Paradox - An Ant on a Rubber Rope

I am sure you know this paradox quite well that's why you are here to read this post but I think you are not able to grasp the solution of the first order differential equation.

Let's forget the calculus solution and do it with intuitive way. It might not provide you the solution but we may have great discussion.

To solve the complex problems like this, break the problem in chunks so start with the shorter version.

An ant is crawling on a stretchable rope at a constant speed of 1 cm/s. The rope is initially 4 cm long and stretches uniformly at a constant rate of 2 cm/s. When will the ant reach to the initial end point (Corner of the 4 cm rope)?

Initially the ant is at the starting point of the 4 cm rope.

After 1 second, the ant travels 1 cm on the rope. Now here consider the rope does not stretch continuously. It means the rope is stretched 2 cm after the end of every second (The stretching time is negligible i.e. a Femtosecond). This thought might change the whole approach but it can be quite easy to understand because if the rope would stretch continuously then it would stretch all the smallest slots of the second as the ant moves ahead. 

So After 1 second, the ant has traveled 1 cm, and the rope is stretched 2 cm uniformly. It means every one cm of the rope is stretched 0.5 cm so complete 4 cm is stretched to 6 cm.

It makes ant's traveled distance 1 cm to 0.5 cm more stretched so after 1 second the ant has traveled 1.5 cm.

After 2 seconds, the ant travels 1 more cm. So the ant is at the 2.5 cm from the start but the rope is stretched again 2 more cm after the end of 2 seconds. This time this increased 2 cm distance will be distributed between existing 6 cm uniformly. It means every one cm of the rope is stretched 0.3333 cm so complete 6 cm is stretched to 8 cm.

 

It makes ant's traveled distance 2.5 cm to '2.5 x 0.33333 = 0.8333'  more stretched so after 2 seconds the ant has traveled 2.5 + 0.83333 = 3.3333 cm and so on

By this way, the ant will reach to the initial end point between 9 and 10 Seconds.

But if you solve this question using calculus, the answer is 12.77 Seconds

L=4 cm (Initial Length of the rope)

v=2 cm/sec (Rope stretching Speed)

u=1 cm/sec (Ant's speed)

 

There is difference in the answers, this is because we took the different approach but it will give you an idea how you will try next time to solve this question for your own satisfaction.

Approach : 2

Initially the ant is at the starting point of the 4 cm rope.

a) After 1 second, the ant travels 1 cm on the rope.

So After 1 second, the ant has traveled 1 cm, and the rope is stretched 2 cm uniformly. It means every one cm of the rope is stretched 0.5 cm. This 1 cm has been traveled by the ant so stretching distance will be (1x0.5)/2=0.25.

Ant will travel 1.25 cm after 1 second.

b) After 2 seconds, the rope is stretched again 2 more cm. This time this increased 2 cm distance will be distributed between existing 6 cm uniformly. It means every one cm of the rope is stretched 0.3333 cm so complete 6 cm is stretched to 8 cm.

If ant would stand still at 1.25 cm then it would have been moved to 1.25x0.3333=0.41666 cm more that is 1.25+0.416666=1.666666667 cm but ant is moving with speed 1 cm/sec so this 1 cm distance traveled by the ant will be stretched with (1x0.3333)/2=0.16666 so the total distance moved by ant after 2 seconds will be 1.666666+1+0.166666 =2.833332 cm

c) After 3 seconds, the rope is stretched 2 more cm. This time this increased 2 cm distance will be distributed between existing 8 cm uniformly. It means every one cm of the rope is stretched 0.25 cm so complete 8 cm is stretched to 10 cm.

If ant would stand still at 2.83333 cm then it would have been moved to 2.83333x0.25=0.7083325 cm more that is 2.8333333+0.7083325=3.5416658 cm but ant is moving with speed 1 cm/sec so this 1 cm distance traveled by the ant will be stretched with (1x0.25)/2=0.125 so the total distance moved by ant after 2 seconds will be 3.5416658+1+0.125 =4.6666658 cm

d) After 4 seconds, the rope is stretched 2 more cm. This time this increased 2 cm distance will be distributed between existing 10 cm uniformly. It means every one cm of the rope is stretched 0.2 cm so complete 10 cm is stretched to 12 cm.

If ant would stand still at 4.6666658 cm then it would have been moved to 4.6666658x0.2=0.93333316 cm more that is 4.6666658+0.93333316=5.59999896 cm but ant is moving with speed 1 cm/sec so this 1 cm distance traveled by the ant will be stretched with (1x0.2)/2=0.1 so the total distance moved by ant after 2 seconds will be 5.59999896 +1+0.1 =6.69999896 cm and so on.

By this way, the ant will reach to the initial end point between 12 and 13 Seconds.

This is an almost same time calculated by calculus solution.

The difference between approach 2 and previous approach is the stretching distance calculation of ant's traveled distance. We took half of the stretching distance in approach 2 and it gets us near the exact answer.

Case II

Now Let's discuss one easy condition in this question. Suppose the ant is at the fixed distance from the initial point. Let's say 1 cm from the initial point but the ant does not move a bit. Only stretching factor of the rope makes it move further.

One thing is clear in this condition, the ant will never reach to the end point.

But it will never be at the 1 cm always so how much will it move.

At 0th second, it is 1 cm from the start.

