OldDog

Sunday morning jazz ...

I get it ... the definition. So, other than the precise mathematical definition, there is no other significance to actual arg(z) value ... no practical meaning other than within the realm of mathematics. This takes me back to my college days where I just had to accept that learning how to play the game ... apply the rules and manipulate the objects ... and not worry about practical application. At the start of this thread there was a suggestion ... implied perhaps ... that there might be some insight to be gained about Daoism by understanding complex numbers. Do you see a connection? If so, can you elucidate?

OK, I see the definition. But why is that angle any more significant than its supplement?

I assumed we were talking about the triangle you described above. The angle of interest was the angle formed by the two adjacent sides with the common point (0,0). The other angle is the supplement of the angle I calculated. So ... 180 - 33.7 = 146.3 deg and 146.3 * 0.0175 = 2.56 rad But, now that you mention it, please explain the significance of the supplementary angle to this discussion.

Oops, forgot radians 33.7 deg = 0.559 rads ... where 1 deg = 0.0175 radians

Sorry, back. Got busy today. OK, since standard math is allowed |z| = sqrt (a*a + b*b) = sqrt (13) = 3.606 and Arg(z) = sin-1(2/3.606) = sin-1(0.555) = 33.7 deg More or less. Guess I thought we could only use methods disclosed in discussion.

Well, I thought about Pythagoras but for some reason felt like standard math, geometry, etc was not legal in this discussion. Similarly could resort to trig functions to get degrees of angle and then resort to some sort of conversion formula to convert to radians. But again, I am not sure what's allowable and what is not. Have we firmly established that standard math is applicable to non-real numbers?

OK, I'll give it a shot ... Starting point (0,0) Endpoint (-3,2) Real part Re(z) = -3 Imaginary part Im(z) = 2 Modulus |z| = |a + bi| = |-3 + 2i| = sqrt of (-3 + 2) = sqrt of (-1) ... and we all know what that means. Did you do this on purpose or did I take a wrong turn? Argument arg(z) ... alas I am at a loss here. Don't know how to calc an actual value in radians.

Most other translators render these opening lines rather mysteriously ... or should I say mystically ... know without knowing. Lok tells you how this is done ... by way of comprehending the universal truth. Grasping the universal truth when you hear about things you see how things are as they are, how things came about. Sounds a lot like Ni Hua Ching.

I am feeling very poetic this morning. So Hinton's rendering has great appeal. In the Ho-Shang Kung Commentary, Dan Reid translates the idea of contentment as knowing sufficiency; misfortune as not recognizing sufficiency.

In one sense the writing is poetic, as RF points out, but poetry itself is often paradoxical because by design it is trying to point to something that cannot be adequately expressed. RF's reflections are poetic and paradoxical themselves, seeking examples of great accomplisment and fullness in his own experience. Whether we understand that or not seems vague and the real meaning elusive. Great eloquence seems awkward. Understanding this we seek refuge what is simple and natural intuitively realizing that from the point of view of the great scheme of things ideas of greatness and value breakdown. That which is considered great may not be so great; that which is common and simple may be of real value.

Yeah, I am not conversant in radians but I looked it up and understsnd the concept. I can visualize degrees but not radians very well except 6 radians is nust short of a circle.

Sorry to see Marblehead go. I'll stick with it for a while. Still confused over what exactly i is. And, no, have never used radians before ... just degrees.

I am used to the term argument meaning something that is passed to the function when it is called ... a la software function. Are you saying the angle is passed to the function arg(z) or that it returns the value of the angle when called?

Got it. But seems like we have defined everything but the i component. I mean everything except the i component can be accounted for in standard (real) math ... arithmetic, geometry, algebra. Still don't understand much about i other than we call it imaginary or nonreal. At this point I don't think trying to perform operations on non-real/imaginary/complex numbers is going to inform much. I'll hide n watch.

Now that'll be interesting. A 3D plot on a two dimensional surface ... i.e. tablet. Sure that won't add to the confusion? Back later ... errands to run.

OK. I don't think we really answered your question about resolving the modulus of 1+ 0i ... which as I understand it would be the square root of 1 .. or 1.

Does this mean that any point on an coordinate system where the X and Y axis are real can be expressed with an imaginary (i) component?

Good analogy. So, we are to think of Im(b) as a function that operates on b and produces an imaginary value. This value can be paired with Re(a) to identify a point on a Cartesian coordinate system, where X axis is real and Y axis is real?

Hold on ... I need to get a rock for my left hand. Of course, it's only an imaginary rock.

Is he? I did not get that. Pretty familiar with the notation f(x) where f is a placeholder for whatever kind of function we might be talking about. The use of f(x) simply reminds us that we are talking about a function. I don't think that is what Wandelaar is saying. I think he adopted the notation Im(z) because I/we seemed to be struggling with the notstion i. Now, if I am wrong about this ... then I am still out in the hinterland.

I know you are. My laughter was at the turn of the phrase " OldDogian number system" Not laughing at you ... more with you. Apologies! Still chuckling though.

I'm sorry, Wandelaar. I am not really trying to be obtuse. Just trying to develop a frame of reference for thinking about this. I honestly thought we had established that the Y axis was not real. Seems I leapt to a wrong conclusion. So, X and Y axis are both real. So you are saying that on this plane defined by real X and Y coordinates there exist points that can be located by real (x,y) positions but they have some other (imaginary) attribute other than their real position. Did I get that right? Asking questions is really the only way to test my understanding.

Well, you have not ruled out that there can be another starting point other than (0,0) ... you seem to have deferred discussion. If there can be some other starting point on a coordinate system described by X being real and Y not being real, then that point must be of the form Re(z),Im(z), right ... consistency, right?

Yeah, thanks LT for stating that. I had always considered it like and undefined-variable. Maybe that is what has contributed to my confusion. Gonna take a bit of time for that to sink in.