Calling all brainiacs

[NA4BH]

You electrical engineer types, go take you a free course at MIT.

http://news.yahoo.com/blogs/technology-blog/college-cheap-course-mit-free-225905903.html

[N2RJ]

Listened/watched a lot of the lectures on iTunes. Really good stuff.

[W2NAP]

very interesting.

[W1GUH]

Calling all Brainiacs?

LIke this?

http://goodcomics.comicbookresources.com/wp-content/uploads/2006/12/Brainiac_K-30.jpg

[N1LAF]

http://www.comicbookmovie.com/images/users/uploads/10849/brainiac.jpg

[N1LAF]

http://media.comicvine.com/uploads/2/25810/477707-brainiac5dc_super.jpg

[NQ6U]

participants are expected to have a grasp of calculus, linear algebra, and advanced high school level physics.

So much for that.

[N1LAF]

Basic Electrical Engineering concepts...

Kirchoff current and voltage laws

1. Sum of voltages in a loop equals 0
2. Sum of currents at a node is 0

1. Voltage Law - Voltage Loop equals 0. Draw a battery with a light bulb across it. Draw the polarities across the battery and light bulb. Starting from the battery positive terminal, in a loop of the battery and light bulb, you have the '+' of the light bulb, then the '-' of the battery. +Vlightbulb - VBattery = 0

Vlightbulb = Vbattery

2. Current Law - Sum of currents at a node is 0. Rewritten, the sum of currents entering a node is equal to currents leaving the node. Example, two resistors tied togther at one end. The tie point is a node. Current flowing through R1 is the same as the current flowing through R2.

[N1LAF]

Impedance of Resistor is R, resistance.

Impedance of an inductor is Ls, where s = jw, and w = 2(pi)(frequency). Higher the frequency, higher the impedance.

Impedance of a capacitor is 1/(Cs), where s = jw, and w = 2(pi)(frequency). Higher the frequency, lower the impedance

[N1LAF]

Vout/Vin = Transfer Equation

Suppose we have a resistor between Vin and Vout, and a capacitor from Vout to ground. Vout load is very high impedance, infinite for practical purposes. Current through the resistor is (Vin-Vout)/R. This same current flows through the capacitor, which is Vout/(1/Cs), which also is VoutCs. Current in equals current out, and the load is infinite, so no current flow through Vout. From this we have the equation of current entering the node is equal to current leaving the node. (Vin-Vout)/R = Vout(Cs)

(Vin-Vout)/R = Vout(Cs)

Vin R - Vout R = Vout Cs

Vin R = Vout(R + Cs)

Vin = Vout (R+Cs)/R = Vout (1 + RCs)

Vout/Vin = 1/(1 + RCs), where s = jw = 2(pi)(f)

Decible = 10Log(Vout/Vin)

Corner frequency: -3dB

10 Log(0.5) = -3dB

Vout/Vin = 0.5 = 1/2

At corner frequency, (1 + RCs) = 2, RCs = 1

For RCs = 1, s = 1/RC, 2(pi)f = 1/RC

The corner frequency, fc, is equal to 1/(2RC(pi))

Here, in the equation, Vout/Vin = 1/(1+RCs), where s = 2(pi)f, as f increases, (1 + RCs) also increases, and 1/(1+RCs) will decrease.

This is an example of a low pass filter.

[suddenseer]

Are we going through the Advanced/Extra exams again? You came close to brushing the skin effect (ouch) I remember several questions on that subject on the First Radio telephony exam with microwave endorsement. About the only thing I did was weekly meter readings, and drive around and measure field strength at specific spots on the map to verify the pattern. I am proof one does not have to be smart, or a brainiac, just work off the ass studying.

[W1GUH]

Are we going through the Advanced/Extra exams again? You came close to brushing the skin effect (ouch) I remember several questions on that subject on the First Radio telephony exam with microwave endorsement. About the only thing I did was weekly meter readings, and drive around and measure field strength at specific spots on the map to verify the pattern. I am proof one does not have to be smart, or a brainiac, just work off the ass studying.

Bingo!

