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"Veritasium" (YT) - "The Big Misconception About Electricity" ?
bsfeechannel:
--- Quote from: adx on March 27, 2022, 03:01:41 am ---The question then remains whether this fundamental nature of the number (and complex plane) has direct relevance to phase of sine waves, or whether phasor analysis merely purloins the property of the complex plane as a "handy trick"?
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If it is only a "handy trick", it is already useful and worthy of our attention as engineers. We want shortcuts to solutions for our engineering problems.
--- Quote from: adx on March 27, 2022, 01:48:48 pm ---Yes, if it "adds" nothing practical or needs to be applied abstractly by some engineers who might then not know what they are doing as clearly.
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Of course it adds practicality, otherwise it wouldn't be taught. Not only that, it adds insight, which is essential for engineering.
Because you don't have to work with AC circuits, filters, control systems, or RF, and you see no use for it in your daily tasks, it doesn't mean that mathematical concepts like complex numbers should be abolished from engineering.
For working with ADCs, for example, a different set of theorems and math tricks are required.
I could conversely say that the Nyquist theorem is a waste of time, if I my job as an engineer didn't involve sampling analog signals. Or that the Viterbi algorithm, without which CDMA, GSM, WiFi, speech recognition and a whole bunch of other technologies wouldn't be possible, that I had to study while in engineering college, is rubbish if my job as engineer had nothing to do with telecom.
SiliconWizard:
Any of our views of what reality is is just a "handy trick".
Alex Eisenhut:
--- Quote from: TimFox on March 24, 2022, 05:34:14 pm ---The German mathematician Kronecker famously said "Natural numbers were created by God, everything else is the work of men."
In that context, "everything else" includes zero, negative integers, rational fractions, irrational numbers, etc., since "natural numbers" in mathematics means the set of positive (non-zero) integers.
https://www.cantorsparadise.com/kronecker-god-and-the-integers-28269735a638
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Kronecker was a bit of dick and a loon. He made Cantor suffer for nothing...
TimFox:
--- Quote from: Alex Eisenhut on March 27, 2022, 06:27:25 pm ---
--- Quote from: TimFox on March 24, 2022, 05:34:14 pm ---The German mathematician Kronecker famously said "Natural numbers were created by God, everything else is the work of men."
In that context, "everything else" includes zero, negative integers, rational fractions, irrational numbers, etc., since "natural numbers" in mathematics means the set of positive (non-zero) integers.
https://www.cantorsparadise.com/kronecker-god-and-the-integers-28269735a638
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Kronecker was a bit of dick and a loon. He made Cantor suffer for nothing...
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Yes, he had a problem with uncountable infinities.
At university, we joked about attending the "Einstein summation convention" that would be held at the "Kronecker delta".
bpiphany:
--- Quote from: SiliconWizard on March 27, 2022, 05:41:02 pm ---Any of our views of what reality is is just a "handy trick".
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This! A vastly under-understood reality-realization.
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