Science & Technology Q&A for Kids (and others) [Part 150]

Okay. Hello, everyone. Welcome to another episode of Science and Technology. Q and A for kids and others. And I see a first question from Natter here that's a little bit non kid like, but they say, may I ask a simple question? Always a bad sign for something. What aspects or elements of a probability distribution can be computed or quantified? And how are these computations used to describe the distribution? All right, let's see how I can do here. Let's say you've got a bunch of people, 1,000 people. Each person has a definite height. Somebody is 5 foot 8, if you're in the US and those are the units or 1 meter, whatever it is, 400 centimeters or something, 1.4 meters. Somebody else is 5 foot 11, somebody else is 5 foot 3. You got a whole bunch of different heights. And so what's the point of a probability distribution? The point of a probability distribution is to tell you for any given height, roughly how many people would you expect to have that height. Now, if you've only got a thousand people, there's nobody who's exactly 1.3742 meters tall. There'll be somebody who is, you know, 1.7 meters tall, 1. But somebody else is 1.74 meters tall. But any particular value, any particular height, there won't be anybody who has that particular height. The idea of the probabilistic distribution is sort of to approximate how many people, to sort of smooth out this thing about what's the chance that you find somebody with a height near this height? So the idea is you take your thousand people and you know their various heights. So what you can make is, for example, a histogram. So what's a histogram? A histogram is you take all these values, what, 1.73, 1.75, another 1.75, a 1.76 or 1.62, all these values and you put them in bins. So the bin might be Everybody between 1.7 and 1.8 is in one bin. Everybody between 1.8 and 1.9 is another bin, and so on. You put everybody into these bins, and then you make a plot, for example, of a bunch of bars where the height of the bar is the number of people in that bin. So that's going to give you this approximation to the probability distribution. It's telling you how many people are there who have a height right around this value. So that's kind of the idea for that. Now, if you do that for actual human heights, you'll typically get a Particular distribution, the so called normal or Gaussian distribution. It's a bell shaped curve. It's bigger in the middle and, and smaller on the edges. So there aren't that many 7ft tall people, there aren't that many 4ft tall adults. So there's this distribution of heights and most people are kind of in the middle. And so you have this curve that is sort of peaked in the middle and has this bell shaped curve with sort of tails on the two sides. Okay, so that's the distribution of human heights. Looks roughly like that. If you look at human weights, for example, you get a different distribution. It's called the lognormal distribution. And it has more of a. It kind of comes up more quickly on the low end and then has a bigger tail of folks who are pretty heavy on the high end. Different kinds of things have different distributions. It's really common for things to have this so called normal distribution or Gaussian distribution. There are lots of, lots of kinds of things in the world where, oh, I don't know, if you're throwing darts or something, you're trying to work out where do the darts typically land. It'll probably be one of those normal distributions of how many got right at the middle of the target, how many towards the edges, and so on. If you're making various kinds of measurements of things, they'll often be Gaussian or normal distributed. There's actually a good reason for that. There's a fundamental math fact called the Central limit theorem that says this. If you take a bunch of quantities and each one is kind of random in a certain range, and you take the average of those quantities, Maybe even just five of them or 10, you take the average of those quantities, then that average will always be normal distributed. If you have enough quantities, you will get the average of enough quantities that is always a normal distribution. So long as those individual quantities are sort of randomly distributed like they're a random number equally picked in a certain range, or maybe they have some different distribution. So long as that distribution has certain properties, basically, so long as it doesn't have a big enough, too big a tail that goes out too far. Then when you average together enough quantities like that, you will always, the average will always have this normal distribution. Now why human heights are normal distributed like that, nobody really knows. The guess is that there are different genes that affect different aspects of us and that when you sort of combine all the effects of those things, they kind of more or less add up. And so you're kind of seeing the average effect of a large number of kind of different genetic instructions. And so the result of that is something which is roughly normal distributed. Now, actually, in a lot of what's done in the use of statistics, particularly in things like medical research, medical clinical trials, things like this, people kind of assume that everything is Gaussian distributed. It's often not correct, but they assume that because that's how you can do some math to work things out. One of the most important pieces of math you can do is answering the following question. Is the thing you're seeing significant, a significant deviation from sort of the typical random behavior or not? So let's say that you are looking at, let's say it's human heights. I don't know what the average human height is. Let's say, oh gosh, I don't know, five foot seven maybe. I don't know, it depends. It'll be different for males and females, but maybe for males it's 5, 8 or 5, 9, at least in the US there's kind of this fiction that heights have the same distribution all over the world, which clearly, obviously from traveling around the world isn't true. But that's a common kind of assumption fiction, so to speak, that the distribution of heights is the same and has the same average values and so on all over the world. Doesn't really matter. But the point here is if you are. But let's not talk about human heights. Let's talk about. Oh, what's a good example? Let's talk about sizes of cookies. Coming off some cookie production line now, pretty good guess that the sizes of cookies are normal distributed, roughly. So there'll be an average cookie size and there'll be a certain range of cookie sizes. And so the question is what? Actually, let's not pick cookies. Let's pick, well, almost anything. Maybe we're back to human heights. There's a question. Okay, this now comes to sort of the heart of the question that was asked about the characteristics of distributions. The first thing to say is what's the average human height? If you take. And there are different meanings to the term average. So a common average is the mean. What's the mean? You just add up all of the values and divide by the number of values. That's the mean. And so that has the feature that. Let's say that you are getting human heights and you've got these, and they're almost all correct. And then somebody put the height of the Eiffel Tower into your data set. Obviously the Eiffel Tower is Very tall compared to a human. But in the mean that will have a big effect because there's some huge, you know, 300 foot, you know, 300 times the height of a human thing that's in there. And when you add up all the numbers, that one very big number will have a big effect on the mean. So, but mean is often a good way of measuring kind of the average of things is just add up all the numbers, divide by the number of numbers. That gives you sort of the average value that you get. A slightly more robust way to do things is to compute so called median. And so how does that work? Well, what you do there is you take all the quantities that you got, all the values you've got, and you sort them into order. So from the one meter tall to the two and a half meters tall person, all ranked in order from the shortest to the tallest. And then the thing that is the median is you get that whole collection of rankings and you say if you go halfway through that list, that sorted list, where do you get to? And that's the median. So it's the thing that's the middle of the ranked list of quantities. So that's a slightly more robust measure because that Eiffel Tower that got into your data set is not going to be totally relevant. It's just going to contribute one thing that's an outlier right at the end of your sorted list of heights. It's not going to pull the average to something crazy. Okay, so that's a way of measuring. Mean and median are ways of measuring what's usually called central tendency of a distribution. Sort of where's the