntax, alone) have failed
> rather miserably 
> and he even explains why this is so: Mathematics is
> a complex system. 
> To reduce it to syntax is to oversimplify to the
> point that the system 
> has been irrevocably changed. He uses the example of
> David Hilbert and 
> his attempts to formalize Number Theory (to reduce
> the system to a 
> representation in syntax, alone), which created all
> sorts of terrible 
> paradoxes-- the entailments had, of course, been
> altered by the 
> simplification process. That's inevitable; the
> organization of the 
> system had been changed. Robert Rosen argued that
> the system had been 
> changed from one that was complex to one that is
> simple.  (It was his 
> view that all formalizations are simple systems and,
> therefore, any 
> system which can be reduced to formalisms without
> loss of information 
> is likewise simple.)
> 
> There is a further relational issue here, that of
> the human mind-- 
> where the complex system of mathematics actually
> exists and which 
> generated the system/language in the first place.
> So, not only is 
> mathematics based on the entailments inherent in
> relational 
> interactivity, within itself as a system, it exists
> in an "environment" 
> on which it depends for everything including its
> very existence, just 
> like any other complex system. The interaction of
> mathematics (the 
> system) with the human mind (the "natural" or
> evolutionary environment 
> of the system) is essential for the existence of
> mathematics as a 
> system.
> 
> The fact that these "truths" can be equally
> illustrative of any complex 
> system is a proof of the exportability of entailment
> patterns, in 
> general: That identical entailment patterns can
> exist in two or more 
> completely different systems made up of entirely
> different "stuff".
> 
> Comments from the group?
> 
> Judith
> 
> Web address: http://www.rosen-enterprises.com
> BioTheory: An electronic journal of general science
> based on the 
> Relational (Rosennean) Complexity Paradigm