It takes 8,400,000,000,000 years to use a Magic: The Gathering computer

you are complicated and no I don't just mean that you like Dungeons & Dragons and 90-day fiance at the same time wow that's amazing no I mean that you as a system are very complex you are an incredible array of interactions between cells and proteins and atoms and molecules mathematically speaking you are very complicated and being a complicated being you can use your ingenuity to make other very complicated things like the computer in your pocket that's never more than 2 feet from you that's selling your personal data to Facebook and things like games one of these games however is so complex that it would take longer than the age of the universe to finish it the facility the moment you have some system with many different components interacting in many different ways that system starts to get complicated your brain and all of its neurons interacting together is very complicated ant colonies are complicated super computers with sentience are complicated but those are very obvious examples of complexity you can find it in less obvious places too and what feels like a lifetime ago I showed you the most complicated board game known to science magic the Magic the Gathering I guess I don't have access to that video anymore but what I did was show you a real deck of Magic the Gathering cards that could operate using the game's own rules as a Turing machine a simple computer and it was rather amazing a few pieces of card stock that could theoretically compute anything but at the time I wasn't able to show you anything actually being computed well that brings us to today but first let's do a quick recap before we jump headlong into things a Turing machine is a theoretical construction of the simplest kind of computer something that computes first conceived by the father of modern computer science Alan Turing in 1936 the original idea consisted of three elements first a tape that extended infinitely in each direction remember this is all mathematical and had some spaces on it where you could put some symbol the second element was a head that could read write and erase symbols based on the third element a program that the computer would follow the computer could also have multiple different states but we'll leave that alone for now what a Turing machine does is take some input on the tape follow the program and then give us some output to read later it's incredibly powerful let's watch one at work right now computer science has come a long way since 1936 today you can just go online find a Turing machine simulator and mess around with it this one is going to perform unary addition it's going to take 2 binary numbers in this case 8 and 2 and it's gonna sum them together for us when we run this Turing machine you can see the head going along the simulated tape reading writing and erasing according to the program you see below and then it gives us some output which is 10 in binary now this seems simple and it is but it's incredibly powerful any real-world computation can be performed on a Turing machine like this but not all Turing machines have to be digital which brings us back to Magic the Gathering my nerdy hobby of choice in a previous video I took this paper by dr. Alex Churchill and his colleagues and I constructed what they recommended as the real-world Turing machine deck but at the time of that video I couldn't even show you one plus one because the researchers themselves didn't know what it would look like in terms of tokens and board states what have you well I'm glad to say that that time is now and if you thought cardboard was complicated before you know it's not that hard to find a game that can simulate a Turing machine that is so called Turing complete as we said when we first looked into this concept starcraft minecraft and even minesweeper can simulate a Turing machine what's impressive about Magic the Gathering though yeah it's a car with my face on it what's impressive about Magic the Gathering though is that so far it's the only offline game we know that can simulate a Turing machine that can theoretically compute anything and because of that there are board States and Magic the Gathering that can literally present an infinite set of possible moves to a player which makes it mathematically as complex as a game can be more complicated than chess or go and all this just thrown at a player by some cards good one let me see your badge don't you run away from it the last time we talked about the Magic the Gathering Turing machine deck where I was explaining the cards and their interactions and the four turns cycle and how everything worked with my friends from the command zone Jimmy and Josh I had everything laid out nicely on an average sized kitchen table but in truth that was really only possible because we didn't really know how many tokens we would actually need there researchers didn't either we didn't know that we didn't know how many dice we would need so I shortcut everything to make it fit nicely on a table and in a video so how big of a table would you need to run the Turing machine deck how long would a game actually take if you wanted to do something like eight plus two and get an output that showed something that looked like 10 well that's where honorary facility member Yan Beall comes