Please do not believe all the nice
things Shri B.M.L. Sharma has said about me. I
find such exuberant eulogies rather embarrassing.
When I was invited to give this lecture I wondered what I might say. I
could read up and recall everything I knew about cartography. After all,
long years ago, as Secretary, Department of Science & Technology I
had a great deal to do with the Survey of India. Even earlier, as
Director of Space Applications Centre, I was close to aerial photography,
thematic mapping and the beginning of an era of extensive remote sensing
from space. I was in touch with activities related to Omega Sonde, the Doppler receivers with the Navy Navigation
Satellites - and beginning of the GPS system. I even made a proposal at
the U.N. that each person should have a human right to know where he is on
this globe at any time, that knowing your location and being able to
communicate with anyone else should become a fundamental human right,
like the right to clean air and water.
So, I could have decided to cull out stories of that era, brought myself upto date by a bit of reading and given you a very
learned lecture, very much in tune with what you might be discussing
here. But that would have been redundant and, perhaps, not much fun. Most
of you know more about these things than I do. Therefore, I have decided
to brave something different, to talk about things which might be of a
cultural interest to all you cartographers, even though somewhat removed
from your personal interest. Also I am sure that many of the young people
in this large audience are not professional cartographers and may not
mind my excursion into topics only peripherally connected with your
discipline.
In general cartography can be considered as a science of relationship;
how far and in which direction with respect to each other lie some points
of interest to us. It is about connections and these connections manifest
themselves in many different areas. Let me start with a familiar but not
a very elementary manifestation. Even while I am talking to you in this
very large hall, my brain is simultaneously engaged in cartographic
activity. I can see that many young people, presumably students, and
sitting and standing towards the back end of this hall. I am already
aware of the rough distance and directions of various doors and windows. I
have already drawn a thematic map including the presence and locations of
women in their beautiful sarees, the
distinguished people on the dais, the dignitaries and delegates in the
front rows, even parts of the audience, listening to me with
concentration, others who are amused and still others who are beginning
to wonder what I might be leading upto. In this
sense, I have been doing a lot of cartography, not only in the space
defined by three dimensions. In fact all of you are doing the same. Our
eyes, ears and other senses combined with our brains are amazing
cartographic equipment. Without their processing we cannot BE.
Let me share with you a few examples of celestial cartography. There was
an interesting observation attempted during the last solar eclipse. The
distances of the sun and the moon as also the size of the moon are fairly
well known now. It was suggested that the diameter of the solar
photosphere could be determined with much greater accuracy than known by
an accurate measurement of the width of the forty odd kilometer,
wide band of totality on the earth. The students in the audience would recognise that this is nothing but the use of the age
old triangulation technique in a new setting. I do not know the result of
this experiment but the use with trays of photo-detectors across the path
simultaneously enabled by satellite time signals was a neat trick. The
exact coordinates of the photo-detector trays were determined by using
GPS receivers.
But how did we find out the distances to the sun and the planets? This
cartography has a fascinating history. Kepler's
laws of planetary motion showed that the orbital period of a planet was
proportional to the three halvth power of the
distance from the sun. Since the orbital periods had been obtained through
long term observation, one already knew the relative scale of the solar
system in the sixteenth century. In other words the planetary distances
were known in astronomical units, an austronomical
unit being the distance between the sun and earth.
The value of the astronomical unit could only be estimated towards the
end of the eighteenth century by observing the transits of Venus and
Mercury against the disc of the sun from widely separated points on
earth. Such transits occur only a few times in a century. In a passionate
appeal astronomer Halley, of Halley's comet fame, had charged the future
generation of astronomers not to make these measurements during the
transit of Venus expected to occur several decades after Halley's death.
It would be recognised that the transit
technique is a cunning use of the triangulation method.
But why couldn't we use Newton
laws of gravitation and mechanics along with the mass of the sun and the
value of the gravitational constant? Surely that and the
;observed orbital period of the earth can give us the value of the
astronomical unit? Of course it would, but how do we measure the mass of
the sun? Measurement of the solar mass requires the value of the
astronomical unit, the orbital period of the earth, value of the gravitational
unit, the orbital period of the earth, value of the gravitational
constant and, of course, Newton. What we have seen in this discussion
then is the use of cartography in measuring masses of celestial bodies,
including that of the sun.
