Friday, June 10, 2011

Can there be both 'rational and irrational' numbers ?

Everyone knows, from the school, that square root 2 is irrational . I still remember the fashionable way in which my school teacher proved it. (for those who do not remember ). As all know, an irrational number cannot be written as a/b where a and b are integers. We know following facts which are proven in fashion in real analysis.
1. Any real number is rational or irrational
2. There are infinitely rational and irrational numbers
3. There are infinitely integers
 'Can we say a given number is rational or irrational ?'. (If it is given in decimal points, number is rational for sure) . What I really mean is if I marked a random number on number line (see how irrational numbers are marked on number line at, who on the earth can say it is rational or irrational ? Since there are infinitely integers it can be a ratio of any two of them. Or since almost all the real numbers are transcendental (  and all transcendental numbers are irrational, there is a higher probability of randomly marked number is being irrational. 
Therefore until being confirmed (or observed) we cannot comment about the rationality of the number. But we can give a probability distribution for the rationality of the randomly marked number. 
According to quantum mechanics, we can say this number is in superposition of states.  i.e. the number is both rational and irrational. Described probability distribution is the wave function. 

Saturday, February 12, 2011

2011 -2020 a decisive decade for mankind

    2011 is the first year of the 202nd decade which is to be end in 2020. This decade is going to be one of the decisive decades in human history due to many scientific, economic and political reasons. We had something similar decade in 1940-1950 where initial steps to the digital revolution kept with the invention of the transistor and Von Neumann and Alan Turing publishing their papers on stored program computers (First Draft of a Report on the EDVAC by Neumann and Automatic Computing Engine by Turing), first nuclear bomb was produced and world power was shifted to US and Russia.
   This decade is similar because by 2020, we are approaching the end of Moore's law (doubling the performance of semiconductor fabrications in every other year ) , there will be plans replace modern computing with quantum computing, reaching the end of the era of fossil fuels and will be having earth with an unpredictable climate patterns.

End of Moore's law and quantum computing

    While we are making the processors smaller and smaller, there is a limit that behavior gets unpredictable according to the laws of quantum mechanics. Then we will face a quantum leap or saturation. But recent developments in quantum computing and nanotechnology say we are not that unfortunate to face a saturation and coming to a dead end. However this will be decided by 2020. If we are going to replace modern computing by quantum computing, programming concepts will entirely be changed. New languages will replace C, C++ , Java etc.

End of fossil fuels

    Despite the end of fossil fuels is not a proven fact, most nations have plans to replace fossil fuels by alternative sources in 2020. Sweden have plans to 100% fossil fuel eliminations in some regions and most other nations have plans cut off the fossil fuel usage by some percentage. Since we are reaching the end of the resource, finding alternatives is a must and otherwise it'll be serious energy crisis. This will be decided by 2020 and there we will be able to say whether we have to travel by carts or not.

Climate change

     Since no proper agreement to limit global greenhouse gases came effective and US and China have not shown a commendable commitment, unpredictable climate patterns may occur by 2020. Even in this year, 2011 we have seen much of them all over the world. (Australia, Brasil, China etc.) . We will probably  start experiencing the effects of global warming in 2020. There we will see the fate of mankind.

P.S. : New world order

    Although shifting the world power from US to China may not happen there will be many world super powers unlike we had in last century. Anyway this matter is a topic of political scientists and does not suit the scope of this blog :)

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