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Misuse of the term "resonance"

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What's wrong with the square root of -1?
Nothing. But there is no real answer. In other words there is no real number you can multiply by itself to get -1. In general that holds true for any negative number. Try to take the square root of a negative number on your standard calculator and see what happens.
 
Ahah. Of course. :) I think I've been spoilt in a lot of real world electrical and programming tasks where a - sign just means do the same action and make it inverted (or tack a - bit on a variable) haha.

It's annoying when math differs so far from the real world. Like multiplying a sine wave with another sinewave. At an instant when both sinewaves are +3v the output wave is +9 volts, no problem. And when the two waves are both -3v the output wave is (of course) -9v. ;)
 
The product of -3 * -3 is +9, sine waves be damned.
 

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It's annoying when math differs so far from the real world. Like multiplying a sine wave with another sinewave. At an instant when both sinewaves are +3v the output wave is +9 volts, no problem. And when the two waves are both -3v the output wave is (of course) -9v. ;)
In the real world if you put two sine-waves into the inputs of an analog multiplier, the output when both inputs are -3V will be plus 9V not minus 9V.

So what multiplier do you have that gives (of course) minus 9V when multiplying two minus 3V inputs together?

Mathematics is used to describe virtually everything that happens in the universe from the life and death of stars to the subatomic behavior of the atom to the operation of all electronic devices. If math differs from the real world it means the math was incorrectly or incompletely done.
 
Nothing. But there is no real answer. In other words there is no real number you can multiply by itself to get -1. In general that holds true for any negative number. Try to take the square root of a negative number on your standard calculator and see what happens.

It works on my TI-84... hehe, I know what you mean although I never really comprehended it... :)
 
Warpspeed,

But we both know that is not the case.
Perhaps "potential power" be a better name for it, but "imaginary power" is what the mathematicians have decided to name it.
But circulating reactive power is very real, and it can offer a circuit designer a real challenge.

Yes, the out of phase power associated with reactance energy storage is just as real as the power dissipated by the resistance. I like to call it reactance power. Its energy per unit time is stored in the electric and magnetic fields of a circuit, and is not lost from the circuit unless there is resistance in its path.

crutschow,

They may be real volts and amps but they provide imaginary power not real power. There is no magnifying of energy or real power, only magnification of reactive power.

Reactive power and resistive power are better and less confusing terms to use.

...(hence in the imaginary quadrant of the complex number plane) and are not carrying real power (watts).

Reactive circuit elements are carrying "real" power represented by an easily measurable voltage and current. The fact that its associated energy is being stored in electromagnetic fields instead of being dissipated as heat does not negate this fact.

The mathematicians decided to define the √(-1) as i (e.g. i² = -1) ...

That is a misconception. "i" is a mathematical operator, not a numerical constant. The numerical constant √-1 is 1/_90° in polar coordinates, not "i". The mathematical operator "i" is defined as "Rotate a real number by 90° counter clockwise (CCW)". Usually "i" by itself is understood to mean 1i, but it should always by understood that it is really an operator. Likewise 5i does not mean i + i + i + i + i . It means 5 rotated CCW by 90°. It is true you can get correct answers by treating it like a constant, but that is only due to its conformal similarity. So 5i³ means, apply the "i" operator 3 times by rotating 5 CCW 270°.

Ratch
 
That is a misconception. "i" is a mathematical operator, not a numerical constant. The numerical constant √-1 is 1/_90° in polar coordinates, not "i". The mathematical operator "i" is defined as "Rotate a real number by 90° counter clockwise (CCW)". Usually "i" by itself is understood to mean 1i, but it should always by understood that it is really an operator. Likewise 5i does not mean i + i + i + i + i . It means 5 rotated CCW by 90°. It is true you can get correct answers by treating it like a constant, but that is only due to its conformal similarity. So 5i³ means, apply the "i" operator 3 times by rotating 5 CCW 270°.
I understand that "i" is a mathematical operator that represents a 90° rotation in the polar coordinate plane and not a numerical constant. I didn't think it was necessary to delve into the complex geometric plane for the purposes of my explanation (You obviously feel otherwise). Incidentally the geometric concept of imaginary numbers wasn't observed until a couple hundred years after the existence of imaginary numbers was first noted so the geometric intrepetation is not required for the study of such numbers.

But wikipedia, among others also states the i² = -1 and Wolfram Mathworld states that i equals the √-1. So what is the misconception, or are wikipedia and Wolfram wrong also?
 
crutschow

But wikipedia, among others also states the i² = -1 and Wolfram Mathworld states that i equals the √-1. So what is the misconception, or are wikipedia and Wolfram wrong also?

Nope, as I said before, i by itself is understood to mean 1i. Therefore i² means (1i)² = -1 which is correct.

Ratch
 
crutschow



Nope, as I said before, i by itself is understood to mean 1i. Therefore i² means (1i)² = -1 which is correct.

Ratch
So what was the "misconcepiton"?
 
...

So what multiplier do you have that gives (of course) minus 9V when multiplying two minus 3V inputs together?
...

Any circuit that multiplies the offsets of the 2 signals (from zero) and maintains the sign.

If you want a simpler example you could rig an opamp circuit to control gain based on imput amplitude, so that;
+2v in = +4v out
+3v in = +9v out
-2v in = -4v out
-3v in = -9v out
the voltage of the output could easily be described as the "square" of the input.
 
Any circuit that multiplies the offsets of the 2 signals (from zero) and maintains the sign.

