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"Veritasium" (YT) - "The Big Misconception About Electricity" ?

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penfold:

--- Quote from: bsfeechannel on April 26, 2022, 12:37:23 am ---
--- Quote from: penfold on April 25, 2022, 08:27:37 am ---But... whilst it is faith and trust, the faith and trust should be in the rationalism and logical framework in which maths exists, as with science where it is the scientific method in which we must trust and believe - it is just a necesary contradiction that we must trust prior work to be valid, though proof and review processes contribute to rationalising that assumption.

--- End quote ---

We don't trust science. Science is just a method for accumulating knowledge based exactly on distrusting current hypotheses.
[...]

--- End quote ---

I think you're adding a bit more weight to "trust and belief" than I intended, I was using it in the sense that to pick up any one "eastablished" topic from "science", whilst it is possible to go through all the proofs from first principals and review the entirity of research and experiments, one must accept/trust/believe that the scientific processs has both been followed and is itself correct. So to clarify, it is not that I am suggesting we must have any trust in 'science the findings/theories/hypotheses", but in "science the method". We must also trust that rationalism is itself correct and capable of producing the answers we are looking for, it has worked so far, but we do not yet know whether we are just chasing our tails. Don't forget that practioners of science make up a very small percentage of the global population, the remaining majority still contains a large number of people who find it easier to accept religious teachings: the easy response would be to question their inteligence but; perhaps it is evident of a set of necesary beliefs that are just part of the human existance but not everybody recognises belief as belief when they believe something.


--- Quote from: bsfeechannel on April 26, 2022, 12:37:23 am ---[...]
I don't know where you had your engineering math courses, and I don't care, but where I learned about math, still in high school, they taught us that math has axioms, or postulates, that are provisional truths, subject to denial if convenient.

It is the case for instance of the so called parallel postulate: true in euclidean geometry; false in, you guessed it, non-euclidean geometry (that one Einstein used for the GTR). 

When we arrived in college, for our engineering degree, we all had this concept in mind. Postulates were accepted as ad hoc truths, we had to prove the deductions from these postulates and then test their application in the lab.

No one told us to trust or believe anything.

If the experience you had with math in your engineering degree is the one you described, I feel bad for you.

--- End quote ---

I'm not really sure why you should feel bad for me, not only because I've not really described my maths education but because I've said nothing to describe how that method of teaching has affected my career or any general metric of success etc. It clearly hasn't done too well to help me justify a philosophical argument on an internet forum, but that is an incredibly small part of my life and one that there's no need for you to feel bad.

I suppose it is only a subtle difference in teaching approaches, as you were taught "...math has axioms, or postulates, that are provisional truths, subject to denial if convenient. ", I don't recall anybody suggesting "denial if convenient", more along the lines of alternative geometries can be constructed from alternative axioms (to varying degrees of validity and applicability to physical things), but ofcourse then require their own treatment... just a pushing vs pulling difference in phrasing I guess.

Nobody in my education has ever asked me to trust or believe anything either, but I accept that in order to actually get along and do some engineering, I won't always be deriving things from first principals and I must often trust what is written on paper and believe it to be true (a more appropriate term may be "to have confidence in").

adx:

--- Quote from: bsfeechannel on April 24, 2022, 04:06:58 pm ---
--- Quote from: adx on April 21, 2022, 04:42:51 am ---Being expected to trust in intellectual authorities with absolutely nil room for deviation is pretty much the definition of faith. All this talk of theorems, deductions and postulates is the setting up of a system to engender belief.
--- End quote ---

There is plenty of room for "deviation". The thing is that no one has been able, as of this day, to come up with something better.

--- End quote ---

Good point. But that is where the problem arises. People can only be expected to 'buy in' up to their own level of understanding (or gullibility), to feel like they are being led on a journey to the "truth". A kind of 'multilevel subjective experience', part of that unwinnable argument. If instead students were told to remain skeptical, not believe a thing, deviate, and revel in their own failure - well, that's not what most people would call an education. If no one believes deviation is possible, they won't try. Postgrad might be the first opportunity the unwashed masses have to think 'deviantly' (or critically).


