I noticed something a while ago. I was cleaning at school and came across a table with 3 columns. In the first column were the numerals 1 to 10, in the second column the binary values for 1 to 10 and in the third column the hex values for 1 to 10.
The curious thing I realized as I studied the table arose from the question “What do these symbols stand for?”
If I were to ask you what the binary value 10 stood for you would probably say “That stands for 2” and this wouldn’t give you too much trouble.
But what does 2 stand for? 2 is as much a symbol as 10.
The French word (read: symbol) for pineapple is ananas.
The English word for ananas is pineapple.
Ananas and pineapple are both symbols that mean the same thing as 2 and 10 mean the same thing. The difference is that the referent of the symbols for pineapple can be pointed to.
Say I ask you to point out 2 to me. You may direct my attention to a pair of nuts and say “There’s 2: 2 nuts”. If I subtract from the image everything that belongs to the nuts (shape, colour, size, position etc) then I am left with nothing.
There isn’t some entity I can point to and say “Look, there is 2”
This isn’t so much a problem in reality. It is a problem with a picture of language we have developed called the picture theory of language. That is the theory that states that all words have a meaning or that meaning is defined as being a correspondence between a symbol and what it signifies. Numbers are words, components of language that have no signified.
The other day at work I was thinking about numbers and how they relate to reality.
I don’t think there is any natural relation between numbers and reality; I believe we first create or discover categories in reality and then associate these categories with numbers.
For example: we create the category “leaf” and then we can make statements like “There are 146 leafs on that tree.”
A more scientific example would be the noticing of certain features of objects such as weight. We could then pick a certain amount of a certain element or object and designate that to be a unit of weight.
This designation is arbitrary. There may be reasons given for choosing this particular amount of this particular element such as how it makes it easier to combine with the measurements of other features of objects such as volume or something.
Still though the designation would be arbitrary because why choose to have a certain amount of space as a unit of volume? It could be said because it makes it easier to relate to other units of measurement; but then we’re back with the question “Why choose that specific something to be the unit for the measurement of that feature?”
But I have gone somewhat off track.
So numbers act as a very useful means for mapping out reality. Science is dealing solely with that part of reality that can be mapped out with numbers; that can be quantified and measured.
The problem is that science has increasingly become religious; especially in its public projection. It tries to say to us that all that exists is what is measurable. That is to say that anything that can’t be talked about in terms of number doesn’t exist.
I believe this is making the mistake of confusing the map with the territory.
There are different kinds of maps all of which are designed with a different purpose in mind.
There are maps that map the varying altitudes of a terrain designed for use by mountaineers and pilots; but they don’t indicate the colour of the terrain, the nature of the terrain and so on.
I think the claim that all that exists is measurable is the same as the claim that all a terrain is, is differences in altitude.