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00:00The End
00:53Whatever your domestic circumstances these days,
00:57palace or one room flat, your life is structured pretty much the same way by science and technology, isn't it?
01:04I mean, look what we all take for granted.
01:09The power that comes out of the wall. That's just a bit of it.
01:16We fly to the moon, engineer genes, computerise nature to play with it and find out how it works.
01:24We shoot film of the Empress Maria Theresa's palace in Vienna so you can watch it on TV.
01:29We boil water to make steam, to drive turbines, to produce the current, to make music come out of the
01:35air.
01:36Or not.
01:40And we expect to go on being able to learn new tricks like that because one of our science-based
01:45abilities is to be able to predict.
01:48That, after all, is what science is about. Learning enough about how a thing works so you'll know what comes
01:53next.
01:54Because, as we all know, everything obeys universal laws.
02:01All you need is to understand the laws.
02:06We're healthier, wealthier, more comfortable, better informed than ever before in history, thanks to science.
02:12And each one of us has more power at a fingertip than any Empress who ever built a palace.
02:40I can, for instance, go to the local library and pick up an almanac that will tell me to the
02:45second,
02:45what time the sun came up here in Vienna this morning.
02:48As a matter of fact, at 6.55, it came up exactly 11 minutes and three seconds ago.
02:55And I know that the Earth's rotation in solar orbit will cause the sun to come up when it's supposed
03:00to,
03:01whether I see it or not, just as I know why this stone will fall like that. Gravity.
03:07And we know that, like we know almost everything else about science, thanks to a crisis that was making all
03:14the headlines here in Vienna about 450 years ago.
03:18And it was a crisis, funnily enough, that was to lead to people wondering why stones did what they did
03:23when you threw them.
03:35In 1535, you wanted a very private crisis meeting with the imperial family, you went for a hunt by the
03:42Vienna Lakes.
03:43What crisis? Luther. And what his Protestants were doing to the Catholic Church. That's what.
03:52So, here's the Pope's man bending the imperial ear with papal plans for an emergency summit meeting to sort it
03:59all out.
03:59Trouble is, the Germans won't come to the Italians, who won't go to the French, who can't stand the English.
04:06After weeks of horse trading, the imperial decision is the northern Italian city of Trento and get on with it.
04:29In Trento, it all turned into a kind of don't do today what you can put off till tomorrow.
04:34Imperial reps would turn up, a couple of cardinals, somebody would go off sick, the Germans would walk out.
04:40Nobody would turn up at two meetings in a row.
04:44Summit preparations took on every appearance of musical chairs.
04:58You're not going to believe this, but for ten years, the church and the increasingly indifferent imperial invitees
05:06went on having talks about talks about what the summit meeting would be about.
05:11Never mind when it would actually start.
05:13These so-called planning meetings were, like all planning meetings, a bureaucrat's delight.
05:19Agenda.
05:24Never mind what he was droning on about, nobody much cared.
05:28By now, as the convoluted Latin sub-clauses filled the air like ecclesiastical ether,
05:35delegates' minds were drifting to matters less exhausting than discussing summit meetings.
05:39Matters like, their expenses.
05:42Utrum nobile svicorum regione stridentine, ad sessiones conciliaris, admit ti bebe,
06:00O.K.
06:05Finally, here on a bitter December day, in the cathedral, they stopped hanging about and got the show on the
06:10road.
06:12Even though only 32 members of the cast had turned up for the opening chorus.
06:15This was where the church was supposed to get a grip on itself,
06:18and over 30 years and five popes, the council did just that.
06:25They made every priest go to school and pass exams,
06:28cracked down on high living bishops,
06:30beefed up the Inquisition and effectively gave it power of thumbscrew,
06:35produced a list of the books you could and couldn't read,
06:37laid down dogma on marriage, purgatory, indulgences, prayer books, worship, you name it,
06:44set up the Jesuits as theological shock troops all over Europe to teach obedience,
06:49and above all, they made it crystal clear that anybody who questioned the literal meaning
06:54of one single word in the Bible would find himself in the cells before he knew what hit him.
07:02Now, in all this great counter-offensive against the Protestants,
07:07the council was to okay something that would change the face of Europe.
