Posted in Psychology & Medicine

Nirvana Fallacy

Humans have a tendency to think in a black-and-white manner, leading us to fall into the trap of the Nirvana fallacy. This is when one compares the real world to some perfect yet unrealistic alternative, causing reality to pale in comparison. Thus, it causes us to believe that many things are not worth doing as they are insignificant compared to this alternative.

For instance, the notion of the drop in the ocean means that we tend not to do altruistic things as we believe that it will not make much of a difference in fixing poverty or cure the world of cancer. Not only does the fallacy apply to how we see the world, but it affects day-to-day life too. People are so afraid of not being able to achieve an ideal, perfect future so ironically they do nothing. This is a major reason procrastination happens, as the person believes that if they do something now, it will be inefficient. They then plan for a perfect opportunity to start doing work, and a vicious cycle begins. Thanks to this way of thinking, people often miss out on a great job opportunity or a lovely girl or a chance to change their life just because it was not perfect and did not live up to their expectations.

In fact, people often fail to see the small steps and only see the big picture. So if someone tries to make an improvement (e.g. going on a diet), others will ridicule that person by saying that going to the gym every week is not going to turn you into an Adonis, ergo it is pointless.

The Nirvana fallacy is also useful in debates. One can create a false dichotomy (that is, a black-and-white argument) and compare someone’s argument to an unrealistic argument. When someone makes a suggestion, you can attack it by pointing out one flaw and show how it is clearly not a perfect solution (even better if you provide an example of the argument failing). This will automatically disintegrate their argument. For example, if someone proposes a new idea, you may point out how someone may abuse the new system or provide a case when a similar idea failed. However, be warned that this method can easily be rebutted with common sense, so one must use it in a convincing way and distract the audience from the fact that it is absolutely ridiculous.

(The Garden of Earthly Delights by Hieronymus Bosch, click for larger image)

Posted in Psychology & Medicine

Egg Of Columbus

After returning to Spain after his discovery of the New World, Christopher Columbus was dining with some nobles. One noble approached him and said:

“Even if you had not discovered the West Indies, another fine Spaniard would have gone to discover it anyway.”

Columbus did not respond and merely smiled. He then asked for an egg, which he placed on the table and asked:

“I bet that no one can make this egg stand by itself.”

All the nobles tried but were unsuccessful and the egg would continue to fall down. Columbus stepped forward and grabbed the egg, which he tapped on the table so that one end would be cracked and flattened. The egg would now stand on its flattened base.
Although the nobles initially complained that they knew that was the solution, the message was loud and clear: once the feat is done, everyone knows how to do it.

This is known in psychology as the historian’s fallacy – a logical fallacy that can be summarised in the words: “I told you so”. Essentially, people assume that people had the same information in the past or that they would not have made the same mistake if they were placed in such a situation. It is another example of cognitive dissonance where the brain finds conflict between a problem and information that could have prevented said problem (which the other person did not have at the time). Therefore, the brain immediately convinces itself that it would have made the right decision as it already knows the answer. This means that we are almost incapable of putting ourselves in other people’s shoes. We label those people as idiots, because they apparently had the same information (they did not) and still could not make the right decision.

People never realise that given the foreknowledge we have now, the Americans would have known about Japan’s plan for attacking Pearl Harbour or that Germany would not have invaded Russia. Although they say “those who cannot remember the past are condemned to repeat it”, we have a tendency to think that people in the past were stupid and we would never make the same mistakes.

Hindsight is 20/20.

Posted in Philosophy

Epimenides Paradox

A Cretan named Epimenides once said: “All Cretans are liars.”
So if Epimenides is a Cretan and he is a liar, then the statement is false. But that means that Cretans tell the truth, and Cretans are in fact liars. So what is the truth? This paradox continues ad infinitum due to the self-referencing nature of the statement.

This is a well-known example of a logical fallacy, or a flaw in a logic. It is also referred to as the Liar Paradox, seen in: “This sentence is false”.
The power of a paradox is best portrayed in the following parable.

A wise woman who worked as a fortune teller was tried for being a witch. In her trial, the king demanded she tell a fortune. If the fortune was correct, she would be drowned. If the fortune was wrong, she would be burnt at the stake. The woman smiled, and replied: “I will be burnt at the stake”.

Posted in Science & Nature

Quod Erat Demonstrandum

1. Let a and b be equal non-zero quantities
        a = b

2. Multiply by a
a = ab²

3. Subtract b²
a² – b² = ab – b²

4. Factor both sides
(a – b)(a + b) = b(a – b)

5. Divide out (a – b)
a + b = b

6. Observing that a = b
b + b = b

7. Combine like terms on the left
        2b = b

8. Divide by b
2 = 1

9. Add 1 to each side and flip over equation

        1 + 1 = 3

Q.E.D. (Thus we have proved)

How is this proof possible?

The source of the fallacy is the fifth step, where (a – b) is divided out.

As a = b, a – b = 0, and dividing by zero is impossible in mathematics.