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Half-life of knowledge

Explore the concept of knowledge decay and evolution, from Oracle9i to halting problems and complex algorithms. Discover the history of programming languages and future challenges in computing. Dive into the depth of mathematical complexities and the survival of lasting knowledge.

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Half-life of knowledge

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  1. Half-life of knowledge Hari V Sahasrabuddhe Kanwal Rekhi School of I.T., IITB hvs@it.iitb.ac.in

  2. what is half-life? Definition: The time required for the quantity of a chemical, drug or radioisotope to fall to half. For example, if the quantity now is 32, and half-life is 10 days, the quantity will be 16 after 10 days, 8 after 10 more days, etc.

  3. Does knowledge decay like that?

  4. Does knowledge decay like that? No, but it may become useless when the situation changes

  5. What is new in Oracle9i? • Oracle Streams (replace Oracle Advance Replication and Standby Databases) • Cluster file system for Windows and Linux (raw devices are no longer required) • (etc.)

  6. MySQL: Changes in 5.0.2 Warning: Incompatible change!NOT a BETWEEN b AND c is parsed as NOT (a BETWEEN b AND c) rather than as (NOT a) BETWEEN b AND c

  7. Even mathematics! Is mathematics necessary? Moving Beyond Myths, published by the National Academy of Sciences, says so, but Prof. Dudley of DePauw University does not agree! (See references)

  8. Halting problem - definition Given a description of an algorithm and its initial input, determine whether the algorithm, when executed on this input, ever halts (completes). The alternative is that it runs forever without halting.

  9. Halting problem - answer Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible inputs cannot exist. We say that the halting problem is undecidable.

  10. Halting problem – informal proof • Let P be a program that reads any program Q and prints 1 if Q halts, 0 if not. • Define P’: • read program Q • simulate P on input Q • if output of step 2 is = 1, go to step 2 • Halt • What happens when P’ is fed to P’?

  11. Halting problem – formal proof Turing’s formal proof is based on Turing Machine, a model of computation with a finite controller coupled to a unbounded memory

  12. Another model of computation -calculus • Allows us to define a recursive function • Foundation for LISP class of programming languages

  13. Decidable but hard problems • Hamiltonian circuit: a circuit that visits all vertices of a given graph • We don’t know how to find one in any arbitrary graph in time limited by a polynomial, any polynomial, of the number of vertices. • If you can solve that one, a number of other problems are solved!

  14. Hard - example • Remember Cramer’s rule? n*n determinant => n (n-1)*(n-1) determinants • Time for n*n determinant equals roughly n*time for an (n-1)*(n-1) determinant • A PC which can calculate a 2*2 determinant in 0.5*10-9 seconds needs almost 1 year to calculate a 19*19 determinant by Cramer’s rule, and 19 years for a 20*20 determinant!

  15. Hard example contd. • We could use a supercomputer. A 60 teraflop supercomputer can calculate a 19*19 determinant in less than 17 hours (but even it will need about 18 years for a 22*22 determinant) • So, faster computers do not compensate for algorithmic complexity

  16. First programmer Charles Babbage described his analytical engine in 1834, and in 1842-43 Lady Lovelace either created or corrected a program for it to computeBernoulli numbers(first defined in print in 1713) (The analytical enginecould never actually be built.)

  17. How many programming languages are there? • Thousands of them! • Main types • Imperative (c, c++, java, …) • Functional (LISP, SCHEME) and applicative (APL) • Declarative (PROLOG)

  18. BCS: Future challenges Conference: Brit. Comp. Soc., 29-31 March 2004 • Two separate reports, on “Grand Challenges” in education and research • Either report identifies seven challenges • Most challenges arisefrom spread of computing to new areas, e.g. embedded systems, memories for life

  19. Identifying lasting knowledge • Abstract rather than concrete • Technology-independent areas, e.g. maths, theoretical CS, architecture, … • Older, still useful knowledge • (if it survived n years it might survive n more years)

  20. What after you graduate? • Self-study and reference skills • library, bookstores, search engines, … • List of references is available • These were gathered using web search

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