Was watching Engineering an Empire on the history channel and the episode was covering the Mayan empire.
They were talking about how the Mayan empire “created” (don’t remember the exact wording used) the concept of zero. Which aided them in the designing and building of their structures and temples. And due to them knowing the concept of zero they were much more advanced than European empires/civilizations. If that’s true then how were much older civilizations able to build the structures they did without the concept of zero?
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The concept of zero as a technology is useful in that it allows us to make math a lot easier.
Zero is necessary to create a space between positive and negative numbers.
Zero is also necessary to create a numbers system that relies on a base that starts over at some point and uses zero as a place holder (like, imagine how much more difficult shit would be if every number after nine was a new number in the same way that 1-9 were).
Zero is such an important idea that multiple empires have invented it independently. The Mayans weren’t the only empire to have made use of zero as a mathematical construct. It was also independently invented in Mesopotamia and India, and probably maybe other places.
Edit: if it helps, look at Roman numerals, which do not have a zero. Try to multiply CCXXXVI by XV in your head without converting them to a base 10 system with a 0 and see how fast you give up.
Because these empires had a concept of a placeholder similar to zero or simply didn’t use them as their systems didn’t use or have any needs. For example, the Romans would not have 0, but ‘nullis’ (nothing).
For example, if you talk to a Roman about how many apples are in your hand if you had no apple in your hand then the Roman wouldn’t say you have zero apple, you simply have nothing. For the Roman, you clearly don’t have *anything, duh.* So, why would such a concept even occur to them?
For the Romans, their system is based on letters. Like II, III, V, etc. and you would combine these letters to form numbers and do overall general math. This allowed them to do basic math which for the most part is designed for record-keeping, taxes, construction, and so on, for the Romans, this was more than acceptable. You don’t need a very complicated system to build a hut or a dam, usually. This also applied to many, many other cultures and civilizations which formed their own system to answer this problem.
>If that’s true then how were much older civilizations able to build the structures they did without the concept of zero?
Suppose you are going to cross a little stream, and you don’t want to get wet so you decide to lay down a piece of wood, and then walk across on that.
How thick of a piece of wood do you need in order for it to not to break when you walk on it?
If you know some things about the wood, how much you weigh, how wide the crossing is, and can do some math, you can figure out a pretty good answer about exactly how thick the wood needs to be. Then maybe you grab a piece that’s a bit thicker than that, and you have a nice bridge.
Or you can just grab the thickest piece of wood you can find, one that looks like it should probably work. You may end up using a bigger piece than you needed, but often this will work out fine in that you can cross without getting wet.
Or, you can just grab any piece of wood you want, and just accept that sometimes that piece will break and you will fall in the stream. After that bad day, you will know to use a bigger piece for that kind of job. Over time and getting wet a few days, you might get good at guessing how thick of wood you need to cross a stream.
Having a good understanding of math will let you make more complicated structures without wasting thick wood on jobs that don’t need it. But if you’re OK with wasting thick wood, or OK with sometimes having a bridge or building collapse, then you can skip over a lot of the math.
This is going to be very trippy but you have to like realize that the way you think about numbers is entirely because you were socialized to think about them this way. Counting itself up to like a dozen is likely built into our brains but beyond that all of math is something we are taught and socialized into. The concept of nothing of course has always existed, but the concept that nothing can be a number isn’t as obvious as it might seem at first, and frankly might even be tied into how we use language and categorize things in our mind.
That said, so long as you’re mindful of the idea that nothing does make sense logically then you can do a lot.
Building a structure doesn’t require mathematics. There are lots of ways to make sure things are level, square, or straight without requiring the mathematical concept of zero.
I´m not sure if my explanation is suited for this sub, as it got quite complex, but i´d like to add this comment anyway in case someone is interested. Other users already made some really nice points, and I’d like to expand on why 0 is important in the development and understanding of mathematics, on top of already mentioned reasons like it being a placeholder in the decimal system.
The key is that 0 is the neutral element for addition. This means that you can always add or subtract zero. Obviously 3+0=3, but we can use this info a little more interestingly.
Firstly, the definiton of 0 can be used to define negative numbers. For example, we can define -3 as the number you need to add to 3 to get the neutral element. Mathematically, this means 0=3+(-3) which is equivalent to our previous equation where the 3 on the left side is transfered to the right side.
Secondly, a neutral element is required for operations on equations. Image you want to calculate something, let’s call it x, and you know that x=34*7. Normally, you would calculate this as x=30×7+4×7=210+28=238. That’s easy enough to make sense. Now imagine you need to calculate something else, let’s call it y, and you know that y=99999997*2. If you calculate that in the same way as before, it’s quite a lot of work. However, we can use a simple trick, which is using the neutral element. We know that 99999997=999999997+0 (obviously), and we know that 0=3+(-3), therefore we can rephrase the equation as y=99999997*2=(99999997+3+(-3))*2=(100000000-3)*2, which is simply 2000000000-6. This is much, much easier to calculate.
While these examples might seem trivial to you, imagine explaining the definition of negative numbers or the trick with multiplication to someone that has never heard of 0, and works in a system that doesn’t use it, like Roman numerals. The use of 0 makes things much more efficient, and is in that sense a prerequisite of inventing/discovering more complex mathematics like derivatives and integrals, but also modern complex mathematics like the quantum theory mathematics that are used for quantum computers, or the general relativity mathematics that are required for gps or space travel. Compare it to how the invention of the wheel is a prerequisite to not just trains and cars, but also to wind turbines, electric toothbrushes or machines like 3D printers, which all use bearings inside that are sort of specialized tiny wheels. Without 0, we wouldn’t have a coherent definition of how numbers work, which would be an enormous hurdle to overcome if we wanted to invent anything that is used in the modern world.
You’re conflating some things. Zero as a concept developed amongst multiple cultures independently thousands of years ago, including Ancient Greece. The type of zero and decimal notation that we use today is a combination of Indian and Arabic in origin.
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