The Inverse Square Law And Society

I have written two previous postings about more that could be done with Sir Isaac Newton's Inverse Square Law. One was "Do We Really Need Calculus", on the progress blog www.markmeekprogress.blogspot.com . This is about my observation that just about anything that can be calculated with calculus can also be accomplished by creative use of the Inverse Square Law.

The other was "Galileo's Paradox And Newton". This explains how Galileo's Paradox, that every number must have a perfect square yet few numbers are perfect squares which proves numbers must be infinite because this cannot be true of any finite set of numbers, is also solved by Newton's Inverse Square Law. As numbers get higher, perfect squares become more sparse according to the Inverse Square Law.

The Inverse Square Law is basically that if a source of light is twice as far away, it will be only one-quarter as bright. This is because the circle of circumference at twice the distance will have four times the area or circumference. Using the Inverse Square Law to explain Galileo's Paradox is simply applying it to numbers instead of space.

Today, I would like to point out that there is still more that is explained simply by this extremely versatile inverse square law.

First, there is one fact about technology, and all human organizations and enterprises, that I would like to establish. The more complex something is, the more room it has for improvement. Consider a chair and table. Chairs and tables are simple devices that have remained pretty much the way they are today since ancient times.

Now, consider a machine. Machines have many parts, and thus many ways in which the parts fit together. This means that machines have a lot of potential for improvement, since each part and each way that each part fits together could potentially be improved.

Technology has progressed on a steep upward curve. In times past, life remained essentially the same for century after century. Then, progress gradually began the upward curve which continues today. Some would consider the Industrial Revolution as the beginning of this steep upward curve. But few people would doubt that there has been vastly more technical progress in the sixty years from 1950-2010 than there was in the sixty years from 1800-1860.

My explanation is that the undeniable upward curve of technological progress is a function of the Inverse Square Law applied to the complexity of technology, based on the fact that the more complex something is the more room it has for improvement. Just as the area of the circumference circle of the Inverse Square Law grows larger as we move out from the point of origin.

Technology has a certain complexity because it is the result of us imposing our higher level of complexity on the lower level of the surrounding environment. This complexity gives it room for improvement, but this improvement usually means more complexity which gives the machine even more room for improvement. Hence the ever-steeper upward curve of technology, and it is all a function of the Inverse Square Law.

It is true that machines become obsolete over time, as more progress is made. But it must be remembered that a machine cannot be considered as an island of complexity unto itself, but exists within the context of the entire society that is progressing.

What about economics? If the Inverse Square Law is as all-encompassing as I am claiming it is, should it not have an influence on economics as well?

It seems to me that Newton's Inverse Square Law actually underlies the fundamental Law Of Supply and Demand. Suppose that a product is in demand, but is expensive. Now suppose that we suddenly start manufacturing four times as many of that product. The price is likely to drop by one-half, according to the Inverse Square Law.

If only the same number of people bought the product after four times as many were produced, the price would probably drop to one-quarter. But the increase in production would likely get more people to buy the product, who did not previously buy it because it was too expensive. This increased demand would cause the product to drop in price to one-half, rather than one-quarter, thus manifesting the Inverse Square Law.

Of course, the real world is complex and it may not work exactly according to these figures for each and every product. But, on the whole, we can safely state that economics, like progress in technology, operates by the Inverse Square Law which is commonly phrased as the Law of Supply and Demand.

Another economic rule which guides how people behave is the Law of Diminishing Returns. If you gained a million (dollars, pounds, euros, rupees, yuan, rubles, pesos, etc.) you would be better off. If you gained two million, you would be even better off than if you gained only one million. But you would not be twice as better off if you gained two million than if you gained one million.

While we cannot be precise with this, because it involves human nature, it is easy to see how this also is based on the Inverse Square Law. The further out something is, or the more that you already have, the less impact something new will make in relation to it's volume.