# Half-life of knowledge

## Presentation on theme: "Half-life of knowledge"— Presentation transcript:

Half-life of knowledge
Hari V Sahasrabuddhe Kanwal Rekhi School of I.T., IITB

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.

First used “Half-life of knowledge”
Fritz Machlup ( )

Does knowledge decay like that?

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

A progression of terms Data: factual information, often numeric
Information: specific knowledge Knowledge: familiarity, awareness, understanding Wisdom: insight, ability to judge Our use of “knowledge” is a bit fuzzy – it fits somewhere in this progression.

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.)

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

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)

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.

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.

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’?

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

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

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!

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!

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

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

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

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

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)