28 February 2014

Copenhagen zoo giraffe

Copenhagen zoo's director, Bengt Holst, took the decision to kill a giraffe because they didn't need it and/or because it was relative of other giraffes there. Of course, animal activists and others protested at the decision but the zoo ignored them. Other zoos, e.g., the one in Yorkshire, offered to take the giraffe, but the Copenhagen zoo ignored them. Holst replied that nothing can make him alter his management style.

Finally, the zoo killed the giraffe. But they also decided to make a spectacle out of chopping to pieces that would be given to feed the lions. They invited visitors, families and children to watch.
Sometimes I simply don't understand. And I think nobody does. Humans are still animals and it will take long time before we evolve to something better or vanish.

23 February 2014

US executioners' attitudes

I write and talk about executions because I lived in Texas and was truly astonished at the barbarism of the laws about death penalty. In fact, prior to my going to Texas, I had never thought about this. Texas taught me that even the most "civilized" states can have have laws that indicate that they are stuck back in time, hundreds of years ago. "How is that possible?", I kept asking and asking myself. Nobody wanted to actually discuss this. This is the worst of all: people do not want to speak about something so obvious, so irrational, so barbaric.What is worse, the executions are done, implicitly, in the name of religion, and, in fact, a very particular kind of religion: the kind of fundamentalism Christianity which permeates US, the one that is based on the evil part of the Old Testament.

Recently, the following article caught my attention. Dr Allen Ault, who was personally giving the final go ahead  for executions in the  State of Georgia, is now talking of the murders he committed.
I knew I killed another human being. Although an execution is state sanctioned it is, by any definition, probably the most premeditated of any murders. In most states, every execution in the coroner's report is listed as a homicide.
I understand him. I would feel the same. Dr Allan Ault's speeches about the barbaric State-sanctioned murders, are all over the Internet now.

Compare him with another death warden, Charles Thomas O'Reilly, of whom I've written before. He is the champion executioner, having given the go ahead in 140 State-sanctioned murdered (in the infamous Huntsville, in Texas. Texas has executed more than 500 people in "modern" times, i.e., since 1982. O'Reilly did 140 of them!)
 I have no reservations, no nightmares. I don't have any intentions of changing my mind, reflecting on how could I have ever done this stuf. If you think it's a terrible thing, you shouldn't be doing it in the first place. You don't do 140 executions and then all of a sudden think this was a bad thing.
Here is an article from an interview he gave when he retired.

Hanging in Texas
The 10 commandments in front of the Texas Capitol
The death bed in Huntsville, Texas

14 February 2014

Changing comment fonts on blogger

I can't believe I spent time doing this, i.e., finding a way to change the fonts on the comments field, but it was easy, thanks to these instructions.  I was prompted to do by Sabio's comment.(Fonts on the comments field were bold (and big and ugly).) So, here is the algorithm:

First, save the current remplate:
Design > Template > Backup/Restore > Download Full Template > Close
Edit HTML > Proceed 
Within the HTML code, just below the lines
/* Variable definitions
insert the code 
<Variable name="sscommentfont" description="Comment Font" type="font"
         default="normal normal 100% 'Trebuchet MS', Trebuchet, Verdana, Sans-serif" value="normal normal 100% 'Trebuchet MS', Trebuchet, Verdana, Sans-serif"/>  
     <Variable name="sscommentcolor" description="Comment Color" type="color" default="#000000" value="#000000"/>
Then, just above the line
#comments {
insert the code
.comments .comments-content .comment-content, .ss{
    font: $sscommentfont;
    color: $sscommentcolor;
Click Save Template. Then go again to
Design > Template > Customize > Advanced
and you will see a new entry, Comment Font, which can be edited.

13 February 2014

Brain scans and beauty in mathematics

Hot off the press:
Brain scans show a complex string of numbers and letters in mathematical formulae can evoke the same sense of beauty as artistic masterpieces and music from the greatest composers. The same emotional brain centres used to appreciate art were being activated by "beautiful" maths. The researchers, from University College London, suggest there may be a neurobiological basis to beauty and their study was published in the journal Frontiers in Human Neuroscience.

Of course, this is not news to people doing mathematics. But it is nice to know that it can be confirmed independently, or that methods are slowly arising for evaluating such things as "beauty", "elegance", etc. Perhaps, one day, we will have some criteria for other kinds of states which belong to the emotional domain, and, perhaps, we will even be able to quantify such things like morality.

Marcus du Sautoy, mathematician and professor for the public understanding of science [Dawkins' successor in this],  said he "absolutely" found beauty in maths and it "motivates every mathematician". [He is almost right. He should remove the pronoun `every' or define the term `mathematician', for there certainly exist `mathematicians' who are not motivated by beauty but, rather, for example, how much money they can raise or how many papers they can publish (regardless where), and other factors.]

Again, we should be careful in generalizing and cautious in interpreting what the news article linked above says, as it concludes by stating that, "in the study, mathematicians rated Srinivasa Ramanujan's infinite series and Riemann's functional equation as the ugliest of the formulae." At the very minimum, most of us know when something is beautiful or not and also know that beauty may not be apparent from the very beginning, and that it may take a lot of ugly, hard, persistent work, frequently by more than one person, in order that this beauty be revealed and finally be written down so that others may admire [or ignore].

10 February 2014

Stopping time property of hitting times

Suppose that Ft, t ≥ 0, is an increasing family of σ-fields of subsets of a set Ω,  such that ⋂ε > 0 Ft = Ft, for all t ≥ 0.

Let F be a σ-field on Ω such that FtF for all t ≥ 0.

Let P be a probability measure on (Ω, F). Assume that each Ft contains every subset N of Ω  included in some set ANF with P(AN)=0.

Let, for each t ≥ 0, Xt be a measurable function from (Ω, Ft)  into a Polish space S, where the Polish space is equipped with the Borel σ-field B, i.e., the smallest σ-field containing all its open sets.

Assume that, for all ω ∈ Ω, the function tXt(ω) is continuous or right-continuous with discontinuities of first kind only.

Let BB, and define TB := inf{t ≥ 0: Xt ∈ B}. Then TB is a measurable function from Ω into [0, ∞] such that {ω ∈ Ω: TB(ω) ≤ t} ∈ Ft, for all t.

Probabilities and Potential, by Claude Dellacherie and Paul-André Meyer.


What measure theory is about

It's about counting, but when things get too large.
Put otherwise, it's about addition of positive numbers, but when these numbers are far too many.

The principle of dynamic programming

max_{x,y} [f(x) + g(x,y)] = max_x [f(x) + max_y g(x,y)]

The bottom line

Nuestras horas son minutos cuando esperamos saber y siglos cuando sabemos lo que se puede aprender.
(Our hours are minutes when we wait to learn and centuries when we know what is to be learnt.) --António Machado

Αγεωμέτρητος μηδείς εισίτω.
(Those who do not know geometry may not enter.) --Plato

Sapere Aude! Habe Muth, dich deines eigenen Verstandes zu bedienen!
(Dare to know! Have courage to use your own reason!) --Kant