Mathmanimals!

math can be. From mathematical b sex to baby animals who are cute little calculators, to the way that math can produce some of the most beautiful living works of art in the natural kingdom. These word problems are no problem at all. Discover this and more as we answer to the angel question should you let your chickens count before or after they've patched? Joining me today is astrophysicist and co host of the podcast Daniel and Jorge Explain

the Universe Daniel Whiteson. Welcome back, Daniel, Hello, thank you very much for having me on. I am happy to be described as an astro physicist because I like to throw my mind out there into the cosmos of the universe, and I'm also a deep lover of mathematics. When I hear math, I don't run screaming, I go tell me more. Yeah, I think that. You know, sometimes some of us, not naming any names, not pointing any fingers, have a complicated

history with math. It's like, you know, it doesn't seem like, oh, this is probably not all that interesting because it's a bunch of numbers and a teacher getting mad at me for not putting them together in the right way on a piece of paper. But it can be really really interesting. And even for people who don't have a big background in math, like you don't. It's you know, obviously some parts of math, especially like the more theoretical you get,

it's it's pretty sort of a dense labyrinth. But when you're kind of looking at the big picture applications of what it can describe and do, like that's accessible to everyone and it can be really interesting. Yeah. And in the end, it's the language of the universe, you know, it's not just the way that we like write physics down and do our theories. We think math is actually like fundamental. We think it controls the way things happen.

So I love when we find things in physics or in biology or in economics that like revealed the underlying mathematics because it shows us like sort of the source code of the universe, like how things are really working deep down exactly. It puts the fun and fundamental it does. And so that's why it's so frustrating to me when I see my kids like developing an aversion to math, you know, because I'm like, come on, math is fund isn't it? And they're like, maybe math worksheets aren't fun.

You know, that's a good point, that's true. But maybe you can just take them out to a field and point out some bees and say like, look, they're doing math, and you can too. So there is a big paradox in evolutionary biology, which is that you have a moles who seem to sometimes behave altruistically and even go as far as to be you social, so you sociality is a social structure that is found in bees, ants, termites,

naked mole rats, where and mostly non breeding. Colony works for the good of the queen and for their fellow members of the colony. So it's this very it's seemingly extremely altruistic, right, you're all working for the good of the queen, for the good of the colony without worrying about reproducing yourself. But this is a big problem because evolution seems like it should always reward genetic selfishness. So if if you can pass on your genes through trickery, thieving,

selfishness or whatever, that should just count. Like mother Nature is not going to judge you. If you get your genes passed on, that's good enough for her. There's this famous Gary Larson cartoon that shows like a bunch of limbings going off a cliff, which is a myth, by the way, they don't you that, but still in this cartoon, one of the limmings has a little inner tube and it's kind of like mugging for the camera, looking very smug because it's the one limbing that's going to survive

this jump off the cliff. And actually this cartoon was used in some of my evolutionary biology classes in college to demonstrate like, well, if you have this one liming doing this thing like cheating with this inner tube, all of the limings should develop this trait soon enough, because that's that's going to be the types of genes that survive.

Like the limmings who were the inner tube and survived the jump off the cliff should all develop that trait because again, like if you survive, those genes are the ones that are going to win out. So I have so many questions already. First of all, you social. Is that like the letter you and social or the word you or like you know, E W E social, it's eu and then social. So it sounds a little bit European, but I'm sure it has another explanation for it. But

my real question is that is selfishness really necessary? Like do most species actually maximize selfishness? I mean, why can't the species get forward by being all nice to each other and just like enjoying life, Like why don't they maximize the joy of sunshine and you know, a drop of water on the leaf and something. Doesn't that make people happy and and make for like happier and more successful children. Why is it all about selfishness? Well, you know,

it's actually true that it turns out. I mean, we can just look around and see that. No, it's not true that all animals maximize selfishness. We can look at humans. I mean, sure we like to say, oh, humans are selfish, but when you really look at human society, we've only gotten this far by working together. And you know, of course, like there's all sorts of problems with society. I'm not going to get into any of those because that's probably different podcasts. But when it comes down to it, we

are a cooperative species. We do work together in order to enhance our survival, and it's somewhat easy to see how this works out in our favor. Like we are not the toughest roughest animal. We could not win in a fight one on one versus a bear, but when we're in a group, we do pretty well. And we all benefit from being in this group because if we are within the group and then we survive, we get to pass on our genes and our children who will

have that same sort of cooperative framework. They're born sort of with the capability of having that cooperativeness and empathy, and then they're raised in the group. So it's sort of this interaction between genetic selection and also social selection, right like when you when you raise your child in a group, they learn the customs of the group and they learn how to interact with people. So we can see how through natural selection, kindness and cooperation can actually

be beneficial to a species. Um But there's this whole other problem when it comes to bees, ants, and termites, because they're not just a cooperative society like humans are, or humans should be. Maybe I should say individual humans have offspring. It's not just the king and queen of human society that have offspring. We're all able to have offspring, and it all benefits us to have a community that's

that's safe and bountiful for our offspring. So working to other, working together helps us all kind of pass on our genes collectively. Um, but with these with bees, ants, termites, and these other you social animals, the individuals in the colony do not reproduce. So you have your hive of bees, your colony of ants. All of the workers are females, The queen is female. The workers do not reproduce, generally speaking, and so it seems like, well, that shouldn't work out

like that. It should only select for the ants that are selfish enough to want to reproduce, or you know, I'm saying selfish and sort of a more evolutionary biology terms, not that there's like a little ant going like ha ha, I'm going to reproduce, screw the colony, but it really should like favor that kind of sneakery. And trickery, it seems like, because it's like, well, how else would these

altruistic genes get passed on? Right, why do they still exist if they're not getting propagated to the next generation exactly exactly, So this is a seeming paradox in order to get to the bottom of this. I mean, there is a hot debate about this in the evolutionary biology community. I mean, I think it's still going on to this day. Like I just read this like scathing research paper about like, oh, well, these guys are all wrong about this, and we can

prove it. It's one of the more controversial topics in evolutionary biology because it is such a fundamental thing that we have to figure out in order to fully understand how natural selection works. Well, why can't evolutionary biologists cooperate when their research about cooperation? Right, there's like selfishness in

the research about cultruism. That's ironic. They've got it. What Jeff Goldblum in the Fly his problem was he didn't like put a bee in the other end of the transporter, so he turned half be because then he would actually be really productive and really cooperatively working on papers together in a hive of researchers. So there are a few theories that I think you have to understand all of them to actually get the full picture of how this works.

