logic – Page 2 – Jineral Knowledge

Process Of Elimination

Posted on 28/01/201215/02/2019 by Jinavie

“How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?” ~ Sherlock Holmes

If there is not enough evidence to come to a conclusion of what is the truth, start by removing the possibilities that cannot be true. If you hack away these impossible answers one by one, you will ultimately end up with the truth. This method is highly useful in a multiple-choice type exam, where you cross off the false answers until only one remains (or take an educational guess from whatever remains). In medicine, a process of elimination can be used to narrow down a differential diagnosis, or to reach a diagnosis of exclusion – that is, a diagnosis that cannot be proven to be true but seems to be the only one that fits since all other diagnoses do not.

Philosophy

Contradiction

Posted on 13/12/201115/02/2019 by Jinavie

A long time ago in ancient China, there was a merchant who sold weapons. He would pick up a spear and advertise it as a spear that can pierce any shield. Then, he would pick up a shield and proclaim that it can block any spear. A wise man who was walking past the merchant questioned: “So what would happen if you took your ultimate spear and threw it at your ultimate shield?” The merchant could not answer.

That is why the word for contradiction, or something that does not make logical sense and cannot co-exist, in Korean, Chinese and Japanese is 모순(矛盾), meaning “spear and shield”.

Science & Nature

Monty Hall Problem

Posted on 18/11/201114/02/2019 by Jinavie

Imagine that you are on a game show and you are given the choice of three doors, where you will win what is behind the chosen door. Behind one door is a car; behind the others are goats, which you do not want. The car and the goats were placed randomly behind the doors before the show.

The rules of the game show are as follows:

After you have chosen a door, the door remains closed for the time being.
The game show host, Monty Hall, who knows what is behind the doors, opens one of the two remaining doors and the door he opens must have a goat behind it.
If both remaining doors have goats behind them, he chooses one at random.
After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door.

Imagine that you chose Door 1 and the host opens Door 3, which has a goat. He then asks you: “Do you want to switch to Door 2?”

Is it to your advantage to change your choice?

Most people believe that as an incorrect option (goat) is ruled out, their odds of winning the car go up from 1/3 to ½ even by staying on the same Door 1 and there is no benefit to switching. However, it is better to switch doors as this will double your odds of winning the car. To illustrate this point, the following three scenarios (with the car being behind Door 1, 2 or 3) can be imagined, using the above rules of the game:

In Scenario 1, you have already chosen the car (Door 1) so Monty Hall will randomly open Door 2 or 3. Switching will obviously lead you to losing the car. The chance of you losing after switching, therefore, is 1/6 + 1/6 = 1/3 (as either Door 2 or 3 could be opened)

In Scenario 2 and 3, because you chose the wrong door (goat) and Monty Hall will open the door with the goat behind it, switching will lead you to choosing the car (no other choices). As the odd of either scenario happening is 1/3 each, your odds of winning after a switch is 2/3 – double the odds of winning after not switching (1/3, the odd of your first guess being right).

Of course, this is only under the assumption that the rules of the game were followed and that Monty Hall will always open a door with a goat behind it. This problem and the answer suggested was extremely controversial as tens of thousands of readers refused to believe that switching could be a better choice. However, as the above illustration shows, the Monty Hall problem is a veridical paradox – a problem with a solution that appears ludicrous but is actually proven true by induction.

Science & Nature

Euclidean Geometry

Posted on 09/10/201114/02/2019 by Jinavie

In 300BC, a Greek mathematician called Euclid wrote a series of texts called Elements. The Elements was a textbook that outlined many principles of mathematics (especially geometry) and it would become one of the most influential works in the history of mathematics. It is composed of a series of axioms (the axiomatic approach) from which many deductions and theorems can be made. Although many of these axioms sound extremely simple and like common sense, the implications are staggering.

The following is Euclid’s Five Postulates of Plane Geometry:

Two points determine a line.
Any line segment can be extended in a straight line as far as desired, in either direction.
Given any length and any point, a circle can be drawn having the length as radius and that point as centre.
All right angles are congruent (can be superimposed).
Parallel postulate: If two lines intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side, if extended far enough.

Using these postulates, mathematicians are able to deduce more advanced theories. For example, the Elements also describes the famous Pythagorean theorem, which states that “in any right triangle, the area of the square of the hypotenuse (the diagonal) is equal to the sum of the areas of the squares of the other two sides” (a² + b² = c²).

Thanks to Euclid’s works, we are now able to accurately model and measure the three-dimensional space around us. Not only did Euclid set the foundations for mathematics, his works were also instrumental in the development of logic and modern science.

Psychology & Medicine

Nirvana Fallacy

Posted on 20/09/201114/02/2019 by Jinavie

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)

Psychology & Medicine

Egg Of Columbus

Posted on 12/09/201110/04/2019 by Jinavie

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.

Life & Happiness

Matchsticks

Posted on 22/05/201112/02/2019 by Jinavie

There are 6 matchsticks. Make 4 identical, equilateral triangles.
The hint is that you must think differently to everyone else. If you think like everyone else, you will never find the solution.
There are 6 matchsticks. Make 6 identical, equilateral triangles.
The hint this time is quite the opposite the first puzzle: think like everyone else.
There are 6 matchsticks. Make 8 identical, equilateral triangles.
The hint for this puzzle is that you must reflect on yourself.

Answers after the break.

(Source: http://fc05.deviantart.net/fs50/i/2009/288/5/4/Matchsticks_by_oh_yesh.jpg)

Continue reading “Matchsticks” →

Philosophy

Epimenides Paradox

Posted on 15/04/201112/02/2019 by Jinavie

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”.

History & Literature

Three Daughters

Posted on 13/04/201112/02/2019 by Jinavie

A man asked how old a man’s three daughters were. The father replied with the following statement.
“The product of their ages is 36.”
“It’s hard to determine their ages from just that.” the man asking replied.
“The sum of their ages is same as the number of my house.”
“I still can’t figure out the answer!” the man replied again.
“My eldest daughter is blonde.” the father said, and the man, now smiling, replied.
“Oh, is that so? Then I can figure out how old your daughters are.”

How old is each daughter? And how did the man figure it out?
A computer cannot solve this problem, as it can only be solved using human logic.

Continue reading “Three Daughters” →

Life & Happiness

Priority

Posted on 02/04/201112/02/2019 by Jinavie

This scenario psychoanalyses how you prioritise your life and what you place the most importance in.

You are out camping, but end up lost in the woods. It has become dark but luckily you find an empty cabin. Under the dim light, you discover the cabin is equipped with a fireplace, a stove, a lamp and a candlestick. In your backpack you only have one match.

What would you light first?