Re: ee's without math

Of course, very few ee's ever use Maxwell's equations. I never have. My fields instructor was a brilliant Japanese guy and we couldn't understand anything that he said. He graded on the curve.

I haven't actually used calculus in about 20 years. I have to have a feel for differential equations and initial conditions and such, but I don't actually have to do it. I use Spice. Anything interesting is nonlinear anyhow.

Being able to do higher math is a kind of mechanical skill. It doesn't necessarily create instincts for circuits or system dynamics.

Some people, like Phil H, can see through the math to the reality, but I think most EE students can't.

Nowadays, computer programs can even do symbolic math and solve equations.

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Yes, well, when I said Maxwell's equations I was kind of meaning the main four that Oliver Heaviside was able to reduce them to. Any decent RF engineer must surely be familiar with those if not the admittedly very abstruse Maxwell originals?

Interestingly Oliver Heavyside had something to say about engineers and math. See page 7 section 8, 9... Although page 5 section 5 is fun with all the name dropping. Maxwell, Poynting, Hertz, Faraday and others.

Mikek

We had the same problem with our High Energy Physics lecturer. He was Italian and a bit vivacious - his English wasn't great to begin with and when excited he slipped into fast Italian. His lectures were almost incomprehensible to us. HEP always looked like stamp collecting to me and it still does. Or as another unsympathetic to HEP physicist put it studying horology by smashing clocks together at ever greater speeds.

That doesn't mean that you can't model it mathematically and have a cute cubic or gulp quartic equation to solve analytically and give you a feel for what is actually going on (or a good starting guess to refine).

Only at the enough to pass exams stage. Higher maths is all about intuiting an answer and then doing the formal algebra to prove that your initial guess was right and communicate it to others unambiguously.

That statement I agree with. I've often wondered why so many EEs find Einstein's special relativity so completely impossible to understand.

Nowhere near as well as a human can yet. But they can do brute force algebra manipulations that would take humans forever and then be full of errors (and have been doing so in some specialities since the 1980's).

Human intuition and computer algebra (or other computer implementation) to avoid silly mistakes is still the optimum for now. I'm not sure that will hold for very much longer as general AI is getting frighteningly good at more and more abstract and thought to be impossible problems.

Maybe not. But they *were* a coveted status symbol. If someone strode into the office with a slide rule hooked to their belt, like a big, swinging dick, you *knew* immediately he was an engineer. Lesser minions were simply in awe. If you want to make an entrance - I mean a

*real* entrance - clutching a calculator simply won't cut it.

You guys are just calling sour grapes. ;)

Mathematical notation is a technology of thought. It enables even mildly skilled users to make correct inferences of a complexity far beyond the reach of ordinary rhetorical thinking.

The problem is mostly how it’s taught at the lower levels. Specifically, the junior-high notion of “simplification” taught us to collect all terms with the same x dependence, with no notion of their size, origin, or significance.

Applied to design problems, that leads to monolithic formulas with big complicated expressions for the polynomial coefficients, which naturally give zero insight.

Keeping the various contributions separate makes it much easier to see which ones are important and how to improve things.

Cheers

Phil Hobbs (Who has no wish to go back to engineering, pyramid style.)

Oh, the 'engineers' of medieval times were war machine builders; those of two centuries ago were steam engine tenders. A modern engineer could be... almost any kind of worker.

The math of Maxwell's equations opens up insights not otherwise available: you can't have a current-sense resistor without associated series inductance, because (insert knowledge of a field construct called Poynting's vector), and you can sense magnets with a Hall device because (insert knowledge of a field effect and its interaction with P-type and N-type doped materials).

To be an inventor, one needs a good imagination and a lot of junk - Thomas Edison

Lots of mathematics is part of the 'good imagination', because it guides around blockages. It's part of the 'lot of junk' because... well, really, I can go years without thinking about Poynting's vector; that's just a dusty reference amid the others on my mental bookshelf. Like other unused materials, it is waiting for use, though: don't we all like to admire the goods in a junkyard?

As for charts, nomographs, and tables "to get them numbers", that's also to encourage visualization, and pure mathematics benefits greatly from visualization; one wouldn't study Bessel functions without a copy of Jahnke and Emde for the pictures...

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Sure, you can fit things with polynomials if that's the only tool you have, but IME there's often a better way. Labfit is a free program which tries all sorts of weird and wonderful equations, usually things you won't have thought of yourself.

Yes, there's certainly better ways; Legendre polynomials for interval-specific things, and Chebyshev polynomials for conjoined segments, for instance, are common ways to shoehorn a problem into that limited shoe. They're ugly.

Even fractals have broad utility, and Fourier representations can beat polynomials all hollow. Give wavelets a chance, too!

<snip>

Or easily converted to impulse counters. :-)

Ed

Heinrich Hertz on his experiments with radio waves:

"It's of no use whatsoever ... this is just an experiment that proves Maestro Maxwell was right—we just have these mysterious electromagnetic waves that we cannot see with the naked eye. But they are there."

Asked about the applications of his discoveries, Hertz replied:

"Nothing, I guess"

Most everything you could say about Maxwell's equations in isolation take up a couple pages, it's Maxwell's equations and _boundary conditions_ that you can write a textbook about.

Heavyside didn't believe EM propagation was possible inside waveguides, he thought you absolutely needed a second conductor. So seems even he sometimes didn't believe what the math was saying.

I often get asked that question about high-energy physics.

"What good is the Higgs boson?"

My answer is usually something along the lines of "Not much, yet. But would we have had electricity if there hadn't been idle gentlemen playing with glass rods and frog legs? We'll have to wait and see."

There are currently some applications of accelerators for cancer treatment. Lately everyone wants his own synchrotron light source for things like materials research on very small scales and time spans. They're still a bit too expensive for extreme resolution lithography, but who knows?

Jeroen Belleman

Heaviside’s dates are 1850–1925.

The Alexanderson alternator, the first CW transmitter, was invented in

1903. It ran at 200 kHz, iirc, using high speed and many many poles. Even at that, it would have needed a 1-km-wide waveguide, so in H.’s era it really wasn’t possible.

Cheers

Phil Hobbs

afaict 1904,

patented in 1903:

Can't resist again, eh? May the fleas of a thousand camels invade your armpits.

No, it is not. Firstly, you can make photons with non-atoms (synchrotron radiation), and second, the selection rules of atomic transitions argue against any photon without exactly spin = 1 (i.e. a single quantum of angular momentum). Photons are spinning massless electric field energies. A quantity of 'the energy required" is NOT enough to define a photon.

More like 200 kW around 20 kHz at least for the big stations.

There is still one usable transmitter in Grimeton, Sweden at 17.2 kHz. It is operated once in June/July and often during Christmas for an hour. Some pictures of the machinery, feeders and antennas at