And we've talked about bees and ants on the show before, and I've kind of discussed some of these things in less detail in terms of like how the math behind this works. But right now we're going to get really deep into it. To get a full understanding about the math of bees and answer termites and so on and so forth. I've never been more ready. That is probably not going to be the only b pun we do to folks, so strap in. So first let's talk about

the kin selection theory. So this is one of the few theories that helps explain how a bee colony could exist. And this actually doesn't apply to the one group of mammals who are used social naked mole rats, which we'll get into a little later. We'll discuss in more detail in just a little bit, but let's just focus on bees, ants, termites. These groups of insects that have a colony of worker females. None of them reproduce, just the queen reproduces, and somehow

this remains a stable system. So the so the workers are all female, like the males are not doing any work. Yeah, basically the males don't do much. They kind of sit around eating until they can go off and mate. And if they don't go off and mate, they actually get kicked out of the colony for being you know, layabouts too lazy to mate. Wow, that's quite I know, all right, you think that just getting to eat food all your life and then going off and mate would be a

pretty good life. But uh yeah, I mean the the only function males really do. I think that sometimes bees will cluster together and vibrate together to increase the temperature of the colony and cold weather, and I think males will actually engage in that as well. But other than that, they just kind of hang it around and wait until they can go and reproduce. Basically, any bee you see going from flower to flower collecting nectar is like chance,

it's going to be a female. So you got like women at the top because the queen is in charge, You've got women doing all the work, and the males are really just around to make more women. Right, it's a very matriarchal society. Congratulations, men, you can finally feel like you are you are being discriminated against in b society. They're being held down by the honey ceiling. So, as we've discussed before on the show, bees, ants and termites

are what's called haploid diploid. So haploid simply means one set of chromosomes, whereas diploid means two sets of chromosomes. So we humans and most other sex having animals are actually diploid. So we get one full set of chromosomes from our father and one full set of chromosomes from our mother, and we take all that, we scrumble it up,

and that becomes us. So that's why we're mostly x X or x Y for example, exactly exactly, and of course, like there are exceptions to this, like there are times when like there are children who will have xx y or like these things, but that on average, most people get one set of chromosomes from their father and one set of chromosomes from their mother. Haploid diploid is a combination of haploidy where you get only one set of chromosomes and diploid e. So this is the way it

works in these insects that are haploid diploids. So female offspring hatch from fertilized eggs and get a set of chromosomes from their mother and from their father like a human, but male offspring hatch from unfertilized eggs, and they will only receive one set of chromosomes from their mother, the queen. So this means that sisters share about seventy five percent of their genes with each other when their father is

the same. And so this is kind of like a little bit of a jump in mauth, Like, wait, how does that work? Because in humans, Uh, it's kind of varies how much we're related to our siblings. On average, it's a statistical average of about fifty pc you're going to be related to your sibling. Uh. And it's the reason it varies, The reason we're not just like always related to a sibling is that we are getting a random grab bag of gene from each parent through the

process of biosis. It's somewhat randomized recombination of genes when our parents create their gammets. So we're getting this kind of like grab bag of stuff, and then we'll probably share a lot of those genes with our siblings. Um, but it's somewhat randomized. So Statistically speaking, we've got about a fifty percent chance of sharing those genes from our

parents with our sibling. But there's a range there, right, Like principle, it's possible to have no genes in common with your brother if you just got like, exactly the opposite version of every gene from each parent. Yes, it's theoretically possible. Yes, it's theoretically possible for that to happen. Uh, you can see like that's sometimes siblings look very similar, sometimes they don't look related at all, So you can and that actually, even looking similar or not related at

all doesn't necessarily mean that you're not genetically similar. You could share more genes with someone who you don't look at like, a sibling that you don't look like, then you do with the sibling that you do look like. It just depends on whether you happen to share some of the genes that code for like eye color or hair color. People always tell me I look like Matt mconackey, but we're not related at all. I'm pretty sure that wasn't a joke, right, No, that was a serious laugh.

It's it's just how stunningly similar to Matthew McConaughey, you like, all right, all right, all right, yeah, so right, so with our sibling, your sister or your brother or your whoever you're about related statistically, you could be less or more depending on which sort of grab bag of jeans you got from your parents when you were a little when you're a little egg in a sperm, and then those combined and then you then there you're you. Uh.

With bees, it's seventy that's way more. It's not always exactly seventy five percent, but on average, that's how related they are to their sisters, uh so much more than humans. So hold onto your butts. This is where we're gonna do some pretty simple I would say math, but it can get a little confusing. I definitely failed some of these quizzes in college because I like get sort of

confused with percentages. But it's easier to do when you're looking at a diagram that somebody made using Pokemon bees. So I will include that in the show notes. Someone made this diagram. I think it's Comby and then like Cambies evolutions. Um, I don't know what the names of those are, but it's a great diagram. So basically the queen gives of her jeans to her daughter, and the father gives one of his genes to his daughter. How

does that work? Well, if you remember earlier what we were talking about is that males results from unfertilized eggs. They are haploid. They only get one set of chromosomes from their mother, so they only have one set of chromosomes they can get of to an offspring. So when they are mating with the queen, while the queen has two sets of chromosomes and she can give you of whatever chromosomes she has, the male only has one set, so he just gives you that that's all he's got

for you. So this means that at least half of the daughter's genes are going to be shared with her sister's genes at a minimum, because she gets they both got like a of their genes from their father if they share their father, So the other half of her genes that she gets from her mother that's a little more randomized, So she'll share about half of that amount

of genes with any given sister. So that means that of like her total chromosomal amount, like she'll of her mother's chromosomes, she has about a chance of sharing that with another sister because it's half of a half. It's so let's see if I get this math right. So you're saying that all the female sisters they have the same gene from their father, because the father only has one, so they all have exactly the same one. They're like identical twins. But the other one, the one they get

from their mom. They have one of their mom's genes,

so they might share it or they might not. Right, basically similar ish, I mean, it's a little it's a little more complicated because it's sets of chromosomes and when when the mother is actually creating her egg it goes through this process of miosis where there's some randomization, so females can actually share more or less related nous through their mother, whereas like they're getting I think basically of their father's genes, because the father really doesn't have, uh

that the amount of genes to play around with that the the mother does because he only gets like one set of chromosomes and that's all he is. And when she makes eggs, like eggs are either female or male, right, even though they have only one of her genes, So the male eggs do they always get the same gene from her or do they get one or the other. They get I think a randomized gene from her, so they are unfertilized, so it's only getting its mother's genes.