Want, or need, to do anything bad enough to keep on keepin' on...you'll get good at it! IMHO, the key ingredient of "talent."

[n2ize]

Basic Electrical Engineering concepts...

Kirchoff current and voltage laws

1. Sum of voltages in a loop equals 0
2. Sum of currents at a node is 0



But can you explain the underlying principle behind why this is true ? Can you explain it in terms of vector (energy) fields ? What can you say about such an energy field ? What is it represented by in mathematical terms. How would I know this if , let's say, I never heard of Kirchoff ?

[W1GUH]

OFMG!!!! Make it stop!!!!! Just kiddin' - fascinating stuff. Just reminds me of all-nighters doing those damnably difficult problem sets!

Then there's Circuits, Signals, and Systems....

Any arbitrary waveform is the sum of pure sin waves.:yuck::lol:

[suddenseer]

Meh, all one needs to know is break the circuit to measure DC current, put your test leads on the correct polarity. If you fry your company's meter, blame it on the janitor.

[KC2UGV]

I registered. Never hurts to get a cert from MIT.

[XE1/N5AL]

I registered. Never hurts to get a cert from MIT.Free courses from MIT! That Romney sure is a swell guy!

[KC2UGV]

Free courses! That Romney sure is a swell guy!

Um, MIT is a private institution... And, it didn't happen while Romney was sitting as a guest board member, either.

[N1LAF]

But can you explain the underlying principle behind why this is true ? Can you explain it in terms of vector (energy) fields ? What can you say about such an energy field ? What is it represented by in mathematical terms. How would I know this if , let's say, I never heard of Kirchoff ?

All your theory and equations are explained here, along with its limitations
http://en.wikipedia.org/wiki/Kirchhoff%27s_circuit_laws

[N1LAF]

OFMG!!!! Make it stop!!!!! Just kiddin' - fascinating stuff. Just reminds me of all-nighters doing those damnably difficult problem sets!

Then there's Circuits, Signals, and Systems....

Any arbitrary waveform is the sum of pure sin waves.:yuck::lol:

The square wave is the sum of all odd integer harmonic frequencies.
http://upload.wikimedia.org/wikipedia/en/math/d/c/1/dc1ca9de7f258a89d3c579f55d29ed05.png

[n2ize]

I've been using MIT's OCW as refresher courses for a few years now. It's a fantastic resource, complete with actual video lectures and recitations. Here is a listing of all the free courses offered.
http://ocw.mit.edu/courses/

[n2ize]

The square wave is the sum of all odd integer harmonic frequencies.
http://upload.wikimedia.org/wikipedia/en/math/d/c/1/dc1ca9de7f258a89d3c579f55d29ed05.png

Prove it..

[W1GUH]

Prove it..

Easy! A low-pass filter after a clipper removes spurious signals generated by the sharp edges in a clipped waveform!

[N1LAF]

Prove it..

Right here...
http://mathworld.wolfram.com/FourierSeriesSquareWave.html

Fourier Series:

http://mathworld.wolfram.com/images/equations/FourierSeriesSquareWave/NumberedEquation3.gif

[n2ize]

All your theory and equations are explained here, along with its limitations
http://en.wikipedia.org/wiki/Kirchhoff's_circuit_laws

What I meant is in the general case what mathematical property of a vector field is required in order for conservation of energy to apply to a closed loop ? It's an important property because it can be applied to not just electrical fields but any type of abstract conservative field or flow field. In short, instead of thinking of it in terms of a finite sum of discrete values along a closed loop (or even an open path) think of it in terms of a continuum. When we look at it this way it translates to the total amount of work done along a path or closed loop in two, three or even multi-dimensions). In short any vector field that is conservative is the gradient of some potential function... and the total work done along any path is simply the line integral along that path. But if the field is conservative, such as an electric field the line integral along a path = total work done along the path = the absolute value of the difference between the potential at the starting point of the path and the end point, i.e. f(P1)-f(p0)... So for a closed loop (path) the start point and end point are equal and we will always have f(p1) - f(p0) = 0. This holds for any conservative field (including an electrical energy field) in any number of dimensions and is the reason why Kirchoff's laws for circuits hold true and is also the reason why thus far perpetual motion machines have failed. It is also why the potential difference between any two points in a conservative (such as electrical) field is the same regardless of the path between those 2 points. The beauty of it is that it is the same underlying theory that unites these laws for different types of conservative energy (or flow) fields is the same.

