Program 05 - "Beginnings of Science"

Music Eh, Eh.Hm.Look up there.Hm.What, what is that?I don't care.Now, look, look, look.Huh?Like a giant lizard, chasing a, chasing a bug across the sky.Bug, bug?No see bug.Bug.Right, right above that big tree, there's a bug up there.No bug, that's not a bug, that's a woff, woff, woff.Did you see, did you see, hah?Like what?That big thing go cross the sky like dat.I didn't see anything, I didn't see anything.It's so bright it hurt my eyes.Ow...ah..Come on, come on, maybe we ought to ask the other guys if they saw anything.Oh, ow, ow...

MusicWe're back with Science 122, where we questionthe Nature of Physical Science."Today, we will learn about the role of the human brainin this program, "Beginnings of Science," and the developmentof astronomy and mathematicsin the Mediterranean region prior to 500 B.C."Hey, that was pretty good, but, hey, don't quit your day job.Hey, I may not be ready for prime time, but then, neither are you.Hey, don't go there.Maybe we should go on with the program.We'll talk about this later.Before we are done with this program we will have tracedthe origin and growth of science from itsbeginnings to Greece of the 5th century B.C.We will see how the development of the human brain goes handin hand with the use of language and the ability to reason abstractly.We will see the connection between calendars, navigationand regularity of the heavenly bodies,and how this relates to causality and mysticism.Counting and the use of numbers marks a huge stepin the advancement of science, a step equallyas large as the use of language.

Finally, we will look at the accomplishments of variousastronomers in the Mediterranean and elsewhere in the world.The importance of these events in the developmentof science cannot be overstated.It is here that we find the underpinnings of our modernworld view, modified though it is, by the scientific method whicharose to overturn the ancient views three and a half centuries ago.Be sure to read these objectivesin the Study Guide and refer to them as you study the lesson.Focussing on the learning objectives will help youto study and understand the important concepts.

Compare the objectives with the study questions for this lessonto be sure that you have the concepts under control.You know, the fact that we are curious about our environmentreally should come as no surprise.As a survival skill, the more we know about the resourcesand hazards of our world, the more tools we havewhich can aid in our survival.Previously we've seen that the scientific learning we do isreally only a formalized version of learning in general.And in order to learn we must receive, organize and classifyinformation about our surroundings.This is impossible, of course, without a brain, and ours does it pretty well.So well, in fact, that it's safe to say that the human brain is themost remarkable and complex structure in the universe.Around 40 to 50,000 years ago an important development tookplace that marks an important step in the growth of whatwe now call, science--the ability to reason and symbolize; to uselanguage; our prehensile thumbs, which allow us to make and use technology.

All these are results of our new brain, and it's exactly thesequalities which are necessary for systematiclearning about our universe.I want to carry on with the idea of the beginnings of science.When we talk about the beginnings of science we're really talkingabout astronomy, because astronomy can be said to be one of the oldest sciences.I'm not sure it's the oldest science, but it's certainly one of the oldest sciences.It's fairly apparent, I think, that if people were sitting around aswe tried to imagine last time, you know sitting around the fire,with the darkness surrounding you, the only shelter a caveand wolves sound out in the distance, that the stars wouldbe very apparent to you and very visible to you and you shouldprobably have a curiosity about what the stars were made of,and also a curiosity about what caused them to move the way they do.Assuming, of course, that you could ever figure out exactly how they moved.

I tried to leave you last time with the impressionthat figuring that out would not be that easy.That's not just something that one person would likely look atand figure all this out, the movement of the stars, the sun and the moon.And even to notice the retrograde movement of the planets wouldtake quite a bit of time, generations of time, if notthousands of years of time for people to get to a point wherethey had some sort of legends or some sort of tribalknowledge about the way in which the way in which the stars moved.

So, keep in mind here that when we are talkingabout beginnings of science, or any kind of science,the part of what we meanby science is the classification system.Right?Good.That's not the only thing there is to science,but the part of it is the classification system.And we all classify things based upon our culture and on our experiences.Our culture helps us to determine the paradigm.Right?We sort our experiences and organize them according to ourcultural beliefs and those cultural beliefs are not something thatan individual creates, it's something that the culture creates.So, our senses tell us that the earth is stationary.We don't feel the earth moving.Although I did have a student in here one semester who claimedthat she could feel the earth moving.That she sensed that the earth actually moved around the sunand that it was revolving on its axis, and she's the only personin all these years that I ever came across who made what seemedto be a legitimate claim to be able to do this.I should point out that she didn't stay in the coursevery long after she made that statement.And I don't know exactly what that means.But,Could be, could be.For the most part, we don't sense this.Right?When we stand watching the sunset, we don't get the sensethat we're rotating around in its orbit, what we get is thesensation of the sun is moving through the sky.It's not too surprising that the earliest paradigms did the same thing.

