October 21st, 2024
One of the great powers of the human mind is its ability to develop more abstract ways of perceiving reality. One of the simplest examples of our powers of abstraction is the linguistic notion of hypernymy.
Hypernymy
Consider the following list of things:
pear, apple, cherry, orange, lemon, fig, apricot, peach
We group all these together under the hypernym “fruit”. There is nothing in nature to suggest that “fruit” exist; we invented the concept of fruit as a way of recognizing the higher principle that there are certain things showing great similarity.
But it doesn’t stop there; even more abstract is the word “food”. All fruits are food, and the concept of food includes other members, such as meat, bread, and great big gobs of greasy grimy gopher guts.
We can take this abstraction process another step higher with the term “living creatures”. All members of “food” are necessarily living creatures; have you ever tried to eat a rock?
We can go another step up in this sequence of abstractions with the word “thing”. All living creatures are things.
This sequence (pear, fruit, food, living creatures, and things) is called “hypernymy” and is merely one of the simplest examples of abstraction. We use sequences of abstractions in many ways that you might not have noticed.
Programming
For example, consider programming. Let’s pick a number: say, 27. That’s a number. But it can also be the contents of a variable. We usually give variables a name; perhaps this one would be named “HowManyMonkeys”. The variable is a more abstract representation of that number, something we can compute with.
But it doesn’t stop there. If you learned to program in the good old days when we used flint tools to program, you would know about something called a “pointer”. This was a variable that pointed to another variable, a higher level of abstraction. “What’s the point of a pointer?” you might naturally ask. Well, pointers were valuable for memory management. You could move big hunks of variables around in memory to close up holes in the memory, and keep track of them with pointers.
But programmers didn’t stop there; they invented an even more abstract concept, the handle. A handle is a pointer to a pointer. It turns out that, for advanced memory management, a handle is even handier (mea culpa!) than a pointer.
So in programming we have the abstraction sequence of number, variable, pointer, and handle.
Money
Here’s another area which has, over the millennia, developed many different levels of abstraction. It all started off with the notion of trading: I’ll give you my cow if you’ll give me 100 bushels of grain. This was all simple and obvious, but it could get clumsy. What if you have only 60 bushels of grain, but you have 25 apples and an autographed photo of Taylor Swift. Perhaps I would swap my cow for those valuable things. But when trades start getting complicated like this, they’re harder to work out.
It didn’t take long for people to develop a scheme to coping with this problem. They cooked up an imaginary unit of value. In Mesopotamia it was called the shekel. The Code of Hammurabi, for example, specified that
“If a man rents a boat of 60-kur capacity, he shall pay one sixth of a shekel of silver per day for its rent.”
Now, there were no coins back then; a shekel was about 10 grams in weight, so the renter would have to produce about 1.5 grams of silver or, more commonly, something that both people agreed was equal in value.
Using this scheme, people were able to make complicated, messy deals by sorting out how many shekels of silver each component of the deal was worth, and balancing the two values. This facilitated commerce.
There were still problems with people disagreeing about the value of different items, as well as the problem of weighing that tiny amount of silver accurately. That problem was solved around 610 BCE (Before Current Era) in Lydia (now part of Turkey) with coins made of electrum (a naturally occurring alloy of gold and silver). These were little blobs of metal stamped with a lion to indicate that they were a standard weight. Therefore, all of these little stamped blobs were of the same weight. However, even though they were quite small, they were still too valuable to be used for most commerce.
Fortunately, inflation worked its wonders and pretty soon these little blobs were of low enough value to be useful for commerce. Even better, some people began making coins out of bronze, silver, and gold, with the bronze coins being of the lowest value.
Now people had real money! Each coin had its own name and declared value. For example, Athens had two basic coins, the obol (small) and the drachma (big). But they divided these basic coins into many divisions of different sizes with intimidating names. Think of “microObol, miniObol, kiloObol, and megaObol” and you’ll get the idea.
Let’s take a moment to recognize that the coin was an abstraction of the idea of “value”. Real objects (cows, bushels of grain, and autographed photos of Taylor Swift) are valuable, but their value is hard to define. Coins have an explicitly defined value; one economist called them “frozen value”. They are an abstraction of that idea.
Coinage was so useful that it has persisted for over 2500 years. People trusted coins because they contained precious metal that was worth the declared value of the coin… well, not always. Governments learned all sorts of dirty tricks for diluting the value of a coin so that they could raise more money. They diluted the precious metal with base metals; they made the coins smaller. When that happened (which was frequent), people lost confidence in the coinage and this damaged commerce. Still, coins remain useful today; how else could you buy sodas from a machine? Of course, none of them contain precious metal equal to their declared value; the governments have been victorious in eliminating coinage as a guarantee of value.
