Mass extinctions linked to climate change

http://www.timesonline.co.uk/tol/news/uk/science/article2726751.ece

The +1 conjecture = ambiguity problem

Firstly there is the issue of a system "actually" containing itself ... a box containing itself.

A box is a simple system with a single relevant function namely to contain things (like a set). Suppose a box could contain its real self. When would it perform this function?

Usually we put something in a box and it there by performs the containing function on that object. But if it can contain itself it forms a closed system, with self-containing an intrinsic feature. Suppose there is a condition which determines whether it performs the containing function on itself or not.

This is very abstract (since boxes don't contain themselves) but when that condition is present the box would contain itself. It would not however be able to contain that condition as well.

If however the self-containing function was triggered by some condition and then operated to contain both the box and the condition the two would always be present together and inseparable within the system.

Whichever way this gets looked at self containing creates an odd man out.

===

This is the ambiguity problem in symbol systems.

A symbol system has two types of symbol: the entities and the operators. For example

1+1=2

Now the system cannot operate on itself because + and = only operate on numbers, and the list of symbols above is an expression.

In computing for example we can express this expression as a string using a new operator the quote marks so

"1+1=2"

is an expression. Now quote marks operate on expressions so we can quote itself

""1+1=2""

However now there is ambiguity. Does this mean "" expression and 1+1=2 expression and "" expression written side by side or does it mean the string containing "1+1=2". It is not explicitly decidable.

This is not self-referential as only a copy is contained, and an inferior copy to lacking the outer most strings quotes.

To really contain itself it needs to contain a reference to itself, say:

S = "S"

But there is ambiguity again because both the S things are symbols. Is this saying that S is the string containing the symbol S (character 83cin ASCII) or the string containing the string called S. Is S a character or a reference to a string?

if we were to PRINT S in a programming language we would just get an output of S.

Another possible output is the recursive """"""..."""""" where S keeps being replace by "S"

But the real thing we wanted to express was self membership which can't be expressed in this language.

The ambiguity problem like the self-operation problem above requires an external switch to decide whether to treat the entity as a reference to the system self, or as the entity itself.

===

In case self-reference seems void as it appears to be in these sterile examples. Consider a robot which like the ones in Japan can play football. When it picks its team it needs to be able to model itself as a member of the team, otherwise it will pick 11 players and try to play along side them making 12!

However it is not good enough just to model a team of 11 robots in its system... it needs to operate on the situation of just one of those robots (itself).

ok phone call...

Simplest Universal Turing Machine

One might think that computational ability would be a more gradual phenomenon: that as one increased the complexity of the rules for a system, the system would gradually show greater computational ability.

But PCE says that's not how it works. It says that above a very low threshold, all systems will be exactly equivalent in their computational capabilities.

http://blog.wolfram.com/2007/10/the_prize_is_won_the_simplest.html?lid=title

i.e. the old argument that if we could just juice up machines a bit more we would get more out of them may be even consciousness is not true.

The +1 conjecture

A self-operating system cannot complete operation in its domain.

If a system could operate on itself, for example a hand grasping itself, then the system would be able to complete the operation intrinsically.

The question then is under what circumstances would it simply complete under itself and under what circumstances would it complete under external circumstances.

If it is a truely intrinsic system then it negates its own operation because it would always complete under itself.

If there is an extrinsic factor that triggers self completion then it can operate on all factors except that extrinsic factor where the result is self-operation.

Thus there must always be one element within the domain of the input which it cannot operate upon, if it is to have self operation.

A set cannot essentially contain itself, because if it could complete under itself it would negate its containing function.

This is why a hand cannot grasp itself, for if it could then to be able to grasp anything else there would need to be an external trigger, which it could not itself grasp. Evidentally in the realm of things there are not rules enough to distinguish that special thing which would cause self-grasping. It is worth exploring this to find the rules...


On References....

The same argument then applies to references. A box can contain other boxes but it cannot contain itself. It contains instead a reference to itself.

However then it cannot then contain also that thing without breaking the reference rule. Thus to have self-membership you need a symbol which has a special meaning i.e. self. and not its obvious meaning.

Now it might seem absurd. If we can model 14 rugby players there is nothing to modelling a 15th and calling it myself. However this is not the system of self modelling. This is simply treating the self as another entity and there is no notion of selfhood.

Formally... and this is where I need to push ahead...

A universal set {A,B,C}

Now the powerset requires no new symbols. Within the rules we can construct subsets at liberty. e.g. {A,B},{A,B,C}

Now if the set {B,C} was to have self membership we would need to create a new symbol with which to reference it. T = {T,B,C} and the system increases by 1

The set of all symbols {A,B,C} and itself has a problem then because it requires a new symbol T, but that creates a new set and so on...Recursively this creates a problem...

