Wednesday, September 2, 2009
(And since I was in any case mooching about a way to interpret some meaning into all the slog of miscellaneous microscopic myopic thinking and doing as being maybe somewhat like that great complex of miscellaneous microscopic myopic biochemical metabolism - a rather disturbing mess up close but actually supporting a worthwhile homeostatic constancy if you stand back a bit. An intricate machine to provide constancy in the face of friction and adversity...so don't forget to dot the i's and cross the t's and put out the rubbish and file the weekly pointless management report because it all does have a point after all, its all part of the intricate metabolism of life - the worthwhile achievement of (more or less) homeostasis in the face of environmental, social, professional, psychological, familial and financial friction and adversity !)
Anyway - it turned out interesting to contrast that 1976 definition of "metabolism" - "the sum total of chemical changes in living matter" , with the slightly less poetic sounding online definition given by Chambers 33 years later in 2009 :
"sum of all the chemical reactions that occur within the cells of a living organism..."
So what has changed ? :
* "changes" has become the more technical and less agnostic "reactions"
* "sum total" , suggesting a complete enumeration of a collection, has become the more quantitative sounding "sum" - which vaguely suggests some sort of chemometric summation of reactions.
* ...and the lovely antique phrase "living matter" redolent of natural philosophy and the Victorians has become the more microscopically correct "cells of a living organism". (I wonder if the newer microscopically correct version is actually correct though...I would have thought a fair bit of metabolism occurs outside cells - e.g. in the action of salivary enzymes and gut acids on food....or maybe that is not counted as part of metabolism proper ?)
The other change in the online definition is that it goes on to add "...including both anabolism and catabolism of complex organic compounds", with these terms (anabolism and catabolism) hyperlinked as I have them. The offline version has both of these as separate dictionary entries but not of course inter-linked (and the entry for catabolism delegates to katabolism)
(I hadn't met these before but have met katabatic and anabatic winds, which are winds that blow down/up the slopes of mountains, as these cool or heat the air immediately above. Hence analogously katabolism breaks down compounds while anabolism builds them up. Nice words, I'm glad I met them).
Anyway getting back to "actabolism" - although Google finds it, its
clear it only makes it into their keyword index by virtue of being
an anagramatical typo' of "catabolism" - see for example
http://www.jipb.net/earticle_read.asp?id=4557 where both versions occur.
So I do actually have freedom to operate here - there is no such word as actabolism -but my derivation is not pretty and also wrong. I really (?) need to replace the "bolism" with something denoting a thought or action, not the "meta", as this prefix supplies (?) the "sum total" part of the concept. Or so I thought with my meagre etymological knowledge
This brings out another interesting contrast between the offline and online definitions of "metabolism". The offline version occurs within the context of an ordered list of terms appearing on the page, whereas the online definition occurs on its own without any context - true there are links to the related terms anabolism and catabolism, but links are completely different if not diametrically opposed, to context. The online definition occupies a whole web page - in fact it is really more fragmentary than that, just a web sentence.
In this case the ordering of the terms in the offline dictionary is quite interesting and informative - it is not strictly alphabetical, in fact when I first looked in the big red book for the word "metabolism" I couldn't find it because this word comes after "metacarpal" and "metacentre" which confused my tiny mind ! Well - thats because "metabolism" does not (apparently), despite appearances, derive from the "meta" root after all - and the offline Chambers collects all of the words derived from the "meta" root together, even if this upsets strict alphabetical ordering.
(This is explained in a note in the dictionary's preface section - "The Arrangement of Entries" :
"...Derivatives are not listed in crude alphabetical order but in a more logical form....etc etc")
How much of that sort of informative and rich non-semantic context that you get from "Arranging the Entries", are we going to lose in the new strictly semantic electronic information infrastructure ?
Are hyperlinks always all they are cracked up to be ? Is the current web too hyper' ? Can / will the web stay the way it is now or do we need / will there evolve some "Arrangement of Entries" ? Maybe it needs to become more of a "semantic manifold", with local contextual structure, density and continuity, and less of a porous semantic web, of tangled links between tiny fragments.
