Class @ MindSay

When we have a line in the old XY plane, we know it by knowing one of its points and then its direction, or slope. The same holds true here. Suppose we have two vectors, r and r₀. These will be the position vectors of points P and P₀, that is, r is the vector from the origin to P, and r₀ is the vector from the origin to P₀. Now, suppose that a new vector a is the vector from P₀ to P, or from the end of r₀ to r. The triangle law gives us that r = r₀ + a.

Now. Let's suppose that we're looking for some line L, and we'll let some vector v be parallel to this line L, and now let's also suppose that a is inside of L, that is, at some point, r and r₀ end at random points on L, and the part of L that lies inside this "boundary" is a. Because v || a and v || L (|| means "is parallel to"), then we can say that a = tv, that is, some scalar t times the vector v gives us the same magnitude as a.

We replace a with tv, then, and we have r = r₀ + tv. This is our equation for the vector of L. We call this a vector equation of L. Our parameter is t. Now, let's give some values to these vectors.

We'll say v = <a,b,c>, then tv = <ta,tb,tc>, and we'll say r <x,y,z>= and r₀ = <x₀, y₀, z₀>. Our vector equation then becomes

<x,y,z> = <x₀ + ta, y₀ + tb, z₀ + tc>. Because L and a are parallel, then their corresponding components are equal.

This means that we have three scalar equations:

x = x₀ + at
y = y₀ + bt
z = z₀ + ct

And these are our parametric equations (see Chapter 11 for more info).

Now, wtf? Let's give a quick example here.

Suppose we have some P₀ = (1,1,1) and we start at the origin, and we want to find the vector parallel to i + j + k. We have r₀ = <1,1,1> and v = <1,1,1>, so we multiply v by t to get , and then we simply add up tthe components: x = x₀ + at = 1 + t, y = y₀ + bt = 1 + t, z = z₀ + ct = 1 + t. Thus, our new r is now <1 + t, 1 + t, 1 + t>. Bam. And by plugging in a new t, say, t = 3, then we can find all the new points on this vector r, like (4,4,4) in our case of t = 3. It's simple. You are given P₀ and v, and you find r.

Now, what if we don't like the parameter t? Let's get rid of it! To do so, we must assume that a,b,c =/= 0, and then we solve each of those scalar equations for t. This gives us

t = (x - x₀)/a = (y - y₀)/b = (z - z₀)/c. These are called symmetric equations. We employ these when we are GIVEN both P and P₀, allowing us to find r and r₀ and thus v (which is r - r₀). This is very useful later when we are trying to find where L intersects various planes and, ultimately, when we need to find some boundary conditions for when we'll apply calculus later on.

Now, if only ONE of a,b,c = 0, then we can still eliminate t in the same way, and we simply remove the entire part of the equation where the letter = 0. Suppose b = 0. Then we just say y = y₀, and that leaves us with the x and z parts equal each other still. This also implies our line lies in vertical or horizontal planes, which can simplify things just a wee bit.

Anyway, usually, we don't care about entire lines. We only wanna know what's going on in a piece of the line. We can do this very simply.

We know that r = r₀ + tv, and we know v = r₁ - r₀. We just substitute back in--r = r₀ + t(r₁ - r₀), and we have

r = (1 - t)r₀ + tr₁, where 0 < t < 1. r₁, by the way, is the same as r, except we've narrowed it a bit to just be from 0-1 for t. This lets us describe a tiny piece of the line and ignore the dumb crap beyond our parameter.

And so, we have all our equations for solving for lines. Now we just have one more little geometric concept. In the XY axes, you knew two lines existed: intersecting lines and parallel lines. All lines either were parallel or they intersected at some point way off in space. In 3-D, there is a third kind of line called a skew line. Skew lines do not intersect and they are not parallel. The easiest way to look at this is by having two people side by side in the middle of a platform on a staircase, where the stairs run up and down from this platform. One runes up, the other runs down. They will never hit each other 'cuz they're to each others' right and left, and they aren't going in the same direction at ALL. Skew lines work like this.

Now for some PLANES! This is not a separate topic. It builds straight from the lines we've just talked about.

