text:
User:Egm6341.s11.team3/sub6

= 6.1 =

Given: p4 and p5 values along the error expression and residual integral term
From by Prof. Vu-Quoc, functions $$ p_4(t), p_5(t) \ $$ expressions are given as:

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$$ p_4(t) = c_1 \frac{t^4}{4!} + c_3 \frac{t^2}{2!} + c_5 \ $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *  $$ \displaystyle
 * }

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$$ p_5(t) = c_1 \frac{t^5}{5!} + c_3 \frac{t^5}{5!} + c_5t \ $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *  $$ \displaystyle
 * }

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$$ c_1 = -1, c_3 = \frac{1}{6}, c_5 = -\frac{7}{360} \ $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *  $$ \displaystyle
 * }

with expression for $$ E \ $$ at $$ p_5(t)^{th} \ $$ term is given as

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$$ E = \left [ p_2g^{(1)} + p_4g^{(3)} \right ]_{-1}^{+1} - \ \int^{+1}_{-1}p_5g^{(5)}dt $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *  $$ \displaystyle
 * }

Find: Expression for p6, p7, E at p6 and p7, the expression for global-to-local variable conversion and values for functions 'd'
(a) Expression for $$ p_6, p_7 \ $$ and $$ E \ $$

(b) Find $$ t_k(x) \ $$

(c) Find
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$$ d_1 = \bar {d}_{2.1} = \bar {d}_{2} = \frac{p_2(1)}{2^2} \ $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *  $$ \displaystyle
 * }

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$$ d_2 = \bar {d}_{4} \ $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *  $$ \displaystyle
 * }

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$$ d_3 = \bar {d}_{6} \ $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *  $$ \displaystyle
 * }

(a)
Having this expression for error $$ E = \left [ p_2(t)g^{(1)}(t) + p_4(t)g^{(3)}(t) \right ]_{-1}^{+1} - \ \int^{+1}_{-1}p_5(t)g^{(5)}(t)dt $$

, we integrate by parts the residual part once again

by noting that

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$$ \frac{d}{dt} \left ( p_6(t)g^{(5)}(t) \right ) = p_5(t)g^{(5)}(t) + p_6(t)g^{(6)}(t) \ $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *  $$ \displaystyle
 * }

then by taking integral over the interval, for this more specific case, in interval $$ t \in [-1, +1] \ $$, we get

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$$ \int^{+1}_{-1} \frac{d}{dt} \left ( p_6(t)g^{(5)}(t) \right ) = \int^{+1}_{-1}p_5(t)g^{(5)}(t) + \int^{+1}_{-1} p_6(t)g^{(6)}(t) \ $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle
 * }

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$$ \left [ p_6(t)g^{(5)}(t)dt \right ]_{-1}^{+1} = \int^{+1}_{-1}p_5(t)g^{(5)}(t) + \int^{+1}_{-1} p_6(t)g^{(6)}(t) \ $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle
 * }

Then re-writing the equations above

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$$ \int^{+1}_{-1}p_5(t)g^{(5)}(t) = \left [ p_6(t)g^{(5)}(t)dt \right ]_{-1}^{+1} - \int^{+1}_{-1} p_6(t)g^{(6)}(t) \ $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle
 * }

2 things must be noted:

 * 1) the rewritten term is the same as the residual term in error as well as the residual next term is of the same format as $$ \int^{+1}_{-1}p_5(t)g^{(5)}(t) \ $$ term.
 * 2) note that by the definition of integration by parts, that was done in deriving expression for $$ \int^{+1}_{-1}p_5(t)g^{(5)}(t) \ $$, we expressed $$ \frac{d}{dt}p_6(t) = p_5(t) \ $$ or $$ p_6(t) = \int p_5(t) \ $$

Therefore,

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$$ E = \left [ p_2(t)g^{(1)}(t) + p_4(t)g^{(3)}(t) \right ]_{-1}^{+1} + \left [ p_6(t)g^{(5)}(t)dt \right ]_{-1}^{+1} - \int^{+1}_{-1} p_6(t)g^{(6)}(t) \ $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle
 * }

, where $$ p_6(t) = c_1\frac{t^6}{6!} + c_3\frac{t^4}{4!}+ c_5\frac{t^2}{2!}+ c_7 \ $$

in same fashion we expand it once more

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$$ E = \left [ p_2(t)g^{(1)}(t) + p_4(t)g^{(3)}(t) \right ]_{-1}^{+1} + \left [ p_6(t)g^{(5)}(t)dt + p_7(t)g^{(6)}(t)dt \right ]_{-1}^{+1} - \int^{+1}_{-1} p_7(t)g^{(7)}(t) \ $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle
 * }

, where we have now

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$$ p_6(t) = c_1\frac{t^6}{6!} + c_3\frac{t^4}{4!}+ c_5\frac{t^2}{2!}+ c_7 \ $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle
 * }

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$$ p_7(t) = c_1\frac{t^7}{7!} + c_3\frac{t^5}{5!}+ c_5\frac{t^3}{3!}+ c_7t + c_8\ $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle
 * }

in order to reduce some error in residual function and noting that this is an error that generated from integration, we want to make 1 function odd such that negative and positive contribution to error would cancel out. Since we note that $$ p_1, p_3, p_5, .... \ $$ are odd functions, we will force with constants $$ c_1 - c_7 \ $$ for this function to cancel out at the interval $$ t \in [-1, +1] \ $$

That is:

They both end at the same point, namely '0'

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$$ p_7(-1) = p_7(+1) = 0 \ $$ $$
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 * style="width:95%" |
 *
 $$ \displaystyle
 * }

as well as the function will pass though origin, in order to enforce the oddity of the function (remember that odd functions are symmetric with origin and, therefore, they pass though origin)

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$$ p_7(0) = 0 \Rightarrow c_8 = 0 \ $$ $$
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 * style="width:95%" |
 *
 $$ \displaystyle
 * }

then by noting that constants $$ c_1, c_3, \ $$ and $$ c_5 \ $$ were already found for lower order 'p' functions and $$ c_8 = 0 \ $$

we plug in the final boundary value to find $$ c_7 \ $$

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$$ p_7(1) = (-1)\frac{1^7}{7!} + \frac{1}{6}\frac{1^5}{5!}+ \left (-\frac{7}{360} \right ) \frac{1^3}{3!}+ c_7(1) + 0 = 0 \ $$ $$
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 * style="width:95%" |
 *
 $$ \displaystyle
 * }

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$$ \Rightarrow c_7 = \frac{31}{15,120} \ $$ $$
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 * style="width:95%" |
 *
 $$ \displaystyle
 * }

Therefore

$$ p_6(t) = c_1\frac{t^6}{6!} + c_3\frac{t^4}{4!}+ c_5\frac{t^2}{2!}+ c_7 \ $$

$$ p_7(t) = c_1\frac{t^7}{7!} + c_3\frac{t^5}{5!}+ c_5\frac{t^3}{3!}+ c_7t \ $$

$$ E = \left [ p_2(t)g^{(1)}(t) + p_4(t)g^{(3)}(t) + p_6(t)g^{(5)}(t)dt \right ]_{-1}^{+1} - \int^{+1}_{-1} p_7(t)g^{(7)}(t) \ $$

$$ c_1 = -1, c_3 = \frac{1}{6}, c_5 = -\frac{7}{360}, c_7 = \frac{31}{15,120} \ $$

(b)
From the equation (3) given in Prof. Vu-Quoc's

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$$ x(t_k) = \frac{x_k + x_{k+1}}{2} + t_k \frac{h}{2} \, t_k \in [-1, +1] $$ $$
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 * style="width:95%" |
 *
 $$ \displaystyle
 * }

, where $$ h \ $$ is the size of an interval, namely, $$ h = x_k + x_{k+1} \ $$

By re-arranging members

$$ t_k(x) = \frac{2x - (x_k + x_{k+1})}{h} \ $$

(c)
From Prof. Vu-Quoc's on expression for function "d"

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$$ \bar {d}_{2r} = \frac{p_{2r}(1)}{2^{2r}} = d_r = - \frac{B_{2r}}{(2r)!} \ $$ $$
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 * style="width:95%" |
 *
 $$ \displaystyle
 * }

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$$ p_2(t) = c_1\frac{t^2}{2!}+ c_3 \ $$ $$
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 * style="width:95%" |
 *
 $$ \displaystyle
 * }

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$$ p_4(t) = c_1\frac{t^4}{4!}+ c_3\frac{t^2}{2!}+ c_5 \ $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle
 * }

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$$ p_6(t) = c_1\frac{t^6}{6!} + c_3\frac{t^4}{4!}+ c_5\frac{t^2}{2!}+ c_7 \ $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle
 * }

$$ d_1 = \frac{p_2(1)}{2^2} = \frac{-1 \frac{1^2}{2!}+\frac{1}{6}}{2^2} = - \frac{1}{12} \ $$

$$ d_2 = \frac{p_4(1)}{2^4} = \frac{-1 \frac{1^4}{4!}+ \frac{1}{6}\frac{1^2}{2!}- \frac{7}{360}}{2^4} = \frac{1}{720} $$

$$ d_3 = \frac{p_6(1)}{2^6} = \frac{ -1\frac{1^6}{6!} +\frac{1}{6} \frac{1^4}{4!}- \frac{7}{360}\frac{1^2}{2!}+ \frac{31}{15,120}}{2^6} = - \frac{1}{30,240} $$

Miscellaneous/Matlab Code for caluclations
--Egm6341.s11.team3.JA 03:07, 4 April 2011 (UTC)

=6.2 =

Given: The Error Expression of the Trapezoidal Rule

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$$E_n^T = I - T_0(n) = \sum_{r=1}^{l} h^{2r}\bar{d}_{2r}\left[ f^{(2r-1)}(b) - f^{(2r-1)}(a) \right] - \left(\frac{h}{2} \right)^{2l} \sum_{k=0}^{n-1} \int_{x_k}^{x_{k+1}} P_{2l}(t_k(x))f^{(2l)}(x)dx$$ $$ \displaystyle(Eq.6.2.1)$$
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

where:
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$$ \bar{d}_{2r} = \frac{P_{2l}(1)}{2^{2r}}$$ $$ \displaystyle(Eq.6.2.2)$$
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 * style="width:95%" |
 *

 * }

Find: Derive the Given Expression
Derive equations 6.2.1 and 6.2.2.

