 Okay, I have 10 o'clock, second lifetime. What would kind of be interesting is if the second life had been created in another country, instead of it being Pacific time, now it would be some other time or universal time or something that would be interesting. But, since it's with San Francisco, it's 8 o'clock. Okay, today I am going to present at 2 a.m. Yes, local time. Really? Okay, I did a presentation earlier, by the way, for people if they were able to. Oh my goodness, okay, all over the place. It's galactic standard time. Okay, have a Mars time, right? Okay, so today I'm going to present on a topic that's been fascinated to that I have found fascinating for some time, which is the idea of analog computing. So the first thing I need to do is kind of look at what we mean by analog and digital. This is a computer today. And I will talk a little bit about what we mean by digital computer. Now, one of the reasons we're doing this is first of all, welcome. We haven't done this, perhaps for a little while, but if you're new to the Science Circle, welcome. And we present people all over the world do presentations to people all over the world. Yeah, there we go. Okay, so digital one and zero. Now in the case of digital, it really means discrete numbers. So in the case of computers, it's binary ones and zeros, but we could mean simply numbers and nothing in between. In other words, a two and then a three and nothing in between and that would mean digital. While you're right, it goes back to fingers and toes, although we've had other bases. So for example, decimal is base 10. Although our time system and such with 60 seconds, 60 minutes is back, Babylonian is 60. And then you've got what's it called VESA digital or VESA decimal base 20. So I'll talk a little bit about that. But in any case, the computers today are based on digital system, particularly binary, particularly electricity on an off. Yeah, there you go base 60 and then what's the there's a there's a vest of whatever base 20 that was used in the Americas and also by the Celts. So any case, let's distinguish between thank you, let's distinguish between digital and analog. So let's just say this is a digital computer. And one of the things we're doing by the way in the science circle and here is, well, analog to me when I think of analog is, and I'll show you here is this is analog. In other words, continuous movement, each increment of movement means we think of it as mechanical because analog is a, well, there's digital and analog but analog is a very natural sort of thing where continuous movement and every part of that movement has meaning. Whereas in digital devices only, as I mentioned, only specific increments like numbers have meaning and anything in between is not. Yes, and we're actually going to talk about that a little bit in other words up until around the 1970s. So any case, one of the things also about us being here is that we have to understand how these systems work or somebody does anyway, because if digital computers are very nice. The business model and technology have advanced to the point where all we have to do is our fingers click and move and drag and such and so billions of people are able to work with them without any understanding whatsoever of what's going on inside. But somebody has to understand what's going on inside in the days of in these days when we had watches and stuff not everybody had to understand what was going on inside but the designers of analog devices like this fine watch or other devices that I'll talk about had to understand numbers, relationships between them, translate that into physical distances. And I as someone pointed out the last time or the last presentation it was really quite actually the presentation today is about the difference between analog computers and digital these guys right here. Okay, so we're going to be talking about more like the ones that look like this analog devices over the years. Yeah, exactly. Okay, so let me show you a simple device now you could think of this is what is this digital or analog I like the commentaries from the audience there. This digital is this analog. Yeah, okay. Okay, that may be more precise is, yes, the definitely the concept is digital. And I'm sorry I can't read that but I like it that you're talking in another language I wish I could read that. The only reason I'm talking in English is because I can't read that or speak it. Otherwise I would love to be able to do this in more than one language. I hope some of you guys will as a matter of fact, well, let's let's say that it's a mechanical device but the concept is digital what I mean by that. Well, first of all, let's look at what this is. This is a device that's been around for many years in fact, a couple thousand years. Because one of the things is if you look and yes it is a decimal system. In other words, it has numbers from one to nine at least. By the way, it doesn't have a zero zeros were not invented back in the Roman days. It was invented basically Hindu, it's a Hindu invention of the. I think about 1000 years ago somebody want to look that up when the zero is invented bank case if you look, there's a replica on the upper left of an abacus from the Roman Empire. So these are not recent devices and they're also worldwide you can see they're from lots of different places. Essentially, let's take a look at what they. Yes, I think so too. Essentially, let's take a look at how these work by looking at the one on the bottom