Saturday, August 31, 2013

Ian Pollock does a very good analysis of secularism here. He argues that secularism is, in fact, unprincipled, but at the same time, it is probably practically necessary.
"I believe that secularism, as imagined above, arises more or less as follows:
• Participation of citizens with differing views in political debate is supposed to be part of the democratic process.
• However, a large fraction of citizens hold some views that are (in the judgment of more sober minds) straightforwardly insane, and would not hesitate to impose the policy implications of those views upon the rest of society if given the ability to do so.
• Religious moderates, religious minorities and non-believers, tacitly recognizing these two facts, promote secularism as a compromise, despite its philosophical bankruptcy and practical pathologies."
I am of the same opinion. I agree that that there is no principled difference between religious beliefs and secular beliefs. However, I also do not see how a multicultural democratic society can exist and thrive without some version of the two main principles of secularism mentioned in the article, especially when there are religious fanatic elements within the society who have no respect for other religious points of view. 

If there is to be tyranny, let it be against those who wish to tyrannize others.

Wednesday, August 28, 2013

Insulin coma therapy was a once wildly popular psychiatric treatment for Schizophrenia in which large doses of insulin were repeatedly administered to patients to produce daily comas, continuing on for several weeks.

Consider this 14-year follow-up study on the effectiveness of insulin coma therapy for schizophrenia that was published in the American Journal of Psychiatry in 1955, and stated "We conclude that insulin coma therapy is effective in restoring the schizophrenic patient to his prepsychotic adjustment." If these researchers could study an intervention (that we now, with hindsight bias, know to be obviously ineffective) on 800 patients for 14 years and still conclude that it was effective, we can imagine how many researchers doing studies with much smaller samples and follow-ups would only end up seeing what they want to see. How much of cherished research today would be discredited two or three decades from now?

Here is another study from another prestigious journal JAMA, that was published in 1958. It compared the effectiveness of chlorpromazine, an antipsychotic medication, with insulin coma therapy, and concluded that there was no difference in efficacy between the two, just that chlorpromazine had the advantage of being safer and easier to administer.

By the time insulin coma therapy was fully discredited by more meticulous and controlled studies, most physicians had already stopped doing insulin coma therapy. Not because they thought it was ineffective (they still believed it effective based on their clinical experience) but because they had found a safer alternative in the form of antipsychotic medications.

(Here is a good article on the rise and fall of insulin coma therapy.)

I think this particular example goes a long way to show the limitations of evidence-based medicine. Of course, the alternative is not to rely exclusively on clinical experience, which is even more faulty. The alternative is clinical experience informed by better and more rigorous evidence-based medicine, but it is just a reminder that we are not there yet. It can, in fact, be demonstrated (as in this paper) that most current published research findings are false.

Tuesday, August 27, 2013

by Dr. Yuval Noah Harari

Personal Lecture Notes from Lesson #2: The Cognitive Revolution

(These are personal summaries and paraphrasings of some of the major points of the lectures that I felt to be important. They are not meant to be comprehensive records nor intended to be reproductions of copyright materials. I encourage you to participate in the course for better understanding.)

Cognitive Revolution: the appearance of new ways of thinking and communicating between 70,000 and 30,000 years ago.

Around 100,000 years ago, Homo sapiens first tried to migrate to Middle East from East Africa but they were driven away by Neanderthals.

70,000 years ago, however, Homo sapiens tried again, and this time they were successful, driving away other human species in the process. 60,000 years ago, they reached China and Korea. 45,000 year ago, they crossed open sea, and landed in Australia (first time for a human species). Later they reached America about 15,000 years ago, again, first time for a human species. They reached America from Siberian Alaska, which would have required them to adapt and survive extreme cold temperatures within a remarkably short span of time.

Signs that something special had happened:

* Humans spread throughout the world and adapted to new ecological conditions very quickly.
* Appearance of new technologies and innovation of existing ones:
Boats or rafts, which allowed them to reach Australia by crossing the sea
Needles: this allowed humans to sew things together, making new clothes, boots, tents, etc. This made it possible for them to endure extreme cold climates.
Oil lamps: this allowed them to explore caves and produce cave art
Constant innovation of spear points and knives (which had prior had been consistently the same)
First evidence for art, religion, trade and complex societies.

Most likely there was some small change in the internal structure of the brain with remarkable results.

Human language was not the first language. Animals had languages before. Nor was it the first vocal languages. Those also existed prior. It is also not the most vocally sophisticated language. So what is special about it?

1) Our language is immensely complex in terms of information transmission. We have ability to take limited number of sounds to produce infinite meaningful sentence.

2) A theory suggests that the vast information capacity of human language evolved so that we could talk about other humans (i.e. gossip). Gossip plays a very important role, as without it it is very difficult to live in a large group and to cooperate effectively with other people. Social cooperation is our key for survival and reproduction. The ability to gossip allowed us to do that. Even today, the majority of human communication in the world is gossip. Gossip focuses on the wrong-doings, on breaking of norms. It acts as a sort of police, and was especially important in the establishment of early complex societies when there was no police as such.

