What do I really love?

[gusl]

I am thinking about applying for an Economics PhD, but given the choice, I would study AI first. The problem is that the good AI schools may not have a space for me, due to a combination of factors, which I won't go into now.

If I want to become a specialist in both AI and Economics, the idea is to study AI first because it's good to be technical first and soften later (please challenge me on this).

But I really don't know what I want afterall. Ideally, I would study both econ and AI, but let's take it one thing at a time.
So, what fascinates me more? Well, this week I think I hit something when I described my one enduring passion as epistemology (See also two entries ago). It's been more or less related to most of my interests, since high school.

How My Interests are Connected with Epistemology (and other areas of philosophy)

From the file below, my CS interests file, I can see that:

* most of the AI interests are strongly epistemological

* under systems, I am interested in formalizing and standardizing ways of modeling things (programs, data)

* under theory
* information theory is about the structure of the world (this sounds bad, help me here). Chaitin is the Gödel of information theory.
* the cryptography research that interests me is like "I can't make one, but know it when I see one" and "I know it but I can't teach it", which is an interesting epistemological state (zero-knowledge proofs, etc.)
* category theory and model theory are about very general mathematical structures: you can talk across areas of mathematics with them.
* A logic is a set of laws for reasoning.

* under applications, you can see:
* Formalization of Existing Mathematics
* Formalization/Structuring/Tagging of Legacy Knowledge: the job that slipped from my hands right after I left Amazon.
* Intelligent Learning Environments: systems that teach. Can we make computers teach people interactively (assume no AI)? Can we structure knowledge in such a way?

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My areas on Interest, by Gustavo Lacerda

I know very little about most areas listed here.
As for the others, marked "*", I know almost nothing, but they sound interesting nonetheless.


AI
--

Machine Learning
Beliefs: Bayesian networks*, belief revision*
Knowledge Representation
Planning
Automated Reasoning, Theorem-Proving


Systems / Software Engineering
------------------------------

Integrated Computing System (TUNES)
Reflection, Introspection
Verification
Data Models, XML, SQL
UML
Programming by Contract
Functional Programming


Philosophy
----------

Epistemology, Causality (see Judea Pearl)


Theory
------

Logic and Complexity
Models of Computation*
Information Theory, Chaitin
Cryptography
Category Theory, Model Theory*, Chu Spaces*
Logics


Application Domains
-------------------

Music
Natural Language
Formalization of Mathematics (Projects like QED and NuPRL)
Physical Reasoning
Economic Reasoning
Scientific Discovery
Formalization/Structuring/Tagging of Legacy Knowledge
Educational Systems: Intelligent Learning Environments
Ubiquitous Computing
Cybernetics, Cognitive Aids, biofeedback

Comments

[gustavolacerda.livejournal.com]

hm.... I would say that's a serious philosophical debate.

Maybe objects in the world carry a finite amount of information, absolutely speaking. In this case, they can carry more or less information. (This was my (perhaps naive) position in making the above statement)

The other possibility is that they contain infinitely much information, so that would make it impossible to distinguish them on that basis. In this case, however, we can only perceive a finite amount of information from each object, so the amount of information depends on the observer as well as the object itself (a picture or model of an object only carries a finite amount of information).

Much like two sea coasts may be compared for perimeter: according to "chaos theory", they both have an infinite perimeter, but if we take surveyors measure the coast mile-per-mile or meter-per-meter, they will both have finite measurements, which correspond more to our intuition of the "real" perimeter.

[selfishgene.livejournal.com]

I would regard information theory as dealing with methods of transmitting and manipulating information. Including methods of building mental or digital constructs as models of external processes. The point of a model is to allow manipulations that we cannot perform on the real process or object. These manipulations result in conclusions about the real process - when done correctly. (Deciding how to do this 'correctly' is exactly the purpose of information theory!)
An example is weather simulations. Meteorologists build a computer model of the weather situation and run that model into the future faster than real time. This allows weather predictions. Better information theory may lead to better models.
In your coastline analogy it would be the job of information theory to predict whether mile measurements are more efficient than meter measurements given the model requirements.

[gustavolacerda.livejournal.com]

I'm thinking now that I was wrong in saying that InfT is about the world itself. Hang on.... no, sometimes the information results about the model shows results about patterns in the world, as you said. So, information is not only an epistemic concept, but a metaphysical one also, since epistemology asymptotically approximates metaphysics (in any non-malicious universe).

Classically, this information will be data, whether analog such as a one-dimensional voltage signal, or digital such as a byte stream. What it can do is measure information content under various interpretations, but I would say that the making of models itself is outside of the scope of InfT.

More interestingly (non-classically?), we can use information theory on higher-level objects, such as models and programs. This kind of recursive thinking is explored by Chaitin, and (I think) Kolmogorov.

How would better information theory lead to better weather models?
I don't understand your adaptation of my coastline analogy.