right and you can see how clever it is essentially what it is a mechanical device so what it does is it uses. Particularly the width of the not with I mean width along the excuse me height with whatever the width along the. The line that contains the beads or the counters on there. So if you look on the bottom right. So the configuration that is used in Japan, you'll see that if you also with gravity if you leave it like this and all the counters. Well, maybe not gravity. Okay, bank case if you look at if you leave the counters the way they are on the far left that those are zeros. If you want to represent a one, you just click up one against the stop in the middle, and you don't have to worry about fine movement you just click it up click. Okay, if you want to do it to you click up the next one if you want to do a three you can see that in the third row from the left there 123 click click click. And four of course would be four up and then the real clever thing about this one is that if you want to do a five you just take the whole thing and when you click it down starting from the top. And so the top one becomes a five and then the four that were above it get clicked down you can kind of imagine this and then you go six. In other words you leave the five down and you go click six seven eight nine 10. I've actually seen the one I saw an action was looked a lot like the one to the bottom left which was I was in Russia about 20 years ago, and they were using abacuses in the store in place of calculators. And that was, and I, and they were very fast. I mean, people with, with abacuses can calculate as fast as you can on a little pen held calculator, or on possibly your iPhone or something. And I was quite amazed that they're able to calculate the basic things you would need for in a store. Okay, so this is a device from many years ago. And essentially, like I said it's a mechanical device but it's really a digital calculator. So let's take a look at this next device. Anyone seen this before anybody recognize this. I've got the name up there but really what that is is that me that's a device that was found in an island off of the Greek island of Antica, which, by the way, was opposite Katera Island. That's what the anti Katera means. Anybody know how old this is. Yeah, this is definitely an analog computer. It was pretty sophisticated. Yeah. It's around there. In other words, they think it's around 100 BCE. So that would put it at what 2100 years or more. But that's amazing for device like that. Now it didn't look like the one on to the right, the bottom right obviously that's a reproduction of it right now. Unfortunately, it looks like what it looks like up upper left, but using x rays and a bunch of other things they found out that oh my goodness. This is a very sophisticated device that used to look like one down to the bottom. And the actual diagram in the middle there shows how the different gearing such worked in it. And as an analog device that are very interested in the movement of the sun and the planets and the moon and such. And so this one actually is able to track and depict where the sun is. Well, for astrology and lots of other purposes. Remember that the word is that astrology was kind of the study of what's out there beyond us before the scientific astronomy came around. And so you've got, but also the idea that the planets and extra terrestrial bodies ruled things on earth. And that's how they have the names of gods and goddesses we were talking about that in trivia just recently here. I mean in some of the trivia questions. So, you've got this device, able to track and depict the path of the sun and the planets and the phases of the moon so they understood relationship wise that if you could track where the moon was and the phases and where the sun was and such you could also predict solar eclipses now that was pretty special to be able to say tomorrow the sun is going to be have a shadow in front of it from the. Excuse me. Yeah, from the moon. They could also predict equinoxes and solstices. There was a calendar in here the Olympic years. So this is a very sophisticated mechanical analog computer from that time period. Okay, let's take a look at another one and see now this is one that not that many people know about anyone seen this one before the word keep who is actually a. I've got a bunch of text here that I have been failing to put here so if you aren't picking up everything that I have, or that I have been saying I could have been putting it up there. So now they have also discovered fairly recently that the ancient Chinese and Hawaiians also had different not systems keep who in this case means like not or talking knots. So the devices had meaning both in color and position. Now think of what it actually did is that for example this was a database it was almost like yeah it could store data anyway. And so this was like a database is for example what if you wanted to go around down a road, think of the think of that baseline piece of rope as a road and you go down the road and you meet these little villages and you go into the village and you count how many young men there are for the army and how many sheep they have and people and so you can do tax records and census records and store all kinds of information, depending on the knots and how many where the positioning of the knots and there was actually a numbering system based on where the knots were along the rope and such it's very sophisticated for the