This is the first installment in a series about social choice and welfare. The structure will be: historical anecdote, followed by “spoon-feeding” the conclusions.

Senate tribunal

Senate tribunal

So, here go:

We are in the 1st century A.C.. Pliny the younger is the current “chairman” of the Roman  Senate. And he is faced with a difficult situation. Consul Africius Dexter was found dead. Was he murdered? Was it an assisted suicide?
The freedmen who worked on his estate are sent to trial in Rome. The Senate is debating their doom.

The Senate gets divided into three groups. In the first and largest group, Pliny the younger convinces the other senators that there is no case for conviction. The death of Africius Dexter was a suicide, or very likely so, and the freedmen should be exempt from charge. The second group, slightly smaller, includes senators who are not willing to clear the freedmen from guilt. But they are not convinced enough to demand a harsh punishment. They opt for exiling the freedmen.
The smaller group, the third, is composed of senators who would have the freedmen all executed.

Most Senators expect Pliny the younger to count the votes on guilt, first, and then on punishment. The outcome in that case would be guilt, and the lesser punishment of exile, not death.

But Pliny refuses. He claims that coupling the options of exile and death and pitting them as a couple against acquittal is wrong. What do these punishment have in common, he asks? Surely, the distance between death and exile is larger than the distance between exile and acquittal. Pliny wants to count all three options as equal, and see what option would gain a simple majority. That is, which option has the larger pool of supporters.
This would mean, conveniently, that acquittal would win.

But that did not come to pass. The third group, the ones who want a death sentence, they “lie” and go over to the second group. Together, they have signed a majority for exiling the freedmen – much to the dismay of Pliny. As he moans in a letter to a friend, that was foul play.

Was it?

Why does -1 * -1 = +1 ?

I have been asked this by perplexed teachers, parents and kids:

Why did them silly mathematicians decide that the multiplication of two negative numbers is positive? What’s the logic?

The first thing is to acknowledge that this is a convention. We could define -1*-1 to be whatever we want. But there is good reason to decide it should be +1.

Let’s try to calculate:

-1 * ( 1 + -1)

Well, -1 is the negative of +1, which mean, by definition:

-1 + 1 = 0

So, -1 * (1+ -1) = -1 * 0

and multiplication by zero must be zero, so we have:

-1 * (1+ -1) = -1 * 0 = 0

But, if we open the parenthesis, we have:

-1 * (1 + -1) = -1*1 + -1*-1

now, multiplication by 1 is doing nothing, so -1*1 = -1, so we get:

-1 + -1*-1 = -1*1 + -1*-1 = -1*(1+ -1) = -1*0 = 0

hence, -1 is the negative of -1*-1, so the latter has to be +1.

What have we used? We used the definition of zero and 1, we used the definition of the negative of a number, and we used the law of distributivity (by which we can open the parenthesis).

We could decide, say, that -1*-1 = -1, but then we’d have to abandon one of the principles mentioned above, and that would make arithmetic rather unpleasant.

The hardships of equality

This post is an attempt to clarify and generalize the main points of:

and explain why equality is an excruciatingly hard goal. Note that equality is meant, first and foremost, to be formal equality in front of the law. I am not interested here in questions of economical equality, although extreme economic inequality often has legal and social repercussions.

What does it take to create equality?
Continue reading

On double and or

A small remark on programming conditionals. This is true for C and C++, but it might be true also for Java and other languages. I haven’t checked all of them.

It is about conditionals.

I’m seeing lots and lots of double OR and double AND in conditionals. In fact, I find it rare to see a single single operator these days. (Sorry, I couldn’t resist the pun). Almost without exception, every multiple conditional I see has the form:

if ((x>0) && (x<MAX_VAL))
   do something....

Which is kind of silly, really. What one should do is use the simple single-operator

if ((x>0) & (x<MAX_VAL))
   do something....

Continue reading

Don’t compress it with that!

We had an issue at work. Our dev. team is managing a php server, which sends and receives binary KET files of constant size (say, 5kb) to production servers. I was rewriting some of the production servers and I notices that sometimes I’m getting TLE files in instead of KET files, and that they are 11 byte too big.

I checked it out. Apparently the dev. team was sending the KET files for compression (via php gzcompress). They were very much surprised to learn that the output files were larger than the original KETs. “Apparently”, they sighed, “gzip is not a very good compression. Let’s find another one”.

Which is the wrong conclusion. They have a meagre chance of finding a compression engine which wouldn’t expand the files. And this is a good excuse to explain this to the rest of the world.

An introduction to data compression

Mathematician’s digest:

Pigeon hole principle → no general compression scheme possible.

Range limitation → Data redundancy → range-specific compression possible.

Prima facie, compression is an impossible task.

Continue reading

What did go wrong?

A few years back, a friend bought me Bernard Lewis’ “What went wrong” and asked me for a review. This is somewhat late – but you might find it interesting.

Lewis’ starting points seem obvious: is the 13th century, Islam was the future. The Islamic centers in Mesopotamia were the peak of civilization. 700 years later, Islamic Mesopotamia is poor and sordid.
He is searching for an answer in culture. That seemed weird to me. Culturally, the east – and especially the Islamic east – was not a lethargic culture.
And I think I have a better explanation now.
Reading material:
Weatherford, Jack (2004). Genghis Khan and the Making of the Modern World (review). New York: Crown. ISBN 0-609-61062-7.


As people are the same, so are socioogical truths. It’s the same story in Israel, today, as well.

Originally posted on Pandaemonium:


At the heart of the current debate about immigration are two issues: the first is about the facts of immigration, the second about public perception of immigration.

The facts are relatively straightforward. Immigration is a good and the idea that immigrants come to Britain to live off benefits laughable. Immigrants put more money into the economy than they take out and have negligible impact on jobs or wages. An independent report on the impact of immigration commissioned by the Home Office in 2003, looked at numerous international surveys and conducted its own study in Britain. ‘The perception that immigrants take away jobs from the existing population, or that immigrants depress the wages of existing workers’, it concluded, ‘do not find confirmation in the analysis of the data laid out in this report.’ More recent studies have suggested that immigration helps raise wages except at the bottom of the jobs ladder where…

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