Eureka! Archimedes!

That was a particularly nice one. Thank you. I thought you were gonna say one is the loneliest number, and I'm just gonna say, what does that have to do with our podcast? Now? We're going to talk about a genius. Today we are going to concentrate on a genius, mathematical genius and inventor, one of the one of the greats. Really, yeah, we are. And in the past we have talked about many fascinating people in tech, uh, most of whom lived

in the twenty one centuries. Today we're going back a bit farther, Yeah, to the point of of two seven b C would be the the year that this fellow was born. And we are talking about Archimedes. Yes, the developer of the T R S A D. I'm kidding, he's definitely a precursor to that. Um. Yes, we're not talking Texas instruments, we're talking Greek ones. So Archimedes was a mathematician, he was an astronomer, he was an engineer and inventor. Very clever fellow, I guess that would probably

an understatement. Oh, yes, one of the fathers of calculus. Not not the calculus that we used today, but precursor again. Uh, well, we've talked about it a lot in in the past two We've talked about the principle of simultaneous discovery, where people more than one person comes up with the same idea. We've also talked about how people to have discoveries build on other people's work. And Archimedes was definitely a founder of many, many of our technologies. Yeah, you would call

him the father of integral calculus. Not not the same thing as Newtonian calculus um, which is of course much later on. So and and Chris has already made mention of one of the famous quotes attributed to Archimedes, which is, give me a place to stand, and I will move the earth and it sounds like something that a megalomaniacal supervillain would say. But in this case, Archimedes is talking about the discoveries he made and what we would call

basic mechanical structures now, things like pulleys and levers. In that case, we're talking specifically about leavers. But our Coimedes really was interested in the relationship of pulleys leavers and how they could be used to do work, and um, he spent quite a bit of time perfecting that, so much so that there are certain inventions that are are associated with him that are related in some form to simple machines, although not all of those inventions are necessarily

straight from uh, from archimedes brain. But we're gonna talk a little bit about some of the things that he did do, and then some of the things that are attributed to him that perhaps he did not do or perhaps just didn't work. There's one in particular that's pretty famous due to a MythBusters episode that we'll get to. It's one of my favorites, actually, Now, Archimedes. Archimedes his dad was an astronomer, so he was growing up, he was exposed to the sciences. Um, he was probably taught

by followers of Euclid, and uh he was. You know, what we know of him is mostly from stuff that was written well after his death, and because of that we can't be completely certain about the details of his life. In fact, there's still some confusion about exactly when he died. It was sometime around two hundred twelve or two hundred eleven b C. He was born in two eight seven b C. Remember we count backwards right, probably confuse the heck out of them at the time. What are we

coming down to? So, yeah, so and so he died around two twelve to eleven b C. And you might ask, well, how did Archimedes die? How did Archimedes die violently? Unfortunately, it was during a sacking of Syracuse, which is that was archimedes home. He lived in Syracuse, in Sicily and at the time it was an independent Greek city state. Before it it was, you know, physically uprooted and moved to New York. Yes, no, yes, not how exactly what happened? No, no, no,

the original original Syracuse. So so in the Romans were in a war with It was a Roman Carthin Carthaginian war, says Carthage, and Rome are in a war with each other in Syracuse got pulled into the middle of that, despite attempts to kind of sort of not do that, but various rulers of Syracuse ended up siding with either Home or Carthage during the the the whole conflict, and at one point in the war, Rome besieged Syracuse and during the attack a Roman soldier came upon Archimedes, and

although there were specific orders to spare the life of Archimedes, the Roman soldier killed him, apparently not knowing the identity of the man he put to the sword. So Archimedes was He was valued by both sides. He was recognized as a genius, and neither side wanted this genius to be destroyed. But as an unfortunate side effective war, sometimes accidents happened. Now why was why did people consider him a genius? Well, one was that he was making incredible

contributions to mathematics. He had found really interesting relationships between things like the volume of the sphere and the surface area of cylinders, and found out interesting ways to to kind of explain those relationships, including a very close approximation of pie um. Bye, we've lost him, haven't had breakfast? Yet. Um. So he was definitely valued for his intelligence, but beyond that,