Now let us start with a special symbol T for self reference

{A,B,C,T}

I guess the problem might be that T has no definition, and doesn't really belong to the same set as the other symbols so it can't be a member at this stage... to explore

Containing Oneself - 3 approaches

The problem then is that a theory seems to always be about something else. Systems must be extrinsic, you cannot have a system which is intrinsic.

The Existential/Essential Approach
=========================
In essential terms, if we take a materialist point of view, then a system embodies itself already... it "is" itself. To contain itself again would require there to be a copy of the system within it, in which case it would have a "similar" system inside but not the "same" system. A box cannot thus contain itself as to contain something being the "nature" (or essence) of the box requires something else to be contained... at best a copy of the box. Likewise a hand can only grasp for something else as to grasp for itself. You cannot for example shake hands with yourself.

It is the chicken and egg situation. To have a chicken you must have an egg etc. To grasp you must already have a hand, so you cannot then grasp that hand... still unconvinced of the apparent "necessity" of this. Why can't these things be true?

The Referencing Approach
===================
Anyway when we say that we must grasp, or box, a copy of the hand or box then we are "referencing" a copy to mean the object.

An entity can thus contain a "reference" to itself. This by itself is not very useful. We would need rules to govern how to model this reference and its relationship with references to other entities.

Also we can try to include the system within itself by referencing its own components. So how many components does a system have? It depends how many components are determined. This is a function of the simplicity of emergent properties and the level of detail. We could reference each atom of a car or we could model its engine parts. The rules that govern these references are very different.

I will explore later a very simple Lindenmayer System

variables : A B
constants : none
start : A
rules : (A -> AB), (B -> A)

This system is already a reference system, it will be interesting to see if it can reference itself.

Ofcourse what does that mean? Because at the end there is only input, interations and output. It still requires a user to see the "similarities" but it is a start at self-identity.

Black Box approach
==============
Finally if we say that two systems that produce the same output from the same input, regardless of their mechanics are identical then we can rephrase the problem as a system which models its own output.

But this is ridiculous! If all the system does is model its own output then it has an undefined output, so what is there to model? How could it be correct or incorrect? If it can't model its own output then it certainly can't model itself.

Now if the system did something useful say model some extrinsic data, and then we ask it to model itself then it would produce the same output and so again cannot succeed.

If we say that it models some extrinsic data, and also reports on its processing, then we are simply adding to the data that it outputs. This is no difference from the first case.

Still however the hand grasping itself says it best. That issue applied to data processing leads to a requirement for all systems to have extrinsic qualities.

If this is true then we cannot have any system which exists independent of its objects, and no system can explain itself.

Now Dave's idea of 2 systems modelling each other. However this closed system is really just one system.

Then we are into Strawson because it seems that the universe is just a single intrinsic system, with no extrinsic source of meaning. That is where people turn to God.

This is a bleak view arising maybe from the replacing of all "things" with references in models. Reality is not a model it is reality, and a model is not reality because it is a model.

However then we begin the very hard work of ontology and epistomology asking how is it that we have referencing at all, and are there really "things" independent of our knowing of them.

The problem is that the idea of "references" suggests that there is things which are linked by a meaning. Crudely this suggests that the link is a new thing and we are in the third man falacy. If it is a new things and we reference it then we have an eternal heirachy of references supporting the last link we made.

References are "implicit" within the process of knowledge, they only exist when we reference and do not exist independent of the things within the reference. They are "meaning" itself, the dialectic between things which are not one another, but at the same time are one another as they are used interchangeably.

If we cannot speak of references without their things, as they themselves are not things, then likewise we cannot speak of things without their references because how would we call them?

The dualism is thus only for teaching purposes. In its organic in-vitro environment there is no problem, they are sides of the same coin... that of Mind.

Still very whooly but getting there...

Referencing, things and reality

Having looked at it there is nothing wrong with T={T}. But try and do this in reality and there is a problem.

Take 2 boxes. Now make a box of all boxes called C. In common sense we'd just put them in a third box, but strickly it is true that third box should be in itself. This cannot be done in "reality" so we would put a third box in and call it C. That is we would "reference" C with something else. Pretty obvious.

Take T = {T}

Actually there are 5 symbols (existing things). There is not one T symbol but two. When we say they are the same thing they cannot be the same thing else there would be only one symbol. In the example they are different things but they reference the same thing, belong to a finite symbol set so we can quantise them the same, and they are constructed in a way that our visual cortex picks out well (especially being made of lines). Nevertheless in "reality" they are different things and all the similarity occurs off the page in what I have been calling "mind". If similarity occurs in the mind then so does difference.