Governments were able to get away with this because of another development. Back in the late Middle Ages, merchants were starting to travel greater distances and meeting at the Champagne trade fairs. They had little problem moving their goods to the fairs, but moving money was another matter entirely — a merchant traveling along a country road with a big bag of money was a prime target for robbers. They needed a system allowing them to buy and sell without actually using money.
The solution was cooked up by the Italian bankers: the bill of exchange. This was rather like a check, but it specified the source bank and the destination bank. A simplified bill of exchange might read like this:
“Nicolo the Italian Merchant orders his bank in Florence (the Bank of Medici) to remit 600 florins from his account to the account of Hermann the German Merchant at his bank (the Metzler Bank) in Hamburg.”
Nicolo would write this up, sign it, and hand it to Hermann in return for whatever Hermann was selling. Hermann would take this to his bank back in Hamburg and give it to them. Here’s the trick: the Bank of Medici would have an agent right there in Hamburg. Hermann’s bank would show the bill of exchange to the Medici’s agent, who would swap the 600 florins for the bill of exchange. Then the Medici agent would send the bill of exchange to the home office, which would deduct 600 florins from Nicolo’s account. This is what would happen with the most trusted merchants.
For most people, the agent would send a letter to the home office requesting permission to transfer the money; the home office would check Nicolo’s account to make sure that he had enough money in his account to cover the payment, then send back a letter authorizing the payment. Given that these letters were carried by messengers on horseback, the process was slow. But it was secure against robbers.
This was paper money — a huge step forward! The idea caught on and slowly, more and more transfers of money were handled with paper rather than people carrying big chests of coins all over Europe. Instead, the chests of coins were moved from one bank in town to another bank in the same town — a short trip that could be made safely.
The next step was to increase the abstraction even further: eliminate the specification of the recipient of the money. In other words, this new kind of money consisted of pieces of money saying
“The Bank of BigMoney will pay 10 ducats to anybody who presents this piece of paper to the Bank.”
This kind of paper money wasn’t secure, as robbers could take it and use it, but it was still a lot easier to use than a bag of coins. We’re still using this kind of money; if you look closely at your dollar bills, you’ll see that they say pretty much the same thing, only for them the bank is the US Treasury.
Of course, this new form of money had its problems. It was only as trustworthy as the bank that issued the bills, and there were all sorts of cases in which banks issued bills which later proved to be worthless when the bank went bankrupt. That took a long time to sort out, and a lot of laws and regulations to protect people from shoddy banks.
So now we’re two levels of abstraction up the chain. We have pieces of paper that refer to coins that represent value. Fasten your seat belts, we’re just getting started.
The next step was to permit ANYBODY to issue these bills; they’re called “checks” and they’re very close to the bills of exchange from the Middle Ages. When you write a check, you are ordering your bank to transfer the specified amount of money from your account to the recipient. He gives it to his bank, which bills your bank for the money, the money is transferred, and everybody lives happily ever after… most of the time.
The use of monetary abstraction has accelerated in the last sixty years. Next, we have “credit cards”. You set up another account, this one with the credit card company. You give your card to the merchant you’re buying from, and he uses it to electronically create a bill that he sends to the credit card company. The credit card company sends him the money, minus a handling charge (typically 3%) and every month sends you a bill, which you normally pay with a check. We’re getting even more abstract here: the money travels from your bank account to the credit card company’s bank account, and from there to the merchant’s bank account — except that this happens in reverse order. Ya follow?
In just the last few years, we’ve seen a new abstraction appear: the smartphone electronic card. You create an account with, say, Apple. You give Apple your credit card number. When you want to purchase something from a merchant, you use your iPhone to render payment through ApplePay, which bills your credit card company, which sends you a bill, which you pay with a check… we’re getting even more abstract. The advantage of this system is that it is fully digital where the credit card must be scanned to make the electronic connection. How very Twentieth Century!
When we get into high finance, we get into even more abstraction, but I won’t burden you with that. Let’s conclude this long, long tale of trade using money. The moral here is simple: because trade plays such a big role in our lives, we have developed ever more complex systems for handling the transfer of wealth between people — and that complexity is managed by ever greater amounts of abstraction.
The moral of this story: the only way you’ll be able to cope with faster change is with greater abstraction in your approach to learning.