So, we have this vector a which is formed by r - r₀. What we want to do now is try and describe a plane it will be located it in. More specifically, we're interested in the direction of this plane. Is it flat, is it slanted, if so what's its slope, etc. To do that, we need our arbitrary point P₀ on the plane and then we need something called the normal vector. We define as n, and it is simply the orthogonal (perpendicular) vector to the plane itself. That is, if you have a plane (like a sheet of paper) lying flat horizontally, n points straight up. If it's vertical, n points to the right or something.

Because n is orthogonal to our vector a, we say that n · a = 0. a = r - r₀, so n · (r - r₀) = 0. But we should just rewrite that as this--

n · r = n · r₀. This is called the vector equation of a plane.

But vectors are often a bit confusing to deal with, so we oftentimes want a scalar representation. To do that, we simply replace n with , r with , and r₀ with ₀, y₀, z₀>. This gives us

· ₀, y - y₀, z - z₀> which can be rewritten as

a(x - x₀) + b(y - y₀) + c(z - z₀) = 0. This is the scalar equation of the plane.

If we collect all the terms together, we can rewrite this one step further as

ax + by + cz + d = 0, where d = -(ax₀ + by₀ + cz₀), and this is called the linear equation in xyz.

Now for a stupid little property. Two planes are parallel if their normal vectors are parallel. It makes sense if you draw it. If two normal vectors are pointing straight up, they are parallel, and this means that their planes lie flat on the ground (like a sheet of paper), which makes them parallel to each other. However, we don't really care too much about planes being parallel, and we're instead curious about planes that aren't parallel. We want to find the angle between them. To do so, we consider only their normal vectors, and it's simply the dot product equation. That is,

cos = (n₁ · n₂) / (||n₁|| ||n₂||).

Another thing that is useful is figuring out the line of intersection. When two lines intersect, they intersect at a point. Well, when two planes intersect, they intersect at a line. This will be line L, and to find line L, we simply go back up to the beginning of this section, and we find some vector v parallel to this line L. To find v, we simply take the cross product of the two normal vectors. Thus,

v = n₁ x n₂.

We can then apply symmetry equations and other things to figure out the overall equation of the line or points on it.

Lastly, suppose we have a random point P₁ in space and we want to know the distance between it and our plane. To do that, we need our P₀ and our normal vector. If we draw it, we can force P₁ to lie on n, and then P₀ lies anywhere on the plane, and all three are connected to make a triangle. By doing so, we see that the distance D is simply the scalar projection of b onto n, where b is the vector from P₀ to P₁. Thus,

D = |comp_nb| = (|n · b|) / ||n||.

We can rewrite this...

D = (|a(x₁ - x₀) + b(y₁ - y₀) + c(z₁ - z₀)|) / Sqrt(a² + b² + c²) , we distribute the a,b,c and regroup according to 0s and 1s:

D = (|(ax₁ + by₁ + cz₁) - (ax₀ + by₀ + cz₀)|) / Sqrt(a² + b² + c²) , we recognize that all the 0th terms are actual points, and so they're given, and so we can rewrite the entire 0th part as some constant d:

D = (|ax₁ + by₁ + cz₁ + d|) / Sqrt(a² + b² + c²)

And that's it! Now let's work some examples!!

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1) Find a vector equation and parametric equations for the line through point (1,0,-3) and parallel to the vector 2i - 4j + 5k.

This is easy. r = r₀ + tv. v is 2i - 4j + 5k = <2,-4,5> and r₀ = <1,0,-3>. tv = <2t, -4t, 5t>, so now we just add to get r = <2t + 1, -4t, 5t - 3>. The vector equation then is r = (2t + 1)i + (-4t)j + (5t - 3)k.

The parametric equations are x = 2t + 1, y = -4t, and z = 5t - 3.

2)  Find the distance from the point (2,8,5) to the given plane x - 2y - 2z = 1.

It's the last formula.  D = |ax₁ + by₁ + cz₁ + d| / sqrt(a² + b² + c²).  Here we have a = 1, b = -2, c = -2, d = -1 (from the plane), x1 = 2, y1 = 8, z1 = 5 (from the given point).