center of the distribution? Where's sort of the middle of things? By the way, if you were to take a physical object and you were to put little masses that corresponded to those different height values and so on, and you were to say where does it balance in the middle? Where is its center of gravity? That will be determined by its mean, by the mean of that distribution. So that's kind of where the middle of the distribution where the sort of central tendency, the, the mass of the distribution is. So the next big thing is the spread of the distribution. Is it the case that Everybody is exactly 5 foot 9 inches tall or is it the case that, well, there's actually some people who are 5ft tall and some people who are 6ft 10 tall and so on, that there's a breadth to the distribution. So the way that that's measured is with, well, usually with a variance or standard deviation. And that's measuring. Well, it's basically measuring kind of if you draw out the distribution, how wide is that? How wide is it? Well, the mathematical definition of that is you take every value, you subtract the mean and you take and you square that and you add that up and then you take the mean of those things and then you take the square root, take the square root to get the variance. The standard deviation is the thing you get from the square. Am I getting that the right way around? I think so. In any case, the main point is forget the, I mean the details of the math. You just type it into Wolfram language. Variance or standard deviation of some distribution, you'll get the answer. But the qualitative story is how wide is the distribution around the peak, around the average, how wide is it, by the way? I should say that the very peak of the distribution is usually called the mode. That's the place where the distribution is highest. That's a very unstable thing because, for example, there might be two peaks in the distribution and they're both vying for which is the tallest one. And it might be very unstable which one happens to be be the very tallest. But in any case, the variance or standard deviation, one square root of the other gives you kind of the width of the distribution. And now the question is if you have a normal distribution, you can make some very definite statements like you can define one standard deviation away from the mean. And that is standard deviation is the square root. Maybe I said that the wrong way around before, but it's like you say, well, the value is for example, 7 + or -0.1. Now there's a whole calculus of thinking about how plus and minus numbers work, thinking about how numbers will uncertainty work. But in a one version of that is that plus minus one tells you where the standard deviation, what one standard deviation away from the mean would be. So seven might be the mean. Seven plus one might be one standard deviation above the mean, seven minus one might be one standard deviation below the mean. So then the question is for a normal distribution, there is an interesting fact which is that 68% of all, if you pick points at random, 68% of the points you pick will be within one standard deviation of the mean. And so that's often called one sigma. That's the sort of one sigma where you get to by going out one standard deviation from the mean two sigma, that goes to 90%. I think by the time you're two times a standard deviation away from the mean, the chance that you are within that range is 90%, you go three sigma, it's 90. Oh, boy. I don't know. Wolfram alpha or Wolfram language will immediately tell you the answer. I'm sorry, I don't carry it around in my brain. I think you get to 95%, maybe by. I've forgotten. In any case, as you go out more sigmas, you get to more 99.999%. So by the time you're at five sigma, it's 99.99 something percent. The chance that you are within five sigma is larger than 99.99 whatever percent. So that means that if you make a measurement of something and you expect it to be this mean value, this standard deviation, and the actual measurement you observe is way different from that, then the chances are that's significant. So, for example, you might say, oh, we've got this background measurement of how much radio noise there is in this area or something. And we see something which seems like it's a signal. It seems like the extraterrestrials are communicating with us or something. And that's a four sigma effect. Let's say that means that you're assuming that you know the distribution, you know what the. You know that the average radio intensity is this. There's a one standard deviation of radio intensity is that. But what you observed is four times further away from the mean than that one standard deviation of sort of spread. So that idea is. So that's kind of another idea is this kind of notion of how many standard deviations. It's also another. The statistics as it's currently practiced, a lot of it developed in the 1930s in connection with agricultural statistics and so on, measuring, you know, did this fertilizer really work when we put it in this field? Things like this. And there are a bunch of different pieces of nomenclature, different ways that things are named for different sort of subfields. So this whole thing I'm telling you about, the chance to be a different distance away, there are lots of words, P values, confidence intervals, Z scores, these are all words that are related to this question about sort of how far away are you from the mean? And if you assume that you have a normal distribution, then you can convert that to probabilities in various ways. Unfortunately, people essentially always assume normal distributions, but it often isn't true. So, for example, in biomedicine, there are some things like human height which are normal distributed. There are things like human weight that aren't. That's log normal, roughly. There are things like different kinds of. If you look at Medical test results, many medical test results. You can see these in Wolfram Alpha. Actually, many medical test results are roughly normal distributed, but some are not. Some have all kinds of exponential distributions and all kinds of other different distributions. By the way, there are just many, many things in the world that aren't normal distributed. So another one that isn't normal distributed is human lifespans. That's a different distribution. It's called the Gompertz distribution, usually which has for the standard mortality curve has a different form. And if you use the normal distribution to work out if you're 95 years old, what's your probability of dying soon, you'd get completely the wrong answer. If you use the normal distribution. Many things have very different distributions. So for example, if you say, what's the average lifespan of an incandescent light bulb? The average lifespan might be, who knows what, a couple of years, let's say. But there's a certain distribution. Not every light bulb immediately after exactly two years goes kaput. There's a distribution of times. And that distribution is yet another distribution. I think it's the Weibull distribution, I think is the right one. That is a common fit for that or another distribution. Another thing you could look for is you're trying to cross the road and you're waiting for a break in traffic and these cars are coming and they're coming at random times. And there's a certain. What's the chance that there is a break between cars that is such and such a length long? Well, that's governed by a thing called the Poisson distribution. Roughly all of these things, there's usually a sort of a rough approximation and then there's a more detailed thing that you get that may depend in detail on the habits of the drivers in the particular area you're in and things like this. But there's a first approximation, which is a Poisson distribution for the distribution of lengths of gaps in traffic when you're going to cross a road, and so on. So any case, that's now other things about distributions. So one thing is, there's a question of is it symmetrical? So in other words, is the chance to be one standard deviation below the mean the same as the chance to be one standard deviation above the mean? So for human heights, again the quintessential normal distributed thing, That's true that it's roughly equally probable to be this amount below the mean and this amount above the mean. Another thing that's classically distributed in normal distribution, although I think is fraught with issues is. Is the IQ distribution. You know, if you do IQ tests as a thing from the 1930s, people had the idea that there would be this parameter. They usually called it G, the parameter of general intelligence, whatever that might possibly mean. What it actually meant was we've got these tests that are, you know, what is. Can you fit these patterns together with this? And so on. Tests that are sort of somewhat disembodied tests that aren't really related to. Which