07:11I mean, put yourself in their position, in a gloomy church.
07:14That was exactly the problem. Religion was boring.
07:18And if they were going to get the crowds back in again,
07:20they really had to put on a better performance.
07:24So, the last vote the council took was just a touch theatrical.
07:29Here's the simple cross in front of which they announced all their decisions.
07:33And here's what they did to it.
07:35The council had gone bananas.
07:38They ordered lights, music, drama, razzmatazz into all the churches
07:42to turn them into a kind of 16th century Hollywood heaven.
08:07This was the stuff to pull the crowds in. We call it Baroque art.
08:29Meanwhile, as they say when the plot's about to thicken,
08:32meanwhile, up here in the Polish port of Frombork,
08:36the plot was about to thicken.
08:43The plan, you remember, with all that song and dance stuff,
08:46was to get them flocking into church, right?
08:48Okay, then what?
08:50I mean, when was then?
08:52Were you in Easter, Lent, or February the 29th?
08:55Because, salvation-wise, what you did in church depended on what the date was.
09:00And that was just it.
09:01They didn't know, exactly.
09:04For instance, if Easter was supposed to fall on the first Sunday after the first full moon,
09:09after the beginning of the spring equinox,
09:11which depended on a moon-sun cycle that couldn't be checked correctly,
09:15except every 312 and a half years,
09:18and anyway that night the moon didn't come up,
09:20and the calendar you were using was nine days out, which it was.
09:23I mean, what?
09:25But church authority was what held the whole of society together,
09:29everybody from the prince in his castle down,
09:30and it depended on the faithful doing what they were supposed to do at the right time.
09:36Small wonder the pope wanted the sun and the moon checked out better than they had been so far.
09:40Well, when they were, here at the castle of Fromburg, his troubles were over.
09:46But not for long.
09:54Because the astronomer-priest here, who had a go at clearing up the confusion in the sky, succeeded.
10:02And in doing so blew everything to kingdom come, if you'll forgive the phrase.
10:06Let me explain why his work was so revolutionary.
10:11See, back at the beginning of the 16th century,
10:14what was up there was what Aristotle said there was, had said, 2,000 years before.
10:19It was a straight common sense, as I see it, view.
10:24Let me show you a model of it.
10:32Here, at the centre of everything, the earth. Static.
10:36Well, you can't feel any motion, can you?
10:38All around here, on concentric crystal spheres, pushed through the sky by angels,
10:44the moon, the sun, the planets and the stars.
10:48All wheeling around once a day in heavenly, unchanging circles.
10:53Well, they do, don't they?
10:55Heavenly motion was evidently circular.
10:57Here on earth, on the other hand, things only moved one way.
11:00In straight lines, up or down.
11:06So, if celestial circles were eternal, obviously, straight line earthly movement had to be the reason we weren't eternal.
11:15Movement special to earth.
11:21Okay, this priest here, in 1512 or so, took a closer look at the heavenly arrangement and didn't much like
11:28what he saw.
11:29Which was Mars, for instance, among others, being very un-Aristotle.
11:33I mean, it appeared, sometimes, to go backwards.
11:38Now, that was supposed to be impossible.
11:41So, people had got round the difficulty with this little gizmo here.
11:46See, there's Mars.
11:48It goes forward on its main circle, while on an extra mini-circle it goes backwards.
11:54Backwards.
11:56Good, eh? Solved the problem.
11:58Trouble was, to make the entire solar system work, in pure Aristotle terms like that, took over 90 of those
12:06little fiddly bits.
12:08It occurred to Copernicus, our priest, that there might be a simpler way that would still be circular,
12:14and that would allow for things seeming to go backwards.
12:18So he came up with this.
12:20If you put the Sun at the centre, and the Earth in orbit, then you know what we now know.
12:26That that view of Mars going backwards isn't real.
12:30It's because it's in a slower orbit further up than Earth.
12:33Most of the time, everybody appears to be going forwards.
12:35And then when we pass Mars, it appears to go backwards.
12:45And then at other times, forwards again.
12:49And similar problems for the whole sky were solved by this sun-centred system.
13:00Copernicus published his manuscript in 1543, just in time for the Council of Trent.
13:05So, you're a church father.