[N1LAF]

I am more into the application than theory.

For example, you have a 12 VDC battery, and you connect four 3VDC light bulbs in series, and connect to the battery to light the light bulbs. The sum of all the voltage drops across the light bulbs is equal to the battery voltage - Kirchoff's Voltage law application. The current into the light bulb is equal to the current leaving the light bulb from then other terminal - Kirchoff's current law application

[n2ize]

I am more into the application than theory.

For example, you have a 12 VDC battery, and you connect four 3VDC light bulbs in series, and connect to the battery to light the light bulbs. The sum of all the voltage drops across the light bulbs is equal to the battery voltage - Kirchoff's Voltage law application. The current into the light bulb is equal to the current leaving the light bulb from then other terminal - Kirchoff's current law application

I'm interested in the underlying theory because it enables us to derive not just Kirchoff's laws but similar laws for any system involving conservative fields in any coordinate system. Which is important when delving into non-standard problems as well as understand from where Kirchoff's (and similar) laws come from and why they work.

This is an issue I had very early on when i was studying Physics in high school. It would drive me crazy when the teacher would just put up a formula on the blackboard and just tell me to plug in numbers to get a result. I couldn't stand just using a formula without understanding why it works and where it came from. I am the same way to date. I am not comfortable using a formula until I can see its derivation or prove its validity.

[W1GUH]

How do you tell if a black box is a Thevenin or Norton equivalent? Can't look inside, just play with the two output terminals.

[N1LAF]

How do you tell if a black box is a Thevenin or Norton equivalent? Can't look inside, just play with the two output terminals.

With both boxes unloaded, the Norton box will be warmer than the Thevenin box

When unloaded, the Thevenin is open circuit, the Norton has a parallel resistor with a current source.

Electrically, they are the same.

[N8YX]

With both boxes unloaded, the Norton box will be warmer than the Thevenin box

When unloaded, the Thevenin is open circuit, the Norton has a parallel resistor with a current source.

Electrically, they are the same.

One of them must be a Davemade. :yes:

[suddenseer]

With both boxes unloaded, the Norton box will be warmer than the Thevenin box

When unloaded, the Thevenin is open circuit, the Norton has a parallel resistor with a current source.

Electrically, they are the same.What about the box with the dead cat?

[WØTKX]

Don't look in that box, you'll affect the outcome...

[suddenseer]

Don't look in that box, you'll affect the outcome...I read Dancing Wu Li Masters as recommended by you, and Carlos. Wanna laugh? I already had a copy, it was in the box of books I ordered after my first divorce. I understand that stuff now, or is it another me?

[W2NAP]

What about the box with the dead cat? you end up with a box and a dead cat. if cat has been dead awhile. you end up with a smelly box, and a smelly dead cat

[n2ize]

One of them must be a Davemade. :yes:

How many pills ?

[W1GUH]

With both boxes unloaded, the Norton box will be warmer than the Thevenin box

When unloaded, the Thevenin is open circuit, the Norton has a parallel resistor with a current source.

Electrically, they are the same.

Aw, you knoew the answer!

OK...here's another one. Saw the solution once, it was very hairy. I believe it was a thesis at the 'tute.

Form the inverse of three logic signals. What you have available is an infinite supply of AND and OR gates, but only TWO inverters.

Ther IS a solution, but I don't know it. Might find web info by googling "Minimum complexity inversion problem."

[suddenseer]

Andor/nordor/neider/noredor.

[W1GUH]

And while we're on the subject.....one of my faves. Posted it before, but it's worth repeating (at least to yours truly.)

It's about AM detectors, diode and product.

Probably all of us completely understand diode detectors. They're pretty intuitive. The AM signal modulates the RF with an envelope that's the shape of the modulating signal, and if that RF signal is rectified and the RF is filtered out, voila! the original modulating signal. Very obvious graphically. Knew that from the very first crystal sets we made.