Solution
From class lecture, we have the following error expression:
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$$ E = \sum_{r=1}^{l} P_{2r}(+1) \left[g^{(2r-1)}(+1) - g^{(2r-1)}(-1) \right] - \int_{-1}^{+1} P_{2l}(t) g^{(2l)}(t)dt $$ $$ \displaystyle(Eq.6.2.3a)$$
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 * style="width:95%" |
 *

 * }

Where:
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$$ g_k^{(i)}(t) = \left(\frac{h}{2} \right)^if^{(i)}(x(t)), \quad x \in [x_k,x_{k+1}] $$ $$ \displaystyle(Eq.6.2.4)$$
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 * style="width:95%" |
 *

 * }

By recognizing that x(+1)=b and x(-1)=a, equation 6.2.4 may be used to solve for three of the parameters in equation 6.2.3 as follows:
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$$ g^{(2r-1)}(+1) = \left(\frac{h}{2} \right)^{(2r-1)}f^{(2r-1)}(x(+1))= \left(\frac{h}{2} \right)^{(2r-1)}f^{(2r-1)}(b)$$ $$ \displaystyle(Eq.6.2.5)$$
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 * style="width:95%" |
 *

 * }
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$$ g^{(2r-1)}(-1) = \left(\frac{h}{2} \right)^{(2r-1)}f^{(2r-1)}(x(-1))=\left(\frac{h}{2} \right)^{(2r-1)}f^{(2r-1)}(a)$$ $$ \displaystyle(Eq.6.2.6)$$
 * style="width:95%" |
 * style="width:95%" |
 *

 * }
 * {| style="width:100%" border="0"

$$ g^{(2l)}(t) = \left(\frac{h}{2} \right)^{2l}f^{(2l)}(x(t))$$ $$ \displaystyle(Eq.6.2.7)$$
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

Substituting these three expressions (Equations 6.2.5, 6.2.6, and 6.2.7) into the error expression in Equation 6.2.3 yields:

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$$ E = \sum_{r=1}^{l} P_{2r}(+1) \left[\left(\frac{h}{2} \right)^{(2r-1)}f^{(2r-1)}(b) - \left(\frac{h}{2} \right)^{(2r-1)}f^{(2r-1)}(a) \right] - \int_{-1}^{+1} P_{2l}(t) \left(\frac{h}{2} \right)^{2l}f^{(2l)}(x(t))dt $$
 * style="width:95%" |
 * style="width:95%" |
 * }
 * }

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$$ \quad = \sum_{r=1}^{l} \left(\frac{h}{2} \right)^{(2r-1)}P_{2r}(+1) \left[f^{(2r-1)}(b) - f^{(2r-1)}(a) \right] - \left(\frac{h}{2} \right)^{2l}\int_{-1}^{+1} P_{2l}(t) f^{(2l)}(x(t))dt $$
 * style="width:95%" |
 * style="width:95%" |
 * }
 * }

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$$ \quad = \sum_{r=1}^{l} \left(\frac{h^{(2r)}}{2^{(2r)}} \right)\left(\frac{h^{(-1)}}{2^{(-1)}} \right)P_{2r}(+1) \left[f^{(2r-1)}(b) - f^{(2r-1)}(a) \right] - \left(\frac{h}{2} \right)^{2l}\int_{-1}^{+1} P_{2l}(t) f^{(2l)}(x(t))dt $$
 * style="width:95%" |
 * style="width:95%" |
 * }
 * }

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$$ \quad = \sum_{r=1}^{l} 2h^{(2r-1)} \left(\frac{P_{2r}(+1)}{2^{2r}} \right) \left[f^{(2r-1)}(b) - f^{(2r-1)}(a) \right] - \left(\frac{h}{2} \right)^{2l}\sum_{k=0}^{n-1}\int_{x_k}^{x_{k-1}} P_{2l}(t_k(x)) f^{(2l)}(x)dx $$ $$ \displaystyle(Eq.6.2.8a)$$
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

By substituting the expression given by Equation 6.2.2 into Equation 6.2.8, the final answer is achieved:

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$$ \therefore E = \sum_{r=1}^{l} 2h^{(2r-1)} \bar{d}_{2r} \left[f^{(2r-1)}(b) - f^{(2r-1)}(a) \right] - \left(\frac{h}{2} \right)^{2l}\sum_{k=0}^{n-1}\int_{x_k}^{x_{k-1}} P_{2l}(t_k(x)) f^{(2l)}(x)dx $$ $$ \displaystyle(Eq.6.2.9a)$$
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

However, this answer is different than the one given in the problem statement. Unless the solution given in the problem statement is incorrect, I believe this is likely due to a misprint in the lecture notes. Had the expression in Equation 6.2.3 been given instead as:

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$$ E = \left(\frac{h}{2} \right)\sum_{r=1}^{l} P_{2r}(+1) \left[g^{(2r-1)}(+1) - g^{(2r-1)}(-1) \right] - \int_{-1}^{+1} P_{2l}(t) g^{(2l)}(t)dt $$ $$ \displaystyle(Eq.6.2.3b)$$
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

Then, by following the same exact steps shown above, the derivation would instead have led to:

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$$ E = \left(\frac{h}{2} \right)\sum_{r=1}^{l} P_{2r}(+1) \left[\left(\frac{h}{2} \right)^{(2r-1)}f^{(2r-1)}(b) - \left(\frac{h}{2} \right)^{(2r-1)}f^{(2r-1)}(a) \right] - \int_{-1}^{+1} P_{2l}(t) \left(\frac{h}{2} \right)^{2l}f^{(2l)}(x(t))dt $$
 * style="width:95%" |
 * style="width:95%" |
 * }
 * }

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$$ \quad = \left(\frac{h}{2} \right)\sum_{r=1}^{l} \left(\frac{h}{2} \right)^{(2r-1)}P_{2r}(+1) \left[f^{(2r-1)}(b) - f^{(2r-1)}(a) \right] - \left(\frac{h}{2} \right)^{2l}\int_{-1}^{+1} P_{2l}(t) f^{(2l)}(x(t))dt $$
 * style="width:95%" |
 * style="width:95%" |
 * }
 * }

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$$ \quad = \left(\frac{h}{2} \right)\sum_{r=1}^{l} \left(\frac{h^{(2r)}}{2^{(2r)}} \right)\left(\frac{h^{(-1)}}{2^{(-1)}} \right)P_{2r}(+1) \left[f^{(2r-1)}(b) - f^{(2r-1)}(a) \right] - \left(\frac{h}{2} \right)^{2l}\int_{-1}^{+1} P_{2l}(t) f^{(2l)}(x(t))dt $$
 * style="width:95%" |
 * style="width:95%" |
 * }
 * }

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$$ \quad = \sum_{r=1}^{l} h^{(2r)} \left(\frac{P_{2r}(+1)}{2^{2r}} \right) \left[f^{(2r-1)}(b) - f^{(2r-1)}(a) \right] - \left(\frac{h}{2} \right)^{2l}\sum_{k=0}^{n-1}\int_{x_k}^{x_{k-1}} P_{2l}(t_k(x)) f^{(2l)}(x)dx $$ $$ \displaystyle(Eq.6.2.8b)$$
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

Which, after making the substitution given by Equation 6.2.2, agrees with the desired final solution. So, by assuming the aforementioned misprint in Lecture 31 Page 3 Equation 2, the error may be expressed as:

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$$ \therefore E = \sum_{r=1}^{l} h^{(2r)} \bar{d}_{2r} \left[f^{(2r-1)}(b) - f^{(2r-1)}(a) \right] - \left(\frac{h}{2} \right)^{2l}\sum_{k=0}^{n-1}\int_{x_k}^{x_{k-1}} P_{2l}(t_k(x)) f^{(2l)}(x)dx $$ $$ \displaystyle(Eq.6.2.9b)$$
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

Egm6341.s11.team3.russo 19:35, 28 March 2011 (UTC)

Given: Kessler's code
Kessler's code is given below

Find: understand Kessler's code line by line
Using $$(p_{2i},\ p_{2i+1}),\ i=1,2,3$$ to understand Kessler's code line by line, starting with the best of Spring 2010

Solution
The Kessler's code is to compute the coefficients $$p_{2n}$$ and the constants $$c_{n}$$ where $$n=1,2,3,...,n$$, according to the following algorithm :

1) $$i=0$$:
 * {| style="width:100%" border="0"

$$p_1(t)=c_1t,\ c_1=-1 $$ $$ (Eq.6.6.1) \ $$
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

2) $$i=1,2,3,...$$:
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$$c_{2i+1}=-\sum^{i-1}_{j=0}\frac{c_{2j+1}}{[2(i-j)+1]!}$$ $$ (Eq.6.6.2) \ $$
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

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$$p_{2i}(t)=\sum^{i}_{j=0}c_{2j+1}\frac{t^{2(i-j)}}{[2(i-j)]!}$$ $$ (Eq.6.6.3) \ $$
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 * style="width:95%" |
 *

 * }
 * function traperror

The input of this function $$n$$ is a integer that ranges from 1 to $$\infty$$. The function returns two arrays $$c$$ and $$p$$, corresponding to the constants $$c_{n}$$ and the coefficients $$p_{2n}$$.

Set initial values for f, g, cn and cd, where the initial value of cn and cd are the numerator and denominator of $$c_1=-1$$, respectively.