13:08What this new system of Copernicus is saying is this.
13:12The Earth moves, although the Bible says it doesn't.
13:15It's no longer at the centre of God's universe, although the Bible says it is.
13:20It's a planet, so heaven and Earth are no longer separate.
13:24And Aristotle is wrong.
13:26Though church authority depends on Aristotle being right.
13:30So, you're a church father.
13:32You pick up this subversive, heretical, revolutionary lunacy.
13:37And what do you do?
13:38Foam at the mouth, right?
13:40Wrong.
13:54The church was far too busy for boring stuff like astronomy.
13:58They were still getting their heads together on the expensive business of making theology theatrical.
14:17You must admit, if nothing else, the end product of all that radical refurbishment by the Catholic Church turned Rome
14:23into one of the most artistic places in the world.
14:39Sorry to drag you away from all the uplifting culture, but we do have to get back to Copernicus.
14:52When the Council of Trent got round to reading what Copernicus had said, they were delighted.
14:57His new system would make calendar reform more precise.
15:01And the business of turning every basic belief regarding the nature of the universe upside down?
15:06A mere bagatelle.
15:08Since from the church's point of view, back here in Fromburg, Copernicus was talking nonsense.
15:13Literally.
15:14After all, astronomy drew lines and circles up there in the sky, but they weren't really there, were they?
15:20They were a mathematical convenience for measuring or teaching astronomy.
15:25While the Copernican system might well have been brilliant mathematics, nobody thought for a second he really meant the Earth
15:31was whizzing around the sun.
15:33Ha! Don't be silly. That kind of talk would blow holes in everything.
15:38Most unfortunately, it was already too late for that kind of talk.
15:42Nothing immediately theologically dangerous, you understand, just some people asking questions about what Aristotle had said about motion on Earth.
15:49What were they up to? Nothing much. Just blowing holes in everything.
16:13Here's Niccolò Tartaglia, expert on that new terror weapon, the cannon.
16:17Trying very sensibly to find out how to shoot it more accurately so his boss, the local duke, can put
16:23his military and political standing up by knocking his enemy's military and political standing down.
16:34In the course of these dynamic deliberations, Tartaglia was to discover something extremely awkward regarding that business you remember about
16:42what Aristotle said on how things moved when they got propelled, in straight lines on Earth and in curves only
16:49in heaven.
16:53Well, the more Tartaglia looked at what his cannonballs were doing, the more it looked as if they weren't doing
16:59what they were supposed to.
17:06The ball went straight, all right, straight out of the muzzle, but it very definitely didn't just stop in mid
17:10-air and fall straight down, it curved.
17:18Now, if the official view of circular motion only happening in heaven was wrong, then stuff about planets on crystal
17:24spheres was wrong.
17:25And if that was wrong, everything was wrong.
17:29Tartaglia, however, was interested only in what could have created a curving trajectory.
17:34Air resistance?
17:46And then, back in Venice, where he lived, Tartaglia found the answer in the most obvious of Venetian places, on
17:52the canals, or the boats in the canals.
17:55And with his mania for practical application, he made the idea available to everybody, because in 1551 he translated into
18:03Italian a book in Greek by Archimedes about why boats floated the way they did.
18:09Now, it doesn't take a genius to see why a book like that would go over big with the Venetians.
18:13A, because Tartaglia wrote it in Italian and not Latin, so the ordinary boat builders and engineers could understand it.
18:20And B, because messing about in boats is the Venetian line of business.
18:24They were, after all, the greatest maritime empire in the world at the time.
18:40So, the book was a rave bestseller.
18:45But the real reason why was what it said about how, when a boat hit the water, it got lighter
18:50by the weight of the water the hull displaced.
18:53The water, as it were, changes the weight of the boat.
19:11Well, if that happened to boats in one medium, water, did it happen to different things in another medium, air?
19:18Things like flying cannonballs, because they were going through the air, just like the boats were going through the water.
19:24That was the burning question.
19:26Well, the answer, said boring, authoritative Aristotle, remember him, the answer was no.
19:34Nothing could change the way an object behaved, because every object had its own unique characteristics and would always behave
19:40the same in every medium.