So, we just plug in.  D = |1*2 + -2*8 + -2*5 + -1| / sqrt(1² + (-2)² + (-2)²) = |2 - 16 - 10 - 1| / sqrt(1 + 4 + 4) = |-25| / sqrt(9) = 5/3.

3)  Find the angle between the planes x + y + z = 0 and x + 2y + 3z = 1.

We'll call the normal vectors of these n1 = <1,1,1> and n2 = <1,2,3>.  Then the cos(θ) = (n1 · n2) / (|n1|*|n2|)

That we just plug in things.  n1 . n2 = 1*1 + 1*2 + 1*3 = 1 + 2 + 3 = 6.  |n1| = sqrt(1² + 1² + 1²) = sqrt(1 + 1 + 1) = sqrt(3).  |n2| = sqrt(1² + 2² + 3²) = sqrt(1 + 4 + 9) = sqrt(14).  sqrt(3)*sqrt(14) = sqrt(42).

So, cos(θ) = 6/sqrt(42), then θ = cos^-1(6/sqrt(42)) = 0.3876 radians.

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Why do you care?

Trajectory from impact is very important from this as an example I can immediately think of.  Magnetic fields are what I'm getting at.  You may induce a magnetic field such that it creates a "magnetic plane" over an area, and you'll have a particle between two of these planes cocked at an angle and such that the particle is also charged and is SUPPOSED to move around, but you don't want it touching the planes or any sort of wall.  But you need to keep that magnetic field to induce electrical current.  Drafting equations gives us an application of magnetic force, then.

For those of us building large skyscrapers in cities that are already polluted with very high buildings and have to deal with winds (looking at you, Chicago), this is also fairly important because it's a good idea to know the distance between X point on building A and Y point on building B (where X and Y are defined because these will deal with maximal wind shear, vorteces, whatever the problem is), and sometimes this location will fluctuate a little depending on the time of year, so you can't just simply take one measurement and be done, but taking the measurements of the "vectors" of the buildings (basically, the height) gives you a sort of "blueprint" any time you need to measure forces of "wind interaction" between the two buildings at ANY point on either building.

And wind can change its nature after dealing with an obstruction, like Building B.

So, we've seen planes and spheres as far as surfaces go. Now we're gonna wrap up the surfaces with the last bit, starting with the simpler cylinders and then generalizing to all quadric surfaces.

Now, one thing you need to do is remove the idea that a cylinder is two circles connected. It's not. A cylinder is a surface that consists of all lines (or rulings) that are parallel to a given line and pass through a given plane curve.

If your given plane curve is a flat circle, and we take every line that can pass through it that is parallel to a given line perpendicular to the circle, you have your circle-based cylinder!

But consider this! Consider the graph of z = x². You draw your XYZ axis and notice that since the function z does not involve y at all, every line is parallel to the y axis and runs through the ENTIRE y axis. And then all you have left to determine is the shape of the graph, which, if you simply do an XZ plane where X is the horizontal, you see a parabola. Extending this infinitely through the y-axis, you get a shape that looks exactly like a folded piece of paper. This is called a parabolic cylinder.

So, you can clearly see cylinders don't even need to be closed!

If you have x² + y² = 1 through the XYZ, then you see it's a circular cylinder, the circle being on the XY plane and then going up and down infinitely, the circles' radii = 1. So, drawing your XYZ axis with Z pointing up, it's just a vertical, circular cylinder. On the other hand, y² + z² = 1 is a circular cylinder that goes in the direction of the X axis.

Now you should know what cylinders generally look like. Consider the parabolic cylinder example again. Mathematically, we are saying that any vertical plane with the equation y = k (parallel to the XZ plane) intersects the graph in a curve with an equation z = x².

And now that that's in your head, let's move on to the general quadric surface.

A quadric surface is the graph of any second-degree equation in three variables, and the most general form is

Ax² + By² + Cz² + Dxy + Eyz + Fxz + Gx + Hy + Iz + J = 0

where A,B,C,D,E,F,G,H,I,J are all constants.

This is gonna get kinda tricky to explain how to draw, so bear with me.

