General > General Technical Chat
"Veritasium" (YT) - "The Big Misconception About Electricity" ?
SandyCox:
--- Quote from: bsfeechannel on March 25, 2022, 01:37:23 am ---
--- Quote from: penfold on March 24, 2022, 03:45:44 am ---My verbal description remains purely verbal and not at all physical, it just describes a physical object.
--- End quote ---
Your DNA is a description of you. But it is a description that can replicate itself and even build an entire you. We can encode your DNA sequence using the letters ACGT. It'll describe you uniquely. It'll be purely verbal, but once decoded to assemble the actual nucleic acids it represents, it'll be an functional polymer.
So, is math the encoding of the "DNA" of the universe? That's what David Hilbert and his program aimed to ascertain until Kurt Gödel screwed it all up.
--- Quote ---Maths is a descriptive language in which the natural phenomena are described, from those descriptions we can hypothesize, test, and refine new theories... the phenomena, including the big bang, relativity, quantum, etc all existed before humans and maths... yet that curiously happened. The language in which these descriptions are encoded - since it can be communicated verbally... is not exclusively physical.
--- End quote ---
I would say math is perhaps language minus contradiction. Since it doesn't admit paradoxes, it is a convenient tool to describe things for which ambiguities would be inadmissible.
I like Al-Khwarizmi's preface when he introduced algebra to the world in 850.
The fondness for science [...] has encouraged me to compose a short work on Calculating by Completion and Reduction [a.k.a algebra], confining it to what is easiest and most useful in arithmetic, such as men constantly require in cases of inheritance, legacies, partition, law suits, or trade, and in all their dealings with one another, or where the measuring of lands, the digging of canals, geometrical computation, and other objects of various sorts and kinds are concerned.
So that's what math is all about: making life easier and less ambiguous.
--- End quote ---
The concept of dimensionality is clearly defined. It is the cardinality of a basis of the vector space. The dimensional of the real numbers is 1 and that of the complex numbers is 2.
Interestingly, there are exactly as many complex numbers as there are real numbers.
Complex analysis is much more powerful than real analysis.
penfold:
--- Quote from: bsfeechannel on March 25, 2022, 01:37:23 am ---
--- Quote from: penfold on March 24, 2022, 03:45:44 am ---My verbal description remains purely verbal and not at all physical, it just describes a physical object.
--- End quote ---
Your DNA is a description of you. But it is a description that can replicate itself and even build an entire you. We can encode your DNA sequence using the letters ACGT. It'll describe you uniquely. It'll be purely verbal, but once decoded to assemble the actual nucleic acids it represents, it'll be an functional polymer.
So, is math the encoding of the "DNA" of the universe? That's what David Hilbert and his program aimed to ascertain until Kurt Gödel screwed it all up.
[...]
--- End quote ---
That's an interesting example, it is also an awful example.
--- Quote from: bsfeechannel on March 25, 2022, 01:37:23 am ---I would say math is perhaps language minus contradiction. Since it doesn't admit paradoxes, it is a convenient tool to describe things for which ambiguities would be inadmissible.
I like Al-Khwarizmi's preface when he introduced algebra to the world in 850.
--- End quote ---
Yeah... you may want to update your reading material, maths has changed a fair amount since then.
TimFox:
--- Quote from: SandyCox on March 25, 2022, 11:26:15 am ---
--- Quote from: SiliconWizard on March 25, 2022, 03:40:28 am ---Complex numbers are just vectors in R², with the property: i² = -1. You can write i as the (0, 1) vector, and the multiplication as a generalization of the cross-product of two vectors. Actually, i² = -1 (or: (0, 1)x(0,1) = (-1, 0)) comes naturally from the generalized cross-product in R².
--- End quote ---
The concept of a cross product is only defined for three-dimensional vectors.
The complex numbers form a commutative ring, more specifically a field and a complete metric space. So calling it a vector space is confusing. It still is a vector space, but with more properties. So let's call it a field.
--- End quote ---
A cross-product of two vectors gives another vector as the product.
The scalar product (or inner product or dot product) of two vectors gives a scalar as the product.
adx:
Oh, oh, where to start.
