Here are a couple of overdue Choate blooper corrections. Regarding the Prime Number Theorem, Choate originally wrote:
I had typed x/ln(x) as the asymptotic limit for the number of primes less than x.
This is incorrect. It should be,
x/log(x)
It should be noted that ln(x) is the logarithm to the base e of x. log(x) is somewhat ambiguous as to the base, but when it is contrasted with ln(x) as Choate does here, it implies that the base is 10. In fact the correct formula uses the base e, and x/ln(x) is not "incorrect" as Choate is claiming. When Choate's error was pointed out, he responded by quoting http://www.utm.edu/research/primes/howmany.shtml, which says that the formula is x/log x. What Choate failed to notice is that the web page clearly states that its logs are to the base e. In other words, the "log x" on that page is equivalent to the "ln(x)" which Choate originally wrote. Choate's original formula was the right one, and in writing that his formula was incorrect, he only displays his own confusion. With regard to his ludicrous model of a spark gap inside a conductive sphere, Choate originally wrote:
The spark gap generates sparks and that builds up free electrons in the space inside the sphere (whether it is gas filled or a vacuum is irrelevant). As that charge builds up it will be all of one type, electrons. Now the electrons repel each other and therefor move in a circular motion with the spark gap as the center. They strike the surface of the sphere and tunnel through to the outside surface where they reside. The amount of charge at any one point is related to the curvature of the surface at that point. Since a sphere is constant curvature the charge will be evenly distributed. It will continue to build up so long as you supply power to the spark gap. In an ideal world it will get bigger and bigger. In the real world at some point insulation breaks down and normal current flow takes place.
He believes that the spark gap emits electrons, which strike the inside surface of the sphere and "tunnel through" to the outside. He says that the charge will continue to build up so long as you supply power to the spark gap. Here is another message in which he made the same point:
This is in addition to the charge that steadily builds up in the shell as the electrons accrete over time. This can be modelled with an integral of the flow rate of the current in the battery (it after all is Coulombs/s). It's not too hard (k * I). (I'm not going to go into what happens as the charge on the shell builds up as we're discussing here the applicability of wave equations as a reliable model).
So what do you get? A hell of a charge that will go bang at some point when some insulation give way.
When it was pointed out how ignorant this idea was, and how it violates Gauss's Law, Choate tried to backpedal by proposing that the battery itself was charged in the first place. He even drew a picture:
2N e- 1N p+
| | | | |-------------| |--------------| | | | | | | | | | | | | |------0 0------------------0 0--| \ \ spark gap switch
It should be obvious that this device fails to generate the phenomena which he describes above. In the first place, since it has a net negative charge, the charge will appear on the outside of the sphere BEFORE THE SWITCH IS THROWN. There is no spark active, no electrons being emitted, yet a negative charge appears on the outside of the conductive sphere. This is an elementary application of Gauss's Law. Then, when the switch is thrown, there will be a spark, and some of the charges will neutralize each other, but of course the net charge will stay the same, by conservation of charge. The phenomenon Choate described of electrons being emitted by the spark gap, moving outward and striking the sphere, and then tunnelling through to make charge appear on the outside, will occur only in Choate's deluded imagination. Furthermore, there will be no "build up" of charge. The charge will be there from the moment the device is put into the sphere, long before the switch is thrown. Throwing the switch will have NO EFFECT WHATSOEVER on the outside of the sphere. Michael Motyka spent several days trying to patiently explain all this to Choate, to no avail. He finally gave up in frustration. Choate is almost completely immune to enlightenment. He has certainly proved that patience and politeness make no dent in his thick skull. We shall see whether blunt frankness is any more effective.