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.
