Evidence of Intent

This post was inspired by “Who Can Name the Bigger Number?“.

“oooooooooooo”, “1100”, “12” and “1.2e1” are different ways of representing the same number.

In coming up with a new representation, the first step is to invent a process by which all members of the old representation can be written in the new one. For example, to convert the “ooo” form to “11” (binary), one would do the following procedure:

1) “ooo” – “”
2) “oo” – “1”
3) “o” – “10”
4) “” – “11”

Addition and Multiplication are defined for the old rep, and to do the same on the new rep, one can convert to the old rep, do the operation, and then convert back. However, most useful reps also have direct ways of doing the same operation. In fact, the usefulness of a rep is often determined by how efficient the operations in it are. (Transforms are used to the same effect.)

Also, in principle the different reps describe the same objects, but this is assuming we have infinite memory and time. For example, to write “1e100” in the “o”-form is impossible, since that would require more “o”s than there are particles in the universe (~1e79).

Representations neglect information that we do not need. Scientific notation, for example, lists only the leading digits of a number and allows us to discard inaccurate digits early in a computation and thus reap the results of error propagation by compacting the expression.

The equivalence of an operation in a higher and lower rep must be proven using mathematics, and not by going through all possibilities, since the higher rep is capable of expressing values that the lower rep is not.

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In music, (more…)

“What is Privacy?” “What does it mean to take something personally?”

Questions in that vicinity are interesting. I was once able to write as a disembodied voice, convinced that I had possession of THE truth, and that description of personal details was unnecessary and distracting. That writing was only ever read by a very small circle, members of whom knew my language, so communication was smooth, and I was assured of the clarity of my truths.

Now? Things are more complicated. People second-guess, attempt to reconstruct your intentions and often mess up pretty badly. There’s too much behind-the-curtain peeking going on.

But isn’t this intended? Believing everything you hear is incredibly naive and dangerous, isn’t it?

Since when were the only two choices trust and distrust? IMO, the appearance of skepticism is too often used to mask the lack of imagination and intelligence. Remember that both creation and destruction are needed for growth. Ideas diversify, and the tree of possibilities grow. Combined with the trimming of critical insight, the mind then takes form. Both steps are needed, a balance must be sought.

How does this relate to the personal aspects of conversation? I think it is much easier to share the methods with which one trims ideas, especially since such trimming is often done in the name of objectivity. It is the sharing of creativities that is rare and technically more difficult, because of personal differences and even privacy concerns. It is that type of conversation that I seek.