But I think it's still goes through the process of myosis. So the male offspring is still getting some randomized genes from its mother, but it's all that's all it's getting. It's getting nothing from the father because it's unfertilized. So the eggs all have one gene and then the male comes along and when he fertilizes, it gives it the other one to make it female. But the male eggs never get fertilized, so they just stay one gene and

stay male. I mean, I would just say, like instead of saying one gene, one set of chromosomes, because like there's many genes within a set of chromosomes. But yeah, just like one set of chromosomes that it gets from its mother, not add percent of its mother's chromosomes, because its mother has more chromosomes than the male even needs. So she that's going through that process of myosis, such that the male offspring is getting, um, what is it? I think the male is roughly related to its mother.

Let me just double check on that. Sorry. See, this is why I fail these quizzes in college. It's complicated. Oh my gosh, it really is. I mean it doesn't seem like it should be right because you're dealing with very simple percentages like a D. But then as you get like a longer line of bees and you're trying to figure out like how much of this be is related to that be, it actually adds up to be

quite complicated. So the queen will share on average about half of her jeans with her you know, she will definitely share half of her jeans with her son. Weirdly, the male be will share a hundred percent of his jeans with his mother because he's like a hundred percent of his genes is his mother's genes. But for her, she's only half related to him because she's only giving half of her jeans to him. Uh. It creates some really really weird scenarios to where well, mothers and sons

always have complicated relationships. Well bees, male bees can only have daughters, they can't have sons, but they can have grandsons because again, like you have, uh, when the queen is laying eggs and she mates. Let's let's call him Jerry is her mate. You can't even really call him the king because he just dies after mating. He has no yeah, exactly, it's got he's got no like uh power in the royal society. So like one time they mate and explode. No wonder the wonder these men know what, mate?

I understand, I do what now? So so the queen mates with Jerry, and Jerry dies, and the the only eggs that the queen is going to use Jerry's DNA for our female because the unfertilized eggs do not use any of Jerry's DNA, and those are the Queen's sons. But Jerry can still have a grandson because one of his daughters could grow up to become a new queen. And if she mates, she can have a son, and through the process of miosis, some of her father's genes

that she's scrumbling up to go into her son. Uh could could like that then will make that son Jerry's grandson. But he can't have any sons, so he has got a skip a generation before he's got a got a grandson, which doesn't really matter to him. Because he's dead anyway, And so most of the queen's children to have no offspring. Right, only if she springs to have a female child which becomes a queen. Well, it's not even too randomized in

terms of female offspring becoming queens. That only happens if they feed them royal jelly, right, And so yes, most of the female offspring will not have uh any offspring.

And the way that this happens, one proposed way is that because um, because they're more related to their sisters than they are to like, potentially their own offspring even um, then it doesn't make sense for them to have to sneak around and try to have their own offspring when they're they share so many genes with their sisters that whatever altruistic gene they have, if they ensure the success of their colony and one of their sisters ends up

being one of the new queens, it's like that increases the chance of all of these genes that they share of getting passed onto the next generation. So usually you think about the next generation and like, I'm trying to lift up the next generation and support the ones that have my genes so they can probably go forward, sort of down the evolutionary tree. But here these people will never but here these beans will never have any offspring.

But you're saying that they're related to their mom them into their siblings, and so they still have a sort of genetic interest in their mother's success even if they're not going to have any kids themselves. It's not really that individually they have any interest in it. It's that it's whether or not the genes that they have, uh, are the same genes that get passed onto the new generation and code for the same behavior. So it's like

they're like, they're these bees have no plans. They're not thinking like, well, if I help out my sister, maybe she'll have a she'll become queen and have a son. There's not like neither the bee nor the genes inside the bee can plan ahead like that or think like that. It's really like, say you have it's about the statistical probability that the genes that they have and they share that codes for the same youth social behavior ends up

getting passed on to the next generation. So it's it's it's counterintuitive because we really think about sort of intention with things like like a kind of uh, you know, I want to give my children a good life. I want to you know, pass on sort of like good qualities to my children, like kindness and happiness and things. But you know, in terms of natural selection, especially when you're looking at something like a B, it's not a

conscious decision of I'm trying to pass this on. It's it's like, if those genes get passed on, you did it, You won, And those behaviors that got passed on through those genes are going to be replicated over and over

throughout the generations. Yeah, and it's even deeper than that, right, because you're saying that that behavior caring for your kids, loving your kids is really just a product of evolutionary pressure that folks that ended up feeling things for their kids are the ones that took care of them and

then propagating their own genes. It is. It is, And I know that for some people that may like feel like, oh man, well then we don't have free will, and it's it's meaningless, and it's like everything in human society is basically a product of evolution, but we have this kind of unique ability to have some fun with it and to kind of have some decision, like if you know, as evidenced by the fact that people adopt children and love them as as you know their children because they

are their children, and that has no like, you know, genetic motivation. It's just because we have developed this empathy and this kindness towards other humans where we realize, like, hey, you know, a family can be anything that we want it to be. So, if anything, we're kind of like giving the middle finger to Mother Nature and saying like, hey, we're gonna be nice whether you want it or not. Right,

and not every behavior is perfectly sculpted by evolution. Right, It's like, if something develops and it's useful for propping any of your genes, it might also have other effects which aren't harmful, like adopting children and also loving them exactly because we live in a society, as the Joker likes to say, but I also like to say it, because through our society we can actually achieve much more in terms of like propping each other up and helping each other survive in a way that takes off a

lot of the selective pressures from us and allows us to be kinder and and have more freedom in terms of what we choose to do with our behaviors, which I think is really lovely. Unfortunately not the case for bees and and ants and and uh also naked molerats. And so this is where I get into part two

of the explanation of what is going on. So unfortunately, kin selection is not the sort of tidy explanation that we would hope for where it's like, okay, so just like statistically speaking, like you know, they share their genes with their sisters, and that would would be able to allow them to like, you know, those genes to survive.

