Antenna Guru

RF is not 'black magic' – It's Synthesis, Optimization, Analysis and Realization.

Tag Archives: Math

A Yen for Yin and Yang

C++This has been an interesting week and it’s only Tuesday…

Yesterday I found myself involved in computer code of all things. I was actually able to dig out some C++ code I wrote for a *.dll way back in the year of ’99. My direct involvement in computer programming was short-lived — there were other people who were pretty good at it already and the integrated development environment simply wasn’t ‘real’ enough for me. Still, and all, it was neat to find (and find useful) an archived project from days gone by.

After that walk down memory lane I worked on the finishing touches of an algorithm that uses Inverse Fast Fourier Transform analysis to automatically tune split ring resonator filters as they are being manufactured.IFFT

But then I had to put that project on hold because the fellow who is commissioning the tuning algorithm wanted new (22 GHz) test fixtures built to test the prototypes he has built so far.

But the test fixture project required me to grind some special holding fixtures so that I could machine the teensy weensy test fixtures in the first place. I don’t have a precision grinder, so I used my mill.

Parallel_grinding_01

I wouldn’t want to do this all the time, but this was for a prototype and it worked out. So now, I’m back to getting those fixtures done, so we can validate the algorithm.

I like going from math books to machine shop and back. It’s interesting and fun to keep up that balance. It’s invigorating, it’s yin and yang.

Parallel_grinding_02
I wonder how that C++ code is going to turn out?

 

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Gödel

Kurt Gödel (Wikipedia)

It’s easier to disregard someone when you leave them out. It’s easier to disregard ideas when we don’t think about them. We sometimes do this when faced with inconsistency don’t we?

Haven’t we learned that consistency is absolutely necessary in order to be logical?

To be logical is to be reasonable… Isn’t it therefore unreasonable to be inconsistent?

Although I am not a professional mathematician, I use mathematical concepts daily. Most of us think that mathematics is the epitome of logical thinking. Most of us would think that arithmetic –the “oldest and most elementary” kind of mathematics there is– has to be self-consistent, but this only turns out to be true so long as you assume arithmetic is self-consistent but don’t try to prove its self-consistency using arithmetical statements.

Officially,

[In] any consistent effective formal system that includes enough of the theory of the natural numbers …there are true statements expressible in its language that are unprovable.

Gödel’s first incompleteness theorem

But hang on a second, this is a theorem saying it is mathematically true that there are mathematically true statements that cannot be proven (or disproven) true mathematically!

Doesn’t that wreck mathematics?

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