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How to Understand Order

Introduction

We are fascinated with order. Our inventions like mathematics and geometry openly show that welove patterns. We have been trying to find patterns everywhere since thousands of years. Logic

and reason enjoy important status in our society because they allow us to discover order andpatterns. Numbers are one of the most fascinating orderly systems invented by human mind. Theyare ubiquitous and we cannot imagine our lives without them. But inside this orderly world ofnumbers, there is a mysterious world of prime numbers. And they seem to defy the order whilestaying firm within this orderly system.

Prime numbers have stimulated minds of great mathematicians since time of the Greeks. In myrecent expedition in world of primes, I discovered that primes can tell us some fascinating thingsabout the nature of order, and how it can be investigated. It is aim of this article to explore thisunusual hypothesis.

Mathematics

Our love for order has given birth to many wonderful innovations. It would be agreeable to say thatmathematics of the most important of those innovations. There is a certain order in the world ofmath. One plus one will always be two, no matter what. Pi is a universal constant and it will stay soanywhere we go. At the same time, this property does not hold for physical constants. Theychange with time and space. So there is an inherent universal order in math. For rest of the article,we will limit our investigation to natural numbers greater than zero.

Within this orderly world of math, some mysterious numbers live. They are called primes. Theirmystery is unfathomable, and potentially lethal. But rather than diving in this mystery,understanding why the mystery exists can tell us something important.

Primes

Primes are numbers divisible by one and themselves. They only occur in natural numbersequence. Let us spare zero for now, it is a mystery in itself. Now let us summarise couple of factsrelated to primes:

Fact 1: Primes are infinite in number.Fact 2: Natural numbers can be factored in prime numbers.

From above, one can clearly see that primes can build rest of the natural numbers. It would be

agreeable to say that primes are primary constituents of natural numbers. They are ‘atoms’ thatcan build rest of the world they come from, namely natural numbers.

Order

As we saw earlier, primes can build rest of the numbers. So when we mix primes and what theycreate, we get an orderly system i.e. natural numbers. But apparently, nobody has been able tofind out any order within prime numbers. They seem to be randomly distributed. And as we saidearlier, they are infinite in number. What does this tell us about the nature of order?

I think this phenomenon in mathematics tells us that it is futile to study an orderly system throughits constituents. The approach to study natural numbers through primes starts with fragmentation

of numbers into primary constituents. But as we have found, these primary constituents are infinitein number. And they also random and totally elusive, beyond all formula and order. From this

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example, it seems unworthy to study an orderly system by studying its fragments. Because we cannever say anything conclusive about these fragments. We can only keep finding more of them.

Discussion

It seems to me that our approach of fragmentation to understand an orderly system is bound to fail.It is clear from the things noted above that primary constituents of an orderly system may berandomly spread out and infinite in nature. In physics, we have encountered such situations wherewe are continuing our search for fundamental particles. I would like to say that it may not be themost fruitful search. We may end up finding that we can divide things infinitely more.

This trouble arises only when we take approach of division. As a unified system, natural numbersare orderly and functional. But when we try to understand them through fragmentation infundamental constituents, the system seems to fail us and evade any investigation.

Conclusion

It was aim of this article to explain that divisive approach to understand an orderly system has a

great chance to fail. This approach has pervaded human mind in recent times. I think that a holisticapproach that sees every part of the system as equal has more potential to create fruitful results.