So was it just a coincidence that early astronomersconsidered the earth to be flat and stationary?Or was there a good reason to think so?Well, we must remember that our focus in this first sectionof the course is the build up and fall of the geocentric paradigm.It's certainly fascinating to trace the development of an idea likethis from the intuitive stage of our primitive ancestorsto canonization by the church.It serves as a reminder of how easily we can convinceourselves that what we want to believe is true, especiallyin a case where there is little evidence one way or the other.This process by which we build and then rebuild our workingmodel of the universe is a mirror of the workings of the humanbrain which, of course, is a requirement for doing science in the first place.So, this is what we want to examine--the growthof this paradigm and how this idea of geocentrism, that the earthis stationary and the stars go around it, became from anintuitive thing, you know, that which we sense, into a paradigmwhich was ingrained not only in the culture, and the religion,and in the politics, and the science, and everything else.Because the question we have to ask is, why a paradigm like this,which is obviously wrong, or which could be shown to beobviously wrong, stuck around for 2500 years.OK?

So this is the, this is our paradigm, right?I mean, this is a paradigm, that, geocentric paradigm,this is what our senses tell us.We're not moving, that the heavenly bodies revolvearound us, and in an egocentric and a geocentric sort of way,we believe that the earth is the center of the universe.I've always thought it was kind of a nice coincidence that thewords, geocentric and egocentric, have the same letters.The idea that the universe is made specifically for us,and it's ours to use and it's inexhaustible,and that everything that we think about is a result of our purposeand our being the superior life form on the earth,is all tied in with the idea of the geocentric theory.The idea that, I'm suggesting here that our egocentrism is partlyresponsible for our belief in geocentrism.And that's one thing that makes it so hard to overcome, especiallywhen the religion that developed with Christianity, and mostof the early religions as well, are very egocentric.That the earth is made for men.

OK, so.Just to switch us back and forth here, just to keep your mind sharp.Our modern paradigm tells us just the opposite.That the earth revolves around the sun, that,and this by the way, is only a few hundred years old.A few hundred years old meaning it's only in the 1700s,late 1600s, that people really began to accept the ideaof heliocentrism, of the earth going around things.So, why do we replace this paradigm?In other words, what happened to replace this geocentricparadigm which is logical, is consistent with the senses,was incorporated into politics for 2500, religion and everythingelse for 2500 years, and is embodied in the authorityof the religion of Christianity.In other words, the question is not so much why did people adoptgeocentrism in the first place, the question is, why did we give it up?It's a really good idea, makes a lot of sense, and it's consistentwith all of our senses, and it's all tied in with everything.

So, the question that we want to try to answer as we go deeperinto this, is, what happened to make this geocentricparadigm no longer viable?And this is really the story of science, at least the scientific revolution.Because what we're finding is that when science is at itsbest, it allows us to understand rationallywhat we're confusing intuitively.Does that make sense?It allows us to understand rationally what our sensesconfuse or what our intuition misrepresents or confuses.That's exactly what we'll see happening here.So, is our brain that distinguishes us most from the other animals?It's our brain that allows us to perceive the universe in the waywe do and to classify it, write about it,draw pictures of it, and talk about it.The development of the human brain took a major leap 40,000years ago or so with the development of languageand the ability for abstract reasoning.The use of meaningful symbols to communicateabstract ideas is the basis for our common reality.Which, of course, is the physical universe.

OK, let's go, you're on.Hey, are you there?No, I think it's crashed.We've been trying some new software and some of it is very disagreeable.You know, Macs really don't like some of the newsystem files, especially if there's extensions.I guess I'll have to do this.That's OK, I'll wake you up later.Now it's time to consider the relationshipbetween the brain and the physical universe.OK.So, in order to use rationality, or intuition,the first thing that's required is a brain.You probably know this, right?Humans have the most advanced brains.On the planet, certainly, and as far as we know, in the universe.We don't know of any other life forms outside of our own planetand certainly the human brain is the most complexstructure we know on the planet.Maybe dolphin brains or whale brains were up there with us,or even a little ahead of us, but still, it's the mostcomplicated structure we know of.

The modern brain evolved quite a long time ago.In other words, looking at archeological or anthropologicalevidence, the size of the human head or humanoid heador anthropoid head was fairly developed around a million years ago.And we assume that going along with this large brain goes theability for abstract ideas and abstract concepts.And also, of course, rational thoughts and religious concepts,and all of these other things that we associate with being human.And, most importantly, I think, with the developmentof the brain it allows us to develop things like technology.And the earliest technology, of course, that was developedby early man was fire and stone tools.

Fire, as we'll see a little later on also links into man's studyof chemistry and the use of substances from the earth,the refinement of substances from the earth.And stone tools, of course, go along with that because theyallow us to manipulate the environment.With a stone tool you can hunt an animal, you can cut down a tree,you can build, you can build structures.So all of these things allowed us to survive in an environmentwhere we might not have been able to survive otherwise.Of course, along with, if you take a rational brain and the abilityto make tools, and the desire to survive, then you have therecipe and the ingredients for a technological advancement.And a technological advancement is going to include not onlymaking tools, but also learning more about the world to put usinto a better position to survive in it.

