Hi Dave,

     Well, how's this for random serendipity? By way of introduction, I work for Lockheed-Martin in Owego; we used to be a happy part of the IBM family years ago, and I remember your name and posts from all the IBMPC fora. Recently I was rummaging through the attic and found my old AT with an IBM Music Feaure in it and thought I'd bring it out of retirement - I had laboriously scored the Hallelujah Chorus, and had a sudden urge to hear it. Once the machine was up I found some software for the card that you'd written. That got me to thinking - a perfectly good IMF wasted in an old machine, but is there a driver/software that I could use with it today on a new machine? A search of the web turned up - Yep, your name! Not so many degrees of separation.. Anyway, have a great holiday season, and best wishes for the new year!

Bill Owen: very cool! Did you get the IMF working? I've taken to just writing MIDI files and letting Windows play them. Can't mess around with the voices as much, but it's simple...

So can anyone (everyone?) see (www.)davidchess.com now? I've replaced the ceoln.pitas.com page under the assumption that you can. *8)

Well, the IMF works as well as ever in the AT with Compose and Playrec (remember them??), but that's as far as I have gone, at least for now. I may keep the AT as a power supply<G>, and use my other machine/soundcard to actually drive it. I should at least capture the MIDI strings I do have, and maybe clean them up. Compose was pretty limited, though the price was right! I do have the IMF Tech manual, so maybe someday... :)

Welcome back from the great void, Davey boy. But where's the input box? Surely this isn't "it"?

The real input box is back! Just like old times...

Heh! Looks like weblogs.com can't see davidchess.com at the moment. Odd place, the web...

I have an old AT sitting on top of the filing cabinet with a Music Feature. Haven't turned it on in a long time but can plug in the monitor controler and run it.

But it isn't amped up with speakers and such, so it will have to wait a while.

HELLO. I CAN SEE DAVID CHESS DOT COM.

What's a springy man?

Hey Dave, I just came across your site... looks like you still try to convince Intel processors doing compositions ;-)

Honestly, the results don't sound much better than in the old days when we were doing the "Music from Big Blue" series. Must have been about 10 years ago ... do you still have the tapes, I was just listening to one of 'em, funny stuff.

I don't have too much time recording these days, some older stuff is available on http://www.mp3.com/bitblue

Happy trails
Andy

Festoon!

Edited by author 01-04-2002 06:06 PM
Re: planes intersecting at a point, etc. The algebraic way to think about this (the way I think about it on a daily basis) is to associate geometric gadgets to subsets of polynomial rings called ideals. For example, every plane curve (say, y=x^2) corresponds to the set of polynomials that vanish there (in this example, all multiples of the polynomial f(x,y)=y-x^2 in the ring R[x,y]). The curve is then the set of points where f vanishes, and multiples of f are exactly the polynomials that vanish on the curve.

There's nothing stopping you from doing this in higher dimensions. For instance, the x-y plane in 3-space is the vanishing set of the polynomial f(x,y,z)=z. The x-y plane in 4-space (represented by the four axis variables x, y, z, t) is the vanishing set of the ideal (z,t) - that is, the set of all multiples of z and t.

There's lots lots more about this (try a quick search for "ideals and varieties"), but the crux of your question was finding the smallest n so that varieties of dimensions r and s meet in a point. This is answered by Serre's Theorem:

Theorem (Serre's Intersection Dimension Formula, ~1964). Let V and W be two varieties in affine n-space. Assume that dim(V \cap W) = 0. Then dim(V) + dim(W) \leq n.

So in particular, 6-space is the smallest one where two solids can meet in a point (or set of isolated points). An example is easy to give: the two "hyperplanes" defined by (x_1,x_2,x_3) and (x_4,x_5,x_6) are each 3-dim'l and meet only at the origin.

This is closely related to my research - feel free to ask more questions. Glad I could finally contribute something.

Graham
http://www.leuschke.org/log/

Whoa! Thanks much; I think I actually understand that. *8)

Given a set of polynomials, is there a straightforward way to tell what sort of gadget corresponds to the set of points where they all vanish? For at least some particular subset of sets of polynomials? That is, can one glance at a set of polynomials and say "oh, yeah, that's a plane sitting in a 7-space", or "that's a line in 3-space" or whatever?

Straightforward? Hope not, or I'm out of a job. Well, you can tell the dimension of the ambient space - just count the variables. You can also say a lot about the dimension of the defined variety - the algebraic version is the supremum of lengths of "prime" ideals between 0 and the defining ideal. So (x,y) in R[x,y,z] defines a two-dimensional gadget because 0 < (x) < (x,y) is a chain of prime ideals of length 2, and no longer one is possible. (The definition of "prime" is a bit technical.) There are computer implementations of this and lots more; the main programs are CoCoA and Macaulay.

I'm right this second attending the national meeting of the American Math Society and listening to talks about exactly this stuff. Maybe I should be doing a web-simulcast for public edification. Nah, maybe not.

It should also be pointed out, wrt the acne medicine, that the levels of suicidal/homocidal behavior referenced in the various articles on the subject haven't been established as higher than to be expected in a control group of non-medicated teenagers. Correlation vs. causality, baby!

"a prefatory flash-forward that assures you that no one important came to harm."

brings to mind:

"She doesn't get eaten by the eels at this time."
"What?"
"The eel doesn't get her...I'm explaining to you because you looked nervous."
"I...I wasn't nervous. Well, maybe I was a little bit concerned, but that's not the same thing."
"Because we can stop now if you want."
"No, you could read a little bit more... if you want."