19:42Well, it was time to call Aristotle's bluff, and you could see he was talking rubbish.
19:47Look, here is a stick, falling through air, and not falling through water.
19:55Maybe Tartaglia's hunch about air resistance having some kind of effect on the flight of cannonballs was right after all.
20:01The answer had to be out there somewhere on the water.
20:04It was, but on a totally different tack.
20:14It was Tartaglia's least favourite student, a guy called Benedetti, who first saw the answer.
20:19Well, he could hardly miss it in Venice.
20:21It wasn't weight that affected how anything moved.
20:24It was surface area.
20:28Broad bows went slowly, sharp bows went fast.
20:32The more surface area there was, the more resistance.
20:43Well, if that happened with water, Benedetti asked himself, did air offer resistance to surface area?
20:50Was that why, say, a downy feather fell so slowly?
21:08If falling down behaved like this, what about the general kind of falling down?
21:13Benedetti decided to drop everything and drop everything, if you see what I mean,
21:17with the aid of some trusting friends below.
21:25First of all, the assistants timed the falls of various balls.
21:34They seemed to fall about the same speed.
21:37But dropping one ball at a time wasn't good enough.
21:40So Benedetti tried dropping two.
21:43Aristotle said weight mattered.
21:45Two balls of different weights would fall at different speeds.
21:50Wrong.
21:52Maybe Aristotle, whose word had ruled everything scientific for over 2,000 years,
21:56was wrong elsewhere, too.
21:58As Benedetti dropped his umpteenth ball,
22:01It struck him that circular motion only being in heaven was rubbish.
22:06Here was earthly circular motion.
22:07And when he tried making his own circular motion, he got the answer.
22:12Circular motion became straight line motion once you released it.
22:28Excuse me.
22:33Well, some more things that weren't supposed to happen were about to.
22:36Here, on what has to be one of the more underwhelming places on Earth,
22:40the island of Vane, between Sweden and Denmark,
22:43both of whom often claim it belongs to the other.
22:46Still, if it hadn't been quite so featureless,
22:49he might have been less observant.
22:51He?
22:52Him.
22:53The one with the crick in his neck.
22:55Danish nobleman,
22:56and the only astronomer in history with a metal replacement nose,
23:00Tycho Brahe.
23:02One evening in 1572,
23:05in his customary position, staring up,
23:08Brahe noticed a new light in the sky,
23:10made a few notes on the subject,
23:11and became the rage of Europe,
23:13because Aristotle had said the sky was perfect and unchanging,
23:17and new stars couldn't happen.
23:19So what was this?
23:21And it had no parallax.
23:26Parallax is the way a thing seems to shift, as you do.
23:29Look, watch this nearby cart, compared with that distant lighthouse,
23:33as I move my view.
23:36See the cart move?
23:37That's a shift in parallax.
23:44The lighthouse doesn't shift,
23:46because it's too far away to show on that small move.
23:49Now you take a giant move,
23:51like the Earth going round the Sun,
23:53anything you watch during that
23:54will have to be a long way away not to shift at all.
23:58And Brahe's new star didn't.
24:00So it was.
24:02A star.
24:09Well, the King of Denmark was so impressed,
24:12he offloaded the island on Brahe as a base of operations,
24:16plus a financial sweetener.
24:18And Brahe turned up here,
24:20dug this hole to put a castle in,
24:21and generally started behaving like a little Hitler.
24:25Nasty piece of work, by all accounts.
24:28Anyway, you'll have noticed the wind.
24:31So did he.
24:32And built his observatory down another hole to get away from it.
24:37Went down this second hole every night for 20 years.
24:40Not much else to do around here.
24:46And whereas all other astronomers were content with the odd observation or two,
24:52Brahe watched everything, all night, every night,
24:55with instruments like this,
24:57for measuring the angle of the heavenly bodies.
25:00And came up with a mountain of data,
25:03which was why he was able to be clever
25:04about the next shock horror in the sky.
25:07The Comet of 1577.
25:10Which, he said, was also a long way out.
25:12And not where Aristotle said it should be in the atmosphere.
25:16And it was coming in through Aristotle's crystal spheres.
25:20Yet no sign of breaking glass.
25:22Maybe there were no crystal spheres.