Start iteration from $$k=1$$ to $$k=n$$

Update vector f according to $$f^k_i=f^{k-1}_ig^{k-1}_i(g^{k-1}_i + 1)$$, where $$f^k_i$$ is the denominator of the factors of $$c_i$$ in (Eqn 6.6.2) as $$i=k$$

Calculate $$c_{2k-1}$$ according to (Eqn 6.6.2)

Update vector f and g, where $$g_i$$ and $$f_i$$ are respectively the numerator and denominator of the factors of $$c_{2i+1}$$ in (Eqn 6.6.2) as $$i=k$$

Calculate $$p_{2k}$$ according to (Eqn 6.6.3)

Add $$c_{2k+1}$$ and $$p_{2k}$$ to the output arrays c and p

 * function fracsum

This function is to calculate the summation of $$n_i/d_i$$ from vectors $$n$$ and $$d$$. The outputs nsum and dsum returns the numerator and denominator,respectively. $$\frac{nsum}{dsum}=\sum_{i}\frac{n_i}{d_i}$$

The function round is used to round off a number to its nearest integer. The function gcd returns an array containing the greatest common divisors of the corresponding elements of the two input arrays.

This is to remove the common divisors from $$n_i$$ and $$d_i$$, while the ratio $$n_i/d_i$$ is preserved.

The function lcm returns the least common multiple of corresponding elements of two input arrays

Egm6341.s11.team3.ren 06:31, 30 March 2011 (UTC)

Results:
The integration results for a), c) and d) are shown and compared in the following table:

The Romberg table for b) is:

(2) Circumference for Ellipse: Method1
From definition of eccentricity of ellipse :

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$$ e = \sqrt {1-\frac{b^2}{a^2}} = \frac{\sqrt{91}}{10} \quad $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle (Eq. 6.7.11)
 * }

From (Eq. 6.7.2), (Eq. 6.7.3), we derive the Integration as:

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$$ C = I = \int_{0}^{2 \pi} a(1-e^2)(1-ecos \theta)^{-2}\sqrt{(1 +e^2 - 2e cos \theta)} d \theta \quad $$ $$ = \int_{0}^{2 \pi} \frac{9}{10} (1- \frac{\sqrt{91}}{10} cos \theta)^{-2}(\frac{191}{100} - \frac{\sqrt{91}}{5} cos \theta)^{\frac{1}{2}} d \theta \quad $$ $$
 * style="width:95%" |
 * style="width:95%" |
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle (Eq. 6.7.12)
 * }

Using WolframAlpha, the exact solution is calculated to be :

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$$ C_{exact} = I_{exact} = 43.8591 \quad $$ $$
 * style="width:95%" |
 * style="width:95%" |
 *
 $$ \displaystyle (Eq. 6.7.13)
 * }

Following the same approaches as in (Eq. 6.7.7), (Eq. 6.7.8) and (Eq. 6.7.9), the integration is computed using the following code:

Results:
The integration results for a), c) and d) are shown and compared in the following table:

The Romberg table for b) is:

(3) Circumference for Ellipse: Method2
The 2nd method of circumference for ellipse follows (Eq. 6.7.4). Similar to previous calculations, the function integrated here is defined as:

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$$ f(\theta) = 4a[1-e^2 sin^2 \theta]^{\frac{1}{2}} = 40\sqrt{1- 0.91 sin^2 \theta} \quad $$ $$
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 $$ \displaystyle (Eq. 6.7.14)
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Using WolframAlpha, the exact solution is calculated to be :

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$$ C_{exact} = I_{exact} = 43.8591 \quad $$ $$
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 $$ \displaystyle (Eq. 6.7.13)
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Which is identical to (Eq. 6.7.13), following the same approaches as in (Eq. 6.7.7), (Eq. 6.7.8) and (Eq. 6.7.9), the integration is computed using the following code:

Results:
The integration results for a), c) and d) are shown and compared in the following table:

The Romberg table for b) is:

Egm6341.s11.team3.Xia 18:00, 31 March 2011 (UTC)

Solution
$$ \sum_{i=0}^{3} C_is^i = \sum_{i=1}^{4} N_i(s)d_i\,$$ $$ C_0+C_1s+C_2s^2+C_3s^3=N_1(s)d_1+N_2(s)d_2+N_3(s)d_3+N_4(s)d_4\,$$ $$ C_0=z_i \,$$ $$ C_1=z_i' \,$$ $$ C_2=-3z_i-2z_i'+3z_{i+1}-z_{i+1}' \,$$ $$ C_3=2z_i+z_i'-2z_{i+1}+z_{i+1}' \,$$ $$ d_1=z_i\,$$ $$ d_2=\dot{z_i}=z_i'\frac{1}{h}\,$$ $$ d_3=z_{i+1}\,$$ $$ d_4=\dot{z_{i+1}}=z_{i+1}'\frac{1}{h} \,$$ $$ z_i+z_i's+(-3z_i-2z_i'+3z_{i+1}-z_{i+1}')s^2+(2z_i+z_i'-2z_{i+1}+z_{i+1}')s^3=N_1(s)z_i+N_2(s)z_i'\frac{1}{h}+N_3(s)z_{i+1}+N_4(s)z_{i+1}'\frac{1}{h} \,$$ $$ z_i(1-3s^2+2s^3)+z_i'(s-2s^2+s^3)+z_{i+1}(3s^2-2s^3)+z_{i+1}'(-s^2+s^3)=z_i(N_1(s))+z_i'(N_2(s)\frac{1}{h})+z_{i+1}(N_3(s))+z_{i+1}'(N_4(s)\frac{1}{h}) \,$$

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$$ \displaystyle N_1(s) = 1-3s^2+2s^3 \,$$ $$ \displaystyle N_2(s) = h(s-2s^2+s^3) \,$$ $$ \displaystyle N_3(s) = 3s^2-2s^3 \,$$ $$ \displaystyle N_4(s) = h(-s^2+s^3) \,$$ $$ \displaystyle$$
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$$ \bar{N_1}(s) = 1-3s^2+2s^3 \,$$ $$ \bar{N_2}(s) = s-2s^2+s^3 \,$$ $$ \bar{N_3}(s) = 3s^2-2s^3 \,$$ $$ \bar{N_4}(s) = -s^2+s^3 \,$$ $$ \displaystyle$$
 *

 * }

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Note for Verifying that : $$ \bar{N_1}(0)=1, \dot{\bar{N_1}}(0)=0, \bar{N_1}(1)=0, \dot{\bar{N_1}}(1)=0 \,$$ $$ \bar{N_2}(0)=0, \dot{\bar{N_2}}(0)=1, \bar{N_2}(1)=0, \dot{\bar{N_2}}(1)=0 \,$$ $$ \bar{N_3}(0)=0, \dot{\bar{N_3}}(0)=0, \bar{N_3}(1)=1, \dot{\bar{N_3}}(1)=0 \,$$ $$ \bar{N_4}(0)=0, \dot{\bar{N_4}}(0)=0, \bar{N_4}(1)=0, \dot{\bar{N_4}}(1)=1 \,$$ $$ \displaystyle$$
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Plot of N1, N2, N3, N4 as a function s Egm6341.s11.team3.rakesh 19:21, 4 April 2011 (UTC)

=Contributing Members =

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User:Abd/Landmark Education/Abd/Participants

It is recommended that participants register accounts at Wikiversity. In general, users with a Wikipedia account may link an account with the same name here, or a new account may be started here if one wishes to keep the accounts separate. Having an account allows all a user's edits to be identified, if they are made when logged-in, and is actually more anonymous, since anonymous edits will display, in page history, the IP address of the editor. Having an account will allow the rest of us to contact you, on your user Talk page, and you can set up your preferences so that you get e-mail notifications of all your Talk page edits. You may also choose to allow direct email contact from other Wikiversity users, and that does not reveal your email address to anyone; your address would only be revealed (to the sender of an email to you) if you choose to respond to the mail.

It may be useful to know which participants are graduates of the Landmark Forum, so feel free to add, to your listing below, the information. As a minimum, having registered an account, you can add this to the list under Participants.

Copy this *before* you press the edit link to the right of the Participants section title.

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To be clear, one need not be a graduate of the Landmark or Est trainings to register as a participant.

Participants

 * Abd 20:09, 6 April 2011 (UTC), originator of this resource.
 * Forum, March 2011 (Boston)
 * Advanced Course (2011, Boston)
 * Self Expression and Leadership Program (2011, Boston)
 * Assisting Program (Boston, 2011 and later)
 * Self Expression and Leadership Program Coach (2011, Boston, and October 2013-January 2014)
 * Introduction Leader Program (Boston and New York, 2012)
 * Seminars (Boston, 2011, and Meriden, Connecticut, 2012 and 2013).
 * Updated 06:18, 29 December 2014 (UTC)


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User:Abd/Landmark Education/Abd/Glossary

Landmark Worldwide uses English terms, words and phrases in special and often unique ways, although there is always a logic to them once you understand the basis of Landmark's work. Sometimes these are distinct from how people use these terms colloquially nowadays. For example, the term "enrollment" is used to mean "enrolling" others in a possibility, so that they are "moved, touched, and inspired," and does not refer to enrolling people in courses. "Registration" is as described below, and, in context, often refers to actually signing up for a course (the generic meaning in the training is the acceptance of an offered choice, but it is also used with the ordinary meaning, i.e, action to formally place one's name in a list of "registrants.").

Every discipline has its own language, borrowing general terms and providing specific meanings. For example, in physics the words "force", "work", "power" are given specific meanings for the mathematical modeling to work consistently, so while "work" means force through a distance in physics, "work" means applying effort, either mental or physical, to everyone else. To a physicist, pressing as hard as you can against a wall and not moving it = no work; but to everyone else, it is a lot of possibly useless work, having exerted a lot of effort to no affect, other than to give your muscles some isometric exercise. So it is with Landmark, it borrows words from common language and gives them specific meanings, creating its own sublanguage, in order to communicate specific ideas in unusual ways. The idea is born out of the educational principle "you don't learn something until you have discovered it for yourself." The unusual usage forces fresh use of the mind to elicit the discovery of whatever is being presented.

