# Complex versus real numbers

Started by August 25, 2009
```invalid wrote:
> "Jerry Avins" <jya@ieee.org> wrote in message
>> Do agree that a real number is a complex number with the imaginary part
>> equal to zero? Then I use complex numbers when I count my toes.
>
> I hesitate to use the term, "imaginary", for it has other connotations
> as already discussed in this thread, but even the so-called "real" numbers
> are just a figment of the imagination.
>
> Ask someone to show you two pencils, then two apples, and then ask
> them to show you "two". If they offer, "2" or "II", point out to them that
> they are indeed symbols that represent two, but not two itself.
>
> Two does not exist any more than does i*2 (or j*2 if you're electrical).
>
> Real numbers are as imaginary as are imaginary numbers.
>
> This is the standard response I give when tutoring those who claim that
> they can never understand mathematics because it is abstract by pointing
> out that they already understand the abstraction that is mathematics.

What do you say to those who claim that exp(ix) is a fundamental
abstraction, and that sin(x) and cos(x) are derived abstractions?

Jerry
--
Engineering is the art of making what you want from things you can get.
&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
```
```Randy Yates wrote:
> Jerry Avins <jya@ieee.org> writes:
>> [...]
>> Some people seem to believe that mathematics is reality and the things
>> we touch are only Plato's shadows on the cave wall.
>
> Define "reality"...
>
> No, really - try it. I have and never reached a final verdict.

Reality is that which does not change when you ignore it.

--
Les Cargill
```
```On Aug 27, 11:08=A0am, Les Cargill <lcarg...@cfl.rr.com> wrote:
> Randy Yates wrote:
> > Jerry Avins <j...@ieee.org> writes:
> >> [...]
> >> Some people seem to believe that mathematics is reality and the things
> >> we touch are only Plato's shadows on the cave wall.
>
> > Define "reality"...
>
> > No, really - try it. I have and never reached a final verdict.
>
> Reality is that which does not change when you ignore it.

ooooh!  i *like* that.

thanks, Les.  that's a tidbit i'll need to remember.

reality is voltage we actually measure and express with real numbers
(and units).

reality is the sound that the tree falling in the forest makes
(whether we're listening or not).

reality is the periodic extension of the DFT (whether Dale D is
observing it or not).

L8r,

r b-j
```
```Jerry Avins wrote:
> Rune Allnor wrote:
>> On 26 Aug, 23:07, robert bristow-johnson <r...@audioimagination.com>
>> wrote:
>>>  I actually used a slide rule
>>> in high school (and got a circular one so i wouldn't have to move it
>>> from one end to the other),
>>
>> You didn't, by any chance, use that slide rule when you
>> first encountered the DFT...?  ;)
>
> I did. I called it a Fourier series then, and used it to compute the
> expected distortion of open-loop Class-B audio amplifiers used as plate
> modulators in radio transmitters. What goes around comes around.
>
> Jerry

There was a graphical tool with the EIMAC (Eitel-MacCullouch) book
The Care and Feeding of Power Grid Tubes.

--

Tauno Voipio (OH2UG)
tauno voipio (at) iki fi
```
```On Aug 27, 1:22=A0pm, Tauno Voipio <n...@sem.pp.fi> wrote:
> Jerry Avins wrote:
> > Rune Allnor wrote:
> >> On 26 Aug, 23:07, robert bristow-johnson <r...@audioimagination.com>
> >> wrote:
> >>> =A0I actually used a slide rule
> >>> in high school (and got a circular one so i wouldn't have to move it
> >>> from one end to the other),
>
> >> You didn't, by any chance, use that slide rule when you
> >> first encountered the DFT...? =A0;)
>
> > I did. I called it a Fourier series then, and used it to compute the
> > expected distortion of open-loop Class-B audio amplifiers used as plate
> > modulators in radio transmitters. What goes around comes around.
>
> > Jerry
>
> There was a graphical tool with the EIMAC (Eitel-MacCullouch) book
> The Care and Feeding of Power Grid Tubes.

i remember Eimac back when i was a ham radio operator in the 60s and
early 70s.  i was WN0CCA and WB0CCA.

they had some really interesting power tubes (that i'd used to lust
after before i started lusting after electric guitars), if you wanted
a 1 KW linear amp (2 KW peak for SSB).  the least interesting were
their forced-air cooled tubes (which is what you saw in most ham
linear amps).  they also had heat-sink coupled tubes (i think you
needed a special insulator the conducted heat and not juice, unless
you were a "grounded plate" amp).  they had the more old-fashioned big
glass envelope tubes (that needed a fan to blow on them).

the most interesting were *water* cooled power vacuum tubes!  they had
little threaded hose connectors on them. (there are some pdfs at
http://www.cpii.com/product.cfm/9/22/75 .)