he also was this great inventor. In fact, during the war, during the siege on Syracuse, he came up with an invention known as the iron hand that played a big part in the defense of the city. Did you come across the iron hand? Actually I did not come across the iron hand. This is different from the iron fist. Yeah, I guess the one is used for defense. The other one you rule with that. It was also sometimes called Archimedes claw. Um, it's a it's a brilliant, brilliant defense

mechanism for that time. It would not work today. But here's what here's what it was. So Syracuse was um, right up against the ocean. Like essentially there was you know, a slight cliff and then you had a city wall that that was I think twenty seven kilometers long back when it stood. It doesn't stand anymore, um, but it you know, then you it was essentially right up against the ocean. So one of the possible avenues of attack was an attack by sea, which is what one of

the venues that Rome was interested in. So, uh, the leader of Syracuse came to our communes and said, I need a way to protect us while from these attacks from the from the ocean. So what our communes came up with was an enormous lever that you would mount on the sides of the city walls. Are actually on the top of the city walls. So you have this huge lever that that extends out over the ocean. Okay, from the end of the lever, you have a rope that drops down, and on the end of the rope

is a grappling hook. Now on the other end, the short end of the lever, you put huge lead weights and you first put them near the pivot point so that the weight of the long part of the lever keeps it level. All right, What you try to do is you try and catch the bow of a ship, a Roman ship with that grappling hook. Once you do, you slide those weights back from the the fulcrum there to the very end of the short arm of the lever.

Now that weight is enough to push that end of the lever down, meaning the long arm of the lever goes up. That's the arm that, by the way, is attached to the rope and the grappling hook. So you literally pull the end of the Roman ship out of the water. You then use the lever to shake the Roman ship and eventually the grappling hook breaks off of it, making the Roman ship fall again, either smashing against the water or the rocks on the base of the cliffs.

That's brilliant, but extremely complicated. It seems like trying to to build the lever. Yeah, however, was incredibly effective. Yeah, so effective that Rome abandoned their sea based attacks. They instead of instead of attacking Syracuse by see, what they did was they set up a blockade further out in the ocean where they're not going to get hit by a grappling hook from the shore, and then they ended

up attacking by land and eventually sacked Syracuse. So while the victory was a a a good one, I mean it was, it was definitely a lauded victory, but it was short lived because all they did was they changed tactics and unfortunately the the iron hand was not as

good at defending against land based attacks good at all. Now, there were other theoretical weapons that some people say actually were built and used against the Romans during this very same siege, and uh, one of the one I was talking about with MythBusters was the the Archimedes death ray. Oh right, you know what I'm talking about here, right right, How he theoretically was able to uh set fire to the sales, Yeah, to the same or actual ships from

a distance. The idea being that he designed a device that would reflect and concentrate light from the sun and direct it at ships, and it would be so intense that it would be hot enough to to set fire to at least the sales of the ship, if not the actual ships themselves. Uh and and and at least some of the reports it was uh said that he used shields and he just polished the surface of the metal shields and arrayed them in a in a shape that would direct the light kind of very concentrated way.

So you have all these different shields that are tilted just so so that the light that they reflect all hits the same spot, sort of like the devices that you used to cook a hot dog or something like that that you used to use a camp. You know, you have your your mirror and you stick your food there, and you know, the sunlight reflects off the inside of the mirror, and except much much larger and stuff I use to fire, Yeah, anyway now that that actually isn't

so far fetched in a way. I mean, he really was interested in catoptrics, which I didn't know was a word, so I'm trying to use it and build it into my vocabulary that I don't know what it is, so please tell me, yes, Well, I actually got that word from H. Britannica's profile on archimedes Um. It is the the part of optics that works with the reflection of

light from mirrors from different types. They could be flat or curved mirrors, but catoptrics is is that, uh study, and he was particularly interested in it, so it wasn't like it was out of character for him to be interested in something like that. But apparently it doesn't so much work well. On the MythBusters episode that they made um, the MythBusters used they they actually tried to build one

themselves and it didn't really work so well. And then they set out a challenge to various groups to try and build old Um a working ur commedees death ray, and they found some success, something where it was warm enough where it could in theory set fire to maybe the sales, but it would it took time, and you know, you had to worry about it being the right time of day for you to be able to do this, And it would really depend on the ship being very

uh well complicit in the burning process, in the sense of if the ship's moving around a lot, then you have to be able to move the ray so that it stays on the same general area in order to keep increasing that temperature until it reaches the burning point. And if the ship's moving, then you may not be able to train the ray on that on that uh moving target fast enough to be able to um to actually get the temperature hot enough to for stuff to burn.

