Tag: mathematics

Posted in Philosophy

Formula Of Love

Posted on by Jinavie

Einstein, considered to be the greatest genius in history, once faced this situation while giving a guest lecture at a university.
A student asked Einstein, who had just finished giving a physics lecture, the following:
“Professor, you have discovered the theory of relativity and managed to formularise it. Could you express love as an algebraic formula?”

Einstein thought for a while, then smiled as he wrote this equation on the board:

LOVE = 2△ + 2□ + 2~ + 4/

The students were confused and asked him to explain it further. He then solved it as shown below:

“The sorrow of having to take a path you must take, yet not being able to resist looking back over and over! The frustration of wanting to follow a path you cannot take! That is love.”

(Source: http://xkcd.com/55/)

Posted in Science & Nature

A Simple Task

Posted on by Jinavie

A plague struck the ancient Greek island of Delos. As the disease ravaged the island, the people went to the oracle at Apollo’s temple for help. This is what the oracle said:

Double the volume of the cube-shaped altar in Apollo’s temple

People considered this a simple task and made a new altar where each side was double the original length. However, instead of disappearing, the plague worsened and people were confused.

Reason being, given that the length of one side of a cube is a, the volume is a³; if one side is 2a, the volume becomes 8a³, or eight times the original volume. Therefore, to double the volume of a cube, the number ³√2 is required. The problem is, whether ³√2 can be found using only compass and straightedge construction (where only the two tools are used to solve a geometric problem).

This problem, also known as the Doubling the cube problem, is one of three geometric problems known to be unsolvable by compass and straightedge construction. In other words, without the help of other mathematical methods, the answer cannot be found.
However, the solution to the above story is very simple.

Find a new god.

Posted in History & Literature

Three Daughters

Posted on 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” →

Posted in Psychology & Medicine

Beer Goggles

Posted on by Jinavie

There’s only one thing other than love that can make a person oversee another’s weaknesses and amplify their strengths – alcohol. The term beer goggles refers to this phenomenon, where a member of the opposite sex appears more attractive due to the influence of alcohol. This is because alcohol inhibits the cerebral cortex where higher order thinking occurs, reducing sexual inhibition and allowing primitive behaviour to surface.
Beer goggles can be utilised to increase the chances of succeeding in courtship if one knows how to manipulate it.

There is even an equation to calculate the strength of beer goggles, produced from actual scientific research and experiments. The equation is:

An = number of units of alcohol consumed
S = smokiness of the room (graded from 0-10, where 0 clear air; 10 extremely smoky)
L = luminance of ‘person of interest’ (candelas per square metre; typically 1 pitch black; 150 as seen in normal room lighting)
Vo = Snellen visual acuity (6/6 normal; 6/12 just meets driving standard)
d = distance from ‘person of interest’ (metres; 0.5 to 3 metres)

Ergo, the more you drink, the further you are from them, the smokier and darker it is and the worse your eyesight, the beer goggle index (ß) rises and the subject becomes more attractive, thus increasing the probability that you will approach that person.

Posted in Philosophy

Two Clocks

Posted on by Jinavie

There are two clocks: a still clock and a clock that is always a minute late.
Which clock is more accurate?

The answer is the still clock – it tells the correct time twice every day, but the other clock is always wrong despite the fact that it constantly ticks.
Sometimes when life gets you down, it is better to stop and rest instead of trudging on forever, always out of sync.

Posted in Life & Happiness

Eleusis Game

Posted on by Jinavie

The victory condition for this card game, named after an ancient Greek city, is quite simple: discover the pre-determined law via induction.
This game needs at least four people, with one person acting the position of God. God decides on a certain law (in the form of a single statement) and writes it down on a paper, thus creating the way of the universe. 
Next, the deck of cards is split evenly between the other players, then one person places a card in the centre. After “the world begins to exist”, God looks at the card and says “This card qualifies” or “This card fails”. The next player also places a card in the centre and the God judges whether it fits the way of the universe.

Players carefully study which cards qualify or fail to try discover the way of the universe. If someone thinks they figured the law out, he or she proclaims themself as the prophet, who begins to take over the role of God to announce whether the cards qualify or not. If at any point the prophet is wrong, he is dismissed. If the prophet correctly judges ten cards in a row, he states his hypothesised law and compares it to the piece of paper. The prophet wins if the two laws coincide, but is dismissed if it is not. When all 52 cards are played without a successful prophet, God becomes victorious.

However, as this is a game, the way of the universe cannot be too complex. To make it fun, the God player must devise a law that is simple yet difficult to discover. For example, the law “Alternate a card higher than 9 and a card lower than 9” is tricky as players tend to focus on picture cards or the colours of the cards. Also, laws such as “Only red cards qualify, except the tenth and thirtieth cards are disqualified” and “Accept all cards that are not the 7 of Hearts” are illegal, as they are too detailed. A God who comes up with such ways of the universe that cannot be found using logic and the scientific method loses his right to play the game. Ergo, the God must seek simplicity that is not easily conceived.

So what is the most successful strategy for this game? Even if there is the risk of being dismissed, proclaim yourself as the prophet as soon as possible for the best chance of winning.

(Source: http://iraka.deviantart.com/art/Playing-his-cards-right-55647521?q=boost%3Apopular%20in%3Aphotography%20playing%20cards&qo=21)

Posted in Science & Nature

Quod Erat Demonstrandum

Posted on by Jinavie

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.

Posted in Science & Nature

Mobius Strip

Posted on by Jinavie

A piece of paper has two sides. However, a Möbius strip has only one side. Ergo, if you walk on a Möbius strip, you walk on both sides and end up on the opposite side on the same location you started at in one trip. Because it has one side, it also has one boundary. This means that if you cut a Möbius strip along its length, you end up with not two rings, but one thinner, longer loop with an extra twist.

A similar structure is the Klein bottle. This structure is a self-paradoxical, single curvature, as its opening meets with its base, making the inside and outside indistinguishable. The entry is the exit, the inside is the outside, and the top is the bottom.

Our universe might be such a space where there is no distinction between the beginning and the end.

Posted in Life & Happiness

Study

Posted on by Jinavie

No Study = Fail
Study = No Fail

No Study + Study = Fail + No Fail

(No + 1) Study = (No + 1) Fail

Study = Fail

Q.E.D.

Posted in History & Literature

Cattle

Posted on by Jinavie

Alison and John are standing in the same cattle field at the same time. John can see twice as many cows as bulls. However, Alison can see the same number of bulls and cows in the field. How can this be, and how many bulls and cows are there in the field?

Continue reading “Cattle” →