3) The most unique feature of human language, however, is to transmit information about things that don't exist at all. Legends, myths, gods, religions. Human language is fictive language. It enables us to imagine collectively and weave common legends.

The ability to create well-functioning groups on the basis of gossip ranges up to about 150 individuals. The secret which enabled humans to cross the critical threshold of 150 individuals to create immensely large and complex societies is fictive language. A large number of humans can cooperate successfully by believing in common myths. Complete strangers who are Christians can cooperate to go on a crusade because they believe in the same God. States are based on national myths, the judicial system on legal myths, economic system on the myth of money, all of which do not exist outside the common imagination of humans.

Take Peugeot, a huge company that employs thousands of complete strangers who work efficiently to produce millions of cars around the world. What is Peugeot? Is it the cars? No. Is it the factories? No. Is it the employees? No. Is it the management or stock-holders? No. The company is a story, a particular sort of fiction. It belongs to a fiction we call 'limited liability companies'. Limited liability company is a company which is collectively imagined to be legally independent of the people who set them up, of the people who invested money in them and of the people who manage them. So if the company takes a loan, it is not the owner or the manager who is responsible for the loan; it is 'the company'. And if the company cannot repay the debt, it is the not the owner or the manager who will go bankrupt, but the company. This was not the case earlier in history, when no such limited liability existed. We have become so accustomed to such companies that we forget that we invented them ourselves and that they exist only in our imagination. The ritual involved in their creation is also not much different from the rituals of shamans. A shaman would do particular actions and cast forth particular spells to call forth a spirit, and here the lawyer and owner wrote the particular 'spells' on a particular paper and once they were signed, hocus pocus, Peugeot was created. The spirit is as real to someone who believes in shaman's magic as Peugeot is real to someone who believes in business laws. Both are, in fact, imagined realities. They are products of common belief, and as long as this common belief persists, it is a real force in the world. It is this power of common belief that allowed Homo sapiens to work together flexibly and effectively in very large groups, and this is something that other human species were unable to accomplish.

Creating large shared stories in this manner also makes cultural evolution possible. In certain conditions, humans can change stories, resulting in rapid innovation of social behavior, without any underlying genetic change. This can happen within decades, unparalleled in the biological world. Female chimpanzees, for instance, cannot stage a feminist revolution to overthrow the alpha-male, unless there is a radical change in their genetics, but because humans possess the power to create and change fictions, women can, and have, remarkably changed the gender roles and relations in human society. Same applies to all the other social and cultural changes that we see in history. From this point onwards, to make sense of the human history, we need to make sense of the shared stories and collective fictions.

Monday, August 26, 2013

Hannes Leitgeb and Stephan Hartmann

Personal notes from lectures of Week 3: Rational Belief

(These are personal summaries and paraphrasings of some of the major points of the lectures that I felt to be important. They are not meant to be comprehensive records nor intended to be reproductions of copyright materials. I encourage you to participate in the course for better understanding.)

Propositions and Possible Worlds

Propositions are true or false at possible worlds, with one of these possible worlds being the actual world. It is possible to show that worlds are identical if and only if the same propositions are true at them; and propositions are identical if and only if they are true at the same worlds.

Propositions can be defined as sets of possible worlds, such that every proposition is identical to the set of worlds at which it is true. Using set theory, we can visualize negation ('not'), conjunction ('and') and disjunction ('or') of propositions in the form of Venn diagrams. Also, the relationship of logical implication between propositions (proposition X implies proposition Y etc.) can be understood as a subset relation (X is a subset of Y).

Postulates of Rational Belief:

For an inferentially perfectly rational person 
1. If capital W is her set of entertainable possible worlds, then she believes capital W. (This is expressed by the logical form 'A or not A'.)
2. She does not believe the empty set. (This is expressed by a logical contradiction of the form 'A and not A')
3. If she believes X, and if X is a subset of Y, then she also believes Y.
4. If she believes X, and if she believes Y, then she also believes X-and-Y, the intersection of X with Y.

From these four postulates, a theorem can be derived stating:
There is always a least or smallest believed proposition ('B_W'), and the person in question believes a proposition if and only if B_W is a subset of that proposition, i.e. B_W logically implies that proposition.

Philosophical implications: 

* Rationality has an information-compressing effect (if we just know the B_W, we can determine whether a particular proposition is believed by the person, is disbelieved, or the judgment has been suspended.)

* Rational belief has a kind of mathematical structure.

All-or-None Belief vs Strength of Belief

While we can categorize beliefs in terms of believing, disbelieving, and suspending judgment on a proposition ('all-or-none'), we can also think of belief in terms of a scale in which we assign a numerical degree to the strength of belief in a position. This means that we can analyse a perfectly rational person’s degrees of belief over propositions in terms of rules of mathematical probability. The strength of belief ranges from probability value of 0 to 1.

