What do LEGO bricks and celestial bodies have in common?

I think something worth mentioning is that a lot of celestial bodies are really just collections of many smaller objects. For example, galaxies are collections of millions of star systems. Each star probably has a few planets. I wonder if how we classify what an “object” is affects the trend, or even causes it

i love how this tiny talking bird is asking the real questions in life. But seriously, this is my new favorite educational channel by far <3

I don't think this is by any design at LEGO, it would also be very hard to make sets with a "forced" distribution. I think it's a naturally arising property from the way things build up. I mean, you can only have a few big pieces (base blocks, big custom monoblocks, etc), while you need a ton of tiny things to fill the gaps, connect blocks, add decoration, and so on. This is why it's so amazing, I think this arises organically.

Guess I'm a bird because the youtube algorithm decided this video was for me

I'm a video game designer and when I make levels, adding clutter to the environments follows the same curve of object sizes for the map to feel "Right" It might be some sort of fractal pattern that we all have a deep intuitive understanding of, that's why the legos follow the same rule. Maybe even our bodies follow the same rule: bone sizes vs quantity; it could potentially apply to anything.

Astrophysicist here, I'm getting my Ph.D. studying galaxy formation/evolution. I wanna start out and say, I really enjoyed the video! It's really interesting to think about how mass is distributed in the Universe and if the same laws of nature that apply to galaxy clusters apply to LEGOs :). First is in regards to the initial mass function (IMF, as we typically call the mass function for stars) you describe here. Indeed the Salpeter (1955) IMF is a power law with an index of -2.35. However, more recently increasingly complex IMFs are used to describe the distribution of stellar masses of stars (see, e.g., Kroupa 2001 or Chabrier 2003) which are more than just a power law. These distributions are more like log-normal distributions, they have a plateau and turn over at lower masses. Even further than "Is it a power law?" it's actually a super open question in Astrophysics right now whether the IMF has evolved throughout the lifetime of the Universe. Second (sort of related), I think your intuition about gravity and the r^-2 power is really awesome, but the dense, star-forming interstellar medium is a little more complex than that. You have to take into account turbulence (collisions within the gasses), stellar feedback (other high-mass stars exploding in the neighborhood), etc. So I am skeptical as to whether or not that's where the Salpeter power law index comes from. It's an interesting connection nonetheless! Finally, at 10:07, I take exception to the statement "...galaxies are formed by stars clustering together into bigger pieces." Galaxy formation is a direct effect of dark matter overdensities, which gravitationally attract baryonic (non-dark) matter to their center, not necessarily groups of stars in space that all coalesce. The stars have to form from the gas reservoir, which needs to be sufficiently dense. In the absence of large dark matter potential wells the diffuse intergalactic gas simply doesn't get dense enough (or if, by some wild chance it would, not enough of it would in order to form galaxies of the mass we see today!). Again, really enjoyed the video! I hope you find the comment helpful 😀 EDIT: formatting (thanks @Speed

This is kind of reminiscent of Zipf's Law. Something to keep in mind is that a relatively small variation from -2, to, say -2.5, is a bit bigger than we might think as it is on a log scale.

The -2 coming from gravity makes good sense, but if a similar pattern exists in a wide range of different settings wherein things are built from combinations of other things (e.g. LEGO sets, IKEA furniture, laserjet printers, motor vehicles, etc.), that would suggest that it's a statistical property instead. I'd be interested in seeing a data where rather than "mass" being the x-axis, it's "mass of component divided by mass of the final product" wherein components of a wide range of different things are included, rather than just being a single category of objects, like LEGO. I think that distribution might provide further insight into this.

it is actually criminal with how small your channel is. Your content is fantastic and so well executed. I can't wait to watch you grow in the future.

This was such an enjoyably nerdy and poetic moment of science. You sound like such a fun friend to have. I hope you are able to make a living creating these videos.

Great video! I’m an acquaintance of the author of the paper. I have a school-aged son and a BrickLink store, so he sent me the paper to read, and then later sent me this video. You did a great job. He’s really impressed, and my son has become a big fan of yours (I already was). If you need any help with Lego, give me a hollar. Or if you’d like to get in touch with Stefan, I know he’d be happy to speak with you. Keep up the great work!