It's it's not enough of an explanation potentially. And we see this because of the pesky naked molerat, which is a mammal uh, a little cutie that looks um sort of like you took a hamster and shaved it, uh and uh put it underground. Don't do that anybody from They're wrinkly, they're flesh colored, you know, they look slightly phallic. But they're really interesting animals. So uh. They are diploid like humans, like most other sex having animals, like all

other mammals. Uh, they you know, get a pair of a set of genes from their mother and from their father. All of them there's none of this like weird genetic shenanigans going on for these naked mole rats like there is for bees and ants and so on. But naked mole rats have a youth social society, which shouldn't make sense,

but somehow it works out. So they have one reproducing dominant queen and subservient worker females who do not reproduce, just like bees and ant colonies, and and they kind of act in a way that's very similar to bee colonies, where you have the queen kind of passing on orders and bullying her underlings. So this brings us to another force that may help create youth social societies, and that's brutal tyranny, so, or, perhaps more gently put the manipulation

on the part of the queens. So both use social insects and naked molerat queens use both chemical and behavioral manipulation to force their colony into compliance. So you social insects use pheromones often that will suppress other females ability to reproduce. So they have these pheromone signals that will

actively suppress female reproduction in their offspring. But we're talking about bees now bees using SMA because I thought that the female bees couldn't reproduce because they're not queens and they needed the royal jelly to be a queen. But you're saying that even without the royal jelly they could somehow reproduce. Sometimes they can sneakily reproduce. While the pheromones do suppress their reproduct of hormones. If you've got to be that maybe is not getting as exposed to that.

Sometimes they do sneakily reproduce even if they're not queens, and that is met with the punishment of having their eggs eaten by the queen. So the queen will go around eating eggs that she finds that are not her own. So it is an extra safety measure to make sure nobody's reproducing but the queen. Uh. And even in terms of like once a queen hatches, right, and if she has other sisters that are being developed into queens by being fed this royal jelly, she will kill them to

make sure that she's the only queen. Uh. There are very few instances where a colony can have two queens at once. That doesn't typically happen. Um. So like once the old queen dies and her pheromones are gone. UH. This signals like the bees to start creating, just feeding royal jelly hither and thither, to like create new queens and to start reproducing until a new queen will emerge

and reproduce for the rest of the colony. But naked mole rats now, there was some research done to see whether they use pheromones to UH for the queen to enforce her monarchy. That research a little it's a little shaky. They're not really sure whether or not. There there was like some evidence that pointed towards maybe some pheromones excreted in the queen's urine that may have some impact, but there have been other studies that were like showing that

maybe it doesn't have as much as an effect. What we do know is that she will physically bully them, like any female that is disobedient or you know, is trying to shirk her work or or go off to mate somewhere, Like we'll get bullied and shoved around and sat on by the queen UH to Like basically this and this physical dominance displays UH seems to inhibit the females reproductive hormones by basically constant bullying makes them less

likely to reproduce actually inhibit yes, inhibits the reproductive hormones, um so, and can somebody else take over? And maybe it's just like physical dominance. Can you get like a really tough muscley one of these things that's born and

eventually take over and be the new queen? Yeah, but generally, interestingly, it seems like that is often passed, like the daughters of the queen, Like, uh, it's usually I think it happens like when the queen is older and like if she's like kind of losing losing her head or her edge, like one, yeah, one of these daughters will take over

the colony. And sometimes, and this is what's interesting and this seems to happen more often in these colonies than with the colonies, is that like the female members, the ones that are sort of being bullied, these workers will try to sneak off and start there like reproduce and start their own colony essentially, and they can manage to

do that. So it's sort of this like release valve of like of these workers sneaking off starting their new colonies, Which makes a lot of sense because in this in this kind of you social situation. It really is sort of just however you can manage, uh, manage it. So like the queen is using kind of brute force to make sure that she's got a lot of support for her offspring. But other females, if they can get away with going off in and reproducing, they will, and bees

in theory probably would too. It's just like in the b society, it's probably a lot more iron clad than these naked molerat societies in terms of preventing that from happening. And what are the men doing in these naked molerat societies? So they also like not doing any work. I think that's a good question. I think they might do more work than than the than in bees. So like there is like brute force being used both in the naked molerat society and in bees and ants and these you

social insects. Uh So, so that's another part of it. I think that adds onto like the kin selection. So if the kin selection is not enough, like you also have this behavior where you're basically having a tyranny which can propagate. We know in human society tyranny's can continue on for generations even if it's not to the benefit

of individuals. But um, but in this case, it's like it's helped even more out by the fact that genetically speaking, UH they do like they do share a lot of genes, even even the naked moleras, even though it's not the same as with U. With the uh bees, like they are often sisters and related to their mother in some way.

But then the next theory, the last theory we're going to talk about, is the multi level selection theory, which is basically that evolutionary selective pressures acts on all levels of life, from genetic to cellular to an individual organism

to a group of organisms. So the analogy used as like a Russian nesting doll, where it's like inside like that little the tiniest Russian nesting doll, Like that's on the genetic level, your genes uh will will often compete and will uh you know, like there're selective pressures happening

directly on the genes at the genetic level. And then you have evolutionary selection pressures acting on your cells individual like cells can compete and interact in interesting ways, which are actually going to talk about a little bit more later. And then you have the individual organism the organism made up of all these cells, made up of all these genes, and then you have pressures acting on the organism itself, like cheetah has to go fast to catch its prey.

You know, a bird flies so that it can like eat insects and escape predators. So you have that the organism itself, like this collective of genes and of cells,

has evolutionary pressures acting on it. And then the bigger step is that a group of organisms has selective pressures acting on it, Like you have, say, um, a group of like lemurs fighting with another group of lemurs over resources, Like you'll have selective pressures fighting at the group level and as well as on the individual level, as well as on the cellular level, as well as on the

genetic levels. So that's why it's that Russian nesting doll um and so kind of like a over probably oversimplified way to look at it. Like in practices, like you know, sperm will compete to reach the egg, right, so like this, these cells, the fastest ones to reach the egg will end up being the ones that survive. Individuals will compete with other individuals or with their environment in order to reach food. And then groups will compete with each other

in order to secure resources for their own groups. So the way that EO. Wilson, who's the famous ant man or maybe I should say entomologists, kind of uses this as a way to explain how altruism and these other these other seemingly paradoxical behavior just conform. So he says, quote in a group, selfish individuals beat altruistic individuals, but groups of altruistic individuals beat groups of selfish individuals. So

you know, this can make sense for humans. Like if we have a group of altruistic individuals, uh, you know that are all working together, and then we have like Jerry. I don't know why I'm piling on Jerry today, but you know Jerry over there, who's like being selfish and not cooperative, Like the group of people who are all being cooperative and kind can end up beating you know, Jerry, Like who's over there just like you know, you know, pounding a stone against a rock and screaming angrily and

you know, not picking up his trash. A whole hunting party can take down a mammoth, and that can feed him through the winter because Jerry's not going to make that kind of kill on his own right, right, if Jerry is just spending all his time like trolling people

on Twitter, like he's not gonna get a mammoth. But there must be multi levels within the levels, Like if you're an altruistic group and you're all helping each other, still you prefer to support the folks who like have more genes um connected with you, right, Like you're gonna help your kids more than other people's kids. And there must be like nuances there also, yes, yeah, exactly, So you know, these kinds of like each of these theories.