After 1 second, rope is stretched 2 more cm. This 2 cm is distributed between existing 4 cm uniformly that makes the total length 6 cm. Every cm is stretch to 0.5 cm so the ant will be at 1.5 cm from the start. That is 25% of the total length.
75% remaining.

After  2 seconds, rope is stretch 2 more cm. This 2 cm is distributed between existing 6 cm uniformly that makes the total length 8 cm. Every cm is stretch to 0.3333 cm so the ant will be at 2 cm from the start. That is 25% of the total length. 75% remaining.

After  3 seconds, rope is stretch 2 more cm. This 2 cm is distributed between existing 8 cm uniformly that makes the total length 10 cm. Every cm is stretch to 0.25 cm so the ant will be at 2.5 cm from the start. That is 25% of the total length. 75% remaining.

It means if the ant does not move, The 'distance to cover' ratio does not change and that's why if the ant starts moving very slowly, it will always reach up to end,  if sufficient time is given and stretching speed is constant.

Case III

Now there is another condition. Suppose the rope gets doubled after every second. Speed of the ant is same i.e. 1 cm / second and initial length of the rope is also 4 cm.

What will happen now ? Will it reach up to the end point?

After 1 second, length of the rope is 8 cm. It means increased 4 cm is distributed between existing 4 cm uniformly. Every one cm of the rope is stretched to 1 cm. The ant will be at 2 cm but length of the rope will be 8 cm.

After 2 seconds, length of the rope is 16 cm. It means increased 8 cm is distributed between existing 8 cm uniformly. Every one cm of the rope is stretched to 1 cm. The ant was at 2 cm and now it travels 1 more cm in 2nd second, as the rope is stretched, the ant will be at 6 cm but length of the rope will be 16 cm.

After 3 seconds the ant will be at 14 cm from the start and length of the rope will be 32 cm.

After 4 seconds the ant will be at 30 cm from the start and length of the rope will be 64 cm.

The stretching speed of the rope is not constant, it is accelerating and that's why the ant will never reach up to the end point.

 

 

Interstellar (2014) - Calculations and Analysis

                                             Interstellar (2014)
                                              Welcome to the Fountain
                                           Quench Increase your Thirst

Fact : 1
Miller's Planet to outside observers orbits Gargantua every 1.7 hours. On Miller's Planet, that means the planet orbits ten times a second around Gargantua , which is normally faster than the speed of light. But since the spin from Gargantua caused space to whirl around it similar to wind, Miller's Planet does not travel faster than light relative to its space as the laws of physics say you cannot travel faster than light relative to space, but space itself is not bound by the speed limit. As such, faster than light travel is possible by bending and twisting space. However, Gargantua would have to fill half the sky in order for it to be so close.

Fact : 2
The time dilation on Miller due to the gravitational forces of Gargantua would be tantamount to the planet moving through empty space at roughly 99.99999998% the speed of light. 

Fact : 3
Gargantua’s mass must be at least 100 million times bigger than the Sun’s mass. If Gargantua were less massive than that, it would tear Miller’s planet apart. The circumference of a black hole’s event horizon is proportional to the hole’s mass. For Gargantua’s 100 million solar masses, the horizon circumference works out to be approximately the same as the Earth’s orbit around the Sun: about 1 billion kilometers.

Fact : 4
Miller’s planet is about as near Gargantua as it can get without falling in and if Gargantua is spinning fast enough, then one-hour-in-seven-years time slowing is possible. But Gargantua has to spin awfully fast. There is a maximum spin rate that any black hole can have. If it spins faster than that maximum, its horizon disappears, leaving the singularity inside it wide open for all the universe to see; that is, making it naked—which is probably forbidden by the laws of physics

Fact : 5
Einstein’s laws dictate that, as seen from afar, for example, from Mann’s planet, Miller’s planet travels around Gargantua’s billion-kilometer-circumference orbit once each 1.7 hours. This is roughly half the speed of light! Because of time’s slowing, the Ranger’s crew measure an orbital period sixty thousand times smaller than this: a tenth of a second. Ten trips around Gargantua per second. That’s really fast! Isn’t it far faster than light? No, because of the space whirl induced by Gargantua’s fast spin. Relative to the whirling space at the planet’s location, and using time as measured there, the planet is moving slower than light, and that’s what counts. That’s the sense in which the speed limit is enforced.


QUERIES 
1. How old is Miller’s planet? If, as an extreme hypothesis, it was born in its present orbit when its galaxy was very young (about 12 billion years ago), and Gargantua has had its same ultrafast spin ever since, then the planet’s age is about 12 billion years divided by 60,000 (the slowing of time on the planet): 200,000 years. This is awfully young compared to most geological processes on Earth. Could Miller’s planet be that young and look like it looks? Could the planet develop its oceans and oxygen-rich atmosphere that quickly? If not, how could the planet have formed elsewhere and gotten moved to this orbit, so close to Gargantua?

2. What is the gravitational time dilation equation for Miller's planet? As there is 60000 ratio between time on earth and time on Miller's planet , to balance the equation what should be the distance of planet from Gargantua, angular momentum as it is revolving around very fast spinning object and Mass of Gargantua ?

3. We all know Gravitational Time Dilation does not affect Mann's planet as it is far from Gargantua’s vicinity. But we also know, almost immediately after the Endurance’s explosive accident in orbit around Mann’s planet, the crew find the Endurance being pulled toward Gargantua’s horizon. From this it appears when crew leaves Mann’s planet, the planet must be near Gargantua. Following diagram is the orbit of Mann's Planet.