25:25But his last discovery really floored Brahe.
25:28The comet was going in an oval path.
25:31Well, A, guess who said that was impossible?
25:34And B, how could a non-circular orbit be regular?
25:38Not wobble about all over the place?
25:40Hmm?
25:47Meanwhile, the Gunners were, unfortunately,
25:50busy demolishing the whole philosophical argy-bargy.
25:53Forget Aristotle, they said.
25:54Watch this.
26:07You aimed, using the forbidden theory of mixed circular and straight line motion.
26:12You hit.
26:21And air resistance was obviously happening.
26:24It helped put the ball on target.
26:25And as for the oval planetary orbits that didn't wobble,
26:29was there some connection between them and trajectories?
26:36Well, guess what happened next?
26:40Yes.
26:41Only this time, the mathematics professor involved
26:44slowed the falling ball process down by rolling his balls down a slope,
26:49marked with numbers at equal intervals to see how long it all took.
26:54He used a pendulum swing to get split-second timing on when he released each ball.
27:01He spent months rolling different weight balls down different angle slopes,
27:06hundreds of times so as to get accurate average figures.
27:09And each time, watching how long it took the ball to go different lengths of the slope.
27:14A third, quarter, fifth, eighth, half and so on.
27:23He measured the time with water.
27:26As the ball rolled whatever distance it was supposed to,
27:29he'd run water at a steady rate into a measuring jar
27:32because he could see immediately from each amount
27:35whether the ball was taking different times to do different bits of the journey.
27:40In other words, if it was accelerating as it went down the slope.
27:53What Galileo was looking for was some kind of law that all falling objects obeyed.
27:59In 1604, he found it.
28:02Everything accelerated as it fell at exactly the same rate.
28:06By Galileo's law, we all learnt at school.
28:09Thirty-two feet per second per second.
28:18It was the first time nature had been described by mathematics
28:21it could be used in any circumstance to describe what nature was doing.
28:25The beginning of what we know today as the scientific revolution.
28:45Now, all that may look very mathematical and esoteric to you,
28:48but in 1605, doing that kind of thing with balls was dangerous
28:54because what Galileo had discovered was the thing that Aristotle said couldn't exist.
29:00A universal law of acceleration that every single falling object on Earth would obey.
29:05And never mind all that nonsense about each object its own unique characteristic.
29:12Now, contradicting Aristotle like that could have made life very hairy for Galileo,
29:17had events not taken a turn for the safer, with a new business proposition.
29:23In July 1609, a friend of his showed him the new wonder machine from Holland, a telescope.
29:29And one month later, Galileo was here in St Mark's Square at Venice
29:33with a financially very attractive idea in long-range optics.
29:39Up here, he said.
29:50Up here, he said.
29:52Look through this, he suggested to a group of shipping merchants.
30:03Galileo's new improved version of the optical gizmo
30:07and that meant that you could spot the ships coming into anchor out there
30:12a full two hours ahead of the average naked eye.
30:16And that meant that you could get out your little commodity list,
30:19ship symbol, cargo, value, and fix the market prices accordingly
30:24because you knew the ship was coming in and your customers didn't.
30:28Nice idea, they said.
30:31We'll take 30.
30:33And here's a fat salary to keep it in the family.
30:47But a bullheaded, arrogant exhibitionist like Galileo
30:52couldn't keep his mouth or his options closed.
30:54And in 1610, he did something only a lunatic would do.
30:58He pointed an even better version of his telescope at the one place
31:03Aristotle and the church said not to.
31:05Up there.
31:06And when he saw what he saw, he compounded the felony by going public
31:11in a little 24-page booklet called The Starry Messenger
31:15that blew 2,500 years of authority and status quo right out of the window
31:22because in a few scribbled illustrations, Galileo took the universe apart.
31:27Look.
31:29Here's the moon.
31:31Not perfect and incorruptible like Aristotle said it was,
31:34but with mountains, just like the Earth.
31:37And millions more stars than there were supposed to be.
31:40And look at this, the unthinkable.
31:42Three or four little satellites going round Jupiter
31:44when everything was supposed to go round the Earth.
31:47And a bit later, here he is saying that even the sun isn't perfect.
