Of Numbers, Ratios, Fascism, Value

So the Greeks viewed geometry in terms of ratios of lengths and sides and stuff hence pythagoras's famous equality etc.

Ratios and equations are directly analagous to weighing scales. Sadly but true it was merchants and accountants whose trade necessitated and began the art of numbers and maths.

It occurred to me today that all numbers can be seen as ratios. Nothing new but never seen clearly to me before...

In elementary algebra we are taught to treat terms separately ... i remember as a kid trying to get my head around the rules : "3a + 4b = 7ab" seemed sensible that is 3 apples and 4 pears makes a pile of 7 apples and pears... not so. The point here is that numbers in reality are of "types" of things which means that we are comaring like with like! A pile of 3 apples is in a ratio of 3 to a pile of 1 apple. It is not in a ratio to a pear. The number 1 then arises through my old enemy of self-reference: everything is in a ratio of 1 to itself. But this is not a self-reference problem because the reference is external to the entity: when we say that an apple weighs as much as itself a priori we imagine an apple on both sides of a scale: but the scale is external to the apple. The self-reference problem is an entity which is by its own nature self-referential e.g. a scale which weighs itself. This annoying problem like a tooth ache still awaits solution.

When we measure the number of things we are not making any qualitative statement about the thing itself. 3 apples does not tell us what an apple is. To say that something is 100 miles long doesn't actually tell us how much space it occupies it simply tells us the ratio of this length to the length which we call a mile. We try to make sense of distances like a thousand miles by taking what we humanly know of a mile and do a bit of mental addition. Of course that mental addition is unrealilistic. 1000 miles is alot more than two 500 mile walks!

My criticisms of economy, employment, capitalism, politics have been aimed recently at the psychology of power and the misuse of people by one another. It is dawning on me that there is another illness in the system - a misunderstanding of numbers. I scanned a book a few weeks ago on this very subject and it has left an impression. David Boyle's "Tyranny of Numbers" looks at first scan as off the pulse but actually it explains more of the ills than my own analysis so far.

It is because we feel knowledgeable about things when we see the numbers, because we feel we know whales by a statistic of their size, or we know the sun by a statistic of it's surface heat, or know the concentration camps by a statistic of the body count. But this is accountant thinking. Does an accountant know an apple when we reads the receipt for 10 apples?

This is at the route of the old saying "knowing the price of everything but the value of nothing".

Value is Quality as Robery Pirsig would say (Zen and the Art of Motor Cycle maintenance) while Number of Quantity as we are familiar with.

You cannot know value when you have numbers, and judgements based on number are void of quality - that is disrespectful of the things being counted - that is in the terminology of this blog; fascism. It is not money that is at fault but numbers, and I propose experimentally that it is not Nazis at fault but numbers.

So far only Natural and Rational numbers have been discussed. A student of Pythagoras discovered - and was drowned for the heresay (Pythagoras in the midst of Nazi number madness) - a group of numbers that do not exist in a ratio to the numbers so far discussed. These are the irrational numbers things like e and pi. They can only be generated by infinite sums of the numbers so far discussed. Here my analogy between ratios and numbers collapses and numbers spin off out of worldly orbit.

Numbers are certainly an odd world, quite removed from qualitative value based reality: yet intersecting with this reality in qualitative concepts like ratio. You can use the methodology of ratio to get a number (more commonly called measuring e.g. 10cm is a length in a ratio of 10:1 with a cm i.e. 10 cm end to end) but you can't then measure the methodology. This has been my argument for many decades against science it doesn't have the tools for self analysis. It is the self-reference problem.

However I must add that pi cannot be measured since it does not lie in a ratio to anything: but we can determine an indefinitely accurate ratio which is as good as measurement. Somehow we have escaped the limitations of our human world of indefinite quality to postulate the existence of exact entities which lie in infinity - how Platonic is that! The mind is certainly greater than reality (greater in a qualitative not quantitative way - how could you measure the mind: What is the meaning when a ruler measures itself?).