Monthly Archives: June 2000

Napoleon’s Academic Conquest of Egypt

I was reading a very interesting book : Napoleon by Vincent Cronin .

It is a wow biography . There is a very interesting chapter on Napoleon’s Egypt conquest . This conquest was not merely a military project but was also a academic adventure . In today’s VERITAS we will only talk about the Academic campaign and not the Military Campaign .

      Napoleon’s plan was to attack Egypt and then take control of the silk route , build a canal and then attack India .But it was also to be a expedition of learning and understanding the ancient civilization.

      Napoleon started recruiting a strange kind of army that consisted of scientists , artists , historians , poets and normal  soldiers too .

Among the people who hie took with him were :

Geoffery Hilaire : Natrulist

Nicholas Conte : Baloon Warfare expert

Dolomieu : Mineralogist

Fourier : Mathematician

Redoute : Painter

 

He also took a huge library on his ships and the evenings on the deck were spent in scientific and philosophical discussions .

Do you know that Napoleon was a amateur Mathematician himself. There is even a theorem in Goemetry called Napoleon’s Theorem !!!

 

      He landed in Egypt in 1798 .

      After he beat the Turks in the battle of Pyramids he became the ruler of Egypt . He published the first Egyptian books . He had the got the type from Europe . His knowledge of the Quoran made him popular with the locals . Now the english admiral destroyed the shpis that Napoleon had used to land in Egypt and napoleon and his troops were stranded in Egypt .

      Napoleon made good use of his time . He formed a Institut de France consisting of the scientists that he got with him . napoleon became its head . The members would meet every five days and discuss science . All members grew thick moustaches . This was the kind of research these dudes did :

Berthollet : Egyptian technique for manufacturing indigo Norrey : Measured Ptolemy’s coloumn Savigny : found an unknown species of water Lilly Viloteau : studied Egyptian Music Larrey : studied Egyptian eye problems.

 

      Napoleon himself along with his friend Cafarelli studied the canal

which in ancient times joined Mediterranean Sea and the Red sea . They would

take 2  roasted chickens with them and spenf the whole day studing the canal.

Napoleon also measured the dimensions of the pyramids .

 

      napoleon also ordered the historians to study the history of Egypt .

He also encouraged the study of ancient egyptian writings : hierographics .

Till now no one knew what the symbols in the writings meant . So the

writings on Pyramids etc could not be understood .

 

      At a session of the institute Lancret presented before Napoleon

a wonderful stone : The rosetta stone . It was 3 feet X 2 feet and

had text written in 3 languages : ancient egyptian hierographics , greek

and domonic . Lancret was an expert in greek and started to decipher

the egyptian writings . He was joined by Champillion who was an expert

in 9 languages . They together deciphered the ancient egyptian language.

 

      This was a major discovery . Egyptians were thrilled . A whole

world of Egyptian History was opened to them .

 

      So we see how much work was done by Napoleon’s  institute while

stranded in Egypt . The sea was blocked and Napoleon’s fleet was

destroyed . He could not go east because the Turks were hostile .

So Napoleon and his institute stayed in Egypt and discovered

Science , history and goegraphy of Egypt .

 

Coffee History

An amusing very short history of coffee :

      Coffee is said to have been discovered by a goatheard in Abysinia His goats started dancing on their hindlegs after eating some red colored berries ( These were coffee berries )  . He took some of these berries back to his village and people found that eating these berries kept them awake during their prayers . This was sometime in 6th century AD .

 

      In 1453 Coffee was introduced in Turkey by ottoman turks . The world’s first coffee shop Kiv Han opens there in 1475 . Turkish law makes it legal for a wife to divorse her husband if he fails to provide for her daily cup of coffee .

 

        When Coffee was first introduced in Italy the wine merchants appealed to the Pope to ban it . It threatened to compete with wine sales.

The pope tasted it and liked it so much that he proceeded to Baptize it !!

 

       In 1607 Captain John Smith introduces coffee to N.America .

       between 1600 and 1650 coffee houses appeared all over Europe .

