Learning From Numbers To Generate New Kowledge- Part 1

I had attended a lecture by Dr.C.R.Rao, a world renowned statistician. I had live tweeted the lecture (@ArchanaRaghuram). Many people had requested for the entire  transcript. I am posting the transcript in three parts.

The difference between the Philosophers, Scientists and Statisticians view of knowledge

Statistics is the science, technology and art of developing human knowledge through the use of empirical data.

 1 Concepts of Knowledge

 Knowledge is what we know, also what we know we do not know. We discover what we do not know essentially by what we know. Thus knowledge expands. With more knowledge we come to know more of what we do not know. Thus knowledge expands endlessly. What exactly is the process involved in generating new knowledge? What confidence do we have in the newly created knowledge and how do we use it. In order to understand these problems let us look at different views of knowledge.

 1.1.         Philosopher’s view of knowledge

 Philosophers maintain that knowledge is infallible. The different instruments for acquiring certain knowledge are:

• Deductive logic or pure reasoning from given premises as advocated by Kant.

The process is the same as that in mathematics, where we lay down certain axioms taken to be true and derive propositions by arguing from them. However, we have to make sure that conclusions drawn from different sets of axioms are not contradictory. The logician Godel proved that consistency of a given set of axioms cannot be established by using the same axioms. He also showed if one contradiction occurs, any contradiction can be established.

• Mill’s inductive logic of reasoning from particular to particular. For example if it is known that in the past, banks refused to give loans if the applicant had filed for insolvency at any time, we conclude that the same will hold in the future. Byinduction, we generally mean arguing from the particular to the general.
• The Indian Philosopher Vivekananda and Einstein maintained that new knowledge can be created only by instinct, reason and inspiration, a process known as abduction and not by deductive reasoning assuming a given set of premises to be true or by inductive inference from observed data. ( “a theory can be proved by an experiment, but no path leads  from experiment to theory”-Einstein).
• The ancient Hindu scriptures mention, perception (pratyksha), inference(anumana), comparison (upamana) and verbal testimony (sabda) as possible instruments for creation of new knowledge.

 1.2 Scientist’s view of knowledge

 Scientists maintain that all knowledge is fallible, i.e., there is nothing like a true knowledge. They create scientific knowledge by the following steps.

 (1)   Build a model for observed data using the information contained in the data or through instinct, reason and inspiration.

(2)   Then generate new data through an experiment or taking observations in nature and see how well the suggested model can predict the observed data.

(3)   If the accuracy of prediction is within acceptable limits for practical applications, the model is given the status of a scientific theory. If not the model is rejected. In either case, research will continue to find a theory which gives   predictions with a higher degree of accuracy. Each time, we replace the existing theory by the new one.

(4)   Sometimes more than one theory can co-exist as Newton’s laws of gravitation and Einstein’s theory of relativity although the latter is more comprehensive than the former. For practical purposes, even sending a man to the moon, Newton’s laws of motion can provide results of sufficient accuracy. Neither of them is strictly true as the following famous scientists affirm.

 1.2.1 Views of some scientists on scientific theories:

  “An experiment does not even establish the relative truth or falsity of a hypothesis but merely furnishes a basis for deciding acceptability”.

                                                -A.H.Copeland (Philosophy of Science, 33,303-316, 1966)

“If you thought that science was certain well that is just an error on your part”.

                                                      -Richard Feynman (Nobel Laureate)

       “In science, fact can only mean confirmed to such a degree that it would be  perverse to withhold provisional assent”

                                                       -Stephen Jay Gould

      “There has not been a single data in the history of the law of gravitation when a      modern test of significance would not have rejected all laws and left us with no   laws”                                       -H.Jeffreys (in The Theory of probability)

       “There is no need for these hypotheses to be true or even to be at all like the truth; rather one thing is sufficient for them-that they should yield calculations which agree with the observations”

                       -Andreas Osiander (1498-1552) in preface to Copernicus De Revolutionibus

 1.2.2 The sad story of Galileo (15 Feb 1564-8 Jan 1642) and the Catholic Church

During the life time of Galileo a large majority of philosophers and astronomers subscribed to the geocentric view that the earth is at the centre of the universe.  When Galileo began publicly supporting the heliocentric view, which placed the sun at the centre of the universe, he met with bitter opposition from some philosophers and clerics, and two of the latter eventually denounced him to the Roman Inquisition early in 1615.