In my opinion, while there's a lot of fighting going on, you know, in terms of like really figuring out, and when I say fighting, it's often like good natured like actually trying to get to the truth of things. It's not just like a biologists being petty, although there's probably some of that, uh you know, it's I think that all of these theories kind of interlocked in a lot

of ways. So like you have you can say, have like a flock of birds, right that like works together as a flock, but individual birds really do want to reproduce, and within that like often like offspring of birds will stay around with their parents and help raise uh, their younger siblings, not only because it like is beneficial because the share genes with their siblings, but it also helps

them trained to become parents. So in that example, you have all of these layers of sort of like selection where you have the flock doing better all you know, sticking together, and then you have the offspring helping raise the new generation of offspring that they are related to. UM. But they are also selfishly getting a benefit from helping to raise their younger siblings because it trains them how

to better raise their own offspring. So that's you know, the individual need to reproduce as well being shown there. So it's really interesting and I think that like when you simplify things to like it's just kin selection or something, you do get uh, some complications that really can't be explained unless you are using all of these other different theories and and nuance like you said, to try to explain it. Well, it's complicated. I can see why biologists

gets sort of heated about it. Are you saying that they're all playing nicely? There's no really like scathing papers being written back and forth, But oh no, there are there are There are some like in a way. It's like I'm almost scared to talk about it because it's like I don't want to like come down on the incorrect side or something, because like I'm not I'm not necessarily an expert on on things like kin selection and

and multi layer multi level selection. So I don't want to get something wrong and like start getting like, you know, knocks on my door in the middle of the night

from angry biologists. Well, you know, there's another level there also, because there must be like academic structures where people tend to support their students who believe in their theory and probably their theory of evolution right against the other academic biologists who are promoting their students to become professors, um, and so there must be the competition between those groups. You have, you have kin selection of your your research assistance.

I get it. Be society may be based at least partially on math. But can these themselves do math? A recent study done at r M i T in Australia suggests that you can train a bee to do basic addition and subtraction. So say you're a bee in this study, you would enter into a maze where you're shown a group of blue shapes, let's say three blue squares. Then you'll enter a second room in the maze with two holes above whole A is four blue squares above whole

B is two blue squares. The correct answer is A. You were supposed to add one blue square to the total for the correct solution. Of course, you don't know this initially because the researchers don't speak B, so you have to do trial and error, either getting a reward of tasty sugar or nasty quinine to help you figure out the correct solution. But then you're presented with a maze in which there are yellow squares instead of blue. This time you have to subtract to get the correct solution.

In the first room, you see three yellow squares, and you can go to the food behind the door labeled with either two yellow squares or the door labeled with four yellow squares. The correct answer this time is two yellow squares, and again you're either rewarded with good food or punished with yucky food for the correct incorrect answers. Well, congratulations, because if you're a B, you'll figure it out kind of.

After a few hours of training, these were able to pick the correct solutions, doing basic edition and subtractions well at least significantly better than chance. They probably only got like a B minus on their report cards. When we return, we're going to talk about more animals who can do math. Clever Hans was a famous German horse in the early nineteen hundreds who purportedly could count and do math. He could stomp his foot the correct number of times when

faced with a math problem. Unfortunately, it turns out that Hans was no math is, but rather a body language expert. He could only get the math problem right if his owner knew the answer, and if he could see his owner indicating there was some subtle facial expression or posture. His owner would probably unconsciously exhibit when Hans was on the right number of hoof stumps. I'm pretty sure this still means Hans deserves that title of clever. But can

other animals really do complex math problems? So what do you think? You think animals can do a math? I think humans struggle with maths. But yeah, I think if we think mathematically, and you know, human brains are similar to human brains are similar to animal brains, I imagine there must be some level of math that they can do. It must be continuum of ability rather than it's solely

a human facility. Yeah, I mean, like we don't have we don't have like an orangutan with a little like a motorboard hat and like smoke a pipe with a chalkboard doing like mathematics with like banana symbols. But pretty close, actually pretty close maybe minus the pipe. Uh. In two thousand and seven, Duke University made macaque monkeys and college students take a math test, which I think if I was a college student, I would be very nervous to

be outperformed by a monkey. I would be is. I would just be like beside myself hoping that I performed better, and I probably wouldn't. So they were shown dots on the screen instead of numbers, because it's kind of unfair to expect a maccaque monkey to know what a number is, like they don't know. Um. The humans were told that they would be shown one set of dots and then another, and then they could select from a range of choices, and the correct choice would be adding the first set

of dots to the second set of dots. So like say you're shown two dots and then you're shown one dot, and then you have like you're on the final screen, you're shown like three dots, seven dots, four dots. The correct answer is three dots because you've added two to one dots. We can't talk to monkeys and explain the rules to them, not yet anyways. We can't also brible them with class credits. So they had to figure out another way to teach these monkeys to try to make

do this math. So they would get treats in exchange for selecting the right answers. And it's interesting to me what they're measuring, Like, they must be measuring the ability of the monkeys to generalize. So they show them a bunch of patterns, reward them when they're correct, and then do they show them a math problem they haven't seen before and seeing if they do it better than random chance? Yes, exactly.