The distances to the nearby stars are determined through parallax
measurements; in other words by observing their apparent movement against
the background of distant stars as the earth goes around its orbit. This
is now possible because we now know the value of the astronomical unit.
However for the stars which are very far away the value
of parallax becomes too small to be measured accurately. This is
certainly so for stars in other galaxies. If stars were like standard
candles of known intrinsic luminosity, their observed brightness could
straight away tell us how far they are. However the stars rightly refuse
to be standard candles. Their rate of energy output depends on their
composition, mass and the stage of their evolution. Like living things
stars are also born and go through period of childhood, youth and old
age. Nevertheless, one class of stars, called Cepheid variables, have a very useful property - their period of
intensity variation depends on their intrinsic brightness. This is
clearly related to the astrophysical processes in stellar evolution and
stellar dynamics. Thus if we can find the period of intensity variation
of a Cepheid we also know its intrinsic brightness. This may not be a
standard candle and by measuring its apparent brightness we can tell how
far it is. Notice the understandings and contortions we go through for
this type of cartography.
Recently a lot of excitement has been generated in the astronomical
community by observations of Cepheid variables in outside galaxies by the
Hubble space telescope. Being outside the corrupting influence of the
Earth's atmosphere, this telescope can observe many more variable stars is external galaxies than was possible with ground
based instruments. The measurements of periods of
variation is also expected to be more accurate. As a result we
have more extensive and presumably more accurate measurements of
distances of a number of galaxies. We can also measure the Doppler
red-shifts of spectral lines emitted by stars in those galaxies. The
red-shifts give the velocity with which a specific galaxy is receding
from us due to the general expansion of the universe. A relation between
distance and rate of recession can give the rate at which the universe is
expanding. Application of Einstein's theory of gravity then gives us the
time, when the universe started expanding - in other words the age of the
universe. All this is true only if the generally accepted big bang theory
of the origin of the universe is correct.
What the new measurements of the Hubble space telescope indicate is that
the age of the universe is significantly less than earlier believed and,
to the embarrassment of several astronomers, some stellar clusters in the
galaxy seem to be older than the universe itself. Parts of the universe
appearing to be older than the universe is the kind of paradox which
delights scientists. It is pregnant with possibilities.
A number of astronomical discoveries of great significance have been made
by using the Doppler effect. Pulsars are said to be rotating Neutron
stars. Pulses of radio waves, visible light or x-rays are observed when
the rotating beacon of radiation is intercepted by the earth. Since the
rotation is essentially unaccelerated, the
timing of the pulse is extremely accurate. However, some years ago a
Pulsar was found to have a cyclical variation of the pulse period. This
was finally diagnosed to be due to the fact that the rotating Neutron
start was itself revolving around an invisible massive object. Accurate
measurements of the Doppler shift in the pulse timing provided the
orbital parameters of the Neutron star, which then led to an estimate of
the mass of the invisible massive object. The mass was found to be so
high that the object had to be a black hole. That, in essence, is the
manner in which theoretically postulated black holes have been
discovered. We can't see them but we can see the effects of their massive
gravity. I suggest to you that this discovery also brings in a class of
cartographic science, helped no doubt by lot of clever physics and
astronomy.
Just one more bit of information and I will stop talking about
cartography in astronomy. When astronauts first landed on the moon, one
of the instruments they deployed was a tray of corner reflectors. A
corner cube reflector reflects an incident beam of light exactly back in
the direction from which it was coming. These reflectors have been used
over the years for laser ranging of the moon. A powerful laser pulse is
directed towards the moon using a large telescope and the time taken by the
light reflected back by the corner reflectors on the moon is measured
using accurate atomic clocks. The distance can be measured to an accuracy
of a centimeter or less. By careful measurements over the years it has
been found, as expected, that the moon is slowly receding from the earth,
this rate of recession is about 5 centimeter a year. The physical reason
for this effect is the tidal friction. While the moon moves away from us
the rotation of the earth is also slowing down. A corroborating result,
recently reported and based on the study of deposits of tidal sands,
suggests that 600 million years ago an earth day was only about 18 hours
long.
Enough of astronomy. I will also resist the temptation of talking at
length about the GPS (Global Positioning System) which enables us, using
a system of geodetic satellites, to determine our position on earth in
three dimensions with an accuracy of about a meter if we are carrying an
appropriate receiver. This has truly revoutionised
cartography and navigation. It is also revolutionising
the manner in which wars are being fought. Everything nice usually has a
horrible reason; that is the tragedy of human species, though I don't
believe it has to be this way.