 

      In 1732 Bach composed “Kafee-Kantate” . This was partly an ode to coffee and partly a protest against the German Govt who prevented women from drinking coffee

 

      In 1901 the first instant coffee is invented by Satori Kato of Chicago

 

 

Range of Physics Week Day 5: Angular Momentum in Quantum Mechanics: Electron Spin

 

      Today we come to the world of the ultrasmall . The world of electrons , photons and other elementary particles .

      And the world here is very different fom anything we can ever imagine . The most important things here are probabilities , uncertainties and quantizations . How does this Change our view of Angular Momentum .

 

      Most important thing : Angular momentum is still conserved .

However the way we imagine it becomes very different . Here is how it

is ( The actual theory is very vast. But here are a few glimpses) :

 

      Lets take an electron : Every particle has a spin quantum number.

It has to be either integral or half integral . For an electron the

spin quantum number is 1/2 ( half ) . This means that en electron

can have the following values of its spin Angular Momentum( z component

actually ) :

 

      +1/2 * h/2*pi          or           -1/2 * h/2*pi

 

An electron ( any electron ) can exist with just these 2 values of

angular momentum . You cannot make a electron have more angular

momentum or less angular momentum by making it spin faster or slower

or doing anything of this sort . So we see a wierd thing here .

Angular momentum becomes quantized . Similarly a particle with a spin

value of 1 can have the following 3 values of angular momentum :

 

    +1 * h/2 * pi    or      0           or      -1 * h/2 * pi

 

But if you put 2 electrons in a system the total spin of the system

becomes 1 and it now behaves just like a spin 1 particle ( ie has 3

values of angular momentum ) .

 

      Particles with half integral spins ( like electrons ) are called

fermions and no 2 of them can be in the same state . This is pauli’s

exclusion principle .

 

      Particles with integral  spins ( like photons ) tend to get together

and are called bosons.

 

      Now the term Electron spin is very misleading . NOBODY has ever

seen a electron spin around its axis . Electon does not even have a axis .

And you cant even see a electon spin around its axis if it did ( would

violate the uncertainty principle ) . So final word : electron does not

spin !!! The spin quantum number is actually means that the electron

has angular momentum even without rotating 🙂 . cool aint it .

 

      So has this spoilt the mood with which we started the week ?

I said that I will take a theory and show you how it applies at

all scales to the Universe . And now we see that our theory has to

change to suit the atomic world . Now let me say that the theory that

we applied to galaxies and cycles was a special case of the real

correct theory of Angular Momentum . And the correct thoery is the

theory that applies to elementary particles . So this theory ( Quantum Mechanics) is the RIGHT theory and all the stuff we studied in schools( Newtons

laws , electricity , magnetism etc ) can be dereived from Quantim Mechanics .

 

      So the theory of Angular momentum does apply to all range in the

Universe . It is just that at different orders of Magnitude the effects

that become important( and dominate) are different .

 

      God created the fabric of the Universe from a single thread ! 

 

Range of Physics Week: day 4 Angular Momentum on a Earth Scale: Coriolis Force

 

      Yesterday we discussed about how Angular Momentum and its conservation produces some effects on an Astronomical scale .

 

      Today we will talk about a effect it causes on Earth. It is called coriolis force .

 

      Imagine a rotating flat disk and you are standing on its end .

Let your mass be m and you be standing at a distance R from the axis

of rotation . Let the disk be rotating at an angular velocity of w .

So your contribution to the angular momentum is m * (R^2) * w . the

m * R ^ 2 is your moment of inertia .

 

      Suppose now to try and move towards the axis of rotation .

Now your distance from the axis be r . Now your new angular momentum

is m * ( r ^ 2 ) * w . It has become less . But it cannot just become

less . It has to be conserved . So you will experience a sideways force !

 

      So a body on a rotating thing , when it moves towards/away from the

axis experiences a sideways force . This is called the Coriolis Force .

 

      So if you move towards the centre of a Merry go around u will

get a sideways kick ( depending on the speed of the merry go around and

ur speed ) .