at the time were not related to anything that people did in practice. I'm not sure that's true anymore because I think with a lot of things one does with computers and other kinds of more formal technical things, that some of those things which were at that time kind of disembodied, nobody would really need this in real life. That's no longer the case. But anyway, classic normal distribution is the distribution of people's scores on those tests with a mean that corresponds to 100 in the units that were used. And I think, oh, gosh, I don't remember. You get out to. There's a. I'm trying to remember. There's a society of people who are very proud of the fact that they score incredibly well on these tests. I forget whether they call themselves the five Sigma Society or something, which means that they are doing, you know, they do the so well in these tests. I assume it's five sigma on the positive direction. That's. That's what they will be proud of. That at one time, I seem to know for quite different sources, many of the members of that rather small, small group that did so well on IQ tests. But in any case, the. The thing is, that's another thing where the distribution of scores is roughly normal distributed, I think. Yeah. So let's see. We were talking about these distributions and some distributions are symmetrical. Some of them have a longer tail in the up direction than in the down direction. Those are distributions that. Well, depending on the sort of distributions with heavy tails of various kinds, that can also mean in both directions. But it can be. The question is, is it. Does it go like a normal distribution which dies off very quickly, it goes mathematically like E to the minus X squared, or does it go more slowly? And there's sort of a big issue of whether if you work out the area under the curve, the integral, whether as you go further and further out, that integral stays finite or not, whether the thing has a tail that sort of keeps going and keeps adding more sort of area as you go further out. In any case, there are these things called Kurtosis, for example, is the thing that tells you there's a thing called skew and there's a thing called kurtosis. Skew tells you something about the relative below and above sort of tail sizes. Kurtosis is something that is above about how far away, how big the tails are in general, if I remember correctly, if you go mathy about it, there are all these so called moments of the distribution which are what you get by multiplying by different powers. You're taking the average of X to the N for different N and so on. So anyway, but the sort of. The main thing about distributions is sort of the most obvious thing people are always calculating is the mean. That for a distribution you can easily use calculus to compute the mean. It's also something where you're adding up all the values and just dividing by the number. The median is a more robust measure of sort of where the middle where the distribution is concentrated. Then you get standard deviation of variance, which are the kind of the width of the distribution. Then you get these various measures of the skewness of the distribution and sort of how supportive the tails are and so on. So a very rough. And maybe I should have done this at a different time when I. Maybe I should do some version of these Q&As where I'm actually typing and showing you things in Wolfram language. Because Wolfram language has really good support for the way that probabilistic distributions work and histograms and all those kinds of things. All right, let's see. Another question from YOLO here. Why are some creatures nocturnal? Why aren't humans? You know, back in the 1990s, when I was working hard on a big science project for most of a decade, I think I went pretty nocturnal. One of my children, when asked something about me, told somebody at a very young age, explained that their father was nocturnal. So it does happen to humans. And whether that's because they're working on basic science projects or because they're doing jobs that need them to be up and about at night, either way. But anyway, I think, you know, the thing about biology is there are lots of different ways to win in the natural world, so to speak. And biology finds these bizarre ways to win. I mean, it finds the ways where you've got a desert and there's never any water there. And so you have these plants that will store water for five years at a time until that one rainstorm comes through. Or you find those creatures that are living in the deep ocean where you would think they're Living near some hydrothermal vent, spewing out sulfur. And they managed to use that in some way. So in a first approximation, in the natural world, biology, through sort of random mutations and natural selection has managed to populate all these different niches. And there's some critters that are up during the day and there are going to be other critters that are up at night. And I think the trade offs of when it's good to be a night creature versus a day creature, there are some things that are good, some things that are bad. If you are, for example, a plant that makes use of sunlight to generate energy through chloroplasts and so on through photosynthesis, then it's kind of, you can't really be sort of shutting down and closing everything up during the day wouldn't be a winning strategy because you just, your leaves wouldn't have a chance to do that, photosynthesis and so on. So there's some constraints like that, but I think for animals it's just, well find a niche which works. Now, there are plenty of things where we get, for example, lots of things about us get synchronized to the sun. I mean, we have these circadian rhythms where we have sort of a daily rhythm where we, you know, things change. Blood pressure, heart rate, all kinds of other kinds of chemical messengers around our bodies have this typical cycle of about 24 hours. And that cycle is kind of, if you, if you just let people in a cave somewhere with no access to sunlight, no clocks, nothing like that, their cycles will tend to be either a bit longer or a bit shorter than 24 hours. But when they're exposed to sunlight and they're like, yes, the sun rises at a definite time of day, they'll tend to get synchronized with the actual light, the sunlight and so on. Now when you go travel to a different part of the world, when the sun is coming up at a different time of day relative to your original time zone, you get jet lag. And the typical, where you can often get jet lag. And the typical reason is that these circadian rhythms that you have are all sort of, they're all unsynchronized. And you know the sun is coming up at this time, but that's the time when, according to your circadian rhythm, you know, that was the middle of the night and your blood pressure is down and your heart rate is down and your digestion is at this level, and so on and so on and so on. And your body is not used to that being the time when you're up and about and running around and so on. And the thing that I think many circadian rhythms, I mean the main one for humans, is driven by the pituitary gland in the center of the brain. And it secretes melatonin and some other things that are sort of in response to sunlight. It's always been a bit unclear whether all the light that comes there is coming through the eyes or whether there's actually some light that manages to make it in through more directly into the pituitary gland. But in any case, that's one source. But it seems like pretty much every cell in our body has some level of circadian rhythm going. And so when we kind of move to a different time zone, it'll be different cells take different amounts of time to adjust and resynchronize themselves to the new time zone. So that's. But I think, you know, it's interesting. I've. I've seen in my life, what is it now, three total solar eclipses. And one of the things that's funny there is that the, you know, during those few minutes, five, six minutes, whatever, four, five, six minutes of totality, that many of the animals that are around just decide very quickly, oh, it's nighttime, you know, birds stop chirping, and then the sun pokes out from behind the moon and it's like, hey, we're just waking up. And there's a giant kind of dawn chorus type thing. And it's really notable that for a lot of these critters, they really are basing their day on whether the sun is up or not. And when there's an eclipse that's all confused and resynchronized and so on, at least temporarily. Let's see. Oh, gosh, lots of questions. Some questions here. Okay, there are a few questions about probability distributions. Let me try and talk a bit about that. So Spare Parts asks, is the normal distribution related to the complexity of the dynamics or is it found all over the place? It's kind of found all over the place, but there are lots of kinds of things that kind of throw it off. So