Another example to illustrate would be an orchestra. If the conductor asks the strings to form one group, and everyone else to form another. He might then ask I want a "group of all groups over here" i'll call the "orchestra". In common sense reality this simply means a group with the strings and everyone else. In the context no one thinks the groups are "real" they are in the "mind".

Now it's a trivial point. No one thinks that what I am writing is itself "real". The writing is just marks on a page, we assume I am talking "about" something "real" and the connection, the understanding and thinking, is "the mind".

What is "in the mind" is not real. So I was wrong "sets" are neither things nor real. They require "action" to become real. Action like things can be referenced but it has its own unique existence. Two actions are not the same thing, even when they look the same. This enters the vast realm of ethics.

Now apply that to materialism, and especially theories of mind. Materialism holds the belief that everything is founded upon a physical reality which is knowable. Clearly referencing cannot be founded upon the things it references that in other words is "mind" cannot be ignored in our account of "reality". Problems then for brain sciences because "the mind" cannot then be the same as "the brain".

Look this argument is so simple...

Why have I spent so long trying to get this argument out... (like about 25 years on and off!!!) its nothing special, but it's implication are I think?

The rules of a system cannot be built within that system.
This is all it is!

Consider. How do you construct a system unless you know the rules? You can only construct a system once you know the rules. Now once you know a game, you can then use that game to write axioms (in a hermeneutic way) but you cannot escape the system now.

Like the anthropic principle, the very presence within a system is a "given". This has been argued to mean that there are many different systems and only some of which can support our presence. This seems like a circularity based upon the rules that have been worked out within this 1 system... that needs some thought. The alternative is that this universe had a special creation to be suitable for life... its interesting how the two ideas are so similar... that "specialness" in general seems to reflect an aspect of the ego.

There is no escape from the system... well within terms of that system. And since a kid I have realised that no theory we can construct has any real value unless it an build things from the start, and since we can't do that it seems and we have to start with a "given" universe we have to just accept the system of rules we call existence and live with it. God given or whatever we want to call it.

So the project (before I forget completely where I'm heading) is simply to create a game and try to build that game within itself to prove one way or another tat it can't be done fromally.

Quine's are a good game where rules are simple PRINT and "{string}". However there is a lot of stuff happening behind the scenes including creating memory which is hidden from the system.

So to propose: a system of characters on a grid (like chess) which have meaning in building characters, so that they can build themselves.

Things to note...
>that the meaning the "user" ascribes is not the same as the meaning the system ascribes (like with Aime)
>that some rules cannot be constructed within the system
>that given the rules a pretty good version of the rules can be built within the system using those rules ... but how good?

What is the constraint on a system that stops it building itself? Formalise that!!!

Consciousness, experiments, systems

What is consciousness?

Brain function correlates well with the "experiences", in that what we become conscious of corresponds with both physical entities and the discrete events caused within the brain.

Clearly naive realism is not true since phsyical objects by themselves do not create experiences, and idealism is not true because brains by themselves do not create experiences "of things".

However quite arbitrary causes like touching the brain and chemicals can create experiences which do not seem to correspond with either the cause.

Cause and experience are not clearly related.

That we do have a correlation under "usual" circumstances, for example when a volunteer sees a chair there is an organised pattern of predictable responses, is probably because the investigator has a similar effect in their brain. So the statement that the brain is corresponding in a orderly fashion to the stimulation, is simply a statement that the patients brain is corresponding in the same way as the investigors. Looking at the chair and then the patient, the investigator having established for themselves that there is a chair there, and then looked for correspondence in the brain of the patient, is really finding correspondence in the brain of the patient which corresponds to their own brain function. Afterall the investigator cannot see what the patient sees by definition, and only make sense of what they say because they come from the same linguistic world in which "seeing chairs" carries a certain language.

If the investigator was blind for example, no matter what instruments existed, they would not be able to make sense of "seeing a chair". It would simply be a pattern of brain activity, and associated words, which corresponded with a chair and its position before the eyes, and also certain predictive elements like being able to tell when a chair was present in a room without touching it. Factually the blind person can establish all this. But to understand from all this what having your own experience of "seeing" is like is beyond the experiment.

So these experiments in neuro-science are unable to shed light upon the nature of "personal" experience precisely because it is personal.

To do that we must go deeper into the nature of existence and personal identity it seems.

