**A never ending story**

The history of the cosmos. In quaternionic physics one equation plays a major role. It is a mixture...

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Recently Leonard Susskind introduced a new type of objects and called them ziggs.See: http://www...

A long time ago (≈1975) I was involved in establishing a world standard for the measurement of the Optical Transfer Function (OTF). It is better known as its modulus, the Modulation Transfer Function (MTF). The OTF combines the MTF with the Phase Transfer Function (PTF). The OTF is a two dimensional Fourier transform of the Point Spread Function (PTF). Thus, it is a two dimensional frequency characteristic used for qualifying imaging devices and chains of imaging devices.

Since the image of a point contains very little energy, the OTF is measured by analyzing the Line Spread Function (LSF).

_{t}can be mimicked by a trail of infinitesimal unitary transforms. Each subsequent trail element has eigenvectors that differ from those of its predecessor. These eigenvectors are also eigenvectors of Ɽ

_{t}. For a single vector, which is not an eigenvector of Ɽ

_{t}, the action of Ɽ

_{t}can be represented by the integrated activity of this trail on that vector. This can be interpreted as the activity of a genuine unitary transform U

_{t}. When a redefiner Ɽ

_{t}is applied to the eigenvector |q> of an operator Q with eigenvalue

*q*, then the eigenvector is transferred into another vector |U

_{t}q>. The expectation value for |QU

_{t}q> is no longer

*q*, but

### The OTF

Dynamic quantum logic

# Abstract

I thought that I knew what a unitary transform is, until I started thinking about it.

(2^n-ons are hypercomplex numbers that are related via the 2^n-on construction. Including n=3 the 2^n-on construction gives the same numbers as the Cayley-Dickson construction. From there the 2^n-ons are "nicer".)

I know the following: