If you happened to catch our last video on "evil" Belphegor's Prime, do check out this cool T-Shirt, Poster, Sticker design... www.bradyharanblog.com/blog/belphegors-prime-t-shirt
Can you please explain how the "lunar math" works before using it. There are so many inconsistencies in this video - and no explanation for how to deal with numbers of several digits...
@@R3lay0 It is harder: Imagine you have a field with 4 horses and another with 3. You take them out to a horse show, and need to tally back up the amount of horses you had to bring them back. You add 4 to 3, 'equalling' 4, so bring back 4 horses and now have 3 less to make money from in the future. Plus will likely have a lot of complaints from the horse show organisers that you left 3 horses for them to deal with, resulting in bans from further events. That all definitely made your life harder!
@@jarlfenrir Well, multiplication isn’t initially intuitive either. It’s not until you get bags with the same number of counters in them that the real life use becomes clear. Similarly with exponentiation, especially above the cubing - tangible intuition isn’t immediately obvious. But an easier system doesn’t require tangible explanation to understand and utilise effectively. Nonetheless this system is a lot less useful of course.
@@JM-us3fr except in this video they obviously mean the element that forms the identity function under the operation in question. Divisible by 1 in the context of prime numbers means the identity function which happens to be 1 under multiplication, but it would also be 0 under addition, and 360 degrees under rotation. Or, in this case, 9 under moon math.
But how can you change a rule set "slightly" - and still keep a convention which is only used by SOME people ON PAPER because it is how they were thought to "do math"...
Jonas Misund because its abstract math boi, math is only linear in that the rules hold or they don’t but changing rules helps you think in a way that lets you reinterpret what you thought, you know its exactly the same as using binary or 16 bit as apposed to the 10 bit decimal system but pretty different as well.
@@expressrobkill Yup. Some people have difficult to grasp it, but there are no absolute rules in maths, we are in the power to define our axioms as we prefer. At all, math is NOT meant to be useful. It's just a bunch of theorems that we can infer through its axioms. Obviously there are some parts of math that are useful in a daily basis, but this creates the illusion that some ideas inside maths are "useless" just bcs you can't use it to bake a cake. If it were true, it would not mock maths anyway; but it is also not true: some concepts just happens to be so advanced that it is only used by a few people.
Perhaps you've misunderstood the purpose of lunar arithmetic. It has no practical application because it's supposed to be a teaching tool. It's easy to learn the simple rules of normal arithmetic without thinking about why those rules work. By creating these new silly rules it forces the student to think about math logically and not just mindlessly adhere to the patterns they're used to. Math afterall is fundamentally just an expression of logic. There's standard conventions, yes, but fundamentally teaching math should be an excerise in logical thinking.
This video is about logic, not arithmetic. It touches on the Godelian notion that rules themselves are symbols and we need more formal ways to process those symbols: To add rules to other rules, multiply to combine rules, perform functions that change rule systems into others, and produce symbols for the results of those processes.
I like the idea, but not the name. Earth and the moon both orbit the same star. 'Interplanetary Prime' is closer but still feels a little wrong. 'Celestial Prime'?
Isn't 10 a prime on the moon? 10*9 is just the smaller one of 9 and 0 which is 0 for the ones digit, and for the tens digit it is the smaller one of 9 and 1 which is 1. Resulting in 10. Right?
Geez, here I was thinking this is the most fun numberphile video in a while; then to my dismay, it receives so much hate. This video embodies the very spirit of real mathematics. To heck with the rules. Pure math should never be constrained by what you think is normal. I wish we could get more of this. Thanks!
But of what use is mathematics that gives wrong answers and is not useful? And if you want to play around with the rules, then what about the different types of primes? Strange that some primes such as 5, are no longer so prime when you consider that complex numbers can also be considered as factors.
You could call this video the Sieve of Lunar Arithmetic based on how well it partitions Numberphile viewers into those with and without a tolerance for abstract thinking.
@@xTurqz A lot of mathematics that seemingly had no relation to the real world turned out to be useful in some field of science later on. You never know if something "useless" isn't going to be the answer to some real problem, or at least point you in the direction of the answer. Secondly, this "dismal arithmetic" clearly is useful as a training tool for people. It messes with your intuition and forces your mind to adapt to new rules. By taking you out of your comfort zone, it makes your mind more flexible and better prepared for learning new maths that you haven't seen before. It's just a fun way to expand your mind a little. I love your username, by the way.
@@zlosliwa_menda though the only thing that this seems usefull to is to teach you how to adapt to new rules and become more flexible. Apart of that it seems pretty useless since the results are inaccurate
It makes me wonder how many new arbitrary operations we could add What if we made two new symbols for this lunar addition and subtraction and used them in conjunction with normal mathematics What if there was an operation where numbers are simply just put together 8 $ 6 = 86?!
What's with all the negative comments. A huge part of maths is about bending the rules and seeing what happens. Complex, negative, and irrational number are all basic concepts to us now but were once seen as pointless or even heresy. Keep an open mind people.
But the ideas of complex, negative and irrational numbers appeared naturally, because people needed these numbers to do stuff they couldn't do without them. On the other hand we already got addition and multiplication which work totally fine. Why do we need to look for another approach to addition? Moreover this technique gives unexpected results... Like you take one "thing" then put another "thing" right next to it and end up with one "thing" you started with? For me 1 + 1 = 1 says exactly this...
But the problem is that what appears to happen is nothing. There was no conclusion apart from, you can do this style of maths and get some different answers that serve no purpose. Kinda hard to get excited about.
I think a function where the greater digit is the the solution for the column isn't more ridiculous than a number where the product of two positives is a negative
Brilliant! Immediately I started to think "now what are the identities?" +0 was obviously the additive identity, but *9 is the multiplicative identity. How peculiar! :D thank you really this was an interesting watch! To answer all of the "but why?" -comments, I think it's a good thought experiment. Taking a closer look like this gives you a bit of insight to the fundamentals of mathematics, which are so often forgotten.
Thank you - it is hard to answer all the "but why" questions - you did a nice job here! Some people will be stimulated and start being curious like you did - like discovering a shiny new gem... Others do not see a direct application to everyday life and think it is probably a silly waste of time... I totally get that and to each their own... But Numberphile has a slight bias towards the former mindset.
Couldn't agree more. The fundamentals of mathematics are so often forgotten, it's hard to meet anyone who remembers them. Namely, the physics of the world we live in had shaped our maths to the degree that people don't even see how things could be different. This video is a nice reminder about this fact and also shows that in the worlds with different physics maths could be completely unusual. Had anyone found physical application for lunar arithmetic most of the "but why" comments would have never shown up.
The interesting thing to me is that the multiplicative identity depends on the base. This immediately raises the followup question, what happens in binary where the identities are the same as in everyday mathematics?
I wish I had heard about this during my Computer Science "Foundations of Higher Math" course in college! At first, I was really hoping that there was some shortcut that this video would teach me. Instead, I learned that trying to apply these crazy rules can really get you to think about _why_ some math rules work the way they do. I wish the video had covered that a bit more at the start, though. It makes much more sense to go into this knowing that these crazy rules aren't for getting a correct answer, but rather to reflect on the logic behind the remaining "normal" things like "what it is to be prime" -- it's not just some crazy concept that your teacher made up for fun, there are some real applications of primes and using lunar math can help us relearn primes from a clean slate with a whole new arithmetic system. By changing one of the core principles of arithmetic, you better understand the place of other principles based on how they changed. Thank you, Numberphile!
That's what I'm really interested in. What do these operators do in binary? Let's make some truth tables! p: 0 0 1 1 q: 0 1 0 1 p+q: 0 1 1 1 p*q: 0 0 0 1 And now, if you're familiar with computer science, you will recognize these as the OR / AND gates. Essentially, lunar math is taking the fundamental operations of binary logic, and applying them to decimal in an interesting way.
Yeah, the results of "Graham's function" are actually not that "interesting". It does grow insanely fast, but (by necessity), their behavior is extremely predictable.
I was immediately unenthusiastic about this video as I initially spent my time searching for some practical application and came up short, but 3 to 4 minutes in, it became a fun logic puzzle to try and reason out at the same speed as you. Excellent video, very fun and thought-provoking
Bro literally same. I was like “ok so how does this all tie in to the real world. Will the rules ultimately result in ‘earth’ arithmetic answers? Or is there some computer program that can use this rule to be more efficient” and then it became clear to me this was just a puzzle and was super happy about it
Maybe there's more to it, a some kind of conclusion or application, or development... or maybe not. But who cares if it's not any of it at all? The investigation itself of the misbehaviour of the basic concepts in the Arithmetic is something worth watching. I truly appreciate and understand the excitement of Mr. Sloane on this one. This approach to mathematics reminds me of something similar (but not so... dismal) that I learned about 30 years ago: 1. Write down a number. 2. Multiply it with the first digit of that number. 3. Do "1." and "2." with the result. If at some point the result starts with 1, then we are hitting a loop, because the procedure will call itself with the same number, again and again. Therefore, we will name the first number (in fact, all the numbers in the sequence) "stable". Consequently, "unstable" numbers will be the ones that grow infinitely, generating sequence that will not contain any numbers, starting with "1". For example, the numbers, starting with n(1) = 52 -> n(2) = 52 * 5 = 260 -> n(3) = 260 * 2 = 520 -> n(4) = 520 * 5 = 2600 ... will be all "unstable", obviously. On the other hand, the sequence n(1) = 24 -> n(2) = 24 * 2 = 48 -> n(3) = 48 * 4 = 192 -> n(4) = 192 * 1 = 192 = n(3) will give us "stable" numbers. Problem: Develop a method for classification of all natural numbers by their new property - which ones are "stable" and which ones are "unstable"? At the first glance it is a boring task, but if you dive deeper, you will witness a mathematical beauty in the logic and complexity that this property will create before your eyes!
“On the mooonnn” is so satisfying to hear. I love how excited this guy gets about math. I remember getting this excited when I started to truly understand basic number theory
Well I guess earthly addition and multiplication still exist. I imagine that all the natural numbers, like us, are born on the Earth, from our familiar operations. When they go on the moon though, they start reacting somewhat strangely!
@@wherestheshroomsyo Thanks for the recommendation, I watched it! I guess the lack of order on complex numbers makes more intuitive sense to me because complex numbers are 2D.
@@wherestheshroomsyo If a and b are complex numbers, then what does a < b mean? And if that does not work, how might we define < and > so that it does work? Compare the real portion first and if equal, then compare the imaginary portion? Or vice versa? Or something else? Or do we need new symbols, maybe something like ? Actually, for each of the 2 portions, we could have a . Or 36 various comparison operators. Or just 6 for real numbers.
@@yosefmacgruber1920 I'll try to address your very first question. When a and b are complex numbers, what is it that a < b is supposed to mean? It depends on who you ask really. I will tell you that the statement is meaningless. The truth is that when using symbols, they can mean anything to anyone. Whether that be what those symbols mean to an individual or the majority of smart math people, it doesn't matter. It is very common, even in good published math, to redefine repurpose reuse and abuse well established symbols, as long as the context is clear and the author explicitly redefines it to be different than convention, that is what is important. However, in a completely practical context, I will tell you that a < b is meaningless for complex numbers. I will tell you that there is no less than or greater than with complex numbers, there is an equal to, and there are useful "comparisons" like talking about the magnitude and angle of a complex number. Keep in mind though that the lexicographic ordering is legitimate, it is just not the same thing as the real number comparisons that everyone learns about. Those are just my thoughts on the topic anyway.
You must first learn the rules to break them! I'm pretty sure this professor has earned his Degree and P.h.D and presumably his job as a professor by learning reeeally well the conventional rules.
if a and b are digits and ab is a 2 digit number ab^2 = abb if a > b, aab if a < b, and any combination if a = b. also if ab9 is a 3-digit number ab9 is a prime only if a > b
I was looking for this years after first watching it and at first I thought this wasn't right because I was thinking the video I wanted had Cliff Stoll.
At first, it looked so silly, but as you started to talk about the primes, this maths became so curious and interesting. We should, definitely, never underestimate que power of maths.
I'm surprised by the comments. As a third year student if mathematics I found it quite interesting. It's just a commutative ring lol. I have to look at rings every day and it's nice to see a new one.
It's an abelian monoid under addition and multiplication. I'm not sure if it's distributive as well. if so, then the non-invertibility is the only unfulfiled requirement for it to be a ring.
@@Friek555 Ah I had a feeling something was off. Either way I'm interested to see what this looks like in binary, I think it'll be either really boring or really interesting haha. I wonder what "ideals" look like, etc. or if you can generalise the notion of a quotient.
@@christopherimanto1732 I think he mentioned that it is distributive in the video, I shall check myself eventually of course. For now I have like three assignments due tomorrow so I have to prioritise for now haha
Supposing that it distributes (which I didn't check but it is claimed that it does), this is actually what's called a semiring (having an additive and a multiplicative semigroup)
well yea but it has applications in that its a mind exercise and allows you to think about things in a different way, i would be happy to see this in school as an exercise or exam question.
This reminds me of the video with Tom Scott talking about how the things science fiction writers have come up with for the way extra-terrestrial cultures view the universe pales in comparison to what we've developed on Earth. This is the kind of system I would expect from some culture from elsewhere in the universe: Completely logical and rule-bound, but completely foreign to our minds. To them, it would make perfect sense and they'd build their entire society and concept of the universe on it, in the same way we've done ours, but when our societies meet, we have completely different foundations for our understandings.
I actually like dismal arithmetic. Lunar arithmetic is just a random name while dismal actually describes the system. For "otherwordly" you could just as well have jovian arithmetic or andromedian arithmatic
I've heard talk of using other "rules" for other planet names already... I was emailing one of the contributors to this video about Martian Arithmetic the other day!
Of course an entirely fair question and asked earnestly... And in anticipation of many people asking this, here's my personal opinion... 1. Because it is fun and creative - and playing with new ideas is good for your brain. 2. Because you never know what "bending the rules" will teach you - what techniques, insights and breakthroughs will occur that may have more useful applications... Just look at much of John Conway's work... So much playfulness and so many games - yet many ideas and insightful mathematics has fallen out of that. Lunar arithmetic is never going to be used to build a bridge or design an iPhone (I certainly hope!!!)... But neither is it just throwing ALL rules out of the window... It is creating new arbitrary set of rules and seeing what happens... What IS a prime number in this new landscape? What pattern do the squares follow? And what light might that shed on more conventional mathematics? Also... If you are not buying that and think it's just nonsensical playing... I say the following... It may be true that this will not cure cancer or help people live longer - but what is the point of living longer if we can't play, imagine, and do fun stuff like this?
Most math doesn't have many direct applications, and most of modern math is just "a toy for bored mathematicians". Even though no one knows how Inter-Universal Teichmuller theory will be used, it still holds value in that it helped solve some conjecture that still doesn't have much application. Pure math is just for fun, for now.
@@numberphile Absolutely fair enough. I am all for fun and creativity, and find your videos fascinating and (mathematically) baffling in equal measure but always feel better for the journey they take me on. Thanks Brady et al., from a happy Tim
But in multiplication... when we shift the second number one place to the left to then add it, that is multiplying by 10.... shouldn't there be a change in that??
actually a neat system, idk why this video got so much hate. just something kinda funny but also kinda cool that people came up with. you guys need to lighten tf up man
there is an interesting thing 3 + 2 = 3 so let is say for example 3 + x = 3, there are multpile solution to this equation it can be one of {0,1,2,3} so 3-3={0,1,2,3} but 3+x=5 then x must be 5 so 5-3=5. The same can be said to 3*2 = 2 so x*2=2 ,x can be {2,3,4,5,6,7,8,9} so 2/2={2,3,4,5,6,7,8,9} but x*2=3 has no solution since there is no number that is less than 2 but equal to 3 so 3/2 is undefined. I can keep going to roots and stuff but maybe im wrong about the division and the subtraction, share your opinions!