True , I was only looking at one of the "freebie" definitions - but even in a
full online entry - e.g. http://www.chambersreference.com/dict/external/site/main/quantity.htm (one of their marketing examples) - you still only get a single definition on a page - there is not the context of similar words to excite the pattern-finding and insight-forming parts of ones attention as you got in 1976. (Interestingly, the structure of that 2009 online page corresponds almost exactly to the design set out in "The Arrangement of Entries" note at the beginning of my big red dictionary of 33 years ago - even though there is no longer really any "arrangement of entries" needed, as there is just one per "page" !)
Well, after all that I still haven't settled on a word to denote , analogously with metabolism, the "sum total of the thoughts and actions of a person - over an hour or day, possibly week (but not a life or even a year)"
Saturday, August 15, 2009
O = N x I
I = the relatively disordered input space of things, from which the emergence. A high dimensional space. Examples : 8 people around a table, a potential 8 way babel; 56 independent nucleons in a plasma ; several billion meaningles stimuli per second presenting themselves to our eyes, ears, taste, skin as we experience (say) a shower of rain.
O = the relatively ordered output space of emergent phenomena. A low dimensional space, viz : 1 polite conversation at the table rather than babel ; one iron atom condensing from 56 nucleons in the plasma ; one conscious subjective experience of a shower of rain.
N = that which transforms the input space into the output space. I suggested this be thought of as a space itself, with a negative dimension, and that some rough dimensional book-keeping can be done :
dim(O) ~ dim(N) + dim(I)
<=> dim(N) ~ dim(O) - dim(I)
So for example the book-keeping predicts that the thing that transforms the huge number of raw sense-stimuli elicited by a shower of rain into a simple subjective conscious experience of a shower of rain, will itself be a very complex space of high dimension. As indeed it is, being a brain with a dimensionality of perhaps 100 billion - the number of interconnected neurons it contains.
OK - so, the existence of an "output" space of low dimension is plausible. In each of the examples we can see the emergence of a coherent new level of reality, with fewer "things" (= lower dimension) than in the lower level, and exhibiting its own novel higher level laws of behaviour. For example iron atoms (once they have caught a few electrons from the plasma) have emergent behaviour such as chemical valence that is nowhere hinted at in the pedestrian lives of solitary protons and neutrons and the nuclear forces that govern their interactions.
And, OK - the existence of a distinct "lower level" "input" space of high dimension also seems plausible - for the iron atom example this is just the 56 independent nucleons in the plasma, a space with dimension at least 56. For the shower of rain it is all the billions of nerve signals elicited on our skin , eyes, ears, smell, taste by the physical effects on our bodies of the shower of rain.
But where does the space "N" come from ? Specifically - why call it a space and why assign it a negative dimension ? Perhaps there are other types of thing that N could be, that also transform a given space of high dimension into a resulting space of low dimension ?
Well it comes about mainly because I like the idea, and thinking about the idea, and seeing where it might go (which might be nowhere). Just maybe there is indeed some abstraction that can be done to find high level structure, in the daily scientific grind of explaining this and reducing that....explanation and scientific reduction as factorisation ? The formula implies an "ontologically opaque" view of things like iron atoms and consciousness - which is to say that, these things are to be regarded as new levels of coherent reality in their own right and they are not ontologically transparent - you can't just look in reductionist fashion through an irrelevant layer of iron atom behaviour and see nucleons, or an irrelevant layer of subjective experience of a rain shower and see neurons firing.
So far though that is at most merely proof-by-narcissism - "its so because I like it and it likes me". I suspect that's as far as I'll ever get - but maybe I can incrementally build a case and then one day do a summing up. Lets start with precedents - that's a good way to build a case in law.
