Misuse of the term "resonance"

[unclejed613]

ok, i just read through this whole thread..... does anybody remember what the original post was?????? ok, the OP didn't seem to understand the use of the term "resonant frequency" applied to a low pass or high pass filter. the simple answer is "if you're talking about passive RL or RC filters, you're correct, they do not resonate, but once you combine R,L, and C elements in the filter (and that includes active feedback and amplification that substitutes for L or C), it has become a resonant circuit, even if the Q has been made less than 1. the L and C elements interact, and there will be a frequency where Xc and Xl are equal, and the circuit will be resonant."


i had a few good laughs while reading through the thread.... we as techs and engineers can be an opinionated bunch for sure..... and seem to enjoy going down rabbit trails.... the thread started as a question about how a certain term is used, and ended up as an argument about whether imaginary numbers were really imaginary (or maybe not)...... (on the other hand.....)

 

[crutschow]

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.

Well "Out there", you certainly are welcome to your Humpty Dumpty world of math. Just don't expect others to follow.

 

[JimB]

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 ...

Consider this, if real human beings were like the characters in the cartoon series "The Simpsons", we would be counting in Octal rather rhan Decimal.

JimB

 

[crutschow]

Consider this, if real human beings were like the characters in the cartoon series "The Simpsons", we would be counting in Octal rather rhan Decimal.

Which would actually be better for interfacing with computers since it is easy to convert between Octal and Binary, but difficult to convert between Decimal and Binary.

 

[JimB]

Which would actually be better for interfacing with computers since it is easy to convert between Octal and Binary, but difficult to convert between Decimal and Binary.

Exactly!

JimB

 

[Warpspeed]

Mathematics can have it's real world limitations.

How about the roman guy trying to work out the cubed root of minus CXVII ?

 

[crutschow]

Mathematics can have it's real world limitations.

How about the roman guy trying to work out the cubed root of minus CXVII ?

Anachronism time.

There were no negative numbers in Roman times (zero either). They basically used numbers to keep track of things they had, such as numbers of sheep or whatever. No need for zero or negatives. So why would a roman guy need the cube root of a non-existent negative number?

 

[Warpspeed]

Anachronism time.

There were no negative numbers in Roman times (zero either). They basically used numbers to keep track of things they had, such as numbers of sheep or whatever. No need for zero or negatives. So why would a roman guy need the cube root of a non-existent negative number?

Yes I know the Romans had no zero or negative numbers.

Which is why I said mathematics "can" have some real world limitations.

 

[carbonzit]

Yes I know the Romans had no zero or negative numbers.

Which is why I said mathematics "can" have some real world limitations.

I think you're looking at the wrong way 'round. It's the real world that has limitations, not mathematics.

(And I'm not talking about Roman or some other ancient math system here.)

 

[Mr RB]

Which goes a long way to explain the failing of pure math to deal well with negative numbers. Negative numbers were just "squeezed in" later. Kind of like the way DOS managed memory sizes over 640kb.

I'd still like to see someone answer this;

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?

PS. I have always loved that Humpty Dumpty quote. It's interesting to note that it came from a math genius...

 

[Ratchit]

Mr RB,

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?

I must be missing something. I fail to see the dificulty. Could you be more explicit in describing the problem?

Ratch

 

[Mr RB]

I think you're looking at the wrong way 'round. It's the real world that has limitations, not mathematics.
...

Actually I believe in the real world *everything* has limitations. And by definition that must include mathematics which is a "thing".

Look at the massive limitation that pure math has where it can't even square a negative coordinate! If it was without limitation why the need to invent that silly i term to kludge the root of 1?

 

[Warpspeed]

I think you're looking at the wrong way 'round. It's the real world that has limitations, not mathematics.

(And I'm not talking about Roman or some other ancient math system here.)

HAHA, The Romans conquered the world and thought their mathematics was without fault or limitation.

You obviously think todays mathematics is also without fault or limitation too.

But the discussion here just goes to show that some well established mathematical pure "concepts" such as infinity, or negative numbers can face some difficulties.

 

[Mr RB]

For Ratchit;
The problems are that squareing the -coords will destroy the sign, and that even if preserving the sign can be accomplished with a kludge, the math doesn't cope with the final root of the - number.