According to this, what should be the orbital period and orbital velocity of Mann's planet for a person on Earth and a person on Mann's planet.

4. How long Dr. Mann spent time on Mann's planet according to him and according to an observer on Earth(Keep its orbital path in mind)? How long did he spend in hibernation for both observers?

5. Why was Endurance able to receive signal from Earth but Earth was not able to receive signal sent by Endurance.

6. When Cooper left Earth, he was 35 Years old and when he returned, He was 124 years old for Murph. 35 + 2 years for Saturn Journey + 23 years for Miller's Planet Journey + 51 years for Black Hole Journey = 111, Where are 13 Years Missing? How Long was Cooper out for himself?

8. What is the Orbital velocity of Miller's planet for a person on Earth and a person on Miller's planet?

9. What is the age of Brand when Cooper arrives at Edmund's Planet?

10. How long Dr. Laura Miller spent time on Miller's planet according to her and according to an observer on Earth? Lets keep in mind that she died minutes ago before Cooper and Brand reached there.

11. Miller’s planet travels around Gargantua’s billion-kilometer-circumference orbit once each 1.7 hours. Could Rom see it moving very fast from Mothership?

12. If Coop and team would try to communicate with Rom from Miller's planet, how would their communication appear? According to Coop how fast would they get response from Rom and similarly how long would Rom get response from Coop & team?

Space Time

Frequently Asked Questions

What is light?

Light is a phenomenon that has particle and wave characteristics. Its carrier particles

are called photons, which are not really particles, but massless discrete units of

energy.

What is the speed of light?

The speed of light is 299,792,458 m/s in a vacuum. The symbol used in relativity for

the speed of light is "c", which probably stands for the Latin word "celeritas",

meaning swift.

Is the speed of light really constant?

The speed of light is constant by definition in the sense that it is independent of the

reference frame of the observer. Light travels slightly slower in a transparent

medium, such as water, glass, and even air.

Can anything travel faster than light?

No. In relativity, c puts an absolute limit to speed at which any object can travel,

hence, nothing, no particle, no rocket, no space vehicle can go at faster-than-light

(=superluminal) speeds. However, there are some cases where things appear to move

at superluminal speeds, such as in the following examples: 1. Consider two spaceships

moving each at 0.6c in opposite directions. For a stationary observer, the distance

between both ships grows at faster-than-light speed. The same is true for distant

galaxies that drift apart in opposite directions of the sky. 2. Another example:

Consider pointing a very strong laser on the moon so that it projects a dot on the

moon's service and then moving the laser rapidly towards earth, so that it points on

the floor in front of you. If you accomplish this in less than one second, the laser dot

obviously traveled at superluminal speed, seeing that the average distance between

the Earth and the Moon is 384,403 km.

What is matter?

The schoolbook definition would be: Matter is what takes up space and has mass.

Matter as we know it is composed of molecules, which themselves are built from

individual atoms. Atoms are composed of a core and one or more electrons that spin

around the core in an electron cloud. The core is composed of protons and neutrons,

the former have a positive electrical charge, the latter are electrically neutral. Protons

and neutrons are composed of quarks, of which there are six types: up/down,

charm/strange, and top/bottom. Quarks only exist in composite particles, whereas

leptons can be seen as independent particles. There are six types of leptons: the

electron, the muon, the tau and the three types of neutrinos. The particles that make

up an atom could be seen as a stable form of locked up energy. Particles are extremely

Spacetime, small, therefore 99.999999999999% (or maybe all) of an atom's volume is just empty

space. Almost all visible matter in the universe is made of up/down quarks, electrons

and (e-)-neutrinos, because the other particles are very unstable and quickly decay

into the former.

How fast does an electron spin?

An electron in an hydrogen atom moves at about 2.2 million m/s. With the

circumference of the n=1 state for hydrogen being about 0,33x10-9 m in size, it

follows that an n=1 electron for a hydrogen atom revolves around the nucleus

6,569,372 billion times in just one second.

Are quarks and leptons all there is?

Not really. Fist of all, quarks always appear in composite particles, namely hadrons

(baryons and mesons), then there is antimatter, and finally there are the four

fundamental forces.

What is antimatter?

The existence of antimatter was first predicted in 1928 by Paul Dirac and has been

experimentally verified by the artificial creation of the positron (e+) in a laboratory in

1933. The positron, the electron's antiparticle, carries a positive electrical charge. Not

unlike a reflection in the mirror, there is exactly one antimatter particle for each

known particle and they behave just like their corresponding matter particles, except

they have opposite charges and/or spins. When a matter particle and antimatter

particle meet, they annihilate each other into a flash of energy. The universe we can

observe contains almost no antimatter. Therefore, antimatter particles are likely to

meet their fate and collide with matter particles. Recent research suggests that the

symmetry between matter and antimatter is less than perfect. Scientists have

observed a phenomenon called charge/parity violation, which implies that antimatter

presents not quite the reflection image of matter.

What are the four fundamental forces?

The four fundamental forces are gravity, the electromagnetic force, and the weak and

strong nuclear forces. Any other force you can think of (magnetism, nuclear decay,

friction, adhesion, etc.) is caused by one of these four fundamental forces or by a

combination of them.

What is gravity?