Usually, quadric surfaces can be rotated and translated about until they reach one of two standard forms:

Ax² + By² + Cz² + J = 0
Ax² + By² + Iz = 0

A note: they do not HAVE to be in THAT standard form. Look at them. You see all three variables x,y,z, and if they are all squared, a constant. The first one will always look like that, but the second could be Ax² + Cz² + Hy = 0 instead. Just so long as one variable is not squared.

In fact, there are six common shapes with formulas associated with them. Here they are--

ellipsoid: x²/a² + y²/b² + z²/c² = 1. All traces (we'll talk about traces in a moment) are ellipses. If a = b = c, then the ellipsoid is a sphere. Looks like a 3D ellipse.
elliptic paraboloid: z/c = x²/a² + y²/b². Horizontal traces are ellipses. Vertical traces are parabolas. Whatever variable is in the first power (in this case, z) indicates the axis (or direction) of the paraboloid. Looks like a rounded funnel.
cone: z²/c² = x²/a² + y²/b². Horizontal traces are ellipses. Vertical traces in the planes x = k, y = k are hyperbolas if k =/= 0, but pairs of lines if k = 0 (we'll discuss this "k" stuff later). Looks like two funnels attached at the tiny ends.
hyperboloid of one sheet: x²/a² + y²/b² - z²/c² = 1. Horizontal traces are ellipses. Vertical traces are hyperbolas. Axis of symmetry corresponds to the variable whose coefficient is negative (goes in the direction of this axis). Looks like two lampshades attached at the smaller ends.
hyperboloid of two sheets: -x²/a² - y²/b² + z²/c² = 1. Horizontal traces in z = k are ellipses if k > c or k < -c. Vertical traces are hyperbolas. The two minus signs indicate two sheets. Looks like a bump down on the ground, and then you mirror this so you have an upside-down bump floating in the sky.
hyperbolic paraboloid: z/c = x²/a² - y²/b². Horizontal traces are hyperbolas. Vertical traces are parabolas. Has varying shapes (just Google Image this sucker).

Okay, wait. Where the hell did this "k" come from, and what are these "traces"? Well, first off, they're related so we hit them both in the same explanation. Second of all, we use them to actually determine how we would draw this sucker.

First off, let's talk about these "traces." Traces are our attempts at taking a 3D object and making it 2D at various angles. To be more specific, instead of graphing something in the XYZ space, we're going to graph something in the XY, YZ, and XZ planes. After that, it's up to our ability to "see in 3D" that will helps us connect these three planes into the 3D space.

Let's consider the surface z = y² - x². From our table, we can see this is a hyperbolic paraboloid, where a,b,c = 1 (the table says x - y, but our problem has y - x. This is okay because it basically means we're going in a different direction, is all. The hyperbolic paraboloid will just have one part negative in this format).

So, how do we draw this? First, we need to draw 3 planes: ZY (make Y the horizontal), ZX (make X the horizontal), and YX (make X the horizontal).

Now, let's start with the ZY plane. From z = y² - x², we need to get this in terms of ONLY z and y (since ZY plane does not care about x). This means we need to remove the x². Well, suppose x is no longer a variable, but is now some constant k. x = k, so x² = k², and we have z = y² - k². You should make the connection that this looks VERY similar to y = x² - c, which is a parabola. So, we're drawing parabolas, and we do so by picking arbitrary values for k. If k = 0, we have z = y². If k = 1, we have z = y² - 1. If k = 2, we have z = y² - 4, etc.

As you can tell, because it's k², no matter what value we put in, it will always turn negative because of the minus sign in front of the k². This means we only look at the parabolas whose z-intercepts are 0 and lower. So you draw them. These are called "traces in x = k."

Now, let's look at the ZX plane. We need to remove y such that we only have a function of z and x, and we do so by, again, letting y = k. This gives us z = k² - x². By letting k = anything, we see that these are upside-down (negative) parabolas whose Z intercepts now start with 0 and go to positive infinity, so we can draw them out just like we did the last one. And these are our traces in y = k.