 

[carbonzit]

HAHA, The Romans conquered the world and thought their mathematics was without fault or limitation.

You obviously think todays mathematics is also without fault or limitation too.

Don't see how that's obvious at all; I believe no such thing.

But mathematics does have one thing all over the so-called "real world": it's extensible. Take √-1: as has been pointed out here, the Romans simply couldn't even conceive of this notion, let alone compute with it. But with the magic of i, it is now a manageable concept.

 

[Ratchit]

Mr RB,

The problems are that squareing the -coords will destroy the sign,...

What is the problem with that? Integral calculus solved that problem long ago by defining a positive direction for a low to high limit of integration and positive value for a differential moving in the positive direction. Who cares if the sign is lost if we are looking for a positive sign result?

Ratch

 

[Mr RB]

...
Who cares if the sign is lost if we are looking for a positive sign result?
...

If someone wants a positive result then they would not "care" about the sign being lost.

As I said somewhere above, I've been doing as lot of math coding for CNC applications where the entire object may exist in negative coordinates, so the input variables are all negatve and the output results must all be negative as all object coords must remain in that negative octant.

And all the math operations on that object need to be universal, so the object can be transposed to positive coords etc.

And the best solution I have found is just to make the sign inconsequential, so I would do;
-x1*-y1 = -x2
and achieve perfect mirror symmetry to
x1*y1 = x2
with an elegant disregard for the "correct" way to do math.

 

[Ratchit]

MrRB,

As I said somewhere above, I've been doing as lot of math coding for CNC applications where the entire object may exist in negative coordinates, so the input variables are all negatve and the output results must all be negative as all object coords must remain in that negative octant.

And all the math operations on that object need to be universal, so the object can be transposed to positive coords etc.

And the best solution I have found is just to make the sign inconsequential, so I would do;
-x1*-y1 = -x2
and achieve perfect mirror symmetry to
x1*y1 = x2
with an elegant disregard for the "correct" way to do math.

You are describing a piecewise continous function. The function changes depending on the parameters.

x2 = -(x1*y1)   if both x1 and y1 are <0
x2 =  (x1*y1)   if both x1 and y1 are >=0

So the math is correct when defined and applied appropriately.

Ratch

 

[The Electrician]

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"

You don't quite have it right; your example should be like this:

'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"" (inches squared, but it should be just inches)

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

In freshman physics we learn that if the units don't work out as expected at the end of a calculation, you've done something wrong.

There's nothing wrong with mathematics; you've just used tried to apply simple multiplication where you need a different function.

Suppose:

xa = 2"
xb = -3"

Then what would xc be? Would it be 6, or -6, or zero, or would it be undefined? Where on the beam would the xc hole be?

 

[Mr RB]

...
You are describing a piecewise continous function. The function changes depending on the parameters.

x2 = -(x1*y1)   if both x1 and y1 are <0
x2 =  (x1*y1)   if both x1 and y1 are >=0

So the math is correct when defined and applied appropriately.
...

Sure, that is a fairly obvious way to tackle the problem that the math has in handling the negative values. It's probably also my preferred procedure most times.

But conceptually I like;
(-)x2 = (-)x1*(-)y1
where the concept of (-) is subservient to the important math processes taking place. The (-) could be arbitrarily assigned, or even a different sign such as;
(left)x2 = (left)x1*(left)y1
or
(up)x2 = (up)x1*(up)y1

as conceptually in the "real world" when working with mirror symmetry and coord systems +,-,left,right,up,down etc are equally valid concepts and can be assigned or interchanged as required without affecting the math.

...

x2 = -(x1*y1)   if both x1 and y1 are <0
x2 =  (x1*y1)   if both x1 and y1 are >=0

If you analyse the whole process it is almost identical to the concept I proposed of *ignoring* the signs while the math is taking place and at the end arbitrarily reinstating the signs to ensure the entire operation remains in the correct octant, and what you have provided is a working procedure for that concept.

xsquared = -(x1*x1)   if x1 is <0
xsquared =  (x1*x1)   if x1 >=0

And essentially this is
-9 = -3*-3