--- Quote from: bsfeechannel on April 24, 2022, 04:06:58 pm ---... I don't think science is a place for faith to thrive.

--- End quote ---

Nor do I. But thrive it does.

It can only get worse as the expectation for human knowledge grows.


--- Quote from: bsfeechannel on April 24, 2022, 04:06:58 pm ---
--- Quote ---Applied mathematics seems there to be endured and never questioned from the outset.
--- End quote ---

1 + 1 = 2. You can question it, but, before that, you need to understand why it is held true that 1 + 1 = 2.

--- End quote ---

I often wonder if 1+1=1.999...

Applied mathematics sweeps right over number theory. (I can only assume that, but there is a nonzero chance that I had a dream that exactly replicated the lesson while I napped, so that monster that was chasing me was really an amusing anecdote given by the lecturer of having a dream of being chased by pi, while neglecting number theory as I slept through it all.)

That all reminds me of a post I drafted but didn't make, about my objection over pi.


--- Quote from: bsfeechannel on April 24, 2022, 04:06:58 pm ---
--- Quote ---When something is as optional as it seems to be, arguments in support are expected to collapse into various logical fallacies.
--- End quote ---

You've got a point here. Cockroaches survive without math. However they're not engineers.

...Or are they?

--- End quote ---

Well I never needed math, not complex numbers anyway. There is a gap. Pure math and physics is different from engineering, that was part of my argument that engineers would get by to some potentially large extent. The fact that they do and have got by seems to have caused you some anguish. It (hopefully not your anguish, because it does seem to be laid on a bit thick) can only get worse as the expectation for human knowledge grows.


--- Quote from: bsfeechannel on April 24, 2022, 04:06:58 pm ---
--- Quote ---But sines are not sqrt(-1). They are real-valued.
--- End quote ---

Alas, you slept through the class where they demonstrated that ALL real numbers are complex, too.

--- End quote ---

If you keep steering the argument to loop back around to that same point, then by the 5th or 6th time I might notice, leading me to reject it on purely contrarian grounds.

Valid though that may be, your point works both ways; if all real numbers can be considered complex, then any complex can be broken down into 2 'reals' with a by definition redundant (some might say nonexistent) imaginary part. Complex is a construction on top of reals, in a similar way to negative numbers are made from positive reals. I don't have to believe that complex numbers are "better" than real numbers, when I can twist my provisional faith to believe that real numbers are more fundamentally "numbery".

adx:

--- Quote from: SiliconWizard on April 24, 2022, 06:07:54 pm ---As we already said, there is no fundamental difference between irrational numbers and complex numbers (when having a non-zero imaginary part.) Both are defined by equations. Neither can *directly* be defined, so if your sense of what is "physical" and what is not is tickled here, both should tickle equally.

--- End quote ---

Doesn't work for me. Irrational numbers fit into a number line, ordered. Complex numbers are not a quantity.

Exact irrational numbers? Then yes (except as by above), but I can define pi as 314/100 and keep going as far as I think I need. "Equations" are a very mathematics thing to say, pi = 314/100 is an equation, 1+1 = 2 is too. They all tickle my sense of what is "physical", but some are less equal than others.

That sense is driven more by what something is than how it is defined. That might sound like a nonsense, invalid to some, but to me I am more interested in the nature or existence of sqrt(-1) than the difference between pi and 3.1415926535897932384626433832795 (well that might be a bad example due to my objection over pi, but you get what I mean).

Reminds me of some scones I made a few days ago (after this post came in) that were such a twisted mess that it wasn't possible to tell where one started or even if they were connected (it was in a rush and experimental). Sizes ranged from full scone to microscopic crumbs (I ran out of liquid, couldn't be bothered adding or mixing more so dumped it out like that, made futile attempts to pound it into homogeneity with scone compressions, then proceeded to tear it into groups of congealment). I remain more alive than dead despite eating it all (except a piece that looks remarkably like a dead baby bird which remains - bad word choice). The question though is this: How many scones were there? Casts the existence (or place in the hierarchy) of whole numbers or integers into doubt.


