What do LEGO bricks and celestial bodies have in common?

if you count up all the things in the universe that weigh between one and two kilograms all the pineapples all the toasters all the prairie dogs and then you count up all the things that weigh between two and three kilograms all the two liter soda bottles all the bricks all the physics textbooks which one will you have more of if you do this for all the weight classes things that are one gram like Lego studs things that are 10 to the power of 40 kilograms like supermassive black holes then what will the shape of the distribution be while you think about that this funny paper caught my attention recently because it's a peer-reviewed physics publication and the subject of their experiment is Lego Ninjago which is just so silly I mean what does that say about the state of scientific research what value could there possibly be in doing experiments with trivial things like toys or food or musical instruments yeah in all seriousness this seems exactly like something I would do in fact I really think this is a clever paper and it seems like something that I would make a video about so I will but why does Lego show up what is the study even about well it's about the question I started off by asking you what is the distribution of mass in the universe we sometimes call this a mass function not to be confused with probability Mass functions or binary Mass functions which are different concepts if you take all the objects in the universe galaxies stars planets dust weigh each one and count them up how many small things should we expect there to be for each big thing some Studies have tried to answer this before so what the authors of this paper did is they asked the same question for Lego bricks and it turns out there's a pretty surprising similarity in this video we're going to learn about the mass distribution of the universe what percentage of all things weight blank kilograms and then we're going to try to reproduce the results of this experiment that was done with Lego bricks and we're not just going to repeat what they did I made a way to expand this experiment to hundreds of Lego sets and the results are really weird I really think we might have discovered some kind of hidden law of Lego and it might just agree with the laws of physics documenting the mass of celestial objects was popularized within the study of stars see the most important factor that determines how long a star will live and what happens when it dies is how massive it is heavy Stars need to perform Fusion faster to keep themselves from collapsing so they have shorter life spans and less massive stars have longer life spans so if we want to learn about the evolution of a collection of stars like a Galaxy for example we need to know the distribution of Stellar Mass when the stars are first formed how many stars will be this big how many stars will be that big we notate this with some function that represents the number of stars per Mass interval that means we can get the number of stars that have a mass within a given range by integrating this function we sometimes call it the salpeter function after the astronomer who introduced it in 1955. using data from nearby Stars salpeder realized that the distribution is very close to a power function there are way more small Stars than there are big stars the exponent that he found fit his data best was negative 2.35 even before that in 1942 Fritz Wiki theorized that all objects in space might follow some common Mass distribution in 2007 a study that looked at data on planets Stars gas clouds star clusters galaxies and Galaxy clusters found that all of them follow a surprisingly clean power distribution the exponent is negative two which is pretty close to what had been found for stars before what that means is that for every thing in the universe that's as heavy as the sun there are four things that are half as heavy as the sun Then There are 16 things that are one quarter the mass of the sun the smaller you get the more things there are and the bigger you get the fewer things there are if you think about a Lego set it's kind of the same thing so back to the paper the authors thought it would be interesting to weigh each brick and count them up and see what the distribution of masses it might make a fun experiment for undergrad astronomy classes they used set number 70656 Garmadon Garmadon Garmadon because it contains a Shark model like the mascot of their University I see the resemblance wait this is actually off brand Racer the shark it seems like this guy is their actual mascot nope how many mascots does this school have once they ran the experiment they found that the mass function for this set was very close to a power curve but even more surprising the exponent was negative 2.13 this Lego set is in line with everything else in space now maybe it's just a coincidence the authors even recognize that possibility and they only did one set if we really want to say anything about how the weights of Lego bricks are distributed we would need to do this same analysis on a large number of sets as much as I would like to buy a lot of Lego sets it's not really financially viable and it's not even necessary either because Lego instructions and part lists are publicly available all we need to do is weigh each part but we should never underestimate the Lego Community the weight of every piece is also available on websites like Bricklink although I think it's for shipping purposes it should be good enough for our experiment so instead of doing all this by hand let's write a program that does it for us it turns out Bricklink even has an API so we could use that to get our set and part info but you need a seller account to use it no problem we'll just do some web scraping I got it working so that the program starts on a Lego sets Bricklink page then goes through each part in the inventory opens that web page and Records the weight because it loads every single pieces page it's not very fast it takes two or three minutes for most sets but it does the job by all means it's faster than weighing and Counting every single element once we have the weights we can plot them as a histogram sure enough there are many more small pieces than large ones but how do we know whether or not this is a power distribution well let's go back to the equation that we expected to follow and we'll take the logarithm of both sides in case you need a refresher a logarithm is the operation that undoes an exponent I'm using log base 10 so log of 10 to the a equals a and 