So it's even if it were an actual weapon, it was not necessarily an effective one, not like the not like the the the lever that he had designed, which was to monsterly effective, effective enough to make the Romans change their tactics. Now, there are also other interesting inventions that we attribute to our commedies, one of which is uh that that he probably did make were planetariums. Oh yes,

they were also called spheres at the time. The Archimedes spears, and it was if you don't know what a planetarium is, a planetarium is essentially a geocentric model of what the h the stars and position of planets in the Sun and the moon, what what it looks like from the perspective of Earth. You know, it's a it's an earth based view of the the galaxies around us, the universe essentially.

And so Archimedes had apparently built one of these possibly that used interesting little gears to mimic the motion of the planets and stars and constellations to keep everything aligned properly and making the move the way they actually do through the sky. And uh, he built a couple of

these apparently, although both of them have been lost. There were other devices that have been recovered since then from shipwrecks and things like that that may either be an actual example of the spheres of Archimedes himself built or maybe built on the same principles that Archimedes used when building his But that's that's one of those things where we have we've heard the record of him building these things, and he certainly had the intelligence necessary to be able

to design such a thing, we just don't have the physical proof of it. Um. Yeah, there was a treatise that he apparently wrote called the sand Reckoner that had to do with um astronomy and his astronomical thought. He actually had had been able to sort of using his tools of his time, he was able to get an eye a reasonable idea of the diameter of the sun, um, you know, through his uh using instruments to observe this.

And this is of course long before people that we sort of associate with um astronomy, you know, modern astronomy, people like Galileo UM. You know. There he was really sort of in a groundbreaking category in this regard. But all there were others who who worked with these principles to um. You know, his work went into uh, several others as well, but UM, I think it's sort of disappeared for a while. UM. And they were the kinds

of things too that stood out. People like Plutarch, the uh um you know, who wrote quite a bit about the famous people of his time, categorized archimedes work. UM and he's you know, these things were well enough documented that he was able to to pull this out. So yeah, I'd like to talk about another real quick legendary Archimedes moment um. This would be another great quote. Yes it does. It has to do with the bathtub. So this is again a possibly apocryphal story. So in other words, this

this may not be true. In fact, I think a lot of historians put this in the realm of legend for for many reasons, one of which is that the solution Archimedes came up with was actually not as not as difficult to to get to as you would imagine. So, in other words, it seems like it's too easy an

answer for Archimedes is almost the argument here. But the the situation was that you had the King of Syracuse who had commissioned a a golden crown, and this golden crown was made, but the king was suspicious of the

golden crown. He thought that perhaps the person who made it actually used silver to make the crown and then coated it with gold in order to UH to cheat the king out of money, essentially because silver was less precious than gold, and therefore by using gold silver in the crown, he could make it for for less money than it would cost him uh to to gather all the materials, and thus have a higher profit. So how do you figure out if it weighs the right amount

for a crown of that general size? Um, how do you figure out whether or not silver was used? Well, silver doesn't weigh as much as gold does. So in other in other words, in order to make a silver crown that would weigh the same amount as a gold crown, you would have to add more silver. Right, So, if you had a cube of silver and a cube of gold that were the exact same size, the gold would weigh more. So in order to make the cube's weigh the same, you would have to have a bigger cube

of silver. Right, So that was that was what Archimedes came up with. He came up with this adea of well, if I use the amount of gold that it takes to create the weight of this crown, let's say this crown weighs let's just say ten pounds. Okay, okay, So for the argument's sake, this crown weighed ten pounds. So what our community said, Well, what if I get ten pounds of gold, and then I use some way to determine the mass of that gold, and then I use

that same measurement for the crown. If the measurements the same, then we can come to the conclusion that the gold that is gold in the crown, if the if it's different, then we can say that maybe there's a different material in here. So what he did was he took a bath. Yes, so this all has to do with the displacement of water by putting the the and again we're just using

this this measurement out of for for simplicity's sake. Putting ten pounds of gold in the bath, he sees how much water is displaced, how far that water is displaced in the bath, and then putting the crown in there, he can see how much water is displaced from there, and the the amount is different than he knows that the two materials are not the same. And supposedly he became so excited by this discovery that he ran out of his home. Starkers, I'm that's not a joke. That's

part of the legend. Know that that part is not what's cracking up Starkers. He was naked as a blue jay running down the road, turning into my kinfolk here. Um so anyway, yeah, completely nude, running down the street and screams out Eureka, which means I have found it also is a quirky, uh dramatic comedy on the sci

