Tuesday, September 22, 2015

What is a living thing?

Read one of the cool working definitions for living things.

Any living thing should have the following attributes:

1. Enough carbon for organic synthesis since our life is carbon-based.
2. Energy for metabolism and synthesis.
3. Catalysts for speeding up and channelizing reactions, otherwise energy will be quickly lost.
4. Elimination of waste, otherwise accumulation of waste will prevent life proceeding.
5. Compartmentalization - essentially having an interior and exterior
6. Hereditary material such as DNA or RNA for replication.

I think we cannot classify virus, retrotransposons or plasmid as life if we adhere by this definition. 

Monday, April 06, 2015

Gene Pool Factory

Evolution by natural selection is the key mechanism by which species retain their mutations in their gene pool. Mutations as such do not confer fitness advantage for the species. If species is imagined as a product of a factory, mutations make the proteins that are the raw materials for the product. The selling factor of the product is the fitness advantage (reproductive or survival). Since the selling factor is determined by demand/supply rather than the raw material the product is composed of, demand/supply is analogous to natural selection. Just as demand/supply determines the selling factor, natural selection determines the fitness advantage through which the species propagates. If the product sells well, the factory will make sure there is a good amount of raw materials in store, similar to the proteins that are conserved through the mutations in the gene pool. I rest my case.

Thursday, October 02, 2014

Richard's Paradox

This is one of the really cool paradox I came across. Find the fallacy in this paradox.

Consider the properties of natural numbers that can be described in, say, the english language. For instance, the property of a number being a prime can be described as "a number x that is not divisible by any other number other than 1 and itself". As an another example, the property of a number that has an integer square root can be described as "a number x that is a product of an integer by itself", etc. 

Now these descriptions can be listed one by one, based on the number of letters present in them. For example, the description "a number that is not divisible by any other number other than 1 and itself" has 61 letters and the description "a number x that is a product of an integer by itself" has 41 letters and so the latter description will be listed before the former description. If two descriptions have the same number of letters then they can be arranged alphabetically in the order of appearance. 

Call a number x as Richardian if x does not satisfy the description listed in the xth row. Thus, 41 is Richardian whereas 61 is not Richardian. 41 is Richardian since 41 does not have an integer square root and 61 is not Richardian since 61 is a prime number. Now this property of a natural number being Richardian that is described can then be listed in a row. Let the row number corresponding to this description be n.

The question is then "is n Richardian?"

If n is Richardian, then by definition it should not satisfy the description in the nth row. But, the nth row description is the definition of a Richardian number and so n will not be Richardian. On the other hand if n is not Richardian, then it does not satisfy the description on the nth row and so it will be Richardian. Thus, n is Richardian if and only if it is not Richardian.

Isn't this cool? So what is the fallacy here?

Wednesday, August 20, 2014

Immanuel Kant Series - Part I

Immanuel Kant (1724-1804) is the foremost and central figure in western philosophy. His greatest work Critique of Pure Reason stands out as one of the most influential philosophical treatise of all times. In the coming series, I am planning to record notes which I find important (and interesting) when trying to understand Kantian philosophy. 

A small note on Kant's view on his days which I thought was interesting. It appears Kant did not enjoy his youthful days. He says:

Many people imagine that the years of their youth are the pleasantest and best of their lives; but it is not really so. They are the most troublesome; for we are then under strict discipline, can seldom choose our friends, and still more seldom have our freedom.

Now on to philosophy. There were at least two outstanding questions related to metaphysics which led Kant to formulate his philosophy. One was Descartes famous cogito ergo sum (I think, therefore I am) and the other was the antagonism between Leibniz's rationalism and Hume's empiricism. 

cogito ergo sum

According to Descartes it is senseless to doubt our existence. The fact that we can think of our existence means that we exist, for sure. Roger Scruton1 remarks "here doubt only confirms what is doubted". However, critical analysis of cogito ergo sum reveals our existence is not vouched by that statement, but rather a thought exists about our existence. cogito acknowledges there is a thought and ergo sum acknowledges our existence. But even when taken together it doesn't mean "I" exists but rather a thought that "I exist". Thus, when Kant was framing his thesis, there was no argument that was readily available to affirm or deny the existence of "I".

Leibniz's Rationalism 

Rationalism is a philosophy that emphasizes that all knowledge is derived primarily from reason and claims to provide an absolute description of the world that is independent of observers experience. Leibniz belonged to rationalist school of thought in which he described the world consisting of infinitely many individual monads each of which living eternally outside space and time. Each monad has a view of reality but ultimate reality is inaccessible to any monad through experience although it can only be realized through reason. Such a reality is more like a surface defined by function of several variables, where each variable is a monad. And experience of reality for a particular monad can be imagined as a restriction of other variables to a constant, during which a section of reality, and not the whole, can be described.

Hume's Empiricism

In contrast to Leibniz, Hume was a empiricist. Empiricism is a philosophy that believes all forms of knowledge are a product of experience and not reason. We gather information only through the senses and so there is no reason to believe reason can alone derive any knowledge. Far from it, it is only through experience all knowledge are gathered. There is no such thing as monad or soul, because experience doesn't tell us if there are any. Also rationalists claims of ultimate description of the world accessible only through pure reason are false since they run contrary to sense perceptions. There could be no single description of the objective universe. Everyone has their view of the world which gets superposed thorough relations. On other words, relationships of experiences only define the objective world and nothing else.

Hume's empiricism and especially this extreme skepticism was unacceptable to Kant and he noted Hume woke him up from "dogmatic slumbers". Roger Scrutonnotes:

Kant did indeed have a lasting quarrel with Leibniz and with the Leibnizian system.  But it was the sense that the problems of objectivity and that of causal necessity are ultimately connected that led him towards the outlook of the Critique of Pure Reason. It was only then that he perceived what was really wrong with Leibniz, through his attempt to show what was really wrong with Hume.


