Changes

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<math>\begin{array}{ccccc}

<math>\begin{array}{ccccc}

x      & = & f(u, v) & = & \underline{((}~ u ~\underline{)(}~ v ~\underline{))} \\

x      & = & f(u, v) & = & \underline{((}~ u ~\underline{)(}~ v ~\underline{))}

\\

\\ \\

y      & = & g(u, v) & = & \underline{((}~ u ~,~ v ~\underline{))}             \\

y      & = & g(u, v) & = & \underline{((}~ u ~,~ v ~\underline{))}

\\

\\ \\

(x, y) & = & F(u, v) & = & ( ~\underline{((}~ u ~\underline{)(}~ v ~\underline{))}~ , ~\underline{((}~ u ~,~ v ~\underline{))}~ ) \\

(x, y) & = & F(u, v) & = & ( ~\underline{((}~ u ~\underline{)(}~ v ~\underline{))}~ , ~\underline{((}~ u ~,~ v ~\underline{))}~ )

\end{array}</math>

\end{array}</math>

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For example, in some applications the discursive universes <math>U^\circ = [u, v]</math> and <math>X^\circ = [x, y]</math> are best understood as diverse frames, instruments, reticules, scopes, or templates, that we adopt for the sake of viewing from variant perspectives what we conceive to be roughly the same underlying objects.

For example, in some applications the discursive universes <math>U^\circ = [u, v]</math> and <math>X^\circ = [x, y]</math> are best understood as diverse frames, instruments, reticules, scopes, or templates, that we adopt for the sake of viewing from variant perspectives what we conceive to be roughly the same underlying objects.

When we consider a transformation in the alibi interpretation, we are thinking of the objective things as objectively moving around in space or changing their qualitative characteristics. There are times when we think of this alibi transformation as taking place in a dimension of time, and then there are times when time is not an object.

When we consider a transformation in the alibi interpretation,

we are thinking of the objective things as objectively moving

around in space or changing their qualitative characteristics.

There are times when we think of this alibi transformation as

taking place in a dimension of time, and then there are times

when time is not an object.

For example, in some applications the discursive universes

For example, in some applications the discursive universes <math>U^\circ = [u, v]</math> and <math>X^\circ = [x, y]</math> are actually the same universe, and what we have is a frame where <math>x\!</math> is the next state of <math>u\!</math> and <math>y\!</math> is the next state of <math>v,\!</math> notated as <math>x = u'\!</math> and <math>y = v'.\!</math>  This permits us to rewrite the transformation <math>F\!</math> as follows:

U% = [u, v] and X% = [x, y] are actually the same universe,

and what we have is a frame where x is the next state of u

and y is the next state of v, notated as x = u' and y = v'.

This permits us to rewrite the transformation F as follows:

<u', v'>  =  F<u, v>  =  <((u)(v)), ((u, v))>

<u', v'>  =  F<u, v>  =  <((u)(v)), ((u, v))>