import blog.xanga.*

 

 

I have recently switched to this wordpress from xanga. It was easy as I had written just one blog in my previous technology blog , so all I had to do was copy and paste it here. But with my personal blog it has a different story. I have written so much in it that now I can’t manually copy, paste and format it on a new blogsite. I wish I had a software which would do this for me. Blogs are growing day by day and people would be changing blog sites more and more as better ones come up. Hence demand for such a software would be rife. Any blogsite which apart from being attractive also has the feature to import blog entries form other blog sites which the writer owns would have a big advantage. So look out for it!

 

 

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Technology and Mathematics :an Introduction(MUST read)

Now why this technology blog when I already have one[here]? Well, to begin with technology is an interest of mine which deserves a category of its own. Hence, this blog. Now why only this technology blog? Well, first of all this blog will not be talking about gadgets , or how to fine tune and speed up your computer[or may be when I have nothing else to write about!] or other such tid-bits; it will talk about two guiding phenomena of technology.

(1) Underlying philosophy in technological advancement.

(2) The backbone of technology-mathematics.

To make matters less ambiguous let me state that when I refer to technology I usually talk about the net and IT revolution. So technology would mainly mean this, until otherwise stated specifically.

Also when I use the term mathematics I mean higher mathematics, and not in the general sense like – hey count nicely, do your maths.

As the complexity of cutting edge technology grows, it will be more and more dependent on mathematics. For many it would seem that this is the era of technology- well it is not. The era of technology is yet to come. Let me give you an analogy to illustrate my point. At the time of Aristotle and Archimedes[of the Eureka fame!] the era of Physics had begun, but it had not reached its mathematical finesse yet. There was a lot of accosting and dating which went between mathematics and physics, but the marriage of physics and mathematics took place with Newton acting as the head priest. And with the culmination of strong bond between mathematics and physics put forward by Einstein. You can call it an age of Physics if you want, but certainly not of technology. Technology is still in its ‘tinkering’ stage with now and then dates with mathematics. There have been many who have used the underlying power of mathematics to change the face of technology. To give you an example I choose the most popular technology[if not the best example to show the relation between mathematics and technology]—Google. It extensively used mathematics to harness the power of net in its new search engine- google.com. For further reading you can have a look at the paper written by Larry Page and Sergey Brin- co founders of Google-here.

Let me finish this introduction by paying tribute to the beauty of mathematics by the proof of infinitude of primes by Euclid.

 

Theorem:

 

There are infinitely many primes.

 

Proof:

Suppose that p₁=2 < p₂ = 3 < … < p_r are all of the primes. Let P = p₁p₂…p_r+1 and let p be a prime dividing P; then p can not be any of p₁, p₂, …, p_r, otherwise p would divide the difference P–p₁p₂…p_r=1, which is impossible. Hence either P itself is a prime number or any prime other than p_1, p_2,…, p_r .Now if P is a prime then we get a contradiction as we assumed that p_r is the largest prime. If there is any other prime number which divides P,say Q, then Q is other than p₁, p₂,… p_r and hence greater than p_r, because all the primes less then p_r[namely p₁, p₁,… p_r-1] are already excluded. Hence Q is a prime greater than p₁-again a contradiction. Hence there are infinitely many primes.

On a personal note, my love affair with mathematics began by seeing the power and beauty of this particular proof. If mathematics could be represented by one theorem, it would be Euclid’s theorem ,which reflects the force as well as beauty of mathematics in a delicate balance.

Happy thoughts!

 

p/s: Another area of interest which deserves a blog of its own is economics. I will start an economics blog soon.

Goodchild: There must be. Your way, the way of intelligence is the way to destruction. You made man make that choice, you made him violate the natural law.
Sky: No, human life has scorned both of us. The chaos to come is of man’s own making. Neither you or I can help him now.

–From movie: Sky(1976)