Biased, are we?

Intelligent systems and Racial bias – a couple of remarks

In, Rose Eveleth talks about the racial bias inherent in Facial Recognition systems. It is an interesting read. I would like, if I may, to make a couple of comments.


I must admit, first of all, that Rose Eveleth is correct. Face Detection and Facial Recognition systems suffer from racial bias. I have used many such systems, and they are all, always, racially biased. But I would just like to elaborate a little bit on that issue.

The underlying problem is simple – you need to train a system on a large “test set” of sample faces. Those “test sets” need to be generated by human beings, at a high cost. There are now two human biases coming into play:

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On the manipulability of votes

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 punishments 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?
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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. The double operator && is the right thing to use when you have a complex conditional with function calls. But when all you do is compare arithmetical conditions? What one should do is use the simple single-operator

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

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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.

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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.