I love that this concept of smaller parts summing to equal bigger parts is kind of intuitive while being simultaneously mysterious. The universe is a strange and magical place.

This is my new favourite Channel!

I love your videos, the way you mix different subjects that at first might seem completely unrelated is fascinating to say the least Warmest regards and best of wishes🌹🌹🌹

3:04 need to say, this is actually called the initial mass function (IMF) . Slatpeter is just one of them, another really used one is Kroupa for example (also named after the scientist like the Saltpeter). Also for galaxies a nrw one tends to show up called the IGIMF which is integrated galactic initial mass function and comes from the behaviour of the initial mass functions of all the star clusters and stars inside the galaxy.

You want me to count every object in my house?! Uh, yeah, I'll get right on that. Respect to NSU to use a Ninjago set for the experiment. Because it shows they jumped up, kicked back, whipped around, and spun, and then they jumped back and did it again. If everyone did the Weekend Whip, the world would clearly be a better place. Nova Southeastern was originally a National Association of Intercollegiate Athletics (NAIA) institution back in the 1982–83 athletic season, which they would compete in their first conference affiliation home in the Florida Sun Conference from 1990 to 2002. The Sharks were originally called the Knights, which was from 1982 until 2004. In 2005, they unveiled the new Sharks logo and athletic mascot. The nickname was selected by the students.

I'm a Lego fan and custom design creator. Small pieces are used to create detail, as well as specific functionality. Since Lego designs typically reflect our world in some manner, it makes sense that lots of small pieces are required to match the fractal and chaotic nature of our world. An interesting research topic would be to do something similar to actual fractals. Or turbulent fluid flow.

I like your theory about why -2 for astronomical objects. Edit: Though actually, I think I just thought of a handwavy variation that doesn't depend on the gravitational constant. Let's say we start with a bunch of really small things (rocks, particles, etc.). Some might merge together into particles that are twice as big, and some might not. then, out of those, some might merge again to form particles of the next order of magnitude, etc. If, at any level, the probability of merging vs. not merging is about even (for any reason at all, which may be different for different types of "things"), then I think the exponent will be roughly around -2. For LEGO bricks, I have a different (half-baked) model that might be worth exploring. We can view a LEGO model as trying to approximate a specific 3D shape using a minimal(ish) number of bricks. With some additional constraints, e.g. there's a limit to how large (or at least how massive) the bricks get, and also limits on individual dimensions (e.g. normal bricks are only so thick). So, they fill in the rough shape with big bricks, then they start using progressively smaller bricks for the details, then even smaller for the tiny details, etc. At some point it bottoms out because they either give up on the level of fidelity, or make bricks that are the exact right shape they need (e.g. human head, flower, window, ...). I feel like these constraints will at the very least naturally produce a power distribution. It would also be interesting (and relevant) to find out whether brick volume is proportional to mass (or maybe larger bricks are less dense, for example)

I have two (very high-level and possibly very wrong)thoughts on this: 1. It could very likely be related to packing small and large pieces in bags(or even some sort of packing algorithm), as the design might be optimised for that. Or some obscure packing problem, for that matter. 2. Smaller pieces are spread out on the surface area of larger parts. So a graph like this is expected. Some more thought on the circley things might give more insights on the exact power of 2 point something. Random extensions to these: For 1. The density of smaller objects are larger because they have more bulky and dense edges compared to light flat surfaces. (I checked this for squares and circles) lego lengths have a higher variance wrt bag sizes, so it won't scale as much. Using this, I tried to see what would happen if we naively take n(legos) \propto vol(bag)/vol(lego), but was off by 0.5 or something. Without looking at the data as it's already 4 am lmao For 2. For VLSI, a design following a somewhat-similar principle, I'd say mass and surface area both scale according to the square of the side, as height does not vary too much. So it should not be very far from 1/mass. Legos often have tall pieces. idk what I'm talking about, though. Also, great video: Can't stop thinking about this :p

This was a very interesting video! Also, as software engineer student, doing stuff like what you did in this video, just because you can, is what got me into this field.