Then there's the product detector. Works because the product of multiplying two sine waves together contains two frequencies; the sum and difference of the two inputs. And following from that is the fact that if an AM signal is multiplied by a sine wave at the same frequency as the carrier, what you wind up with is and AM signal with a carrier frequency of 0, and the sidebands are the original audio.

The question is, what is the signals and systems connection between the two detectors?

Extra credit....

Did the first person to ever make a diode detector use systems theory, or was it obvious by inspection?

[N1LAF]

Aw, you knoew the answer!

OK...here's another one. Saw the solution once, it was very hairy. I believe it was a thesis at the 'tute.

Form the inverse of three logic signals. What you have available is an infinite supply of AND and OR gates, but only TWO inverters.

Ther IS a solution, but I don't know it. Might find web info by googling "Minimum complexity inversion problem."

I did find the solution, simulated it, and it does work.

x = a & b & c; // == three ones
y = a & b | a & c | b & c; // == at least two ones
z = a | b | c; // == at least single one

//Here are our 2 inverters
g = !(y); // zero or single one
h = !(x | g & z); //zero or two ones

x1 = g | h; //zero or single, or two ones
y1 = g; // zero or single one
z1 = g & h; // zero one
a1 = b & c & x1 | (b | c) & y1 | z1; //three zeros or ...
b1 = a & c & x1 | (a | c) & y1 | z1;
c1 = b & a & x1 | (b | a) & y1 | z1;

http://puliu.blogspot.com/2005/04/3-inv-by-two-inverters.html

[W1GUH]

Well, I'll be dammed! I'm sure you've check it out for validity. Much simpler solution than the one I saw 40 years ago!

Thanks, Paul.

[N1LAF]

http://paulfelgate.com/hamisland/Inv3use2.jpg

[W1GUH]

Argh!!!!! "He blinded me with Science!" ARGH!!!!!! Looks like work!

Thanks, Paul

[n2ize]

Well, I'll be dammed! I'm sure you've check it out for validity. Much simpler solution than the one I saw 40 years ago!

Thanks, Paul.

Actually it's a tricky but pretty straightforward Boolean algebra (logic) problem. Incidentally there is a way to test for existence of a solution(s).

[W1GUH]

No takers on the detector question?

[n2ize]

No takers on the detector question?

I'm not too familiar with "systems theory" in the specific context of electrical engineering. I am more familiar with it as an abstract theoretical concept.

The Boolean question was interesting. I should run an online tutorial or online class in Boolean algebra. I don;t know if anyone from this particular forum would be interested.

[W1GUH]

Thanks, John.

If you're a Boolean guru, and your words seem to say that, maybe you can add some information to this...

I once heard briefly that there can be Boolean algebras that have more than two values, but the number of values has to be a power of 2.

Ever hear anything about that?

[n2ize]

Most definitely arises in the context of Boolean algebras. In terms of a finite Boolean algebra the arity the number of n-ary operations is a power of 2 and there will always be 2 to the nth power possible argument values for each n-ary operation. Thus for a 0-ary operator there are 2^1=2 possible 0-ary operators. For a 1-ary (unary) there are 2^2 = 4 possible operations including negation (NOT), identity operator, and constant operators. For 2-ary (binary) there are 4^2=16 operations for 3-ary (ternary) there are 16^2= 256, for 4-ary there are 256^2, etc. Likewise there are correspondingly 2^0, 2^1, 2^2, 2^3, 2^4 for possible arguments.

More here

http://en.wikipedia.org/wiki/Switching_function


I am not a guru of Boolean algebra which is why I would love to do an online class or study group to first consider the basics and then tackle more advanced and challenging examples.

[ab1ga]

The question is, what is the signals and systems connection between the two detectors?


Applying an AM signal to a diode detector is equivalent to multiplying it with a raised square wave at the carrier frequency?

[W1GUH]

Applying an AM signal to a diode detector is equivalent to multiplying it with a raised square wave at the carrier frequency?

Bingo! Give that man an R.G. Dunn!