Gravity is the force that causes objects on earth to fall down and stars and planets to

attract each other. Isaac Newton quantified the gravitational force: F = mass1 * mass2

/ distance2. Gravity is a very weak force when compared with the other fundamental

forces. The electrical repulsion between two electrons, for example, is some 10^40

times stronger than their gravitational attraction. Nevertheless, gravity is the

dominant force on the large scales of interest in astronomy. Einstein describes

gravitation not as a force, but as a consequence of the curvature of spacetime. This

means that gravity can be explained in terms of geometry, rather than as interacting

forces. The General Relativity model of gravitation is largely compatible with Newton,

except that it accounts for certain phenomena such as the bending of light rays

correctly, and is therefore more accurate than Newton's formula. According to

Spacetime,General Relativity, matter tells space how to curve, while the curvature of space tells matter how to move. The carrier particle of the gravitational force is the graviton.

What is electromagnetism?

Electromagnetism is the force that causes like-charged particles to repel and

oppositely-charged particles to attract each other. The carrier particle of the

electromagnetic force is the photon. Photons of different energies span the

electromagnetic spectrum of x rays, visible light, radio waves, and so forth. Residual

electromagnetic force allows atoms to bond and form molecules.

What is the strong nuclear force?

The strong force acts between quarks to form hadrons. The nucleus of an atom is hold

together on account of residual strong force, i.e. by quarks of neighboring neutrons

and protons interacting with each other. Quarks have an electromagnetic charge and

another property that is called color charge, they come in three different color

charges. The carrier particles of the strong nuclear force are called gluons. In contrast

to photons, gluons have a color charge, while composite particles like hadrons have

no color charge.

What is the weak nuclear force?

Weak interactions are responsible for the decay of massive quarks and leptons into

lighter quarks and leptons. It is the primary reason why matter is mainly composed of

the stable lighter particles, namely up/down quarks and electrons. Radioactivity is

due to the weak nuclear force. The carrier particles of the weak force are the W+, W-,

and the Z particles.

How are carrier particles different from other particles?

Carrier particles, such as the photon, gluon, and the graviton are hypothetical. They

are thought to be massless and having no electrical charge (except W+ and W-). Force

carrier particles can only be absorbed or produced by a matter particle which is

affected by that particular force. They allow us to explain interactions between

matter.

How old is the universe?

Today's most widely accepted cosmology, the Big Bang theory, states that the

universe is limited in space and time. The current estimate for the age of the universe

is 13.7 billion years. This figure was computed from the cosmic microwave

background (CMB) radiation data that the Wilkinson Microwave Anisotropy Probe

(WMAP) captured in 2002.

What came before the Big Bang?

The Big Bang model is singular at the time of the Big Bang. This means that one

cannot even define time, since spacetime is singular. In some models like the

oscillating universe, suggested by Stephen Hawking, the expanding universe is just

one of many phases of expansion and contraction. Other models postulate that our

own universe is just one bubble in a spacetime foam containing a multitude of

Spacetime, universes. The "multiverse" model of Linde proposes that multiple universes

recursively spawn each other, like in a growing fractal. However, until now there is no

observational data confirming either theory. It is indeed questionable, whether we

will ever be able to gain empirical evidence speaking in favor these theories, because

nothing outside our own universe can be observed directly. Hence, the question can

currently not be answered by science.

How big is the universe?

The universe is constantly expanding in all directions, therefore its size cannot be

stated. Scientists think it contains approximately 100 billion galaxies with each galaxy

containing between 100 and 200 billion star systems. Our own galaxy, the Milky

Way, is average when compared with other galaxies. It is a disk-shaped spiral galaxy

of about 100,000 light-years in diameter.

What is the universe expanding into?

This question is based on the popular misconception that the universe is some curved

object embedded in a higher dimensional space, and that the universe is expanding

into this space. There is nothing whatsoever that we have measured or can measure

that will show us anything about the larger space. Everything that we measure is

within the universe, and we see no edge or boundary or center of expansion. Thus the

universe is not expanding into anything that we can see, and this is not a profitable

thing to think about.

Why is the sky dark at night?

If the universe were infinitely old, and infinite in extent, and stars could shine

forever, then every direction you looked would eventually end on the surface of a star,

and the whole sky would be as bright as the surface of the Sun. This is known as

Olbers's paradox, named after Heinrich Wilhelm Olbers [1757-1840] who wrote about

it in 1823-1826. Absorption by interstellar dust does not circumvent this paradox,

since dust reradiates whatever radiation it absorbs within a few minutes, which is

much less than the age of the universe. However, the universe is not infinitely old,

and the expansion of the universe reduces the accumulated energy radiated by distant

stars. Either one of these effects acting alone would solve Olbers's paradox, but they

both act at once.

If the universe is only 13.7 billion years old, how can we see objects that

are 30 billion light-years away?

This question is essentially answered by Special Relativity. When talking about the

distance of a moving object, we mean the spatial separation now, with the positions of

us and the object specified at the current time. In an expanding universe, this

distance is now larger than the speed of light times the light travel time due to the

increase of separations between objects, as the universe expands. It does not mean

that any object in the universe travels away from us faster than light.

Source:- thebigview.com

Flatland

In Flatland, a "jail" is a circle drawn around a person. Escape from this circle is impossible in two dimensions. However, a three-dimensional person can yank a Flatlander out of jail into the third dimension. To a jailer, it appears as though the prisoner has mysteriously vanished into thin air.

