The nature of number

[Whateverist]

Hello .. anyone still here? I've had an idea about your wiggling number line mappings, jon.

Ok lets play with this can we now do anything with it?
Well I have found you are not restricted to just comparing one number at a time, you can compare a series of numbers to a second series.





So to draw this up we only need the outer parameters of the two series and a function point



You will notice that the direction of the resultant series is in the opposite direction to the original series.

So we can either reverse the order of the numbers, or, if you prefer, just multiply by the opposite of each number.

Another issue is that the spacing of the whole numbers in each series (which I think of as the scaling on your number lines) is not identical. If this matters to you one way to fix it would be to move the location of the point which serves as the fulcrum for the rotating line.

If you multiply by 1, the fulcrum point is exactly midway between the two number lines. But if you multiply by 2, to maintain equal spacing between numbers you would have to move the fulcrum twice as far from the line containing the results as from the line containing the numbers which are multiplied by 2. The larger the number you multiply by, the greater the distance to the line containing the results. So I imagine placing the fulcrum point on a slider between the two lines. Now the length of a 'unit' on the starting line and results line can be equal.

With this adjustment there is no longer any problem with multiplying by zero. When multiplying by zero the fulcrum would simply be hard up against the results line at the zero point. All numbers on the starting line go only here.


[Alternatively, we can keep the fulcrum fixed midway between the two lines but allow the multiplication but allow the spacing of the numbers on the results line to increase when multiplying by numbers greater than one and shrink when multiplying by positive numbers less than one. In that case, when multiplying by zero the spacing between numbers becomes zero and any particular segment of the results line shrinks to zero too.]