day. And this was down in South America. Yeah. Okay. I didn't know about that. That's that's good. Thank you for sharing this device anyone familiar with this one. Well, now that's that's an interesting point, Castle is that the origin of writing. I was thinking about that myself. And since I have a moment here I think I'm a little head, because I didn't put the text earlier, but the actual origin of writing, if you look back at the Phoenicians and other peoples of that area at the time is that and some of the earlier empires, Babylonians and well, much earlier and that Samarians and such is that. Yeah, exactly, is that writing began kind of in fact actually if you don't mind, let me just pop in what I know about it is that the is they needed to keep track of things for their own purposes like taxes and whatever. And so they would make a little clay ball and or vessel and drop little clay balls into it and then seal it and that became the first kind of record of those sorts of things and that would represent the number of people in a village or something. And then, instead of making the clay vessel with the little balls and dropping in it which is kind of a difficult because how do you get to the balls you have to break open the little clay vessel and you know it's, then they decided to make symbols for a horse or for a person or for whatever it is they were fishes or something. And those then they could press onto clay rather than to make the little clay balls, or they could press on to the clay container. So now all of a sudden those little symbols represented animals and at some time, some and the and the symbols at one time looked like the animals or the objects and then pretty soon the symbols became basically represented the sounds of the objects and much like we have today and in at least English and relate related languages is that some of the symbols actually represent the sounds, rather than the objects but in other parts of the world, the symbols represent the objects as well so yeah, yeah like the hieroglyphs that was kind of another thing but that's very interesting I'm glad you brought up the idea of language. Okay, so this particular device was, as we've mentioned before this one was like the anti cathedral device this one was analog. What we mean by that is that every movement has a meaning that is you move it a tiny little bit and it represents something. Well, there were digits because you're talking time. And when you're talking time or you're talking specific places so you can't really distinguish it's kind of hard at all of these overlap a little bit, as far as whether it's pure. Exactly. That's who. So I'm not going to, you know, from the semantics of whether it's a particularly analog or digital but the idea is that since you're talking about analog objects like astronomical objects. Those don't like click like seconds on a clock that you don't just see Mars going, and then it goes over a little bit. It moves in through the sky in a continuous moment. Good, good for us otherwise the earth would be, you know, would be jumping every a little bit. In other words, we move in a very smooth pattern. So, like the Antikythera device, the Astrolabe was used for astronomical observations, which were then used for navigation I'll consider people that travel back and forth between Asia and Europe and Northern Africa and such is that essentially they needed to be able to find latitude they need to be able to find have some idea where they were in a day and night and so they use devices like this in order to be able to do that. Yeah, there you go. In order to be able to do that and one of the things I find. Well, actually the Astrolabe then became the sex or the the later version of it became the sextant. I think when you're talking about Captain Sparrow is probably now that's course fictional and character there in Hollywood movies but used a sextant which was kind of a later version of some of these. Now what's interesting I think about this also is you is the cultural aspect, you could actually see that first first of all the devices all dependent on gearing and such you can see one of them broken apart more or less on the upper right and the gears there, but you can also see that the development began in the area that kind of was in the middle between far Asia and far left. Or far west Europe and the device was passed on particularly since the Islamic world had the one of the big cities of knowledge of the time some of the cities in the in that area including Baghdad and stuff while Europe was somewhat in the still in the backwater is that there are also people Jewish people who were not welcomed in Europe but they were in the Islamic world or at least accepted in the Islamic world so they were able to shuttle back and forth between and help to bring some of the technology from the Islamic world and then of course by nature of the Islamic world being between China and Europe, being able to bring knowledge back and forth, in addition to things like spaghetti. As mentioned that last time, you know, and spices, other things. But in case if you look at the chronology on there, you've got the early versions and then for other versions and then the European versions in in the middle ages and into the Renaissance and they're I found one here there's an Iranian version in 20 that was made just five years ago. And they were also used for astronomical observation and then for navigation because you where they were. Yeah, I'm, yes, all