If we peel a Flatlander from his world and flip him over in three dimensions, his heart now appears on the right-hand side. All his internal organs have been reversed. This transformation is a medical impossibility to someone who lives strictly in Flatland.

A Flatlander can visualize a cube by examining its shadow, which appears as a square within a square. If the cube is rotated, the squares execute motions that appear impossible to a Flatlander. Similarly, the shadow of a hyper- cube is a cube within a cube. If the hypercube is rotated in four dimensions, the cubes execute motions that appear impossible to our three-dimensional brains.

In Flatland, Mr. Square encounters Lord Sphere. As Lord Sphere passes through Flatland, he appears to be a circle that becomes successivley larger and then smaller. Thus Flatlanders cannot visualize three-dimensional beings, but can understand their cross sections.

A Mobius strip is a strip with only one side. Its outside and inside are identical. If a Flatlander wanders around a Mobius strip, his internal organs will be reversed.

The mystic Henry Slade claimed to be able to change right-handed snail shells into left-handed ones, and to remove objects from sealed bottles. These feats are impossible in three dimensions, but are trivial if one can move objects through the fourth dimension.

Source : Michio Kaku's Parallel Worlds

Fourth Dimension

Flatlanders cannot visualize a cube, but they can conceptualize a three-dimensional cube by unraveling it. To a Flatlander, a cube, when unfolded, resembles a cross, consisting of six squares. Similarly, we cannot visualize a four-dimensional Hypercube, but if we unfold it we have a series of cubes arranged in a cross like tesseract. Although the cubes of a tesseract appear immobile, a four-dimensional person can "wrap up" the cubes into a Hypercube.

In Christus Hypercubus, Salvador Dali depicted Christ as being crucified on a tesseract, an unraveled hypercube. (The Metropolitan Museum of Art. Gift of Chester Dale, Collection, 1955. © 1993. Ars, New York/Demart Pro Arte, Geneva)

Cubism was heavily influenced by the fourth dimension. For example, it tried to view reality through the eyes of a fourth-dimensional person. Such a being, looking at a human face, would see all angles simultaneously. Hence, both eyes would be seen at once by a fourth-dimensional being, as in Picasso's painting Portrait of Dora Maar. (Giraudon/Art Resource. ® 1993. Ars, New York/ Spadem, Paris)

The shadow of a hyper-cube is a cube within a cube. If the hypercube is rotated in four dimensions, the cubes execute motions that appear impossible to our three-dimensional brains.

Source : Michio Kaku's Parallel Worlds

Fifth Dimension

If we lived in a hyperdoughnut, we would see an infinite succession of ourselves repeated in front of us, to the back of us, and to our sides. This is because there are two ways that light can travel around the doughnut. If we hold hands with the people to our sides, we are actually holding our own hands; that is, our arms are actually encircling the doughnut.

If a rocket disappears off the right side of a video-game screen, it re-emerges on the left. If it disappears at the top, it re-emerges at the bottom. Let us now wrap the screen so that identical points match. We first match the top and bottom points by wrapping up the screen. Then we match the points on the left-and right-hand sides by rolling up the screen like a tube. In this way, we can show that a video-game screen has the topology of a doughnut.

Source : Michio Kaku's Parallel Worlds

Worm Holes

If we insert our hands into the window from two different directions, then it appears as though our hands have disappeared. We have a body, but no hands. In the alternative universe, two hands have emerged from either side of the window but they are not attached to a body.

In this purely hypothetical example, a "window" or wormhole has opened up in our universe. If we look into the window from one direction, we see one dinosaur. If we look into the other side of the window, we see another dinosaur. As seen from the other universe, a window has opened up between the two dinosaurs. Inside the window, the dinosaurs see a strange small animal (us).

Source : Michio Kaku's Parallel Worlds

View from Voyager 1

Michael Goes Climbing

Two women stood talking in the sunlit streets of old flushing* three hundred

years ago.

They were talking, as their descendents

do today, of their children, of their husbands’

wages, of the price of food. Suddenly one of

them broke off and, pointing to a little boy

cried, “Ah, there goes that Michael! I can

hardly keep my hands off that little rascal!”.

“Why?” asked the other turning to look

at a lively little boy who walked past with

his hands in his pockets.

“I never saw such a spoiled, proud and

useless rascal of a boy in my life! Cried the

first. “He is never happy unless he’s making

mischief or doing something to call attention

to himself. He must always be the first. He’ll

come to a bad end, and I hope I shall live to

see it.”

The other woman thought for a while. She said, “Ah well, daring some-

times turns to courage.

He’s a bold little rascal; he’ll never make a poor, respectable citizen like

his father; he’ll go far but whether on the right road or the wrong one, who can

tell yet?”

Meanwhile the boy had passed on into the market place. He was idling

about in the sunshine on the look out for mischief. All at once he saw it calling to

him. Workmen had been salting* the church spire, and their ladders starched

invitingly from earth to steeple.

II

All children like climbing up into high places to see if the world looks any

different from an apple tree or a housetop; over and above this love of climbing

Michael had, as the woman said, an argue to think that had never been done

before. As he gazed at the spire, an idea leaped into his mind – he would the first

person in Flushing to stand on the golden ball beneath the weather-vane.

