Friday, December 26, 2008

The First Principles of my Career

A post I just read over at Evolving Thoughts got me to thinking about my first First Principles experience that had a real effect on my life. Prior to that, I was accustomed to working examination questions from first principles rather than spending the effort to memorize the curricula - I managed a reliable C+ to B- with that approach and that kept me below the notice horizon. But that really only had the effect on my life of failing to develop good study habits. So I do not recommend it to high school students.

I'll copy my comment to that post here because I think I said nicely what it was:

On the subject of the philosophical 'NOT':

1: George Spencer Brown, "The Laws of Form", specifically on the subject of division.

2: negation seems not to be understood by the 'subconscious'; the concept to be negated is simply asserted and the negation ignored. This has serious implications for those of us with bad habits we need to change. It may also be related to how come it took so long - longer than '0' - to become properly handled.

3: the Schmidt Orthogonality Principle, which asserts that all logical (i.e. Boolean) propositions can be constructed using only expressions of the form ~(A & B). This has considerable consequences in the field of logic design as used in VLSI chips. It is also a good interview subject...


~A ::= ~(A&A)
(A&B) ::= ~(~(A&B)&~(A&B))
(A|B) ::= ~(~(A&A)&~(B&B))
(A^B) ::= ~(~(A&~(A&B))&~(B&~(A&B)))

and in fact this last is how the first computer I ever worked on (Elliott 4100 series) actually implemented XOR functions in the ALU's Adder unit. It is a pretty and symmetrical diamond-shaped image when viewed as a logic schematic.

What really launched me into computers in my late teens (1966) was the visceral realization/apperception of the one-to-one relationship between the formal abstract logic (of the philosophical texts used in the Philosophy department at my University) to the actual physical electronic circuits which implement those logical equations, which in so doing perform useful computations. Without any visible moving parts. And I have to say that was a surprisingly hard association to make. The electronics was pretty easy, very basic Ohms law and simple semi-conductor junction physics; the philosophy and Propositional Calculus was equally straight-forward, something I learned and did well at in 2nd Form (UK equivalent to 6th grade). But there is something very different about the mind-set, or context, or something. I remember it took about a year of struggling to internalize an equivalence between ~(A&B) and the simple circuit of two diodes, a resistor, and a transistor. One of the few Aha! moments I can remember when it struck.

I'll probably revisit this again later. Right now I have to pack for our trip to Phoenix tomorrow.

No comments:

Post a Comment