Survival is what it's all about, right?I mean from the point of view of a evolution,and the point of view of advancement.It also, the rational brain also allows us to have language.We take language so much for granted because most of us have it.Some of us don't use it very well, but most of us have the ability to use it.We suspect, meaning, we, meaning archaeologists andanthropologists that the use of language evolved around 40,000years ago with the developmentof our modern species of man, Homo Sapiens Sapiens.If you're not aware of human history, early human history,around 40,000 years ago, a different type of human startedto appear in the fossil record in Europe and other places.And that particular species, our modern species, did things likebury their dead and drew pictures on cave wallsand performed very elaborate rituals which leave verydistinctive archeological markings.The other species that was present at this time, the socalled Neanderthal, did some of these things like bury the dead,but people who study this sort of thing, look at the bonesand the skulls of Neanderthal and make the claim that thestructure is not there for the delicate manipulationof the tongue which is responsible for language.And many people would argue that Neanderthals may have gruntedin and formed some sort of sounds, but the ability to verywell rounded vowels and very short consonantsprobably wasn't present until that time.

So, you can see what advantage language gives us, right?Because without language, if I learn something, if I am ableto watch the stars and figure out something, if I can'tcommunicate it to someone else, then it dies with me.But with language I can communicate it not onlyto progeny and other relatives, but I can also communicate itto the rest of the village or the rest of the tribe, and then we can talk about it.And I say, "Well this is what I think happened," and someoneelse can say, "No, this what I think happened," and we cancome to sort of a common understanding.In other words, language allows us to generate and share a common reality.And it's really that common reality that defines what reality is.Think about this.We were talking before about internal reality, the spiritualside and the external reality, the physical side.And most of the time we have trouble deciding which is which.But if I talk to you and I say, "You know, I saw this thing lastnight up in the sky, and it looked like this," and I describe itto you and you say, "Well, I was watching the sky lastnight and I didn't see anything like that."And everybody else who was sitting around the fireat the same time also didn't anything, then I'm going to startto think that maybe what I saw was inside me and not out there.Right, but if we're sitting around the fire talking about thisand I say, "I saw this thing," and you say "Aw, I saw it too.And everybody else says, "Yeah, I saw something."Then we may not agree on what it was we saw, but we'll all agreethat there was something out there that's common to everyone. And so, with language, we also develop the abilityto distinguish on a group basis between individual spiritualrealities and sort of physical realities that exist for everyone.

It also, of course, when you take the concept of languageand combine it with the sense that we have of needingto understand things, it allows people to sitaround and figure out reasons for things.In other words, you can sit around and say, "Well, you know thatweird light was in the sky last night, what do you think that was?And someone else can say, "I think it was just your imagination."Someone else would say, "No, I think it was one of the godswho couldn't sleep that night and was angry and so he came outat night," and you can then form some sort of an idea about what you think it is.And, of course, the explanations that you give are going to bedone in the context of your paradigms,in the context of your cultural beliefs.And this is essentially what we see happening.And, of course, we put this all together and what we come upwith is the fact that people could not help but notice, wonderabout, talk about, and make judgments or speculations about the stars.About what they were and what was going on.

So, it's easy to see, if you take all these thingstogether why people became astronomers.At least why they had this wonder about what wasgoing on with what's in the sky.Most of us know the date most of the time.How do we know?If you did not know the date, how would you find out?"I would use my modem to call the National Time Standardin Boulder, Colorado, to synchronize my internalclock which measures the time in seconds from January 4, 1904."That's very interesting, and I'm sure that's what most of us would do.But some people might use a calendar."That is what I said.I would use my electronically synchronized internal perpetual calendar."You know the calendar is based on the movements of the sky,and also the relationships of the sun and moon and the timeand location of the sunrise and sunset.One of the major advancements, of course, which requiresthe knowledge of the stars is the use of calendars.Why do people care, other than just curiosity, why do wecare where the stars are at a particular time?It tells us the season, right, among other things.But, if you are a person who, maybe we need a littlebackground on the history of development here,one of the major technological advancements of mankindin civilizationwise was the domestication of cropsand the domestication of animals.In other words, people at one time early on probably were migrators.

Today, anthropologists call this transmigrators who follow herds and animals.That is, like in the northern country you follow the caribou,and further, in temperate climates, you followanimals up and down the mountains.The animals move up the mountains in the summer timeand when the snow comes to the mountains, they move down into the low lands.So, if you were part of a nomadic group of peopleor transhumanists, as they're called, following these groupsof animals, you might notice for example, that at certain timesof the year when you pass on the way down the mountain,that certain kind of crop is growing, a certain kindof seed or something is growing here.Then you might eventually begin to understand that, well, let's see,last year I ate some of this stuff and I dumped someof the stuff I didn't want here.And this year I come back and there's stuff growingwhere I left stuff from last year.I mean the connection between the seed of a plantand a plant going through that entire cycle of growthand fruiting and harvesting is also a connection that we can't take for granted.So the idea here is that once you understand that you can stayin one place and you don't have to follow the animals around,but you can keep the animals in pens and that you can plantthings and they'll grow, you have to understand that ithappens within the growing season.

The growing season may depend upon water.It may depend upon temperature.It may depend upon hours of daylight.But all three of those things are seasonal in most places.You know one of the side effects of keeping track of the seasonsis the tendency to connect events causally.It's part of human nature to be curious.We just can't help but wonder why.Think about this.If two events always occur in the same sequence, isn't it naturalfor us to assume that one causes the other?We do this in everyday life.And five or six thousand years ago when there was probably nodistinction between science and other types of learning,it's not surprising that our ancient ancestors did sofor the stars and other seasonal patterns.After all, today we ascribe these same patterns to the sun.

We distinguish between one event which causes anotherand two events which are controlled by the same cause.But, I'm getting a little bit ahead of things, here.So the calendar becomes very important because if you livein a place where there's a short growing area as you would havein medium elevation in the mountains, for example,even in the tropics, you'd find that if you planted things too early,when the seedlings were little, a late spring frost would kill theseedlings and then you'd be, then you'd have to plant over.But if you plant too late in the spring and something which hasa long growing season, you find if you plant it too late,then in the fall, before it had time to fruit, an early fall frostwould kill it off and you wouldn't have any crops.So it's very important to plant the cropsin the window of the growing season.So it becomes very important to be able to predict when it'slikely, it's the right time to plant so that you'll miss the springfrost on the early end and this fall frost on the late end.It also, of course, relates to navigation.And very early apparently the early Phoenicians, for example,were very good sailors across the Mediterranean were ableto navigate reasonably well by using the stars.Recognizing that a certain star is at a certain location, is nothingmore than just recognizing a certain direction.So, calendars and navigation become a good reasonto understand what's going on with the stars.With me so far?Nothing too difficult here, I assume?

OK.So, keep in mind now that the heavenly objects have this regularity.The regularity of the sun, of the stars, and the sun and the moon,it's relatively easy to figure out.The moon's more difficult to predict, but still it hasa fairly regular monthly cycle.The planets are very irregular.

Now why would we care where the planets are?What difference does it make, I mean, if you could navigate,for example, by watching a particular star riseon the horizon at a particular time,why would you care about the planets?If you could read the sun, moon and the planets.You wouldn't want to follow them by accident, so you'dkinda like to know where it is, OK, like that.Part of it has to do with the idea of causality.One thing causes something else.And we have a need to understand this sort of thing right?I mean in our everyday lives, if you do something and asa result your spouse or your parents or somebody gets madbecause you do that, then if you do it often enough, you beginto understand that one sort of behavior causes another sort of behavior.Is it like that with the heavens as well?The ancient Egyptians, for example, now again a little background here.The ancient Egyptian civilization was down in the middleof Africa, not up near the Nile Delta where Egypt is now,but down about a thousand miles down into centralAfrica, right in the middle of the desert.The only water supply there was for growing things camefrom the flooding of the Nile which happened every spring.The flooding of the Nile, as we know today, is causedby the fact that the Nile originates up in the mountainsin central Africa in Tanganyika or Kenya or someplace in there,and when the snow melts, it causes the Nile to flood.All the ancient Egyptians knew was thatat a certain time of the year the Nile flooded.And, of course, it's the flooding of the Nile.It's a big event, if that's your only water supply for the whole year.

The Nile floods, it spreads out over the flood plain.It releases silt and water and irrigates the land.So, the Egyptians happened to notice that around the sametime the Nile flooded, the star that we call Sirius, actuallythe brightest star in the sky, just began to rise on the horizon.In other words, you watch all year and the starSirius is up for about six months of the year.Remember how the stars sort of migrate around the sky?And it turns out that just about the time the star, Sirius,appears on the horizon at sunrise, that very soonthereafter the Nile floods begin.

So the Egyptians had this whole thing worshipping the star,Sirius, and believed that the star, the appearanceof the star, Sirius caused the Nile to flood.Wouldn't you make that connection too?If every year you begin to see this star appearing.The star's been gone for six months and suddenly this very bright star appears.And Sirius is the brightest thing in the sky exceptfor the sun and the moon and Venus.A very bright star appears, and within a few weeks,like clockwork, the Nile floods come.Doesn't it make sense to connect this causally?To say that the star, Sirius, causes the Nile floods?So, here we see the beginning of the allianceof what I call here, the religious and the secular, in our societies.That a religion in Egypt developed around the appearance of Sirius.There was a big festival, a worshipping of the god,Sirius, because, after all, you have no wayof knowing, maybe this year the god, Sirius, will bemad and won't cause the Nile to flood, unless you're nice to him.Right?It may be hard for us to see this because, you know, we don'tworship things in this sort of way.But it's a very common thing for, I hate to use theword, primitive, but I guess I have to.For primitive cultures to worship things like that.And, of course, I note here that any explanation is better than none.I mean if you don't have an explanation for why the Nilefloods, and you have this chain of events, one thing leadsto another, then it's because we have this need to explainthings, any explanation at all seems better than no explanation.

Also, part of the human pschye is the concept of mysticism.Because there are so many things we don't understand and perhapscannot understand, there will always be a certain amount of mystery.So, what exactly is mysticism?"It is a mystery to me how my operating system works.Is that what you mean?"Not exactly.We have to distinguish between mystery and mysticism.So, look up the word, mystic, in the dictionary."My dictionary says, one, spiritually significant or symbolic.Two, pertaining to mysteries known only to the initiated."That sounds basically right.But, you know, for us it's useful to connectmysticism also with the concept of destiny.The connection is that if events are destined, then there justmight be some way to find out ahead of time what is destined to happen.So, looking for clues in the stars or in tea leaves or in omens just might work.So, this concept of mysticism will recur throughout the course.So, it's a good idea to take a few minutes now to think about it.When you encounter the term in future programs be sure to stepback for a minute, and stop and make sure you understand thecontext in which we're using the term.I asked the question earlier why would you care about wherethe stars are and where the planets are.