@@KanalDerGutenSache He said substraction and division were not allowed but why, though? Is it because those multiple or undefined solutions would pop up everywhere?
This kind of thing is a great showcase of the creativity of mathematics. People don’t readily understand that math is actually an extremely creative endeavour, and when told that it is can’t wrap their mind around how it could be. The reason is that math is traditionally terribly taught as just a rigorous system of algorithms that you use to robotically crunch through numbers. In such a world math becomes this rigid boring system of absolutes. People don’t realize that mathematicians play with “absurdities” like these all the time. Indeed the only restrictions within mathematics really is that whatever craziness you cook up is logically internally consistent. It’s through playing around like this and saying... well what if I imagined I could do this... that mathematicians have made some of the most profound discoveries, found some of the most beautiful abstractions. The very concept of negative numbers, the number zero, algebra, imaginary numbers, infinity, were all at one point thought of by many as laughable.
I'm a bit confused in one aspect, Is it really ok to work in base 10? I mean, a base 10 number x=x(n)x(n-1)...x(2)x(1)x(0) [where x(i) is the i-th digit of x base 10 (the standard base)] is defined this way: x=x(n)*10^n+x(n-1)*10^(n-1)+...+x(1)*10+x(0) (being + and * the usual add and product)
Yeah, that's the problem I always have with these kind of digit by digit operations. After thinking about it a bit though, I realized that it works as long as you start by defining the numbers 1-9 and 90. Then you can make larger numbers because 90*90 = 900 and so on, and you make the 'base 10' numbers by multiplying the digits by 90, 900, etc instead of multiples of 10.
over the last few weeks I've been investigating Lunar primes, trying to determine if a number (with a 9 in it) is prime just by looking (i.e. with having to check) I've also been generalising it, into all bases. (with a Lunar prime having to contain the largest digit of the base) so far I've made a lot of progress, but still have a long way to go to get a general solution
in logic algebra (1's and 0's) + is the OR gate and * is the AND gate when I tried to apply that on decimal I got that AND should be the biggest number that are both bigger than or equal to (the smaller) and OR should be the biggest number on anyone of them (the bigger) very similar...
One of the most interesting videos in a long while. I think it's fascinating that it's distributive. I'll have to take a look at them myself, when I'm not working on other mathsy stuff haha.
What a pleasant surprise to see Neil Sloane on Numberphile. I've had the pleasure to read his great book on coding theory. Given the quality of his book, I'm not surprised at how well he manages to presents this odd piece of arithmetic. Great video!
I think you'll get a contradiction when trying to do that, since for example ab+99=99 for any a and b, so trying to do 99-ab for any a and b will give you 99. Subtraction isn't unambiguous which is a condition for it to exist as a function in lunar arithmetic
subtraction and division are built on the principle that there's an unique solution to a+x=b and a * x=b for every a and b (unless b=0), but we have already that 1+2=2 and 2+2=2, and 1 * 1 = 1 and 2 * 1 = 1. (up here, b-a is defined as the unique solution x, resp. b/a is defined as the unique solution x)
Also while additive and multiplicative identities exist (9 and 0) there isn’t a unique additive and multiplicative inverse function such that for any a you can find a unique b such that a + b = 9.
This is really interesting. I have toyed around with creating my own rules for arithmetic, but never got anything that I thought would yield interesting results. However this video is encouraging to try it more.
Half this comment section might faint if they’d found out about geometric algebra or lambda calculus. I’d love to hear mathematicians’ opinions on the degree to which day-to-day mathematics is arbitrary / a human invention. I also like the name lunar arithmetic because it makes me wonder how extraterrestrials’ mathematics might differ from our own. Nice video
To the thing with extraterrestrial math: It should work in the same way, if you have a cookie and take another one, 1+1 will always equal 2. This is something interesting to wrap your head around and get a new point of view at mathematics. But if you want to use it to keep track of your warehouse stock, it would be messy and not applicable.
Agreed, but you could imagine, very hypothetically, a species evolved with a natural awareness of quantum phenomena developing a kind of mathematics more suited to superposing waves than to counting cookies. Maybe such a type of mathematics would make quantum physics obvious and cookie counting bizarre.
@@uuaschbaer6131 Your second comment here highlights why topics like these are so important. And why our natural numbers and basic arithmetic might not be any more fundamental than something like lunar arithmetic. The only thing our number system really has over lunar arithmetic is additive and multiplicative inverses.
Anton Ellot No, because you are already fundamentally assuming that if you have a cookie and have another and combine them, that this somehow means adding. There is nothing fundamental or real about it. You are merely failing to get rid of that assumption in your brain. Lunar addition is just the max function or Ramp operator of Earthly arithmetic. Now, take a pile of sand and drop it on another pile of sand. How many piles of sand do you get? 1. So by your own reasoning, 1 + 1 = 1. Oh, what was all that nonsense about one arithmetic being more real and applicable than the other!
I like how many ppl comment that this video is nonsensical or that they "got dumber after watching it" but it really helps to see maths from another perspective imo, what's possible? What's something we take for granted but can be really important to understand?
Unfortunately the people who don't understand why this is interesting are exactly the people who would benefit from learning this. It's kind of like asking "what's the point of having other languages when we've got English?" The answer is it's a whole new way of thinking that completely changes your perspective on things.
I think it is mathematics, it's just not worth talking about it. There are so many other ways to twist your brain and learn to view things from a different perspective and still useful for something. At least make a game out of it, or make it somehow more interesting, but not the way it is represented in this video. I'm not saying that this is possible, but you don't have to upload everything that you make, some stuff can go to the "maybe later, if we get a better idea to go with it" pile. There is no application for this, not even the slightest and if there would be in the future (which I doubt), the whole thing is so easy and self explanatory that if someone would come across something that would use this weird system, could describe it and invent it in 5 minutes, maybe 10. Anyone. Those who did learn something from this video, please tell me, pleeease: What did you learn????
Nice one. But how do you get the ordinal numbers 1, 2, 3, 4, ... By definition every number is 1 higher than the before. But 1+1 = 1. You never come to 2. Even if you say 9 is 1 it doesn’t work. So how is the lunar number sequence constructed?
It just occurred to me that in Lunar Arithmetic, zero still has the property that any number multiplied by it equals zero and any number added to it equals that number. It makes me wonder if you could come up with a variant of this ruleset where equations behave differently if you don't remove zeroes from the start of a number.
Although I do find most of the Numberphile videos enjoyable, I think this was the best video here in a while. This was a completely new topic to me and shows that a lot of what we think of as rules for math are actually agreed upon conventions but there really isn't anything stopping someone from creating new conventions and seeing what happens.
@@atrumluminarium Sometimes people call things like this rigs (a ring without negatives, hence missing the n), because it still has all the other ring properties.
This video was a treat, thank you!!! I'm surprised that a little bit of algebra can put so many Numberphile viewers off. People defending the "rules" of arithmetic... Seriously? Are you sure you're watching the right channel? This isn't "bending the rules". There are no rules. We make the rules, any rules, plug in some symbols and watch what happens. It can be confusing and scary, yeah, but that's the funky world of algebra for you! Endless possibilities! This video is just a taster. Conventional arithmetic (what you learned at school) is, as the name implies, a convention - a particular set of symbols and rules we have agreed to use that is special in no way other than that we've agreed to use it for everyday purposes. But we're here for the maths, not counting apples :D Where's your sense of adventure, people?
Because it's fun! Not everything has to have a distinct purpose behind it. You can play golf for the sake of playing golf, and you can do math for the sake of doing math. This just a mathematical game of mini golf
({0..9},max,min) is an example of a distributive lattice which is also a semiring. Lunar arithmetic makes the numbers polynomials over this semiring (which form again a semiring), and these "lunar primes" are the irreducible polynomials. Even if its based on operations as simple as "max" and "min", there are lots of applications of lattice theory, from geography to quantum mechanics. Look at Wikipedia for semiring and lattice. Don't forget that all the electronic devices in our lives are based on arithmetics in Z2={0,1} with 1+1=0!