My first precedent is the example of functional notation and spaces-of-functions in mathematics. Don't let that put you off - its very unlikely I know anything more about this than you do and in fact writing this little bit puts me in mind of finding out where this functional notation we all take for granted really came from. Since it is no less metaphysical and wacky in its own way than my "negative dimensional reducing spaces"
Take a few maths equations :
y = x + 2
y = x^2
y = x^2 + 4x + 4
y = sin(x) + cos(x) + 4x + 4
- these represent the daily calculational grind of multiplying this by that and adding it to the other to get some answer for some reason - and I would wildly guess that up until the beginning of the 19th century there was no higher level of abstraction than this. Though there was certainly an enormous level of skill in manipulating these equations.
But then somebody said "lets think of x^2 +4x +4 as consisting, actually , in a thing called a "function" operating on another thing called "x" - we will now represent the calculational rule x^2 + 4x +4 as being the formal product of a function, with x :
f(x) = x^2 + 4x + 4
and these "functions" will live in their own function space and we can take formal products of functions with other functions - in the above example , if
g(x) = x + 2
h(x) = x^2
f(x) = x^2 + 4x + 4
then f(x) = h(g(x)) so that f = hg
....standing back a bit - where on earth did that functional abstraction come from !? - its a huge innovation. You take an equation like
x^2 + 4x + 4
- which we can all understand as instructions to do some stuff on our calculators - and do an abstract factorisation of this into a thing called a function, "f", existing in some weird function space, acting on a thing called "x" , existing in a (less weird) space of numbers !? Its bizarre, only we are used to it so it seems bland.
The encouraging thing is that this apparently willful not to say whimsical piece of abstraction turned out to be very fruitful in mathematics in the long run.
(Which is not to say that my own wilful abstraction and factorisation of emergence and (soon) reductionism and scientific explanation and (after that ) certain physical processes, into formal products of spaces, and associated dimensional book-keeping, will be so productive).
Friday, April 24, 2009
- The emergence of life from an ambient "soup" of inanimate molecules.
- The emergence of consciousness from a cranial soup of neural networks and other brain parts that are not conscious
- Computational emergences - Cellular Automata :
Examples : Life by John Horton Conway ; many examples in Stephen Wolfram's A new kind of science. The general idea is a simple algorithm, repeated application of which leads to totally unexpected "emergent" behaviours and patterns. There are well known examples from (computational) biology - along the lines of, simple postulated individual interactions from which emerge coherent behaviours of schools of fish, flocks of birds etc ; simple rules of growth and development which lead to emergent morphologies of coat patterns etc on animals.
- The emergence of a coherent regulated society from the (more or less) free participation of millions of individuals.
Both the big and computational emergences have a kind of implicit payload of rabbit-out-of-the-hat magic and rare privilege - events that you are unlikely to see very often and only in special staged situations, such as at the primordial birth of life, or of consciousness, or on running a computer program like Conway's Life or on occasional witness to the impressive synchrony of a flock of birds or school of fish. But they are (in my view) no different to everyday emergences...
Little Emergences :
- 8 people sitting at a table at morning tea discussing a single topic, one speaker is speaking. One topic and thread emerging from a complex of 8 different people.
- an iron atom : 56 protons and neutrons sitting at a table at morning tea discussing a single topic - how to be an iron atom. One coherent and very useful metal atom emerging from 56 unruly nuclear personalities.
- a well designed computer program interface, marshaling millions of pixels and bits of information into a simple coherent metaphorical world with which the user interacts.
Unifying Small, Large (and Computational) Emergences : Dimensional Reduction
My idea for a metaphysics of emergence, is a factorisation into
(1) an input factor space (I) of relatively high dimension
(2) an output product space (O) of relatively low dimension
(3) mediation of the transform from input space to output space by a complex (i.e. complicated) intermediate factor space (N) of negative dimension.
So that we may write formally as :
I x N = O
dim(I) + dim(N) = dim(O)
In words - an input space of very high dimension is formally composed with a negative dimensional space to yield an output space of low dimension - the dimension of the product space is the sum of the dimensions of the two factor spaces.
For a visual metaphor - we might think of the intermediate space as being like a lens, which transmits and transforms a coherent input scene into a transformed coherent output image. All three of the elements of this metaphor have themselves internally a coherent space-like structure, and with a formal composition of the lens space with the input-scene-space generating a coherent but transformed output product space.