He turned his eyes around. No one was looking Michael began to climb up

the ladders. At the top of the tower there rose a slated spire, crowned by a

golden ball and weather vane. Michael at the last found himself sitting on the top

of the ball, holding on by the van. He was hot, out of breath and not a little giddy.

Presently he heard workmen moving below. He did not bend over to look,

or speak. He was not going to be pulled before Flushing had been seen him. He

died away, and Michael sat resting.

At last he felt ready to give the town a surprise. He pulled himself to his

feet, and, keeping firm hold of the weather vane, managed to stand on the top of

the ball. It was well that he had a cool head and iron nerves.

Someone must have looked at the vane by chance and seen his little figure

outlined against the blue sky and cried out .In a minute or two Michael was

delighted to see the market place full of people who had rushed out of their

shops and houses to gaze at the giddy sight. It was wonderful have all those eyes

and hearts fixed upon oneself !

III

But Michael did not intend to stay there until he was taken down, to be

handed over his father and punished before the crowd. After a little he prepared

to descend of his own free will.

He learned over the ball. The ladder had gone. The workmen had taken it

away!

A sudden feeling of sickness and giddiness came over Michael. He mas-

tered it. No doubt the people saw what had happened and would send for the

ladders.

But to wait for rescue was a poor sort of end to his mischievous adventure.

He would come down alone, even if it coast cost him his life.

The spire at the base of the ball was only half slated. And Michael saw

some hope of gaining a foothold on the old part. He put his arms round the top of

the ball and left his body swing down; he was just able to feel the first slate with

his toes. Those to d were sod with iron toecaps, for Michael was hard in his

shoes. Michael kicked with his armoured toes till the slate broke and fell in; then

he got a foothold on the wooden laths beneath. *

He rested for a minute, with aching arms and a stiff body. He could not slide

down with his arms around the ball; for the middle of the ball was much too big

for his arms. He must let go his hold on the ball, and some how grasp the spire

below. One false movement, and he would be thrown to his death on the hard

ground below.

Slowly he begins to slide his hands together at the top of the ball, and then

downwards over its sides. Every inch is packed with peril; every inch pushed

him backward toward death. It seemed to him that he would be too weak to hold

on when the time came for him to grasp the spire.

But at last the steady, deadly creeping of his figures brought him to a point

where he could bend forward. With a sudden snatch he caught the base of the

ball.

IV

The next moment he was kicking out a stairway in the old slates on the

spire, and climbing down rapidly. He reached the foot of the spire, lifted the

trapdoor* of the tower, ran down the steps, and was caught by his father in the

church.

The streets were filled with white-faced people telling each other that never

in their lives had they seen anything so dreadful as that child leaning backward

in the air.

“ I said he’d come to a bad end!” cried a woman, wiping the moisture from

her forehead with a trembling hand.

“Wait and see!” replied her neighbor.

They waited. Michael took care to maintain his reputation for mischief,

until his father lost all hope for him and sent him to sea. Suddenly he grew tiered

of the wrong road and determined to give the right one a trial. As the women had

foreseen, he marched down it with the same courage and determination.

***

One day an old woman visited her bedridden neighbor. “ Have you heard

the news?” she cried. “The English fleet has been destroyed off Chatham. What

a victory for little neighbour? Do you remembered the day be climbed the church

spire? Who could have guessed then that whole world would ring with the name

of Admiral Michael Adrianzoon de Ruyter?”

(Adapted from The Children’s Encyclopedia)

Note – During the 17th century the English and the Dutch often fought

against each other on the high seas. There were great seamen on both sides.

As the Admiral of the Dutch Navy, de Ruyter won several victories over the

English. There was great fear in London on one occasion when he sailed up

the Thames victoriously. He is considered the greatest seaman ever produced

by Holland and one forth greatest ever in the world. You may be interested to

now that as a young man de Ruyter came to India with the Dutch merchantships.

*A town in Holland

*Covering the spire with pieces of slate.

* The slates were fixed on a framework of wooden laths. When the slates were broken the

laths would appear.

*A door in the roof.

The Glorious Whitewasher

[This story is an incident in The Adventures of Tom Sawyer, by Mark Twain.

Tom has been troublesome at home; moreover, after playing and fighting

with the other boy he had came home late at night. His aunt saw the state of

his clothes and decided to turn it Saturday holiday into a day of hard labour.]

I

Saturday morning came, and all the summer world was bright and fresh and

full of life. There was a song in every heart and cheerfulness in every face. The

hill beyond the village was covered with summer green and it lay just far to

seem enough a wonderland of joy-dreamy, restful, and inviting.

Tom appeared on the pavement with a bucket of whitewash and a

long-handled brush. He surveyed the fence, and at the uninspiring sight all

gladness left him, and a deep sadness settled down on his spirit. Thirty yards of

broad fence nine feet high. Life to him, seemed hollow, and existence a burden.

Sighing, he dipped his brush and passed it along the topmost plank, repeated the

action, did it again, compared the insignificant bit of whitewashed space with

the far-reaching continent of unwhitewashed fence, and sat down on a tree-box,

discouraged. He began to think of the fun he had planned for this day, and his

sorrows multiplied. Soon the free boys would come tripping along on all sports

of interesting adventure, and they would ridicule him for having to work. The

very thought of it burnt him like fire. He got out his worldly wealth and examined

it bits of toys, marbles, all worthless things. They were enough to buy an ex-

change of work, may be, not enough to buy half an hour of pure freedom. So he

put them back into his pocket and gave up the idea of trying to buy the toys. At

this dark and hopeless moment an inspiration burst on him nothing less than a

great, magnificent idea.

