Beyond Newton · Modern Times

Beyond Length Times Breadth

We all know from our earliest days in school that to find the area of a rectangle is to multiply its length by its breadth. The formula usually looks something like this:

A = L x B

The ‘x’ in this case being used to describe the operation ‘multiply’ – that is to say, timesing. This is not a post on the intricacies of number theory.

The first thing that most people will have missed in this instance is that to apply this formula, you first need a rectangle.

Only in the rarest of occasions do you ever find a rectangle in nature; on a farm, where fields are enclosed by fences or hedges, more often, they are an irregular shape. It all depends on who did the enclosing. More mundane but industrial products are rectangular and are so on account of their being easy to manufacture. Ease and cheapness work hand in hand. Nature has far more elegant and sensible solutions that arise out of nature’s laws directly. The hexagon is nature’s choice, as in the beehive. Nature doesn’t count the cost, nature doesn’t have to.

We have here two radically different approaches to the world. The first is dependent on establishing a rigid rule, the rectangle; the other derives the solution out of the creative forces of nature itself. We will return to this, later.

What Is An Equation?

The simple equation given above is an abstraction; well that’s pretty obvious, isn’t it? A rectangle can be any size and the equation applies to all of them. Any length, any breadth and you have an answer. So instead of having a book that has all the areas for different sizes of rectangle, we can remember the simple equation instead – or, on seeing a rectangle, be reminded that we’d forgotten it.

The process of abstraction is one that is invariably materialistic, though. Here we establish the length and the breadth using arbitrary measures; the ‘inch’ is less arbitrary in that it springs from the length of the thumb. The foot and yard equally so. The danger we are unaware of is that we have to use the ultimate abstraction to determine how many of these ‘commodities’ there are: number.

Number And Measure.

The way we measure a rectangle is something we have to do, have to understand before we can do it. This is not a natural procedure, for all its being so obvious. The problem with ‘obvious’ things is that it is something you’ve been taught.

Number is not something one finds in nature, not at least in the form we use it. Numbers do exist in nature, but do so in a way that is a million miles away from what we think it is. That’s for an upcoming post on Russell and Whitehead’s “Principia Mathematica” – but please do not run: I will be discussing the issue of 1+1 = 2 and doing so in words, not mathematical jargon.

If you are going to measure something, you first have to want to measure it. This will seem odd to the bloke who measures out the parking bays, but it’s no less true for all that. Parking bays do not measure themselves any more than a hillside marks out the fields. We enclosed the field, and on selling it, the buyer wants to know how big it is. There’s another consideration too, that a rectangle knows nothing of: the wise farmer will take a few spades of soil to see how good that soil is – and measuring that is far less easy. Unless you happen to have an eye for it, as a good farmer will – he’ll be able to determine the quality in the blink of an eye; a chemical test will take weeks and will be far less certain. The quality of the soil will put the price of the field up or down accordingly. To the purchaser of a commodity, like a rectangle of printer paper, it is meaningless. The commodity has had all its qualities stripped away.

You get what you pay for, and nothing else!

And yes, we’ve drifted into the turbulent waters of price here. Only price is another measurement, only using a different ruler. We are still in the realm of number, and if you are in the realm of number. If you are going to find anything out, you have to use it: fields don’t measure themselves. But their fertility does grow by itself, and that is nature’s secret. A secret that no number will ever tell you about.

What is important to notice here is number is something we live with all the time. It is part and parcel of any modern culture, yet it is something that doesn’t exist in nature. As mentioned, it does exist, but not in the way we employ it. If we are to truly understand nature, we must understand how our usage of number is our own creation – and in having understood it, only then can we begin to understand the things we are trying to measure. We cannot understand the true nature of nature itself if we are contemplating the veil we threw over it.

Einstein remained at this point in his ability to think: he saw the world as number. He saw the veil that covers nature like a dust sheet, and not what was beneath it. It cannot be otherwise if one wants to force the subtlety of nature into a clumsy, ineffective equation. For all its power, his famous equation e=mc2 veils something vastly more powerful and vastly more dangerous than even the horrifying bombs we have today.

Thankfully Einstein’s equation is difficult enough for most scientists to leave it alone; they tie their hands together with their thoughts on number and will pick at the threads of the dust sheet instead of prodding the shape underneath it. The first you can measure, the second you can’t.

It’s how nature works. Knowing the difference is the first step in using its power wisely, and sometimes it means leaving it alone.


One thought on “Beyond Length Times Breadth

  1. If you look at nature with eye of mathematician you will find numbers , if you look at nature for the natural joy of it you will find wonder !


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