I wonder if an answer to the "extra credit" is actually knowable, e.g. was the diode detector invented though systems/signals analysis, or by gut inspection?

Thinl I'll go and bone up on the history of this. It'd be fascinating to see how AM was actually invented. Any reading suggestions?

[W1GUH]

Most definitely arises in the context of Boolean algebras. In terms of a finite Boolean algebra the arity the number of n-ary operations is a power of 2 and there will always be 2 to the nth power possible argument values for each n-ary operation. Thus for a 0-ary operator there are 2^1=2 possible 0-ary operators. For a 1-ary (unary) there are 2^2 = 4 possible operations including negation (NOT), identity operator, and constant operators. For 2-ary (binary) there are 4^2=16 operations for 3-ary (ternary) there are 16^2= 256, for 4-ary there are 256^2, etc. Likewise there are correspondingly 2^0, 2^1, 2^2, 2^3, 2^4 for possible arguments.

More here

http://en.wikipedia.org/wiki/Switching_function


I am not a guru of Boolean algebra which is why I would love to do an online class or study group to first consider the basics and then tackle more advanced and challenging examples.

Thanks, John. Thinking about what those "extra operations" could be is starting to make my head spin!

Guess it would be unique ways to combine the different values.

Wonder if anyone's working on making this practical. Would a computer that uses a four value Boolean algebra be more efficient than our usual, run-of-the-mill 2 value?

Maybe I'll apply for a government grant to study this issue!

[NQ6U]

I wonder if an answer to the "extra credit" is actually knowable, e.g. was the diode detector invented though systems/signals analysis, or by gut inspection?

It was the result of a systematic investigation by one Jagadish Chandra Bose (http://en.wikipedia.org/wiki/Jagadish_Chandra_Bose). From the Wikipedia:


J.C. Bose was the first physicist who began an examination of inorganic matter (metals and certain rocks) in the same way as a biologist examines a muscle or a nerve. He subjected metals to various kinds of stimulus—mechanical, thermal, chemical, and electrical. He found that all sorts of stimulus produce an excitatory change in them. And this excitation sometimes expresses itself in a visible change of form and sometimes not; but the disturbance produced by the stimulus always exhibits itself in an electric response.

[n2ize]

Thanks, John. Thinking about what those "extra operations" could be is starting to make my head spin!

Guess it would be unique ways to combine the different values.

Wonder if anyone's working on making this practical. Would a computer that uses a four value Boolean algebra be more efficient than our usual, run-of-the-mill 2 value?

Maybe I'll apply for a government grant to study this issue!

Boolean algebra is an algebra of 2 values, namely 0 and 1 or, used in electronics on/off, true/false, bits, etc. Nonetheless it is based on the set {0,1} upon which various operations are defined i.e. (AND ^) (OR V), (NOT ~), etc. Of course the operations will work on other values comprised of 0 and 1, i.e. bit vectors so for instance A = (1,1,0,0) and B = (1,0,1,0) =>
A^B = (1,1,0,0) ^ (1,0,1,0) = (1,0,0,0)...
and we can make infinitely many combinations of values and combinations of operations.


Would a computer that uses a four value Boolean algebra be more efficient than our usual, run-of-the-mill 2 value?

. Yes, we could used for example a 3 or 4 (or more) value (voltage) logic based on say, {0,1,2} or {0,1,2,3} and we could build a computer based on such a logic system but, will it be more efficient ? Not necessarily since adding more voltage states within an electronic device not only adds to overall complexity but can make the process of differentiating between signal and noise more difficult since we would have an increased number of "states" to detect and deal with. I believe these are among the reasons why they settled on a 2 value logic. Plus it is easy, on off. 0 volts & 1 volt, etc.

[kb2vxa]

"...was the diode detector invented though systems/signals analysis, or by gut inspection?"
Neither, Edison didn't know what to do with it but De Forest did.

[W1GUH]

Boolean algebra is an algebra of 2 values, namely 0 and 1 or, used in electronics on/off, true/false, bits, etc. Nonetheless it is based on the set {0,1} upon which various operations are defined i.e. (AND ^) (OR V), (NOT ~), etc. Of course the operations will work on other values comprised of 0 and 1, i.e. bit vectors so for instance A = (1,1,0,0) and B = (1,0,1,0) =>
A^B = (1,1,0,0) ^ (1,0,1,0) = (1,0,0,0)...
and we can make infinitely many combinations of values and combinations of operations.