II

He took up his brush and calmly resumed work. Ben Rogers came into view

presently –the very boy of all boys whose ridicule he had been dreading. Ben

was eating an apple, and seemed to be in high spirits. Tom went on dipping the

brush into the bucket and whitewashing, and paid no attention to Ben. Ben con-

templated him for a moment and then said, “Hi-yi! You are in trouble, aren’t

you?”

No answer! Tom surveyed his last touch with the eye of an artist, gave his

brush another gentle sweep, and surveyed the result as before. Ben went up and

stood by the side of Tom. Tom’s mouth watered for the apple but he stuck to his

work.

Ben said, “Hello, you’ve got to work, hey?”

Tom turned round suddenly and said, “Why, it’s you, Ben? I wasn’t

noticing.”

“I am going swimming, Tom,” said Ben. “Don’t you wish you could? But of

course you prefer to work”.

“Why, isn’t that work?”

Tom resumed his whitewashing and answered carelessly, “Well, may

be it is and may it isn’t. All I know is, it suits Tom Sawyer.”

Now, you don’t mean to say, Tom, that you like it

The brush continued to move. “Like it? Said Tom. “Well, I don’t see why I

ought not to like it.

Does a boy get a chance to whitewash a fence every day?”

III

That put the thing in a new light. Ben stopped eating his apple. Tom swept

his brush back and forth softly like an artist-stepped back to note the effect again,

while Ben watched every movement and got more and more absorbed. Presently

he said, “Tom, let me whitewash a little.”

Tom considered, and was about to consent; but he changed his mind. “No-

no-I suppose it would hardly do, Ben,” he said. “You see, Aunt Polly is awfully

particular about this fence; it has got to be very carefully; I supposed there isn’t

one boy in a thousand, may be two thousand, that can do the right way.”

“No- is that so? Oh come now –lemme* just try-Only just a little-I’d let you

if you were me. Tom.”

“Ben, I would like to, honestly; but would Aunt Poly like it? Well, Jim

wanted to do it, but she wouldn’t let him; she wanted to do it, and she wouldn’t

let Sid. You see this is the front fence and Aunt Poly is awfully particular about

it. Now don’t you see how I’m caught? If you were to try whitewashing this

fence and anything was to happen to it....”

“Oh! Come, I’ll be just as careful. Now lemme try. I’ll give you half my

apple.”

“Well, here, take this.... No, sorry, I can’t let you. I am afraid.......”

IV

“I’ll give you all of it.”

Tom gave up the brush, pretending to do so half-heartedly. And while Ben

worked and sweated in the sun, the retired artist sat on a barrel swinging his

legs, eating his apple, and lying plots to take in other boys.

Boys came along every little while; that came to laugh, but remained to

whitewash. By the time Ben was tired out, Tom had sold the next chance to Billy

Fisher for a kit in good repair. And when he was out, Johny bought the next time

chance for a dead rat and a string to swing it with, and so on and so on, hour after

hour. And when the middle of the afternoon came, Tom was just rolling in wealth.

He had, in addition to the things mentioned, twelve marbles, a piece of blue

bottle glass to look through, a key that wouldn’t unlock anything, a piece of

chalk, a tin soldier, six fire-crackers, a kitten with only one eye, a dog-collar-but

no dog-the handle of a knife, and a number of other things of the kind. While

others bore his burdens for him, he had a nice, good, idle time all the while-

plenty of company-and the fence had three coats of whitewash on it. It was just

magnificent! If he had not run out of whitewash he would have ruined every bit

in the village.

Tom said to himself that it was not such a hollow world after all. He had

discovered a great law of human action without knowing it –namely, that in

order to make a man or boy desire a thing it is only necessary to make the thing

difficult to obtain. The boy contemplated with pleasure the possessions that has

come into his hands, and then got up and walked home to report.

“It’s all done, Aunt, the whole fence,” he said to his aunt.

“Tom, I hate your lying so,” said Aunt Polly and marched out to see for

herself.

“Oh, Tom,” she said in surprise when she saw the fence, “you can work

when you want to, only you hardly ever want to,” She took him home and gave

him the best apple she had, and allowed him to go and play.

The country of the blind – I

*Adapted from the story by H.G. Wells.

I

Three hundred miles and more from Chimborazo, in the wildest wastes of

the Andes in Equador, there lies that mysterious mountain valley cut off from the

world of men, called the Country of the Blind.

Long ago the valley was connected to the outside world by a difficult moun-

tain pass, and some people from Peru settled down in the valley. It had all that

the heart of man could desire: sweet water, rich green pasture, plentiful trees

and a fine climate. The settlers did very well indeed up there and their cattle and

sheep did well and multiplied. But one thing their happiness, and spoiled it

greatly. A strange disease came upon them-they all began to lose their sight

gradually. The children born to them were born blind.

While this was happening, there came a terrible earth-quake and landslide.

One whole side of the mountain slipped and came down with a tremendous

noise and filled up the mountain pass, cutting off the little green valley forever

from the exploring feet of men.