So they don't want to just train them to do the same types of math problems over and over again, so they are introducing novel math problems and training the macaques that they do want to get the math correct. So they found that not only were the macaques good at doing the math, they did almost as well as the college students. So I think that we should be giving the maccas a degree and asking what the college

students they've been up to clearly not studying. No, But I mean it makes sense because as humans we don't necessarily do We're not at least taught to do math in terms of looking at groups of dots and then trying to add them and just visually doing the math really quickly. We have this symbolic system which really works

out well. We have incredible brains that are so good at like nesting concepts that it really cuts out a lot of this like uncertainty and having to make this really quick calculation of like how many dots are there, because we can just we have the number five, and we can store all that information within this concept of five and then learn, you know, uh, five minus two is three I'm pretty sure, and so like. But with the macaques, they don't have that symbolic uh representation that

they can fall back. So it's actually not too surprising to me that they're good at just seeing a number of dots and kind of getting like what that quantity is. If anything, I would say that it I would think that sometimes animals might even be better at that than humans because they have to rely on that much more, whereas humans we have symbolic thinking that we can use that animals don't always seem to be able to demonstrate.

It's fascinating to imagine what's going on inside the monkey's brain, you know, has it developed some basic mathematics as it found some like tricky work around to find the solution of these problems? Or is any workaround? Is any solution of these problems then defined as mathematics. I can imagine the monkey sees the first group and then the second group, and it solves the problem by saying, oh, I want

the third group to be both of them. It's not like actually coming up with the concept of the larger numbers, just like recognizing that these two things emerged. I'll argue, right exactly, and it's it maybe is partially just like combining these two visuals in their head and thinking about

what that combined visual looks like. And some some more evidence that this is sort of a math sense rather than actual like human type math is that well, what's interesting is both students and macaques struggled when the ratio of like the the math was like really close. So basically, if you have a similar of dots relative to the total.

So like when they had to choose between like eleven and twelve dots, because you have a lot of dots and then they're only off by one versus having to choose between five and seven dots, or even like, uh, five and six is easier to differentiate between than like twelve and thirteen, because like, once you get more dots, it's like, even though they're both, both of those sets

of solutions are only off by one. It's harder to see that with the larger proportion of dots than like you see five, you see six, it's a little a bit easier to see the difference there. Absolutely, I know that just from like writing exams that you've got to put potential answers that are pretty similar to really figure out if the students have any idea how to do it or they're just guessing exactly. Yeah. I wonder how the monkeys feel when they see like none of the

above as an option. They're like, oh, man, that's that's fair. That's when they start throwing poop. The students too, to be fair, and so can the monkeys do more than just add to the test. Other math concepts like subtraction or multiplication? What can they do? Can they do integration? No? I don't think they can do integration. I haven't seen

anything that suggests they can do multiplication. I think the most is it seems like simple addition, subtraction, and counting are sort of the things that uh primates seem to be able to do. Um. But you know, you might think, like, okay, that makes sense, right, they're really close to us evolutionarily, like it would make sense that's sort like our basic animal cousins can do math. Um. But surely, like really a stupid animal couldn't do math, like a chicken, Like

they're not very bright. But actually there's evidence that chickens can count. And not only can they count, they can do it at a very young age, so they can count themselves before they've hatched. But ump, bump, that's my that's my chicken joke of the day. I've fulfilled my chicken joke of the day. Quota, So right after they've hatched, about three day old chickens are able to understand basic amounts and basic summation. Uh So these baby chickens are presented with a game of Peek a boo or I

guess pekaboo. Okay, that was my second chicken joke. I promise I'm done with chicken jokes. Um. The the way that the study was done is based on the fact that baby chickens seem to like more stuff than less stuff, which is weird. They don't actually know why. Like you have some objects, like a group of objects, they will walk over to the bigger pile of objects, and they will to the smaller pile of objects. And it's not really clear why they prefer more stuff. I guess they

just like to live extravagantly. They're greedy little chickens. They don't believe in tidying up, right. They're not these clean freaks. No, no, no, they they like yeah, like they are like more stuff, give me more stuff. It's a little scary if you think about it. There are so many chickens in the world. So if they decide that they can demand more and

get more stuff, and they rise up against us. Um. So they these baby chickens are shown these two opaque screens where the researchers drop these little balls behind uh and so like when they're dropping the ball, they can see the ball, but once it falls behind the screen, they can't see anymore. Um, so when like they dropped one ball behind screen A and three balls behind screen B and release the baby chicken, the baby chicken goes towards screen BE because it's like, ah, yeah, I'm gonna

get more balls, gonna get some balls. Us just really excited about collecting little toys. It can both conceptualize and remember basic amounts. That is really exciting in event itself.

But then the researchers got more tricky with it. So they dropped like some balls behind screen A and then drop some balls behind screen B. But then they moved some of the balls from screen B back to screen A, so that now there are actually more behind screen A than screen B, whereas originally when they had first dropped it, there was a higher amount behind screen B. So yeah, so this chickens. The little chicks can't see behind the screen,

but they can see the researchers hands moving things. So like so say like they drop um, like one ball behind screen A and then dropped four balls behind screen B. Then they pick up one ball from behind screen BE lifted up so the chicken see that ball, and then move it behind screen A, pick up another ball, move it behind screen A. Now, so the chicks have seen that they've just moved two balls behind screen B over to screen A. So now they should prefer screen A

because now it's actually had more balls than screen B. But that would require them to understand that they're removing quantities from screen B adding it to screen A, and remember that screen A now has more balls. And they do They figure that out like about eight of the time, which is a really high success rate. Uh So, yeah, so a little baby chicks can do very simple math. Uh so, yeah, sign them up for Harvard. Little baby

chicks are definitely better at math than little baby humans. Well, there have been research studies done on human infants as well. Uh And one of the problems actually with testing infants is they don't seem to have this weird preference for

more objects that baby chicks have. So, like you put a baby like in front of some objects, uh like a young enough baby like even something with like candy, they're not necessarily going to just like crawl towards a pile with more candy or something when they're super young, because they don't have a concept of like, you know, I need to get that more candy that's only for

older children. So for really young children, our best way of measuring their interest is something is I gaze, because the longer they stare at something, the more interested or surprised they are by something. They seem to like novelty. So that's one thing we've established, is they'll stare at something that is new or surprising to them. And so like, basically when researchers show them the same kind of test that they do with the chicks, except that they will

do like impossible math problems. So they'll put like one ball behind a screen, two balls behind another screen, move one of the balls back to screen one. So they would expect when you lift up the screens, screen A has two balls, screen B has one ball. But then if you lift the screens and like screen A still has like one ball and screen B has like three balls, they stare and they're confused. They don't understand what's going on.