31:51It's got spots.
31:53And then the clincher.
31:54Venus looked like the moon sometimes, waxing and waning.
31:58And that meant that we were seeing it illuminated differently
32:01as it went round the sun.
32:03So all of this was visible proof that Copernicus was right after all.
32:10Everything went round the sun.
32:15Even then, Galileo might have managed to keep things sweet
32:19had it not been for one breakfast time
32:21when his boss's wife, the Duchess of Tuscany,
32:25asked a friend of his if all this didn't mean
32:27that when the Bible said the Earth stood still,
32:30it was wrong.
32:33Well, in a polite letter explaining things to her,
32:37Galileo said yes, and not to put too fine a point on it,
32:40scientifically speaking, the Bible was wrong.
32:44And then everything hit the fan.
32:51And then everything hit the fan.
32:58Now, the conventional view of what happened next
33:01is that the church decided to arrest Galileo and shut his mouth for good.
33:04Well, he was arrested and shut up.
33:06But only after an infuriated church had bent over backwards not to.
33:16They said, look, we know you're right,
33:19but you can't just spring it on the masses.
33:21You've got to let us tell them slowly.
33:23Galileo told them to get lost.
33:25Then he was arrested.
33:27Copernicus was prohibited and that, for the Catholic Church, was that.
33:50Well, fortunately, Galileo hadn't blown it for everybody.
33:53Not up here in Austria, in the Protestant town of Effeding.
33:57And why are we here?
33:58Well, you recall Brahe.
34:00He'd finally gone off to work in Prague,
34:03still worried about those wobbling orbits.
34:07You remember the comet he saw coming into the solar system
34:10on an oval orbit and couldn't figure out
34:13how an oval path would remain stable without rolling around.
34:17Like an oval wine barrel did when you put it down.
34:20Well, it was wine barrels that provided the answer.
34:22The same shape barrels they're delivering here now.
34:25Brought to this castle back then in 1613 for a wedding.
34:34The groom was a local maths teacher, a fellow called Johan Kepler,
34:38and his blushing bride, the adopted daughter of the people who lived in this castle.
34:43Now, Kepler had just come back from Prague, where he had been Brahe's assistant.
34:47And being a short-sighted fellow, had tended to concentrate on the paperwork and the calculations,
34:52rather than actually staring up at the sky.
34:55So when he saw the local Effeding delivery men checking the wine in his barrels
35:00in what he took to be a rather imprecise manner.
35:03I mean, same dipstick, but different shaped barrels.
35:10He decided to take a look at wine barrel mathematics,
35:13a piece of cake when you had cut your teeth on measuring planetary orbits,
35:17which is what he'd been doing night and day for 11 years,
35:19trying to make sense out of what Brahe had left behind when he died.
35:23A gigantic pile of nocturnal note takings.
35:40Apart from convincing Kepler that the planets did go round the Sun,
35:45Brahe's mountain of data revealed something that shocked Kepler rigid.
35:49Mars was circling the Sun, but it was speeding up and slowing down as it went.
35:54And when he checked the figures to see if he'd made a horrendous mistake,
35:58he realised that all the planets were going at different speeds.
36:02The further out from the Sun, the slower.
36:05But why?
36:08And then Kepler made a great conceptual leap of the imagination.
36:12He thought of something that would lay the foundations
36:14not only of a theory for why planets moved slower or faster,
36:18or went in orbits that weren't circular.
36:20What Kepler was thinking about was a theory that would do nothing less
36:24than explain how the entire universe worked.
36:28What Kepler worked.
36:56What Kepler worked.
37:01The only explanation for the figures was a kind of magnetic force from the Sun,
37:06strong near it and weaker further out.
37:08A force pulling the planets into orbital paths, like Benedetti's swinging stones,
37:13or into lopsided orbits that sped up close in and slowed down further out,
37:18and stayed that way because the force was always there to keep the planets repeating exactly the same path.
37:25But was he right?
37:29It took Kepler four years to work it out.
37:33Mars wasn't changing speed at a regular rate in a circle, and nor were the other planets.
37:38It was doing it in an ellipse, and it was doing it like clockwork,
37:42the change in speed exactly relative to the distance from the Sun.
