RSA: Renata Salecl – The Paradox of Choice

In this video, we see an artistic representation of a talk given by Renata Salecl about the ramifications of this overwhelming amount of choice we have (especially in the U.S.). In this talk she mentions the role that capitalism plays on this topic. I am not posting this as my declaration against capitalism and my support for socialism by any means. I personally do not have enough information to willingly give my opinion. In this talk however, we are certainly given a compelling argument against capitalism as it acts as the catalyst to overwhelming choice which leads to a life of misplaced values and always failing to meet one’s own expectations. Enjoy.

 

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Infinite Primes

I’m currently taking a class called computational number theory. In the class we are learning a variety of things from cryptography, quadratic reciprocity, to (the simple sounding) primes. In class we learned about something called a twin prime pair which is a pair of integers p, p+2 which are both prime. Some examples of these are; (3,5), (5,7), (11,13), (17,19), (29,31) …

Now it has been proven that there are infinitely many primes. I will not do the proof unless it is requested, and it is pretty easy to believe given that we have infinite numbers. But are there infinitely many twin primes? Again, simply using our intuitions of probability we want to say yes (given, again, that we have infinite numbers). Amazingly enough however, intuition is not a proof and NOBODY has proved it!

Recently in the world of mathematics however, a man by the name of Yitang Zhang from the University of New Hampshire proved a theorem this year which is similar to the unproven theorem above. What he proved is called the bounded prime gaps conjecture, and what he showed was that there are infinitely many prime numbers p, q where p < q and q – p is less than or equal to 70,000,000.

This is an amazing feat and the proof is said to be upwards of 160 pages long. This also sheds light on some hope that perhaps our tantalizing question above might one day be proven.

On this topic of primes, I will leave you with a fun video. I hope you enjoy.