An Explanation of Direct And Inverse Proportion

Introduction

At least one of my other posts How Distance Reduces The Power of Radio Waves (not yet published) requires an understanding of mathematical proportionality. In particular it requires an understanding of Inverse Proportion. So I have written this article to try and clarify it. It gives an explanation of the two types of proportion, otherwise known as variation, which are:

  1. Direct Proportion,
  2. Inverse Proportion otherwise known as Indirect Proportion.
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Manual Search Using Binary Chop

The Problem To Be Solved.

A good friend of mine had found that an Excel spread sheet no longer had a formulae in a particular cell. It had a number there instead. This meant that any changes in other cells associated with the missing formulae had no effect on the result in the TOTAL column. He wanted to go back to a time when the spreadsheet had the correct formulae in it. He had many backup files and feared he might have to examine each file until he found when the problem occurred. So I advised him of a quick way to examine his backups using a binary chop method to look at just a few critical files.

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The Faster-than-Fast Fourier Transform

Improving The Fast Fourier Transform

The Faster-than-Fast Fourier Transform can replace the Fast Fourier Transform to save processing time when digitising an analogue signal.

For a large range of practically useful cases, MIT researchers find a way to increase the speed of one of the most important algorithms in the information sciences. – Larry Hardesty, MIT News Office.

You can read it all here: MIT News Office.

Well this might be the case but it could so easily be that everyone takes it at face value and embodies this algorithm into all new electronic sound and video processors. We may then find all our music and video content degraded as a consequence. Then it will be too late. With the Faster-than-Fast Fourier Transform processing sound and video is quicker and cheaper so we’ll be stuck with it. Musicians who prefer analogue sound reproduction may find this degrades digital sound further. On the other hand it could improve the quality.