Please use this page to express definitions of these terms as used by Landmark. Discussion of these definitions should take place on the attached Talk page (the "Discuss" tab, usually above). If there are disagreements, we should attempt to find consensus on the Talk page. This resource is intended to explain how these words are actually used by leaders of seminars in Landmark, and by Landmark Forum graduates in the Landmark community, not to propose these definitions as the "correct" meanings of the words.

Feel free to write definitions, and sign them with. Feel free, as well, to write brief comments or alternative definitions.

These definitions have not been approved by Landmark Worldwide.

 * Act. A command, a bold statement given by brain when one is held accountable for a failure (or perceived failure) in performance. It is often not said verbally but it is very loud inside the brain. It is what one says to people when they confront him and hold one accountable for something not done well or well enough. For example: DON'T TEACH ME!!, I KNOW IT ALL, GET LOST, I WILL SHOW YOU WHO I AM, etc. Now this way of being has impact of self and even though our ACT is not expressed verbally but it does show up in our way of being. It results in lack of power, well being and self expression. The experience of the one being his/her ACT and the people around both have experience which lacks JOY, Self Expression and happiness and there is no access to possibility or fruitful activity until it is acknowledged, resolved or dismissed.
 * Agreement/Alignment For agreement is merely a condition of content in which everyone is going to same place. Alignment, on the other hand, is a context in which everyone is coming from the same source" sercotec-lf
 * Already always listening.™ Undistinguished pre-existing interpretations that shape, color and influence the way people experience their relationships with people, circumstances, and even themselves. Examples may include: rolling your eyes as you see a number or person you recognize calling your phone as you, before they have even spoken to you, decide you already know something about how that call will go. grantlam
 * That little voice in your head, the voice of your imagination, and the interpretations it is constantly making. AnyTDorH

 * Advanced Course. The second course in the "Curriculum for Living." Whereas the Landmark Forum Deals with personal reality the Advanced Course deals with collective reality.
 * Aliveness. Occurrance when you get yourself in the game instead of spectate it and you are aware what you are doing at that moment. sercotec-lf    The sense of vitality one experiences when in action, while performing an action when not impeded by the filters, patterns and limitations laid down in the past.
 * At effect. Usage is "at the effect of [some circumstance]"; to be a victim of circumstances or dependent upon them for success. See also At cause. Abd
 * Authenticity. When one is being consistent with how one portrays oneself with others and with oneself. When one is authoring one's life from a point of view of Self rather than reacting to the outside world or another's expectations or one's own familiar patterns. grantlam
 * Breakthrough. Freeing yourself from some limitation that allows you to achieve immediate and permanent quantum leaps in performance and quality of life.  Achieving unprecidented success in line with a stated aim that you had previously had trouble acheiving. grantlam
 * When "the light bulb clicks on in your head" and you "get it" and it causes a discrete change in behavior. AnyTDorH

 * Breakdown. A breakdown happens when some action in line with a stated possibility, intention or commitment is frustrated, stopped or thwarted. grantlam
 * When things don't go as expected or intended, or when you don't do as you said you would -- "not keeping your word" --, also known as a loss of integrity, a loss of workability. AnyTDorH

 * Complete. When one is complete with any aspect of the past and therefore the past has no constraint on who one is being or how they are acting in the present. In communication, being complete is the experience of one being left with no lingering resentments, regrets or "unfinished business". One can declare something complete even when an aim has not been achieved if one wishes to move on.  This is termed "being complete with being incomplete". grantlam
 * Cost. (as used in Rackets™). The undesirable impact of one’s reactive, self-serving, nasty ways of being and acting. See also Payoff. Abd edited by grantlam
 * The costs of rackets™ are love/affinity, vitality/well-being, self-expression, and satisfaction/fulfillment, all of which fall under aliveness. Shinigami Realm

 * Change. (versus transformation). Change begins with a something that is made different in distance (from here to there), time (from now to then) or form (for example, from a square to a circle). An aspect of the nature of change is that change causes the persistence of the something being changed. grantlam
 * Change is a gradual continual shift. Transformation is a discrete jump.  A caterpillar transforms into a moth or butterfly, but the metamorphosis that happens in the cocoon is change.  Improvement and evolution are in the world of change.  It is a case of more, better, different.  Transformation is about accepting something as it is - "no change" - such that it is fully appreciated for what it is, which causes disappearance. From this space of nothing, something new, unique and immediately relevant arises or can be created.  Change = a+1, Transformaton = a+0. AnyTDorH

 * Choosing vs. Deciding When presented with choices, an automatic reaction is to pick something over another thing - deciding. Deciding is related to other "*cide" words (suicide, insecticide, genocide), and is the result of applying reason to eliminate alternatives, effectively killing them off. Usually a single thing is left and that becomes the decision.  Choosing is about making a choice purely for the sake of choosing, not applying reason, not applying logic, not removing or disqualifying the other choices.  I have purposefully not quoted the Landmark definition of decision and choice as that is copywrited material by them. Everyone likes to use reason, but ultimately, at the bottom of every decision or even proofs, is either fundamental choice or reason:  "I choose to believe ..." or "I choose to trust ..." adding "because" makes it a reason.  By using reason, one then absolves oneself from responsibility for the choice, it becomes the fault of the reason or the reasoning process if it fails.  Choice demands responsibility for making the choice. AnyTDorH
 * Clearing The most common analogy is of a field, and removing the stones and stumps and whatever obstacles are there in the field, that interfere with the functioning of the field: whether to grow something, or to play a game, or something else. The abstraction in this case is a mental construct in which possibilities can be placed, created. The clearing is like a vacuum, and can draw things towards it.  If the thing in the clearing is "I'm no good" then it draws things that supports that attitude.  You are then a clearing for "I'm no good".  If you want the possibility of contribution to the world to be in your clearing, to draw those flavors of possibilities and opportunities, then you would need to remove the "I'm no good" thing from your clearing. AnyTDorH
 * Context. Context is your occurring world; the total of how the world around you, and the people and things in it (either in totality, or in a given situation), show up for you. Nearly all context in which humans live is created. As a "meaning-making machine", it forms the setting and the background of your story and you tend to take actions based upon it in response. And you take it for granted and don't realize it: the one thing your occurring world doesn't automatically occur for you as, is context. For example, for a fish, water is a major part of his context. A fish has no appreciation of water, it's just there, life consists of dealing with it all the time, he 'swims in it'. No other fish has ever been out of water for any length of time and come back to tell him what it's like, so the fish doesn't know anything but water, and nothing else is possible to him. (The difference is, the fish's context of water is beneficial to him, and he can't overcome it and survive. You, however, might "swim in" a context that isn't altogether beneficial to you, and that you can overcome. By contrast, responsibility is an empowering context.) When your life sucks, when you're in a negative or disempowering context; the way to break out of it, to overcome the negative or disempowering context, is to distinguish something (see Distinguish, Distinction). Then you can see your disempowering story as a story, and take new action in alignment with reality; or take on one or more new ways of being that might work better for you. MakeItRain
 * Curriculum for Living™ The basic Landmark curriculum, which includes The Landmark Forum®, The Advanced Course®, The Self Expression and Leadership Program, and The Landmark Forum In Action Series. Since the courses have gone online in 2020, the Curriculum has the Introduction Leader's Programme instead of the Self Expression and Leadership Programme and there is no mention of the Landmark in Action Seminar Series.
 * Disappear. To "disappear something" is to eliminate or evaporate it, such as to disappear a complaint. This is done by fully acknowledging it for what it is and what it isn't such that it no longer has any hold over you, and no longer "sits in your space" or clearing.  See Change vs Transformation. JF, edited by Abd (discuss • contribs)
 * Distinction. A distinction is a linguistic phenomenon that brings something into being as a presence, for which previously there was no presence. It brings something into contrast so it stands out where previously it did not show up as a thing. grantlam
 * The idea of a distinction comes from Taoism, when you name something as beautiful, not beautiful comes into existence as well. It also comes from sublanguages created to facilitate an area of thought or information -- the example of physics used above.  A distinction is simply a term, a word, used to name something to facilitate the abstraction, discussion and/or use of that thing. AnyTDorH