of the things yes all over that world that I think one of the things they're finding is more and more that there's a lot of cultural back and forth, maybe more than realize sometimes. Okay, so this device is a little closer to the modern time period. Now, this one itself also has a some stories associated with it and let me put some text up there is essentially. Yeah, Ada that exactly I'm I included both people up there because I think that's important for one because I think some people who are important to history have been overlooked by people who write history. And the other part is because she actually played a quite a part we usually think of this we usually call it the Babbage engine or whatever, but they both played a part. And let me tell you a little bit about it essentially 200 years ago when industrial machines were starting to be used in the first areas that were part of the industrial age is that he designed a device for calculating polynomial equations polynomial that were used for approximations of all kinds of numbers. And the only way else to do it was long hand calculations, in other words tables of numbers for logarithms and trigonomic metric values and stuff helped engineers and astronomers and others in order to create some of the machines they needed and calculations they needed. Okay, how many people here you can raise your hand I won't see you in second life there. But you can raise your hand. How many of you guys have gone to tables of numbers whether trigonometry logarithms statistics. Yeah, me too. And it's still used in for p values and stuff in statistics I mean technically you can run those out yourself. But we still use some of those tables of numbers, and creating tables of numbers back then we didn't have a computer to do it or calculator. So it's done by hand, and anything done by hand that's time consuming like that to create a whole book or tables and numbers out to however many decimal places. That's a lot of work. So the idea is that Charles Babbage wanted to create a machine that could do it for you so you could have one of these machines and do it at the time you needed and so now he was a little bit ahead of the time. So, actually, he was only able to do a scale model of what's called the difference engine which is the one on the left was built in his time but a full scale model was required too many gears too much precise machining, all that stuff so it wasn't actually realized in his time but people after he died started working with it now where does a love ice come in. Well, so Babbage thought of this as a machine to help people to generate astronomical calculations he was he did astronomy and other things, as well as tables of numbers. But a love lace when she looked at particularly the drawings for the analytical machine which was never built. But, well, that's a replica there on the modern replica is. Yes, there was. In fact, as a matter of fact when I was in the military in the 1980s, Ada or was the accepted language. Computer language. Okay, so any case what she looked at is she looks at these machines. Yes. And she looks at these machines and she goes, Oh my goodness. A general digital computer can become a thinking machine. This is more. And so she was also in addition to writing some of the first instructions for how this thing works in other words she understood the principles and wrote them in a way so other people could understand it. Is that while Babbage is credited with being kind of the father of the first digital computer a love laces credited with being the first computer programmer, and also the first person to realize the, what the potential was of general digital computers. So she was probably 100 years ahead of her time as far as that goes. And actually this next one is something I didn't know about. I thought I knew about most of these devices but when I was doing a little research. I found this, because I wanted to find what was between say Babbage is machine and IBM. And I found out, first of all, let's take a look at the machine in the middle. That was called a Pascal calculator. Yeah, there you go. And while, and I don't know whether it was sophisticated, kind of like the one in the middle. In other words, I know it had gearing and such. And it was based on a what's called the Leibniz wheel, which is a stepped wheel that you see up to the upper left. In fact, all calculators pretty much mechanical ones, even up until into the 20th century, had those devices in them to be able to step when you basically crunch the numbers. In other words, things went around and they stepped and moved up numbers and such and that was developed back in the 1600s. They do. Now, the thing is with the, this is definitely digital. And it's definitely, well, okay, it's mechanical digital. It's, but it's definitely decimal. In other words, 10 digits. The thing, excuse me, the thing is that, I don't know, you can figure that one out. The thing about this is that unlike that big unwieldy machine that Babbage had developed, or thought of this is, this is from 1850 to the about 1800. And this was something that as you can see, this is kind of like the laptop of calculators, so to speak, back in the 1900s, or 1800s, is because you could actually, they were inexpensive enough, and you could, yeah, you could do basic arithmetic and stuff and you stick that you do the little sliders and you could do big multiplication problems and all kinds of stuff like that for about 50 years. And then the last