The next step here then was the belief of the Sumerians thatthe stars and their locations could influence human destiny somehow.Well, maybe they can, and maybe they can't.We certainly know that Sirius influences the flooding of the Nile.Influencing the behavior of the people, right.So there is a connection.They began way back in early times, the idea that if youcould know ahead of time where the stars and where the planetswere going to be, it was believed that you could then predictcertain types of events, things like flooding and rainsand climate, but also other kinds of events.A sort of generalization evolved here that if you could predictfloods and climate and other meteorological events thenwhy not be able to predict human events too?In other words, if maybe the stars are favorable at some timesfor doing other things besides planting.Like, for example, going to the neighboring country and plundering and looting.The Babylonians, it's really the Babylonians to who we owea lot of our current misunderstandings and alsoa lot of our current myths about the stars and influence on people.

The Babylonians were really the first astrologers.I want to make a distinction here between astronomy and astrology.Astronomy is watching the stars and knowing where they areand predicting where they're going to be.Astrology is taking that information and using it to tryto predict things that are going to happen in the future.The Babylonians were very much into the prediction of the future.In other words, they were the ones who gave us the legacy of whencertain stars and planets line up.Did that create sort of, some sort of influence which then caninfluence human affairs in some predictable sort of way?In other words, they thought the stars were gods.And since the gods in the Babylonian system werein control of human destiny, if you could do what the gods weredoing you might be able to figure out what the gods had in mind for us.So the motions of the heavens then became tied inwith the idea of destiny and this leads to our modern concept of astrology.And by the way, up until the 1970s or even 1980s, muchof the information that astrologers in our modern timeswere using was about 2500 years out of date because they werestill relying upon some of the stuff from the ancient Babylonian times.This has now been updated.

Now astrologers can buy computer programs and planaterianprograms and that sort of thing to find out where the stars actually are.And much of the information that was used to make theseastrological predictions was 2500 years out of date up until very recently.Please, the idea here is not that you memorize all of the detailsabout the Sumerians and Babylonians, but to lookat the progress that's made in terms of the writingand the mathematics and the way the ideas evolved from one to the other.You know the idea of counting in arithmeticis second nature to some of us.Even it we're not good at it.Having been taught the rules of arithmetic at a very young age,it's difficult for any of us to imagine how hard it must havebeen to figure out those rules in the first place.The importance of numbers, arithmetic, algebraand geometry really can't be overemphasized.Now, don't panic.

This course is not really about calculations per se, but it isnecessary for us to understand the important role thatmathematics plays in the development of science.The Babylonians had figured out tables of squares and square roots.This is a pretty hard thing to do, isn't it?I mean, we can, if I want to know what the square root of 7 is,I can go to a table and look it up, or I can go to a calculatorand punch in the number 7 and press the square root key.But how do you figure out the square root of 7, if you don't know?You don't have the calculator?There's a way to do it.I learned it somewhere back in second or third grade,but it's not an easy thing to do.I mean, you look at it and you say, "Let's see, 2 squared is 4and 3 squared is 9, so 7, the square root must be somewherebetween 2 and 3 and make a whole bunch of approximations,and you try 2.1, and that doesn't work, and youtry 2.2 and you keep adding decimal places.It's a fairly complicated process to do this.Why would you care to know the square root of a number?And who cares what the square root of 7 is anyway?What's the point?Proportions is one thing.And keep in mind that there are formulas for area.And these people were amongst the earliest farmers.

So, suppose that you know, for example, that you have enough seed to plant.I'll use modern units.That you have enough seed to plant 700 square feet of land.Right?How big a square is 700 square feet?See what I mean here?You know that you can plant an area somehow that's 700square feet, so how big is it on the side?How much land do you have to till to plant that much seed?Well, of course, each side here is going to bethe square root of 700 isn't it?Because when you multiply the square root of 700by the square root of 700, you get 700.So, if you have a circle, and you want to know how much,how big the circle has to be to plant a certain amount of stuff in it.You have to know the radius of the circle.And the area of the circle is dependent upon the square of the radius.OK?

So, the other thing here is the idea of geometry and Pythagorean triples.Does anybody know what a Pythagorean triple is?You can figure I'm probably going to tell youor I wouldn't have asked the question.But, does anybody know what it is?The numbers 3, 4 and 5 are called Pythagorean triple.The three numbers that have a very special relationship to each other.Does anybody know what the relationship is?They are consecutive, but that's not the only.I'll draw a triangle.A triangle is a geometric figure.If I draw a special kind of triangle; that is one that hasa 90 degree angle in it, called a right triangle, and then drawthe third side of the triangle between the two right angles,it turns out that if this side is 3 in length, and this side is 4 inlength, then this side is 5 in length.In other words, if you make a triangle that has a right anglein it, there are three numbers which willdescribe the lengths of the sides that will work.You think all numbers will do this?Why would you care about this?I mean why would you care about this sort of geometric figure?Sure.Even in those days people like to build square buildings.It's much easier to build something if you build it squarebecause all the sides are the same length and all the beams are thesame length, if you build it with square corners.