===

On the subject of systems suppose we had a 2D phase diagram of a system with 2 independent variables. That system can establish nothing greater than its own state. To model that phase diagram (without being that system) it must have more state variables than the system it is modelling. Is this true?

Also... philosophers and scientists are not looking to model the brain. They are looking to explain the brain. That means to provide a high level model of the elements of the brain.

So the suggestion then is that higher level state variables are available for systems which approximate the behaviour, which is actually produced by much more intricate lower level workings.

For example we might reduce the function f(x) = x ^ 10 to a binary description which states whether the function is high or low, since it appears to go along slowly before rising very fast through the (1,1) co-ordinate and away.

So a general theory of "scales" in theories is required to look at what might be considered a good enough explanation of th brain? afterall how good do we need to explain it before we might say we understand ourselves?

Add to this the fact that consciousness is not a low level phenomena either. We are conscious only of very high level entities, not the vast amounts of minute data available in any situation.

Free, Bound variable + misc

A notion I was thinking of using before is already defined in maths...

A free variable is a symbol which has an external use. A bound variable has a particular use within the expression and so has no external meaning. Bound variables have closure of meaning while free variables must link to the outside.

A closed expression (a black box) can only replicate "all" the output of a open expression, it cannot determine "which" value a free variable takes.

This is the concise way of expressing the problem I had with "Aime" my 1996 AI experiment. Aime was written in a hermetic box seeking whether "feedback" could explain consciousness. It became apparent very quickly that anything that operates within a closed box has no meaning to the outside world.

Arguing further now, an AI machine must be able to link with its environment in order to mix with other agents ... i.e. as required by the Turing test.

Now any computer program, being just a collection of bits, is a number. There are a finite number of programs (given that no-one is ever going to write for ever, and no machine could ever write for ever).

One of those programs is the Mind Machine (MM) and we assume that humans have found it. Now the MM takes some input. There must be a finite amount of input for the MM to discover itself ... given that humans have done so. So that input is also a finite number. So the MM and the input data together form another single finite number.

Now we have to give the MM a machine on which to run else we would need to code how to build it, another number. And another number to build that machine and so on forever. So we give it a machine. Maybe like in Hitchhikers Guide to the galaxy it needs to build a new machine * x before it can get started

OK some problems here since maybe working out the start data is non-computable... anyway that is a start on a method of proof...

Miscellaneous ...

Vertical/lateral thinking - step by step proof/deduction forward and leaps followed by working back.

Could there ever be "artificial life". That is a question very closely related to this blog and one that will become more central after this initial work is done. Can the mind be artificial is the current project since we can use self-reference more easily to test ideas.

Hermeneutics seems more relevant as time is progressing to. I just need to find a nail for the coffin of deductive/logical/mechanical process thinking to show that fixed within rules we cannot escape to investigate those rules.

Rules btw might be the foundation to work with. Even set theory has rules that define what is a good and a bad formulation and process.

So the question is what rules define the rules? or if we define a rule how do we know that the rule is being followed? or if we define the word "rule" how do we know that it is being used correctly?

All these questions come down to the old point that the question "what is reason?" can't be answered without reason so it presupposes the answer.

Or the famous Anthropic principle http://en.wikipedia.org/wiki/Anthropic_principle which I would want to expand to the mind. We need a mind before we can even do the investigations into Life (carbon or anything else) and existence.

btw the issue of can things be their own foundations didn't get anywhere in set theory. I wanted to show that T <> {T} but the following suggests its quite consistent...

Consider a U = {T, A} where T = {T}
so T' = A

Now P(U) = { {}, {T}, {A}, {T, A} }

and consider a new universe of the elements of P(U) = U1

Given the definitions above this universe has 3 members U1 = {T, {A}, U}

so now T' = { {A}, U}

I was hoping for a contradiction. But actually if T' = A = { {A}, U} then

A = { {A}, U }

So A u T = { T, {A}, U } which is a perfectly consistent universe! I think...

anyway my brain hurts now so off to pub :-)

Not, Truth and the Universe

When we create any proposition we are at the same time eliminating other "similar" propositions.

This process of elimination is called "negating". Without negation all propositions would have the same standing.

The negation process occurs under a universal, or a context. This is most clearly seen in set theory where A n A' = U gives the set of all things under discussion. U is not "All things" simply the limit of the discussion.

Given any proposition we have a relationship to the limit of the discussion through the "not" operator.

Truth and Falsehood lie outside the Universal as shown by Godel since statements can be true but cannot be proven within the Universal.

However a proposition which is deemed true gives rise to false propositions through negation.