First, my concern over sqrt(-1) in electrical engineering, penfold has it right: "and the j is an operator rather than a quantity ... it is stretching it a bit far to say that it is a physical quantity".
I don't think it is any sort of tautology to say mathematical concepts are not real, if one then goes on and asserts that some part has physical relevance. Not all engineers are naturals at maths and can easily identify where that link appears (ie goes from nothing to something without explanation). Some people here seem to be struggling with it too - perhaps from over-familiarity.
Does the 'value' sqrt(-1) have innate physical relevance for anything like phasors (or even quantum mechanical wavefunctions)? In other words, would these engineering uses suffer some fatal breakdown if they were replaced by two 'ordinary' numbers without some extra special property added? I genuinely didn't know as a student, although I slowly learned they are simply 'hack vectors' and more akin to polar to Cartesian conversion than some mysterious fact of mathematics. (But whether mathematics has more of a reality of its own is a different and much more interesting question.)
I too read the bit about Gauss suggesting "lateral" and thought that might have helped set the pedagogical direction for engineering uses, but I have no problem with the word "imaginary" or the reason it was originally used, especially if this lateralness is not truly innate (ie, an illusion).
"Waffley texts" I meant anything that is used as or perhaps is an "argument from authority" fallacy (per Wikipedia), eg Steinmetz says so so it must be true. Steinmetz says it is a handy trick, so if I read that right, it is an answer to my question that sqrt(-1) has no direct / special / innate physical relevance (because it is a handy trick).
My issue with the 'physicality' of sqrt(-1) is that it is so meaningless in engineering and unrelated to its original reason for being, that it allows what is really two numbers to be called one, and that is all it is used for (and to conjure up sine waves). I don't have an issue with negative numbers because they are not two numbers masquerading as one; the sign bit (unitary minus operator) has a genuine reason for being. I don't have an issue with vectors because they don't masquerade as one quantity. As penfold illuminated for me, a phasor is effectively a de-glorified scope screenshot or v vs t plot, for repetitive sinewaves - the entire signal. Complexians would call that "a number".
I've already posted what I think about zero etc, but I have no problem ascribing some potential physicality to all real numbers, because they embody the principles of proportionality (linearity), repeatability, measurement, divisibility etc - even noise. I have never seen the "beauty" in mathematics (I can't even begin to understand what that means), but I think A/D converters are wonderful things.
I think i is icky, because +-sqrt(-1) is wholly less useful than +-sqrt(+1), yet multiplying by either has the same type of effect (an arbitrary phase shift, eg 90 or 180 deg). Let us not forget that i is composed of the multiplicative identity and unitary minus. Hmm, it's getting late, better head off before I say something I'll agree with.
The rest can wait.
bsfeechannel:
--- Quote from: adx on March 25, 2022, 04:04:02 pm ---"Waffley texts" I meant anything that is used as or perhaps is an "argument from authority" fallacy (per Wikipedia), eg Steinmetz says so so it must be true. Steinmetz says it is a handy trick, so if I read that right, it is an answer to my question that sqrt(-1) has no direct / special / innate physical relevance (because it is a handy trick).
--- End quote ---
Steinmetz has no authority. His application of complex numbers to the analysis and design of AC circuits does. The authority comes from the logical soundness of its approach, the agreement with the facts and the solutions it brings, confirmed ad nauseam all over the world.
--- Quote ---My issue with the 'physicality' of sqrt(-1) is that it is so meaningless in engineering and unrelated to its original reason for being, that it allows what is really two numbers to be called one, and that is all it is used for (and to conjure up sine waves).
--- End quote ---
So, because you see no meaning in i or j (probably because you're already refractory to math and physics) you say it should be forgotten altogether for the whole engineering, although an entire industry exists around the concept. But what do you suggest to replace it, to easily solve AC circuits? Are you some kind of new Steinmetz with an even better approach?
--- Quote ---The rest can wait.
--- End quote ---
The rest is becoming impatient.
Navigation
[0] Message Index
[#] Next page
[*] Previous page
Go to full version