```Dnia 30-10-2009 o 01:05:10 glen herrmannsfeldt <gah@ugcs.caltech.edu>
napisa&#2013266099;(a):

> robert bristow-johnson <rbj@audioimagination.com> wrote:
>
>> well, you'll have to judge if i act like that.  from where i stand,
>> all's i'm saying is that real (meaning that they really exist)
>> physical quantities are measured as real numbers.
>
> Many physical quantities aren't necessarily real.
> Index of refraction is usually complex.
> Closer to DSP, impedance is often complex.
>
> -- glen

You are misleading quantity (or index, proportion)
with property.
Percentile is a quantity.

Any property (physical) is real.
Non real things doesn't exist
by the actual definition of reality
and the real things we name properties.
Maybe in english there is no specific words to desribe reality
so I may not be as specific as I wish.

It doesn't mean that imaginary numbers
can only describe non existent "things".

I don't know what you mean by idex of refraction
but I'm sure that it is usualy described in complex form
bu it doesn't mean that it is magical.
They are existent dependencies worn in a nice 2dimensional form.

There is nothing strange to use imaginary to describe reality,
it is just an agreement, nomenclature and tool
of description.
It's a language.

--
Mikolaj
```
```Dnia 31-10-2009 o 09:38:06 glen herrmannsfeldt <gah@ugcs.caltech.edu>
napisa&#2013266099;(a):

>>> Another place where complex numbers seem more than just an abstraction
>>> is the evanescent wave:

No, it just possess human readable interpretation
in this specific case
so we are very lucky.
Complex numbers are just a method (tool) of 2D dependence representation,
in this case 2D electric vs magnetic field dependence at once.

> Impedances and dielectric constants by their effect on currents,
> voltages, and electric fields.  Voltages and currents have phase,
> but impedances don't.

Impedance has "phase". That makes it complex.
Phase means delay (from number of origins,
energy flow and transformation an loses)
and this is real, it physicaly exist.
We can describe it in a pair of bonded real equation
but it looks nice in just one
in special field of numbers.

--
Mikolaj
```
```"Jerry Avins" <jya@ieee.org> wrote in message
> Jerry Avins wrote:
>
>   ...
>
>> Yes. I used to program my IMSAI Nova from the front panel toggles.
>
> IMSAI and Nova 1200
>
>> Jerry
> --
> Engineering is the art of making what you want from things you can get.
> &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
A friend of mine had an IMSAI.

I played around many years ago on the TX-0 http://en.wikipedia.org/wiki/TX-0
in which  the first 32(IIRC) 18 bit words of memory could be either core, or
by changing a switch, a matrix of switches.  Just toggle in a program and
press the run button...
--Phil

```
```On Nov 1, 11:53=A0am, Jerry Avins <j...@ieee.org> wrote:
> Jerry Avins wrote:
>
> =A0 =A0...
>
> > Yes. I used to program my IMSAI Nova from the front panel toggles.
>
> IMSAI and Nova 1200
>

i remember seeing one of them.  <shudder>.  fortunately for me, i
didn't have to deal with it.  the first microprocessor i ever had to
enter code into was the Motorola M6800D2 kit.  still hand-assembly,
but a hex keypad beats binary toggle switches any day in 1975.

r b-j
```
```On Nov 1, 2:22=A0am, stevem1 <steve.martind...@gmail.com> wrote:
>
> OK, back to the ~original question,

that's not the original question.  the original question was what does
LT offer that FT does not.  there was something about frequency in FT
being a real physical quantity (where "s" might be more abstract) and
i stated that negative frequency in FT had no physical manifestation
whereas it did exist mathematically in the FT.  then from that the
discussion went on about (my paraphrase) if e^(iwt) exists physically
(because if e^(iwt) *does* exist physically, then so also does
negative frequency).

> why is the LT defined for postitive values of "t" ?
> At one point I thought this had something to do w/ turning on the
> signal at time "0"

there are definitions for the LT that has meaningful definition for
negative t (called the "double-sided" LT).  since t=3D0 is arbitrary,
there is no reason it can't be.  one problem is that there are many
signals (like decaying exponentials) that cannot be "turned on" all
the way back to t=3D-inf and be expected to converge for the FT.  it
*can* converge for the LT but only if "sigma" (the real part of "s")
is greater than the "alpha" in e^(alpha*t).

one reason that the single-sided LT is useful (but applicable only to
signals that are always zero for t<0) is that both the differential
equation *and* the initial conditions (at t=3D0) get integrated into the
LT elegantly, whereas with classical diff eq, first you solve the diff
eq (leaving you with a number, equal to the DEQ order, of undetermined
constants) and then those constants are solved for by use of initial
or boundary conditions.

r b-j