i used to get QST magazine and on the back cover, they had an ad with
this big 1/2-MW tetrode or pentode that was about a foot in diameter
and 18" tall (with two big threaded water in and out connectors).
standing next to it on a featureless white floor and backdrop was a
toddler in diapers and the caption "Introducing our new baby!".  as if
ham operators would have any use for some 500-MW transmitting tube.

hey Tauno, thanks for stimulating some 40 year old synapses that i

geez, i'm getting old.  (and i know i ain't as old as you, Jerry.  i
can remember JFK and RFK, but it doesn't go much farther back than
that.  it's interesting that the siblings, same generation, were still
in the game until this month.)

L8r,

r b-j
```
```Jerry Avins  <jya@ieee.org> wrote:

>Some people seem to believe that mathematics is reality and the things
>we touch are only Plato's shadows on the cave wall.

You should look up Max Tegmark and the Mathematical Equivalence
Principle.  It's a serious theory that says exactly what
you just said, but probably untestable.

Steve
```
```robert bristow-johnson wrote:
> On Aug 27, 1:22 pm, Tauno Voipio <n...@sem.pp.fi> wrote:
>> Jerry Avins wrote:
>>> Rune Allnor wrote:
>>>> On 26 Aug, 23:07, robert bristow-johnson <r...@audioimagination.com>
>>>> wrote:
>>>>>  I actually used a slide rule
>>>>> in high school (and got a circular one so i wouldn't have to move it
>>>>> from one end to the other),
>>>> You didn't, by any chance, use that slide rule when you
>>>> first encountered the DFT...?  ;)
>>> I did. I called it a Fourier series then, and used it to compute the
>>> expected distortion of open-loop Class-B audio amplifiers used as plate
>>> modulators in radio transmitters. What goes around comes around.
>>> Jerry
>> There was a graphical tool with the EIMAC (Eitel-MacCullouch) book
>> The Care and Feeding of Power Grid Tubes.
>
> i remember Eimac back when i was a ham radio operator in the 60s and
> early 70s.  i was WN0CCA and WB0CCA.
>
> they had some really interesting power tubes (that i'd used to lust
> after before i started lusting after electric guitars), if you wanted
> a 1 KW linear amp (2 KW peak for SSB).  the least interesting were
> their forced-air cooled tubes (which is what you saw in most ham
> linear amps).  they also had heat-sink coupled tubes (i think you
> needed a special insulator the conducted heat and not juice, unless
> you were a "grounded plate" amp).  they had the more old-fashioned big
> glass envelope tubes (that needed a fan to blow on them).
>
> the most interesting were *water* cooled power vacuum tubes!  they had
> little threaded hose connectors on them. (there are some pdfs at
> http://www.cpii.com/product.cfm/9/22/75 .)
>
> i used to get QST magazine and on the back cover, they had an ad with
> this big 1/2-MW tetrode or pentode that was about a foot in diameter
> and 18" tall (with two big threaded water in and out connectors).
> standing next to it on a featureless white floor and backdrop was a
> toddler in diapers and the caption "Introducing our new baby!".  as if
> ham operators would have any use for some 500-MW transmitting tube.
>
> hey Tauno, thanks for stimulating some 40 year old synapses that i
> didn't realize i still had.
>
> geez, i'm getting old.  (and i know i ain't as old as you, Jerry.  i
> can remember JFK and RFK, but it doesn't go much farther back than
> that.  it's interesting that the siblings, same generation, were still
> in the game until this month.)
>
> L8r,
>
> r b-j

In the sixties, I dreamed of big Eimac tubes. I still
have a linear with a pair of Eimac 3-500Z's.

--

73, Tauno, OH2UG (since 1960)
```
```Tauno Voipio wrote:
> Jerry Avins wrote:
>> Rune Allnor wrote:
>>> On 26 Aug, 23:07, robert bristow-johnson <r...@audioimagination.com>
>>> wrote:
>>>>  I actually used a slide rule
>>>> in high school (and got a circular one so i wouldn't have to move it
>>>> from one end to the other),
>>>
>>> You didn't, by any chance, use that slide rule when you
>>> first encountered the DFT...?  ;)
>>
>> I did. I called it a Fourier series then, and used it to compute the
>> expected distortion of open-loop Class-B audio amplifiers used as
>> plate modulators in radio transmitters. What goes around comes around.
>>
>> Jerry
>
>
> There was a graphical tool with the EIMAC (Eitel-MacCullouch) book
> The Care and Feeding of Power Grid Tubes.

Yeah. I used that too. It didn't work much better for me.

Jerry
--
Engineering is the art of making what you want from things you can get.
