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?
In: 395
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.
Latest Answers