company that made one of these, I read, went out of business in 1915 probably because you know, we're a year up in particular was pretty occupied 1915. And then you had basically well let me let me throw up some of the text here because I'm talking talking but for people that have more visual backup. This was called the arithmometer. And it was used in from run thing now. The reason why you don't see these after World War One time period is it was superseded by calculators that were developed by companies such as the International Business Machines IBM in the early 90s. But, and I mentioned that the key to the working mechanism of computers was this, excuse me, was this Leibniz wheel that was actually designed in the 1600s. So that's rather interesting. By the way, does anybody know how IBM came into being some reason I've got a little more time than I had on the first presentation I think because I had like a here again I if I miss the text. I may miss some of the things I need to or would like to say okay. I didn't know that one, but essentially what I tell my students because when we go over the development of technology and such is that you can look it up let me see I probably have a minute to look up a couple things here real quick. Does anyone know about this let me give you a, you know, give you a little. Okay, I'm going to do Wikipedia here I don't use that for everything but it's a good general thing. Does anybody know about what's called the jacquard loom. Yes he was the other contemporaries, essentially they co invented calculus and things like that okay so the jacquard loom was the first device, and it was early late 1700s and what that device did is essentially they said, Okay, just like some of those earlier devices is there I mean, in order to weave fabric you need a person and you need a skilled person programmable exactly so you need a skilled person and so couldn't we do this with a machine. And so the card in France made punch cards and they stuck the punch cards on the machine the punch cards programmed what the weave would be voila you could. And that's a is voila okay not okay whatever so any case you you make the pattern on the on the weave, you could do it for inexpensively you don't have to have skilled labor and like a player piano exactly. And so you are able to make any more inexpensive items and etc so I kind of set the whole chain in motion. Well this particular punch cards were later created by, or there was a immigrants the United States name Herman Hollerith, and he, let me see I'm looking up his little computer here I'm looking, I'm looking for a Hollerith cards, punch cards, okay, but in case he is punch cards in order to store data. And there we go. Okay, you can look under if you want you can look under here but he's it to store data, and particularly for census in the United States in the 1990s. And when they had to go around with like pen and paper, they took them seven or eight years to tabulate everything which in the United States the census is every 10 years and they're going. Oh my goodness by the yeah that's how I started programming with punch cards. So they go my goodness you know by that we have so many immigrants coming in that by the next decade for example it may take quite a long time to do the census. And so he goes, Okay, I, immigrant, Herman Hollerith here. How about these little cards and so he did he created a machine to read the cards of course people had to punch it in and able to do the census in about two years whereas it took three years or three times that earlier. And then he created a company with the punch cards and he merged with another company and the bottom line is that the company became international business machines, which was IBM. Okay, not everybody knows that background to but kind of interesting. So, in the early, so 100 years ago you had companies like international business machines and let's see what was a digital. I was trying to think of a couple other ones that did the electronic, excuse me first the mechanical calculators and then the electron electrical ones and such like that. So now, in the 1930s and 1940s when we did. Yeah, exactly DC. Perfect. Yeah, that's what I was looking for is. Yeah. And so here's just an example of how these analog or let while it's not say analog computer anymore these early, early types of calculators computers were used for different purposes. The most probably most known is the one up at the upper right, which was used by the way in the 1920s I learned that it was used machines like this were commercial machines that were invented in Germany used for commercial purposes. But by the 1930s with the enigma machine they also enigma was a company, and they made this machine for encryption and decryption. And then, in order to decode those encrypted messages. The US and British worked on machines in order to try to decrypt the message and you've got the American machines as I understand them yes exactly that was the the movie that I'd forgotten about the name. The ones down at the one the ones in the United States were destroyed but the one down on the bottom is a picture of one from British by the way the word bomb BOMB. They come from the same word does anybody know why it's called that that's kind of an, in fact, how come the explosive things called the same thing. How come there's a dessert called the same thing that may give you a little more clue. It refers to the I know actually it refers to round. So what you have down