Fi network. Yes, that is anyway, So Eureka, that's that's where we get that when when you have someone who makes a discovering screams out eureka, they are essentially paying homage to Archimedes, which, again, since this is a potentially apocryphal story, we might just be paying homage to a legend. Well, apparently the bathtub part is what's probably apocryphal, but the

crown part apparently is true. Um, they do. They do seem to feel, or at least Britannic Adust seems to feel that that that he was asked to determine whether or not the crown was actually gold apparently really did happen. Yeah, and and then you know, you would want somebody like Archimedes to do this because he was thinking scientifically in

this case. And the reason you might say, well, why don't they just scratched the crown and see if they're silver and they bite it like your coin, right, Well, the problem here was that the crown was considered to be almost a holy relic. It was because you're the kings of the Greeks were they would trace their lineage back to God's and so you couldn't destroy the crown in any way because that was an front to the gods.

So he had to find a non destructive way to test this without you know, without actually causing any sort of damage to the crown, which makes it way more difficult. Um. And then we have another object that is attributed to Archimedes, although it's very possible that it actually predates his lifetime and it's just that he observed it and then was able to apply it elsewhere, which is the Archimedes screw. Yes, you know, well, how could it not be Archimedes invention?

It has his name right there in the name. Well, yeah, McDonald's isn't named for somebody named McDonald, so you know there's a name. A name is is a tricky thing sometimes, but yes, he did. He did observe the principle that uh, you know, the hydrostatic principle using using the screw to raise water, which sounds counterintuitive at first until you realize

how this is implemented. It's actually a screw that is, in general, the screw is encased in a tube and then you lay it in a at an angle whereof you know, one end is raised at the top and the other end goes into the water. So you've got one end that that descends into the water, and you have one end that's above the water level. You start turning that screw and what it does is it scoops the water and the water travels up the screw just because of the principle of the screw as you turn

it within this tube. Now there's you know, you might have some leakage issues where some of the water leaks back down to the next level down. But as as soon as you start turning that screw in a nice clip, eventually the water starts coming to the surface, and the the speed that you turn the screw will counteract the

leaking problem. And since it's just leaking to the next level down, it essentially becomes a non issue once you get to a certain speed and you can actually lift water out of out of a body of water that way, and this was often used in our commedes time two pull water from say a lake and put it into an irrigation system. The Greeks and Romans were both very

big on irrigation. Yes indeed, um, yeah, Actually that reminds me of there's an infant toy that has three or four little plastic balls and there's a screw inside and if you push down and it's encased as you said, in it and not in a tube. It's actually sort of a it's not conical, but it does get narrower at the top than it is at the bottom. And when you press down on the plunger in the center,

it makes the screw turn. And the faster you push it, the higher the balls climb up the screw until you stop,

and then they know spin back down. I mean there's you know, not hydro static, there's no water, and but yeah, it's the same kind of thing, and you can sort of if you've seen that, that's you can sort of imagine that because it's you don't often see an archimedes screw in practice, although you you you can see them in practice if you were to go to certain hydro electric plants, they would be used in practice in reverse because then what you do is you turn the If

you happen to pour water on the top of the screw, it will make the screw turn. So you know, turning the screw will bring water to the top. But if you pour water on the top of the screw, it makes the screw turn, so it's the reverse action. Well, that means that if you are able to position the screw so that a flow of water is constant on the top of it, then the screw will keep turning.