It seems to be like, like that's our best measure that we can get that they can understand this math because they're like staring at it longer. It's pretty tough, I guess to do experiments with infants and so like, kudos to anybody who figures out how to do these experiments. But I'm always skeptical that we're like really understanding what's going on inside these infants based on like, you know, where their eyes are pointing. I get that it's the

best we can do. That doesn't necessarily mean that it's actually telling us what the infants are doing, right, right, that something totally different is going on. It is it's a significant problem, right, Like for the baby chick experiment, right, Like we have of this weird innate thing that the chicks do, which is we want more stuff, give us more things. We're going to Vegas. Like these chicks, uh

are ambitious little money makers. So like we can easily see that what preference the chick has for the most the most stuff. Babies don't act that way. We can't like get a baby to do what we want necessarily in an experiment. So yeah, the the eye gaze is the best metric that we often have for really young infants. But it's certainly something that it's like definitely up to interpretation, like what that means, Like does that really mean they

think it's a wrong answer? Um, you know, like it's it at least into like the I think most we can say is that it indicates when we compare eye gaze, right, like, if they spend less time gazing at something than something else, it indicates they see the difference between the two things, right, that there's a difference in there, like something different is happening in their brain when they look at the thing that they're staring at longer versus the thing they're not

staring at as much. Whether that means they like get that it's a wrong answer, It's hard to say whether or not that's true, but it seems to indicate that it's like the best indication that we have that they're like not expecting that, which is interesting because we also see that with physics problems, like they see they seem to have sort of this innate understanding of conservation of momentum. Like you have a tiny ball hit a big ball,

and the big ball goes flying off. They stare at that longer than an appropriate response from the big ball, which seems to indicate maybe it's unexpected to them. Babies can do physics. You're saying, exactly, see it, Daniel, Even a baby could do your job. Sometimes I feel like an infant when I gaze at the wonder of the universe. I know lions wouldn't strike you as such, but they're secretly nerds. Lionesses can tell the size of a competing

pride based on the number of simultaneous roars. In a study, researchers found that with a great degree of accuracy, lionesses could figure out whether a recording of lions featured fewer or more potential rivals than their own group, and they chose to either run towards the speakers for a fight or to retreat based on whether or not they since there were more lions or fewer. Wolves too, are able to distinguish between larger numbers of treats versus smaller numbers

of treats and choose a can of treats accordingly. Unfortunately, in a research setting, it seems like dogs failed this test, meaning that in our domestication of dogs we may have bred the ability to do math out of them. So sorry, spot, but speaking of spots, when we return, we're going to find out the math behind animal spots. While spots and stripes, like the code of a leopard or tiger, may appear flashy and attention grabbing to us, out of context in

their natural environment. These clever markings help them blend into their surroundings, and it depends on the time of day to Leopards hunt at night in dark, tree dense areas, so those spots help them blend into the shadowy modeled moonlit forests, and a tiger stripes helps it hunt in tall grass where the shadows and patterns of the grass

help it blend effortlessly into its environment. And while being orange looks flashy to us, to its main prey who have more limited color vision, the tigers can become practically invisible. So Daniel, I think it's relatively well known, like hey, you know, like spots and stripes serve this uh evil

utionary function right for like camouflage mimicry. Uh. It can even be more complex things like in zebras sort of this illusion this barber Pole effect where when you get a group of zebras, it's hard to tell which way the stripes are going, which makes it hard for predators to figure out the direction that the hurt is moving. But the question is not like why they have these stripes in terms of like why there are evolutionary pressures, but like how their bodies can even form stripes, Like,

how could that even happen? Like why would there um pegman or melanin producing cells ever arrange themselves in that way even by chance? Right, because you have to create the organism out of the cells, and so the cells have to like organize themselves in such a way to make these macroscopic effects from the microscopic cells. That's pretty

fascinating exactly right. As you probably know through physics, like when you have sort of a great number of things, right, like you have a randomization of things over great numbers, it has this diffusion effect of kind of smoothing things out, so like for for spots and stripes, it's a little bit surprising because you would think that, like if you have random movement of like pigment cells, you wouldn't get organized patterns out of that. You would get some kind

of diffuse pattern. And this has been a question for quite a while. In fact, Alan Turing was on the case way back in nineteen fifty two. Of the many things that he did, this was one of the problems he was interested in, which is fascinating. I never knew

this about Turing. He accomplished so many things, so his paper The Chemical Basis of Morphogenesis looked at basically these sort of mathematical models of how stripes and spots could occur in animal skin for scales doesn't matter, just he was looking at whether the random movement and into her action of proteins, uh that my code from element or

pegment could produce these patterns. And basically he was able to show mathematically that you could have situations in which random movements of protein through tissue could actually result in an organized pattern. And it was this extremely advanced bit of math and evolutionary theory for the time. It's kind of incredible he was able to come up with this. Of course, the issue though, which turn didn't necessarily factor into his paper, which to be fair, I think the

paper was more of a mathematical exploration. It wasn't literally trying to figure out, say, like how a zebra gets it stripes. It doesn't take into account the fact that cells don't move in an entirely random way. They are actually like I know that we don't think of cells as having autonomy, but they do, like they actually move in um like purposeful ways. They do in a way

and although they don't necessarily they don't have brains. They don't have nerves because of course, like our nerves and our brains are made out of cells, and even a single neuron is itself a cell, but they do have chemical reactions that happen throughout the cell that will cause it to move in certain ways and act in certain ways. So when you trigger chemical reaction, I mean, that's how our brains work, you know, we have chemical reaction that

creates the synaptic firing um. So that so basically you can have a cell move in what seems like a very purposeful and almost cognizant way, but it's simply through

chemical reactions happening throughout the cell. And of course you scale that up to a whole organism, then the organism really does have this kind of like purposeful thinking and movement, which kind of ties back into what we're talking about, you know, earlier on in the episode, where you have like cells on the cellular level acting in a certain way, having evolution pressures on them individually, and then you scale that up and the organism made out of cells also

has evolutionary pressures on it, and you actually see this happening rather beautifully in these studies of zebra fish. So, zebra fish are these cute little fish. If you've ever owned an aquarium or been to a pet store, you've probably seen them. They have these blue and white horizontal stripes. They're very pretty, really cute little fish. I've had a few throughout my aquarium owning days. But the research done on them is amazing, Like the amount of information we're