Cartography is about distances and directions. Therefore it is also about
size, shape, architecture and topology. And that is what Physicists,
chemists and biologists are studying all the time. Just consider the
difference between graphite and diamond. Both are made of carbon atoms.
The unbelievable difference in their physical properties comes entirely
from the difference in the way they are put together - in their
architecture. About five years ago a new class of carbon molecules was
discovered. One of these contains sixty atoms and has the shape of a
soccer ball. This molecule has remarkably different properties, many of
which are being still explored. It is also remarkable that these
molecules can be produced by lighting an oil lamp and collecting the soot
on a plate held above the flame. It has been suggested that these
molecules might have had a distinct role in the living world. I have
wondered sometime whether the believed efficacy of my mother's way of
making SURMA by burning a wick soaked in mustard oil or GHEE was based on
the secret properties of carbon sixty. Crystalline beauties of all kind
depend on specialized structures and precise distances of the constituent
atoms.
We know, of course, that these depend on the structure of atoms
themselves and the basic laws of Nature. Indeed these laws and properties
of materials are understood by studying the structures themselves.
Biology provides, perhaps, the most dramatic examples of the critical
role of size, distance and shape in ensuring that living things are what
they are and function and evolve as they do. The replication of DNA, in
fact the whole science of genetics, functions by recognising
structures. So does the immune system without which we would not survive
very long. Our sense of smell comes from the fact that we have various
types of receptors in our noses with which molecules of specific
volatiles make an exact fit and there issues a signal to our brain which
gives us a sensation of rose smell, lavender or whatever. Our taste buds
work in a similar fashion. The major enterprise of modern biology is to characterise various biological structures, different
type of receptors and even to create some molecules and complexes to work
like keys for some naturally occurring 'locks' we want to neutralise. Search for new antibiotics, even design
of vaccines against new diseases is an enterprise in which a whole lot of
work falls in this category.
We may be impressed with what we know today about the art and science of
cartography and about navigation. But we should retain some humility in
the face of what many birds, bats and bees, even crickets, can do with
great ease without any instruments, telescopes and other aids. Indeed I
could mention turtles and many other species of fish and other animals
whose capabilities in this regard are far superior to those of unequipped
humans. We are barely beginning to understand, for example, how some
birds can find their way across thousands of kilometers to the same
winter breeding grounds every year, overcoming all kinds of weather enroute. It seems they do use the earth's magnetic
field but as a backup they also sense the band of polarized light from
the sky, essentially to steer by the sun without having to look at it.
How their ancestors discovered that this could be done remains, of
course, a mystery. I suppose much more is learnt by different species
through evolution than we can intellectually understand.
Bats are nocturnal animals. They do not depend on external illumination
to see. They do not have eyes like us but they can locate a cricket or a
moth from a distance as large as twenty meters and follow it. They see
and navigate with the help of an ultrasound
radar. The processing system of their radar. The processing system of
their radar is a marvel of sophistication, still a subject of
investigation by communication researchers including defence
radar experts. Their distance measuring capability, as also of direction
determination, is truly, astounding. But there is more to the story of
bats hunting moths. It turns out that some species of tiny little moths
have also developed the capability of detecting when they are being
illuminated by a bat ultrasound signal. Not only that, from the strength
of the signal received they know whether the bat will be able to detect
the tiny reflection from their body. If their estimation indicates that
the bat is still unaware of their existence they just drop to the ground
to escape detection. If, on the other hand, the signal is strong and in
their judgement the bat has already spotted
them, they go into a set of chaotic movements, trying their best to dodge
the fast approaching bat. Sometimes they escape, often not. I wonder what
type of cartography and navigation academics bats and moths go through
when they are young.
We have been talking about distances, directions and shapes - essentially
of relationships in the physical world. Are there any well-defined
measures of proximity or distance in the realm of ideas? I tend to feel
there are. New concept often seem to arise from
sources which are often obscure and completely unrelated.
Thoughts move in peculiar ways. Does creativity have a
logic? I have only a tentative hypothesis in this regard. In the
world of concepts, architecture, shapes and
personality matter more than distances and directions. There does remain
the possibility, for example, of mathematics and theoretical physics
being inspired by music; not only by a specific piece of music perhaps
but by the sheer musicality of music... but this is becoming another
realm altogether and therefore a good time to stop.
Thank you for attention.
