Explainability of Universe in perspective of human being.

The term explainable AI is around for a while now. Modern human try to understand everything rather to merely use it. It is verified with the fact the exponential rising of edutech based startups viz. Coursera, EdX , Udemy , educative, udacity , unacademy just to name a few.
Philosophers have always tried to understand nature and explain it to common folk.

But the question remains same, how complex is it to understand an underlying mechanism of a phenomenon. Do we need to make a basic assumption before understanding it or every process is explainable without requiring any underlying assumption.

As it turns out, no mathematical theorem or any maths can be proved without any prior assumption and generally we don’t weigh if the particular assumption is built upon some other more basic assumption. The most basic assumption in most cases are found experimentally. Mathematically we say them as axioms or postulates which scientists community regard as "self evident".
For example-
From basic
1. if a=b then b=a
2. if a=b then ac= ab when a,b,c are real numbers.
To less basics

1. It is possible to draw a straight line from any point to any other point.
2. It is possible to describe a circle with any center and any radius.

Physicists call them first principles.

Every proof requires assumption. Likewise to understand anything people usually believe a basic assumption to be undebatably true to set a starting point.

A Possible Analogy

Let me put an analogy which is the sole reason for writing this article . Isn’t it?
People have always learned from analogy with other subjects.

The fundamental theorem of arithmetic states that :
Every natural number greater than 1 is either a prime itself or can be factorised as a product of primes that is unique up to their order.

Simply a natural number is either prime or can be expressed as a multiplication of prime numbers.
Like 2(prime), 3(prime), 4=2×2, 5(prime), 6=2×3 and so on.

A prime number is a natural number which is divided by 1 or the number itself. Like- 2,3 5,7,11 etc.

The same way either a process existing in nature (think why natural numbers are called natural) is the self evident assumption itself or it is built upon several underlying assumptions, remember in nature assumption may be basic or complex that I would explain you further.

Like in the past, people experimentally assumed that objects fall to earth or the earth is flat, so people understood the processes built upon those assumptions that you can easily find in the ancient texts(many of them are religious texts like bible) back then.

With the progress of people and science, assumptions changed based on experiments and experience. But the style to understand natural processes remained same which is built upon some other assumptions.

So .. assumptions are just like prime numbers, uniquely identified. We understand a process or phenomenon based upon those unique assumptions and process itself as a combination(sometimes simple operations and often complex operations) of underlying assumptions.

But again sometimes(less often) unknowingly and often beautifullly during our exploration of processes, we encounter some processes which don’t seems to be the combination of our basic prior knowledge assumptions.
Like when quantum mechanics showed it’s properties and uniqueness , no prior knowledge or assumptions could explain them be it Newtonian science or even realtivity . Amazing we discovered another prime number(unique scientific assumption)!

These processes adds more set of assumptions to our existing set which human try to use to further explain processes more accurately and precisely.
Like quantum mechanics is now used to explain even simple Newtonian phenomena and sometimes used in conjunction with relativistic assumptions in hope to explain the other processes more finely.

So quantum mechanics , relativistic assumptions fits in the definition of our prime assumptions. Aren’t they?

They are unique and cannot be explained with simpler assumptions like with Newtonian or Euclidean assumptions. But we can use these prime assumptions to explain composite phenomena by their combination.

With the advancement and rapid growth of our researches, human hope to find more prime assumptions like these.

Dark matter and dark energy are possible candidates of our next prime numbers(unique scientific assumption).

But as the mathematics say, there are infinite prime numbers but more densely found near 1 and becomes very scarce with the rise.
Like there are 8 primes between 1 to 20 and 3 primes between 80 to 100.

See the below graph of density distribution of prime numbers.

In Number theory, Prime number theorem states that “Primes become less common as they become larger by precisely quantifying the rate at which this occurs.”

There are many processes which we don't really know how they work but we experimentally see their results and we try to explain them on the basis of those prior scientific assumptions. We can get a close estimate by this but we don't really can know them untill we actually discover a concrete prime assumption.

Mathematics says we can never accurately predict a n’th prime number, there’s no formula of it, we can only estimate it with some relative error.
Like if someone ask you to tell (10^52)th prime number ,will you or your computer be able to tell accurately? Ask your CS professor.

Like Prime Number Theorem says
“The prime number theorem is equivalent to the statement that the nth prime number Pn satisfies
Pn ~ n*log(n)

The asymptotic notation meaning, again, that the relative error of this approximation approaches 0 as n increases without bound. For example, the (2×10^17)th prime number is 8512677386048191063, and (2×10^17)log(2×10^17) rounds to 7967418752291744388, a relative error of about 6.4%.”

A better approximation is

Again considering the (2×10^17)th prime number 8512677386048191063, this gives an estimate of 8512681315554715386; the first 5 digits match and relative error is about 0.00005%.

This way we estimate the mechanism of many processes without actually knowing concrete mechanism behind that. That mechanism can only be unleashed by rapid growth of researches.

With that being said I believe there are infinitely many unique physics theories which are waiting to be discovered but difficult to find with the rise. A healthy and better environment and research friendly world and mindset is all that human kind need.