I can't believe how many commenters didn't understand the bit about teaching this to kids who don't understand carrying was a joke! Lighten up, guys. Numbers and operators are only symbols and there's no harm in defining them some other way just to see what happens. It's not like normal arithmetic is threatened by this.
The notation is rather confusing though. These things are like vectors so some surrounding brackets or something would help. I'll accept + and × though as they match Boolean algebra.
Why does it have to have a purpose? It's experimenting and having fun, It's looking at something different, and learning, and yes, playing with it. Why can't so many of the people watching this just enjoy it for the sake of it, and feel it's somehow of less value because of some perceived lack of purpose? There are banks of computers on this planet trying to find larger and larger prime numbers. Is there a point to that? No, we know there are infinitley many, so searching for bigger ones is just pointless, still looking though aren't we? I'm sure many in the comments enjoyed those videos, revealing impossibly large seeming prime numbers, but for some reason taken a dislike to this. It's puzzle solving, pure and simple. Solving a twisty puzzle is pointless, by the definition given by many here in the comments, but it's still satisfying and fun to do, and that is all the "point" needed to make something worthwhile. Have fun, enjoy it, solve a puzzle, thats enough for me, and you never know, in a 100 years time, the relevant application will arise that this is a perfect fix for. If I want to sit and pop bubble wrap I'm going to do it, for no reason or higher purpose beyond the simple act itself. I do it because I am human, and humans have wonderful, outrageous, nonsensical, unlikely and crazy brains, and you know what? I think that is a fact worth celebrating.
Simple algorithms are used in public schools to help slower kids get right answers. Paint this fence. Paint this wall. Hey, some kids still don't get the right answer. We need a simple algorithm. Paint this fence. Paint this wall. Hey, some kids didn't get it right. Buy my curriculum reform! Easier fence to paint. Easier wall to paint. Buy my teacher training program!
So, "kids have trouble with carries", which I don't believe But look what happens when you multiply 17 by 24 using Lunar Arithmetic at 2:21. There is a carry
" it is just placing the number in a different place," Where else could you have placed it ? Where else could you place a carry ? For anyone confused by carries Lunar Arithmetic serves no useful purpose other than to confuse them further.
why when multiplying several digits and you're picking the 'smaller' the last digit is not zero. for example in 12 times 12, normally we have: 12 12 --- 24 120 --- 144 but in 'lunar arithmetic' the zero for the second summand doesn't exist: 12 12 --- 12 11 --- 112 rather than: 12 12 --- 12 11**0** --- 110
If you happened to catch our last video on "evil" Belphegor's Prime, do check out this cool T-Shirt, Poster, Sticker design... www.bradyharanblog.com/blog/belphegors-prime-t-shirt
Please make next video on the basel problem
No!
@@kevinhart4real why?
That video turned me on to recreational math and I have never considered myself a "math person". Consider it sold! $$$
Can you please explain how the "lunar math" works before using it. There are so many inconsistencies in this video - and no explanation for how to deal with numbers of several digits...
I like the way this mathematician loves what he is doing, you can see it in his eyes, the way he speaks, he smiles ... Beautiful.
+
Went to the comments in search of this one :)
I enjoyed the enthusiasm as well, charming man
Agreed. :)
Like Futurama's Prof Farnsworth as a warm, kindly mathematician!
It's Neil Sloane, creator and maintainer of OEIS
Arithmetic is hard, let's make it easier!
*Actually makes it harder like a boss*
Is it really harder or are we just use to the "normal"?
@@R3lay0 It is harder: Imagine you have a field with 4 horses and another with 3. You take them out to a horse show, and need to tally back up the amount of horses you had to bring them back. You add 4 to 3, 'equalling' 4, so bring back 4 horses and now have 3 less to make money from in the future. Plus will likely have a lot of complaints from the horse show organisers that you left 3 horses for them to deal with, resulting in bans from further events. That all definitely made your life harder!
@@andrewsparkes8829 That's less useful, not harder
@@Reashu I think it actually might be harder for children because it has no apparent reflection in daily life. Even the rules might seem simpler.
@@jarlfenrir Well, multiplication isn’t initially intuitive either. It’s not until you get bags with the same number of counters in them that the real life use becomes clear. Similarly with exponentiation, especially above the cubing - tangible intuition isn’t immediately obvious. But an easier system doesn’t require tangible explanation to understand and utilise effectively. Nonetheless this system is a lot less useful of course.
Neil Sloane looking up a sequence on his own web site is undeniably badass.
How did I only just realise that this Sloane is that Sloane
@@gormster Yes, I wish I'd learnt java a way back, too :)
@@xyzzy2602 what?
Why is that badass?
it's deniably badass
This is actually how Enron did their accounts.
Taking the floor of their expenses, and the ceiling of their revenue, right?
Something went en-wrong
🤣🤣🤣🤣
Clever
🤣🤣🤣🤣
But what is 1?
*insert strange Vsauce music*
First of all, what are bricks?
The successor of 0. 0 axiomatically exists, and so does the successor function.
Jason Martin axiomatically?
@@JM-us3fr except in this video they obviously mean the element that forms the identity function under the operation in question. Divisible by 1 in the context of prime numbers means the identity function which happens to be 1 under multiplication, but it would also be 0 under addition, and 360 degrees under rotation. Or, in this case, 9 under moon math.
What are frogs?
“Lunar Arithmetic maths” can be be abbreviated “LUNA-TIC maths”
Because it's absolutely bonkers haha
Still correct.
Ideas like this leads to deeper understand of abstract concepts. Love this.
Good on you.
Indeed, it's nice to change a rule set slightly and see what peculiarities come out as a result.
But how can you change a rule set "slightly" - and still keep a convention which is only used by SOME people ON PAPER because it is how they were thought to "do math"...
Jonas Misund because its abstract math boi, math is only linear in that the rules hold or they don’t but changing rules helps you think in a way that lets you reinterpret what you thought, you know its exactly the same as using binary or 16 bit as apposed to the 10 bit decimal system but pretty different as well.
@@expressrobkill Yup. Some people have difficult to grasp it, but there are no absolute rules in maths, we are in the power to define our axioms as we prefer. At all, math is NOT meant to be useful. It's just a bunch of theorems that we can infer through its axioms.
Obviously there are some parts of math that are useful in a daily basis, but this creates the illusion that some ideas inside maths are "useless" just bcs you can't use it to bake a cake. If it were true, it would not mock maths anyway; but it is also not true: some concepts just happens to be so advanced that it is only used by a few people.
The first numberphile video were I felt I got dumber by watching it
this is the first video from this channel that i couldn't finish.......
Perhaps you've misunderstood the purpose of lunar arithmetic. It has no practical application because it's supposed to be a teaching tool. It's easy to learn the simple rules of normal arithmetic without thinking about why those rules work. By creating these new silly rules it forces the student to think about math logically and not just mindlessly adhere to the patterns they're used to. Math afterall is fundamentally just an expression of logic. There's standard conventions, yes, but fundamentally teaching math should be an excerise in logical thinking.
This video is about logic, not arithmetic. It touches on the Godelian notion that rules themselves are symbols and we need more formal ways to process those symbols: To add rules to other rules, multiply to combine rules, perform functions that change rule systems into others, and produce symbols for the results of those processes.
TheJaredtheJaredlong I had to think harder to do what he said, rather than what you’re supposed to do.
I checked. First skip for me for 5 months.
Or is it called Parker maths?
No because the squares make sense here. 😄
sadly a lunar square would be impossible.
not quite maths but they gave it a shot
KD Money o
KD Money Yes.
_Lunarithmetic_
_Lunatic_
Lunahoax*bullshit= Nasa
How tf do you say that?
@@fanimeproductionst.v.3735 Just say Lunarithmetic.