--- Quote from: SiliconWizard on April 24, 2022, 06:07:54 pm ---adx, you seem to be convinced that "real numbers" are physically real, while "complex numbers" are just a tool from human's imagination. That itself is a belief. It looks like the more accurate would be to say that you're "more comfortable" with real numbers, not that they inherently make more sense.

--- End quote ---

My attempts to explain have possibly made my views seem more certain than they are. I do think real numbers inherently make more sense in some situations, based on observation, and resulting suspicion then having not yet found something to explain it (away). If you want to build a definition of belief that includes skepticism as a form of belief then you wouldn't be the first, and is fine given my recalcitrance in the face of consensus. But you could hardly call my description here "faith". In any event it is consistent with my argument that mathematics pits belief against belief - like these ones.

Real numbers have a certain inevitability to them in a field of work like engineering. Applications would fail if some numbers went missing (say voltages >12 or numbers with an odd integer part, or negatives even), or at least be severely impacted. If complex numbers lose a whole axis, you just use a vector. No need to concoct from an impossible equation to have a new dimension imagine itself into being so you can say that has "phsycial relevance". It seems so synthetic. Hard for me to believe it is anything else.


--- Quote from: SiliconWizard on April 24, 2022, 06:07:54 pm ---sqrt(2) is one solution of x^2 = 2. i is one solution of x^2 = -1. Big deal.

--- End quote ---

Sqrt(2) can be approximated onto the same number line as 2. i (or really 1i) must remain orthogonal to -1. I think that is a big deal.


--- Quote from: SiliconWizard on April 24, 2022, 06:07:54 pm ---And, you have a problem with complex numbers because they are actually "two quantities" rather than just a single one.
But then you're OK with manipulating both sin and cos values, which are two quantities linked together.

--- End quote ---

My problem is with people saying complex numbers are a quantity for seemingly no reason beyond what was drilled into them. Sin and cos are linked together by the sides of a triangle. Real and imaginary are linked together by insanity.

It's not really an argument anyway. I have no more a problem with complex numbers being two quantities, as I have with vectors. Unless you mean the word "number", which I will have to learn to take with a grain of salt.


--- Quote from: SiliconWizard on April 24, 2022, 06:07:54 pm ---Ultimately, I'm not sure this has really anything to do with science or reality, but mostly just with perception.

--- End quote ---

Maybe, but my argument is that perception has driven complex numbers to this place, people seem more concerned with these perceptions than what the realities might be.


--- Quote from: SiliconWizard on April 24, 2022, 06:07:54 pm ---And IMHO, the universe and its physical reality does not freaking care about our qualms regarding numbers. It probably doesn't care about numbers altogether. Your perception does, and it's fine. Just maybe do not assume that you hold a "physical truth" just because it appears so in your own perception.

--- End quote ---

I don't know how you can say that (actually I do but I'm just saying it for effect). The universe is full of "thermometers" of continuously-varying stuff - maybe not numbers as we know them (we can't define a scale for something until we know what "1" is), but with quanta, it's as close to unavoidable as I think possible. So I have no real option other than to assume "physical truth" for potentially any mathematical object. That's not to say I "believe" or have "faith".

TimFox:
"Sin and cos are linked together by the sides of a triangle. Real and imaginary are linked together by insanity."
The second sentence in that quotation is both absurd and offensive to those with mathematical education.
Just because you find something to be icky does not render it insane.

HuronKing:

--- Quote from: TimFox on April 27, 2022, 03:39:09 pm ---"Sin and cos are linked together by the sides of a triangle. Real and imaginary are linked together by insanity."
The second sentence in that quotation is both absurd and offensive to those with mathematical education.
Just because you find something to be icky does not render it insane.

--- End quote ---

I tried to tell you guys. He can't stop worshipping at the altar of Rene Descartes. That's actually the religion here.

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