The position of the church as explained by Cardinal Bellarmino in 1615 was similar to what Osiander thought a century earlier that the church would raise no objection if Galileo stated his theory as a mathematical hypothesis, “invented and assumed in order to abbreviate and ease the calculations”, provided he did not claim it to be a true description of the world. In 1916 Galileo agreed not to advocate his views and  he was cleared of any offence. When he later defended his views in his most famous work, Dialogue Concerning the Two Chief World Systems, published in 1632, he was tried by the Inquisition, found “vehemently suspect of heresy”, forced to recant, and spend the rest of his life under house arrest.

   1.3 Statistical view of knowledge

   All knowledge derived from observed data is uncertain with the degree of uncertainty depending on the amount and quality of available data. Unlike in science, in real life action has to be taken on available knowledge however meager or uncertain it is. We are always seeking answers to questions like: What career should I choose? How do I invest my money? Should I go abroad for higher studies or continue in the country? Should I take drug A or B for my headache? There are no definite answers to these questions in view of uncertainties in available information, but decisions cannot be postponed.

To the human mind tuned to deductive logic over several centuries, formulating rules for decision making under uncertainty which can go wrong posed a challenging problem. It is only in the beginning of the last century, it was realized that knowledge, however meager, is usable if we know the amount of uncertainty in it, in the sense that we can formulate optimum decision rules, i.e., with minimum loss, which is the subject matter of statistics developed as a separate discipline in the last century. The fundamental equation of statistics may be stated as follows:

      Uncertain                     Knowledge of                              Usuable

                                    +      of amount of              =       

     Knowledge                  uncertainty in it                            knowledge

   1.3.1 History of statistics

Statistics has a long antiquity but a short history. Its origin can traced back to the primitive man who put notches on trees to keep an account of his possessions. As early as 5000 BC, kings used to carry out census of populations and resources of the state for selfish reasons. When democratic governments were formed, it was the task of the governments to collect information about the people and on the resources of the state to make short term policy decisions and formulate long range plans for improving the living conditions of the people. The information collected by the government was called official statistics (data collected of the people for the people by the government). The word statistics was coined by the German Scholar Achenwal in the middle of the 18^th century to mean data, analysis and use by the government.  The first State Statistical Bureau was established in 1800 in France.

 It is interesting to note that Shakespeare came close to invent the word statistics or statistician. He used the word ‘statist’ in his drama Cymbeline in 1600 and ‘statists’ in plural in Hamlet in 1609 to denote, perhaps, officials connected with the state.

  The first nongovernmental use of statistics is in computing life insurance rates based on the data of births and deaths, called Bills of Mortality, in the 17^th century. During this period analytical studies were made on death rates from different diseases and the growth of populations in different regions of a state. In 1900, Karl Pearson used concepts of probability to test scientific hypotheses based on observed data in any field of enquiry, which is the beginning of the modern theory of statistics. The theory of statistics was developed during the period 1900-1940 by R.A.Fisher, J.Neyman and A.Wald Statistics was introduced as a separate subject of study and research in universities in the decade, 1940-1950.

The second half of the last century saw the development of statistics as the science and technology of using information as the main tool in all areas of human endeavour from scientific research, designing and controlling the quality of goods, medical diagnosis, national security, giving evidence in courts of law in cases such as disputed paternity and authorship, detection of fraud and to making personal decisions. As R.A.Fisher said in a speech delivered at the Indian Statistical Institute in 1952:

       “Statistical science is the peculiar aspect of human progress which gave 20^th      century its special character.   It is to the statistician the present age turns for       what is most essential in all its more important activities”.

 I shall give some examples to show how statistics works in different activities.

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