@@fanimeproductionst.v.3735 You can also say Luna - Rythm - eek !
so, 19 appears to be the smallest Interstellar Prime (both on Earth and Moon)
I like the idea, but not the name. Earth and the moon both orbit the same star. 'Interplanetary Prime' is closer but still feels a little wrong. 'Celestial Prime'?
Isn't 10 a prime on the moon? 10*9 is just the smaller one of 9 and 0 which is 0 for the ones digit, and for the tens digit it is the smaller one of 9 and 1 which is 1. Resulting in 10. Right?
Kyle Holler But 10 x 1 = 10, right? If I understood this correctly at least
Oh yeah it is, I forgot
Tidal primes
Good job identifying the identity Brady! You are more mathematically clever than you give yourself credit for.
Geez, here I was thinking this is the most fun numberphile video in a while; then to my dismay, it receives so much hate. This video embodies the very spirit of real mathematics. To heck with the rules. Pure math should never be constrained by what you think is normal. I wish we could get more of this. Thanks!
Good for you! ;That's how I feel. :)
But everyone wants something different from Numberphile I think.
You can't please everyone all the time.
@@numberphile keep it up the great work! Always inspiring!
Yeah, the most numberphile video I‘ve seen so far
But of what use is mathematics that gives wrong answers and is not useful?
And if you want to play around with the rules, then what about the different types of primes? Strange that some primes such as 5, are no longer so prime when you consider that complex numbers can also be considered as factors.
Yosef MacGruber Abstract thinking. Answers your question.
Wait, this is THE Neil Slone? Of OEIS fame? That's so cool! More Neil Sloane videos!
More coming!
From the Slone's gap video? Awesome!
yes! THE Neil Sloane!
its not spelt slone
You could call this video the Sieve of Lunar Arithmetic based on how well it partitions Numberphile viewers into those with and without a tolerance for abstract thinking.
Thanks for making a comment like that so now I don't have to!
Abstract thinking is useful when what you’re thinking about could actually have some use SOMEWHERE in the real world
@@xTurqz A lot of mathematics that seemingly had no relation to the real world turned out to be useful in some field of science later on. You never know if something "useless" isn't going to be the answer to some real problem, or at least point you in the direction of the answer.
Secondly, this "dismal arithmetic" clearly is useful as a training tool for people. It messes with your intuition and forces your mind to adapt to new rules. By taking you out of your comfort zone, it makes your mind more flexible and better prepared for learning new maths that you haven't seen before. It's just a fun way to expand your mind a little.
I love your username, by the way.
@@zlosliwa_menda though the only thing that this seems usefull to is to teach you how to adapt to new rules and become more flexible. Apart of that it seems pretty useless since the results are inaccurate
It makes me wonder how many new arbitrary operations we could add
What if we made two new symbols for this lunar addition and subtraction and used them in conjunction with normal mathematics
What if there was an operation where numbers are simply just put together 8 $ 6 = 86?!
What's with all the negative comments. A huge part of maths is about bending the rules and seeing what happens. Complex, negative, and irrational number are all basic concepts to us now but were once seen as pointless or even heresy. Keep an open mind people.
Indeed.
But the ideas of complex, negative and irrational numbers appeared naturally, because people needed these numbers to do stuff they couldn't do without them. On the other hand we already got addition and multiplication which work totally fine. Why do we need to look for another approach to addition? Moreover this technique gives unexpected results... Like you take one "thing" then put another "thing" right next to it and end up with one "thing" you started with? For me 1 + 1 = 1 says exactly this...
But the problem is that what appears to happen is nothing. There was no conclusion apart from, you can do this style of maths and get some different answers that serve no purpose. Kinda hard to get excited about.
I think a function where the greater digit is the the solution for the column isn't more ridiculous than a number where the product of two positives is a negative
Totally right
Brilliant! Immediately I started to think "now what are the identities?" +0 was obviously the additive identity, but *9 is the multiplicative identity. How peculiar! :D thank you really this was an interesting watch! To answer all of the "but why?" -comments, I think it's a good thought experiment. Taking a closer look like this gives you a bit of insight to the fundamentals of mathematics, which are so often forgotten.
Thank you - it is hard to answer all the "but why" questions - you did a nice job here!
Some people will be stimulated and start being curious like you did - like discovering a shiny new gem... Others do not see a direct application to everyday life and think it is probably a silly waste of time... I totally get that and to each their own... But Numberphile has a slight bias towards the former mindset.
Couldn't agree more. The fundamentals of mathematics are so often forgotten, it's hard to meet anyone who remembers them. Namely, the physics of the world we live in had shaped our maths to the degree that people don't even see how things could be different. This video is a nice reminder about this fact and also shows that in the worlds with different physics maths could be completely unusual.
Had anyone found physical application for lunar arithmetic most of the "but why" comments would have never shown up.
The interesting thing to me is that the multiplicative identity depends on the base. This immediately raises the followup question, what happens in binary where the identities are the same as in everyday mathematics?
fdagpigj E well, even though the identities are the same, there's still that quirk that there's no carry... so there will still be differences. :-B
??.
I wish I had heard about this during my Computer Science "Foundations of Higher Math" course in college!
At first, I was really hoping that there was some shortcut that this video would teach me. Instead, I learned that trying to apply these crazy rules can really get you to think about _why_ some math rules work the way they do. I wish the video had covered that a bit more at the start, though. It makes much more sense to go into this knowing that these crazy rules aren't for getting a correct answer, but rather to reflect on the logic behind the remaining "normal" things like "what it is to be prime" -- it's not just some crazy concept that your teacher made up for fun, there are some real applications of primes and using lunar math can help us relearn primes from a clean slate with a whole new arithmetic system. By changing one of the core principles of arithmetic, you better understand the place of other principles based on how they changed.
Thank you, Numberphile!
I love these wild constructions of un-intuitive systems! So fun to dive in to their oddities. I love that 9 is the multiplicative identity.
i feel like this has lots of fun properties that are more readily apparent in smaller bases. might have to go mess around with lunar binary for a bit
Check out the paper in the description.
for a bit ;)
That's what I'm really interested in. What do these operators do in binary? Let's make some truth tables!
p: 0 0 1 1
q: 0 1 0 1
p+q: 0 1 1 1
p*q: 0 0 0 1
And now, if you're familiar with computer science, you will recognize these as the OR / AND gates.
Essentially, lunar math is taking the fundamental operations of binary logic, and applying them to decimal in an interesting way.
wait where'd the rest of my comment go? The "view more" button isn't appearing...
Danatronics I can read your comment just fine. Your phone might just be broken
Oddly enough, in this number system, Graham`s Number is a degenerate number series, and all itterations equal exactly 3.
Yeah, the results of "Graham's function" are actually not that "interesting". It does grow insanely fast, but (by necessity), their behavior is extremely predictable.
I was immediately unenthusiastic about this video as I initially spent my time searching for some practical application and came up short, but 3 to 4 minutes in, it became a fun logic puzzle to try and reason out at the same speed as you. Excellent video, very fun and thought-provoking
Bro literally same. I was like “ok so how does this all tie in to the real world. Will the rules ultimately result in ‘earth’ arithmetic answers? Or is there some computer program that can use this rule to be more efficient” and then it became clear to me this was just a puzzle and was super happy about it
Maybe there's more to it, a some kind of conclusion or application, or development... or maybe not. But who cares if it's not any of it at all? The investigation itself of the misbehaviour of the basic concepts in the Arithmetic is something worth watching. I truly appreciate and understand the excitement of Mr. Sloane on this one.
This approach to mathematics reminds me of something similar (but not so... dismal) that I learned about 30 years ago:
1. Write down a number.
2. Multiply it with the first digit of that number.
3. Do "1." and "2." with the result.
If at some point the result starts with 1, then we are hitting a loop, because the procedure will call itself with the same number, again and again. Therefore, we will name the first number (in fact, all the numbers in the sequence) "stable". Consequently, "unstable" numbers will be the ones that grow infinitely, generating sequence that will not contain any numbers, starting with "1".