You can make that screw to work. You can have that screw uh use you can use it to drive a generator, an electric generator, and thus you can create electricity from water. That's just one way. I mean, there are turbines as well. I mean, it's not the only method of of using water to drive an electric generator, but it is one way. Yeah. I was actually thinking of the Tesla turbine when you mentioned that, um, which is also a fascinating thing. We have an article on

the website about that as a matter of fact. Not it's not using the same exact principle, but it's also a way of using water to to uh to turn a turbine. That's not, you know, something what I would think of a typical But anyway, I digress, and we again we should point out, I mean, we've mentioned it a couple of times, but it bears repeating that they the actual Archimedes screw. There are at least some indications that this was being used in Egypt, uh well before

Archimedes ever had his name attached to it. Yeah, completely by chance. Um A few months ago, I was reading the uh the Biography of Cleopatra by Stacy Schiff. It's very popular there for a while, UM, and I hadn't really read a lot about ancient Egypt. But he Archimedes was actually in contact with, uh, some of the scientists in Alexandria, which at that time, Alexandria and Egypt was probably the world center of learning, or at least one

of the top uh centers of scholarship, you know. And um, he apparently was was in contact with them and had spent some time in Egypt before he went to Syracuse. Uh. So it is not at all unlikely, um that he wouldn't have you know that that he would have had contact with those uh, those scientists over there and gotten some some cool ideas, you know. And he also was attributed with the creation of a game. Really yeah, did

you hear about stonemacheon or stomachion. I have heard of it, but I didn't realize this was this was related to our comedies. It's attributed to him. It's a it's a game that you play with these different shapes. It's almost like having a puzzle in a way, like these shapes. If you if you put them all together in one way, it will create essentially a square. But the idea is

to use those shapes to create other recognizable shapes. And it's really an exercise and creativity like seeing seeing the potential of geometry to build um shapes that are more organic, so things like you use them to build a tree or the example I saw was an elephant. Um, which is kind of it's just kind of interesting. Is the idea that you have to use all the shapes in the group to create a recognizable object, an interesting object.

And uh so that's also attributed to Archimedes. But again this is another one of those attributions that we can't be completely certain is accurate. It's just one of those another another interesting thing of something that Archimedes may have had a hand in. Um. So shapes actually yeah, um looking for something. Darn it all right, hang on, well, well you look and then we will pick up alright,

speaking of shapes. Um, you know, he was he was involved with many He published a lot of his work, and there there is an indication that he may have had other work that he either didn't publish or that was later lost. Um. Again, there's been a lot of time that has passed now since he is he has left us. But um, one of the things we do know that he was fascinated with shapes. Um. He was able to, uh to figure out the surface area of a spear sphere of radius r. Remember this back from

your mathematics classes. I have a vague memory of it. Yeah, yeph s equals for pie r squared. Yeah, and the volume is two thirds of the cylinder in which it is inscribed. H v equals four thirds pie r cubed. I have not had to know those those formula and so long, but they came back to me as soon as I saw that. And apparently, uh, he was so excited about this that this is actually, uh what his

tomb was arked with. Marcus Tullius Cicero found his tomb, which had been overgrown with uh greenery, let's say, and um, probably about a hundred and fifty years or so after he died, and found that his uh, his tomb had been inscribed with a a sphere or had been marked with a sphere inscribed in a cylinder. And that's uh, I just think that's fascinating. I mean, going back to what I learned about geometry and um uh calculus. I

think of people who came much later than that. But you know, in general, but Archimedes really had a huge influence on many many other people. Of course, his writings were known to uh, to the Arabic world. A lot of a lot of scientists and mathematicians from that era in in later centuries were able to take his work and build upon it. Um, and it's just uh, it's just cool stuff. He also did lot with with mathematics as it was, you know, working on place value systems

UM and lots and lots of different things. He wasn't he wasn't. Uh he was, I would say, polly mathic. Yes, you know, somebody who is is um well, has has knowledge in multiple areas, very knowledgeable about a variety of mathematical and science topics. And we'll probably talk about other individuals who fall into that category as well. Um for example, I eventually we're gonna have to do a full profile

on Leonardo da Vinci. Yeah, because but that's another famous polymath from from history that that you know, really was instrumental in the whole idea of of invention, you know, really embracing that part of genius and uh, I would say Archimedes was a great you know, uh forefather of that of invention as well. Now granted, he's also a very good example of the the raise uh necessity is the mother of invention. When you've got romans attacking you, you find it really necessary to find a way to

make them stop. And then he wrote that song you know, fifty Ways to Love your lever. Alright, So that wraps up this discussion on Archimedes. If all of you folks out there have in a particular people you would like us to come straight on, either in the deep past or even modern day, whichever, let us know. You can send us a message on Facebook or Twitter. Are handle there is tech Stuff h s W or you can email us. That address is tech stuff at how stuff works dot com. Chris and I will talk to you

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