37:47Close in, going fast, taking a month from there to there.
37:51Far out, going slow, a month from here to here.
37:54But these areas...
37:57exactly equal.
37:59You'll notice that I'm drawing little triangles like Kepler was.
38:02That's because that's how they measured orbits.
38:04You split the orbit into zillions of little triangles,
38:06and used them to tell you the area and the approximate length of the orbit.
38:11And that's why Kepler's new method for measuring wine barrels,
38:15which incidentally proved the dipstick method was fine,
38:17was such a big deal for astronomy.
38:19It was immensely accurate.
38:21Look.
38:23Kepler split each barrel into zillions of little cross-sections like that.
38:28Each one of which, on the edge, would look something like this.
38:34Now, a rectangle is easy to measure,
38:37and you fill this one almost with a little triangle.
38:40That little leftover bit there is minimal.
38:43That's why I keep using the technical term zillions.
38:46The more sections you make,
38:49the smaller those little leftover bits there become.
38:51And if you have an infinite number of sections,
38:54you get no leftover bits at all,
38:56and total accuracy on the curve of a barrel,
38:59or the curve of an orbit.
39:03Which was all amazing stuff,
39:05and advanced the state of the art of orbital dynamics, as it's called.
39:08But it did create a problem almost as big as the one it solved.
39:18Kepler might have been a genius at getting the sky to work according to his sums,
39:22which left only the mind-boggling problem of working the sums out.
39:26Every time you wanted to check something,
39:28you were back to that ridiculous business of horsing around with zillions of little triangles.
39:32There had to be a better way than this.
39:45Well, when it came to sums, here was the place.
39:48Holland. The home of sums. Commercial sums.
39:52And, flat, sober and cosmopolitan, the Dutch loved science, if it made money.
39:58That's really all Amsterdam got worked up about.
40:00Financial matters, cash flow, bridging loans.
40:05Incredibly, they didn't care about what the rest of Europe was burning and torturing people for.
40:10The dull middle-class Dutch let you say and do and think almost anything you liked.
40:16The first truly tolerant nation in Europe.
40:18And because of it, knee-deep in refugees.
40:21One of which, a French thinker called René Descartes, in 1637,
40:27came up with an entirely new way of looking at everything.
40:29Including, of course, balls in the sky.
40:32Look.
40:33However I move, I'm either going along or up, aren't I?
40:37Descartes tried setting that movement against two scales.
40:41One showing how far up, the other how far along.
40:45So, run me by again with numbers.
40:49Up one, along five.
40:51Up two, along 16.
40:55Up three, along 25.
40:57And you could describe any movement like that on Descartes' new graph.
41:03Now, suppose I want to do that with a cannonball.
41:06Say I want to shoot it out at 100 feet per second, like this.
41:11Here's the trajectory.
41:13Here's the scales.
41:14Call up y and along x.
41:17So you can describe this trajectory in x's and y's.
41:20And you could put in Galileo's law, Tartaglia's air resistance, speed, anything.
41:25And fire your cannon on paper, because now you could fire it in an equation.
41:33Now, you see what that means?
41:35With a system like that, there's no more mumbo jumbo.
41:37Just mathematics that you can now use to describe and predict everything.
41:43Even the stuff you can't handle, like the planets.
42:05All you needed to get the really precise data you could now handle with your fancy new maths was instruments.
42:11And there were none better than those made in mid-17th century England.
42:23Calculators, logarithms, slide rules, vacuum pumps, microscopes,
42:27theodolites, quadrants, thermometers, barometers, clocks.
42:31The new instruments and techniques made it possible to examine everything
42:34from the microscopically small to, more important for us, the astronomically large.
42:40And start getting really accurate figures.
42:58The fellow who put it all together, literally, why Benedetti's stones went off in a straight line when you let
43:04them go,
43:05why Galileo's balls fell at the same rate, why Kepler's planets went fast in round the sun and slow far
43:10out from it,
43:11and the clever way that Descartes could turn trajectories into algebra.
43:15The fellow who put all that together was the first person in history who could have explained mathematically what I'm
43:20about to go through now,
43:21and why the whole universe goes through it.
43:24What am I talking about?
43:26This.