 * Distinguish. To take something from an undifferentiated background and bring it to the foreground. Shinigami Realm
 * Effect. See At effect.
 * Empty. No content, not real, made up, no substance. Generally used in conjunction with "meaningless" as in "empty and meaningless" see "meaningless" below. AnyTDorH
 * Enrollment. A kind of sharing that causes a new realm of possibility to be present for another such that they are touched moved and inspired by that new possibility. This is not to be confused with Registration. grantlam
 * Force. (versus power. Force is not a distinction recognized by Landmark. Personally, I feel that 'force' should be a distinction -- force as distinct from 'power', since within the Landmark technology, the two terms are so often used together, and so often contrasted against one another -- so I'll attempt to generate one for you here that will work for you.) Access to the distinction between force vs. power, lies in the outcome, the result. Power produces outcomes that will fall into place without a whole lot of resistance, and that once in place will stay in place indefinitely. Force can produce outcomes, but force nearly always meets with resistance. Force frequently produces outcomes other than what the person applying the force wants, or had in mind. Force produces unintended consequences. No one likes being forced, after all, and most anyone will seek ways to thwart whatever or whoever is trying to force something on them. And when force produces an outcome at all, that outcome will stay in place only for as long as the force can continue to be applied effectively. Once the force goes away, or is removed, or is met with an opposing force; once someone who is unhappy with the outcome produced by force comes up with a way to get around the force, or force back, or to evade the punishment that it threatens, the outcome produced by force is going to unravel. Power is, by its nature, successful. Force, by its nature, isn't successful, and certainly isn't powerful. Access to power lies in force-free communication. MakeItRain
 * The Landmark Forum. An accelerated learning experience, set up as a guided dialog between the instructor and participants designed to bring about a transformational shift in the participants' effectiveness and quality of life in three and a half days. The first course in the "Curriculum for Living," The Landmark Forum® is the entry point for all Landmark programs. grantlam
 * Genesis of Identity. The you who you identify with, as generated from a series of incidents at key points in early life where your unconscious mind (see IT) automatically directs you to become a certain way to survive a series of stressful and potentially life threatening breakdowns in important developmental situations.
 * The first incident is said to occur in childhood when you rely on adults/caregivers to get your needs met and "Something happens" where your needs for sustinance, security etc. aren't met, and then in a state of fear, your brain thinks "There's something wrong", and assuming your access to resources and safety depends on your ability to manipulate or influence relationships with caregivers, it comes up with something and decides that you must be a certain way to cope with and survive the situation.
 * The second event occurs in adolescence when you have a strong need to bond with your peer group. Then "Something happens" which makes you feel left out and your brain goes straight to, "I don't belong!" and again it comes up with a fix and decides you must be a certain way to survive.
 * Then thirdly, as a young adult, just as you're out in the adult world, just finding your way towards leading a life of independence, when "Something happens" where something interrupts the process and you panic and your brain processes this as "I'm on my own!" and so the third level of identity, as a way of being is created to survive in life.
 * These could look like #1 Being nice and supportive, #2 Being attractive, #3 Being a perfectionist.
 * This then forms your identity - where you habitually go when under stress, who you think you are, who others see you as and how you show up in the world. It is so relentless that you, the thinker, is trapped in it!  The key here is that your brain landed on these ways of being automatically, based on the circumstances and what you knew at the time, and you did not have time to think it through, and still don't as the survival instinct is so strong, it overrides conscious thought.  But as these events occurred during a time of stress, it created a strong imprint in the neural pathways of the brain and whenever you get to this or a perceived similar area of life, you automatically go to this behaviour, regardless of how relevant or useful it is.  You have no control over this person you think you are - until you distinguish it - see it for what it is and make another choice in a situation that is simiarly stressful.  Then you can lay down a new neural pathway with great power and you get to choose what kind of person you wish to be, based on the current and real situations you are facing today.  This leads to great levels of success and elevated performance in whatever you're up to in life, in a very short period of time.
 * Graduate. A person who has completed The Landmark Forum. edited by grantlam
 * I. The distinction of the structure and patterns people have come to identify with, and form identity from, as being a collection of fixed characteristics, attributes, survival responses and experiences from the past. See Genesis of Identity. Shinigami Realm
 * A pattern of patterns of neurons firing, see Genesis of Identity. Abd

 * Informative learning. Learning that increases what people know and adds to their skills by bringing new knowledge to an existing worldview and frame of reference. Compare to transformative learning. Shinigami Realm
 * Integrity. Integrity is a state or condition of being whole, perfect, complete and unimpaired, in perfect condition. For a person, integrity is a matter of a person’s word. The extent to which who you are reflects the person you intend to be. Grantlam (discuss • contribs) 01:02, 23 September 2016 (UTC)
 * Integrity is well defined in a dictionary and covers all usage in Landmark. It is presented, though, from a perspective of workability.  The more workable, the more integrity, the less workable, there is a loss of integrity.  Keeping ones word is associated with integrity -- agreeing with common usage -- but in Landmark, it is a progression.  Not keeping your word, means you were inauthentic about your word.  Inauthenticity leads to unreliability, which reduces workability, and thus a loss of integrity.  If you say you will be at a meeting at 5pm and show up at 5:10pm, there is inauthenticity, and there is the loss of 10 minutes of time, reducing the workability of the meeting, which may have to still end on time, so there is less time for discussion, information sharing, etc. which can lead to incompleteness, which reduces workability.  Thus a lack of integrity, a loss of integrity, or simply, no integrity. AnyTDorH

 * IT. A reference to the machinery of the mind, the automatic patterns of neurons firing that get set up in our unconcious minds at a young age before we could control how our brain, thoughts and responses function. See Genesis of Identity; Strong Suit
 * IT is used in the context of being distinct from our true Self and often overshadowing our authentic Self expression, such that we forget our Selves and the true Source of our being - our sense of human being, our humanity - separate from our body's automatic and unconscious processes and actions. [ R Blueberry]
 * IT always interprets current circumstances through a lens of what it knows - memories and past experiences - and uses examples of these in relation to current circumstances in order to generate actions, ways of being and responses. IT is designed for survival at all costs.  Therefore actions taken from this place are limited and often have costs hidden to our conscious minds.  This is distinct from the Self which, being on the other side of the void, the no-thing that IT is, has access to ALL possibilities and does not need to sacrifice or short cut anything in order to take actions in the world of performance.
 * Life, as in "yourself and your life." Our entire set of relationships with people. Grantlam (discuss • contribs) 01:04, 23 September 2016 (UTC)
 * Listening In Landmark Education, "Listening" does include the action of actually listening to another person in the common sense, but also includes a state of being. In this regard, the qualifying statements are similar to "... in your listening".  This state of being is recognized as providing a coloration to your listening to what others are saying, and to what is happening around you, even if no sound is hitting your ears.  It is the application of interpretation, and the recognition that we are always applying some sort of interpretation to our sensory input.  By recognizing that we are applying color, and the color that is being applied, we can then choose that coloration.  The state of being is referred to as "your clearing", and that clearing provides the coloration, the interpretation, and the responses produced. AnyTDorH
 * Meaningless. The absence of inherent meaning. Grantlam (discuss • contribs) 01:04, 23 September 2016 (UTC)
 * Used in conjunction with "empty" as in "empty and meaningless". This sentiment comes from the opening chapter of the book of Ecclesiastes, by the said Biblical teacher and philosopher who wrote this in reference to life, outside of a healthy relationship with God.  A relevant dictionary definition here is: implication of a hidden or special significance . [ R Blueberry] Meaning is the association of things with other things.  This is an action of interpretation, of creating "story".  Since it is made up, it is not real, and therefore empty.  People tend to use "meaning" to ascribe substance and value to something.  But since the meaning is made up, empty, it is really meaningless, without substance, and thus subject to change, alteration, transformation, or disappearance. AnyTDorH
 * In modern philosophy, this concept of life being "empty and meaningless" is summed up in Nihilism. However, as a mindset, this is considered to be pecimistic and can lead to depression and other serious mental health problems.  In reaction, it generates positive thinking and false positive attitudes unrelated to reality - hopeful, wishful or magical thinking.  However, in the Landmark Forum, it is stated clearly, that even drawing this as a conclusion is using the brain to imply meaning and so is not reality, it is more of "IT", the mechanism of the mind.  In fact, that life can be experienced this way is in itself empty.  It is often phrased "It is empty and meaningless, that life is empty and meaningless".

 * Occur Used in the plural form, as in "how it occurs ...", in an active form "occurring" and in the past tense "how it occurred ..." . The interpretation of something.  Occurring applies story, reason, to what happened, or to how you think about something.  Occurring is a subconscious summarization and associative process that hits the conscious mind as real, as truth.  It is difficult to recognize this without training.  Someone yelling at you could occur as they being angry; or you thinking they think you are deaf, or stupid; or as an urgent notification of something you need to pay attention to; or something else.  Thus when trying to describe what happened, you may include that interpretation unknowingly, when it is really how it occurred to you. AnyTDorH
 * Payoff. A payoff is something one gets out of certain ways of being and acting that is not immediately obvious. Grantlam (discuss • contribs) 01:04, 23 September 2016 (UTC)
 * This is used in relation to the hidden side of a Racket, where you get a benefit that is not obvious to others and sometimes not even yourself. Where it feels good to do something that has unwanted consequences which keep the habit around.
 * Possibility. A phenomenon in language that creates a new future now. Grantlam (discuss • contribs) 01:04, 23 September 2016 (UTC)
 * Power. The rate at which an intention is turned into a result Grantlam (discuss • contribs) 01:32, 23 September 2016 (UTC)
 * Present. Being Present is to be truly listening with a quiet mind. You are not thinking of what you need to do next or what you are going to say next. Instead, you are fully present in the conversation. You are hearing every word.
 * Racket.™ A persistent complaint combined with a fixed way of being. Rackets are maintained because of payoffs (see payoff) and persist until dropping the racket (and thus its associated cost) is chosen. Abd
 * It is a term related to Mafia rackets, defined as a type of organized crime in which the perpetrators set up a coercive, fraudulent, extortionary, or otherwise illegal coordinated scheme or operation (a "racket") to repeatedly or consistently collect a profit. It is often designed to appear lawful or necessary and have a glorified front to hide or distract from unlawful activities.
 * Because there is a brain pathway of pleasure associated with the behaviour, despite the unwanted consequences it is something that tends to continue, especially when we are running our lives in an automatic, unconscious way.
 * The down side of rackets is a loss of love, vital energy, or something else good which is sacrificed for a short term, personal gain.
 * Because of the anti-social nature of the behaviour, it is presented as a false positive way of being so it seems like a good action but has a hidden nastiness which undermines our sense of humanity.
 * An example is: going to work and smiling at the boss while thinking I'm right, he's wrong. I'm good, he's bad - which leads to taking action to undermine the boss such as gossip or choices that justify your position and make them look bad or wrong.
 * Reality. That which is real either independently of language (e.g., a car) and that which is real only in language (e.g., a concept). Grantlam (discuss • contribs) 01:32, 23 September 2016 (UTC)
 * Reason. An excuse we invent to justify choices we make. That would be Ambrose Bierce's definition. When choices are made according to "reasons," they are distinguished as the "machine" operating, based on assumptions about truth and reality. Genuine choice operates on another level. Reasoning is not denied, but distinguished as rooted in our stories about reality. NOTE: This is not a Landmark term. Just the generic meaning of the word is used in Landmark programs.Grantlam (discuss • contribs) 01:32, 23 September 2016 (UTC)
 * Reasonable. To justify acting or not acting based on reasons and justifications. Grantlam (discuss • contribs) 01:32, 23 September 2016 (UTC)
 * Registration. See also Enrollment. Some action that registers a commitment to the future, for example registering for a gym membership. Grantlam (discuss • contribs) 01:32, 23 September 2016 (UTC)
 * Resentment. A poison people swallow hoping it will kill the other person. NOTE: This is not a Landmark term. Just the generic meaning of the word is used in Landmark programs. Grantlam (discuss • contribs) 01:32, 23 September 2016 (UTC)
 * Responsibility. “Responsibility begins with the willingness to take the stand that one is cause in the matter of one’s life. It is a declaration not an assertion, that is, it is a context from which one chooses to live.  Responsibility is not burden, fault, praise, blame, credit, shame or guilt.  In responsibility, there is no evaluation of good or bad, right or wrong.  There is simply what’s so, and the stand you choose to take on what’s so.  Being responsible starts with the willingness to deal with a situation from the view of life that you are the generator of what you do, what you have and what you are.  That is not the truth.  It is a place to stand.  No one can make you responsible, nor can you impose responsibility on another.  It is a grace you give yourself – an empowering context that leaves you with a say in the matter of life.” (Werner Erhard) MakeItRain
 * Self-Expression and Leadership Program. The final course in the original Curriculum for Living®., this program expands one’s natural capacity for providing leadership and making a difference as a natural self-expression. Grantlam (discuss • contribs) 01:32, 23 September 2016 (UTC)
 * Speaking into the listening. Effectively communicating to another such that the communication is heard in the way in which the speaker intended. Grantlam (discuss • contribs) 01:32, 23 September 2016 (UTC)
 * Stinginess. Deliberately holding oneself and one’s contribution ‘close to the vest’ and without generosity. Grantlam (discuss • contribs) 01:32, 23 September 2016 (UTC)
 * Story. A "story" is an account or interpretation of past events often mistakenly taken for what actually happened. Grantlam (discuss • contribs) 01:32, 23 September 2016 (UTC)
 * Strong Suit. A way of being and acting one relies on to produce results and make it in life. Grantlam (discuss • contribs) 01:32, 23 September 2016 (UTC) Also called a "winning formula" or "winning way." --Abd (discuss • contribs) 22:10, 17 October 2017 (UTC) It is developed and locked in place during a stressful period of life when the young person experiences a failure in being - where your natural way of being doesn't appear sufficient to deal with a situation that seems important to you and you sense that you are judged or are being compared to others and coming up short.  Then you look at someone else who IS considered successful there and think, "I can't be...trait...like...admired person...so I'll be...instead."   The new trait is used to be successful and "make it" in life in order to get acknowledgement and acclaim but it is exhausting, unsatisfying and limiting as it prevents any other possible way of being from being available to the person and those under their influence.  It is also tiring because every time it's used, it reminds you of the original incident of your failure and your judgement (on yourself) that you're not good enough.  It is distinct from the Genesis of Identity as that happens automatically, and here, although there seemed to be something to survive, you had time to make an informed decision on how you'd do that.
 * Superstition. The system of ideas, beliefs, social and cultural assumptions, and taken-for-granted conclusions, etc., through which an individual interprets and interacts with the world, other people, and himself or herself. Shinigami Realm NOTE: This is not a Landmark term. Just the generic meaning of the word is used in Landmark programs. Grantlam (discuss • contribs) 01:32, 23 September 2016 (UTC) In Landmark it is taken a step further, to challenge the fixed impression of identity and reality by examining the words "I" and "is".
 * Throwing your hat over the wall. Committing to an outcome without knowing how it can be accomplished, comes from a story told by Irish writer Frank O’Connor of two boys standing beside a tall orchard wall, wanting to pick apples.  They didn't know know how they'd get over the wall but they did know they'd get in trouble if they came home without their hats so they threw them over the wall and climbed after them.
 * Transformation. The invention of a new realm of possibility for yourself and your life. Grantlam (discuss • contribs) 01:32, 23 September 2016 (UTC)
 * The invention of the realm is a necessary condition, but not sufficient for transformation. Without resultant new actions in alignment with the possibilities populating the realm, the invention is just a mental exercise. AnyTDorH
 * Transformation is used in the sense of a new state of being where the experience is generated from the Self, as a Self-expression instead of from the identity, from the fixed, repetitive patterns of behaviour.

 * Transformative learning. Transformative learning, gives people an awareness of the basic structures in which one knows, thinks, and acts in the world. From that awareness comes a fundamental shift that leaves people more fully in accord with their own possibilities and those of others. Grantlam (discuss • contribs) 01:32, 23 September 2016 (UTC)
 * Transformative learning is contrasted with Informational Learning. Informational learning increases knowledge and ability.  Transformative learning results in new perspectives and new abilities (and sometimes disabilities).  The common example is of learning to ride a bicycle.  Very little information is provided, like "pedal".  Suddenly the learner gets balance and is able to ride the bike without help.  They have discovered it for themselves, and may never lose the ability to ride a bike.  The experience, the learning, transforms the person, their perspective and their abilities.  Before they couldn't, now they can. And, a whole new world or realm of possibilities is opened up. AnyTDorH

 * Trump Card. The card you pull out to deflect a challenge to your Act. It appears as an unspoken taunt, challenge or gesture such as "Get lost!" or "Why should I? You're a loser anyway".  It is so consistant it is extremely predicable when someone is being their Act and don't realise it, they will simply act out this way every time.
 * Upset. All upsets that occur in life come from one of these three things: 1. A thwarted intention. You had some intention to be fulfilled and it was thwarted in some way. 2. An unfulfilled expectation. You expected some result and it didn't happen. 3. An undelivered communication. You withhold something that needs to be said, or someone withholds from us, and we get upset. see: https://www.coachruben.com/the-three-elements-of-an-upset/

 * Unreasonable. Not to be mistaken for irrational; it is going beyond one’s reasons, justifications and considerations to act on something one is committed to. Grantlam (discuss • contribs) 01:32, 23 September 2016 (UTC)
 * Unreasonable Request. A request that requires one to go beyond one’s reasons, justifications and considerations to act on something one is committed to. Grantlam (discuss • contribs) 01:32, 23 September 2016 (UTC)
 * Vicious circle.™ The human tendency to collapse what happened with the story we tell about what happened. Grantlam (discuss • contribs) 01:32, 23 September 2016 (UTC)
 * The story creates a clearing, a listening, for that which supports the story, resulting in more occurrences of things that further support the story, forming a self supporting vicious circle. AnyTDorH

 * What happened. Consensual reality, "objective," aside from judgment, blame, right/wrong, good/bad, and other forms of "meaning." What happens occurs to us as it is analyzed by the Already Always Listening to be good/bad, etc. If my ex-wife told me she had a problem with what I've done, that's what happened. If I say that she was unreasonable, that's my story about it, not what happened. See also Story. --Abd NOTE: This is not a Landmark term. Just the generic meaning of the word is used in Landmark programs. Grantlam (discuss • contribs) 01:32, 23 September 2016 (UTC)
 * Winning Formula. See Strong Suit. The Winning Forumula was a later term for this distinction.

Terms with "™" are known to be trademarked by Landmark Education.

Definitions to be added

 * Alacrity
 * Assertion
 * At choice (vs. at effect)
 * At stake
 * Being
 * Choice
 * Commitment
 * Communication
 * Competencies
 * Complaint
 * Complete
 * Conspiracy
 * Dimensions
 * Fixed way of being
 * Generate is to choose to create thoughts of possibility and making it happen. Also, making a list of effective actions to move it forward.
 * Gossip
 * Got it. means you understand what the other person is saying.
 * Ideals
 * Incomplete
 * Language
 * Levels of Self
 * Looking good
 * No agreement
 * More, better, different
 * On the court (or in the stands)- playing the game of life by taking actions and being in the game, not watching from the bleachers.
 * Principles
 * Presence of a person
 * Realm of survival/Realm of enrollment
 * Self (with a capital S)
 * Sharing
 * Significance
 * Source
 * Stand
 * Standards
 * Technology
 * Touch, move, or inspire (define the whole phrase as an indicator of enrollment + define each term)
 * Transform (versus change)
 * Upset
 * Values
 * Velocity
 * Vitality
 * What's so


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User:Borkzorkorc

borkzorkorc I am. nerd-geek bridge & unabashed learn-o-phile.

This Space Intentionally Left Blank ...   hee :-)

Borkzorkorc 22:02, 6 April 2011 (UTC)

title: User:Borkzorkorc


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User:Groverjones

groverjones

title: User:Groverjones


text: Category:Survey research and design in psychology/Tutorials/Multiple linear regression


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Action Research

Action Research, also called Participatory Action Research pursues action (or change) and research (or understanding) at the same time (Dick, 1999). Richards and Morse (2007) categorise Action Research as ethnographic research, specifying that Action Research challenges the researcher-participant relationship. Action Research is not conducted on people, but with people. Participants are part of the discussion on what will be researched, how it will be researched and what happens to the findings. It is a reflective, democratic practice. which values what people know. Action Research is generally about achieving change through helping participants reflect on a situation, a practice, a process. The aim is generally to change this situation, practice, process.

Prerequisites
Participants and researcher have to have shared goals. Stakeholders want to improve a situation.

The researcher and the participants
The research is led by participants, and the researcher’s role is to provide expertise on how to address an issue.

Data collected
Can be qualitative or quantitative, depending on what participants want to research.

Results
Participants own the results of the research and use it to change a situation, solve a problem.