So today, of course, you go to True Value Hardware or someplaceand you buy a carpenter's square which has a right angle builtinto it so you know how to make it square.But if you don't already have the carpenter's square to do it,what you can do is to draw, is to take a piece of ropeand tie knots in the rope at equal intervals.And so that the length of the space between each knot is the same.So then, to make a square angle, a right angle, you take that ropeand you lay it along here and you mark off three lengths of ropehere, and then you mark off another rope that has four unitson it and then you have two people who sort of splay those things out like this.Someone else with a third rope that has five knots in it cancheck the distance along here and when that distance is equalto five, then you know that these two things are at a right angle.It's called a Pythagorean triple for reasons that we'll see nexttime, because it was the Greek philosopher Pythagoras whofigured out what the relationship is.Does anybody know what the relationship is?It has to do with the sums of the squares of the numbers.OK.Three squared is nine, four squared is 16 and five squared is 25.It turns out that in general, any three numbers who fit thisrelationship, you can use to make a right triangle.

Another set of Pythagorean triples, for example, are the numbers 5, 12 and 13.So we know today that there's a general relationship herebetween the three sides of the triangle in terms of the sums of the squares.The Babylonians and Egyptians didn't know this.What they knew, were that there were several sets of numberswhich you could use to make squares, but the generalrelationship which said, "A squared plus B squared equal Csquared," was not discovered for another 500 years or so.So, its a fairly sophisticated arithmetic;a fairly sophisticated geometry.Also, certain rules of arithmetic, like addition and subtraction.You notice I'm avoiding the word, math, here as much as possible.But, we know certain things about arithmetic, don't we?We know, for example, that 3 + 2 is the same as 2 + 3.This is the stuff we all learn very early on in our lives,so we know that 3 plus, that 3 x 2 is equal to 2 x 3.There are certain simple rules about how to add and subtract.We know.Do we know that multiplication is like adding?Yeah, it is.Even so.If I multiply 2 x 3, what am I really saying here?I'm saying that it's really 3 +3.In other words, I'm adding the number 3 to itself 2 times.And if I say 3 x 3, I'm adding 3 + 3 + 3.OK?

So multiplication is really nothing more than a shorthand for adding.It doesn't make much difference for small numbers.Right?Because I can look at this and say, "OK, well here's 1 x 3,and here's 2 x 3, and here's 3 x 3," and I could actually count them if I wanted to.Here's one row of 3 and here's two rows of 3 and here's three rows of 3.If I want to multiply 517 times 419, it's going to get a littlecomplicated making 417 things and making 519rows of them and counting them.Right?So we learn these very simple rules of arithmetic that helpyou to multiply so that we don't have to count.So these things were fairly established by 2500 B.C., or I should say by 1000 B.C.You know, every culture has an astronomy.Here in the Nature of Physical Science we tend to focuson the Mediterranean astronomy because of its direct linkto our modern scientific world view.Because there were planted the sees for the scientificrevolution which spread throughout Europe 2000 years later.

So later on in this program we will considerthe astronomy of some nonwestern cultures.But what we see here beginning with the Sumerians is what'scalled the cradle of civilization as far as the Western world goes.In Sumeria we see the development of writing.We see the development of counting and numbers.We see the development of bronze, metallurgy and we see thedevelopment of very accurate calendars and astronomicaltables, keeping track of where the planets are and where the starsare, and, of course, this all involves the concept of writing.The cuneiform form writing, you've heard the word, cuneiform, before?The cuneiform writing was basically done by taking a quilland poking it into a piece of clay so that you hadsymbols which could be superimposed.The symbols were usually sort of V shaped, that's the shape thatyou get when you, if you cut a quill of a feather.And you can stick this in various anglesand the symbols all mean something.

Notice here that at this time, by 3000 B.C.,the Sumerian writing had about 2000 symbols.How many symbols do we have in our alphabet?We have 26, right?It's a lot easier to learn 26 symbols than it is to learn 2000 symbols.You can imagine that only those people who studied very hardand had lots of time to study would even know how to write at all.Everybody can learn the alphabet by the time you're age 5 or 6,but if you have 2000 symbols to learn, it takesa lot longer to become proficient with it.By 2500 B.C., another 500 years had passed, the number of symbols had been reduced to about 600.It's a pretty major advancement, isn't it, in 500 years?To reduce your writing symbols from 2000 down to about 600?So that means that the writing was developing very quicklyand that more people were able to learn how to read.The Sumerians also had fairly good basicmathematics, a number system based on 60.You know what that means?The number system based on 60?We have a number system based on the number 10.But the Sumerian number system was based on 60 which meansthere were 60 separate symbols representingthe numbers instead of 10 symbols as we have.But we have the digit 0 through 9 which are 10 different symbols.And when we run out of symbols we start a newcolumn and use the same symbols over again.You can also do this with 60 symbols, it's just that it'sa little more complicated with 60 symbols.