1. Roger Scruton, Kant: A Very Short Introduction, Oxford University Press; Revised edition December 6, 2001.

Saturday, July 19, 2014

Modern Science and Collaborations

Three months back there was an article in Nature (Policy: Free Indian science dated Apr. 02, 2014) discussing the status of science in India and how it should be free from government and bureaucratic interference. This is a good article and points towards the right direction. At the end of the day, science like religion should be de-coupled from governance. This is just basics. This article also brings to the fore the legacy of good science pursued under prominent Indian scientists decades back which leaves us wondering whether the era of monumental ingenuity by lone scientists, are over. Contemporary science often presents itself as a collaborative enterprise devoid of towering geniuses. This is an upsetting view, especially for Indian science because there has not been a single Nobel prize or Fields medal winner after our independence, despite our success in collaborative endeavors such as space and pharmaceuticals. Here I attempt to argue that in science, the era of individual geniuses are not over so that we can hope to reclaim the past legacy (provided we take much needed reforms). In fact, far from it, I claim that in disciplines requiring extensive collaborations, towering geniuses are inevitable outcomes as much as in the disciplines of minimal collaboration. To see this, we need to analyze the structure and the philosophy of science. 

Science is not one single entity. There are at least two main divisions: formal sciences and experimental sciences. Formal sciences can be typically characterized by analytical propositions, i.e., those propositions that are true by their inherent meaning and not how they relate to the real world. In formal sciences like mathematics, theoretical physics/computer science and logic, the progress is largely determined by individual efforts with little scope for collaboration. This is simply because of the structure of these sciences. In these sciences, a new progress cannot merely shelter known propositions. Any new theory should subsume old theories: not just reconciliation of known ideas but proper inclusion of known facts. It is not mere accommodation of known doctrines in the new framework but explanation of available actualities within the new framework. Special relativity includes Newtonian mechanics and not merely accommodates it. Any result that holds true for a vector space should hold true for a Hilbert space. On the other hand, collaboration involves exchange of ideas, although can aid in the formation of a grandeur theory, often works on the level of ideas than on intuition. Encompassing theories are invented purely on the levels of intuition where collaboration has minimal influence. Therefore, there are ample scope for geniuses, who can stand out from the ordinary, by building a better bigger theory. This doesn't mean the progress is linear and a great theory, as a giant leap in our understanding, can take its time to arrive. In these systems of thought, history determines who is great and who is not. Blessed are those scientists who were recognized during their lifetimes. Such recognition need not always happen and certainly we cannot expect them to happen during the short window of our times. Events that leave footprints in the history of science are separated in time far greater than the average human life. For instance, it took more than 160 years for special relativity at appear (it was proposed in 1905) after Newton passed away in 1727. In my opinion, Paul Erdos, the hungarian mathematician could easily be one of the great historical figures who died in the recent past. Currently, Terrence Tao is considered an extraordinary mathematician and history has the potential to elevate him to a genius like David Hilbert. Therefore, at least in the case of formal sciences, where collaboration is of limited importance, we can expect history to determine superiority. And often history repeats itself.

In the case of experimental sciences, it can be argued that today's science has increasingly become collaborative. Several reasons could be attributed to it, including availability of information, increased networking, abundance of scientists etc. However, it is important to recognize that the very nature of these sciences allow exchange of ideas at the fundamental level. This is because experimental facts cannot be derived from a well-defined and agreed set of axioms. Whatever be the reasons for collaboration in these sciences, it is not straight-forward to see why they should result in geniuses. Thomas Kuhn, in his classic book, The Structure of Scientific Revolutions talks about normal science and paradigm shifts. Basically, progress in science proceeds in three distinct phases. Prescience that lacks a central paradigm comes first. In this phase scientists scramble to define a central defining principle. As an example, in the beginning of 20th century there was struggle to define a unit of inheritance until Gregor Mendel established its laws. This prescience phase is usually followed by normal science. Normal science is a puzzle-solving exercise proceeds by development-by-accumulation and attempts to refine and strengthen a central paradigm. This phase is extremely productive and keeps scientists in business. In this developmental phase,  the works of professional scientists who conform to the central paradigm are acknowledged and honored. Scientific results that doesn't reconcile with the central paradigm are not considered as refuting the paradigm but viewed as a mistake of the researcher. For example, in modern times, any result that do not conform to the central dogma of molecular biology would be considered as a blunder of the researcher in designing an experiment. As results anomalous to the central paradigm appear in increasing frequency, there comes a crisis point in science when a new paradigm that accommodates the original framework as well as the anomalous results, emerges. This is a period of revolutionary science when contradictory theories and ideas are reconciled and merged into a broader framework. There have been several revolutionary periods in the history of science. In the recent times, negative experiments of Michelson-Morley in 1887 (that attempted to validate the theory of aether) and eventual emergence of special relativity in 1905, marks one such period in experimental physics. This phase also brings in towering researchers. These pioneering scientists are stalwarts who question the central and well established principles, just to come up with an inclusive framework.

Thus, regardless of whether science is formal or experimental, pioneers are bound to arise and the need of the hour for Indian science is to create an environment that works to this advantage. The rise of such glorious scientists whenever contradictions overwhelm normal science, reminds of the classic verse in Bhagavad Gita:

paritrāṇāya sādhūnāḿ
vināśāya ca duṣkṛtām
sambhavāmi yuge yuge

Saturday, June 21, 2014

Experimental and Formal Sciences

The difference between experimental sciences and formal sciences is the difference between Reductionism and Reductio ad absurdum. 

Reductio ad absurdum is simply not possible in any experimental framework and is the hallmark of sciences based on formal logic.