If you want a simpler example you could rig an opamp circuit to control gain based on imput amplitude, so that;
+2v in = +4v out
+3v in = +9v out
-2v in = -4v out
-3v in = -9v out
the voltage of the output could easily be described as the "square" of the input.
Creating gain that is dependent on the input envelope could create that sort of response, I suppose, but it would not be simple, and it wouldn't work at DC.
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the voltage of the output could easily be described as the "square" of the input.
No, the square of a negative number is a positive number.
 
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No, the square of a negative number is a positive number.

Sure, I understand that is correct in terms of pure math. What I am trying to describe is that real world can and does differ from a pure math model.

By using sinewaves and squares in my example it has brought to your mind pure math solutions (since both are pure math constructs), which I don't think has made the point. I'm not saying the math is wrong, I'm saying the real world can and does work differently to the math.

Forget sines and squares and consider a physical object, say a beam with a centre coord and a right and left side. You can arbitrarily assign + and - coords to either side of the beam as you wish.

Now there are 3 holes on either side of the beam their positions referenced with relative coords to the beam centre point, so that the position of 3rd hole xc is determined by the positions of the first 2 holes;
xa = 2"
xb = 3"
xc = (xa*xb) = (2*3) = 6"

and on the other side of the beam;
xa = -2"
xb = -3"
xc = (xa*xb) = (-2*-3) = -6"

So where in pure math we assume that (-a*-b) = +c in the real world the sign can be arbitrarily assigned to either side of something real, and the sign has a much lower importance than the requirement that an *identical operation* be carried out on both sides of something with mirror symmetry.

So I guess my premise is that in pure math we need (-a*-b) = +c but in the real world the case is very commonly that the same operation must be carried out on both sides of the zero, and the sign is much less important and can be arbitrarily assigned to either side of the mirror. Either before or after the operation or inverted as needed without affecting the operation.

And so within a real world "mirror symmetry" model I have no problem with the square root of -9 being -3.
 
Mr RB, your mind is definitely has accompanied the rest of you to your location.:D
 
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Mr RB, your contention that the "real world" can and does differ from a pure math model is not true. Everything that happens can be described and defined by a pure math model, from subatomic behavior to the operation of the universe. It's the cornerstone of the technical world. It doesn't require any modifications or exceptions to the mathematical rules (although some of the math is obviously very complex and far beyond the ability of most mortals to fully understand it).

But you can certainly live in you own world of non-standard math if you like and modify whatever math definitions you find convenient to do so. But you will have difficulty conversing accurately with the rest of the technical world who do follow the standard math rules.

You example with the beam would be normally done by saying that the position of the third hole on the negative side is simply -(xa * xb) = -(-2 * -3) = -9. If you want to say -2 * -3 = -9, then when is -2 *-3 = +9? Whenever you find it expedient? Never?

The technical world depends upon everyone following the same mathematical rules, even if they may not alway seem the most common-sense. Otherwise there would be chaos. If a technical subject or process in the real world can not be accurately described using standard mathematical rules then likely it can not be accurately described at all.
 
As a bemused bystander, this thread appears to have all the potential of a blockbuster going nowhere but round in circles thread, just like a cat chasing its tail.:D

A bit like threads on Ohms Law, and how AC flows through a capacitor.:eek:

JimB
 
But a cat must enjoy chasing its tail, or it wouldn't do it.;)
 
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You example with the beam would be normally done by saying that the position of the third hole on the negative side is simply -(xa * xb) = -(-2 * -3) = -9.
...

Exactly! And proves my point quite well. What you have is apply a math kludge -() to try to cover the failing of the math to perform the actual real world operation.

Now your new kludge formula fails to satisfy the coords on the other side of the beam so that if you apply the same forrmula to the positive numbers you get -(+2*+3)=-6 when the result should be +6. You have exactly the same failing of the pure math you have just inverted it.

In the real world the process is the same on the LEFT side of the beam and the RIGHT side (not I used left and right rather than + and - to make a point) the + and - are subservient almost to the point of irellevance. They can even be assigned AFTER the math process has been done so they had no effect on the math at all.

The pure math approach does not cope well with the mirror symmetry of the real world which requires that IF the same operation is to be carried out on either side of the divide the same and simplest math should be used on both sides.

As another real world example I have done a lot of vector coordinate math over the last year for CNC applications including generating CNC paths, object scaling (requires -mult and -div) 3D vectors and speeds (requires -square and -root) etc. And the absolutely best approach was to perform identical operations for both + and - coords.

If you have to do a 3D pythag that requires summing 3 squares and a root on 3 negative coords how do you do it?

...
If you want to say -2 * -3 = -9, then when is -2 *-3 = +9? Whenever you find it expedient? Never?

I like that. When it's expedient. Mastery over the tool rather than subservience to the tool... In the same way that a master craftsman might use a screwdriver as a chisel when it's expedient.
 
Mr RB, your mind is definitely has accompanied the rest of you to your location.:D

Hehe. :D

I love taking a stance on the fringe of logic and seeing how far that border can be pushed. Especially when in the company of smart men that may appreciate that the standard assumptions can be challenged, even if tongue in cheek.

Isaac Newton would have not imagined that in the future the best way to do large calculations would be in base2 with huge numbers made of 1's and 0's. That's just a completely "out there" math idea, until of course you realise it's the best way to do math in the real world. ;)
 
Isaac Newton would have not imagined that in the future the best way to do large calculations would be in base2 with huge numbers made of 1's and 0's. That's just a completely "out there" math idea, until of course you realise it's the best way to do math in the real world. ;)

No.

It's not "the best way to do math in the real world". Oh, it may be the best way for binary computing machinery to do math in the real world; it certainly isn't the best way for human beans to do math ...
 
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