Now and then someone will give me Endeavour stuff, such this coin and photos of HMS Endeavour.
The other day Mark Jones sent me this photo of Space Shuttle Endeavour.
Month: December 2013
Micro-consulting and mentoring
Sometimes a quick answer to a question is priceless. It can even be valuable to know that you could get a quick answer to a question, even if you never ask. For example, if your company is considering doing something new, knowing that there’s someone to help could make the difference in the decision to go forward.
Next year I’ll be offering this sort of micro-consulting and mentoring. For a monthly retainer, I will be available to answer questions and give advice. This would be for questions I could answer on the spot or with minimal research; anything more involved would have to be a separate consulting project. You would be guaranteed my availability for a certain amount of time per month and a quick turn-round on correspondence. (My response might be “I don’t know,” but I’d get back to you promptly.)
I’ve done some of this kind of consulting, and clients have found it very valuable. I’d like to do more of this next year as a way to fill some of the interstitial time between larger projects. I also expect it will lead to larger projects, e.g. “We like your idea of what we should do. Could you do it for us?”
If this sounds interesting to you, please contact me.
Heisenberg, Gödel, and Chomsky walk into a bar …
Seth Godin tells the following joke in The Icarus Deception:
Heisenberg looks around the bar and says, “Because there are three of us and because this is a bar, it must be a joke. But the question remains, is it funny or not?”
And Gödel thinks for a moment and says, “Well, because we’re inside the joke, we can’t tell whether it is funny. We’d have to be outside looking at it.”
And Chomsky looks at both of them and says, “Of course it’s funny. You’re just telling it wrong.”
Related: A priest, a Levite, and a Samaritan walk into a bar …
Visualizing Galois groups of quadratics
Yesterday Jack Kennedy told me about a graph he’d made as part of a project he’s working on and I asked if I could post it here.
The Galois group of a quadratic polynomial x2 + bx + c is either A2 or S2. If b2 – 4c is a perfect square, the polynomial has rational roots and the Galois group is the trivial group A2. Otherwise there are distinct irrational roots and the Galois group is the two-element group S2.
As b and c range over integers, color a pixel yellow if the group is A2 and black otherwise. This produces the image below.
Note that what appear to be the crossed lines y = ±x intersecting at 0 are actually the lines y = ±(x+1) intersecting at (-1,0).
You can find a larger image here. View the page source to see the JavaScript that produced the image. The page is calculating and setting the value of one million pixels, and yet the time to render the page isn’t even noticeable.