However, there are problems in relating the all-or-none belief categorization with the degree of belief categorization. This is manifested in the Lottery Paradox. 

Lottery Paradox:

Considering a fair 1000 ticket lottery that has exactly one winning ticket. It is therefore rational to believe that one ticket will win. 

For a joint theory of rational belief and rational degrees of belief, we’d need to set a probability limit for strength of belief beyond which we can say that the proposition is ‘believed’. Let’s suppose the limit is 0.9. If the strength of belief is more than 0.9, the proposition is believed.

Based on this, we do not believe that ticket 1 of the lottery will not win (Probability of winning is 0.001). We also do not believe that ticket 2 will win. We also do not believe that ticket 3 will win. And so on for all the 1000 tickets individually. This entails that it is rational to believe that no ticket will win! This is of course contradictory with what we saw earlier, that it is rational to believe that one ticket will win.

How to resolve this paradox is still a matter of some dispute.

Week 3 of Coursera Social Psychology course deals extensively with three famous sets of experiments:
1) Milgram experiments on obedience to authority figures

As all these experiments are quite famous (refer to wikipedia links) I would not go into any detail here. Even though I had knowledge of all these experiments before, it was quite chilling and insightful to see the video recordings of the original experiments (the lecture materials included Obedience, Milgram's documentary on his experiments, and Quiet Rage, documentary by Zimbardo).

The take-home message, so to speak, is the immense power the situational factors have on our behaviors, something that we are, in general, blind to. Under certain circumstances, people will continue to obey orders, despite reluctance, that they can apprehend to be morally objectionable, if the orders come from an authority figure. Under certain circumstances, people will conform with the group opinion and behavior, even if it means contradicting something one knows to be obviously correct. Under certain circumstances, when people in positions of authority become deindividuated, they will easily slip into a mindset in which they subject others to degrading, brutal and inhumane conduct. 

This vulnerability lurks within all of us.

Sunday, August 25, 2013

Hannes Leitgeb and Stephan Hartmann

Personal notes from lectures of Week 2: Truth

(These are personal summaries and paraphrasings of some of the major points of the lectures that I felt to be important. They are not meant to be comprehensive records nor intended to be reproductions of copyright materials. I encourage you to participate in the course for better understanding.)

Liar Paradox

The vocabulary of L_simple does not contain the word ‘true’ but English does contain the term 'true' already in its vocabulary. So, a definition of truth for English as a whole should allow us to derive sentences that talk about the truth of sentences. This can, however, lead to the famous Liar Paradox, which can arise when a sentence refers to itself.

* The sentence that is introduced by a star symbol is not true.

Applying the truth predicate: 
'The sentence that is introduced by a star symbol is not true' is true if and only if 'The sentence that is introduced by a star symbol is not true' is not true. 

This conclusion is of the form 'A if and only if not A', but that is a logical contradiction.

The Tarskian Hierarchy

Kurt Gödel famously proved in his so-called incompleteness theorems that there will always be sentences which in some sense talk about themselves. 

In our definition from before, we defined the truth predicate 'true' for all the sentences of L_simple, but the truth predicate itself was not a member of the vocabulary of L_simple. 
The truth predicate and its definition do not belong to L_simple, but to a different language. The language in which we stated our definition of truth for L_simple. 

When we define truth, we are actually dealing with two languages at the same time: 
1) The object language. That's the language for which one defines truth. 
2) The metalanguage, the language in which one defines truth for the object language. 

L_Simple doesn't contain the word 'true' but meta-language of L_Simple does. Would this lead to Liar Paradox? 

To state the truths of this meta-language, we'd have to create another meta-meta-language, which would use a new truth predicate 'true_1' which doesn't occur in the meta-language. And so on and so forth.

We can construct such a hierarchy of meta meta and so on languages and Tarskian truth definitions on top of it. While none of these languages is expressive enough to speak about the truth or falsity of all of its own sentences, they can speak about the truth or falsity of all the sentences at the previous stages in the Tarskian hierarchy. 

Consider, however, a universal language, a language in which one can express everything that is meaningful at all. It is not possible to state a formally correct and material adequate definition of truth for such a universal language. Such a definition would have to be carried out in some language again. If the definition is formulated in the universal language itself, it would lead to the contradictory conclusion of the liar paradox. So there is no universal language for which one could state a satisfactory definition of truth in the Tarskian sense. If a natural language such as English is universal, then we cannot state a satisfactory definition of truth for it as a whole, only for fragments of it.


Hannes Leitgeb and Stephan Hartmann

Personal notes from lectures of Week 2: Truth

(These are personal summaries and paraphrasings of some of the major points of the lectures that I felt to be important. They are not meant to be comprehensive records nor intended to be reproductions of copyright materials. I encourage you to participate in the course for better understanding.)

