Thursday, April 11, 2019

A Travelers Definition of Infinity

Now I am not a mathematician nor is the upcoming subject the usual fare for this blog, but here goes anyway.

The concept of infinity has bothered me for a long time. It first really bothered when I was learning calculus and heard that there is always a very small remainder in the typical calculus answer. I foolishly allowed this trivial observation to undermine my confidence in the mathematical strength of calculus. In my mind, I was learning a failed technique that was not perfect. Now, some sixty years later, I am confident that any calculus calculation can be as accurate as we desire, despite being incapable of achieving absolute perfection.

So what might an infinitely small error look like?

I was recently on a long drive in the Moses Lake, Washington area, traveling at the speed limit, when a container truck passed me. After complaining silently about his excessive speed, I began to wonder about the included angle made by the two sides of the rapidly disappearing truck. The angle was large when the truck was close but rapidly became smaller as it increased distance. The angle would become infinitely small at some distance (I thought) but no, it would never become zero. So, I wondered, what is infinity?

This must be a case of defined infinity. Here, "infinitely small" must be a shorthand term for 'too small to worry about'. We could always find an included angle with a value, even if the truck was located on a planet orbiting a distant star. The result would be real but how could it possibly have a physical influence on our local reality?

With this example in my background, I am free to think about the equation

Y = A_infinity x 1/B_infinity.

Does Y equal 1, zero, or infinity? It would depend upon the equality of the two infinities.

So there you have it. A travelers definition of infinity.


Sunday, March 3, 2019

Basic Elements of Mechanical Economics

[The discipline of Economics attempts to bring coherence to exchanges of products, labor and money. Coherence is impossible without some commonality in understanding the interrelationships of three exchanged groups. The following examples attempt to provide insight into the interrelationships.]

When a foreign producer markets a product in the USA, he finds himself selling the product for American dollars. When the sale is completed (no matter what the actual original product cost as measured in any currency), the foreign producer has exchanged ownership of a product for ownership of dollars. In this way, the foreign producer has become an owner of dollars which places him in the same position as all native American owners of dollars.

Welcome to America!

When an American citizen exchanges his labor for money, this citizen finds himself selling ownership of labor hours in exchange for ownership of American dollars. In this way, the American laborer has become owner of dollars which places him in the same position as all other owners of dollars.

It great to be an American!

Now we should ask what is so nice about owning American dollars? Possession of dollars gives access to future ownership of any asset for sale in the dollar economy. Access is bounded/restricted only by the number of dollars available.

Hooray for the free market!

Fortunately for some, money can be given away as if it were a Christmas gift certificate. In this way, the recipient becomes an owner of dollars which places him in the same position as all other owners of dollars.

Hooray for giving!

The difference between money and gift certificates is that money is accepted everywhere while gift certificates are accepted only in the store that created them. The key concept is that both money and certificates can be (within their respective limits) traded for anything for sale. The environment surrounding creation of gift certificates will provide a useful backdrop once we overcome the misleading circumstance that certificates are commonly purchased for cash.

What a convenient parallel!

We have here the basic elements of micro and macro economics.  A change of ownership is an exchange.  Products, labor and money exchange mechanically as directed by their owners.  Exchanges between few owners is micro economics, Interactions between many owners is macro economics. Parallels between money and gift certificates provide a generally unrecognized link between micro and macro economics.

Let's tie these basic elements together!

The mechanical money blogging effort (found on this site) is focused on building coherent relationships between products, labor and money. The above examples display basic mechanical interactions found in past postings and expected future posts. These relationships will continue to underlay future mechanical economic logic until (or unless) better basic relationships are found.



Monday, May 28, 2018

One Way to Run an Economy

There is more than one way to run an economy. Today, let's explore a single way.

In our imagination, we have an isolated island with it's own currency. With sunny days and pristine beaches, they wish to join the wider world's economy.

They collectively decide to advertise their island, offering a one week stay for XX.XX in their currency or YY.YY in a number of other currencies. It seems to me that they are setting their own foreign exchange rate. They would need to decide among themselves how the divide the cost of providing that one week experience.

OK. With a plan in place, they begin the experiment. After one year, they find that they have a booming business. They have more people arriving than they can handle. What do they do? Change the exchange rate? Put people on a waiting list? Send guest home dissatisfied?

Whoa. We have too many possible answers! We need to more accurately examine how this island's business is economically arranged. Let's assume that government has been issuing local currency in exchange for foreign currency. This local currency has been obtained from a stable system of taxation that results in an agreeable balance within the island's economy.

Returning to the problem of excessive success, the island government decides to decrease the exchange rate, which results in a decrease in the amount of local currency for each unit of foreign currency. In other words, the price of a week on the island has increased in terms of foreign currency. This action stabilizes the tourist industry but leaves it running at a high and nationally profitable level.

Let's continue this story for 50 years. Our island has a stable, successful tourist industry. Government routinely spends part of the foreign currency and saves part in the form of bank deposits and safe investments in the currency of foreign origin. After 50 years, large sums of reserves are held in some nations.

Could this really happen? Think China? Think Japan? "Whoa!" someone shouts! "Those are both exporting nations. Just the opposite of this story." Hold that thought until later in the article.

Now we add a new twist to the story. An enterprising journalist (who is also an amateur economist) notices the large sums held by a single nation. He also notices the large number of tourist on vacation. He writes a story. The story is read by a politician. We have a political moment.

The story expresses concern about the large overhang of potential spending by this single island economy. There is concern that people are off vacationing rather than working, which just continues the trend long in place. Something must be wrong, but an exact problem and suggested solutions are not part of the article.

Eager politicians begin blaming this island nation for causing unemployment in other nations by failing to spend all of it's earnings (Like the critics were doing?).  Politicians begin expanding the argument by complained that vacations spent on the island could have been provided in-nation to reduce the unemployment numbers and improve the balance of payments. Obviously, according to some politicians, the island nation was doing some things wrong. Maybe the exchange rate was not correct.

This seems to be a good place for ending the story. The political story has developed into something that we can learn from. A single government is controlling the exchange rate. The method of money exchange allows the controlling government to claim a repeated annual share from the labor and resources provided by the entire economy. The situation has gone on long enough to attract the attention of media and political elements.

Except for the critics, everyone seems happy with the stable economy described. Is there REALLY a need for change?

I would suggest that need for change is in the eye of the beholders. The island described is neither China nor Japan, but the effects on reserves and unemployment can be made to sound the same. Every national economy has the ability to arrange a division of resources within it's borders. Whatever arrangement is made has potential interactions with other national economies, which will be developed if mutual benefits for each side can be found.

The economies and economic interactions we have in today's world are the result of political and individual decisions on thousands, maybe even billions, of levels. The illustration provided in this article is just one way to run an economy.