Taking as an example a small emergence - conversation at morning tea - the input space has dimension 8, which is the dimension of the conversation space if all 8 individuals talked independently and simultaneously ; the output space has dimension 1 - the single coherent conversation that occurs. The dimensional reduction is mediated by a relatively intricate set of social mores, hierarchies, and behaviours - but which in this metaphysics we will notate and size as a negative dimensional space of a certain dimension - in this case -7.
A living creature enjoys a coherent high-level existence within a space that is quite distinct from the melee of chemical reactions that it is supported by. Furthermore by comparison with the lower substrate - it is a much simpler, lower dimensional space. High level laws of behaviour, nutrition, reproduction operate at this level. Just as in conscious life, our brains build for us an experience of a seamless space of streets, trees, flowers, colours, selfhood....that is both quite distinct from the substrate of our brain and the actual physical activity of the external world, and also vastly simpler.
But what is the point of introducing the mathematical fictions - the negative dimensional space , and the abstract composition of spaces ?
The main idea is that this analysis is philosophically useful - but also with a hope for empirical potential in that it suggests a way to predict or measure the dimensional size of these internal engines of emergence. As a philosophical guide, the analysis recommends that, where we see simple ("low dimensional") behaviour or structures emerging from a complex ("high dimensional") input substrate, then we should expect that this emergence will always be mediated by a complex intermediate structure,with a (negative) dimensional "size" almost as high as that of the input substrate.
And as an engineering guide, the analysis recommends that (for example), where we wish to engineer software interfaces or societies that are simple and coherent, we should in general expect that the internal engines of organisation that generate these interfaces and societies will be complex and messy. And vice versa we should perhaps be wary of simple and elegant internal engineering data and object models and political ideologies - according to the metaphysics-of-emergence formula, this internal elegance will be achieved at the cost of emergent societies and software interfaces that are less coherent and more complex.
So what does the complicated intermediate negative dimensional space N look like ? It is no more possible to visualise a negative dimensional space than it is to visualise other mathematical inventions such as negative numbers and potential energies : but we can say that it encapsulates a forest of dimension-reduction-engine-room internals that actually get the job of dimensional reduction done...constraints, relationships, surfaces, volumes, intersections, knottings and braiding of dimensions, dynamic censoring and suppression of dimensions...that our new metaphysics parlays into a space-like structure.
Philosophically this analysis is in contradiction to the cellular automata view - it encourages us to look for complex machinery underlying simple emergent phenomena, rather than simple machinery. (Obviously this particular antagonism will require some explication in view of the long history and many examples and proponents of cellular automata explanations of emergent phenomena).
Freeman Dyson wrote an essay entitled "Why is Life So Complicated". He meant, why is the machinery of life so complicated. He writes "It seems to be true, both in the world of cellular chemistry and in the world of ecology, that homeostatic mechanisms have a tendency to become complicated rather than simple"
My answer would be - the machinery of life is complicated because
(1) the non-living world (I) with which it interacts is complicated : dim(I) is large
(2) life itself (O) is - almost tautologically - simple : dim(O) is low
(3) the machinery of life (N) is therefore mathematically required by the metaphysical emergence formula to be complex since
dim(N) = dim(O) - dim (I)
Life is complicated because there is a higher level metaphysics governing emergence, and for the same reasons that societies are complicated, the laws of nuclear physics that make iron atoms possible are complicated etc.
The simplicity of life itself - as opposed to the machinery that supports life - is perhaps the key part of this equation. One of the striking things about a living creature is its coherence and unity of purpose - how so many intricate parts mesh into a coherent whole that....swims, runs, searches for food, mates....has a being. But this is another way of saying that life itself - the end product of all of the machinery - exists in a rather low dimensional space. Indeed one way of explicating "being" is that it is a space of dimension 1 - this is the dimension of the thread of existence that we envisage for ourselves, stretching linearly back into the past and into the future.