when you have a bunch of kind of independent random probabilities showing up and you're adding them up and you're doing all this averaging of those, then you get a normal distribution. But as soon as you get kind of long range order, big correlations between different things that are happening, you won't, you'll get something different going on. So I think what tends to happen is when, if there really are lots of completely independent things Going on at any scale, whether that's a scale. I mean, the normal distribution shows up at the level of things to do with particles and the probability to find a particle at a certain distance, well, in a harmonic, even at the level. Very basic questions about how particles propagate from one place to another at the very smallest scales, there are normal distributions that show up there. And you can think about that kind of normal distribution as being the result of all these different paths in quantum mechanics being added up. And the sum of those paths gives you sort of averages that they're all independent and they sum up in a way that gives you a normal distribution. So even at that scale, you're getting normal distributions in the. When you're looking at, oh, I don't know, properties of galaxies and things, you'll find lots of normal distributions when you don't get normal distributions, when, for whatever reason, the different things you're looking at are not all independently random, when there's some connection between them. So, for example, a good example of this is when you have something like a gas with a bunch of molecules bouncing around, and it's about to condense into a liquid, There start to be all these correlations between the molecules. And so things which in the case of the gas would be a nice normal distribution, that's no longer true when things are sort of all correlated to make the liquid. So, for example, in a gas, another thing that's basically normal distributed is the distribution of speeds of molecules in a gas. It actually has a. Depending on how you work it out, it's V squared E to the minus V squared, the Maxwell Boltzmann distribution. But the core of that is a normal distribution. Another one of these Gaussian distributions. But as you get to the point where the molecules aren't all bouncing around and independently hitting things, but they're all kind of glomming together like they do in a liquid that no longer works. There are many places where, for example, that distribution shows up. It shows up in, well, it's said to show up and distribution of speeds of people sort of bouncing around in a crowd and things, although I don't know whether the data for that is particularly good, but lots of other places like that. Let's see, it's a question from. Does PI have a normal distribution? It's a little bit confusing because there's another property of numbers like PI, that's whether PI is normal. And the word is unfortunately being used in a different way there. So a normal distribution is what's the chance that you have a particular value and that's this E to the minus X squared type distribution Normal in the sense usually used for the digits of PI is does every number, does every digit in the digit sequence occur with equal frequency? Does every block of digits occur with equal frequency? And so on. And yes, you can sort of. Well let me think. How would you get. Not so obvious actually how you connect those two. I think it's just a coincidence of words that one is called is the digit sequence normal and the other is a normal distribution. I mean people always like to say it's the standard. So it's a kind of a branding of ideas, so to speak, more than it is a connection between ideas. Let's see, you know, I see this note from that Google says whatever that means, the average human height is 5 foot 9 or 5 foot 10 in the U.S. yeah, I mean that's roughly right. I mean I think that, you know, all this claim of it's the same all over the world. I remember years ago being in Japan at a train station and it's like I'm about average height for average height for the uk, I'm a little bit lower than average height I think for the U.S. maybe I'm not sure I'm five foot nine, give or take. So maybe I'm, who knows. But you know, at a train station in, in Tokyo in the 1980s at least it's like, like I get off the train and I can see over everybody's head and now maybe that's changed, I don't know. But it's certainly not the case that, that everywhere in the world the average height is, is the same. Even though bizarrely the World Health Organization has data that sort of, you know, that has a height distribution that kind of assumes that. Something I never really understood any case. Let's see, Let's see, there's some questions here. From Sam asks says I read there's a puzzle over why no new body plans developed since the Cambrian period. In my kind of machine learning view of adaptive evolution, what's happening there? Yeah, well, body plans are hard to change. I mean the body plan means you've got arms and legs and you know, you've got a head and, and things like this. Maybe you've got a tail most of the time. I mean the real issue is when a critter has children and maybe one of those children is sort of slightly different from the parents and better as most children claim that they are relative to the previous generation, at least for a while. But any case that Some child organism is definitively better. It manages to crack those nuts more easily, it manages to climb the tree more quickly, it manages to do whatever it does more quickly. The problem is many changes that you might make from the parent organism lead to disaster. It's like the creature, you know, can't manage to break its way out of its egg, or the creature is, you know, can't digest any of its food. Or the creature, you know, something goes horribly wrong. And so the issue is, can you get to something where it's sort of, it's incrementally, it's just a tiny bit different. And because it's very different, the chances are you'll just go off into something which is completely hopeless, just doesn't work at all. But so you need these little incremental changes. But it's hard to go from, you know, feet, legs to wheels, for example, by little incremental changes. Now some incremental changes do work, like if you're going from four legged critters to two legged critters, there's probably some intermediate case where you know, yeah, you're more or less four legged, but you can stand on your hind legs and do things. And then it becomes easier in successive generations to stand on your hind legs. And then eventually it's like, forget that crawling around on four legs, you can just stand on two type thing. Or similarly, if you're about to fly or something, it's like, well, you can flap and you can manage to jump a bit further by flapping and so on. And then eventually you take flight and you can be flying around with wild abandon, so to speak. So there are these things where you can get from here to there by making a small change. But eventually that small change becomes a big effect, so to speak, a big functional effect, I think in terms of kind of the overall body plans. It's an interesting question, the extent to which you can get there from here by incremental changes. Can you get to a dramatically different configuration? I mean, it's kind of like there are things that's certainly quite well studied in geometric mathematics. When can you get from one sort of configuration of things to another continuously? So for example, a very, very straightforward example is if you have a piece of string and you tie it around the pencil or something, if it's going zero times around, you can deform it easily. But once it's turned around the pencil once, you can pull it and push it and whatever else. But unless you explicitly unwind it, you can't get it off so to speak. That's kind of a topological way in which the thing is sort of distinguished from the one winding number and zero winding number case. So it's just. It's a bit unclear under what circumstances kind of the changes in body plans can be done incrementally and when they cannot. It's actually a good question. I should look at it given a definition because I've been studying recently very simple programs that can kind of emulate what happens in biological evolution. I was sort of surprised and pleased that one could do it with programs as simple as I'm using. And you can kind of see how, let's say you're trying to make a pattern that lives as long as possible by following these rules and then dies out. Well, if you randomly mutate these rules, it'll find all these different ways to live a really long time, but then die out. And the. You can kind of see hard to have a theory of it. I don't yet have a good theory for describing, you know, what was the idea that it had that allowed it to live longer. You can see it visually. It's pretty obvious, you