Category Archives: Uncategorized

I’ve been to Greece often enough that I’ve picked up a bit of (modern) Greek. Like anyone in  my situation, I’ve had fun spotting Greek words with Englishs cognates based on Greek roots, popping up with unusual meanings in unusual contexts. … Continue reading →

Time for another break from research (at least the normal kind). I seem to be always discovering fundamental Laws of the Universe, especially about teaching. I’d like to share some of them with you.  They are each called “Wadge’s Law” … Continue reading →

Nothing says fun like formal power series! A formal power series is a (usually) infinite polynomial in x. For example 1 + x + x2 + x3 + x4 + … This is an expression, not a number. If we … Continue reading →

Lucid is based on a simple temporal logic. The time model follows from formalizing iteration as it appears in imperative programs with, say, while or for loops. In this model there is a first or initial time point, and every … Continue reading →

In the last post we introduced eod (end-of-data), a special sentinel value used to mark the end of a finite Lucid stream. Streams in Lucid are all formally infinite (non terminating) but we can use eod to represent finite streams … Continue reading →

As I’ve already explained, Lucid can be understood as functional programming with an added time dimension. What about other dimensions? In particular, what about a space dimension? The late Ed Ashcroft and I discovered this possibility when we tried to … Continue reading →

And He took the five loaves and the two fish, and looking up to heaven, He blessed and broke and gave the loaves to the disciples; and the disciples gave to the multitudes. So they all ate and were filled, and … Continue reading →

The Liar Paradox is simple enough to explain – is the following statement true or false? This statement is false. If it’s true then it’s false, but if it’s false then it’s true  … nothing works. In my not-so-humble opinion, … Continue reading →

In the last post there was plenty about Gödel but not much about Grammar and Go-the-game. Time to pay my debt! Basically I said that Gödel’s results proved that no fixed set of facts and rules can on their own form … Continue reading →

More than eighty five years ago  Kurt Gödel proved, roughly speaking, that no fixed set of a formal facts (like 23+14=37) and rules (like x+y = y+x) can establish the truth or falsity of every theorem about arithmetic over the counting … Continue reading →