there is those round cylinders. And so, yeah, like that. There you go. And you. Yeah, exactly. I'm just glad when they're, wow, maybe boom also but the cylinder there you go perfect that's why I like to have people from different languages and cultures because we usually can come to the easily share our knowledge. You can see a reconstructed machine down there on the right and essentially these things as if you saw the movie you can see them you know click click click click click and trying to reconstruct or D. Okay, and then the upper left, you've got a northern bomb, northern bomb site and what that one did was that was a analog device that told the pilot or the bombardier went to well bombardier really went to release the bombs and it was, you had to have wind and the speed of the airplane and where the bomb is supposed to hit and stuff and so it was a more precise way to bomb a city than they had before, which was very imprecise. Okay, and then it brings us to this device here which some people in the audience may have used anyone happened to use this when I went first went into college. I had one of these not a calculator because it was before electronic calculators. Okay, yes slide rules, and there are various types of slide rules some are used for in airplanes, or at least back early air airplanes, where you put in the wind speed and the distance and the gas and all that you could figure out whether you're going to make it or how much cash you had to have. There's one down there on the bottom right which calculated nuclear radiation, an old one up on the upper left and then one that is a more recent version on in the middle of the yellow one. But these were invented back there is for 350 years and they're invented. Yeah, back in the until the 1970s when you had electronic calculators now. I'm going to show you something here if you give me just a second. I'm going to pull something out from behind the screen. I built this earlier. This morning, and it's kind of cool I think. Okay, this is a you can do a copy of this this is a working. So let me let me pull it up a little bit further I think you can get a copy of it let me make sure I got all the pieces here while I'm doing that. So it works. There's three pieces to it if you want to make a copy. And I'll show you how these worked. Yeah, okay there we go. So let me step back a second so I can see this thing. Okay, now the other thing by the way if you don't get everything the way I'm saying it right now this the textures I had for for making this come from here. And this and you can actually see on this website that you can move this is a virtual slide rule online, and you can move the slider around and you can move the middle piece around the same way I'm going to do here in just a second. Yes, it was made in Japan, but and apologies to people because this is at the time this was not very. It was considered insulting is that if you look very carefully it says made in occupied Japan what that means is this was. I had read I read between the two time periods here that the US forced Japan to put on about 50% of its goods they had to put made in occupied Japan rather than made in Japan. And so apologies for that I didn't even notice it said that until recently got politics. But in case let me show you how this works and if you want to see a video for how this works is, you can go to a video I made five years ago that show how a slide rule works and I think I use the same one five years ago. Yeah, 2D digital representation of 3D object. So let me show you how this works. And what I'm going to do is I'm going to do a couple simple ones you can do logarithms and trigonometry and stuff but what I'm going to first do is I'm going to do squares cubes, multiplying and dividing. See the squares and the cubes are rather easy. And so those those I'm going to do first is essentially what you do let's do a 4.7 squared. And what I need to do is let me see get some windows out of the way here, and I got to zoom in. But what I do is I go to and adjust my camera control. Okay, so what I do is in order to make this work is you go to 4.7. Let me put it in the screen since I got a little bit of time here, because let's calculate 4.7 to the squared. So the first thing you do is you take your cursor and you put the cursor on 4.7 on the C scale. So the C scale is the one, the bottom one of the middle area. So let me see I'll adjust this to 4.7 here. And then what you do is you can read it directly in other words right above it on the scale that says a B scale which is two ones up or the one if this is the middle line right here see whoops not that one. You can read it and it says 22 and indeed 4.7 times squared is 22. The other thing is like if you wanted to do 4.7 cubed you go up to the B scale on here which is the or excuse me K scale. So what you do is 4.7 on D here. And then you read 1.04 on the case scale, which is above that. Yeah, you can actually go back and look at my video and I do the same thing in my video here or play with it yourself. And the reason and then it says 1.04 but since basically if you kind of you have to use your head a little bit but if you go five times five times five that's 125 so 101.04 it must be really 104. Now there's people had tricks like this in order to to make it to come up with the right calculation. I think that slide rules were not for precision but you could have at least a what's called three significant figures in other words at least two or more significant