Banach-Tarski-Theorem

I wonder why I did not post this when I first read it, but because I just crossed that topic again, here is a nice, even though not formal and not technical sketch of a proof of the banach tarski theorem at irregular webcomic.

On moral and ethic

Just two quick links to videos on youtube. I will not comment on the degree of agreement I have with those, just take them as initial input for discussing those and the relevant foundational topics:

Noam Chomsky and Peter Singer on abortion

Peter Singer and Richard Dawkins: Interview on morality

I think, especially without knowing to much on the foundation of Peter Singer's ethics, these videos raise interesting questions about how to define ethical/moral behaviour. The second video suggests that moral behavoiur according to Singer tries to minimize the infliction of pain towards living beings. Beyond the discussion about vegetarianism that dominates the interview, one should also consider the "side-effects" of our current life style. Even if you doubt effects like global warming, it is obvious that we have driven many species to the edge of extinction and moreover, done considerable damage to indigenous peoples all over the world.

Assuming a decline or at least a unchanged situation, what does this imply dealing with the future harm of yet unborn animals (including humans)? What kind of trade off can we afford? Is there some kind of cost-benefit analysis weighting the benefits of our life style versus future harm? How do you measure those factors? Actually, is it even justifiable to think about cost-benefit analysis when talking about pain and suffering? Furthermore, who is to take responsibility for our life style? Even if I try to live a "green" life, due to being trapped in our rather wasteful society, I will cause harm. In fact, most of us are certainly opportunistic conformists, just following the mainstream of society.

(dual) n back

I just learnt about the concept of n back tests. Basically, you are presented tokens from a sequence and your task is to determine whether the current token matches the token N steps back.
This can of course be done in parallel with multiple sequences, called "dual", "triple" (..) N-Back, although I haven't seen any implementation of a triple (k, m, n)-Back with different periods in each sequence.

There is a paper which claims to establish a connection between playing dual n back and fluid intelligence. There is also a wired article summarizing the paper.

Check out the flash game presenting a visual and an audio sequence.