For example, the numbers, starting with n(1) = 52 -> n(2) = 52 * 5 = 260 -> n(3) = 260 * 2 = 520 -> n(4) = 520 * 5 = 2600 ... will be all "unstable", obviously. On the other hand, the sequence n(1) = 24 -> n(2) = 24 * 2 = 48 -> n(3) = 48 * 4 = 192 -> n(4) = 192 * 1 = 192 = n(3) will give us "stable" numbers.
Problem: Develop a method for classification of all natural numbers by their new property - which ones are "stable" and which ones are "unstable"?
At the first glance it is a boring task, but if you dive deeper, you will witness a mathematical beauty in the logic and complexity that this property will create before your eyes!
Reminds me of the max-plus algebra in which addition is replaced by the action of taking the maximum, and multiplication is replaced by the addition.
ScienceClic salut! Vous ici! Une prochaine vidéo sur ce sujet?
Vous ici
Is "lunar arithmetic" an algebra though?
@@ambidexter2017 How is even defined the subtraction? 7+8 = 8, 8+9=9, so 9+8-(8+7)=9-7=9-8 so that 7=8?!
Coucou ! On reconnaît les fans de maths et de physique, on regarde tous les mêmes vidéos !
"We're whalers on the moon! We carry a harpoon! But there ain't no whales, so we tell tall tales, and sing our whaling tune!"
I take it you have a degree in fungineering
“On the mooonnn” is so satisfying to hear. I love how excited this guy gets about math. I remember getting this excited when I started to truly understand basic number theory
the hendrix shirt only verifies everything further
This makes me question whether the concept of "bigger" or "smaller" can exist in a number system that doesn't have a standard way of incrementing.
Well I guess earthly addition and multiplication still exist. I imagine that all the natural numbers, like us, are born on the Earth, from our familiar operations. When they go on the moon though, they start reacting somewhat strangely!
You should look up a video on why the complex numbers do not have an ordering, it's fascinating. I think Dr Peyam has one.
@@wherestheshroomsyo Thanks for the recommendation, I watched it! I guess the lack of order on complex numbers makes more intuitive sense to me because complex numbers are 2D.
@@wherestheshroomsyo
If a and b are complex numbers, then what does a < b mean? And if that does not work, how might we define < and > so that it does work? Compare the real portion first and if equal, then compare the imaginary portion? Or vice versa? Or something else? Or do we need new symbols, maybe something like ? Actually, for each of the 2 portions, we could have a . Or 36 various comparison operators. Or just 6 for real numbers.
@@yosefmacgruber1920 I'll try to address your very first question. When a and b are complex numbers, what is it that a < b is supposed to mean? It depends on who you ask really. I will tell you that the statement is meaningless. The truth is that when using symbols, they can mean anything to anyone. Whether that be what those symbols mean to an individual or the majority of smart math people, it doesn't matter. It is very common, even in good published math, to redefine repurpose reuse and abuse well established symbols, as long as the context is clear and the author explicitly redefines it to be different than convention, that is what is important. However, in a completely practical context, I will tell you that a < b is meaningless for complex numbers. I will tell you that there is no less than or greater than with complex numbers, there is an equal to, and there are useful "comparisons" like talking about the magnitude and angle of a complex number. Keep in mind though that the lexicographic ordering is legitimate, it is just not the same thing as the real number comparisons that everyone learns about. Those are just my thoughts on the topic anyway.
Stop and look at all the books around him. He's probably read them all. I'm so jealous of his drive.
Imagine the enthusiasm of James Grime + 40 years and you get Neil Sloane. So wonderful to listen to people who truly love what they are talking about.
For some reason that's relaxing.
I have to say, the moon visuals and especially the recordings of the moon landing make this video just amazing.
Every time he says "one plus one is one" one math teacher feels his connection with the ISS...
And I get "F" for "alternative ariphmetics"
You must first learn the rules to break them! I'm pretty sure this professor has earned his Degree and P.h.D and presumably his job as a professor by learning reeeally well the conventional rules.
if a and b are digits and ab is a 2 digit number
ab^2 = abb if a > b, aab if a < b, and any combination if a = b.
also if ab9 is a 3-digit number ab9 is a prime only if a > b
He reminds me of Cliff Stoll. So much energy and passion and joy for maths. Love seeing these types of personalities!
I was looking for this years after first watching it and at first I thought this wasn't right because I was thinking the video I wanted had Cliff Stoll.
The best part is Buzz Aldrin on the background saying "Roger, _Neil_ ".
At first, it looked so silly, but as you started to talk about the primes, this maths became so curious and interesting. We should, definitely, never underestimate que power of maths.
Oh "great". At first it looked "silly" but then he seduced you into his lunacy.
Cristobal Jorje Stop being butthurt. It is a fun litte exercise to do and see what happens, it doesn't have to change your world view.
I'm surprised by the comments. As a third year student if mathematics I found it quite interesting. It's just a commutative ring lol. I have to look at rings every day and it's nice to see a new one.
It's not a ring. The addition is not invertible, so there is no additive group.
(For example 2+2=2=1+2, so 2 has no additive inverse)
It's an abelian monoid under addition and multiplication. I'm not sure if it's distributive as well. if so, then the non-invertibility is the only unfulfiled requirement for it to be a ring.
@@Friek555 Ah I had a feeling something was off. Either way I'm interested to see what this looks like in binary, I think it'll be either really boring or really interesting haha. I wonder what "ideals" look like, etc. or if you can generalise the notion of a quotient.
@@christopherimanto1732 I think he mentioned that it is distributive in the video, I shall check myself eventually of course. For now I have like three assignments due tomorrow so I have to prioritise for now haha
Supposing that it distributes (which I didn't check but it is claimed that it does), this is actually what's called a semiring (having an additive and a multiplicative semigroup)
This is one of my favourite Numberphile videos. More abstract stuff like this!
also just wonderful editing of lunar dialog (and also not overdone)
I adore Neil!! He is so enthusiastic and giddy!! More of him please
Art for art's sake
Math for math's sake
Some call it mathturbation.
well yea but it has applications in that its a mind exercise and allows you to think about things in a different way, i would be happy to see this in school as an exercise or exam question.
modern math?
The way that last "There are infinitely many primes" clicked into my brain was SO satisfying. This paper and explanation are both wonderful!
This reminds me of the video with Tom Scott talking about how the things science fiction writers have come up with for the way extra-terrestrial cultures view the universe pales in comparison to what we've developed on Earth. This is the kind of system I would expect from some culture from elsewhere in the universe: Completely logical and rule-bound, but completely foreign to our minds. To them, it would make perfect sense and they'd build their entire society and concept of the universe on it, in the same way we've done ours, but when our societies meet, we have completely different foundations for our understandings.
Now Calvin & Hobbes math problem (5 + 6 = 6) makes a lot more sense
When Stupendous Man crashes two planets together, the biggest always survives!
I was waiting for someone to say that. Brilliant!
I actually like dismal arithmetic. Lunar arithmetic is just a random name while dismal actually describes the system. For "otherwordly" you could just as well have jovian arithmetic or andromedian arithmatic
I've heard talk of using other "rules" for other planet names already... I was emailing one of the contributors to this video about Martian Arithmetic the other day!
How does dismal describe it, please?
I think Lunar describes it perfectly since if you use it... you become a lunatic :)
@@MateusSFigueiredo It's a play on the word decimal; this system destroys the rules of the rather dismal decimal arithmetic we learn in school.
It is the arithmetic system used by lunatics.
I don't know what's weirder: The concept of lunar arithmetic, or the fact that there's an older British gentleman wearing a Jimi Hendrix shirt.
But... why though? What purpose does this serve? Is it just a toy for bored mathematicians, or does it serve some actual function?
Of course an entirely fair question and asked earnestly... And in anticipation of many people asking this, here's my personal opinion...
1. Because it is fun and creative - and playing with new ideas is good for your brain.
2. Because you never know what "bending the rules" will teach you - what techniques, insights and breakthroughs will occur that may have more useful applications... Just look at much of John Conway's work... So much playfulness and so many games - yet many ideas and insightful mathematics has fallen out of that.