in Beal was able to take using computer science on the level of Aria the original Magic the Gathering Turing machine paper code calculate and run everything himself to give us the numbers and the math that we are looking for please go watch yawns full video it's over 20 minutes long and does a wonderful job describing everything it's in the description of this video but for now I want to show you the longest game in the universe in his analysis Yan created a Turing machine that could compute two plus three he then through some very clever transformations put this in the language of the Magic the Gathering Turing machine from the original paper you should watch his video for all that fancy work but he found that you need a slightly larger table than I used to do this the average Magic the Gathering card is about 63 millimeters wide this means on the average kitchen table you might be able to fit 25 or so magic cards or card tokens perfectly side-by-side to compute two plus three in a game of magic though you would need a table over two and a half thousand kilometres long and if you're at one end of it it would take the best human marathoner five days to reach the other side on top of this table would be sitting almost 41 million creature tokens for our tape and if you stack them on top of each other there'd be over two times taller than Everest and weighs 72,000 kilograms but this is just all the token stuff actually playing this game would be a creature type unto itself recall that to make our physical Turing machine work we need to go through a number of steps and those steps involve going through a four turn cycle of a Magic the Gathering game and manually placing a lot of plus one plus one counters on our creature tokens these counters signify where the head of our Turing machine is and what that head will be reading writing or erasing now most Magic the Gathering nerds like me use this to denote a lot of counters a d20 a dodecahedron so each one of these can put up to 20 counters on one of our creatures however with like 40 million tokens that means a lot of dice add it all up with millions of powers and toughness --is you would need in terms of D 20s about 20 trillion dice now I have a lot of dice but this is a whole nother level I would need 1.7 percent of the entire planets plastic production diverted towards me playing one game of magic together which is absolutely ridiculous think about someone looking at a spreadsheet somewhere and be like what what 2% of all plastic is going to what or like me getting on the phone you're like yeah that's right yeah all the plastic so when you have tens of millions of tokens and trillions of dice how long would it actually take to play a game of match of the gathering where we both win and compute something like 2 plus 3 well as Yan estimated with me while we were emailing back and forth it would take around 17 trillion turns and remember during those turns we are going along the table manually switching all the dice indicating all the counters if all of these little interactions if we are quick about it and they only took maybe a second a single second on average to play this game and for it to finish it would still take 8 years 84 ye 805 eight point four trillion years that is 600 times older than the universe just just think about this timeline for a second I sit down from you across from you at a table and I take out this deck of cards and I go ok so what I'm gonna do first is I'm gonna exile your hand you're gonna do nothing so I'm gonna grab right Longley animator and I'm gonna start bouncing this to my hand and card is gonna set up and remember you have no hand you can't do any step I just have to make sure I switch the power and toughness on the 5 million 5 million fairy 2,000 miles over there so just one second oh my oh my balls oh my little paws [Music] burnt interceptor deployed [Music] Oh Oh I knew that protocol was a good idea obviously a physical Magic the Gathering Turing machine is wildly impractical even more impractical than I first thought when I was researching this topic the point is it's possible sure the Sun would have burnt out many times over by the time you finished a single game but hey it's possible a game that can compute anything man I love it mostly this card with my face on it that's what I like until next time REM what do you do with my bone what I want to see my bones for a second thank you so much to the facilities very nerdy faculty for directly supporting the creation of this video the main source of revenue for the facility comes from our faculty and from our patreon especially today I want to thank research assistant Michael O'Brien and visiting scholar Patrick Holt if you want to join the facility's staff and our patreon and our disk orbit right now literally hundreds of nerds are talking with each other giving me episode ideas and sharing photos of their pet spiders you can go to patreon.com/scishow science videos today for a nerdier tomorrow thanks for watching

Channel: Kyle Hill

Views: 386,289

Keywords: kyle hill, because science, magic the gathering, turing machine, the facility, computer, kyle hill channel, kyle hill magic the gathering, kyle hill mtg, engineering, learning, math, physics, science, stem

Id: uDCj-QOp5gE

Length: 12min 13sec (733 seconds)

Published: Thu May 14 2020