Showing posts from October, 2009

The countability of real numbers

Natural numbers (symbol N) are positive whole integers starting with either 0 or 1. It is obvious that there are an infinite number of natural numbers, and that they are countable. By starting with the lowest natural number and counting long enough, you will eventually reach any other chosen natural number. Integers (symbol Z) are countable as well. The set of integers contains zero and all natural numbers as well as their negatives. To count them all, just start with 0, then 1 and -1, then 2 and -2, etc. Rational numbers (symbol Q) are those numbers that are expressible as fractions, e.g. 1/2. Rational numbers are also countable. For an idea of how to count them, imagine a two-dimensional grid that has integers on each axis, and contains infinitely many horizontal and vertical lines, one for each integer on the respective axis. To count all rational numbers, start at (0,0). Then, count all intersections on the border of the square between (-1,-1) and (1,1). Then, count all intersect

Somali pirates, Italian mafia, and radioactive waste

Looks like the story about Somali pirates has some twists and turns. Johann Hari : As soon as the government was gone, mysterious European ships started appearing off the coast of Somalia, dumping vast barrels into the ocean. The coastal population began to sicken. At first they suffered strange rashes, nausea and malformed babies. Then, after the 2005 tsunami, hundreds of the dumped and leaking barrels washed up on shore. People began to suffer from radiation sickness, and more than 300 died. Ahmedou Ould-Abdallah, the UN envoy to Somalia, tells me: "Somebody is dumping nuclear material here. There is also lead, and heavy metals such as cadmium and mercury - you name it." Much of it can be traced back to European hospitals and factories, who seem to be passing it on to the Italian mafia to "dispose" of cheaply. In other news , the Italian mafia is reported to have sunk as many as 30 ships of toxic waste off the coast of Italy. Johann Hari makes perverse conclusion

Gay rights worldwide

In a time when the civilized world is slowly progressing towards equal rights for gays and lesbians, it is interesting to look at this map and see what world regions have the harshest penalties for homosexuality. Source: Wikipedia It's striking to see how many countries have penalties as harsh as death, or life in prison. In much of the Caribbean, the penalty is 10 years. In Jamaica, it is "10 years of hard labor". Fascinatingly, the South African Republic is an exception - same-sex civil marriage has been legal there since 2005.

Jaw bone created from stem cells

  Fantastic! In a couple of decades, it may be standard practice to replace older people's worn out joints by growing new joints from the patients' stem cells. Let's hope for similar breakthroughs that will allow the growing and replacement of people's organs, as well. Now consider IBM's efforts to develop techniques for quickly and cheaply sequencing a person's DNA . These types of breakthroughs may allow a person's DNA to be sequenced when young, and reproduced when the person is older. The DNA in your cells gets damaged as you age, but a digital copy of your DNA takes a snapshot at the age at which it was sequenced. Live another 50 years, and the breakthroughs that will be achieved during this time may allow us to continue living much, much longer!

Religious zealotry vs. child molestation

In March 2008, an 11-year old died from undiagnosed but treatable diabetes as her parents prayed by her side without even considering taking her to a doctor. Now, the parents have been sentenced leniently by a judge who sympathized with them. Quotes from the article: During the sentencing hearing, Leilani Neumann, 41, told the judge her family is loving and forgiving and has wrongly been portrayed as religious zealots. "I do not regret trusting truly in the Lord for my daughter's health," she said. "Did we know she had a fatal illness? No. Did we act to the best of our knowledge? Yes." Dale Neumann, 47, read from the Bible and told the judge that he loved his daughter. "I am guilty of trusting my Lord's wisdom completely. ... Guilty of asking for heavenly intervention. Guilty of following Jesus Christ when the whole world does not understand. Guilty of obeying my God," he said. Compare this to child molestation. If the parents were mad in

Progress in tiny nuclear batteries

  BBC article with a photo of the battery. PhysOrg article with comments.

Half the human population is evil

A study performed at the Faculty of Economics and Management in Magdeburg confirms my intuition that nearly half of all humans are inherently unempathic, even downright evil, but simply hide their psychopathy most of the time, because civilization expects that from them: The Pleasure of Being Nasty We introduce the joy-of-destruction game. Two players each receive an endowment and simultaneously decide on how much of the other player's endowment to destroy. In a treatment without fear of retaliation, money is destroyed in almost 40% of all decisions. See Figure 1 - Destruction frequency over time . At least 25% of people will cause gratuitous harm to a random stranger if they can do so at no cost, while up to 50% will do so if they can also deny it.