know, often, oh, it makes these triangles and other things, and that's how it manages to. To live a long time here. So the thing is, if you're doing that at the level of body plans, whatever that means, you could say, can I characterize the overall shapes that I'm getting that are fitness successful, as in they make the thing live a long time? And can I see whether once I'm committed to some particular path, can I see, is there any way to kind of get to a different body plan? And for example, let's say you make a perturbation, you kind of change the environment, you change what makes the organism be fitter. Can you kind of divert it to use a different body plan? I don't know. I mean, I think this is an interesting question of sort of how creative has biology managed to be? Is biology kind of just. It's got this one idea and it's kind of seeping out into all these nearby things that sometimes gradually progressively get further away, or is there that really. It's affected by both. What's the space of possible animal shapes? So, for example, when you see kind of typical science fiction animals, there are these nice books of the strange creatures described or presented in different science fiction books, movies, whatever else. And it's like, what do the aliens look like? Oh, they might be green. Oh, they might have. Oh, do they have two eyes? Do they have two arms? Things like this. Sadly, I would say the vast majority of sort of science fiction aliens are not particularly creative. They're basically just deformed versions of the standard body plan from our planet. Whether it's quite possible that if one saw something that wasn't like that, one wouldn't recognize what on earth it was. It might look like it was just some piece of a rock or something and it wouldn't look like. And obviously I'm a singing, dancing alien type thing. But it's this question of can you sort of imagine and does biology manage to imagine sort of what's the set of things that are reasonable animal shapes that you can reach from sort of from where we are? And what's a set that. Yes, they are possible, but they're disconnected from where we are. You know, I will tell you a couple of examples that I have studied in some detail. One is mollusk shells might even have one. Let's see, good mollusk shell here. Here we go. Here's a mollusk shell. So they grow in this kind of, in a, in a kind of spiral pattern. And depending on various parameters of growth, they'll. They'll have different kinds of whorls here. There'll be very flat shells, there'll be very pointy shells and so on. And one of the things that you find which sort of surprised me, the paleontological literature thought differently and it wasn't quite right, is that if you take different parameters of the growth of these organisms, pretty much any choice of parameters that isn't completely crazy like that doesn't just lock in the animal and leave it no hole to go outside, so to speak, or something like that. Any non crazy collection of parameters. There is actually a mollusk shell that you find somewhere out there in the world that is the shape that would correspond to that choice of parameters. From very pointy to very flat to very wide to very, et cetera. So that's one case. Another case that I've tried to study and never really got this finished was shapes of leaves on plants. So you see some shapes, but people have talked about different kinds of leaf shapes forever and ever. I mean, even in antiquity, people were describing leaf shapes because they were like, this is the herb to pick up that's going to cure this disease. This is the plant that oops, don't pick up that plant because it's poisonous type thing. And people try to distinguish those things by shapes of leaves. There's a chap called Theophrastus who wrote some treatises on plants which had a lot of stuff about shapes of leaves. And so there's all this terminology about compound leaves. Those are leaves with lots of little leaflets, simple leaves. Those are leaves that are just one big leaf. There are leaves that are serrate leaves, which means they have a serrated edge. There are dentate leaves that look like somebody bit a piece out of them. There are lancelot leaves, I think, which are like things that are pointy, like a lance. And there's a whole bunch of classification of other kinds of qualitatively described leaf shapes. Well, the question that I had was, if you look at the shapes of all these different leaves, what does that distribution of shapes look like? In other words, are all the sort of possible shapes achieved by some particular model actually realized? What's the space of possible leaf shapes? I don't know the answer to that. I had a very simple model of the growth of leaves. It's a little bit tricky because the growth of leaves, as you think, like the veins in a leaf. The question is, are the veins first or last? In other words, do the veins get laid down and then a leaf fills in between them? Or does the leaf fill in and then the veins come in sort of after the shape of the leaf has been defined? It's a mixture. The really big veins get laid down first. It's a bit like with humans, where the big blood vessels get laid down and then the angiogenesis of little capillaries, little tiny blood vessels, they just sort of fill into wherever there's tissue. And it's kind of the same with leaves. So there's an overall architecture of the leaf that is a separate thing from the sort of venation of the leaf that comes in later. But anyway, I had a simple model of sort of this branching process that leads to a whole range of different leaf shapes. I don't fully know whether those leaf shapes cover all the ones that are seen, but that's an interesting case where you can actually make a kind of set. I made a nice little thing. This is now, gosh, 30 years ago now, but things. In my book New Kind of Science, there are these. There's sort of a page that shows kind of how the shapes of leaves vary. Characteristics of the shapes of leaves vary with the parameters of the growth process of the leaf. And what's interesting is as you change those parameters continuously, the shapes change discontinuously just because the way things sort of accumulate. When you have these sort of filling in, recursively filling in pieces of leaves, what happens is, as you change the parameter, it discontinuously changes from, oh, these two pieces of the leaf are going to all join up and come together to, it's going to be quite separate and they're going to be poking out differently. So it's a case where you can kind of study the path of evolution and see a continuous change of one parameter leads to a discontinuous change of shape. And I think that's what has happened a bunch of times in biological history that things. But while you still have that continuous change of the underlying parameter, that's what it takes to be able to survive. But this sort of discontinuous, oh, now you're on two legs rather than four. It isn't. Well, sometimes it's really discontinuous in these leaf shape examples and sometimes it can be done more continuously. But anyway, you have a sort of a discontinuous change of functionality behavior. Let's see. Oh, let's see. Ah, people are commenting that Japanese kids get taller because they're eating more meat. Red meat could very well be the only question to ask, which I don't know the answer to is, is it, is it the, you know, there's growth hormones that determine our, our growth. And in fact, one of the most bizarre things is that you would think you just grow continuously taller and taller and taller, but actually the pituitary gland secretes growth hormone and it often does it at night. And if you're a kid, you might discover that just a tiny bit you grow discontinuously. Like one day you'll grow, you know, a millimeter or something and then the next, and you won't, you know, overnight. One night you'll grow a millimeter and then you won't, It's a discontinuous growth process and that's associated with the secretion of growth hormone. I think that leads to various biochemical processes that lead to growth. And so, you know, one thing is, oh, if you have more nutrition, more protein and so on, you will be able to build better, stronger, longer bones and so on. Another is, oh, that cow was fed growth hormone to make it get bigger, faster, the more efficiently to make meat and so on. And when you ate the meat from that cow, it was mixed up with a bit of growth hormone and that got in you and caused you to grow. So I think that, yeah, no, I, I, I, I don't know. I don't know what, yeah, I think the DES is commenting average people gotten taller everywhere because of nutrition and modern medicine. I think the answer is yes. You know, but the funny thing is, obviously we know how tall people were a long time ago because we have skeletons and things. And my impression is that people say, oh, people are getting taller. But I