Of course, we carry some vestage of this around with us today.There's 360 degrees in a circle, right?How many minutes are there in... 60, and 60 seconds per minute.So we carry this around in our time as well.There's a good reason why the number 60 is used.Can anybody think of why?Why 60?It's a very even number.The number 60.You can divide it by 1, 2, 3, 4, 5, 6, 10, 12 and 15.In other words, it's a number that has a lot of factors so that it'svery easy to arithmetic with the number 60.It may be hard for us to think in terms of a number systemwhere you have 60 different symbols, but in terms of usingit mathematically, it's a very nice number.Because it has all these different factors.It can be divided and multiplied by any of these numbers very nicely.Sumerians also developed formulas for the areasand volumes of simple figures like squares and cubes,and also had a very crude approximation of the number pi.Remember last week in lab you determined the number pi,or some of you did, determined the number pi by measuringthe circumference and diameter of a circle and comparing them.You may think, "Well, gee, anybody can do better than 3, it's 3.14, after all.But still being able to recognize that, that ratio existsbetween the circumference and diameter and being ableto measure it closely enough to come up with the number 3is a pretty major accomplishment for a veryprimitive society, by 2500 B.C.

OK, that's 5000 years ago, give or take.

So, the Babylonians were very famous for beingclose astronomical observers keeping very detailed records,and in making very accurate measurements.By accurate measurements I mean to know where a planet is youhave to have some sort of a coordinate system like a graphof some sort and you have to have some sort of a reference point,and you have to be able to measure degrees up and degreesaround from north or east or some other fixed direction.Plus you also have to have the ability to record all this stuff.So, notice the timeframe here.Accurate measurements, the Babylonians were making by 1000 B.C.That's 1500 years after the Sumerians were developing their writing.Fifteen hundred years went by before much advancement took place.In another 300 years they had taken the idea of making accurate measurements.Three hundred years now.This is older than our country, right?In 300 years the idea of simply making the measurementshad gone into keeping accurate records--300 years, OK.

So the Babylonians had a very accurate calendarbased upon the lunar month of 29 1/2 days.They recognized what we know today to be an 18 year lunarcycle, so that the tides and other lunar things repeatthemselves over that time.They invented the seven day week.Why is there a seven day week?Why not an eight day week or four day week or five day week?It's because of the moon cycle, right?.Seven days is roughly one quarter cycle of the moon.So, in roughly four weeks, 28 days, you have nearly a full moon cycle.And so the seven day week comes about as a result.We'll come back to this idea of the number seven a little bit lateron as being sort of having mystical significance and so forth.Also, a year of 360 days.In other words, they didn't have the exact length of the year down.Remember when we talked last time about lookingat the solstice and measuring the maximum extent of the sun.Keep in mind that near the solstice the sun standsstill for a few days, for about two weeks.So being able to tell exactly when the sun reaches that point is very difficult.

So, today, of course, we know what day it is every dayof the year and we buy new calendars, so it's veryeasy to know how long the day is.But, the Babylonians, by around 600 B.C. hadfigured out that there were 360 days.They had 12 months of 30 days each.It was kind of strange when you think about it,because there are actually 13 moons in the year.And it would make a lot more sense even in ourown times to have 13 thirty day months.I think it's 13 twenty eight day months which comesout to 364 days or something like that.So, exactly why the 360 days, well, 360, multiple of 60, right, 60 x 6.OK, so the Babylonians knew about the sun and the moon and five planets.The five planets they knew about were: Mercury, Venus, Mars, Jupiter and Saturn.Those are the five planets outside of earth that youcan see with the naked eye from earth.They knew about the zodiac.In other words, they recognized that the sun went through afixed path, the same path every year, and they had alreadyfigured out the constellations that the sun passes through.So they knew that at a certain time of the year the sun wouldrise in a particular group of stars and those starsalready were beginning to be given names.And they were making very accurate predictions of sunrise and sunset times.They understood, for example, that day lengthis different, different times of the year.It's fairly sophisticated stuff for 700 B.C.I only want to mention Egyptians in passing because it's hardto talk about early civilization without mentioning the Egyptians.

The Egyptians certainly contributedto the civilization of those times.But the Egyptians were very much an isolated community.Unlike the other trading communitiesin the Mediterraneanthe Egyptians were isolateddown there on the Nile River a thousand miles from the coast,and so they depended mostly upon the floods, much more than theydid on trade and they didn't really seem to be much in the wayof great philosophers, and they left few records.They didn't write much except on coffins and on tombs and so forth.So much of what we know about the Egyptian culture comesfrom the interpretation of what's written on people's tombs.They did have a much better idea of the number pi,because they were great builders as you know.They also had a fairly good calendar, but their calendarwas based upon the Nile floods rather than upon the stars.

The Nile floods were the most important thing in Egyptian culture.So that's all I want to say about the Egyptians.Although we do focus on the astronomy of the Westernworld there were many cultures which had developed superiorastronomies to those in the west.Unfortunately, these were unknown to the Western worldduring the development of our scientific paradigmsin the early centuries of the Christian era, and evenwell into the teen centuries.With the discovery of the New World in the late 15th centuryand the subsequent devastation of its cultures, nearly all theastronomical traditions, which were mostly oral, were lost forever.