figures two decimal places in some cases. So let me also show you say how to multiply and I'm going to put the text on here so you can follow it because it's a little bit harder. You want to multiply 2.3 times 3.4. The first thing you do is you line everything up like it is, and then you do to point you find 2.3 on the D scale by moving the little cursor here so let's move this to 2.3 on the D scale which is right. Right there. Okay, got it. Now this is a little little trickier follow it here is what we're going to do is we're going to move the center not the slider. And so what you do is you move the 1.0 part this is for doing that 1.0 in order and you move it down to where it's over 2.3. So let me see I gotta zoom in to look at this thing. Yeah, okay so where it is right there 2.3 got it. And then you go over to the. You move the cursor to 3.4. See if I if I done this every day it would be the same way as people do stuff with or with computers these days and you wouldn't have it wouldn't be as awkward as I'm doing in other words this would be just second nature the same way we do with computers these days and then you move it over to 3.4 which is where's 3.4 3 point well there's pie the 3.4 must be there and then you read down and low and behold if you actually look at the number it read 7. Actually, let's see am I reading this right 7.8 on the line D. Okay. And that is the answer to what we want in other words we're multiplying 2.3 times 3.4. Let's try one more. And what I'm going to do is the first thing you do on most these ones is you go to the middle scale and move everything back to where it all lines up on the left there so we line everything up here in the left. Got it. Okay. And what we're going to do is we're going to divide 4.5 by 7.8. And so what we do here is kind of backwards a little bit but essentially you put the cursor on 4.5 in the D scale. Where's 4.5 looking for 4.5 the D scale which is here. There's 5 yeah 4.5 the D scale and then you move the middle bar so that 7.8 the one we're dividing by is over the top of that. So I've got to move this so that 7.8 is over the top of that. Let's see where's 7.8 is over the top of that. And if you read carefully over here you'll see that the answer comes out as let's see 5.65 or 5.66 or so. And the actual number is 0.576 I think if I did it right or close to it. Yeah, so you can actually read to a couple decimal places or even two or three depending about three significant figures, which is pretty cool. You know, I think that is most cool, particularly if all you needed was somewhat of a rough answer. Okay, so now so that was used here again I like I said I used it when I was first going to college. Okay now let's take a look then about how let's take a look about how computers are used today. In other words the modern computer digital computer and really it's quite simple. See if you can follow this otherwise what I'll do is I'll do a. One of the people asked me for a presentation on logical circuitry and how computers work and so let's take a look is that. If you look at the upper left hand corner you'll see that back in the 1600s also and actually I think his name was mentioned earlier is that. Von Leibniz co invented calculus with Isaac Newton one was in the UK one was in Germany they co invented around the same time. I mean they couldn't just chat on their iPhone or you know, do Twitter or something. They weren't probably sharing information like that back in those days you had to go oh hey did you hear this or whatever. Wow that too problem so so but essentially they were playing at the same time with this stuff. And but also Von Leibniz invented kind of binary binary arithmetic in other words the ones and zeros. Well, long time later what is a one or zero but one or zeros can be portrayed in lots of ways. But one way we look at it is basically electron electricity on or off. In other words a one can be electrostrusting on and off is a zero. The way we often look at that is because a transistor will with a little bit of electricity will allow electricity to go through it. So essentially that becomes a one and if electricity didn't go through it becomes a zero. But ones and zeros are also portrayed in hard drive for example as magnetic direction of the particles and so it's not always electricity. But for the most part you can kind of think of it as one equals on and zero equals off. But this slide is also showing you that just the simple idea of ones and zeros can represent very complex information. So how does that work let's take a look real quick if you look at the slide. You'll see on the bottom left see if you can follow this is when we say 45 what do we mean in other words 45. Yeah, it is. So we say 45 what do we mean that what we mean is there is we have a numbering system a decimal. Let me see if I can do this in text decimal system. And so we have say 10,000 column and the 1000 column and 100 column and 10 column and ones column, which are really just multipliers of 10. In other words, if you go from the right to the left it's just 10 to the zero 10 to the one 10 to the two 10 to the three 10 to the four, or did I make. Oh, I missed one and 10 to zero 10 to up I missed the, let's see 10 to 10 to one 10 to two 10 to three 10 to four. Okay. Exactly. And if you understand converting one to another, then that's fine. And then things like hexadecimal and whatever, don't throw you but if you don't, it can be I know it throws my students. So the idea is that what