 

      Now our Earth is also a rotating system and the Coriolis force

produces some interesting effects here too .

 

        A projectile when moving on the Northern Hemisphere of earth

experiences a deflection towards its right . Similarly in the southern

hemisphere there is a deflection towards the left . Missile designers

have to take care of this because the deflection can be very big for long

range missiles .

 

      Winds on the surface of earth move from high pressure to low

pressure areas . If earth were not rotating the winds would be parallel to

isobars . But earth ghoom rahi hai ! so the coriolis force comes and the

winds are deflected to the right on the Northern Hemisphere !

 

      Coriolis force is a very visible phenomenon . River beds are dug

deeper on one side the on the other( right side on the Northern Hemisphere) .

 

      Coriolis force has also resulted in a lot of hype . People claim

that water in the sinks drain/move counterclockwise in the Northern

Hemishere and clockwise in Southern Hemisphere . But this is not because 

of the Coriolis force . The flush/sink designers make it look that way !

Coriolis force cannot deflect the fast moving water in a small sink .

The sink would have to be hundreds of metres in radius to produce a

visible effect . Could we say that here we have an application of

Angular Momentum in Commerce !!! 🙂

 

We even have a poem about Coriolis force :

 

May the Force be with you

————————–

 

On a merry-go-round in the night,

Coriolis was shaken with fright.

Despite how he walked,

‘Twas like he was stalked,

By some fiend always pushing him right.

 

 

kyon ? ghumaa diya naaa ? 😉 

 

Range of Physics Week: Day 2 : What is Angular Momentum

      Most of us would probably be familiar with the basic theory of angular momentum . But for completeness sake here it is in a very very abridged format.

 

      Angular momentum is a measure of a body’s tendency to continue to spin around its axis or revolve around something else . It depends on

2 things :

 

1) The distribution  of the mass in the body . A body whose mass is close to

   the axis is more diffcult to start and stop rotating. A body whose mass

   is far away from the axis is easier to rotate / stop rotating .

 

   Also for the same distribution the heavier body is more difficult to

   stop/start rotating .

 

   This factor is called Moment of Inertia . Its symbol is I .

   This is the counterpart of mass in linear motion .

 

 

2. The angular velocity of the body : You would appreciate that it is

   easier to make slowly rotating body stop and more difficult to

   make a rapidly rotating body stop . The angular velocity of a body

   is the speed( velocity to be exact ) of its rotational motion . Angle

   covered in unit time . Lets call this factor w

 

 

   So we define angular momentum as I w

 

 

   But we also need a direction for this quantity . Why ? To differentiate

   between say clockwise and anticlockwise rotations . So some people defined

   a direction of motion to perpendicular to the plane of the rotation of

   the body and the direction is given by the “right hand rule” .

   If you wrap your fingers in the direction of the rotations then the

   the direction of the thumb gives you the direction of the angular momentum.

 

   For example if u stand and look at the clock then the direction of

   angular momentum of the second hand is right into the clock ( at right

   angles) .

 

 

   Now another important thing about angular momentum is that if

   you want to change it you have to apply an external force ( torque) to

   it . The angular momentum of a system left alone( and of the whole world)

   remains constant . That means that angular momentum is a conserved

   quantity.

 

  Even if you want to change the direction of motion you still have to

  apply an external torque .

 

  Why does a moving bicycle not fall ? The reason is that to make it fall

  we will have to change the angular momentum of the wheels and to do

  that we will have to apply a large external force ( at the right place ).

  So it is the rotation of the wheels of a bicycle that give it stability.

  The faster it moves the more stable it is .

 

  That is why a top keeps rotating and does not fall . That is why

  bullets that spin on the way to the target have more stability

  than those that dont . That is why all rockets/satellites are deliberately

  made to rotate .

 

  Rotation gives the body stability . It takes a large torque to change

  the direction of rotation of a rapidly rotating body . So it is more stable.

