Everything Everywhere Daily: History, Science, Geography & More - Zero, My Hero: A History of the Number Zero

Starting point is 00:00:00 This episode is about nothing. Not in the sense that Seinfeld was a TV show about nothing, but rather it is literally about nothing. It's about the number zero. A number that few people bother to give much thought to, yet without it, modern mathematics wouldn't exist, and neither would any of the digital technologies you are using to listen to this right now. Learn about the fascinating history of zero and why it took so long to develop on this episode of Everything Everywhere Daily. What if your perceptions about the past were wrong? ThruLine is a podcast that takes you back in time to uncover the parts of the story that may have gone unnoticed. It effectively turned day into night.

Starting point is 00:00:53 And how it shaped the world now. Time travel with us every week on the ThruLine podcast from NPR. This episode is sponsored by G Adventures. These are very troubled times. Even though things are starting to get better and more countries are opening up, people are still hesitant to travel. and that is totally understandable. That is why Gadventures has announced its new Travel with Confidence Plus collection. The Travel with Confidence Plus collection are 37 tours in 27 countries

Starting point is 00:01:21 that have increased safety and sanitation protocols to protect you and other travelers. These tours will have smaller group sizes, private transportation, and cheaper options to get your own room, as well as more personal space. Gadventures has also earned the World Travel and Tourism Council's safe travel stamp for their health and hygiene protocols and has implemented the Adventure Travel Trade Association's COVID-19 Health and Safety Guidelines. The Travel with Confidence tours are available for booking today, and we'll be departing from October 2, 2020, to the end of 2021.

Starting point is 00:01:53 For more information and to book your tour, click on the link in the show notes. Zero was a relatively recent development in the big scheme of human history. To understand how it came about, we have to go back to the beginnings of mathematics, which today we call accounting. People developed numbering systems to describe real things in the real world. You would have three chickens or four sacks of grain. Numbers weren't an abstract concept. They were tied to actual things, and written systems of numbers were designed to keep track of things.

Starting point is 00:02:28 In other words, it was accounting. There's no need to describe zero of something. If you didn't have something, you just didn't have it. There's no need to keep records of nothing. The idea of not having something isn't complicated. children learn about zero as soon as they can learn to count. It's a pretty easy idea to grasp. However, expressing the concept of not having something in the form of a written number,

Starting point is 00:02:51 the same as one, two, or three are numbers, took some time. The primary use of zero for us is in representing the absence of a value in a number. The zero in 201 represents that there is nothing in the tens place of that number. This use of a placeholder for a value of a number was where the earliest uses of zero appeared. The earliest system of written numbers that we know of comes from ancient Babylon. The Babylonians had what is known as a sexag decimal numbering system. It was based on 60 digits, whereas our numbering system is based on 10 digits. The Babylonian system used a space instead of a number to indicate something didn't have a value. Eventually, they came to use a double slash to

Starting point is 00:03:33 indicate the same thing, but it wasn't really the same as a zero. It was more like using punctuation, and they never used it at the end of a number, which could cause a great deal of confusion. The only way you could tell certain numbers apart would be in context. It would be like, not knowing the difference between 530 and 53 in our number system. The zero is what tells us the magnitude of the number. Other cultures independently developed this placeholder system for their written numbers. The early Mayans in Central America developed a similar placeholder character, which really didn't function the same as a true zero. Early Chinese Chinese had developed a proto-tool for calculating note as counting rods. Like the Babylonians,

Starting point is 00:04:13 they would just leave a space for where a value should be rather than using an actual number for zero. The first real record of a true zero comes from India. The Baxhali manuscript, an ancient mathematical text written on Birchbart, uses a dot symbol as a zero. The carbon dating of this text places back to around 250 CE. Another Indian text, the Arabejita, is the first recorded use of a zero in a decibel-based system. This system dates back to about 500 CE, and the Arbahita even explains the use of a decibel-based system by saying, from place to place, each is 10 times the proceeding. The person who is credited with discovering the zero that we know today is the Indian mathematician and astronomer Brahmagupta. He developed the earliest concept of zero not just as a

Starting point is 00:05:00 placeholder, but as a full-blown number complete with mathematical rules. He even plays zero into a system with positive and negative numbers. One place you'll notice that is totally absent in the early development of zero is Europe. The Europeans were really late to the party when it came to zero and for adopting a decimal-based system of numbers. There was no real independent system of zero which developed. For the ancient Greeks, the problem was a philosophical one. They didn't have a zero or even a placeholder value in their numbering system.

