Tag Archives: mathematics

Who are you?

After spending the last 20+ years in your body and mind, you probably know exactly who you are.  Well, you would certainly think so!  Ironically, most can’t seem to find the time to ponder this question.  We are often too busy doing laundry, working, raising our family, hanging out or doing other things like finding Pokémon; partly because this question may not be important to dwell upon.  But thinkers like Socrates, Plato and Jesus often referred to the following as the pillar to one’s life: Know thyself.  In other words, if you don’t know who you are, then what’s the point of living?

In this post, I will use a proof by induction to explain who you are.  Induction is a mathematical principle used to answer certain questions.  It is analogous to falling dominoes.  Once one domino is knocked over, all other dominoes fall in sequence.  The implication of this is quite far-reaching. dominoes

To start, let us simplify the world as two separate entities: physical and mental.  The physical world consists of everything you can touch, see, hear, smell and taste.  The mental world consists of everything inside your head.  Clearly these two “separate” worlds are highly integrated and related to one another.  The physical world is easier to explain and less abstract; therefore, we will start there.  Once we are grounded in these principles, we can then abstract to the mental world.

We first need to know where ideas come from.  All thoughts inside your head were created for you and built in a predictable manner, similar to when two different Lego blocks come together to form a “new one.”  The example I often use to explain this is the following: a wheelbarrow is composed of three different components (ignoring the handle).  The first is a box, which is a placeholder to move the desired object we want to move.  The second is the wheel, a truly important invention.  And lastly, the axle allows the wheel to rotate around so that we can move the object from one place to another with minimal effort.  The wheelbarrow could not have been invented without first inventing a box, a wheel and an axle.  When these three components were put together in a specific order, we were able to create a new object:

Wheel + Axle + Box -> Wheelbarrow

Generally:

Object A + Object B + … + Object X -> New Object A

This example demonstrates that in order for new objects to be created, it must have come from already existing objects.  As a matter of fact, any physical object in this world can be broken down into separate components as was shown above.  If you accept this premise, then we are more than half way there.  This is exactly how ideas are created inside your head as well.  There is no such thing as an original idea.  All ideas stem from other ideas, which were simply put together in a different order, just like a wheelbarrow.  However, the ideas you have inside your head are highly dependent on the time and the place you live in.  If you didn’t have the wheel, axle or box invented yet, then you wouldn’t have the idea of a wheelbarrow either.  Therefore, you need to be present during a time and place where those components exist; otherwise you would never experience or see a wheelbarrow in your life.

The reason why the wheelbarrow example is so powerful is because we first invent in our minds before we develop our ideas in the physical world.  This allows us to look at objects we have created and then go backwards to see how we thought of these new ideas.  It is as if we projected ourselves into a physical object, which is usually referred to as art.  Hence the same formula applies for purely abstract objects too:

Idea A + Idea B + … + Idea X -> New Idea A

Now the crucial part here is that since each new object or new idea feeds into the “next new object” or the “next new idea”, it forms a clear pattern known as the inductive step in mathematics:

New Object A + Object B -> Newer Object C

New Idea A + Idea B -> Newer Idea C

Note that Object/Idea B does not need to be novel in the preceding example.  If we had just invented the box (New Object A) and assume that the wheel and axle already existed (Object B), then we can create Newer Object C, the wheelbarrow.  This implies that each new object or idea comes from existing objects or ideas.

To complete the proof by induction, we also need to state how the very first idea was created.  This is called a base case in mathematics.  Our base case consists of a new-born child knowing nothing about the universe it is born into.  Surely, most animals have instinctual characteristics that they are born with.  However, their ideas are generated from their environment and their experience with it.  This means that if the very first idea of a new-born child was created for it without their permission or control, and assuming the inductive step is correct (that each new idea feeds into the next), we can conclude that there is no free will, but that all ideas and objects just follow this simple process of creation when provided with the right components.

The objects in this world, whether mental or physical, are highly dependent on where and when you were born.  If you were born in a remote village in Africa you would have different thoughts inside your head.  If you were born 500 years ago you would have different thoughts inside your head.  If you were raised by a different family you would have different thoughts inside your head.  Therefore, who you are, has never been up to you because you do not control your environment and you didn’t get to choose where and when you were born.  Otherwise everything inside your head would be different and you would be a different person.  You are just merely a process which provides one piece at a time from which your personality is built for you, not by you.

You may ask, “how this information is helpful to me?”  Imagine a man getting angry each day at the sun when it goes down.  This man is yelling, furious for the start of darkness and cold.  However, if he knew that the sun was obeying the laws of physics and following a well-defined process which was out of his control, he would be less inclined to feel such outrage against the sun setting each day without asking for his permission.

sun_rising

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A theory & proof on “The One”

People often bounce the idea of soul mates around: “I think he or she is THE ONE for you.” But is there such a thing? Yes, absolutely. We can mathematically prove this with a thought experiment. However, just like any other proof, we need to make an assumption:

 A human changes through time and we will assume that we know of all changes a human life undergoes in his/her entire life.

Now, take a woman and randomly pull two men from the entire world. If we know exactly how the woman and the two men will change through time, then one of the men will be a better match than the other. Let’s keep the better match and randomly pull another man from the world. We continually do this comparison until there are no more men left in the world. The last man standing is “The One.”

Of course, it isn’t very realistic to know that 1 out of billions of people on the planet is best for you. But if you agree with the proof above, then we can reduce the sample size to something more feasible – which includes everyone you will and have met in your entire lifetime. Running through the same analogy again, we come to the same conclusion: One of them will be The One for you.


A rigorous mathematical explanation for the proof given above

There are X traits/personalities/attitudes that exists in a human being which can be scored using S.  The score for a trait is a function of time, therefore, making it a time-dependent variable denoted by tAn ordered pairwise-set for two individuals A and B is created, meaning that SXt(A,B) does not equal SXt(B,A)In other words, Person A’s preference through time does not equal to Person B’s preference through time.

We need to find the maximum for this function:

max ∑ SXt(A,B) + SXt(B,A)

for all paired individuals A,B with respect to time t scored on traits X

The world population is estimated to be 7.4 billion and let’s assume that we meet 100,000 people in our lifetime, which is probably a gross exaggeration.  This equates to crossing paths with 0.0000142% of the world’s population!  In contrast, we will never meet 99.9999858% of the world.  Wow!

Since the majority never cross paths, they must be independent sets, which then gives us the ability to quantify a score based on the desired traits an individual prefers through time.  Using the ordering principle defined above, we can order the scores obtained for each individual to determine the best match between each couple.  We then eliminate each person from our set by pairing the highest scored pair first.  And continue eliminating them until there are no more possible pairs left to choose from.  Each of these pairs will be correctly paired with The One, even though they will never meet.

For the case where a couple does in fact cross paths, it is certainly more complicated in nature.  However, we would know that such a pair must have a higher score than any pair of their respective pairs in the 99.9999858% data set.  This is certainly less likely to occur, which is why it is considered a rarity to spend one’s life with The One.”

My proof doesn’t state that a person will actually meet their perfect match; instead, my proof shows that such a person exists.