is 45 in a computer well, there are no fours and fives in a computer, there's only ones and zeros so how do you do that. So essentially, then have to compute. So for binary, you have to have basically two, in other words series of two, like 64, 32, 16, 8, 4, 2 and 1. And so if you have a number like 45 you take the highest number that can go into it this case 132. So you go through it. Okay, so now you have zero times 64 plus one. Let's see I'm going to do it in text one. I gotta watch my time to times 32 plus zero times 16 plus one times eight plus one times four plus zero times two plus one times one and that equals to 45, which what that means is that in a computer 45 is stored at as one zero one one zero one. And all numbers are stored that way in computers. Well, it's not just numbers that are stored in the computers. In other words, in the early days all they used was numbers but what if you want to represent your name. In other words, how is a V or an I stored, how is a character from another language stored. In other words, let's see, let's see if this will do this for me. Okay, so for example, how is this stored in. Oh, it didn't, it didn't do it because on my computer didn't do it. I was trying to do Thai language, because up on the upper right are the some Thai letters so how are those stored in the computers. Well, you've got the idea is ASCII was the table that was invented in 1965 to store basically European languages, but there's a lot of other languages other than European languages. So, in the 70s 80s in particular you have a storage called Unicode which can with more ones and zeros, it can represent up to 110 different languages. And so that's essentially how a letter is stored in the computer. So, great. How do you store a letter you just stored as a pattern of ones and zeros. The same way you store number except it's used in context. The same way you do arithmetic operators like that one that stored is just a bunch of ones and zeros, but how do you store colors. Okay, who's an artist out there. How do you create a color, like purple or something. I'm going to make sure everybody's out there because I'm staring at the board and not you guys. Yeah, okay, so what is that what do you what do you mean by RGB values. Yep, combine based colors exactly. Okay, so you'll see down at the bottom right that in a computer, all the colors are stored as numbers. Now the reason why you have F F F E 64 or D 96 or something under is that is simply another numbering system, which is based 16 hexadecimal. And those are really just numbers it just that they're shortcut ways of representing the numbers, because the numbers are basically eight ones and zeros, or a decimal number bigger. So it's just a it so colors in a computer are just stored by the intensity, how much red green or blue you have exactly based colors hue and saturation so you just store them as a bunch of ones and zeros. You're beginning to get a pattern here is that everything in the computer. Okay, I have about a minute so how does how are sounds stored. In other words, how are you able to hear me right now, because it's the exact same thing. How it what is a sound. A sound is frequency exactly frequency. Plus, well in this case, a frequency because a wavelength is a distance rather than a times and intensity, so to speak, in other words, amplitude. So all we're doing is just assigning numbers to the frequency and the amplitude, and then sampling them about very often 14,400 times a second for CDs. And that is sounds. Okay, so now you know everything about how a computer works. Yes. Okay. So that is my presentation for today. I hope you enjoyed that I'll be glad to answer some questions or comments or such I try to hold it to an hour. If you want to know more about computers and how they work. But he said, yeah, I'd love to know computers, logical circuits that stuff. And I'll be glad to show you exactly how a computer works also next time. Of course, you guys are always can stick around as long as you want. I need to kind of wander off to first life, but I appreciate you being here because I, this would mean nothing if I'm talking to myself. I learned a whole lot from people from all over the world. I mean, that's why I'm here. Really. Yeah, because people are all over the world. One thing I can't change is the world's round and there's time zones and. Yeah, please. I think you can now what you may have to do is oh hi is you what you may have to do is to. There's three parts to it. So you may have to get all three parts make sure you get all three parts, but you're welcome I'll just keep it up there. And you can get copies to it now remember this is just one type of slide rule in a lot of slide rules what you have to do like this one is to. But you can find that in other words you can find a lot of different types of slide rules right here, and you can even make your own and stuff. But remember that for example there are scales for logarithms or scales for lots of different things. And sometimes you have to do one thing on one side flip it over. And get the answer on the other side. And so they're a little more complicated, but you can. It's kind of cool. Okay, have fun. I appreciate it. Thank you. Let's do a lot of such lectures like a college in second life it would be interesting. Yeah, I think so too. The courses is a small courses and all the lectures would be just great. Maybe second life here will be like next month I don't know after July next year is it a joke.