think that the archaeological evidence does not always support that. I think there have been periods of human history where people have been shorter and other periods where they've been where they've not been shorter. Certainly, you know, if you go into, you know, houses in England, for example, that were built in the, I don't know, 1400s, 1500s, you know, you're, you're always crouching down to get through doorways. Now, I assume that's because people were shorter back in the day as opposed to just conventions were different about how tall you built the doorways. I'm not absolutely sure about that, but I looked at this at one point and the archaeological evidence for changes of human height are not as convincing as you might have thought. And there do seem to be, I think, dips in human height rather than it just being, oh, we've been getting taller all the time. Just wait until there are humans born on Mars where the gravity is lower and where presumably in their own growth. Because how do you sort of the way growth works. The thing that's most important in things like height is the length of long bones. That's sort of the skeleton, quite literally the framework that we kind of get built around. And one of the things that happens, the growth plates at the end of long bones, which are these areas where there are cells that continue to divide that make the bone longer. It's just at the ends that that happens. And the amount of growth there depends on kind of how much pressure is put on the bone. And so there are that. That's. So I think I. Well, I guess I don't know for sure what happens in a Martian, you know, the Martian kids story, but my guess is that they grow a lot taller. But maybe that's wrong. The. Okay, so apparently people want to know why. Why are we all getting heavier and fatter and so on. I mean, I assume that's because of the way that food has evolved. I mean, I think that there's, you know, and, and people. It becomes very kind of controversial kind of. I mean, it, it's complicated because. Okay, first point to make is that different times in history, it has been cool or not cool to be bigger and heavier. Like Henry viii. Famously, there are all these portraits of Henry VIII looking extremely portly. Well, in those days, that was a thing you did to look cool, so to speak. It's like, I'm rich enough That I can eat so much that I can weigh 400 pounds or whatever it is. That was a sign of success, so to speak. At other times, it's like, be as slim as possible, because that's the cool thing to be, I have to say. There's also the question of. It used to be the case that most humans were growing their own food and were doing subsistence farming or whatever else. And it was a very short loop between kind of where the food came from and the person eating the food. In modern civilization, obviously, that's got a lot longer. And lots of these sort of effects of food can be generated by sort of tweaking the chemistry, so to speak, in a way that is quite different from what the chemistry was back in the day when we were evolving. That doesn't necessarily mean that the way we were evolved was the best way to be because life expectancies were probably 25 years old or something back in the stone age or whatever, and we probably don't want that today. And probably at that time, people were continually sort of dying from starvation and so on all over the place, and that's not what we want. So it's a little bit unclear where you turn the dialogue, but there's certainly lots of. Kind of deliver sort of the effect of food quickly that, you know, it's very different from what we evolved with. I mean, you know, one of my own favorite foods, chocolate is a heavily refined thing that isn't, you know, kind of, you know, what you would even if you were in the place with the cocoa plants. You know, the giant cocoa bean is not the immediate thing where you can just pull it off the tree and be. Be eating your bar of chocolate type thing. So it's, you know, it's one of the cases where what we were evolved to is not the situation we're in. For better or worse. And it might not be worse. I mean, there's nothing that, you know, I think most people would feel that human civilization has been a net positive for people. And, you know, there are aspects of there. It's. It's a, you know, I think it's a. It's a complicated balancing act. The. Yeah, Des is commenting on the so many variables. It's. It's difficult to figure out. You know, I occasionally I've sort of tried to pay attention to these various different kinds of diets and so on, and it's like the. Eat more meat, eat less meat, eat this, eat that. Okay. First thing, that's a super big surprise if you start thinking about it scientifically is that there's a whole range of different diets that one can eat, and they all more or less work. It's not the case that. And why is that? Well, the reason that is is because we're made of proteins, and proteins are made of amino acids, and there are about 20amino acids. And living things basically contain those same 20amino acids. Well, plants don't contain a few of them, but animals, they contain those amino acids. So if you're eating something that was meat from an animal or something, then fundamentally the molecules that it has, the units of molecules that it has, are just the same ones that we need. And the fact is that you're mixing and matching the things from what you're eating and managing to recruit them for the things you need them for. It's also always been a big surprise that, like, in our. Every red blood cell, every hemoglobin molecule in every red blood cell in our bloodstream has an iron atom in it. Where did those iron atoms come from? Well, there's. You're eating enough iron that somehow there are atoms that sort of come out of that, and those are appropriately arranged to be delivered into the centers of the cages that are in hemoglobin proteins to be able to capture that iron atom. And like, for example, well, vitamin B12, for example, has a cobalt atom in it. And that goes to the right places. Or, you know, the. Famously, the thyroid gland uses iodine. And, you know, you manage to get iodine from sort of anywhere, and it somehow finds its way to your thyroid gland and gets put there. So the thing that the first bigger, big sort of science surprise is you can eat all kinds of different diets. And it basically works because you basically get all the things you need. Now, sometimes you don't quite get all the things you need. There are vitamins that tend to be smaller molecules that you can't make for yourself so easily. And with proteins, you can kind of mix and match the amino acids to make a new protein, so to speak. But with, with these small molecules, there may be too much kind of chemical energy that's needed to go from one to the other that you kind of have to just get that molecule. Or, or, for example, you could just need a certain kind of atom because the only way you'd. You'd go, if you don't have enough iron, you're going to get eventually anemia from where you. Where you, you know, which is deficiency disease of not having enough iron. And your red blood cells won't, won't be work as well, etc. Etc. Etc. You won't be able to make as many and so on. And that's something where there's no way around it. If you don't have enough iron atoms going into your body from your diet, it just, you can't make it work because, you know, the only way you can, you can't make iron from anything else, at least not without a nuclear reactor or whatever. So it's, you know, certain things we kind of need for sure in diets. But as I say, the big surprise to me or to sort of science surprise is that it works to get all these different things from different places and you can kind of more or less have it work. So that means that the 0th approximation is you can eat sort of any reasonable diet and it'll work okay. When you go past the zeroth approximation, some will work better than others. And I certainly don't understand and I've tried to follow a little bit the different theories of kind of what, you know, both the physiological, nutritional, psychological, kinds of aspects of when you're of kind of what causes you to absorb more and not. And so on and how exercise plays into that. I'm no expert in these kinds of things. I have tried to understand some of the basic science and I found some of it kind of confusing. And it's one of those fields where people hold one view and the exact opposite view. And that's always tends to be that the real story is somewhere in the middle. But you know, it's often vigorously held on either extreme. The. By the way, I mean, this whole question about are there things that we do today that in the future will realize that was an incredibly bad idea health wise? I expect the answer is yes. I think one general principle is sort of do nothing too extremely because that sort of if you're in the