Truth and falsity are ascribed to descriptive or declarative sentences, or to what is expressed by descriptive sentences. Descriptive sentences express propositions. What does the sentence 'Snow is white' express? It expresses that snow is white.

Traditionally truth has been defined as correspondence with reality. The meaning of ‘corresponds to’, however, is far from clear. 

The Polish philosopher Alfred Tarski was the first person to state a precise definition of truth in familiar terms.

The Truth Scheme

Tarski suggests two requirements for a satisfactory definition of truth: It should be formally correct and materially adequate. 
By 'formally correct' Tarski means that the definition should be precise, free of contradictions, and it should have the right form. 
By 'materially adequate' Tarski refers to an equivalence sentence. This equivalence sentence is of the form (T): A is true if and only if A. 
'Snow is white' is true if and only if snow is white.

Let us call (T) the truth scheme, and let us call each of its instances a truth equivalence. 

A definition of truth for the descriptive sentences of a language L is materially adequate if and only if the definition implies all truth equivalences for language L. 

Truth scheme is not itself the intended definition of truth. 

It is important to note that we are dealing with a definition of truth for the descriptive sentences of some given language L, not a definition of truth for all sentences of all languages. 

Let's create a simple toy language 'L_simple' that contains only descriptive sentences, and define truth for that.

Truth for L_Simple

(Predicates are terms that express properties or relations). 

Here is the complete vocabulary of L_simple. 
Names: 'Socrates', 'Plato' 
Predicates: 'is a teacher of'. 
Logical symbols: 'and', 'or'. 

These are the grammatical rules of L_simple: 
If we put a name before 'is a teacher of' and another one after it, we get a sentence of L_simple. 
Finally, for every two sentences of L_simple, if we put an 'and' or an 'or' between them, then we get sentences of L_simple. 

We can now define 'truth for L_simple' in a Tarskian manner. 

For all sentences x of L_simple: 

if x is the result of putting together the name 'Socrates' with the predicate 'is a teacher of' and with the name 'Socrates' again, then x is true if and only if Socrates is a teacher of Socrates; (same case for Plato)

if x is the result of putting together the name 'Socrates' with the predicate 'is a teacher of' and with the name 'Plato', then x is true if and only if Socrates is a teacher of Plato; (and vice versa)

if there is a sentence y of L_simple and a sentence z of L_simple such that x is the result of putting together y with the logical symbol 'and' and with z, then x is true if and only if y is true and z is true. 

if there is a sentence y of L_simple and a sentence of z of L_simple such that x is the result of putting together y with the logical symbol 'or' and with z, then x is true if and only if y is true or z is true.

All truth equivalences for sentences in L_simple are derivable from the definition above. In other words: The definition of truth for L_simple is materially adequate.

Recursive Definitions

You would notice that in the definition of truth the term 'true' does occur on the right-hand sides of some of the various parts of our definition. 
Does this mean the definition is not formally correct? No, that is not the case.
The truth condition for the complex sentence is determined by definition from the truth conditions for the simpler sentences and the truth condition for the latter of these is determined ultimately by maximally simple sentences, which are formulated without invoking the term 'true' anymore. 

The definition of truth given above is therefore a recursive definition. Languages that are defined from a given vocabulary in such a precise recursive manner are called formal languages. (Linguists and philosophers of language also believe that recursion is true of natural language in general.)

Explicit Definitions

Every recursive definition can be transformed into a standard definition without any kind of circularity, using concepts from set theory. 
This second version of the definition of truth would look like this: 

For all sentences x of L_simple: x is true if and only if x is a member of all sets capital Y of sentences of L_simple for which the following holds: 

For all x': if x' is the result of putting together the name 'Socrates' with the predicate 'is a teacher of' and with the name 'Plato', then x' is a member of capital Y if and only if Socrates is a teacher of Plato.

And so on with other parts of the definition. 

Friday, August 23, 2013

Scott Plous

Personal notes from lectures of Week 2: The Psychology of Self-Presentation and Persuasion
(These are personal summaries and paraphrasing of some of the major points of the lectures that I felt to be important. They are not meant to be comprehensive records nor intended to be reproductions of copyright materials. Social Psychology is the most fun course I have had on Coursera so far, and all the concepts mentioned below are presented in lectures with brilliant illustrative examples and experiments.)

Attribution Theory: Deals with how people interpret behavior, their own and that of others. It's important because our interpretation determines our further behavior.

According to Harold Kelley our interpretations of behavior are in terms of i) something about the person ii) something about the situation iii) something about the occasion. The attribution will be based on i) consensus ii) distinctiveness and iii) consistency.

A behavioral outcome is attributed to a person when there is low consensus (other people do not behave the same way), low distinctiveness (behavior happens in a variety of different situations) and high consistency (behavior is consistently displayed).

