Lost in Translation

|1 + 0i] is the distance between (0,0) and (1,0), which is 1. Does this mean that |1 + 1i| is the distance between (0,0) and (1,1), which is the square root of 2? EDIT: Is the modulus |z| another way to say the length of the arrow?

Bold added by me. Im(b) does not produce an imaginary number. Rather, it takes a complex number with an imaginary component and returns the imaginary component. Here's an analogy. You have a bicycle. The bicycle has many components, e.g. handlebars, frame, pedals. chain, seat, tires, etc. We can store the bicycle as a variable called z. z = bicycle Now imagine we have a function called "frame." The "frame" function takes a whole bicycle and returns the frame component of it. frame(bicycle) return information on the frame component of this bicycle If we apply the "frame" function to the bicycle variable we might get something as follows: z = bicycle ("Extra-wide easy-grip handlebars", "Huffy Women's Beach Cruiser, #28, pink", "Ultra EZ pedals", "Tungsten chain", "Faux-Leather Extra-Soft Seat", "Double Knobby sand tires", etc.) frame(z) = "Huffy Women's Beach Cruiser, #28, pink" This function has not produced a bicycle frame. It has merely isolated the frame portion of the bicycle and returned information on it. So let's take this back to the complex numbers. We have a complex number in the format of "A + Bi", where A equals the X axis on a graph and B equals the Y axis. If we have a point on the graph (2,3), e.g. X=2, Y=3, then we can express this as 2 + 3i. z = 2 + 3i The function Re(z) isolates and returns the A portion, e.g. Re(z) = 2. The function Im(z) isolates and returns the B portion, e.g. Im(z) = 3. That's all Wandelaar has been saying to this point.

At the risk of getting political...

I'm still very interested! Imaginary numbers have always been my bete noir so anyone who can help me tame them is welcome.

Remember basic training? Brain off. Follow orders, quickly!

Ah, ha! So if we have a point (3,2) where X=3 and Y=2 then Given z = (3,2) Re(z) returns the 3 part and Im(z) returns the 2 part. It's syntactically the same as 3 +2i, just expressed in a different notation.

I don't want to put words in anyone's mouth but it seems we may need to back up slightly. In the above quote, Wandelaar is introducing something called a function, a very basic calculus concept. When he writes "Re(z)" what he is saying is that there is a function called "Re" that relates to a variable "z". I assume "Re" is short-hand for "Real." Similarly "Im" is probably short-hand for "Imaginary". What is a function, you ask? Well, it's basically an algorithm, a set of ordered steps that perform an action on an argument expressed as a variable. For example, let's make a function called "Christmas" that takes as an argument a variable called "child." This would look like this: Christmas(child). The definition of Christmas(child) could be something like follows: Christmas(child) if child is good then bring lots of presents otherwise bring a lump of coal There's nothing magical about functions. They are just a convenient way to encapsulate logic into a reusable component. I am sure that at some point Wandelaar will give a definition of the functions he has introduced.

The symbol "i" is a notation symbol. Check! Good to know. Not to be confused with an algebraic variable. Got it.

You've hit the nail on the head. I look around and I see a lot of pain. We feel pain when we fear for our future. We feel pain when we are jealous of others. We feel pain when we feel obligated to help someone in need. We feel pain when receive help but are then made to feel beholden. We feel pain when we are lost or confused. We feel pain. Hierarchy upon hierarchies. Stratum within strata. It's big and confusing and scary, and we're just small children trying our best to not get eaten when the wolf comes to the door. But the big bad wolf is always there. You can hear him breathing. We pretend he's not. If only we can pretend just a little bit harder... But pain has an upside. It's a motivator. It's a catalyst. It's a necessary ingredient in the process of inner awakening. It's alchemical in nature. But it is dangerous. It can kill. It can drive some men to become saints while dragging others to hell. Respect pain, but don't fear it.

Thank you for this. It's true that there is a lot of dark in this world, but there is also a lot of light. You can't have the one without the other. When I was young I was angry. I had this ideal of what the world should be and was pissed off that it wasn't. I ranted. I was sarcastic. I was a dick. In the end the only person who cared was me, and the only person suffering was me, so I made a choice. I chose to focus on me and let the rest go. I chose to become a little lighter, a little brighter, and in that small way make the world a little better. Yes, I still get angry, and yes I still lash out. But now I try to let go of anger as soon as I feel it. I try to apologize as soon as I've offended. Work in progress... Thank you, Rideforever, for this moment of honesty and intimacy. As others have said, you are in good company. -LiT

? Please continue your lesson. Even if few people today find benefit there are still untold people in the future who may find this fascinating.

Ah, but they DO know how to help themselves. They do this by playing the victim or the savior and demanding that you chip in, "pay your fair share", and the like. Do what you can. Maintain your center. Try to not get caught up in it. If all else fails then run for the hills.

2 + (-3i) or do you prefer 2 - 3i?

Finally, something I can get behind! That reminds me, I am all out of single malt...

technically, 20 + 20 == 40, yet the magnitude is square root ( 20 * 20 + 20 * 20) or square root (2 * 20 * 20) == 20 * square root (2) I never said that. You quoted a quote of Rideforever that I had quoted earlier. That's an issue with the software TDB uses. You're not the first person to do this...

I agree. This is the real question, isn't it? If we perceive our bodies (e.g. our bodies are a possession) then "we" must be something other than our bodies. I cannot refute this logic. By the same token what is to prevent our bodies from being able to perceive themselves? If we ever construct artificial intelligence it will surely notice that it exists. Will the AI suddenly claim to not be the code from which it was written but rather an observer of the code? That's actually an interesting question...

And what if it simply can't be known? What if our perceptions are all we have, and all we ever will have? We perceive we have bodies. That is very easy to do. It takes a lot of effort to force ourselves to perceive that we are disembodied perception. Maybe we are, I just don't know. I'm not refuting your line of reasoning, I'm just taking the Occam's Razor approach that the simplest solution is probably the best solution.

It seems this line of thought is simply substituting one body for another. Where formerly the "body" was made of flesh and blood, now the "body" is made of a kind of disembodied awareness. I fully appreciate this kind of pursuit and find value in it, but ultimately I don't think it solves the problem. If anything it creates a new problem, that of ego fragmentation, or if you prefer "soul loss." In my opinion it is the integration of flesh, mind, and soul that coupled with the acceptance that we live as all three that is the path to liberation.

I wholeheartedly agree. The ego hides behind the illusion that the ego is destroyed. saying "I want to have no ego" is like a man cutting off the branch upon which he sits. I have no answer to this.

Here's another experiment. Pick up a large rock - three or four pounds is sufficient. Hold the rock against your belly. Feel the essence of the rock, its ancientness, its nobility. Allow yourself to blend with the rock, become the rock. Now drop the rock on your foot. What is it that is screaming?

I have no problem with politicians not doing anything. In fact, I wish they did less! I'm happy knowing that they spend their days talking and having dinner parties and kissing babies, as long as they leave me the hell alone!

We use the language that is available to us.

I was watching MMK on TFC. I'm sure @Earl Grey knows what I'm talking about! Which reminds me, how close is the nearest Chicken Joy...?

I understand that, but even if you were limiting your definition of light to the electromagnetic spectrum the results would still be amazing!

You are correct. Perhaps I should have been more precise. Although the topic centers on manipulating X,Y coordinates on a graph I was speaking in general, algebraic terms.