Today we can reconstruct some of the informationwhere there are written records or artifacts.However, we will probably never know the true richness nor theextent of mysticism and astronomical skills of the New World people.I do want to mention just in closing here that to avoid beinglabeled as ethnocentric, we have to point out that there weremany other cultures who were great astronomers.I tend to concentrate on the Mediterranean because thoseare the ones that actually had ties to our modern science.But there were some other people in those times who were muchbetter astronomers than the Babylonians and the Sumerians.One of these was the Maya.The Maya had built a great culture in Central Americawhich involved a calendar which was much better than theBabylonians, also based on the number 60.But they also had writing which was much more advanced thansome of these earlier civilizations.And, of course, the fact that they were isolated in the New Worldmeant that there was no contactbetween the Mediterranean and these groups.Even the Native Americans, the Indians of the SouthwesternUnited States had a fairly well sophisticated astronomy.There are all sorts of, I guess you could call them, astronomicalartifacts that you find scattered all over the West, all the way upinto Montana and even up into Canada.

One of the most famous of these is something called theMedicine Wheel which is a huge wheel with spokes laid out in rocks on the ground.It's about a mile in diameter.And literally it's, if you look at it from the sky, what you see isa wheel with spokes where the spokes and the wheel are rocks and paths.And it turns out that if you stand at certain places on the wheel,it will mark the directions to solstice and equinox sunrises and sunsets.It marks the rising of certain stars at certain times of the year.So, rather than keeping written records in the traditional senseof written records, this marks some sortof a device to keep very close track of astronomy.The Chinese, of course, had developed an entirely separateand entirely independent catalog of the stars.Much of this was unavailable to the Western World until thetime of Marco Polo when the east and the west began to talk to each other.By then the western astronomers had already rediscoveredthe material that had been lost during the Dark Ages,and during that time the Chinese had pretty muchgiven up on the idea of science and progress.A couple more things really quickly.

The Polynesians had a very well developednavigational system based upon the stars.In fact, each of the Polynesian islands had one particular starwhich was associated with the islands.The Hawaiian Islands, the home stars were Castor and Polex.So if you wanted to navigate, for example, from Tahiti to Hawaii,you had to go far enough north so that Castorand Polex would come directly overhead.From Tahiti the two stars are here.As you sail northward they get higher and higher on the horizonand when they're directly overhead, you know that you'reat the right latitude for Hawaii, so then you hadto adjust your east west direction to find it.The last of these is Stonehenge.I don't know if I have a picture of Stonehenge or not.Yeah.This is I guess the things that are disturbedor covered up in the background.

Stonehenge is a very famous monument.Does anyone know where this is?It's in England.It's in northern England.It dates from some very early, around maybe 100 B.C. or 200 B.C., something like that.And again, this is incredibly sophisticated.The stones are largely destroyed, but there arepillars and arches and so forth.Again, when you stand in certain places, stones line upwhich mark the sunset and sunrise locations of the solstices.Not only that, but the ring around the outside, here,actually consists of two rings.You can see some of the stones arranged in a white ring.Just recently people have discovered that if you movestones around this ring at the proper intervals, keeping trackof the sun and the moon, when the stones on the inner circleand the outer circle line up, it means that there's an eclipseseason and an eclipse is likely to happen.It must have been very strange because many times whenthere's an eclipse season, meaning that eclispses are likely tohappen, the eclipses never occur in a particular place.

So, the guys who were running Stonehenge were ableto predict when they were likely to be eclipses, but mostof the time they wouldn't have seen those eclipses.Maybe one out of every 20 times when the stones line up therewould actually be an eclipse at that spot, even though therewould be an eclipse somewhere elsein the world that they wouldn't know about.So, the idea here is that people had reached fairlysophisticated levels of understanding by the timewe get into the ancient Greeks around 500 B.C.Well, we've now set the stage for the next step in our questto understand the Nature of Physical Science.That step is removing the supernatural from the heavensand replacing it with a mathematical, mechanical model.That's in the next program.

In this program we've seen how the ability of the human brainto reason abstractly, allows for the use of language,and mathematics but also for symbolic and metaphorical thinking.All of these are important tools for understanding the universe.And also for defining a shared reality.Still, we see, before the Greeks, little distinction between thesupernatural and natural, or between the physical and spiritual worlds.You know that the spiritual and physical worlds should be sohard to distinguish really isn't surprising.Taking what we have learned previously about the natureof paradigms and perceptions, we've also seen how thedevelopment of language and mathematics allowed for theuse of symbols, and how the reduction of the numbersymbols is a form of technological advancement.So next time we'll examine the Greek cultureand its contributions to the Nature of Physical Science.Well, that's it.We're out of time.Remember, when it comes to science, get physical.Bye.Say goodbye."Goodbye and thank you for joining us.Be sure to tune in next time."Hey, that was really good.You sounded really professional.That's the way you're supposed to do it.I'll bet it those new.....Music