Starting point is 00:05:29 They had a very difficult time getting their heads around the idea of nothing. In fact, debates about nothing, and they don't have a very difficult time. the physical concept of a vacuum lasted well into the Middle Ages in Europe. Most people listening to this are at least somewhat familiar with Roman numbers, which also has no zero. Latin numbers are great for numbering things like Super Bowls or WrestleMania's, but they are horrible for doing things like multiplication or division. The way zero came to the modern world is through Arabs and Persians. They adopted the decimal system created in India and began using it themselves. The Persian mathematician Muhammad Ibn Musa El Chorizmi wrote the text which became the source for the use of the decimal numbering system.

Starting point is 00:06:09 The book, titled Alchorismi on the numbers of the Indians, was eventually translated into Latin and was the primary vehicle for popularizing the Indian number system. Zero and decimal numbers eventually arrived in Europe in the 11th century in Morish Spain in Andalusia. Because they were brought to Europe by Arabs, they became known as Arabic numbers, even though the numbers originally came from Indian. It was the Italian mathematician Fibonacci, also known as Leonardo of Pisa, who was the first European mathematician to really adopt zero in the Hindu Arab number system. The fact was it was just way easier to do math in this system than it was with Roman numbers. By the 15th century, most mathematicians in Europe were using zero in the Hindu Arab numbers, but most business people were still using Latin numbers for the bookkeeping. It wasn't until the Renaissance was in

Starting point is 00:06:57 high gear in the 16th century that zero in the number system was for. fully adopted in all of Europe. Zero is a unique number with properties that no other number has. Anything multiplied times zero is zero. Anything added to zero is the original number. You cannot divide by zero. As one of my math professors used to say, dividing by zero will send you to hell. It does not make sense, and no, it does not give you infinity if you try to do it. In calculus, zero divided by zero can have a value depending on the function which is used, but that is well beyond the scope of this podcast. For those of you who took calculus, just think back to Lopital's rule. Anything to the power of zero is one, and zero to the power of anything is zero.

Starting point is 00:07:41 Zero is the only number that is neither positive nor negative. However, zero is an even number. It fulfills all the requirements of an even number if you sit and think about it. There are some cases where mathematicians have defined certain values using zero by convention. Zero raised to the power of zero is defined to be one, and zero factorial. is also defined to be one. The square root of zero is just zero. In computer science, zero is also extremely important. Zero is one of the building blocks of everything digital. My voice you are hearing right now is nothing but encoded sound waves into millions of ones and zeros. Spreadsheets and databases have even caused us to rethink the concept of zero. If a cell in a spreadsheet has nothing

Starting point is 00:08:22 in it, the value isn't zero. It's null. The difference between null and zero is subtle, but zero is called the cardinality of the nel set. If there's nothing in a cell spreadsheet, then there are zero things in it. But the moment you type a zero into the cell, there is something in the cell, and there are no longer zero elements, even if the only element is zero. Got that? So zero is really important, and it wasn't always something that humans had. So take a moment of some time greater than zero, and give thanks to the number that means absolutely nothing, yet absolutely everything. Executive producer of everything Everywhere Daily is James Macalah. Special thanks to everyone who supports the show over on Patreon. Please remember to leave a review over on Apple Podcasts. Even a simple review can really help

Starting point is 00:09:13 the show get discovered in the sea of other podcasts that are out there.

Everything Everywhere Daily: History, Science, Geography & More - Zero, My Hero: A History of the Number Zero

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