&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
```
```Tauno Voipio wrote:
> robert bristow-johnson wrote:
>> On Aug 27, 1:22 pm, Tauno Voipio <n...@sem.pp.fi> wrote:
>>> Jerry Avins wrote:
>>>> Rune Allnor wrote:
>>>>> On 26 Aug, 23:07, robert bristow-johnson <r...@audioimagination.com>
>>>>> wrote:
>>>>>>  I actually used a slide rule
>>>>>> in high school (and got a circular one so i wouldn't have to move it
>>>>>> from one end to the other),
>>>>> You didn't, by any chance, use that slide rule when you
>>>>> first encountered the DFT...?  ;)
>>>> I did. I called it a Fourier series then, and used it to compute the
>>>> expected distortion of open-loop Class-B audio amplifiers used as plate
>>>> modulators in radio transmitters. What goes around comes around.
>>>> Jerry
>>> There was a graphical tool with the EIMAC (Eitel-MacCullouch) book
>>> The Care and Feeding of Power Grid Tubes.
>>
>> i remember Eimac back when i was a ham radio operator in the 60s and
>> early 70s.  i was WN0CCA and WB0CCA.
>>
>> they had some really interesting power tubes (that i'd used to lust
>> after before i started lusting after electric guitars), if you wanted
>> a 1 KW linear amp (2 KW peak for SSB).  the least interesting were
>> their forced-air cooled tubes (which is what you saw in most ham
>> linear amps).  they also had heat-sink coupled tubes (i think you
>> needed a special insulator the conducted heat and not juice, unless
>> you were a "grounded plate" amp).  they had the more old-fashioned big
>> glass envelope tubes (that needed a fan to blow on them).
>>
>> the most interesting were *water* cooled power vacuum tubes!  they had
>> little threaded hose connectors on them. (there are some pdfs at
>> http://www.cpii.com/product.cfm/9/22/75 .)
>>
>> i used to get QST magazine and on the back cover, they had an ad with
>> this big 1/2-MW tetrode or pentode that was about a foot in diameter
>> and 18" tall (with two big threaded water in and out connectors).
>> standing next to it on a featureless white floor and backdrop was a
>> toddler in diapers and the caption "Introducing our new baby!".  as if
>> ham operators would have any use for some 500-MW transmitting tube.
>>
>> hey Tauno, thanks for stimulating some 40 year old synapses that i
>> didn't realize i still had.
>>
>> geez, i'm getting old.  (and i know i ain't as old as you, Jerry.  i
>> can remember JFK and RFK, but it doesn't go much farther back than
>> that.  it's interesting that the siblings, same generation, were still
>> in the game until this month.)
>>
>> L8r,
>>
>> r b-j
>
> In the sixties, I dreamed of big Eimac tubes. I still
> have a linear with a pair of Eimac 3-500Z's.

Speaking of forced air and special sockets, I still have a 4X150A in the
attic.

Jerry
--
Engineering is the art of making what you want from things you can get.
&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
```
```On Aug 27, 5:58=A0pm, Jerry Avins <j...@ieee.org> wrote:
> Tauno Voipio wrote:
> > robert bristow-johnson wrote:
>
> >> i remember Eimac back when i was a ham radio operator in the 60s and
> >> early 70s.  i was WN0CCA and WB0CCA.
...
> >> hey Tauno, thanks for stimulating some 40 year old synapses that i
> >> didn't realize i still had.
>
> >> geez, i'm getting old.
>
> > In the sixties, I dreamed of big Eimac tubes. I still
> > have a linear with a pair of Eimac 3-500Z's.
>
> Speaking of forced air and special sockets, I still have a 4X150A in the
> attic.

dunno what the 4X150A is but i remember the 3-500Z.  it was the
classic old glass envelope 500 W triode (usually in grounded grid, it
seemed very weird to me that the driver was connected to the cathode
filaments, there was no separate heater and cathode, still seems
weird).  Heathkit had a linear amp with a pair of them (don't remember
the model number, but it matched their SB-102 SSB transceiver, it was
green).  these were really common in ham linear amps.

what was the *cutting* edge back then was the Signal One CX7 which had
nixie tubes for a digital readout and some other digital circuitry.
other than the power amp tubes in the back end (it might have been
Eimac heat-sink coupled tubes, can't remember), it was all solid
state.  cost more than \$2K and back around ca. 1970, \$2K was a lot of
money.  i lusted after that one too.  i also lusted after the Robot
Slow-Scan TV.  my H.S. chem/physics teacher had a nice Swan
transceiver (he was the person that administered my Novice and
Conditional Class Amateur license exams, i could barely get to 13
words/minute, but i did well on the theory test).

i could only afford a Heathkit HW-100 and a few ancillary thingies
(like the SWR meter).  i made a homemade end-fed long wire antenna
(earlier i had a center-fed dipole).   i wasn't the loudest kid on the
block.  i might have mentioned this before, but the informal phonetics
i used (instead of "W B zero Charlie Charlie Alpha") was "W B zero
Casselton's Commie Adolescent".  (the town i lived near was Casselton
ND.)

geez, memory lane.

r b-j
```