Lastly, it's the YX plane. We gotta get rid of z, so we let z = k. This gives us k = y² - x². Suppose k = 0, then we have y² = x², or + y = + x. This is two lines (y = x, y = -x), so we draw out those two lines and basically make an X on our YX plane. Now, if we let k = 1, we get 1 = y² - x². Manipulating, we get x² = y² - 1, or +x = + sqrt(y² - 1), which is a hyperbola that opens up and down. By letting k = -1, we get the same thing, only this time the hyperbola opens left and right By continuing to change k, we get hyperbolas that keep filling up the space left in that plane, and these are our traces in z = k.

Now, the hard part is trying to put this all together in the XYZ space. First, you definitely need to draw the XYZ axes. Now, taking one at a time, say, starting with x = k, you need to sort of "lightly draw" each parabola. In the 2D traces, you drew parabolas above and under each other because k changed the z-intercepts. Here, you'll also be changing the front-back (assuming you draw a standard XYZ axis system, where X points front and back) to accommodate x = k. It's not really THAT hard. You know how to T Table stuff: plug stuff in for, say, X, and then plug something in for Y and find Z, and just keep doing this.

Doing the same for the y = k traces, you simply also account for left-right (assuming standard XYZ coordinates where the Y axis goes left and right) changes, too, as y changes with k.

And then you do the same for the z = k traces, accounting for up-down movement as z changes (standard XYZ coordinates have Z axis going up-down).

And then you can MAYBE see the picture.

In all seriousness, you will probably never be asked to manually graph such an oblique shape. It's really too complicated. Ellipsoids, spheres, cones, and paraboloids are easy, but hyperbolic paraboloids are really just ugly looking when trying to do them manually. You will probably only graph them in software (like Mathematica, MathCAD, MATLAB, etc.), but you will most likely be expected to graph the traces. And, really, that's the important part. As long as you can see what's going on in each of the planes, that's more important than seeing the overall picture because in physical analysis, you will be a LOT more concerned with 2D mappings than you will ever be with the entire 3D object. So this is fine for those of us who can't think in 3D (I know I can't....).

So, let's do some problems.

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1) a. What does the equation y = x² represent as a curve in R²? It represents a parabola whose absolute minimum is 0 and has an infinite domain.
b. What does it represent as a surface in R³? It represents a parabolic cylinder whose absolute minimum is 0 and infinitely extends along the Z-axis, opening in the positive Y direction.
c. What does the equation z = y² represent? In 2D, this represents a parabola whose absolute minimum is 0 and has an infinite domain on the ZY plane. In 3D, it represents another parabolic cylinder whose absolute minimum is 0 and infinitely extends along the X-axis, opening in the positive Z direction.

2) Reduce the equation to one of the standard forms and classify the surface: 4y² + z² - x - 16y - 4z + 20 = 0.

Oh, boy. Well, first, let's group things up and move that 20 out of the way: 4y² - 16y + z² - 4z - x = -20.

Now, let's complete the square for the y. We look at 4y² - 16y. We pull out the 4, 4(y² - 4y), take half the coefficient of the one-degree term, 4/2 = 2, then square this, 2² = 4, and we put that back in there and add to both sides of the equation.

4(y² - 4y + 4) = -20 + 16 (we're ignoring the z and x parts for now, and it's +16 because of that 4*4 on the left side). That gives us 4((y - 2)²) = -4.

Now we gotta do the same thing for z² - 4z, which actually turns out to be the very same except we don't have to deal with the obscure 4, so we get (z - 2)² = -4 + 4 = 0.

Because we ALREADY manipulated the -4 from completing the square with Y, we simply pull in the Y terms, put them with the Z terms, and bring back that X term we had to do nothing to--

4((y - 2)²) + (z - 2)² - x = 0. Now we just divide by 4 to get rid of that coefficient.

(y - 2)² + ((z - 2)²)/4 = x/4. This is an elliptic paraboloid because the two squared terms are positive, and there is one term that is not squared. This moves in the direction of the X-axis because the X is not squared.

3) Find an equation for the surface consisting of all points P for which the distance from P to the x-axis is twice the distance from P to the yz-plane. Identify the surface.

First, let's let P = (x,y,z), that is, just some arbitrary point.  We need the distance from P to the x-axis.  The x-axis, of course, is simply any arbitrary (x,0,0).  So, the distance between the two is just D = sqrt((x - x)² + (y - 0)² + (z - 0)²).  That's just D = sqrt(y² + z²).