Lunar arithmetic is never going to be used to build a bridge or design an iPhone (I certainly hope!!!)... But neither is it just throwing ALL rules out of the window... It is creating new arbitrary set of rules and seeing what happens... What IS a prime number in this new landscape? What pattern do the squares follow? And what light might that shed on more conventional mathematics?
Also... If you are not buying that and think it's just nonsensical playing... I say the following...
It may be true that this will not cure cancer or help people live longer - but what is the point of living longer if we can't play, imagine, and do fun stuff like this?
Most math doesn't have many direct applications, and most of modern math is just "a toy for bored mathematicians". Even though no one knows how Inter-Universal Teichmuller theory will be used, it still holds value in that it helped solve some conjecture that still doesn't have much application. Pure math is just for fun, for now.
@@numberphile Absolutely fair enough. I am all for fun and creativity, and find your videos fascinating and (mathematically) baffling in equal measure but always feel better for the journey they take me on. Thanks Brady et al., from a happy Tim
All math is just a toy for mathematicians. What physicists do with it later is physicists' business
@@numberphile I just hope they'll never get the idea to teach lunar arithmetic to kids, that would screw up the next generation.
For 2 digit numbers squares:
If the number is AB, if A>B then AB squared is ABB, and if A
It gave me insight I never had.
Gonna go experment with mars arithmetic.
Thank you!
How can someone dislike the enthusiasm of Mr Sloane???
I really like this guy's style of problems, I want more of him!
But in multiplication... when we shift the second number one place to the left to then add it, that is multiplying by 10.... shouldn't there be a change in that??
actually a neat system, idk why this video got so much hate. just something kinda funny but also kinda cool that people came up with. you guys need to lighten tf up man
there is an interesting thing 3 + 2 = 3 so let is say for example 3 + x = 3, there are multpile solution to this equation it can be one of {0,1,2,3} so 3-3={0,1,2,3} but 3+x=5 then x must be 5 so 5-3=5.
The same can be said to 3*2 = 2 so x*2=2 ,x can be {2,3,4,5,6,7,8,9} so 2/2={2,3,4,5,6,7,8,9} but x*2=3 has no solution since there is no number that is less than 2 but equal to 3 so 3/2 is undefined.
I can keep going to roots and stuff but maybe im wrong about the division and the subtraction, share your opinions!
There is no "-".
@@KanalDerGutenSache He said substraction and division were not allowed but why, though? Is it because those multiple or undefined solutions would pop up everywhere?
oof the comments
In other news it's really cool that you got to interview Neil Sloane himself!
Just when I thought today couldn't get any better, I've found the real-life Professor Farnsworth and this math confirms his identity.
This kind of thing is a great showcase of the creativity of mathematics. People don’t readily understand that math is actually an extremely creative endeavour, and when told that it is can’t wrap their mind around how it could be. The reason is that math is traditionally terribly taught as just a rigorous system of algorithms that you use to robotically crunch through numbers. In such a world math becomes this rigid boring system of absolutes. People don’t realize that mathematicians play with “absurdities” like these all the time. Indeed the only restrictions within mathematics really is that whatever craziness you cook up is logically internally consistent. It’s through playing around like this and saying... well what if I imagined I could do this... that mathematicians have made some of the most profound discoveries, found some of the most beautiful abstractions. The very concept of negative numbers, the number zero, algebra, imaginary numbers, infinity, were all at one point thought of by many as laughable.
I'm a bit confused in one aspect, Is it really ok to work in base 10?
I mean, a base 10 number x=x(n)x(n-1)...x(2)x(1)x(0) [where x(i) is the i-th digit of x base 10 (the standard base)] is defined this way:
x=x(n)*10^n+x(n-1)*10^(n-1)+...+x(1)*10+x(0) (being + and * the usual add and product)
Yeah, that's the problem I always have with these kind of digit by digit operations.
After thinking about it a bit though, I realized that it works as long as you start by defining the numbers 1-9 and 90.
Then you can make larger numbers because 90*90 = 900 and so on, and you make the 'base 10' numbers by multiplying the digits by 90, 900, etc instead of multiples of 10.
Is there an alternative?
These numbers are more like vectors in disguise.
Basically it's Boole algebra for decimals
What a huge dork. He's delightful and should be in more videos.
These kind of videos are the best. Since I'm no numbers wiz and things frequently go over my head, might as well have some fun with nonsense
Glad you enjoyed it.
All mathematics is just fun with nonsense until someone comes along and finds an application
professor farnsworth took a day out of his delivery service to show us this
over the last few weeks I've been investigating Lunar primes, trying to determine if a number (with a 9 in it) is prime just by looking (i.e. with having to check) I've also been generalising it, into all bases. (with a Lunar prime having to contain the largest digit of the base)
so far I've made a lot of progress, but still have a long way to go to get a general solution
Progress update?
in logic algebra (1's and 0's) + is the OR gate and * is the AND gate
when I tried to apply that on decimal I got that AND should be the biggest number that are both bigger than or equal to (the smaller)
and OR should be the biggest number on anyone of them (the bigger)
very similar...
One of the most interesting videos in a long while. I think it's fascinating that it's distributive. I'll have to take a look at them myself, when I'm not working on other mathsy stuff haha.
cheers - have fun with it
What a pleasant surprise to see Neil Sloane on Numberphile. I've had the pleasure to read his great book on coding theory. Given the quality of his book, I'm not surprised at how well he manages to presents this odd piece of arithmetic. Great video!
Is there no way to formulate subtractions and divisions
I think you'll get a contradiction when trying to do that, since for example ab+99=99 for any a and b, so trying to do 99-ab for any a and b will give you 99. Subtraction isn't unambiguous which is a condition for it to exist as a function in lunar arithmetic
You can figure that out if you like
subtraction and division are built on the principle that there's an unique solution to a+x=b and a * x=b for every a and b (unless b=0), but we have already that 1+2=2 and 2+2=2, and 1 * 1 = 1 and 2 * 1 = 1. (up here, b-a is defined as the unique solution x, resp. b/a is defined as the unique solution x)
@@Ocklepod oh nice
Also while additive and multiplicative identities exist (9 and 0) there isn’t a unique additive and multiplicative inverse function such that for any a you can find a unique b such that a + b = 9.
This is like learning a different dialect of maths.
I remember seeing this math in Calvin and Hobbes :P
His teachers were not impressed.
brilliant editing of the Neil Armstrong audio clips into the video!
This is really interesting. I have toyed around with creating my own rules for arithmetic, but never got anything that I thought would yield interesting results. However this video is encouraging to try it more.
This is quite cool! Not that useful in everyday life, but could be useful in a very nerdy party trick
Half this comment section might faint if they’d found out about geometric algebra or lambda calculus. I’d love to hear mathematicians’ opinions on the degree to which day-to-day mathematics is arbitrary / a human invention.
I also like the name lunar arithmetic because it makes me wonder how extraterrestrials’ mathematics might differ from our own. Nice video
To the thing with extraterrestrial math:
It should work in the same way, if you have a cookie and take another one, 1+1 will always equal 2.
This is something interesting to wrap your head around and get a new point of view at mathematics. But if you want to use it to keep track of your warehouse stock, it would be messy and not applicable.
Agreed, but you could imagine, very hypothetically, a species evolved with a natural awareness of quantum phenomena developing a kind of mathematics more suited to superposing waves than to counting cookies. Maybe such a type of mathematics would make quantum physics obvious and cookie counting bizarre.
@@uuaschbaer6131 Your second comment here highlights why topics like these are so important. And why our natural numbers and basic arithmetic might not be any more fundamental than something like lunar arithmetic. The only thing our number system really has over lunar arithmetic is additive and multiplicative inverses.
Anton Ellot No, because you are already fundamentally assuming that if you have a cookie and have another and combine them, that this somehow means adding. There is nothing fundamental or real about it. You are merely failing to get rid of that assumption in your brain. Lunar addition is just the max function or Ramp operator of Earthly arithmetic. Now, take a pile of sand and drop it on another pile of sand. How many piles of sand do you get? 1. So by your own reasoning, 1 + 1 = 1. Oh, what was all that nonsense about one arithmetic being more real and applicable than the other!
