The Hindu Business Line : Can you tell if any sheep are lost without counting them?

MEET John D. Barrow, a math professor at the Department of Applied Mathematics and Theoretical Physics, University of Cambridge. His new book is "about the biggest subject of all"— infinity. Yes, The Infinite Book from Jonathan Cape (www.randomhouse.co.uk) is "a short guide to the boundless, timeless and endless". Infinitely more surprising is that Barrow writes in understandable prose, not something you would normally expect of a mathematician. For instance, explaining that infinity and boundlessness are not the same thing, he writes, "There are finite things, like the surface of a snooker ball, that have no boundary at all. A fly could walk around it forever without encountering an edge."

Accountants know counting, but did you know there is a way of thinking about numbers without having a system of recording them? The most primitive intuition is to add to or take away from what you have got, points out Barrow. "If you put a stone on the ground every time one of your sheep enters the field in the morning and then take a stone away as each one passes back out at sundown, you can tell whether any sheep have been lost without ever counting them." If only drawing up final accounts was that simple!

Is there a limit to what we can think? Contrary to popular perception that there's no limit, the author informs, that the brain can represent about 10 raised to the power 70 trillion — a finite number — possible thoughts based on the number of neural configurations. However, there are only about 10 to the power of 80 atoms in the entire visible Universe, he hastens to add. "The brain is rather small, it contains only about 1027 atoms, but the feeling of limitless thinking that we possess derives not from this number alone but from the vastness of the numbers of possible connections that can exist between groups of atoms." How difficult then should attempts be to simulate the brain!

In the chapter `Making Infinity Machines', the author introduces the challenge of a `super-task': "Whether a computer could ever carry out an infinite number of calculations in a finite time." The fastest computer on Earth — the NEC Earth Simulator — can carry out 40 trillion calculations per second when it acts alone, he informs. You can join several computers together to raise the speed, yet it would be finite.

"Realistic super-tasks need actions to take place, rather than mere subdivision of the records by book-keepers," argues Barrow, and draws attention to Alan Turing who had shown that there exist mathematical operations that cannot be carried out by any computer in a finite number of computational steps. "They are called uncomputable operations and their existence is closely associated with the famous incompleteness theorem of Kurt Gödel, which teaches us that there exist statements of arithmetic that we can never prove to be true or false by using the rules of arithmetic." Uncomputable tasks cannot just be calculated by performing the same trick over and over again, adds Barrow. Perhaps, arriving at the correct profit is one such task. Infinitely useful, literally too, within a finite number of pages. Useful material.

Bulky company

Bharat Law House (www.bharatlaws.com) has brought out a useful tome for CAs, consultants, companies and secretaries: Company Law Ready Reckoner by D. K. Jain. It runs to almost 1,500 pages and as you would've rightly apprehended, the index is missing; a flaw that is partly redeemed by the detailed list of contents. However, the presentation is good, and concepts are explained using points, sub-heads, and charts. The language is easy to read, even passages where the author cites case laws.

Jain collates not only the appropriate Rules with the Sections but also the relevant circulars, guidelines and forms, supplemented by specimen letters that may be required.

Godrej Consumer Products has announced a second buyback of shares through the open offer route. For more on the topic, help is readily available in Part X of the book. Sections 77A, 77AA and 77B are highlighted. Godrej has stated in a note to the bourses that the buyback is pursuant to Section 77A(2)(b) of the Companies Act, the SEBI Buyback Regulations and is subject to the approval of shareholders by postal ballot.

Jain discusses the three sources from which buyback can be made — terms and conditions to be complied with before buyback, two modes to choose from, declaration to be filed with the RoC and SEBI, and a host of pre buyback activities such as filing of Form 23 and maintaining a register for letter of offer despatched.

`Independent director' is a phrase that we've been hearing in those threatening calls for deadline that the regulator issued a few days ago. On that, there's input in a chapter on Corporate Governance. So, I decided to look for `vanishing companies' that the Kampani Karya Mantri has been vigorously pursuing through chief secretaries and police chiefs of various states to get FIRs filed. I'm still searching... to the point of vanishing, almost!

BooksOfAccount@TheHindu.co.in

D. Murali

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