Salience: the attention-grabbing property of a stimulus. Research shows that salient stimuli are more likely to be viewed as causal. Perception of causality is a function of attention, and attention is a function of salience. 

For instance, an interrogation video which focuses on the suspect is more likely to be taken as a false confession on the suspect's part than another video which focuses on interrogator for the same interrogation. Salient people are also more likely to become scape-goats when there is a problem.

Kelley's framework has generally been supported by research, except that people don't often pay attention to consensus when deciding causal attribution. 

False Uniqueness effect: a false belief that when it comes to our behavior, we are more unique than we really are.

The fundamental attribution error is the tendency for people to underestimate the impact of situational factors and overestimate the role of dispositional factors in controlling behavior. 

Actor-Observer Differences in Attribution:
People downplay dispositional explanations for their own behavior (as actors), but mainly when the outcome is negative. Pattern is reversed when the outcome is positive. It's basically a self-serving bias. There is also, however, a role of salience. To the actors, the situation is the most salient thing, while for the observers, it is the actor. 

Attitude-Behavior Inconsistency: We often behave differently from the attitudes we hold.

Two prongs of cognitive dissonance theory:
* Holding two incompatible thoughts creates a sense of internal discomfort ('dissonance')
* People are motivated to reduce or avoid psychological inconsistencies

Two flavors of dissonance
Predecisional dissonance, in which dissonance influences decision
Postdecisional dissonance, in which dissonance after a judgement affects later judgements

Self-perception theory:
Individuals determine their own attitudes in part by their observations of their own behaviors and circumstances

Two-sided appeal: When a person arguing for a case brings up the objections first and answers them. This is more likely to persuade the audience. 

Attitude inoculation: The process by which people become immune to attempts to change their attitudes when they are initially exposing them to weak arguments against their position, and they are asked to respond to those arguments. This strengthens their attitude, such that when a stronger argument or attack is made later on, people are resistant to persuasion.

Central and peripheral routes of persuasion: Central route utilizes facts and relevant arguments to case, while peripheral route tries to persuade by association with something not really relevant. For instance, advertisements can sell a product by telling us facts about the product (central route) or by showing an attractive model endorse the product (peripheral route).

Fear can be effective, as long as people are given specific steps to avoid the threat (otherwise it may backfire, leading to denial of threat)

6 Short cuts to persuasion: 1. Reciprocity 2. Scarcity 3. Authority 4. Consistency 5. Liking 6. Consensus

Consensus information doesn't always have an impact of causal attribution, it often does have an impact of persuasion. Sometimes emphasizing the severity of a problem (such as saying that one in every four women is raped) can have the unintended effect of normalizing that problem by means of consensus. 

Techniques of Social Influence:

Foot-in-the-door technique
People are more likely to comply with a large request after they have accepted a smaller one

Door-in-the-face technique
People are more likely to comply with a smaller request after they have rejected a larger one

Low-ball technique
Once people commit themselves to honoring a request, the request can often be increased without them withdrawing from the commitment. 

Scott Plous

Personal notes from lectures of Week 1: Social Perceptions and Misperceptions
(These are personal summaries and paraphrasing of some of the major points of the lectures that I felt to be important. They are not meant to be comprehensive records nor intended to be reproductions of copyright materials. Social Psychology is the most fun course I have had on Coursera so far, and all the concepts mentioned below are presented in lectures with brilliant illustrative examples and experiments.)

Our perception of the world, and our psychological construction of reality, is powerfully influenced by where our attention in directed, by context, by past experiences, expectations, and many other psychological factors. 

Change blindness: Changes in visual field are not noticed while our attention is focused elsewhere. These may include significant changes, such as while paying attention to a video of a card trick and eyes focused on the card, we may not notice that magician's clothes have changed, or the background has changed, etc.

Our visual perceptions are a combination what is out there and what is going on within our visual system. Our visual systems have certain in-built predispositions and tendencies that lead them to process social information in very particular ways.

A confirmation bias is a preference for information that's consistent with, or confirms, a preconception we already hold, and to disregard the information that challenges it. Even when the counter-evidence is noticed, the tendency is to explain it away.

Our social perceptions and social expectations have a significant affect on the person about whom the expectations are held. Our expectations can lead people to behave in ways that confirm our expectations. This is a sort of self-fulfilling prophecy. Consider the security dilemma. For example, North Korea believes that South Korea is aggressive, and under that belief starts arms. South Korea perceives the armament as an act of aggression, and begins arming in defense. This is interpreted by North Korea as a confirmation of their belief that South Korea is in fact aggressive. 

Another type of self-fulfilling prophecy is Pygmalion effect, which is the phenomenon in which the greater the expectation placed upon people, the better they perform.

Behavioral confirmation takes place when people's social expectations lead them to act in a way that causes others to confirm these expectations. The behavior that is induced in people as a result of these expectations linger on even when the person holding that expectation is no longer physically present.