II

The strange disease ran its course among the little population of the iso-

lated valley. But life was very easy in that valley, there beings no thorns, snakes,

or wild animals to harm them; and the seeing had become blind so gradually that

they scarcely noticed their loss and easily got accustomed to the new life. They

guided the sightless youngsters here and there until knew the whole valley

marvelously, and when at last sight died out aming them, the race lived on.

Generation followed generation. Their tradition of the greater world they

had come from gradually and became a mere children’s tale. The little commu-

nity grew and developed its own way of life. There came a time when child was

born who was fifteen generations from the time of the earthquake and landslide.

At about this time it chanced that a man came into this community from the

world. This is the story of that man; his name was Nunez.

Nunez was a mountaineer, an intelligent and adventurous sort of man; he

was from Bogota near Quito. He was acting as guide to a party of Englishmen

who had out to Equador to climb the mountains .One night he was found missing

from the camp. In the morning the party saw the traces of his fall. His track went

straight to the edge of a frightful precipice, and beyond it every thing was hid-

den. Shaken by the disaster, the party gave up the trip and returned to Quito.

But the man who had fallen lived.

He fell the precipice into a mass of soft snow, lid down a steep slope

unconscious, but without a bone broken in his body. Then he rolled down gentler

slopes, and at last still, half buried in the masses of soft snow that had saved

him.

III

In the morning he heard the singing of the birds in the trees far below. He

was in a pass between the mountains; and far below he saw green meadows and

in their midst a village, a group of stone huts built in an unfamiliar fashion. He

slowly climbed down precipices and walked down slopes, and at about midday

came to the plain, stiff and tired out. He sat down rested in the shadow of a rock.

As he looked at the village, there seem to be something extraordinary and

unfamiliar about it. Things looked surprisingly neat and orderly in the valley; the

house in the village stood in a regular line on either side of a street of extraordi-

nary neatness. But not a single house had a window, and the walls of the houses

were painted in different colours with extreme irregularity. They were grey in

some places, brown or black in others.

“The good man who painted these walls,” said Nunez to himself, “must

have been absolutely blind!” As he went towards the village, he could see at a

distance a number of men and women resting on piled hips of grass, and nearer

the village, a number of sleeping children. Three men walking one behind and

other were carrying buckets of water. Nunez shouted to them. They stopped and

turned their heads this way and that, as if they were looking about them. Nunez

waved his arms at them, but this scarcely seemed to have any effect on them

“The fools must be blind,” said Nunez to himself. Nunez went nearer, and now

he could plainly see that the men were blind .He was sure that this was the

country of blind .All the old legends of the lost valley came back to his mind,

and through his thoughts ran the old proverb: In the Country of the Blind the one

eyed man is King.

IV

Nunez advanced with confidence and greeted them politely. He explained

that he came from the country beyond the mountains where men could see.

“Let us lead him to the elders,”said one of men, and took Nunez by hand to

lead him along. Nunez drew his hands away.

“I can see,” he said.

“See!” said one of then men.

“Yes, see,” said Nunez, turning towards him, and stumbled against one of

the buckets.

“His senses are still imperfect,” said the second blind man. “He stumbles

and talks meaningless words. Lead him by the hand.”

“ As you please,” said Nunez, and was led along laughing.

It seemed they nothing of sight. Well, in course of time he would teach them.

Soon a crowd of men, women and children all with their eyes shut and

sunken, crowded round him folding him and touching him, smelling at him and

listening to his words.

“A wild man out of the rocks,” said his guides to the crowd.

“Bogota,” Nunez explained. “From Bogota, beyond the mountains.”

“A wild man speaking wild words,” said one of his guides. “Did you hear

that –Bogota?”

“Bogota,” repeated the boys in the crowd. That became Nunez’s name in

the Country of Blind.

“Take him to the elders,” said some one in the crowd. They pushed him

suddenly through a doorway in to a rook black as night. Before he could stop

himself he stumbled over the feet of a seated man and fell. He threw out his arm

as he fell, and it struck someone’s face. He heard a cry of anger and a number of

hands seized him. First he struggled, and then finding it useless, he lay quite.

“ I fell down,” he said. “I could not see in this black darkness.”

“He stumbles and talk meaningless.” One of his guides explained.

V

Nunez heard the voice of an older man question him. He found himself

trying to explain the great world out of which he had fallen, ant the sky; and the

mountains and sight, and such other marvels to these elders who sat in the dark-

ness in the Country of the Blind. But they would believe or understand nothing of

what he told them. During the long years of isolation the names for the thing s of

sight had faded and changed in their language, and they had ceased to interest

themselves in anything beyond the rocky slopes above their village .As for Nunez,

they dismissed his words as the confused speech of a being with imperfect senses.

But they were very sympathetic about his difficulties, and asked him to have

courage and try to learn.

The eldest of the blind men explained to him life and science and religion

.He told him that time was divided into ‘the warm’ and ‘the cold’ (that is how

they distinguished between day and night); it was goods to sleep in ‘the warm’

and work in ‘the cold’. Nunez remembered how, although he had arrived at

midday, he had found the whole village asleep. Then the old man said that it was

late and that they must all retire to bed .He asked Nunez if he knew how to sleep.

Nunez said he did, but before sleep he wanted food.

They brought him llama’s milk in a bowl, and rough, salted bread, and led

him into a lonely place to eat. Afterwards they all retired to bed till the cold

mountain evening woke them to begin their ‘day’ again.