Are some people more intelligent than others? - A Mathematical Perspective

People consider some to be more intelligent than others. For example, most of us would agree if I consider newton or Einstein to be more intelligent than you. But is this really true? First off, what is intelligence? At birth everyone is (more or less) at the same level. Then why is it that some people are good at studies, while some just aren't?

In my opinion, intelligence is all about making rational decisions given the information/knowledge you possess. People are different because the definition of being rational is different for each of us. For some of us, the act of crossing the road carefully might be rational. For others, most rational thing is to cross the road as quickly as possible. These beliefs are based on prior experiences. Someone who has witnessed a road cross accident might prefer to cross it carefully. Those who got fired because of being late might consider a hush hush approach towards crossing.

Bottom line: People are different because of different experiences they possess. This can actually be explained mathematically by a principle most of us are familiar with. Its called 'Bayes Rule'. Bayes rule seeks to find a hypothesis h with high probability given an observation D. Imagine this: You go to your kitchen, find a chair that was used to reach a cookie jar which is now empty. This is observed data D. Probability of this happening is P(D). Now, you can have a set of hypothesis h belonging to set H (representing all possible hypothesis). For instance h1 can be "My daughter must have stolen the cookie". h2 = "A thief stole a cookie as he was hungry". We don't know which of these are true, all may be equally likely. However if we did observe our house to be messed up (typical indicator of stealing), it increases chances of h2 to be true. This rule may be summarized mathematically as:

Our definition of rationality is based on how our knowledge is updated by this rule. By our experiences, we form various P(D)'s and P(H)'s that direct our thinking.

Back to the original question: "Are some people smarter than others by birth?". According to bayes rule "NO". It is our experiences that lets us update probability distributions of likelihood of events/hypothesis. These probabilities guide our actions. If someone makes an intelligent choice despite this, then he/she just got lucky.

Einstein and Newton are intelligent because of their experiences. Some take their experiences for granted. For instance, most of us would just pick up and eat the apple if it fell on our head. Instead, newton reasoned as to why it happened. Is this an indicator of superior intellect? He decided to do a different action (reasoning instead of eating) which is a manifestation of past experience. He must have observed/experienced that its rewarding when you reason every small aspect.

Why do some people learn faster than others? Is it because of genetics? If so, it is again a propagation of ancestral experiences. It might be the case that they worked hard in their childhood (more experience), thereby improving their intellect. Hence, they don't have to work as hard as you to pick things up.

So, in conclusion: "All people are born with the same intellect. It is their experiences that define them. To some extent you decide your experiences, so you control how intelligent you want to be."