Regular, conventional mathematics has enough interesting and useful aspects to keep one busy for a lifetime. This is just silliness.
I like how many ppl comment that this video is nonsensical or that they "got dumber after watching it" but it really helps to see maths from another perspective imo, what's possible? What's something we take for granted but can be really important to understand?
Thank you
So what's possible? What did you learn from this? Please tell me.
Unfortunately the people who don't understand why this is interesting are exactly the people who would benefit from learning this. It's kind of like asking "what's the point of having other languages when we've got English?" The answer is it's a whole new way of thinking that completely changes your perspective on things.
Because it isn't mathematics.
I think it is mathematics, it's just not worth talking about it. There are so many other ways to twist your brain and learn to view things from a different perspective and still useful for something. At least make a game out of it, or make it somehow more interesting, but not the way it is represented in this video. I'm not saying that this is possible, but you don't have to upload everything that you make, some stuff can go to the "maybe later, if we get a better idea to go with it" pile. There is no application for this, not even the slightest and if there would be in the future (which I doubt), the whole thing is so easy and self explanatory that if someone would come across something that would use this weird system, could describe it and invent it in 5 minutes, maybe 10. Anyone. Those who did learn something from this video, please tell me, pleeease: What did you learn????
Nice one.
But how do you get the ordinal numbers 1, 2, 3, 4, ...
By definition every number is 1 higher than the before. But 1+1 = 1. You never come to 2.
Even if you say 9 is 1 it doesn’t work.
So how is the lunar number sequence constructed?
It just occurred to me that in Lunar Arithmetic, zero still has the property that any number multiplied by it equals zero and any number added to it equals that number.
It makes me wonder if you could come up with a variant of this ruleset where equations behave differently if you don't remove zeroes from the start of a number.
Imagine how many completely exotic forms of mathematics we could create by changing the fundamental functions of each of the operations
This is one of the best videos on UA-cam....
Thank you, Numberphile
He's so into it! I love it!! Man, he reminds me so much of Richard Feynman!
Fun fact - "lunatic" comes from the word "luna", which means "moon", because people once believed that changes of the moon would make you go crazy.
He sounds so proud when he says there are infinitely many lunar primes.
I usually have a similar emotion whenever I come to the QED of a proof.
Although I do find most of the Numberphile videos enjoyable, I think this was the best video here in a while. This was a completely new topic to me and shows that a lot of what we think of as rules for math are actually agreed upon conventions but there really isn't anything stopping someone from creating new conventions and seeing what happens.
So its a group without the inverse axiom (the name eludes me, monoid?)
It would be a ring-ish thing since it has two operations and they are distributive! Groups and monoids only have the one operation.
@@diligar but rings have inverses. There's probably a thing along the lines of a double monoids
@@atrumluminarium Sometimes people call things like this rigs (a ring without negatives, hence missing the n), because it still has all the other ring properties.
It is a semi-ring.
This video was a treat, thank you!!!
I'm surprised that a little bit of algebra can put so many Numberphile viewers off. People defending the "rules" of arithmetic... Seriously? Are you sure you're watching the right channel?
This isn't "bending the rules". There are no rules. We make the rules, any rules, plug in some symbols and watch what happens. It can be confusing and scary, yeah, but that's the funky world of algebra for you! Endless possibilities! This video is just a taster. Conventional arithmetic (what you learned at school) is, as the name implies, a convention - a particular set of symbols and rules we have agreed to use that is special in no way other than that we've agreed to use it for everyday purposes. But we're here for the maths, not counting apples :D Where's your sense of adventure, people?
but why?
Because it's fun! Not everything has to have a distinct purpose behind it. You can play golf for the sake of playing golf, and you can do math for the sake of doing math. This just a mathematical game of mini golf
({0..9},max,min) is an example of a distributive lattice which is also a semiring. Lunar arithmetic makes the numbers polynomials over this semiring (which form again a semiring), and these "lunar primes" are the irreducible polynomials. Even if its based on operations as simple as "max" and "min", there are lots of applications of lattice theory, from geography to quantum mechanics. Look at Wikipedia for semiring and lattice.
Don't forget that all the electronic devices in our lives are based on arithmetics in Z2={0,1} with 1+1=0!
how is this person 80 years old. I dont get it
Edit: aah i get it now. 80*1=10. He must live on the moon
He always look extremely satisfied with the math at the end....More than any other human on planet earth
I can't believe how many commenters didn't understand the bit about teaching this to kids who don't understand carrying was a joke! Lighten up, guys. Numbers and operators are only symbols and there's no harm in defining them some other way just to see what happens. It's not like normal arithmetic is threatened by this.
Yeah, people are so narrow minded...
The notation is rather confusing though. These things are like vectors so some surrounding brackets or something would help. I'll accept + and × though as they match Boolean algebra.
Absolute mad lads, they actually invented new mathematics, it is out of this world
Did you know:
Arithmetic spelt backwards is lunar?
Friends!
And Eurovision Cyan backwards is "checks out"
!arithmetic si sdrawkcab tleps citemhtirA !esnesnoN
But only if youre on the moon
The more you know!
Why does it have to have a purpose? It's experimenting and having fun, It's looking at something different, and learning, and yes, playing with it. Why can't so many of the people watching this just enjoy it for the sake of it, and feel it's somehow of less value because of some perceived lack of purpose?
There are banks of computers on this planet trying to find larger and larger prime numbers. Is there a point to that? No, we know there are infinitley many, so searching for bigger ones is just pointless, still looking though aren't we? I'm sure many in the comments enjoyed those videos, revealing impossibly large seeming prime numbers, but for some reason taken a dislike to this.
It's puzzle solving, pure and simple. Solving a twisty puzzle is pointless, by the definition given by many here in the comments, but it's still satisfying and fun to do, and that is all the "point" needed to make something worthwhile. Have fun, enjoy it, solve a puzzle, thats enough for me, and you never know, in a 100 years time, the relevant application will arise that this is a perfect fix for.
If I want to sit and pop bubble wrap I'm going to do it, for no reason or higher purpose beyond the simple act itself. I do it because I am human, and humans have wonderful, outrageous, nonsensical, unlikely and crazy brains, and you know what? I think that is a fact worth celebrating.
Yeah. You’d think this channel was called Numberphile or something!? ;)
These comments reveal how little most Numberphile viewers actually know about how maths work. Sad :-(
Simple algorithms are used in public schools to help slower kids get right answers.
Paint this fence.
Paint this wall.
Hey, some kids still don't get the right answer. We need a simple algorithm.
Paint this fence.
Paint this wall.
Hey, some kids didn't get it right.
Buy my curriculum reform! Easier fence to paint. Easier wall to paint.
Buy my teacher training program!
I don't enough high for understand this
lol 😏
I'm extremely high, and I don't understand this.
His voice is so soothing.
Could have dwelled a little longer with the mechanics of why these operations are
Commutative, Associative and Distributive
THIS IS MY FIRST ENCOUNTER WITH ARITHMATIC. THIS CHANNEL IS GREAT TO LEARN FROM!
Forget everything you learned in this video.
So, "kids have trouble with carries", which I don't believe But look what happens when you multiply 17 by 24 using Lunar Arithmetic at 2:21. There is a carry
" it is just placing the number in a different place,"
Where else could you have placed it ?
Where else could you place a carry ?
For anyone confused by carries Lunar Arithmetic serves no useful purpose other than to confuse them further.
That's distribution actually, not a carry.
So kids have trouble with carries but will understand distributions.
Is that what you are saying ?
By the way. What the heck is a distribution ?
why when multiplying several digits and you're picking the 'smaller' the last digit is not zero. for example in 12 times 12, normally we have:
12
12
---
24
120
---
144
but in 'lunar arithmetic' the zero for the second summand doesn't exist:
12
12
---
12
11
---
112
rather than:
12
12
---
12
11**0**
---
110