 

Range of Physics Week: Day 1 : Some “Philosophical” Remarks

 

      First lets examine the question : Why is there so much rotation

      in the Universe . Any star , any planet , any galaxy , any anything

      rotates . Why is that ?

 

      Let me answer that by sating that this is a bad question .

      The reason is that rotation is a natural degree of freedom and

      you cannot ask a body ” why do you rotate?” . If you go someplace

      in the Universe and a body is rotating u should not ask Why .

      If you go someplace and some body is not rotating Then u SHOULD

      ASK : “why are you not rotating ? ” Because it is strange if

      a freely suspended body does not rotate. Not rotating is strange ,

      rotating is not strange .

 

      If a body is not rotating that means that there is a perfect

      balance of forces(torques) from all sides . That is usually

      not possible ( the probability is very small ) . And a body

      if it starts rotating , then it is very difficult to make it

      stop . You have to apply the right amount of force and the right

      place and only then it will stops . And if by mistake you

      apply a little bit extra or a little bit less force or

      force at a little bit different angle then all your efforts are

      useless because the body will not stop rotating . Just the

      nature of the rotation will change . So the probabilty that a

      random force will start a rotation is VERY LARGE but the

      probability that a random force will stop the rotation is VERY SMALL .

 

 

      So we se that there is a HUGE number of things in the UNiverse

      which keep rotating . Things made of all sorts of constiuents,

      things rotating in all sorts of wierd ways . But the amazing thing

      about Physics is that all rotations , of any body is explained

      by the Theowy of Angular Momentum . One concept( Angular Momentum)

      describes all rotations .

 

      Some people feel that there is nothing great about it  .

      A ball rotates , a electron rotates . So if u treat the electron

      just like a ball then the same theory should apply .

 

      But notice that this is wrong . Lets examine the rotation of

      a ball . It consists of a huge amount of smaller pieces and when

      we say that a ball rotates it actually means ” The pieces away

      from the axis are revolving around the axis ” . So in a sense

      there is a revolution and not a individual piece rotation .

      And each of these pieces are in turn made of smaller pieces .

      Have you ever seen a INDIVIDUAL PIECE spin ???? No .

      In the observable world around us there is nothing like a

      individual piece . Everyhing we see around us has millions and

      zillions of pieces in it . So a theory od spin for a cricket ball

      applies to a piece made of millions of smaller pieces .

      But an electron is a individual piece ! In the truest sense of

      the term . So should the same cricket ball spin theory apply to

      it ???????

 

      So it is not obvious that the theory of angular momentum that we

      made of a cricket ball should apply to the electron as well .

      But it does apply . And there is the power of the ideas of Physics !

      We will see later that we do need some modifications to

      apply the same theory to the electron and the ball . 🙂

 

      This is why I want to demonstrate the scalability in Physics .

      That this kind of a thing is not obvious . But still it happens .

      And that is what makes Physics so fascinating . 

Range of Physics Week

Hi ,

 

      For the next five days we are going to talk about Angular momentum .

      The aim is more sentimental than academic . I want to demonstrate

      the range at which a basic concept of Physics is valid .

 

      So we are going to take a concept of Physics( Angular Momentum )

      and take it to all scales : The scale of the Universe ( 10 ^ 15 metres),

      then we will take the same concept to a earth scale( 10 ^ 2 metres )

      and then we will take the same principle into the depths of

      subatomic particles( 10 ^ ( -15 ) metres ) . So you will be

      able to see that a single law of Physics can be applicable for

      30 orders of magnitude !!! We will see how it changes its form

      at various scales and what parts remain the same .

 

      If you take a step back and see what it means you would feel

      a sense of wonder . Do you know of ANY other subject/idea

      apart from Physics that has such a Universal validity ?

      You take it anywhere and it still works !

 

      Einstein said ” Everything else is for the time being !

      But an Equation … An Equation is something for Eternity “

 

      The agenda for the next five days :

 

Day 1 12 June : Curtain raiser , some general/philosophical questions.

Day 2 13 June : What is Angular Momentum . Definitions .