When we define a proposition then it follows that this is being done under a larger context that allows for the propositions negation.

The negation of the Universal, i.e. the set of things we are not in discourse about, is not defined and creates a limit for "existence" within set theory. Thus existence is assumed for the elements of a universal (may even be the same thing).

The "God paradox" arises then when we use the elements of a set A to build the Universal, because the Universal contains both A and A' and so A cannot construct U.

Take the example of brains. The set of things to do with cognition are limited to "Brain". Then if we make an identity between brain and our experience, and we acknowledge that we know nothing outside our experience, then we know nothing outside our brain, the brain becomes the Universal. But our brain was originally defined as a subset of our knowledge. A creates U and so A' has no existence! We are simply eliminating elements to force U to A rather than explaining U.

U cannot be explained in terms of a subset since U = A & A'

A set such as T = {T} assumes an ontology: T, T', {T}, {T'} and a greater U. work this out...

In Hegelian logic a proposition A, entails its counter proposition A' and the possibility of a new set {A, A'} forces the U to expand to encompass it.

Hermeneutics may b of interest. This would say that we must take all the elements together to explain the whole system. It cannot be done heirachically bottom up, or top down.

Hermeneutic systems and their elements

OK the problem "the God paradox" occur when we try to found the elements of our universal upon themselves. What we have in fact is a hermeeutic circle where the collection of elements taken as a whole defines the world in which we can justify - as consistent - our elements. God is both the elements of our word and the collection of our world. You cannot reduce to the elements and throw away the aggregates and you cannot take the whole and ignore the elements that come together to make that whole.

Democritus and Paremenides I understand put forward 2 hypotheses in ancient Greece... that the world was built up from atoms in the first ase and that the world was divided down from the universal. They are both parts of the hermeneutic circle. The whole system and its parts must be taken together as a dialectic.

In the system T = {T} we have an interesting system where the aggregate {T} is also the only element. This is the simplest hermeneutic system.

I am undecided whether it is to be shown that you cannot create such a system and it be hermeneutically part of another system, or to how that such a system is internally consistent.

In 1994 I had a thesis called "harmonic structuralism". The idea was that given competing systems, the system with the least contradictions and conflicts that was the largest also (i.e. the system which accounted for the most harmony) was the ethically better system. So while the Nazi system may have been internally consistent to some existent it had a huge fracture in it that maybe the democratic system does not.

Axioms n beyond

OK so axioms and logic do seem to have some value in this. The consciousness conundrum can be formulated very simply ... this is informal I'll spend some time to make it precise later...

If we postulate that there are things, and then use those things to explain how we came to postulate that there are things then we have a theory in terms of the thing we were trying to explain. It would be impossible to have a theory not in terms of things so we can't replace that original postulate.

More generally a theory must be in terms of what it is not, otherwise we are taking it as an starting assumption... an axiom. We can't prove an axiom we can only show that it is consistent with other axioms.

The question then of how we arrive at axioms is beyond axioms then. It must be accepted by reason that we can generate propositions as a fact. That cannot be the work of the brain!

===

Set theory again. On a table let us take some red beads and put them in a box and some yellow beads and put them in a box we have 2 boxes which might be described as the red box and the yellow box. The red box is not actually red, and the yellow box is not actually yellow. Our table universe (U1) has only 2 entities, namely the two boxes.

Now if we were to think about the box of boxes; in the analogy, we would create a big box for the two boxes and then we would have a new universe (U2) with 1 box (namely the box of boxes of universe U1). What we obviously can't do in the physical world is to put the big box in itself.

Now in set theory it is assumed that all subsets of a set already exist, so set theory says that in universe U1 the set of boxes {red box, yellow box} exists automatically which is the same as U1. However it is not an actual box.

When we actually build that box we get a new universe with 1 member. Only once that set is constructed does is actually exist, but to make it a member of its own construction is a problem.

If it didn't exist then it would bring its own constrcution down. If it does exist then it makes itself exist. The existence of the set depends upon itself. e.g. if T = {T} then T needs to exist to create T (so it doesn't really exist). If T does not exist then T = {} which exists.

Now we can create sets simply by chosing our ontology, and we can change subject to make sets disappear. Now with T = {T} what ontology do we have? or what universe is that a member of? To create T we must already have T.

The set of all Universes which have "blue" as a member. Which universe is T in?

===

Having shown to myself today (almost like Descartes) that there is a "just is" feature of experience that at the root our experiences just are, I'm now ledt thinking how far does "just is" go. Obviously the arrangement of things in my room can be changed, it is not "just is". So what rule divides that which "just is" and that which can be investigated, understood and changed?