Now we need the distance from some P to the YZ plane.  The YZ plane is just some (0,y,z).  So, we find the distance between P and this plane, which is D = sqrt((x - 0)² + (y - y)² + (z - z)²) = sqrt(x²) = |x|.  We have our two distances, BUT our condition was that the distance from P to x-axis is TWICE the distance from P to the YZ plane, so instead of just

D = sqrt(y² + z²) = |x|, we do D = sqrt(y² + z²) = 2*|x|.  And then we square all sides to get rid of the radical:

y² + z² = 4x².  This takes the general form of a cone, and because not all axes are equal in length (radius of 1, radius of 1, and radius of 2 from that 4x²), this is in fact an elliptical cone.  So, our answer is...

y² + z² = 4x², elliptical cone

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Why do you care? Ever use Solid Works or AutoCad to build 3D stuff? Know those neat little features that'll automatically cover the entire surface in one little design you created, like pinholes or ridges or even fillets? You get that "instant copy and paste" thing by these sorts of equations since ALL solid objects are engineered through these types of equations.

And if you're any good at physics, if you have such a nice design, you know just how to increase a number oh-so-slightly to turn those two cone-shaped funnel things attached at the small ends into a little bit of a wider attachment and keep going until you can maximize what you need done (like shortening the gap in order to increase velocity if it were an air tube, per se, or increasing the gap in order to give it more structural support).

    I never thought of myself as particularly attractive, smart, or socially advanced -- certainly not rich. It was odd, then, to meet two men possessing everything that I lacked. Though modest, they had everything in their hands. The Lexus, a couple of grand to blow, nice shoes, stories of traveling the world. I had the choice of keeping up with them while questioning my own abilities or staying behind.

    There's no gap between poverty and excess, no medium between dim and blindingly bright. At least not here. Now more than ever I can't find a place in this world. I'm beginning to question if I ever will.

   

    "Why are you wearing a hospital bracelet, mate?"
    "I got into a fight. Didn't win."

If you ever take an Ethical Reasoning class, basically through EVERYTHING you believe in as ethical and moral and throw it out the door!  And I am not shittin you!

 

Now granted the ethical reasoning class I went to is a class of 6 total classes to become a drug/alchol counslor in the state of NE, so we had to learn a couple of laws that are used as a drug and alchol clients and counselors.  And half of us were either just starting the classes and the other half were working LDACs or Social Workers who work with addicts.  What just boggles those of us new to these classes is the fact counselors have to juggle not just the federal law on confidentiality but also the State Law of reporting abuse of any kind!  Thus why you take the Ethical Reasoning class and find out that everything you normally would think and do is WRONG!!!!!!!

 

When a counselor deals with issues we have 4 main choices to choose from after we do our ethical reasoning and decision:

 

1.  Legal and ethical, or

2.  Legal and unethical, or

3.  Illegal and ethical, or

4. illegal and unethical

 

Out of our four choices, we were told that we really do NOT ever want to choose #4 but that we would choose #s 1-3 all the time in our wide range of issues and decisions.  Amazing huh?  That we would choose illegal and ethical or legal and unethical but trust me after dealing with some secenarios that actual counselors had to deal with, you would be amazed at how many times you would choose illegal and ethical or legal and unethical!  We were also told and it made total sense that when laws are in conflict with this profession, the bigger wins except when smaller is tougher!

 

Then we got a very brief introduction into the Stages of Ethical/Moral Reasoning.  Which made EVERYONE's brains go to mush!  We were taught that Lawrence Kohlberg is the champion of research in the area of moral development and if you are going to buy any books (modern) to make sure you look in the back to make sure that Kohlberg is listed as a source.  Paiget took a lot of works include Freud's (which was pointed out that Freud may have been wrong on a lot of things in a lot of ppl's views but he was right on a lot of things that are used across the board by many ppl!)  and even though Paiget is now dismissed with a lot of his research in moral reasoning, he is credited with having accelerated the effer to understand psychology of moral reasoning which includes Kohlberg's stages of of Moral/Ethical Reasoning that we use today. 

