Many mathematicians found patterns in the nature and came up with great concepts. For example, arithmetic in early days was only limited to counting positive numbers. Then came integers, fractions, rational, irrational numbers etc. There came a set up of numbers which are transcendental numbers like pi and e.
What is this ‘e’?
Let’s say, our wealth in a bank grows by 1% every month. We can say it grows by 12.7% at the end of year. Let’s say our wealth grows by 0.05% every day. Wealth at the end of year grows by 20%. Let say our wealth grows by a very very small amount for an infinite period, the growth will be a constant e.
This is what a continuous but infinitesimal growth that we see around.
Mathematicians used the naturally occurring patterns to improve the understanding of the nature’s laws
A paradox is simply for us which is contradictory with our existing understanding or logic or rules.
If one travels back in time and kill their grandfather before he conceives one of their parents, which precludes their own conception and, therefore, they couldn’t go back in time and kill their grandfather.
A horn with finite volume but infinite surface area. We can never paint this fully, but fill it with finite amount of paint
It seems like one can replace any component of a ship, and it is still the same ship. So they can replace them all, one at a time, and it is still the same ship. However, they can then take all the original pieces, and assemble them into a ship. That, too, is the same ship they began with (??)
Humans are limited in our understanding of Time, space and logic. For us time is always linear, all our logic seems to be jumbled up when we approach infinity and we think what is right in our mind is correct in the world.
Can these paradoxes help us learn any way ?
Humans must have thought that there cannot be transcendental numbers before their discovery.
We perceive time linearly. Hence we have a certain way of language. Can there be organisms which perceive time non-linearly and hence their language is different?
For a kid, who for the first time faces comes to terms that are other’s needs beyond self, might see it as a paradox.
By extending our understanding, we go beyond these paradoxes.
Logic is man made. It is our understanding of the nature. It cannot fully explain the rules of nature which are not man made.
Culture is man made. It is our beliefs and norms. It is no solution for nature’s creation.
Beauty lies in the eyes of beholders
Why is it that we see beauty in only certain way when it comes to nature. We see beauty in mountains, beaches, trees but are scared of floods, earthquakes etc. How is it that the nature which produces amazing things gives these problems?? If we are of truly understand the nature, would we see if for what it is : indifferent yet utterly tremendous.
Human perception is limited. By understanding this, we have hope for transcending. Science, for one, accepts this and expands its understanding. We need to be less dogmatic in our culture to evolve our understanding. By being defensive, we only limit ourselves.