On another list Wei Dai posted some questions. At this time I wish to
attempt some answers to be placed on public record. These were
excellent questions.
Wei Dai wrote>>>
>Here are my questions:
>How does math really work? Why do we believe that P!=NP even though we don't
have a proof one way or the other?
Math is composed of three levels of abstraction:
(1) Patonic forms that exist outside of space and time
http://plato.stanford.edu/entries/platonism/
(2) Cognitive systems that consist of information processing
(algorithms, logic, probability networks)
Exmaples:
http://en.wikipedia.org/wiki/First-order_logic
http://www.cs.ubc.ca/~murphyk/Bayes/bayes.html
(3) Human artifacts that consist of human created categories and
representations of things (ontologies)
http://en.wikipedia.org/wiki/Ontology_%28computer_science%29
When doing human mathematics, we are attempting to match (2) - our
cognitive systems of logic which exist inside space and time to (1)
the platonic forms which exist outside space-time. We can thus
legitimately assign true/false designations to mathematical
assertions. (a postulated platonic form may explain or fail to explain
the operations of our computations- if the postulated platonic form
fails to explain empricial properties of computational systems we
assign the designation 'false' to the mathematical assertion. If the
postulated platonic form does explain empricial computational
properties we have empirical evidence for calling it 'true'). (3) -
ontologies - data models - programming languages - are 'secondary
mathematical properties' (analgous to 'secondary physical properties'
such as color in the physical domain). These are human inventions
which we use to reflect upon (reason about) mathematics.
>How does induction really work? Why do we intuitively know that, contra
Solomonoff Induction, we shouldn't believe in the non-existence of
halting-problem oracles no matter what evidence we may see?
See above. Be careful to seperate out the notion of induction as an
empirical mathematical *procedure* (system which exists inside space
and time), from the notion of the abstract platonic form which that
procedure represents (this is the algebraic relation or category which
has a platonic existence outside space and time).
When doing Induction we engaging in generalizations. This is the
process of modifying our postulated explanations about platonic forms
(relations, categories) as new information comes in. (see above - we
are attempting to match our own finite information about platonic
forms with the platonic forms themselves). The probabilities and
uncertainties are not properties of the platonic forms themselves.
They simply reflect our own uncertainities about these platonic forms,
arising from the fact that we are finite beings existing inside space
and time.
>Is there such a thing as absolute complexity (as opposed to complexity
relative to a Turing machine or some other construct)?
Yes there is. See above. Asbolute complexity is a platonic notion
which exists outside space and time - it is what enbables one to fix
the 'mathematical identitiy' a given Turing machine existing inside
space and time.
>How does qualia work? Why do certain patterns of neuron firings translate
into sensations of pain, and other patterns into pleasure?
Qualia arise from the fact that there are many different ways to
*represent* the same reality in logical terms. Ontology is the means
through which the mind *reflects* upon mathematics. An ontology is a
way of *communicating* (representing) logical meanings. To do this
the mind has to divide reality up into *objects*, *attribites* and
*relations*. See wiki entry on ontology:
http://en.wikipedia.org/wiki/Ontology_%28computer_science%29
But any given ontology is a *secondary mathematical property* - it is
an invention of the mind, not a feature of reality itself. There are
many different ways of *dividing up* reality into an ontology, and
hence the mind ends up with many different ontologies. An order to
create an integrated logical view of reality, the mind has to have a
way to translate between all the different ontology. The logical
meaning of a concept is thus:
A collection of ontologies
A way to translate between them in order to integrate them.
And this way of representing logical concepts are what generate
Qualia. To summarize: Qualia are logical *represenations* of the
meaning of concepts consisting of onotologies and ontology merging -
this is compatible with global workspace theory - see -
http://vesicle.nsi.edu/users/baars/other/BaarsFranklinTICS2003.pdf
and information integration theory see
http://www.biomedcentral.com/1471-2202/5/42
>How does morality work? If I take a deterministic program that simulates a
neuron firing pattern that represents pleasure, and run it twice, is
that
twice as good as running it once? Or good at all?
There are three levels of abstraction in morality, just as there were
in mathematics:
(1) Objective platonic forms
(2) Calculational (cognitve) processes which perform moral
calculations
(3) The outputs of (2) - the human created ethica/political systems,
memes and rules
Your question is asking about the value of utilitarianism.
Utilitarianism attempts to calculate an 'over-all' utility for many
different agents and in recommends the outcome that maximizes this.
As a caculational device (2) , it is a reasonable over-all guide to
morality (a good 'rough approximation') but it is not a complete
theory of morality. Here's what wrong with it:
(a) it is merely a calculational device (2), which fails to get at the
underlaying explanatory principles of morality (the platonic forms).
(b) Even as a pragmatic calculational device, utiliarianism fails
since it cannot handle *reflection* - utiliarianism only deals with
external (operational behaviour) of agents and cannot say what an
agent should want (internally, in terms of internal mental states).
As per your specific question above, in general the program run twice
would be better than the program run once, but this only 'in general'
- in a specific context it may be worse (due to the fact that
utilitarianism is only an approximation to morality and far from a
complete theory). Nor would it be true even in general that the
outcome is twice as good.
For your information, the three kinds of platonic telelogical forms
and the moral theories which deal indirectly with them are as follows:
Virtues - Internal moral properties of agents. (Characteristics -
exmaples 'tricky', 'generous', 'helpful'). Handled by deontological
theories of morality. See for instance:
http://www.iep.utm.edu/v/virtue.htm
These theories have serious limitations. They are a '1st
approximation' to morality only.
Morals - Decision Making. The process of decision making resulting in
external consqueneces. ie Interactions with others. Consequentialist
and utilitarinaism theories of morality handled by decision theory.
See for instance:
http://en.wikipedia.org/wiki/Consequentialism
http://en.wikipedia.org/wiki/Utilitarianism
http://www.rep.routledge.com/article/Q023?&authstatuscode=202
Decision theory/Utiliarianism/Consequentalism is a more general theory
of morality than the theories of Virtue ethics (in fact decision
theory superceded and subsumes theories of virtue ethics). It's in
effect a '2nd order' theory of morality which is the current human
'state of the art' in morality. But it has weakness (see above). It
is not the last word.... (read on)....
Aesthetics - Aesthetical properties are the most general type of
values. The theories capable of dealing with these properties are the
most general type of moral theories. They are a '3rd order' moral
theory which includes and supercedes both virtue ethics and decision
theory.
Aesthetics. See:
http://en.wikipedia.org/wiki/Aesthetics
I do not choose to reveal you what these theories entail at this time,
since these theories are what supercede and resolve all the problems
of ordinary decision theory and utilitarianism (for instance solving
the puzzles of 'reflection'). Be patient. All will be revealed to
this list in good time ;)
>Why am I me, and not one of the billions of other people on Earth, or one of
the many people in other parts of the multiverse?
You are here asking for an identity condition. This requires the
advanced theory mentioned above (the one I'm not revealing yet) - I
have told you that this theory deals with aesthetic values.
>makes me think that intelligence != optimization process. Does anyone have a
counterargument?
Not at all, you are very astute Wei my friend. Intelligence is indeed
*not* reducible to an optimization process for reasons I tried to
explain above.
Yours
Geddes uplifted
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Received on Sun Nov 11 2007 - 22:46:00 PST