. Yes, we could used for example a 3 or 4 (or more) value (voltage) logic based on say, {0,1,2} or {0,1,2,3} and we could build a computer based on such a logic system but, will it be more efficient ? Not necessarily since adding more voltage states within an electronic device not only adds to overall complexity but can make the process of differentiating between signal and noise more difficult since we would have an increased number of "states" to deal with.

(facetious) ->> Gotcha!!!! Couldn't BE 3 values if it was truly using a boolean algebra! <--- You KNOW I'm just bustin'!

All you say about the question of efficiency are certainly hindrances, but they're pretty much practical, engineering issues to deal with, and it could be that, if a processor that uses a four value system built as a research project demonstrates that it could be the next Big Breakthrough in computer power, you can bet those engineering issues would be solved & the technology would eventually be as commonplace and humdrum as our traditional 2 value hardware.

As a concrete example of potential efficiency gains, An architecture where each "bit" represents four values instead of just 2 would result in narrower buses. And say, for argument's sake that the logic for each of those "super-bits" was developed to the state that 2 value silicon is now*....would that not be a significant effeciency gain?

*Or close. Say, the individual elements occupy an area that results in more power/area than the two value architecture.

But that's the key, isn't it? What potential efficiencies would going to such an architecture yield, if any? Sounds like some time spent with google-fu! Wonder if there's someone in academia out there doing a Ph D thesis on this? Or some guy in his garage/basement?

[n2ize]

;408353](facetious) ->> Gotcha!!!! Couldn't BE 3 values if it was truly using a boolean algebra! <--- You KNOW I'm just bustin'!

It depends. In simplest terms a binary boolean algebra is a set A on which we define binary (^ & V) & unary operations such that a set of axioms are satisfied. But... what about ternary, quaterny algebras ? And the degenerate (trivial) boolean algebra.



All you say about the question of efficiency are certainly hindrances, but they're pretty much practical, engineering issues to deal with, and it could be that, if a processor that uses a four value system built as a research project demonstrates that it could be the next Big Breakthrough in computer power, you can bet those engineering issues would be solved & the technology would eventually be as commonplace and humdrum as our traditional 2 value hardware.

Are you referring to a ternary or quaternary computer as described here. Just want to make sure we are thinking on the same page.

http://en.wikipedia.org/wiki/Ternary_computer

[suddenseer]

I seem to have nothing but reluctance at this point.

[KC2UGV]

...clip...
Yes, we could used for example a 3 or 4 (or more) value (voltage) logic based on say, {0,1,2} or {0,1,2,3} and we could build a computer based on such a logic system but, will it be more efficient ? Not necessarily since adding more voltage states within an electronic device not only adds to overall complexity but can make the process of differentiating between signal and noise more difficult since we would have an increased number of "states" to detect and deal with. I believe these are among the reasons why they settled on a 2 value logic. Plus it is easy, on off. 0 volts & 1 volt, etc.

Enter, Quantum computing... :)

[WV6Z]

I seem to have nothing but reluctance at this point.

Also glad to report that I was drinking beer and getting laid rather than plodding through this faggotry when I was a teen.

[n2ize]

Enter, Quantum computing... :)

^^^ Yes !

[NQ6U]

I seem to have nothing but reluctance at this point.

And resistance, which is futile.

[W1GUH]

Also glad to report that I was drinking beer and getting laid rather than plodding through this faggotry when I was a teen.

Touche'! Guess this topic brought out my inner geek. Must confess the whole subject of computational efficiency fascinates me -- must after the regurtitaion....no...this was a straight puke, hurl, spew!

Thanks for the slap in the face -- I really, really needed it!

[W1GUH]

[QUOTE=W1GUH

It depends. In simplest terms a binary boolean algebra is a set A on which we define binary (^ & V) & unary operations such that a set of axioms are satisfied. But... what about ternary, quaterny algebras ? And the degenerate (trivial) boolean algebra.




