On mathematics

Mathematics is regarded as a demonstrative science. Yet this is only one of its aspects. Finished mathematics presented in a finished form appears as purely demonstrative, consisting of proofs only. Yet mathematics in the making resembles any other human knowledge in the making. You have to guess a mathematical theorem before you prove it; you have to guess the idea of the proof before you carry through the details. You have to combine observations and follow analogies; you have to try and try again. The result of the mathematician’s creative work is demonstrative reasoning, a proof; but the proof is discovered by plausible reasoning, by guessing. If the learning of mathematics reflects to any degree the invention of mathematics, it must have a place for guessing, for plausible inference.

George Polya (Induction and Analogy – Mathematics of Plausible Reasoning – Vol. 1, 1954)

Known knowns, Unknown unknowns

Reports that say that something hasn’t happened are always interesting to me, because as we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns – the ones we don’t know we don’t know


Gaza Blitz hailed?

It is important to keep this in mind given the accusations of “disproportionality” being hurled at Israel from all directions. They are hogwash. The Jewish state cannot be faulted — but rather should be hailed — for investing precious human capital and limited financial resources to develop a technological miracle: Iron Dome. By intercepting in the last week upwards of 400 rockets destined for Israeli civilian centres, the anti-missile defence system saved countless Israeli lives. Likewise, it also saved Palestinian lives, which surely would have been lost in the event the IDF was forced to retaliate for a direct hit, say, on Tel Aviv.

This is in stark contrast to Hamas’ practice of concealing weaponry in residential buildings, schools, hospitals and mosques, thereby guaranteeing the unnecessary loss of life despite the precision of Israeli strikes.

via Gaza| National Post

Ah! This piece of writing is as crappy – biased – hogwash – etc. etc. (are these the right words?, am at a loss of what words to put here) as it can get. And it is not language that is at fault, by the very idea. The idea that Israel can do anything it wishes, without fearing any consequences is what is through an through present in this line of thoughts. The state of Israel has become the new “Untouchable”. The writer glorifies the killing and pounding of the Gaza region, with a logic that is truly cigol. What he claims as a mere “hogwash”, is the reality which the state of Israel is desperately trying to hide, and this with full support of the corporate and major media houses.  Maybe the author is trying to make this fact oblivious (and wants us to be also ) that Israel is the occupying force, and they hold superior fire power. To say killings and bombings should ” but rather be hailed” the author is making an ideological analogy to the holocaust. If someone on the other hand with same argument had replaced Jews instead of Gazans, and justified the killings, there would have been a huge  cry over this. If these killings can be justified, no wait, rather hailed now, why are the Israelis so much adamant that people see the faulty logic and the tragedy of the holocaust. I think this is the same only with the Israelis taking up the place of executioners with impeccable cigol to support their actions.

After all as Orwell says:

War is Peace | Freedom is Slavery  | Ignorance is Strength

And this is what is exactly being practiced here.

Oh and will I get a phone call for this?

‘to criticise Israel can create major problems. Journalists spoke to us of the extraordinary number of complaints which they receive. We have presented our findings to many groups of media practitioners. After one such meeting a senior editor from a major BBC news programme told us: “we wait in fear for the phone call from the Israelis”. He then said that the main issues they would face were from how high up had the call come (e.g. a monitoring group, or the Israeli embassy), and then how high up the BBC had the complaint gone (e.g. to the duty editor or the director general).’ (p. 2)

via | medialens

May be not because I am not a journalist, neither is my blog very famous!

A parable on…

A Parable

Once upon a time, in a far away country, there was a community that had a wonderful machine. The machine had been built by most inventive of their people … generation after generation of men and women toiling to construct its parts… experimenting with individual components until each was perfected… fitting them together until the whole mechanism ran smoothly. They had built its outer casing of burnished metal and on one side, they had attached a complex control panel. The name of the machine, KNOWLEDGE, was engraved on a plaque  set in the centre of the control panel.

The community used the machine in their efforts to understand the world and to solve all kinds of problems. But the leaders of the community were not satisfied. It was a competitive world… they wanted more problems solved and they wanted them solved faster.

The main limitation for the use of machine was the rate at which data could be prepared for input. Specialist machine operators called ‘predictors’, carried out this exacting and time consuming task… naturally the number of problems solved each year depended directly on the number and skill of the predictors.

The community leaders focussed on the problem of training predictors. The traditional method, whereby promising girls and boys were taken into long-term apprenticeship, was deemed too slow and too expensive. Surely, they reasoned, we can find more efficient approach. So saying,  they called the elders together and asked them to think about the matter.

After a few months, the elders reported that they had devised an approach that showed promise. In summary, they suggested that the machine be disassembled. Then each component could be studied and understood with ease… the operation of machine would become an open book to all who cared to look.

Their plan was greeted with enthusiasm. So, the burnished covers were pulled off, and the major mechanisms of the machine fell out… they had plaques with labels like HISTORY and GEOGRAPHY and PHYSICS and MATHEMATICS. These mechanisms were pulled apart in their turn… of course, care was taken to keep all the pieces in separate piles. Eventually, the technicians had reduced the machine to little heaps of metal plates and rods and nuts and bolts and springs and gear wheels. Each heap was put in a box, carefully labelled with the name of the mechanism whose part it contained, and the boxes were lined up for the community to inspect.

The members of the community were delighted. Their leaders were ecstatic. They ‘oohed’ and ‘aahed’ over the quality of components, the obvious skill that had gone in their construction, the beauty of designs. Here, displayed for all, were the inner workings of KNOWLEDGE.

In his exuberance, one man plunged his hand into a box and scooped up a handful of tiny, jewel-like  gear wheels and springs. He held them out to his daughter and glancing, at the label on the box, said:

“Look, my child! Look! Mathematics! ”

From: Turtle Speaks Mathematics by Barry Newell

You can get the book (and another nice little book Turtle Confusion) here.



I have coined a new term: cigol.
The term may have some meaning, google gives it as a surname for many.
But for me it is something, which I am suffering due to.
To guess the meaning read the term backwards.

And you will get it!

Now there is a term illogical which is already existent, but when I mean cigol, it is
not exactly illogical. There is a differnece. The difference is that
illogical would mean devoid of logic. But in case of cigol, the logic is
very much there, but is reversed. They are very much applicable to babus.
For example if something is supposed to help you, they make it in such a way
that it becomes unhelpful, deliberately.

I would love to cite a lot of examples, but alas I cannot for reasons known to all.

Some thing from this book needs no title…

I love the artist or scholar whose activity is like the bee
pursuing the delicious nectar of the flowers. The bee has no
mind to become a renowned authority on which flowers
contain the best nectar; the bee simply loves nectar. In all
probability, the bee, through his actual experience will soon
have a fantastic knowledge of the flower geography of his
neighborhood-as good perhaps as any human scholar who
“studies” botany. And I say the bee really knows the flower
much better than the botanist. The botanist merely knows
about the flower; the bee knows the flower directly. The more
analytically minded reader might well ask, at this point, just
what I mean by “knowing about something” versus “knowing it
directly.” I wish I could answer him! The distinction is so
difficult to explain rationally, and yet it is of such vital