```
```Jerry Avins wrote:

...

> Yes. I used to program my IMSAI Nova from the front panel toggles.

IMSAI and Nova 1200

> Jerry
--
Engineering is the art of making what you want from things you can get.
&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
```
```Phil Martel wrote:
> "Jerry Avins" <jya@ieee.org> wrote in message
>> glen herrmannsfeldt wrote:
>>> Jerry Avins <jya@ieee.org> wrote:
>>> (snip, someone wrote)
>>>
>>>>> This is because the magnitude of the imaginary component of a complex
>>>>> signal is a real signal.
>>>> Of course. All things measurable are real. "Complex" numbers are merely
>>>> a clever and useful bookkeeping scheme for manipulating related pairs of
>>>> real quantities.
>>> Or pairs of real numbers are a convenient way of measuring complex
>>> quantities.  Impedance and index of refraction are both complex, and for
>>> similar
>>> reasons.  We can separately measure resistance and reactance, or
>>> the real and imaginary parts of the index of refraction.  (The imaginary
>>> part comes from absorption.)  Both are due to
>>> the interaction of electrons with atoms, and with each other.
>>>
>>> Often the available materials are fairly close to ideal, such
>>> that we can separate the quantities.  Resistors do have inductance,
>>> inductors (except superconductors) do have resistance.
>> Complex numbers are a clever and useful way to represent those quantities
>> in cases where phase shift has meaning.
>>
>> Compact notations expand out ability to comprehend (same root as in
>> prehensile) complicated things. Vector analysis, quaternions, complex
>> numbers, matrix algebra .. without them, we'd be hard pressed to express,
>> let alone understand, some phenomena as concepts. Nevertheless, being
>> built up from simpler stuff (Shall we go back to Peano's axioms?) thay
>> constitute the HLLs of math. Ultimately, all running code executes
>> assembly language.
>>
>> Jerry
>> --
>> Engineering is the art of making what you want from things you can get.
>>
> &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
> Well, I'd say machine code rather than assembly, though there's usually a
> 1:1 mapping.
>
>    --Phil

Yes. I used to program my IMSAI Nova from the front panel toggles.

Jerry
--
Engineering is the art of making what you want from things you can get.
&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
```
```stevem1 wrote:
> On Nov 1, 12:22 am, Jerry Avins <j...@ieee.org> wrote:
>> Randy Yates wrote:
>>> Jerry Avins <j...@ieee.org> writes:
>>>> Randy Yates wrote:
>>>> [...]
> < snip >
>> I suggest that one has a much better understanding of what a Fourier
>> transform is having done this by hand with sines and cosines than by
>> turning the crank on pairs of complex exponentials. I don't suggest that
>> it is more efficient.
>>
>> Jerry
>> --
>> Engineering is the art of making what you want from things you can get.
>> &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
>
> OK, back to the ~original question, why is the LT defined for
> postitive values of "t" ?
> At one point I thought this had something to do w/ turning on the
> signal at time "0"

I don't know what M. Laplace had in mind, but I do know that LTs are a
formalization of Oliver Heavyside's operational calculus (D operators
and all that) which he developed to simplify the solution of homogenous
linear differential equations with constant coefficients. These are
usually accompanied by initial conditions, which account for any past
history that might exist. (Heavyside also invented the step function, an
integral of an impulse.)

Jerry
--
Engineering is the art of making what you want from things you can get.
&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
```
```"Jerry Avins" <jya@ieee.org> wrote in message
> glen herrmannsfeldt wrote:
>> Jerry Avins <jya@ieee.org> wrote:
>> (snip, someone wrote)
>>
>>>> This is because the magnitude of the imaginary component of a complex
>>>> signal is a real signal.
>>
>>> Of course. All things measurable are real. "Complex" numbers are merely
>>> a clever and useful bookkeeping scheme for manipulating related pairs of
>>> real quantities.
>>
>> Or pairs of real numbers are a convenient way of measuring complex
>> quantities.  Impedance and index of refraction are both complex, and for
>> similar
>> reasons.  We can separately measure resistance and reactance, or
>> the real and imaginary parts of the index of refraction.  (The imaginary
>> part comes from absorption.)  Both are due to
>> the interaction of electrons with atoms, and with each other.
>>
>> Often the available materials are fairly close to ideal, such
>> that we can separate the quantities.  Resistors do have inductance,
>> inductors (except superconductors) do have resistance.
>
> Complex numbers are a clever and useful way to represent those quantities
> in cases where phase shift has meaning.
>
> Compact notations expand out ability to comprehend (same root as in
> prehensile) complicated things. Vector analysis, quaternions, complex
> numbers, matrix algebra .. without them, we'd be hard pressed to express,
> let alone understand, some phenomena as concepts. Nevertheless, being
> built up from simpler stuff (Shall we go back to Peano's axioms?) thay
> constitute the HLLs of math. Ultimately, all running code executes
> assembly language.
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.
>
&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
Well, I'd say machine code rather than assembly, though there's usually a
1:1 mapping.

--Phil

```
```On Nov 1, 12:22 am, Jerry Avins <j...@ieee.org> wrote:
> Randy Yates wrote:
> > Jerry Avins <j...@ieee.org> writes:
>
> >> Randy Yates wrote:
> >> [...]
>
< snip >
>
> I suggest that one has a much better understanding of what a Fourier
> transform is having done this by hand with sines and cosines than by
> turning the crank on pairs of complex exponentials. I don't suggest that
> it is more efficient.
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.
> =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF

OK, back to the ~original question, why is the LT defined for
postitive values of "t" ?
At one point I thought this had something to do w/ turning on the
signal at time "0"

```