center of the distribution, you're more likely to be not anything extreme has high risk associated with it, so to speak. But yeah, I mean, I would be, you know, that over the course of time, things that one thought were harmless turn out not to be harmless, things one thought were harmful turn out not to be as harmful as one thought, and so on. It's complicated and it's very complicated because there's so much variation in the effects different kinds of things have on different people. I mean, it's always very confusing that when people do trials of drugs and things like this, they'll try them on 100 people and it'll work on five of them and nobody will know why, it's that five. And it's very, very confusing. Let's see, Des is asking what diseases have afflicted humanity for most of our history that would stunt growth? Well, I don't know for sure, but I think a bunch of things. I mean, there's some very physical ones to do with, you know, bones and skeletons and so on, but I don't know. I mean, for example, I don't know. Through most of human history, most humans had lots of parasites living in their gut. I mean, all of us have a microbiome that consists of bacteria living in our gut. They have a nice sort of symbiotic relationship with us, you know, digesting food and producing other products that we can then digest and so on. But it's still true in some parts of the world, but it used to be true pretty much universally that people had much larger parasites living in their gut. And whether that had an effect, I have no idea. Were the little parasitic worms or something living in your gut getting all the benefit of the things you were eating, and so they weren't being able to be used to grow you, instead they were just growing worms? I don't know. I don't think so, but I'm not sure. The. It's. Let's see. You know, one of the things that's often claimed these days is that people are commenting about living longer and so on. It's often claimed that caloric restriction, just eating less lets you live longer. I don't know how true that is. I'm always a little bit suspicious. It's kind of like, well, yes, if you sort of. Let's say you have some machine that can run in its lifetime a billion times, and you say, I want it to live longer. Well, one way you can make it live longer is by running at half speed. So those billion things take twice as long to have happen. And I kind of always wonder with some of these strategies to kind of live longer but live slower, so to speak, that, you know, you don't. You don't eat as much. Well, maybe your brain works more slowly or something like this to kind of. And that what you're really seeing is we all get some amount of sort of total amount of this or that activity, and you can kind of spread it out differently. I don't know if that's true. I mean, there's evidence for all kinds of things to do with the way that metabolism and insulin and so on work depending on different amounts of food intake and so on. And I'm not sure I. I think it's all a bit up in the air what the story there is. I think it is probably the case that if you eat an outrageously large amount, that that's probably not good for you. Although I have to say the people I know who've made it to 100, for example, I'm trying to think, well, this is true universally, but it's true. Well, I know more people, needless to say, who made it to 95 plus. And I have to say the vast majority say, oh, I didn't do anything terribly special. I smoked, I did this, I did that, I did all kinds of unhealthy things and I just lucky and that I made it to this point and it's not. And sadly you see people who are very kind of fit and so on and something terrible happens and they die quite young. So I think it's. I don't really know. I know there are various kinds of projects to kind of study the habits of people who make it to 100 and things like this. I don't think I know kind of a good general picture of what's been found. Puts is commenting. If you consume less energy, your metabolism basically your burning of things in your body will go more slowly and maybe that will cause less damage to occur. Yeah, I just don't know. I mean, I don't know whether that. Whether the burning of things, the metabolism and so on is important for every thought you have, so to speak, takes a certain amount of energy and burning of things. It probably doesn't work this way, but it's like, okay, we get a certain number of. Of thoughts effectively and we can't. And we can say, yeah, let's do it at a slower rate. And you know, every time we have. Let's say every time we have a thought we are sort of destroying something. It doesn't work that way. But imagine that then, you know, we'd have a certain number of thoughts and we could spread them out or compress them. And I don't think it's obvious that the. Whether. Whether what matters is the rate or the total amount of. Of something. So, for example, one theory would be if you are sort of metabolizing too quickly and so on, that you produce, you know, you usually the term, a common term is oxidative stress and that you. That when things are happening quickly, that there's sort of irretrievable damage that's produced. But if things are happening more slowly, the damage has more of a chance to repair itself in real time. That is if you're, you know, if it's going too fast, things go wrong. A wheel falls off here, another wheel falls off there, and the whole thing goes splat. Whereas if you were going a bit more slowly and only one wheel fell off, and you can kind of run on three wheels if you're a car or something, and then you can reassemble the other wheel. But that doesn't work if two wheels have fallen off before you've got the chance to reassemble that fourth wheel, so to speak. So, I mean, I can see how that could work, but I'm not sure it's very clear how that works. I mean, there are a lot of things in biology that are sort of quite mysterious in this regard. Another one that's always mysterious is the dose dependence of things like drugs that you can end up with, oh, it has no effect if it's below this amount. And then suddenly when it's above that amount, it has a big effect. And, you know, these things are probably hints about sort of the bulk organization of biological organisms. And the way that, you know, for example, it has no effect because you're gradually blocking some particular site on some particular molecule. And it really doesn't have any effect until you pretty much blocked everything. Because even if you have some unblocked, you can still do that particular thing using the unblocked ones. And it's only when they're basically all blocked that things dramatically change. So I think. That's a thought there. I see. Could we have evolved out of needing an appendix because of diet? So, you know, in our intestines, the sort of the food's going through and being digested and it's being all squidged around and there's this sort of little dead end in the typical anatomy. And that little dead end, people have sort of always assumed that's kind of useless. And it can get infected because it gets full with bacteria that are not kind of the good bacteria you want, but they are an infection that makes the whole thing get bigger and start giving you lots of pain and all kinds of things like that. And it's really very common surgical operation to remove the appendix, to just cut off that little piece of that little sort of dead end in the intestines. People have always said the appendix is just a sort of a quirk of evolution, that the intestines evolved some way, and it was just sort of a thing that got left over and didn't matter much. So it got left there. Even though it causes us trouble in modern times now Is that really right? It's one of these typical things in science and biology and so on. It's like, well, maybe that's not actually right. Maybe Dependix is useful because it's a place that's kind of like a harvesting point for some of the bacteria in the microbiome in our guts. Probably there are plenty of other harvesting points, but maybe it's just a convenient harvesting point. That was a thing that was actually evolutionarily useful, although probably not necessary, but useful. And so then the question would be, if you change diets and so on, is it the case that the bacteria in one's gut change enough that maybe the appendix isn't so useful as a garden anymore? Maybe the fact that it was a useful garden depended on the idea that you would have nasty parasitic worms and so on. And, you know, you'd need this kind of place that was safe from those or something. I don't know. One thing that's the case. So microbiomes, if you sort of try and analyze a microbiome for a typical person, I don't know, I've done mine a few times. You have hundreds of different kinds of bacteria of many different families of bacteria. And there's a couple of things that are interesting about that. One is that a given