References and resources for Action Research

 * Dick, Bob (1999), What is action research? Available on line at http://www.scu.edu.au/schools/gcm/ar/whatisar.html
 * Kemmis, S. & McTaggert, P. (1988). The action research planner. Geelong, Victoria: Deakin University.
 * Herr, K. & Anderson, G. L. (2005). The action research dissertation: a guide for students and faculty. Thousand Oaks, Calif.: Sage Publications. This book provides a broad and clear overview of the varieties of action research. It shows that action research is appropriate not only for a dissertation, but also a deeply rewarding experience for both the researcher and participants. This book helps students understand the ways action research dissertations are different from more traditional dissertations and prepares students and their committees for the unique dilemmas they may face, such as validity, design, write-up, ethics, and defence of the dissertation.
 * Wadsworth, Y. (1997). Do it yourself social research (2nd ed). St. Leonards, N.S.W. : Allen & Unwin, 1997. UC Library HM48.W3 1997
 * Wadsworth, Y. (1997). Everyday evaluation on the run (2nd ed). St. Leonards, N.S.W. : Allen & Unwin. UC Library: H62.W23 1997

See slso

 * Qualitative research

title: Action Research


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User:Organicfood101

Health Advantages of Natural Food And Why It really is Essential To get Them

title: User:Organicfood101


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User:CBennett

Reflective Practice Analysis

War as a political construct and philosophical debate has been generally accredited to Chinese military philosopher Sun Tzu and his opus magnum ‘Art of War’, still considered a defining piece of literature on the topic of military theory. Games such as chess and the Japanese Go have existed throughout history in one form or another, representing both the battlefield and military strategy. Archaeologists have even discovered miniature infantry figurines symbolising Ancient Egypt and Sumerian armies. As a philosophical text Tzu sought to remover the element of chance from warfare; through a realist paradigm this decision appears rational, as chance is based on several internal and external factors outside of the soldier or player’s reach. In doing so, a greater emphasis is placed on military prowess becoming a defining characteristic. For example, in the game of chess it is not the ‘capturing’ of the most pieces that defines the victor, but the one capable of out-manoeuvring the other.

French Marxist theorist and founding member of the ‘Situationalist International’, Guy Debord, created the Game of War as a representation of the works of Prussian military general Carl von Clausewitz. Debord’s fascination with Clausewitz was based on the inexplicable military aptitude of the significantly smaller Prussian army and how, through Clausewitz utilisation of military strategy, was able to defeat the French revolutionary during the Rhine campaign of 1793-1794 and later, Napoleon’s invasion of Russia in 1812. From this point onwards however, we see a departure from Clausewitz’s principles outlined in On War. Whilst Debord attempted to capture the realism of the battlefield on the game board by constructing an artificial reality, this had the opposite effect of limiting the player’s sense of self. Clausewitz had intended to reveal the humanity expressed during war, ‘War, and the form which we give it, proceeds from ideas, feelings, and circumstances’. This being said however, The Game of War still requires players to adopt specific skills intrinsic to military thinking e.g.: evaluating their own abilities and potential in order to out-play their opponent and their forces. Of this, Debord Situationist International refers to the four objectives hoped to be explored whilst in ‘battle’: Provocation, Psychogeography, Détourment and the individual’s participatory creativity; of these it is détourment that represents the conflict against a capitalistic society.

The détourment defined by Debord and the Situationist International was perceived as a multitude of subversive pranks; otherwise considered a form of recuperation, it constituted forms of a capitalist system against itself. This concept had previously been exhibited by both the Surrealist movement with Rene Magritte’s poster ‘C’eci n’est pas une pipe’, an example of rejection towards the rationalisation and homogenisation of society. In addition the Surrealism was the priori movement known as Dadaism, where by creating anti-art cultural works they sought to mock the transient meaninglessness of capitalism and the war needed to perpetuate the system. The abstraction of détourment can be witnessed in the game of war through the player’s analysis of strengths and weaknesses of variously positioned pieces; be they structure, infantry or Calvary by devising strategies and employing decoys over coming the opponent, the victor hopes to achieve their objective. Further examples of military chess such as Christopher Weikhmann’s Koenigspiel are thought to have adapted chess whilst incorporating the philosophical teachings of Sun Tzu and Clausewitz. Although Weikhmann claimed that his game ‘was not designed to serve merely as a pastime but that it would furnish anyone who studied I properly a compendium of the most useful military and political principles’, he was not without scornful critics. Of this, war gaming culture as represented by Weikhmann, as an adequate adaptation to realism fails to convey what more could be gained ‘than basic terminology and principles of warfare’, than knowledge that could be learnt through military literature. As a tool to understanding the individual’s potential by subverting the norms of society, Guy Debord’s Game of War can be judged a success. Nonetheless, in regards to Clausewitz On War it can be said that although military chess attempted to capture the realism of actual warfare, it only succeeded in resembling it rather than simulating conflict. It is peculiar then for the player to see this game as a reversal of the original meaning. In reference to the genre of war-games, this awkward relationship was succinctly described by McHugh whom noted ‘In some ways it might be considered as having the same relationship to later war games as the game of Monopoly bears to current business games’

The game of Monopoly was intended to illustrate the negative consequences of concentrating land into the hands of the independent few. Elizabeth J. Maggie Phillips created the game hoping it would help explain the Georgist pre-eminent theory held by Henry George. George’s economic ideology and philosophy resulting in his ‘single tax’ theory held that the individual’s right to their intellectual property was without exception, but everything that exists within nature, with particular emphasis on land, was of communal property. This being the case it is clear to see how Phillips had hoped to expand on this throughout Monopoly. Furthermore, the tax gained from landing on the property of another, according to Georgist economic theorists transposes the suggested ‘single tax’ of land into the game-playing realm.

Originally patented as ‘The Landlord’s Game’, the social implication of the game was to show that the concept of rent bettered the proprietor whilst depriving the tenant; causing a monopoly of resources. One of the many reasons Monopoly is considered a gaming success, is in part thanks to the organic development over the years. After the game’s formal publication in 1906 it entered academic circles, used as a teaching tool by Professor Scott Nearing, who taught in the finance department of the University of Pennsylvania. Over the years various additions had been made to the game, mainly by Phillips after renewing her patent, to include: a change of street-names, symbolising the transferable qualities of the game; the inclusion of a ‘Monopoly’ card, allowing the user to charge a higher rent on the basis of wealth accrued; and counters indicating the degree of improvements. Nonetheless, it wasn’t until Charles Darrow that Monopoly began receiving widespread popularity. Although this is not to suggest that Monopoly became an instantaneous success.

According to Salen the fundamental problem with many fledgling games is identifying the elusive ‘sweet spot’, which is described as when the player stops thinking of the mechanics of the game, due to a loss of self-consciousness. In understanding the mechanics of a game one can play the game. This analysis draws a distinction between ‘playing’ and ‘enjoying’, labelling them as different on the basis understanding. Herein lays the critical criticism on Monopoly. Arguably an enjoyable game to the many socio-political theorists, Georgist economists and students whom aided in its initial development, Parker Brothers failed to see its mass-market appeal stating it was ‘too complicated, too technical…took too long to play’, as well as listing ‘52 fundamental playing errors’. Despite the fact that one might claim the rules are overly complex, the sweet spot is achieved through the game’s mechanics. Whilst cooperative games have there place in society by engendering a sense of mutual partnership and community, it could be asserted that in a Pluralist society cooperation of resources would result in opposition groups, cooperating to achieve a monopoly. In regards to opposition and competition, a key aspect to all versions of Monopoly is the struggle. In a two-player game such as chess, the game is direct competition. In the case of Monopoly which allows up to four-players, this introduces an element of diplomacy. Though Salen claims that Monopoly does not result in ‘combining against a mutual foe’ as there is ‘no effective way to either help or hinder anyone else’, it is through idiosyncratic game-play where non-regulatory rules become established norms. If we are to accept this, then diplomacy becomes a turn-by-turn tool used and denied when seen fit, further adding to a sense of realism attributed to property realty. The terminology of ‘kingmaker’ finds its origins during the War of the Roses, set in England (1455-1487) and was used to describe the qualities of Richard Neville, 16th Earl of Warwick. The term itself has entered mainstream culture to mean ‘a person or group with such influence to decide royal or political succession’; it can therefore be suggested that the value of said kingmaker initially outweighs that of any potential successor. This does not mean that said individual can gain a political or royal hegemony, their power is only realised when transferred to an adequate candidate.

Andrew McNeil’s Kingmaker allows the player to build and control the military might of various noble families; this establishes a fair playing ground as both Houses have an alternating quantity of resources readily available. Whilst a hierarchy of power resulted in few direct royal conflicts, warring Barons and knights was an accepted norm in the distribution of land. However as Huizinga notes, each player would mutually respect the other as their equal regardless of royal affiliation ‘We can only speak of war as a cultural function so long as it is waged within a sphere whose members regard each other as equals or antagonist with equal rights…’. This recognition lf equality is paralleled in Kingmaker through McNeil’s adherence to the characters central to the War of the Roses, e.g.: Nobles such as Neville, Beaufort and Percy; historically established titles, Earl of Essex and Duke of Exeter; and essential ecclesiastical offices, Archbishop of York and the Bishop of London. In reference to the king making process McNeil’s game-play explanation turns the game into a pedagogical tool allowing the players to gain a basic understanding of English geography, medieval history and the medieval hierarchical system. In addition to this, if not more importantly, it causes the user to comprehend the military strategies possible based on terrain and alliances, as well as accepting their own military limitations.

Unlike the contemporary definition of a kingmaker where the individual decides the victor based in their preference, certain requirements must be achieved in order to win the game. Although the game states that an Archbishop can decide ordain a king by divine decree, should a player be lacking, two Bishops at Westminster Abbey will suffice. This rule is a slight detraction from an accurate re-telling of the war. When Edward of March reached London one Bishop of London, Thomas Kempe, unofficially ordained him King at Westminster Abbey. Despite the lack of dice, supposedly removing the element of chance in the game, the use of random events cards surely re-introduces luck to the game. Events such as Serf uprising, Tempest as sea or the Bubonic plague would have been considered a blessing or curse depending on the individual location, as Huizinga believed ‘the fall of the dice may signify and determine the divine workings; by it we may move the gods as efficiently as by any other form of contest’. With this in mind, the winner is often defined by the player’s use of diplomacy. Should a certain character become too strong or hostile weaker players tend to form alliances of mutual understanding; nonetheless, the pretence of diplomacy will only exist for as long as it holds value.