Day 3 14 June : Cosmological scale : Galaxy Formation, Accretion Discs Day 4

15 June : Earth Scale : Coriolis Force and its effects Day 5

16 June : Subatomic Scale : Angular momentum in Quantum Mechanics

Diophantine Equations

Diophane was a Greek Mathematician in whose honour a whole field of mathematics is named . The fied is Diophantine equations and is a part of the number theory . ( Number theory is a field that deals with numbers and their properties 🙂 .. sometimes I make such informative statements )

 

      Okay . Now the difference between Diophantine Equations and other kinds of equations is that in Diophantine Equations we insist on integral solutions . That means that we dont want decimal solutions .

For example one Diophantine Equation can be :

 

      1027x + 712y = 1

 

Note that we have one equation in 2 variables and we are supposed to find integral solutions to the problem . One solution is x= -165 and y = 238 .

Of course there may be others.

 

      One famous incident related to Diophantine equations : One day

Hardy( Ramanujan’s mentor ) went to visit Ramanujan in the hospital

(Ramanujan was suffering from tuberculosis ) . Hardy says that the cab

he took had a very uninteresting number 1729. Ramanujan smiled and said :

1729 is the smallest number that can be expressed as the cube of two

numbers in two different ways . What Ramanujan had solved was the Diophantine

Equation :    a^3 + b^3 = c^3 + d^3

 

 Fermat’s last thoerem is also an example of Diophantine Equation .

He said that there cannot be a solution to the equation :

 

x^3 + y^3 = z^3 .

 

Note that u are allowed only whole numbers in place of x,y and z .

 

      There is no general way to solve problems of this kind .

Hilbert the famous German Methematician challenged mathematicians

to find a algorithmic approach to solve problems of this kind .

But it doesnt work ! In fact there are theorems which say that

given a Diophantine Equation there is no way to determine if it

has a solution or not . 

Lightning flashes

Hi,

 

      I am sitting here with a copy of Feynman lectures on Physics volume II . There is a very interesting chapter in this :

” Electricity in the Atmosphere” . And a very interesting section in this chapter describes Lightning . I will share some excerpts from this section.

 

 

      He considers the case of a cloud with a negatively charged bottom over a flat country .

 

 

 

 

            |                 |

            |                 |  <- a -vely charged cloud

            |                 |    

            ————————-

                 

                   

                   /                   <-  a step leader

                  /

                 

                          

 

 

 

      —————————————————-

      +   +   +   +  +  +  +  +   +  +   +   +   +    +   +

                                    positively charged ground

 

 

 

      It all starts with a “step leader”  which is not as bright as the lightning . It is a “rod” of -ve charge that moves rapidly from the cloud ( at about 1/6 the speed of sound ) . It goes down for about 50 metres and then stops . It waits for about 50 millisecs and then starts again then it pauses again and starts again . thus forming a series of steps on its way down to the ground .

The “step leader” ionizes the air in its path as it goes down .

When the leader touches the ground u have a “wire” from the cloud to the ground . The -ve charges near the lower part of the leader ( part near the ground ) now get “neutralized” . This produces the lightning flash .

Very bright . Now the charges higher up in the leader get “neutrazized”

and the flash travels upwards. So the lightning flash that we see moves from the ground to the cloud !!! This is called a “return flash”.

 

 

      The current in a lightning stroke is about 10,000 Amperes !

 

      Now after some time ( 1/100 sec ) another leader comes from the cloud . This time no pauses . It comes from the cloud to the ground in one swoop .  It travels along the same path that it had created earlier .

This is called ” dark leader” . As soon as it touches the ground ZING ! a return flash rises upwards. One more flash . This keeps happening  in rapid succession : 5 times , 10 times and can go upto 40 times along just one path .

 

      Feynman goe on to describe more complicated types of lightning flashes . But we wont go into that .

 

 

      The series of books ( Feynman Lectures ) is very very beautiful .

A must read for anyone with any interest in Physics.

 

      Forgive my diagram but u cant draw neatly using a keyboard 🙂