I bought a 1000 page book on the subject at the university bookstore yesterday. It’s actually very simple theory. They’re programmed in a bizarre language called Ladder Logic that is a throw-back to the days of relays.

What’s worrying me is that the whole book doesn’t mention anything about simulation. My buddy and I are wondering if this is an oversight, or if they build plants and turn them on without first simulating their “PCL”. Uh, electronics engineers tend to look down their noses a bit at chemical engineers; I hope we’re being too harsh and there are standard tools for simulation.

I’ve dreaded the day we turn this thing on ever since we bought it. I guess nothing really awful can happen until the ethanol output tanks start filling up.

]]>D= 27[YYYYYY + ZZZZZZ + 5YYYZZZ – YYY – ZZZ + 1]

which will be positive for positive real Y and Z sufficiently large, and hence there are three distinct solutions for X for generic (Y,Z).

However, this doesn’t cover the case when Y and Z are both complex.

]]>X = XX + 2YZ

Y = ZZ + 2XY

Z = YY + 2XZ

and so the inverse circulant has first term

XXXX + 2YYZZ – 2XYYY – 2XZZZ

but using the det=1 rule this becomes … whatever … still doesn’t look like 1 or 0 to me, but then these aren’t primitive idempotents. Besides, I’m far more likely to have made a stupid mistake than you have.

]]>For instance, 3P =

1 1 1

1 1 1

1 1 1.

Probably this comes about because I believe that they can be transformed (by S P S^-1 ) into the three primitive idempotent diagonal matrices that look like this:

1 0 0

0 0 0

0 0 0

which clearly have no inverse. I think that the only idempotent matrix with an inverse is the unit matrix. Gosh, it will be embarassing if I screwed this up.

Meanwhile, my buddy is signing for the $30 million loan tomorrow and we are underway to build the ethanol plant. I promised to design the electrical controls (be afraid, be very afraid, a misprogrammed 36 million gallon ethanol distillation plant burns very well).

And I decided to do the NNLO calc for the Mass snuark term using the traditional technique of vacuum and creation and annihilation operators. That means that I have to first write a blog post that describes how to convert from snuark (geometric) QFT to standard QFT. Schwinger showed how to do this in the 1950s. The standard QFT is easier to program.

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