It remains crucial for the player to perceive games not only within a sphere of strategic possibilities ‘but are also spaces of representation of things both real and make-believe’; in this way the player can gain a greater understanding of the representative world created through game-play. Anders Fager’s Comrade Koba card based strategy game reworks the Soviet Purges of Josef Stalin, becoming a turn based game of chance and misdirection. Whilst a system of representations – based on gender, sexuality, race or class – enables an alternative imaginative discourse to exist, such a Chess or Monopoly, the fundamental structure of Comrade Koba does not allow for multiple interpretations. This can bed considered the main downfall or criticism for games following the rigid formation of history; the use of external prior knowledge, assumptions and expectation fail to alter the historical background. The reality from which the game is abstracted remains unchanged.

The basis of the game follows ‘Koba’, one of Stalin’s many nicknames, and an era of Soviet history known as the Great Terror. At a time of suspicion, internal conflict and betrayal each player represents a member of Stalin’s political cabinet. Vying to prove their loyalty by accusing others, players move one to two character cards closer or further away from Koba. The purpose of this lateral movement is representative of the supposed randomness of the Purges, where at times a Politburo member’s survival was defined by the proximity. It therefore becomes vital for the individual to be aware of other players’ movement; questioning the motives as genuine, a bluff or a double-bluff. On this, Roger Caillois emphasises, in regards to more cerebral gaming, ‘…the risk for the player of missing his stroke, at the threat of defeat’. As each character receives three character cards it heightens their chance of survival, at the same time minimising it due to the increased probability of ‘accusation’. Comrade Koba remedies this by selection on the basis of misinterpreted game-play and plays on the individual’s belief of a higher knowledge; doubt therefore must remain a certainty in order to maximise enjoyment. In the case that the end result comes in advance to either the individual or all involved, the purpose of the game is lost.

Bibliography

Clausewitz, Carl von. On War. Palgrave, MacMillan. 2006

Evans, David. Appropriation. Massachusetts. MIT Press. 2009

Huizinga, Johan. Homo Ludens. Routledge.2002

Perla, Peter P. The Art of Wargaming. Annapolis, Maryland. Naval Institute Press 1990

Salen, Katie; Zimmerman, Eric. The Game Design Reader: A Rules of Play Anthology. Massachusetts. MIT Press.2006

Website

The Guardian. “Hard times turn to gaming, but not everyone will be a winner”  Accessed: 01/04/2011

title: User:CBennett


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User:Nobody60/Nils/God and Quantum Physics

<God '''God is a higher field of consciousness in the cosmos. God is the enlightenment energy. God is love, peace, happiness and a higher truth. Man needs a cosmic consciousness. Man has to think nondualistic. Man has to feel himself one with all. Physics can help to understand God. One can realize a life in God only through the enlightenment. The path to enlightenment goes via the spiritual exercises.'''

God and Quantum Physics
According to some quantum physicists (Hans-Peter Dürr, Amit Goswami, Michael König), there is behind the material world a hyperspace that can be regarded as an afterlife or a heaven. Basis of this assumption is the proved (verified) phenomenon of quantum entanglement. If two entangled (by contact "mentally" connected) photons (light particles) can communicate over a large spatial distance much faster than light (immediately), there must be a higher dimension (a hyper-space) through which this is possible. Because the special theory of relativity from Einstein shows that signals spread out in the traditional dimensions of space can do this not faster than light speed.

Evidences for the nature of the hyperspace are not yet available. There are the string theory and the many-worlds interpretation of quantum physics. If they are verified a multi-dimensional universe (multiverse) can derived from them.

The French physicist Jean Emile Charon (1920-1998) developed the complex theory of relativity, meaning that there is a photon gas in the interior of an electron, which can form structures and is a kind of inner memory of the electron. The consciousness of man can for Charon be stored in electronic memory (see Biophotonics). Since electrons have an eternal life, the German physicist Michael König made in the 1980s the hypothesis that essence electrons form in the body of a man an eternal soul. They continue to exist after the death of the man and incarnate again later on into a new body on the earth. For the existence of a soul independent of the body speak, according to some scientists, the findings of the near death research, the reincarnation research and the after death experiences of the 16th Karmapa. [http://www.buddhismus-heute.de/archive.issue__37.position__5.de.html The death of the 16. Karmapas, Dr. Mitchell Levy (germ.)].

'''The physicist Burkhard Heim (1925-2001) made a quantification of space and time with the extended quantum field theory. He assumed that the space is filled with tiny quantum and that there are also time quantum.''' Spiritually formulated, one would say that the universe exists out of light (an ethereal substance). A mystic can feel this. The hyperspace is not empty, but filled with "light". So Burkhard Heim was able to calculate the hyperspace beyond matter. Overall he found a twelve dimensions universe. Charon and Heim are previously little-noticed in the current physics. But things can change. Outsiders may be the mainstream.

'''The German quantum physicist and mystic, Michael König (b. 1957) published in 2010 the book, "Das Urwort (The physics of God)." In it he made the Firstword-theory. Our universe is an idea of God. All begann with the wish of God that a cosmos with thinking beings should be there. He spoke a mantra (ELI) and the multiverse was started. Consciousness is the center of the universe from which everything is developing.''' Michael König has worked up the theories of Charon and Heim and extended. This enabled him to confirm through quantum physics, what was found by the enlightened ones and mystics of all time by the inner exploration of their consciousness. With his Urword-theory he connects the traditional knowledge of the mystical philosophy with quantum physics.

In accordance with the traditional Indian philosophy our entire universe exists out of three primary areas, the material cosmos, the afterworld and the heaven (God, Light World). Through spiritual practice, a person can develop a light body and ascend to higher realms of consciousness. On earth, there will be a golden age in the future, based on the association of spirituality and science. "And God's light will flood through all people, (...) all love each other, they will laugh and be happy." (Michael König, Das Urwort, p. 265.)

'''God is a higher dimension of consciousness consisting of energy, love and information (ELI) in the center of our multiverse. From this center, the Eta-particle (basic light-quantum) flow and form the heaven, the afterworld and the material universe.''' After the teachings of hinduism at the end of time everything flow back into God, and after some time of rest the dance of Shiva starts again. But it will take an eternity, until everything dissolves in God. Until then, we can live as happy souls in the multiverse. Or as unhappy souls, if we prefer this.

'''The mathematician Klaus Lange has reviewed the theory of Michael König, that God is a high density of energy (light, love, consciousness) in the center of our multiverse. He found two things who can be tested experimentally.'''(Der Mathematiker Klaus Lange zur Urwort-Theorie.) Now we just have to wait until the test takes place. Science will make a quantum leap.''' Love is the essence of the universe. We do not fight against each other anymore, but together we build up a happy world.''' We create the paradise on earth and after we die we all get up into heaven. Until then, it can still be a long way, as the previously unsuccessful attempts to prove the string theory show. But we can be optimistic because the near death research, the reincarnation research and the visions of the enlightened point towards provability.

American Physics Professor Amit Goswami
A key supporter of this theory is the American Physics professor Amit Goswami from the University of Oregon. He wrote the book “The Conscious Universe” in 1992. In his book, Goswami describes the most important discoveries of today’s quantum physics. He also develops his philosophy regarding monotheistic idealism. The monotheistic idealism explains that everything in the cosmos belongs together, to one consciousness, to God. This world view is also found in the philosophy of yoga. In this philosophy, consciousness is the primary substance of the cosmos. Consciousness can be seen as God, as a higher dimension which resides over our material cosmos. Enlightenment should be the centerpoint of mankind’s thought patterns. '''The new world view of physics says that we all belong together, that we are all connected. We live in one cosmos, and are of one energy. We are all connected through the higher dimension in a spiritual sense.''' When we are aware of this, we can let go of egotism and pay more attention to the good of all. Goswami: ''From the beginning of the field of Quantum physics in the year 1900, physicists have indicated that we can change our perspective of things. From 1982 came results from a Lab experiment in France where Alain Aspect and his colleagues conducted an experiment that could show the connection between quantums to a higher dimension.'' ''In this experiment, an atom produced two photons which went in opposite directions. Afterwards, these photons still influenced one another without exchanging any type of signals. What is significant here is that these two particles influenced one another after this separation without exchanging signals. When the rotation of one of the two photons was altered, the rotation of the other changed accordingly and in a measurable way.'' ''Einstein proved long ago that two objects in space and time can never influence one another immediately as everything can only function within the maximum speed that is the speed of light. It was thought that every signal is bound to space and only needs a certain amount of time to move itself through space. Photons freed from atoms in the course of an experiment can influence one another in a particular territorial distance within the blink of an eye, quicker than the speed of light. In conclusion, this control element could not have moved itself through space and therefore it must be implied that the influence it had occurred in another dimension of time and space.'' Hamilton: What was your special discovery? Goswami: ''I was fortunate enough to recognize, via quantum physics, that all the paradoxes of this field could be solved once we take into account consciousness as the basis for all existence. I recognized that consciousness is the primary form of reality. A higher reality exists over our material cosmos which consists of consciousness energy.'' ''The universe is a conscious universe which is generated via consciousness. Consciousness is the only reality that exisists outside of the physical space and time. Consciousness isn’t an ephiphany of material, rather a result of the brain. Consciousness doesn’t come from material, rather, it can influence material in and of itself. The world of manifestation comes from a transcendent world of ideas.'' ''The brain researcher John Eccles identified that the nerve signals in the brain are based on quantum waves. Here is the big point of connection between the spiritual and the material world. The spirit is energy which is separate from the body which can affect the brain as the tiniest particle of our cosmos via quantum particles.''
 * Interview with Amit Goswami (by Craig Hamilton, Quotes)