43:28Galileo's accelerating fall, now.
43:33Benedetti's outward swing, now.
43:38Kepler's orbits with their changing speeds.
43:44And the slowdown as I go over the top.
43:48And the same again.
43:50Galileo's accelerating fall,
43:54Kepler's orbits,
43:56and the outward thrust of Benedetti's centrifugal force.
44:02Fortunately for the fellow who made sense of it all,
44:05he didn't have to go through this.
44:08He says he just sat and watched this.
44:15He reckoned the force that made things fall was the same downward pull as the one Kepler said held the
44:21planets as they swung around the sun,
44:23and stopped them flying off like Benedetti's stones,
44:26because this force attracted everything to everything else.
44:29He worked out a formula for how the force should operate based on how far apart things were.
44:35Well, he knew the Moon was 60 times further out from the centre of the Earth than he was,
44:39so he tried his formula on the Moon.
44:42The pull of the Earth ought to be acting like a hold on the Moon,
44:45counteracting its tendency to fly straight off into space by exactly the amount of force required to keep it in
44:52orbit at that distance.
44:52So our genius, using an advanced form of infinitesimal calculation, you remember Kepler and the wine barrels,
45:00worked out where the Moon's path ought to go if the force acted, as his formula said it should, that
45:06far from Earth,
45:07at 44 thousandths of a foot per second, bending the Moon's path inwards.
45:12Sure enough, that's just what the Moon did, to the edge.
45:19His formula explained what everything else did too.
45:22Planets, pendulums, apples, fairground swings, everything.
45:32The force Newton-named gravity kept the universe balanced, made it work, and brought Heaven and Earth together in one
45:40great equation.
45:43And just as his formula would tell you when what went up would come down,
45:47so it told his friend Edmund Halley when the great comet he saw leaving the solar system in 1680 would
45:53come back,
45:54exactly 77 years later.
46:03We end the story where we began, here, in the Empress Maria Theresa's palace in Vienna.
46:10Because the year Halley's Comet was due back, 1757,
46:14there was a fellow here who was, so to speak, to dot the I's and cross the T's on the
46:18whole affair.
46:19He was a Jesuit astronomer, and mathematician, engineer, geographer, geodeticist and general genius,
46:26called Roger Boscovich.
46:28Now, Boscovich had done a lot of work on comets,
46:31like how to get a very accurate handle on their trajectory from any three observations.
46:37And he'd put in a prize-winning paper to the French Academy of Sciences,
46:41he was one of their foreign correspondents, on the interaction between Jupiter and Saturn.
46:45And it was through that enormous gravitational tug-of-war
46:49that the returning Halley Comet had to come on its way back into the solar system.
46:53The question was, when?
47:00That's why the Boscovich work was kind of vital to the French astronomers watching for Halley,
47:06because it told them that the comet would be returning late,
47:09even before they picked it up on their telescopes.
47:11Thanks to Boscovich, they knew it would be 19 months late.
47:15I said Boscovich ended the story for another reason, too.
47:19He was, among his many talents, like fixing the cracks in Maria Theresa's library,
47:24also science advisor to the Pope.
47:26And it was mainly due to him that the prohibition on Copernicus would be lifted.
47:35Fittingly, the great work went back into general circulation on the library shelves of Europe in 1758,
47:42the same year Halley's comet finally came back.
47:45Ultimate physical proof that Newton had been right, that the universe was ruled by mathematics.
47:52Well, that was the end of friend Aristotle, and magic crystal spheres in the sky,
47:57and questions science shouldn't ask, and the beginning of our modern world dominated by science and technology,
48:03and the confidence they give us to explore everything from subatomic particles to the ends of outer space without fear.
48:10Mind you, you need the confidence.
48:13If, as Kepler said, and Newton proved, it all does work like clockwork.
48:18There is nobody out there to care.
48:21Well, it may be fun to explore nature, to boldly go where no man has gone before.
48:27But in Newton's universe, you're no longer the centre of attention while you do it.
48:32You're on your own.
48:33Just a cog in the cosmic clock.
48:36legal Elite 4
48:36ss
48:48ss
48:54ss
49:04mass
49:34VIOLIN PLAYS
49:52VIOLIN PLAYS
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