Considering how important and obvious zero is to educated people today, zero is a surprisingly difficult concept. Most children under the age of five cannot grasp it at all and it was unknown for most of human history. The Romans somehow managed to run an empire without knowing zero and zero didn’t make it into European arithmetic until Fibonacci introduced it in 1202. The power of zero was only fully discovered in AD 628 by Brahmagupta. Some civilizations had used zero previously, but it was probably “something closer to a punctuation mark between real numbers, rather than a number in and of itself.” Brahmagupta was the first known mathematician to use zero for addition and multiplication and this has been heralded as and “a total game changer … equivalent to us learning language,” and “one of the biggest mathematical achievements in human history” because this was the essential foundation of algebra in which both sides of an equation cancel each other out. This was also the foundation of accounting where zero is the essential concept of every balance sheet where assets and liabilities (plus equity) must always equal zero. Zero = balance. In the natural world, negative numbers are less apparent than in finance so Brahmagupta may well have discovered the mathematics of zero by thinking about accounting. Negative numbers were not widely accepted in Western mathematics until the 19th century!
Today few people in the West know of the 7th century Indian mathematician… Brahmagupta. This is a pity because he has a fair claim to have made the most important discovery in the history of mathematics.
Brahmagupta discovered nothing. More specifically he was the first mathematician to recognize the significance of zero – that it was a distinct number in its own right. Brahmagupta did not stop at nothing, he also saw that zero could be split into two equal but opposite components.
Zero, according to Brahmagupta, was the number which resulted from adding any number to its negative partner.
Zero is the sum of five and minus five, fifty and minus fifty, or of any… number and its negative partner.
Zero = X – X
This insight allowed Brahmagupta to become the first person to understand how to calculate with negative numbers. Today most of the rules laid out by Brahmagupta for calculating with zero and negatives still form the bedrock of modern mathematics…
Brahmagupta’s conceptual trick, splitting nothing into two equal but opposite components, continues helping us make sense of the world in surprising ways. On the biggest of all scales cosmologists use it as a way to conceptualize how the universe was created from nothing, in the big bang, and may one day return to nothing, in a big crunch. On the smallest scale particle physicists use Brahmagupta’s idea to explain how matter is created from nothing. Particles… can be created from nothing provided they are created together with their equal and opposite anti-particles.
Scientists at the CERN particle collider now routinely create particles and their anti-particles – electrons and positrons for example…
Surprising as it may sound Brahmagupta’s mathematics and the process of creating matter and anti-matter can help us think more clearly about the workings of our modern monetary system. It may even help us understand where macroeconomic policy is going wrong.
The connection between the mathematics of zero and that of finance becomes apparent when one looks at the language originally used by Brahmagupta to describe his mathematical laws. The following are three examples of his laws:
A debt minus zero is a debt.
A fortune minus zero is a fortune.
A fortune subtracted from zero is a debt
Note that Brahmagupta chooses to call his positive numbers fortunes and his negative numbers debts. He recognized, as do modern day accountants, that the combination of a fortune with an equally sized debt was exactly zero.
Recognizing that equally sized fortunes and debts sum to zero and therefore can be created from zero is the key to demystifying our banking and monetary system.
It is often said that banks have the power to create money from thin air and that this is the source of their fantastic profits. Although this is true it is, quite literally, only half of the story.
The scientists at CERN can create matter from nothing only if they also create its offsetting opposite anti-matter. Similarly banks are only able to create money from thin air provided they create, at the same time, the offsetting opposite amount of anti-money, otherwise known as debt.
In short our modern banks are the particle accelerators of the financial system. They conjure money and anti-money, fortunes and debts, from nothing.
Unfortunately, George Cooper’s analogy soon gets weaker:
It is informative to extend this analogy a little further. When particles and anti-particles are created from nothing energy is ‘consumed’ and when they later recombine to annihilate one another this energy is then re-released. There is an… opposite process of energy capture and release associated with the creation and destruction of money and debt.
When a bank makes a loan it splits zero into a fortune (money) and its equivalent debt. This process releases new spending power into the economy [and can produce] a burst of economic energy. Conversely when, at a later date, the money is recombined to annihilate the debt, both money and debt vanish and an equivalent amount of spending power, economic energy, is withdrawn from the economy.