While social perception can be distorted by a number of factors, however, it can also operate with surprising efficiency. Thin-slicing is a term used to describe the ability to make accurate judgements based only on "thin slices," i.e. brief observations or small samples of behavior. Social judgments can be made with surprising speed and accuracy, even when they're based on just a single photo or the sound of somebody's voice, or a few brief video clips of behavior. 

Even in direct encounters, social impressions are formed with great rapidity, even if the encounter is to last a long time. The first few seconds of interaction between strangers is often the most important time for the creation of social judgment, and will have significant consequences on how their future interaction will develop. First impressions are hard to over-come, especially if they are bad.

Monday, August 19, 2013


Constantin Brancusi, Mlle Pogany, 1913
Sculpture at Museum of Modern Art
Photo credit: Bryce Edwards on Flickr
See this 2 min video at MoMA website on how this rather exquisite work of art became the subject of ridicule when it was first exhibited.

Sunday, August 18, 2013


Wissam Shawkat's calligraphic drawing for the 
cover of the Canadian edition of Shereen el-Feki’s Sex and the Citadel.
It depicts archaic Arabic words for sex.
(Source: ArabLit )

Saturday, August 17, 2013

Hannes Leitgeb and Stephan Hartmann

Personal notes from lectures of Week 1: Infinity
(These are personal summaries and paraphrasing of some of the materials in the lectures that I felt to be important, with possible additions of personal impressions. They are not meant to be comprehensive records nor intended to be reproductions of copyright materials.)

Let us see how set theory in mathematics can help us understand infinity. The Principle of Extensionality states, in essence, that two sets are identical if and only if they have the same members.

There are two different ways of comparing the size of sets. One can, for instance, say that if X is a proper subset of Y (all the members of X are members of Y, but not vice versa), then X is smaller than Y. Another way of doing so is to pair off members of the sets with each other. Set X {A,B} can be paired with Y {1,2} but not with Z {1,2,3} because Z has a member that has no corresponding pair. So X and Y are of equal size, but both are smaller than Z. Normally these two methods lead to the same result, but in case of infinite sets, this can lead to a paradox, first realized by Galileo.

P1. If X is a proper subset of Y, then X is smaller than Y.
P2. If there is a pairing off between members of X and Y, then they are of equal size.
P3. The set of even natural numbers {2, 4, 6…} is a proper subset of the set of positive natural numbers {1,2,3,4,5,6…}.
P4. There is a pairing off between the even natural numbers and the positive natural numbers. (Each even natural number can be paired with its half. 2-1, 4-2, 6-3,…)

From P1 and P3 we conclude that the set of even natural numbers is smaller than the set of positive natural numbers, while from P2 and P4 we conclude that the set of even natural numbers is equal in size to the set of positive natural numbers. This is a logical contradiction.

Galileo concluded from this that infinite sets cannot be compared in terms of size. That is, P1 and P2 do not apply to infinite sets. Another response is to distinguish between two senses of ‘equal size’. These two senses are different and distinct, such that in one sense the set of even natural number is smaller in size, while in another sense it is equal in size to the set of positive natural numbers. In this case we end up with two ways of extending the concept of size from finite to the infinite.

In turns out, however, that the way of pairing off members of sets offers us a precise, consistent and systematic way of building a notion of what it means for sets to be of equal size. The first sense only tells us about inequality, but not really about equality. The pairing off method can also be used to distinguish inequality. For example, X has less members than Y, if members of X can only be paired off with a proper subset of Y, and not with all members of Y. Therefore, this way of comparing set is the one we ought to utilize.

Using this way of comparing sets, we can even define what an infinite set is:
A set is infinite, if and only if all the members of the set can be paired off with at least one of its proper subsets.
(For example, the set of positive natural numbers can be paired off with the set of positive even natural numbers, which is its proper subset)

“Infinity amounts to a kind of self-similarity property. Much as with fractals in geometry. An infinite set contains something which, in terms of size, looks like itself.” (Lecturer’s words.)

The definition of infinite set was by Richard Dedekind, and Georg Cantor developed an elegant theory out of it. One may be tempted to believe at this point that all infinite sets are of equal size (they can be paired off with each other) but this is actually not the case. George Cantor showed by his brilliant theorem that infinities are of different sizes. In particular, he demonstrated that the set of natural numbers is of smaller size that the set of real numbers (their members cannot be paired off with each other). Furthermore, he showed that the set of real number is smaller than yet another infinite set (the power set of the set of real numbers), which is in turn smaller than yet another infinite set, and so on to infinity. Cantor also showed that one can measure the sizes of infinite sets in terms of new numbers, the so called transfinite cardinal numbers. Cantor believed that if all the transfinite cardinal numbers are taken together, they do not form a set anymore. They form what he called 'absolute infinity', an infinity whose size cannot be measured in terms of set theory. This absolute infinity Cantor believed to be God.


