Lambda the Ultimate

I'm working on an alternative viewpoint on information theory which does a little to support the idea of semantics. This work is Arrow, which is being coordinated with and for The TUNES Project. Basically I take the perspective of arrows (objects with a standard interface of 2 references, much like CONS-cells only information-centric instead of construction-centric) instead of bits as fundamental. My position paper is lacking though, due to my lack of time for the project at the moment. However, this will change shortly. Anyway, the TUNES list has discussed this kind of thing several times.

Maybe you really mean that the fundamental repsn is bits plus arrows? Or rather that you're representing a subclass of information (the relationship between "simple" sets - maybe I'm naive in thinking you can argue one is a subset of the other).

Related to this is a question that is at the heart of the modern debate with the "creationist science". Is the sequence of evolutionary events the result of a blind chance or an "intelligent design"? In a more mathematical formulation, how to tell if a sequence of numbers a[n] is truly random or can be generated by some deterministic function f[n]?

This is a difficult question. Statistical tests are of little help: deterministic pseudo-random generators can yield random-looking results. Such "designed" algorithms as "decimal digits of PI" produce irregular, random-looking, infinite sequences. Another example is Mandelbrot sets -- exquisitely complex and yet generated by one of the most simplest mathematical processes.

Kolmogorov suggested that a sequence can be called random if any of its descriptions is no shorter than the direct enumeration of its elements. Alas, young Chaitin showed that this test is undecidable.

BTW, this example indicates how profoundly stupid are the questions such as "given a sequence of several numbers, tell the next number", which are typical of SAT, IQ and other standardized tests.

Representation in arrow is something relative. Consider embeddings of elements in category theory. The implict idea in bit-wise information theory is that finite inductive representations are all that are to be dealt with, and that any other abstraction cannot be dealt with as transparently as it can.

But more to your point, the selection of either reference of an arrow represents an analogy of a bit of information, and bit sequences are chains of these selections concatenated.

As for the subset (or -class) proposition, I'd rather say that bits force you to represent things with finite inductive forms, meaning that every type is coerced into a fundamentally finite inductive type non-transparently.

Finally, part and parcel of the arrow theory is that information does not have a universal class, or that a single representation or perspective holds more appropriately than any other. A lot of this comes from category theory, but category theory is not general enough.