This analogy fails to explain whether or not economic “energy” is created through creating money (debt) because it doesn’t always work. For example, a monetary expansion can only create an economic stimulus during a recession when the creation of more money can get people to spend more and stimulate demand. On the other hand, if everyone is already fully employed, and the amount of money doubles, no new energy would be created. All that new money would just cause pointless inflation.
Similarly, if new money is created and given to people who will hoard it, no energy will be released. That is what happened when the Fed nearly quintupled the monetary base by loaning over four trillion dollars to US banks. The banks just hoarded the money and zero energy was released (and zero inflation). Money creation ( = debt creation) is only useful if it motivates people to do more work.
And reducing debt/money doesn’t necessarily reduce economic energy either. For example, bankruptcy eliminates debt=money and it should ideally increase work because it is designed to fix a situation where someone’s debts are too large to possibly repay. An impossible financial situation is dispiriting and makes rational people give up. Forgiving impossible debts creates the freedom to start anew and gives the incentive to start working again. The debt-forgiveness of our bankruptcy law is similar to the ancient Biblical ideal of Jubilee which was thought to be as wonderful as the word sounds. Actually, it is fortunately that no full Jubilee ever actually happened because it would have wiped out all debt which would actually have been an economic disaster. But the selective jubilee of bankruptcy is an important way to create economic efficiency and justice.
Most people probably disagree with the idea that bankruptcy is important for economic justice and jubilee, but without bankruptcy, debt leads inevitably to slavery because if someone cannot escape a debt that is impossible to pay given their income, then that person becomes a kind of slave to his creditor. Indeed, some scholars of slavery have argued that debt peonage is the main mechanism that causes slavery and bankruptcy is the way to avoid that.
Every person’s debt is another person’s asset (savings) so to see what happens to economic energy we also need to look at that other side of debt forgiveness too when debt/savings is destroyed. Eliminating someone’s savings can increase work by the formerly wealthy person due to what is called the income effect or wealth effect. For example, people who inherit great wealth or win the lotto typically work less as a result, and conversely, destroying the savings of extremely wealthy people tends to increase their desire to work and be productive too because they can’t just rely as much on their savings to support their lifestyle.
Whether or not ‘economic energy’ is created by creating money=debt=savings is a lot more complex than the analogy of matter/antimatter, but debt clearly does not hurt future generations (contrary to what most people think) because every debt for one person is always exactly equal to another person’s asset. Total net debt is always zero just as Brahmagupta realized when he used this insight to develop the concept of mathematical zero.
One of the most important concepts in economics is the concept that total debt is always zero because debts and credits always add up to zero. That is also the revolutionary concept behind double-entry bookeeping which is the foundation of modern accounting.
Just as there seems to be much more matter than antimatter in the universe (for unknown reasons), there is also more wealth than debt because although all financial wealth is balanced by debt, there is also real physical wealth like land and capital that exists independently of debt.
Guess how much money I have earned from writing this blog? Here it is:
I’m rich in zeros!
UPDATE: There is some debate about whether mathematicians in Cambodia used zero for arithmetic even earlier than Brahmagupta, and the Mayans independently developed a sophisticated usage of zero in Central America. When the Muslims brought zero to Europe where it was first popularized by Fibonacci, some authorities tried to suppress it.
Medieval religious leaders in Europe did not support the use of zero, van der Hoek said. They saw it as satanic. “God was in everything that was. Everything that was not was of the devil,” she said. Wallin points out that the Italian government was suspicious of Arabic numbers and outlawed the use of zero. Merchants continued to use it illegally and secretively, and the Arabic word for zero, “sifr,” brought about the word “cipher,” which not only means a numeric character, but also came to mean “code.”
When Fibonacci introduced zero to Europe around 1202, it was part of his introduction of the entire Hindu-Arabic numeral system that the whole world uses today. Previously, Europe had used Roman numbers which do not include zero and were not compatible with algebraic manipulation. The first known use of the word zero in English was in 1598. Although division by zero is still undefined, that is a foundational concept underlying calculus so zero is important even in a situation where it is undefined.