The First Synthetic Cell

Yesterday, the creation of the first synthetic cell was announced by Craig Venter, one of the greatest biologists of our era. This is the first self-replicating organism on the planet whose parent is a computer.

After a fifteen year journey (during which he also decoded the human genome), Craig Venter's team successfully made a complete synthetic genome, transplanted it to a bacterial cell, and booted it up in the cell to produce a new species. The genome was designed on computers and created from four bottles of chemicals. Then, the chromosomes were assembled in yeast. One of the major obstacles was to boot up the genome in the bacterial cell, since the transplant chromosomes were rejected and destroyed by the recipient cells. Advances were made to remove restriction enzymes from recipient cells and insert chromosomes with methylated DNA in the cells.

Other problems in the project were debugging issues. Initially, the transplanted chromosomes did not support life because only one base pair was deleted. This led to the development of debugging programs that made the production of the life-supporting synthetic genome possible.

One interesting aspect of this genome is that it has watermarks embedded in it for identification. Using a specific code, the names of the authors and the website of the genome were spelled out in the genome.

This amazing breakthrough has vast implications. Firstly, it tells us about the basic recipes of life as well as the dynamic nature of it. It also provides technical advancements such as the production of vaccines and production of new and useful species, such as algae that can make oil out of the carbon dioxide in the atmosphere. We can only begin to imagine what might come out of this astonishing revolution.

Irrationality Proofs

Number theory has always been a fascinating topic to me. If one stops and thinks, the concept of irrational numbers is a very intriguing one; numbers that we cannot determine the exact value of. For example we cannot locate the exact value of √2 on the number line. I find this idea very strange and curious.

To be more precise, irrational numbers are those that cannot be expressed as the ratio of two integer numbers. One interesting approach is to examine irrational numbers by continued fractions. Every number can be written as a continued fraction in the form of

This is an alternative to decimal representations, which is not based on a specific base number. For example:

Irrational numbers are in fact produced from infinite continued fractions. For example:

The value of a number can be approximated to different accuracies by truncating the continued fraction at different poinst.

Determining the continued fraction for an irrational number is also very interesting and I might cover it in a later post. In this post, I am going to prove the irrationality of some numbers such as √2 and π.

Irrationality of √2:

This is proof by contradiction. Let’s assume there is a simplified fraction a/b which is equal to √2.

a/b=√2

a=b√2

a^2=2b^2

∴a^2 | 2

∴a|2 since a∈Z

Since a is even, b cannot be even (since a/b is a simplified fraction).

Since a is even, there should be an integer k for which a=2k.

(2k)^2=2b^2

4k^2=2b^2

b^2=2k^2

∴b^2 |2

∴b|2 since b ∈Z

But b cannot be even. Since a and b are both even, a/b is not a simplified fraction. Therefore, by proof by contradiction, √2 is irrational. Specifically, this is called proof by infinite descent.

Irrationality of π:

This proof is much more difficult and interesting. We are again going to use proof by contradiction. Since this proof involves a lot of exponents, derivatives, and integrals, I have written the proof in Microsoft Word and I am going to upload it here as images.

In future posts I might show irrationality proofs of other numbers as well as proof of transcendence, which is another interesting property of some numbers.

Computing a Theory of Everything

Stephen Wolfram has initiated an interesting approach in studying the physical universe. He tries to create our physical universe out of the much more diverse computation universe, the vast abstract universe of computation and mathematics.

Wolfram has created Mathematica and Wolfram|Alpha, two very powerful mathematical/computational tools. He is also the author of "A New Kind of Science" (which is available online). Wolfram has established a new kind of science (as he calls it) which examines the complexity of systems from very simple computational rules.

In his talk at TED, he outlines this idea and how it relates to our physical world, in the sense that our seemingly complex universe could be the product of simple rules which could be simulated in computers. Wolfram has done much research on this issue and has actually created universes that come very close to ours.

I personally believe that this approach is very valuable and successful. Our understanding of nature lies in understanding complexity in systems consisting of different parameters. Not only will this approach make contributions to theoretical physics (hopefully), but it will also allow us to understand much more complex systems such as those in biological organisms. Something as complex as the brain can only be studied from this approach.
As a matter of fact, a very interesting field named Computational Neuroscience is being established. Many mathematicians, programmers, neuroscientists, and physicists will come together to study the brain from a computational point of view. I personally cannot wait to see what will come out of this in the upcoming years.

Neil Turok's TED Prize Wish

Neil Turok is the director of the Perimeter Institute for Theoretical Physics and a very successful physicist. I was rather shocked when I came upon his Prize Wish video at TED. Alongside his successful academic life, he manages to be quite active in helping other people and providing aid and education in Africa. I think this is an interesting and moving talk by him that really shows some important values:
http://www.ted.com/talks/neil_turok_makes_his_ted_prize_wish.html

Some Interesting Quotes

Here is a list of some interesting quotes that I have encountered here and there. I tried to put them in order from my most favourite to least, but it's not that easy. Here is what I came up with:

"It is not complicated; there is just a lot of it."
Richard P. Feynman

"Life is a sexually transmitted disease."
R. D. Laing

"Physics is like sex. Sure, it may give some practical results, but that's not why we do it."
Richard P. Feynman

"Genius is one percent inspiration, ninety nine percent perspiration."
Thomas A. Edison

"In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in poetry, it's the exact opposite."
Paul Dirac (1902 - 1984)

"We must not forget that when radium was discovered no one knew that it would prove useful in hospitals. The work was one of pure science. And this is a proof that scientific work must not be considered from the point of view of the direct usefulness of it. It must be done for itself, for the beauty of science, and then there is always the chance that a scientific discovery may become like the radium a benefit for humanity."
Marie Curie (1867 - 1934), Lecture at Vassar College, May 14, 1921

"It is our choices that show what we truly are, far more than our abilities."
J.K.Rowling