getting out of these tiny fish is mind blowing. So Professor Shigero Kondo's lab of Osaka University found something incredibly cool when it comes to zebra fish is color creating cells. So zebra fish have light color cells called xanthophores and dark color cells called melanophores, and these cells interact in a beautiful and incredible way, almost like a ballet. So the light cells have tendrils that they used to navigate

and since their environment. When these tendrils touch a dark cell, the dark cell will run away from the light cell because there's a chemical reaction that occurs in the dark cell that is triggered by the light cells tendril that causes the cell to move away from that direction. But the light cell meanwhile gets the chemical signal to actually move in the direction of the dark cell that is

now moving away from the light cell. And so this reaction it's almost like magnets, right, like when you have a opposite polarity magnets or same polarity magnets, sorry, like and you push the same polarity against the same polarity, it will push it away. Uh you know, it's it's like that, but with these cells. Uh, and like where one cell is chase literally chasing the other through this this chemical reaction. And so what you get is like this battel a of these dark and light cells and

as they're chasing each other. Uh. In the zebra fishes development, it will create uh, this kind of straight line. It's like these these bluish lines that run horizontal across its body. And so it'll create this these stacked lines of stripes. So you see this like incredible way in which like the cell's autonomy, like the way that the cells actually

move has this huge impact on animal patterns. So the cells themselves, they're not just like autonomous making up their own minds, and they're not just random you're saying, they're sort of sensitive to their environment and they queue off of effects and that can create these larger scale patterns exactly how a kid goes to sort of like how a kid goes to lunch and elementary school and ends up sitting like at a table of other girls or at a table of other boys, and then you end

up with like a girl table and a boy table because they're queuing off what everybody else right, right, yes, exactly, or in this case, like chasing each other around, or like you know in Star Wars you have like the light side chasing the dark side all the time or something. Maybe that's not a good Star Wars reference. I'm not sure. Uh, but you know this, you know you would think then, okay,

so Alan Turing got it all wrong. It's actually through these like chemical reactions and these cells that actually make them behave in these specific ways. But that research was not for nothing. In fact, mathematical biologist Dr Thomas Woolley is combining Turing's theory and the modern research on zebra fish into a new mathematical framework that aims to describe all sorts of natural patterns, from stripes to spots, even two tiny hexagons that these cells form that can create

these very complicated patterns. Because if you look at animals like from fish too, octopuses to uh two tigers, and to to like like the the awful lot. You have so many different interesting patterns. It's not just stripes and spots. It's like these rosebud patterns and leopards and like all

sorts of beautiful interesting patterns and fish. It's it's really interesting to me that we're slowly starting to be able to find mathematical models that interact with our understanding of how the cells work, and combining those to be able to describe like how you know, say, like a puffer fish's skin ends up being this beautiful canvas of patterns. This is something which I think is really beautiful that

you see all over science. Actually, this emergent phenomena. We have rules, it's sort of the lower level to govern how really small things interact, and then you get these incredibly complex, sometimes beautiful effects at a larger scale which can be sort of simple to describe in their own

level of mathematics. You know, in physics we have like tiny particles which come together to make atoms, which make all sorts of different kinds of materials which can come together to make chemistry and life and all sorts of amazing stuff. So I love seeing sort of signs done at these different levels and seeing the connections between them.

That's really fascinating. Yeah, it's I also just love the fact that you have this little tiny fish that my memory of the zebra fish is like my first experience owning fish, Like it came in this little tiny fish bowl and like with this neon colored pebbles and it's like, here's your little bag of fish food and you feed it that, and then I like did some online research and it's like, you shouldn't have this fish in this tiny little thing, So then I got a bigger aquarium

to put it in, this like tiny cute fish. But even in this single fish who just loved munching on the little little flakes that I gave it, Uh, there is so much to learn about the way that it sells are interacting and how the math of how these stripes form that um it maybe decades before we even fully understand how the zebra fishes stripes form, so like, there are so many biological and mathematical mysteries just in this single teeny tiny fish that it's like when you

think about all of the life on Earth that would have this apply to them. It's kind of gives me a little bit of a headache, but in a good way. We might have to recruit an army of maccaque monkeys and clare chickens to help us with his research. Al Right, baby chickens and maccaques, we got, we got some serious numbers to crunch. Stop stop throwing that poo, and you

stop packing on the floor. Well, it's funny you talk about zebra fish because I had friends in grad school who are biologists, and they always had to go into the lab at four am to feed the zebrafish. And so I know that zebrafish are like a common thing in research. But when I was a kid, we had little fish with neon stripes on them, but we called them neon fish. Is that the same thing? No, there are there's the neon tetra. I actually have some of those right now in my fish tank. Those are a

different fish. I wonder if they get along or if they argue about whose bright Well that's I have actually had to both of them at the same time, and mine there was a little bit of chasing, like generally speaking, like fish can do a little bit of tail chasing and nipping um that sort of normal behaviors between like even within the same species. Like if you get guppies, they're going to be constantly chasing each other. That's how they bully each other. So we have fish bullying and

naked mule red bully bullying, naked mule rat bulling. Yeah, animals are all bullies. No, that's not the message of this this episode. The message is that it's altruism. Matth is cool and math explains kindness exactly. Matthew is love, right, matthe is love exactly. Well, on that note, thank you so much for joining me today. Daniel, Um, how about you tell the people where they can find you, because I have a feeling they would really be interested in

the stuff that you do. Well, thanks very much for having me on. Always super fascinated to learn about any aspect of science and unraveled mysteries of any part of the universe. But normally I'm a particle physicist at UC Irvine, but I'm also the co host of a different podcast called Daniel and Jorge Explain the Universe, where we talk about black holes and neutron stars and tiny particles. In the beginning of the universe and the end of the

universe and all the zebra fish in between. I like to think that some star systems are just a bunch of zebra fish swimming out in space in an infinite universe. Everything happened, so there is a fish star somewhere out there. Of course, there's got to be a fish shaped galaxy somewhere out there. I wonder if stars bully each other. Oh, I mean, they do seem to chase each other right. Sometimes.

You can find the show on the internet at Creature feature Pot on Instagram, at Creature feet Pot on Twitter. That's f F E T. That is something very different. You can also send me an email with your questions, comments, pictures of your cute animals, pictures of your zebra fish at Creature feature Pot at gmail dot com. And thank you so much for listening. If you leave or rating in review, I read all of the reviews and they make me happy and they really help out the podcast,

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