Chaos  Chapter 5 : Billiards  Duhem's bull
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Formal Metadata
Title 
Chaos  Chapter 5 : Billiards  Duhem's bull

Title of Series  
Part Number 
5

Number of Parts 
9

Author 

Contributors 

License 
CC Attribution  NonCommercial  NoDerivatives 3.0 Unported:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and noncommercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
DOI  
Publisher 
Joe Leys, Étienne Ghys, Aurélien Alvarez

Release Date 
2012

Language 
English

Producer 

Content Metadata
Subject Area 
00:00
Area
Complex (psychology)
Collision
Direction (geometry)
Surface
Projective plane
Mathematical model
Line (geometry)
Regular graph
Weight
Parabola
Mathematics
Computer animation
Velocity
Mathematician
Friction
Position operator
Stability theory
03:30
Cue sports
Infinity
Trajectory
Similarity (geometry)
Game theory
Table (information)
Mathematician
Matching (graph theory)
Initial value problem
Nearring
Ellipse
05:42
Complex (psychology)
Computer animation
Manysorted logic
Direction (geometry)
Trajectory
Game theory
Friction
Condition number
08:25
Area
Point (geometry)
Cue sports
Dot product
Rational number
Real number
Multiplication sign
Direction (geometry)
Trajectory
Mereology
Arithmetic mean
Computer animation
Meeting/Interview
Velocity
Physicist
Finite set
Right angle
Table (information)
Position operator
Initial value problem
12:39
Mathematics
Computer animation
Chaos (cosmogony)
Mathematical model
Quantum state
13:11
Mathematics
Computer animation
Chaos (cosmogony)
00:07
understanding of celestial objects it is an old dream the some people say they can read their best start please but we predict collisions between planets it I what could gravitation projects some planets the With or should we rather expect and the stability of the solar system the the but he's a delicate question the did but as always in mathematics but faced with a problem that is too difficult is that the 1st look for simpler situation Henry man for consider this parabolic the and the the if we launch a ball is subject to its weight direction for which we see that the pond is analogous to that of a man who tried to stop his movement seems to regular model complex solar system with let's take a boat that is the of the ball was still subject to its way into the reaction from now the movement is really and if you can in let's take away the weight of the box but keep the reaction force of the surface but this into G8 due him the philosopher of science presenting the work the mathematician other Mark published in 1898 an article entitled on surface With opposite the material maths slide that it is more friction candles he describes her line that John Mitchell called but under consideration when the initial position on matters and the direction of its initial velocity the geodesic defined area you can do why am I he
03:33
imagined a full head of the move Fred we support him the homes passages between his game list fixed in the home actually lost we really get have 1 of the officers that you want to study extend the Ford's toss infinity Shirley is some fancy a mathematician 4 match in launching all for him and at end the 1st the different except book 1 that isn't quite close out of does thinking here is a rectangular billion I should do about then another almost the same way 2 simpler 2 balls father trajectories them very close yeah an elliptical billiard table
05:10
president near and ate I know still To here also 2 balls with similar initial conditions have trajectories that remained close together it is as if we were trying to death 6 on the 4th without but that's head of a
05:44
circular on by but now the 2 nearby trajectory parent game they heaped upon In the 1st goes off in 1 direction and the other is a completely different direction their futures quickly become very different can do the here is he also without any
06:32
friction there are 3 circular obstacle let's call them MCA now it's as if we are observing Ojeda 6 on us with 3 let's take a ball and she if we well trajectory and then see that then be In periodic trying to get but the other periodic audits there was beautiful he said but if you choose any work Rick the 3 letters a he under the condition the consecutive letters are different for example ABC ABC C then there is a periodic trajectories visits the bumper successively indeed ordered dictated by the wording question that you see complexity of the situation for each word there's a periodic trajectories and there are lots of sorts for example the word gay scene being seen being seen Is it trajectory that pertains to hit us once every 11 rebounds it will hit on Burke Of course we must aim precisely very very precise the but I the an all this makes 1 think
08:26
of the real numbers what we regularly some of the periodic these are exactly the rational as an example 123 over 999 it 0 . 1 2 3 1 2 3 1 2 3 and so on while To over 7 is equal to 0 . 2 8 5 7 1 2 a time 7 1 2 8 5 7 1 and such a rational number when it does not they for example are table is similar some trajectories chaotic an are described by periodic word and the letters do In scene others In are described by means still others visit ATP concede a finite number of times and then they escaped to never to return here is to OEMs that
09:33
are geodesic the tools to the removal of the area they are all those dots coming back from nearly ended she far away from through Song keep turning around the right hole another those Toronto left are all those more complicated 1 I 1 hole we stood here are the photo in Hong Kong there would be geodesic that will go to infinity 1 by finding the right others like kind at home the imagine the His always been knickers companion suddenly deciding to shoot on Twitter at noon despite this complication before I know it was actually accuracy the initial position on the part of the former head of his boat and the direction of the initial velocity the geodesic that these point with foot during its movement wouldn't be fixed it would be quite different initial conditions and not known mathematical but Park I appreciate the subtlety not mathematically practically give watch these it did at the same point start almost in the same direction they follow almost then a separate green red and blue 6 have completely different future if the war lounged on the Salafist questions from a position that is given Joe Mexican With a speed that is given Joe Maddock could then mathematical deductions can determine the trajectory of the in determining this trajectory but for the physicist these deductions for ever you should so far all of this applies to GSA billiard ball trajectory can this be applied the everyday life of for instance the movement of the
12:41
planets the the but the question of telling my future it's still there