The video explores the evolution of number systems, from ancient tally markings to the modern decimal system. It highlights that numbers are not a human invention, but a concept that has been independently discovered in various civilizations. The video also discusses the potential of alternative number systems, such as binary and base-12, which could make arithmetic operations easier. It suggests that the current decimal system might evolve in the future due to new discoveries or technological advancements. The video concludes with a discussion on whether mathematics is invented or discovered, and invites viewers to explore these ideas further on platforms like Nebula and Curiosity Stream.
1. Numbers are hidden pieces of information in all of our daily interactions, from the quantity on money to the age on a birthday cake.
2. The numbers we use today are the result of thousands of years of invention and refining by various ancient civilizations.
3. Ancient civilizations independently came up with forms of basic telling where counting was tracked by lines drawn in the earth.
4. Once a number gets big enough, a basic tally becomes unmanageable.
5. The natural solution to this is to separate the tallies into groups.
6. Different cultures started to develop different systems of groupings.
7. The modern tally uses one of the popular options groups of five, reflecting the numbers of fingers on a hand.
8. The counting system became even more different over time as different cultures tried to improve their systems.
9. The next step was to create some kind of shorthand symbol, like Roman numerals which wrote five tallies as a V and ten tallies as an X.
10. The Greek civilizations had a similar idea and created separate symbols to represent different numbers, creating a math alphabet.
11. The modern number system, called place notation, is based on the first fully developed instance by the Mayan civilization around 2,000 years ago.
12. In the callee system, the ungrouped lines are conventionally written at the end, but this is not the case with the modern number system.
13. As we go from right to left each digit in the modern number system represents the multiple of a factor of 10.
14. We have four in the ten thousands place, two in the thousands place, one in the hundreds place, and so on.
15. The two major assumptions with our modern number system are the use of positional notation and the use of base 10.
16. Non-base 10 systems are already being used in the modern world, for example, the way we measure time with 60 minutes in an hour and 60 seconds in a minute, or the fact that there are 360 degrees in a circle.
17. Classical computers are completely based on a base two system, binary, which means that every number can be written using only two symbols, zero and one.
18. Binary has a nice simple mathematical alphabet with just two symbols, which makes its multiplication and addition tables easy to memorize.
19. However, the downfall of binary for human use is that the numbers get long very quickly.
20. The decimal system already works pretty well in terms of our three rules.
21. The octal system, which is based on eight, and the duodecimal system, which is based on twelve, are two examples of alternative number systems.
22. The octal system has two factors, four and two, which allow you to do simple integer hopping of the base.
23. The duodecimal system has more factors, which makes it easier to remember the multiplication tables.
24. The jura decimal system, which is base twelve, has the best of both worlds.
25. While the decimal system gets the job done really well, even minor changes like using a slightly larger base has the potential to make basic arithmetic much faster.
26. It's possible that sometime in the future, humans might use a totally different number system that'll allow them to do bigger and better things.
27. One version of this unique number system is called Quetta imaginary base, and it uses the imaginary number i as its base.
28. This system can represent almost every complex number using only these four digits.
29. Another very unique number system represents numbers as tangled knots, which allows you to do mathematical operations in a more visual and geometric way.
30. Decimal is so useful that it allows children to do calculations that even the best mathematicians would have had a hard time with before because they weren't using sophisticated enough number systems.
31. The question of whether mathematics is invented or discovered is an age-old question and there are good answers to both sides.