All posts by Duncan Gray

The Philisophical Logic of the Universe

So Kurt Gödel figured out completeness, or more importantly incompleteness. So what good are they. I haven’t yet found whether this universe must not be inconsistent. It seems intuitive that it must not be inconsistent, otherwise the inconsistent objects may very well start a chain that would devour the entire universe.

So … Hey … theoretical physicists out there … Could it be that particle/anti-particle pair annihilation is the meeting of two objects that form a paradox … in 1 dimension … Then the event horizon, being a surface … closed, finite support, bla bla bla … is the interface between to regions that represent an approach to a “boundary of inconsistency” wherein nothing can cross the boundary, but only rather approach it? This is a question of the philosophy behind it all, just like Schrödinger’s cat.

The equations of the pair I don’t know at all. The equations that represent the space near the event horizon, I do know. There is a 1/x^r term at the event horizon, so it has a pole there. But there are equations that seem to lead to a paradox. Xeno and Ramanujan come to mind. Xeno was naive and L’Hôpital trunps Xeno to let us pass the threshold. Ramanujan was not so uninformed and produced his work to demonstrate some of the really tough problems of the maths.

SOoo …

Is the universe complete … or is it consistent … ???

Just a thought I had.

Noise and Guitar Pickups

OVERTURE

The noise of a passive, linear, single-port circuit is a very simple thing. Single port needs explanation. Simple is a relative term.
Single port means that there is no other input to the circuit. For the pickup this is tricky since the ambient magnetic field of the world is, in fact, a significant port into the pickup. The electric field is a source, but not as strong. That stray-field source will be assumed to be set to zero for this discussion, but I will bring it back and analyze it in another post.
Simple means that, to someone who knows complex mathematics and the Johnson noise theory, it is simple. The pickup will be modeled as either an impedance or a conductance that has a series or parallel voltage source or current source that drives a noise signal. The six words you need to know are Impedance, Admittance, Resistance, Conductance, Reactance and Susceptance. There is a pretty good write-up at All About Circuits


IMPEDANCE

So, it is obvious that you need to know the complex impedance, in detail, of the pickup. The real part, as proved by Shannon using Boltzmann, gives the noise source capability. It is an interesting footnote that it is called Johnson noise because J. B. measured the stuff. Then old Harry did the work to relate it to quantum theory. Along those lines and at roughly the same time, all this randomness was really important because Claude was really interested in how much telegraph data could be shoved through a wire over the background noise. It took 20 years from the resistor noise findings and the information part of the puzzle. But I digress.


MEASUREMENT

Measuring a pickup’s impedance is no small feat. The impedance can get as high as a few Mega-Ωs … it is polluted by the cable that comes out of the pick (or worse, some folks won’t let you hack their guitar apart and you have to measure with tone and volume in the way – how rude!) then finally it is infected with noise that it … well … picks up. Oh, yeah, I almost forgot … the impedance is non-linear due to the iron in the middle so we have to be careful of that factor. The cable pollution is known in the network analysis world as measurement plane management and is a little tricksy to fix up. I have done this by hand and using built-in facilities of an impedance analyzer. The noise removal is (I am boldly stating based on theory, but you know how that goes) easier to remove.


MEASUREMENT PLANE

Hewlett-Packard … er … Agilent … unh … Keysight have a really nice write-up on how to take the fixture plumbing out of a measurement. That plumbing is alternatively known as the test head, test adapter, harness. For a Guitar Pickup it isn’t much of anything, but we can also de-embed the hookup cable. How’s that for nice magic. The write-up correctly uses T-Parameter matrix mathematics to eliminate the effect-on-reading of the parasitics between the meter and the DUT. I mention that here so that you will know that I didn’t just hold my tongue right and fudge the numbers when I get around to presenting numbers.


NOISE

Did you know that at the end of time, nothing … I mean nothing … correlates. OK, so I’m a drama queen. Formally, in the limit as time approaches infinity, the correlation between two arbitrarily close, but still distinct, sine wave signals is precisely 0.0. When it comes time to measure any sine stimulus, as long as it is a little bit away from interfering noise, integrate the sine multiplication (AKA a Goertzel Transform, just multiply by the I and Q of the frequency being tested) and you have the best estimate of phase and frequency of the KNOWN frequency component in the sample. This is the theory part. The math is true, but the practical problem of noise is what I worry about. I am hoping that I don’t have to go to … like … an hour per frequency point.

Today

I’m struggling with how to get a thing done. I’m not talking about mowing the law, I’m talking about dreams. I watched the story of Rick Hall … someone who wanted to be somebody.

He pushed really hard and got kicked out.  The guys who really succeeded (The Swampers) loved the music, but didn’t have some kind of chip to grind with an ax off of their shoulders.

So here I am.  Make it beautiful, don’t fuss too much about it, don’t worry about the mistakes.  But never settle.