Why We Might Use Different Numbers in the Future

they're hidden pieces of information in all of our numbers from the quantity you see on your money to the age on a birthday cake but numbers haven't always been this way in fact the numbers that we use today are the result of thousands of years of inventing and refining many ancient civilizations independently came up with forms of basic telling where counting was tracked by lines drawn in the earth but once a number gets big enough a basic tally becomes unmanageable because every time you want to know how many there are you have to count them all even when the tallied number is small it can be hard to distinguish what it is without counting like could you tell me what this number was just from looking at it the natural solution is to separate the tallies into groups but it's at this next stage of the evolution of number systems that different cultures started to the fudge while the modern tally uses one of the popular options groups of five reflecting the numbers of fingers on a hand different cultures use groupings that were as small as three and the Babylonians used groupings as large as 60 the counting system became even more different over time as different cultures tried to improve their systems generally 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 the Greek civilizations had a similar idea and created separate symbols to represent different numbers creating a math alphabet was a major accomplishment but while these ancient systems required remembering more and more symbols as you wanted to use bigger and bigger numbers the modern system manages to write every positive whole number with just ten symbols so these old systems were really just more sophisticated tally systems because you still had to add together all the symbols to figure out what number was being represented take this number for example even if you were familiar with the Roman numerals it would take you a bit of time to add all the symbols together to figure out what number this was but if I write the same number in our modern notation you can tell at a glance so what is the modern number system and where did it come from this system is called place notation in the first instance of a fully developed version of it with by the Mayan civilization around 2,000 years ago while in the callee system is a convention of writing the ungrouped lines at the end the number is still the same if you switch around where they're placed but this is not the case with our modern number system the assumption that we make when we see the number 42 is learnt at such an early age that it can be easy to forget that it's there at all as we go from right to left each digit represents the multiple of a factor of 10 so 42 is really 4 times 10 plus 2 times 1 and 42,000 199 is really 4 times 10,000 plus 2 times 1000 plus 1 times 100 plus 9 times 10 plus 9 times 1 another way to say this is that we have four in the ten thousands place two in the thousands place one in the hundreds place and so on so not only do we look at a number and assume that it uses place notation which historically hasn't always been the case but we specifically assumed that each place in the number is associated with a factor of ten now as you'll remember from the earliest days of tallying there's no base number that our system inherently needs to be centered around and historically different cultures have used different numbers in fact the original Mayan system used 20 as its base number so the two major assumptions with our motto numbers are the use of positional notation and the use of base 10 is it possible that there's a better number system out there like our ancestors before us might we one day discover a new and better one well there are actually already non base 10 systems being used all the time 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 these are carried over from the ancient Babylonians makes 60 systems on a larger scale classical computers are completely based on a base two systems binary this means that every number can be written using only two symbols zero and one classical computers have a physical reason for using binary because fundamentally computers are just a bunch of on-off switches if the computer reads out these on-off switches that translates to the binary number below it but humans don't have a similar restriction so what makes a number system good or bad for humans we've already learned a few lessons from the historical number systems that are no longer in use we stopped using tallies because we wanted a system that lets us know what the number is with a quick glance this requires creating a mathematical alphabet a set of symbols with a widely agreed-upon meaning but it's also possible to have too many symbols so we're looking for a balance we want one that's easy to do operations like multiplication and addition on so what about binary it's got a nice simple mathematical alphabet with just two symbols which means it's multiplication and addition tables are really easy to memorize but the downfall of binary for human use is that the numbers get long very quickly the biggest four-digit number is 1 1 1 1 which is only 15 in decimal even just 500 in decimal is 1 1 1 1 1 0 1 0 0 in binary so like the tally system the binary system is hard to read at a glance FISMA decimal system already works pretty well in terms of our three rules let's look at a couple of paces closer to 10 in a couple of his popular math books Isaac Asimov discusses the benefits of the octal system which is based on Apes and the duodecimal system which is based on 12 while we can use the first eight symbols of the decimal system to write numbers in base 8 a base 12 system requires two additional symbols which will borrow from the English alphabet take a look at the size of the multiplication table and the largest four digit number for each system if you were going to remake our number system would you trade having numbers that tend to have some extra digits in exchange for having an easier time stable to memorize if you're thinking you'd rather just stick with the decimal system consider this the easiest times tables to remember are the ones that are a factor of the base number decimal being base Ken has easy 2 & 5 times tables because when you divide by those numbers you get integer in other words two and five are factors of ten this means that their multiplication tables always follow a regular pattern despite having a smaller x table an octal system base eight also has two factors four and two but unlike with decimal these numbers allow you to do simple integer hopping of the base half of 8 is 4 half of 4 is 2 and half of 2 is 1 whereas half of 10 is 5 but then half of 5 is an innate whole number what about the jura decimal system face 12 well it has the best of both worlds way more factors and better simple Harling than the decimal system the factors of 12 are 2 3 4 and 6 so each of these follow an easy-to-remember pattern in the x table and if you're worried about running out of fingers just get a little creative all of this is to say that 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 that's said it seems unlikely that we'd go through all the trouble of completely changing our number system unless there was some kind of new discovery that fundamentally changed the way we do math but just like negative numbers weren't always a part of everyday life maybe sometime in the future some new technology is developed which makes imaginary numbers part of everyday life this would call for a number system that easily incorporates imaginary numbers number systems like this actually already exist one version is called Quetta imaginary base and uses the imaginary number to eye as its base it can represent almost every complex number using only these four digits another very unique number system represents numbers as tangled knots these allow you to do mathematical operations in a more visual and geometric way 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 and just like it would have been difficult for them to imagine the number system that we use today 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 thing you know all this talk of numbers has got me wondering different civilizations came up with different ways of representing numbers but they all still perform the same mathematics one plus one still equals to independent of what system you're working with so on one hand it seems like numbers were a creation of humans as different civilizations came up with different numbers but on the other hand all of these different representations represent the same ideas so is mathematics invented or discovered this is an age-old question and there are good answers to both sides that's why I'm making a video about it over a nebula Nebula is a streaming video platform built by creators before creators it features names like minutephysics real engineering Wendover productions and more nebula is a place where we can try out new content ideas without the pressure of the YouTube algorithm I was apprehensive about going down a more philosophical path on YouTube as it's a bit of a jump from my regular content but nebula makes it possible for us creators to follow our passions and try new things normally nebula is $3 a month but we've partnered with our friends at curiosity stream to get you free access to nebula with a curiosity stream subscription so curiosity's dream is a different subscription the streaming service which specializes in high quality documentaries including names like David Attenborough and astronaut Chris Hadfield they're currently running a 40% off promotion it's their version of a care package for these trying times thought-provoking documentaries to keep yourself and your loved ones engaged over the coming weeks so you're literally getting to streaming services for the price of 60 percent of won that's a pretty good deal if you'd like to check out both platforms I've linked them both in the description but to get the two-for-one deal sign up to curiosity stream at curiosity stream comm slash up and Adam watching your favorite creators try out new ideas and the soothing voice of David Attenborough might be just what you need right now thank you for watching and I'll see you in the next episode [Music] [Music] [Music]

Channel: Up and Atom

Views: 338,969

Rating: 4.8928571 out of 5

Keywords: The Hidden Assumption Behind All Numbers, up and atom, numbers, number systems, ancient number, ancient, history of numbers, history, math, mathematics, math video, video, explainer, science

Id: JS40jPaogM4

Length: 11min 54sec (714 seconds)

Published: Sat Apr 18 2020