Are you referring to a ternary or quaternary computer as described here. Just want to make sure we are thinking on the same page.

http://en.wikipedia.org/wiki/Ternary_computer

Not talking about any specific "whatever" -- don't even understand why you ask that question, except possibly to maintian your legendary obtuseness & unwillingness to talk specifics about concrete ideas?

Just sayin' that the difficulties about implementing the hardware would probably be very well understood and probably not be a major impediment to developing a machine using a higher-order (if that's not the correct word, mil pardon!) boolean algebra if it was shown that there was a decent probability of realizing major efficiency gains.

As for your first point, I don't even know WTF you're talking about. Earlier, you asserted, in response to my query, that a boolean algebra must have 2 **n values...then you back off. Felling slippery?

I'd say that, to gain maximum efficiency gains and to be robust with no inconsistencies, this postulated machine would necessarily use a "complete" boolean algebra.

UNLESS some researcher finds an incomplete algebra that DOES yield the desired effieincy gains while avoiding possible difficulties in using a complete algebra.

[n2ize]

[QUOTE=n2ize;408371]

Not talking about any specific "whatever" -- don't even understand why you ask that question, except possibly to maintian your legendary obtuseness & unwillingness to talk specifics about concrete ideas?

How can we talk about anything in concrete terms when you refuse to acknowledge what type of engineering marvel you are trying to describe ? You mentioned a 3 or 4 element computer or something along those lines but you don't want to be more specific as to what type of device you are referring to or envisioning. Are you refering to a ternary or quaternary computer that used 3 or 4 voltages or signals i.e {0,1,2,3} ? or one that uses {0 1} ?


Just sayin' that the difficulties about implementing the hardware would probably be very well understood and probably not be a major impediment to developing a machine using a higher-order (if that's not the correct word, mil pardon!) boolean algebra if it was shown that there was a decent probability of realizing major efficiency gains.

There are different schools of thought in this arena. There are those who have proposed > 2 bit computing models and such models have even been constructed long before electronics was even invented. many ideas are geared towards faster processing speeds, quantum computing, etc. No doubt we will see new breakthroughs in these areas of active research.


As for your first point, I don't even know WTF you're talking about.

Fundamentally an "algebra" is a set of operations on elements of a set S such that certain rules defining the algebra are satisfied. The set S can be almost anything, i.e, integers, real numbers, a set of sets, sets of n-tupes i.e. (x1,x2, x3,...xn) which is the basis of Linear algebra, or , in the case of the boolean S= {0,1} on which we apply the set properties of union ^, intersection v , and complementary ~ or 1-X.



Earlier, you asserted, in response to my query, that a boolean algebra must have 2 **n values...then you back off. Felling slippery?

Not backing off. What a said before applies to operations, i.e. 2^(2^1) unary operators 2^(2^2) binary, 2^(2^3) ternary, ...,2^(2^n) n-ary operators and 2^n argument for an operation of arity n For example there are 2^(2^1) = 4 unary operations, f(1)=0, f(0) = 1 (negation) and f(1)=1, f(0)=0 (identity) and 2^1 arguments 0 and 1.



I'd say that, to gain maximum efficiency gains and to be robust with no inconsistencies, this postulated machine would necessarily use a "complete" boolean algebra.
UNLESS some researcher finds an incomplete algebra that DOES yield the desired effieincy gains while avoiding possible difficulties in using a complete algebra.

"Completeness" in a purely algebraic context is mainly derived from specific set bounding properties and the subsequent completion of specifically defined axiomatic properties. As far as building a functional machine, either in theory of practically the underlying abstraction should have enough "completeness" (so to speak) as to allow for the desired functionality. It's, for lack of a better term, a "signal to noise" issue.

[KA9MOT]

I signed up! Thanks Bob!

[K7SGJ]

http://paulfelgate.com/hamisland/Inv3use2.jpg

It's not that I'm completely stupid. In this case a wee bit slow, But I am keeping up to this point, so far. I think have a good handle on everything except for one thing. Are the good guys the green or the brown?