Coursera Course: 
by Dr. Yuval Noah Harari

Personal Lecture Notes from Lesson #1: The Human Family
(These are personal summaries and paraphrasing of some of the materials in the lectures that I felt to be important, with possible additions of personal impressions. They are not meant to be comprehensive records nor intended to be reproductions of copyright materials.)

There is no unbrigdeable gap between history and basic sciences like physics, chemistry and biology. History in the next stage in the process of ongoing complexity in the universe.

Three main revolutions of history:
1) Cognitive Revolution: 70, 000 years ago. Homo sapiens evolved unique cognitive abilities. 
2) Agricultural Revolution: 12, 000 years ago.
3) Scientific Revolution: 500 years ago.

Homo sapiens belong to the Family of great apes. (All the Genera in a Family spring from a common ancestor.) Chimpanzees are our closest relatives, the two species splitting apart just 6 million years ago.
There used to be many other human species (belonging to the genus Homo). Humans first appeared in East Africa, about 2 and a half million years ago, evolving from a genus of apes called Australopithecus (means 'southern ape'). Around 2 million years ago, some of these humans left Africa and settled in various part of North Africa, Middle East, Europe and Asia. Due to different climates and geographical features, these populations began to evolve in different ways leading to different human species.  

In Europe and Middle East, there was Homo neanderthalensis ('man from the Neander valley'; first remains were discovered in Neander valley in Germany). 
On the island of Java in Indonesia evolved Homo soloensis ('man from the Solo Valley').
On Flores, another Indonesian island, evolved Homo floresiensis ('man from Flores island'). Unique thing about Homo floresiensis is that they were dwarfs, having the maximum height of about one meter. 
In Asia evolved Homo erectus ('the upright man', called so because of their height). They were tall, up to 1.9 meters. They are the most successful human species ever in terms of how many years they managed to survive. From about 1.5 million years ago to until about 500,000 years ago, they existed for 1.5 million years (contrast with: Homo sapiens began to evolve around 200,000-300,000 years ago; our prospects of outliving this record are bleak).
From Denisova cave in Russia fossilized remains of a finger were found, whose DNA did not match with any other human species, leading to the inference that there existed another human specie in Central Asia called Homo denisova. 
Meanwhile, evolution of new human species continued in Africa, for instance Homo rudolfensis ('man from Lake Rudolph') and Homo ergaster ('working men'; many tools were found along with their bones). Homo sapiens also appeared in East Africa, around 200,000-300,000 years ago.The world was the home to at least six human species (that we know of) simultaneously. It is surprising, and somewhat suspicious, that there is now only one human species in the world. 

Common characteristics of genus Homo:
1) Large brains, compared to other species (Larger brains, while having their advantages, have disadvantages too. For instance, human brain accounts for 25% of our energy expenditure at rest, while brains of other apes require only 8% of the energy of the body. Large brain needs more fuel, and hence more food intake. This means ancient humans had to spend more time looking for food, compared to other animals. Another toll the larger brain took on the body was that the human body became much less muscular.) It is not obvious that this a good survival strategy. A chimpanzee of 60 kg is five times more stronger than a man of 60 kg. Why the human brain became so large during evolution is a great mystery.

2) All humans walked upright on two legs, freeing the upper limbs, leading to the development of fine musculature of hands. Humans began to construct and use various tools. The manufacture and use of tools is a defining characteristic by which archeologists recognize ancient humans. This led to extra strain on the spine, leading to back aches, stiff necks and various other musculoskeletal problems that we humans so commonly experience. 

Women had to bear extra burden, as upright posture required narrower hips, and therefore narrower birth canals. So while the heads of the babies grew bigger, the birth canal of women grew narrower, creating an obvious problem. This led to greater fatality during childbirth. The evolutionary solution was to give birth earlier and earlier. "Humans so to speak are born prematurely" [lecturer's words]) As humans are born under-developed, they require extra care and attention on part of the parents for survival. This usually cannot be accomplished by a single mother alone. There is a saying that it takes an entire tribe to raise a human child. As a response, humans developed strong social ties with each other. Because humans are born under-developed, it also means during childhood, the eventual development can be significantly influenced by socialization and education. 

For the large part of their evolutionary history, humans were not the top predators, they were rather preyed on. They survived on vegetables, small animals and left overs of bigger animals. Many of the early tools were not for hunting, but rather for breaking open the bones of dead animals to feed on bone marrow, which some researchers believe to be the niche of early humans. Other bigger scavengers like hyenas and jackals left little else of the dead for humans to eat. Only in the last hundred thousand years did humans become top predators on Earth. This is practically overnight in evolutionary terms, and therefore humans are not well-adjusted in this position. Many of our large scale behaviors such as wars and our treatment of the ecosystem are consequences of this over-hasty jump. 