10 to the log of a also equals a looking at our equation we can use some logarithm rules to simplify the right side multiplication inside a log is the same thing as addition outside also exponents inside a log are the same as multiplication outside it looks like we just made our equation more messy but really log of something each of these is just a number and this is just the equation for a line Y equals Alpha X plus b what we've done is we took this power equation which is curved and we turned it into a linear equation so if we plot the log of the number of bricks against the log of the mass then it should look like a straight line and it does the slope of this line is the exponent so if your data is curved and you want to fit a line to it logarithms often do the trick that's one of the reasons you'll see log plots in so many fields once we fit our line we have the slope and therefore the exponent for Garmadon Garmadon Garmadon I got basically the same results as their experiment so I think our process works I'll make it so we can just enter a set products number and it runs the whole analysis gives you the plots and displays the best fit slope I generated a random five sets and then picked one from those that seemed big enough to be a good sample and I did that a few dozen times the results are totally unbelievable every set has a slope of negative two of course there's some variation there are some small sets that have a more uniform distribution and sets that have Unique Designs like a boat might have a big hole piece or Technic sets might have hundreds of these little pegs but the overwhelming pattern is negative two once again that is the same distribution of all things in space the interpretation of this number is for each piece of a given weight there will be about four pieces that have half that weight therefore 16 that have one quarter of the weight and so on this pattern appears to apply universally to Lego sets and if it applies to most sets it also applies to all the Lego bricks in the world if one of you watching this is a Lego designer or has some kind of industry knowledge or maybe if you know someone you can show them this video I just need to know is this some kind of design standard at The Lego company does it have to do with manufacturing or playability or Warehouse economics or something that would make them ask designers to include this particular distribution of parts or maybe is it some cognitive thing maybe the way we construct things we start with big pieces and then add smaller ones as we make details I don't know if you've made a Lego model of your own creation try out this experiment and let me know what the results are I think even after writing this program and trying it out a few dozen times this needs more investigation is it just Lego or does this work on everything maybe you can come up with a way to count every object in your house please improve my code try it out yourself come up with other ways of counting I don't know I think this is really interesting besides not understanding the Lego problem everything following this negative two slope is really weird in astronomy the reason it's weird is because all of the different objects in space are formed in completely different ways for example stars are formed from molecular clouds collapsing and fragmenting into smaller pieces but galaxies are formed from Stars clustering together into bigger pieces even if there was something about the creation process that ended up making things follow this distribution why would it apply to so many classes of objects there's really only one similarity that all matter in space has and that's gravity the gravitational force in classical mechanics is proportional to one over the distance squared or R to the power of negative two this might be the negative 2 that we're looking for pretend that the universe is made up of all these balls of rock floating around maybe some of them have already congregated into a bigger Rock and some haven't if Iraq is deciding where it'll group to of course being heavier makes the force stronger but being close makes the force stronger faster so it'll require adding a lot of rocks before the force from the big rock becomes so strong that the new rock choses the big one over the close one that means that we get more small groups than big ones and in theory the distribution should be proportional to 1 over Mass squared but whether this is really where the negative 2 comes from is a big Maybe before we end I'd like to tell you about this video sponsor brilliant if you want to learn more about Stellar Evolution or gravity or maybe you need to study data science to make a Lego analyzing program of your own then brilliant.org is the best place to do it brilliant has thousands of lessons on stem subjects from foundational math to Quantum information so whether you want to dive into a new topic or just practice your problem solving skills in a fun way they'll have something for you while preparing for this video I worked through Brilliance lessons on the life cycles of stars in the astrophysics course and the lessons are so interactive that I found myself understanding things conceptually that I never even got from my degree in physics to try brilliant free for 30 days visit brilliant.org physics for the birds or click on the link in the description the first 200 subscribers using my link will get 20 off an annual premium subscription big thanks to brilliant for sponsoring this video and thank you for your support maybe we shouldn't even be asking this question why negative two there might not be any fundamental law behind it it could just be chance or maybe it's some unproven mathematical thing like how a lot of other random variables tend to follow a normal distribution but when the physicist inside of me sees this pattern showing up in completely unrelated situations I can't help but think that there's some reason for it Mass distributions for stars are a relatively important topic in Stellar physics but the universal Mass function does not have a lot of literature surrounding it I hope that watching this video inspired some of you to think more about it and if not anything else I really hope that some of you take the Lego investigation further I need to know why parts are distributed by weight so cleanly whether it's a universal law or not I think it's really cool foreign

Channel: Physics for the Birds

Views: 183,104

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Id: AaLwBdRXslM

Length: 13min 11sec (791 seconds)

Published: Mon Apr 17 2023