 

LDACs and other counselors always look at their final decision they make for a client and then look at what stage of Moral/Ethical REason they are using.  And what is so upsetting but not suprising is that once a person starts working as any form of counselor, their Moral/Ethical Reason goes from what they dub a Jr. High level after a few years working back down to an Infant level.  Because they start out with good intentions and follow through with them, they get in trouble either via their organization or the law for being a truely ethical and moral counselor!  So after that, they revert back to the infant level to cover their butts because they have been burned!

 

There are three main catagories of Moral/Ethical Reasoning that are then broken into 6 stages that we use today:  (I am going to use an example from our ethics manual)

 

Stage 1:   If I don't take the course I'll get in trouble.  (Infant-Concerned with self)

Stage 2:  I need the CEU's, so I'll take the course.  (Toddler-Concerned with self)

These two stages fall into the Preconventional Level of Reasoning that the majority of ppl revert back to once working in a counseling and other profession after a few years.

 

Stage 3:  I'll take the course because I know the presenters are truly wonderful human beings and I want them to like me. (Jr. High-Social/Group Concern)

Stage 4:  I'll go because my boss told me to and thus it's my duty.  (Law & Order-Social/Group Concern)

These two stages fall into the Conventional Level of Reasoning that the majority of ppl who do NOT work in counseling professions funtion at (before they become counselors!) and the level that the majority of those ppl in professoins as Police Officers, Medical professions, Judiciary professions, and the Military function at.

 

Stage 5:  I'll go because I have accepted a job as a counselor, and have thus also accepted the responsibility to discharge my duties in an ethical manner.  (Negotiation to find balance)

Stage 6:  I'll take the course out of respect for dignity of my clients, who deserve, simple by virtue of being a human, to be treated in accordance with the highest possible ethical standards.  (Individal vs. Social)

These two stages fall into the Postconventional, Autonomous, or Principled Level of Reasoning that very few ppl ever fall into.  What is so suprising is that the US Constitution was written to these two levels by 30-45 year old White men who were slave owners and they thought and wrote like this when the Constitution was being constructed.  The same with the Magna Carta.  Any Country that has been through a lot and still flurised and wrote laws and other things at this level have flurished and have functioned orginally at this level of Reasoning!

 

Amazing isn't it.  And I am not done with the things I have learned!  We also had to learn about putting 4 factors into play after we came to our Decision and our Rational of why we got there.  Those Rules as they were dubbed in our class are:

 

Beneficence--the duty to promote welfar of, and prevent harm to, all persons we serve.  Whic extendes to the community and is a must for all counselors to pursue. 

 

Nonmaleficence--the duty to do no harm Sounds Wiccany to me if you ask me!  This actual principle is traceable back to Hippocrates.  In other words, we have a duty to avoid potential harmful multiple relationships with not only our clients but their families.

 

I was very happy to hear in this class, that I and my friend that went to this class who are Pagans, were NOT the only ones that had a HUGE problem with Nonmaleficence.  In reality there is NO such thing as doing NO HARM to ANYONE!  And when a few of us brought this up to the Ethics Presentors, it was explained to us that we are correct, somone is ALWAYS going to get harmed in what ever decsioin we make and our job is to ethical come to a decision as to who is going to get the least amount of harm presented to them!

 

Rspect for Client Autonomy--duty to recognize the client's right to make her/his own decisios, at the same time the substantial influence we have over those decisions and the potential conflict between duty to respect client autonomy and the duty to prevent harm

 

Justice-- the duty to treat individuals fairly, provide equal access to services regardless of race, disability, appearance religion age gender ethnicity intelligence, sexual orientation, national ancestory, martial economic educational or social status

 

Then after learning all about these lovely things, we got told there is of course no book that we can resort to when we have delimias.  Suprise Suprise!:P

 

Anyway, I got a lot out of the class even if I didn't agree with some of the decisions that were eventually made by unknown counselors scenarios that we were presented and had to make our own decisions over!  But that is why in the Ethical/Moral Reasoning class there is truely no right or wrong answer to any of your decisions!  This class was to help you think in an ethical manner and then be able to explain your decision and WHY!  We learned to always ask WHY we came to any decision in anything more than 5 times because then and only then would we come to the true understand at what is at the core of our ethical reasoning!