One of the factors important in this jump in food chain status was the domestication of fire. By about 300,000 years ago, some humans were using fire on a daily basis. Fire enabled humans to cook. This opened up immense options of what foods human could ingest, as most foods like wheat and potatoes can not be digested unless they had been cooked. Another advantage is that cooking kills various parasites and germs in the food. It also made chewing and digestion easier for humans, compared to other animals. This led to development of smaller intestines, and because large intestines require immense energy, shorter intestines could've allowed for the development of bigger brains by taking away the competition for energy utilization. 

The real change in the predator status came after the appearance of Homo sapiens. When Homo sapiens arrived in Middle East, most of Eurasia was already populated by other humans. What happened to all the other human species? There are two conflicting theories. 

1) Interbreeding theory: Homo sapiens bred with other human species in Middle East, Europe and Asia, and modern humans are the result of that interbreeding. The only people who are maybe pure Homo sapiens are the Africans.

2) Replacement theory: This theory challenges that different human species had sexual interest in each other, and says that any potential offsprings of interbreeding would have been infertile. This means that all modern humans are pure Homo sapiens.

If the replacement theory is correct, then differences between races are negligible, as all humans have the same genetic package. If inter-breeding theory is correct, then there are possible genetic differences between races. Chinese may have erectus genes and Europeans may have neandethal genes. 

Until recently, replacement theory was more popular, not just because of evidence, but also because of political reasons. This changed in 2010, when the neanderthal genome was published. When compared with our genome, it was discovered that about 4% of genes of Middle Easterners and Europeans have Neanderthal genes. Shortly afterwards it was discovered using DNA from the finger found in Denisova cave that 6% genes of modern Melanesians and aboriginal Australians are actually Denisovan genes. This shows that there was at least some interbreeding between different humans. 4-6% of DNA, however, is not enough to account for a complete merger of populations. It appears that around 50,000 years ago, sapiens, neanderthals and denisovans were at a borderline stage, where they were almost distinct species but still capable of inbreeding on rare occasions. 

How did Neanderthals die out? One possibility is that sapiens out-competed them. If sapiens were more sophisticated than neanderthals in their techniques of hunting, then they would have claimed more and more of the food resources. Another more likely possibility, however, is that this competition was not a peaceful affair. Tolerance is not a human trademark. This may have resulted in 'the first and most successful ethnic cleansing campaign in history'.

The genocides are speculation, but what we do know is that no sooner Homo sapiens arrived in a particular area, the other human species went extinct. The last remains of Homo soloensis in Java are from 50,000 year ago, just when Homo sapiens arrived in Java. Homo denisova went extinct 40,000 years ago, Neanderthals 30,000 years ago, and the dwarfs of Flores island 12,000 years ago. 

Imagine how the modern world would have looked like if Neanderthals still existed. Would Christianity have claimed, for instance, that Jesus died for the sins of all humans or just Homo sapiens? Would American Declaration of Independence have stated that we hold this truth to be self-evident that all members of the genus Homo are created equal? Would Homo sapiens still have believed themselves to be the epitome of creation, separate from the rest of animal kingdom as they do now?

I am taking various online courses on Coursera these days, and to make the best use of them, I will post my lecture notes (sometimes extensive, sometimes not so) on this blog for some of the lectures. Hopefully many of the readers will find them to be instructive as well (apologies to those who would not). For those who have time and are interested, and go ahead and try out the classes for yourselves.

Saturday, August 10, 2013

The cardinal sin of the modern marriage is to wed without love.

Friday, August 9, 2013



Drawing by Jenny Yu
(contrast adjusted)

Tuesday, August 6, 2013

"If the diagnostic judgment of mental illness is an evaluation – an expression of our values – rather than simply a description of the facts, then mental illness cannot be an objective matter; it cannot be a feature of the fabric of the world, independent of our own perspective."

Tim Thorton, Reductionism/Antireductionism (Essay include in The Philosophy of Psychiatry: A Companion)


Eric Gill, Ibi Dabo Tibi (1925)
Wood engraving on paper
Image from Tate collection

The title 'Ibi Dabo Tibi' is a reference to Song of Solomon 7:12. The relevant sentence reads in Latin as ibi dabo tibi ubera mea. This is generally translated as: 
'there will I give thee my loves' (for instance, see King James version)
But if you go by the literal meaning of ubera, the translation becomes:
'there will I give thee my breasts' (see Douay-Rheims 1899 American Edition, which makes more sense to me if you see the context)

The engraving beautifully plays on both these versions. 
Below is the translation by John Cunyus of 7:12 and 7:13

Let us rise up early
and go to the vineyards!
Let us see
if the vine blossoms,
if the flowers
give forth fruit,
if the pomegranate blooms!
There, I will give 
my breasts to you!

The mandrakes
gave their scent
in our doorways!
All my fruits,
old and new,
I saved for you!

 

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