person tends to have a certain microbiome. And even if you take antibiotics that go zap all these bacteria in your gut, a thing that I've. Ever since I started paying attention to microbiomes and things, I've been very reluctant to take antibiotics because I'm like, I want to preserve all these bacteria, but it's not a. But anyway, even if you sort of wipe out all this population for any given person, it seems like the populations tend to come back in the same kind of way. Like, you end up with, I don't know all the names of the different kinds of bacteria, but you end up with some number of this family and that family and so on. Even, for example, identical twins wind up with different microbiomes. It's just very unclear what it is, but it seems to be a constant in a particular person. Even if you kind of wipe out the populations. So they have to come back from a few members to sort of come back, they'll end up coming back in more or less the same proportions. Not clear why. I mean, maybe it has something to do with the actual geometry of the intestines. I don't know. It's. I think there's a question of if you really change your diet, how does it change Your microbiome. I'm sure it does. You know, can you tell what the effect of that is? Does it make a. You know, does it have a. Could you say, I'm gonna. I'm gonna architect my microbiome to be just this way so that I will have. Well, nobody really knows what the. What the. What the thing you want to have there is. So maybe one day in a few years, people will be saying, oh, I'm eating more tomatoes, because the number of staphylococci or something in my. Maybe you don't get those. Those may be only. Only bad bacteria. I'm not sure the number of some kind of bacterial family in my gut isn't high enough. I should eat more tomatoes or whatever, because those. Those guys really like that. I mean, in the microbiome, in the gut, there's a whole complicated ecosystem of, you know, one bacteria consumes one kind of thing. It excretes some kind of thing. Another bacteria picks up what it produced and metabolizes that. It's a whole zoo in there of organisms that are interacting. All right, well, I think some. There are more questions related to these topics. Am rudo I'm not sure I would be happy to see a firefly as big as an albatross. Also, is it possible to measure somehow the intelligence of dinosaurs? That's an interesting question. That's an interesting question. I mean, I think that, first of all, I think measuring quotes. Intelligence is a fraught business to begin with. I mean, I think that for humans, it's like, what does it mean? Does it mean. Does it prove that you're intelligent, that you can make a science discovery? I don't know. I mean, the main thing it proves is that you can make a science discovery. Why you can make a science discovery. It may have many, many different origins. I mean, certainly it can be all about strategy of what should you study. And you can be pretty bad at doing the detailed analytical steps. Maybe you're really bad at those steps. You just use a computer to do them. And then does that make you, you know, just. Do you get notches down for intelligence because you're using a computer to do these things, you're not doing them in your own brain. Or it's just such a messy concept of, you know, if what you want to measure is how well somebody does on some particular task, well, you can measure that. Whether you can generalize that, as people thought one could from the 1930s to a coefficient of general intelligence or an IQ, an intelligence quotient that's Just extremely unclear. And when it comes to jumping to animals, it's so hard to tell what sort of counts as intelligence. So, for example, I remember, oh, gosh, so many things. I mean, like, when I was a kid, there was a popular television program. I think it was called something like Bird Brain of Britain, which was, you know, this is a, you know, I have to say this is a British kind of type of thing, culturally, that it was a thing where they would have video of birds pecking at milk bottles. In those days, people would leave milk bottles, you know, outside with milk deliveries and so on, and there would be kind of a. Can the bird figure out how to peck through the milk bottle that's had this thing put on it and that thing put on it? And you would see these different kinds of, you know, crows were famously pretty good at these things. And, you know, they would be kind of like the. The bird is kind of looking around and trying to figure out which angle to put peck at and, and so on. And it's like, is that a measure of bird intelligence? Unclear. And then you look at these tests people do and different kinds of animals. And, you know, one I saw was opening a box, a wooden box that had various kinds of. Of things that were sort of latches on the box. And, you know, you, you see, oh, there's a. I remember in the video there, there was a polar bear trying to open the box. And I'm sorry, but its paws are just too big to move the little latches on the box. And pretty much you could see the polar bear was pretty much getting ready to just smash the box, which it quite possibly would have been able to do. But in any case, it's just very unclear how you'd measure these kinds of things and what it would even mean if you ask a question, like if you define some particular kind of thing. For instance. Well, let's take an anthill. You know, that's a complicated structure built by ants that are individually, you know, have whatever 50,000 neurons or something and might not be considered, depending on what your definition is. You know, it's hard to. The collective intelligence of the ants is certainly much greater than the individual ones. And then for the dinosaurs, I think one of the questions would be, were there dinosaur artifacts? Now, there are artifacts for many kinds of creatures, whether it's beavers building dams or these pufferfish making these very elaborate kind of mandala like patterns on the sand and so on. There are lots of kinds of ways of imprinting on the natural world the effect of what animals are doing. So we could certainly ask, did dinosaurs build houses for themselves? I don't think we know the answer to that. I think the answer is probably absolutely not. But I don't think we know. I mean, for example, were there dinosaurs that dammed rivers like beavers tried to do, or were there dinosaurs that would garden things to make a nice thing where they would cultivate some particular kind of plant? I don't think we know. Could we figure that out? Well, I think our best hope will be to find essentially archaeological evidence of something like that of which none has been found. And some dinosaurs have been preserved sort of in an in life type configuration. But, you know, it's an interesting question whether what kind of artifacts. I mean, I know, for example, you know, tracks are something like, you know, tracks made by the feet of animals and so on. That's the thing people have studied going back a long way, I think even to the Cambrian period. Those things exist also excretion from animals that people study that and you can look at tracks and things with that. And that's another way one can get a sense of the behavior of the animals as opposed to just purely the shape of the animal as it got turned into a fossil. But I think it'd be an interesting question whether there are things constructed by critters in the ancient past that are things constructed out of stuff other than their own bodies that one can identify. Did they move things around? That would be a terribly shocking thing if one day one found a trilobite, a collection of trilobites. There are lots of trilobite herds that one finds fossilized and so on. You know, you find a trilobite herd that somehow drawn a hexagon that's arranged things in a hexagon or where even the trilobites are arranged and, you know, doing a hexagonal dance right at the moment they got fossilized. Nothing like that's ever been found. But it would sure be interesting if it was found. It's kind of like alien intelligence here on Earth. You know, could we find it? What would it be like? You know, could we. Or is it the case that, you know, the trilobite configurations that we actually find are super, you know, indicative of something that is kind of very is, you know, the great civilization of the trilobites, but we just don't recognize it. And I think I have to go back to my day job, which I think is actually also a live stream here, talking about Wolfram language design, about sound and vision characteristics of Wolfram language design. So we move from the trilobites and their potential visionary activities to our visionary activities with image processing and so on. So thanks for joining me. And I see there were a lot of other questions I didn't manage to get to today. I look forward to talking about them another time. All right. Bye for now.