In general , humanity has been trying to find the truth. This is the struggle that has helped us grow with our use of intellect and wisdom to acquire knowledge. Solving problems was/is a component of this journey. Mathematics played a major role in this regard. But is it possible that some of its fundamental concepts might not be able to give the true picture?

For example , an equation is considered to be fundamentally true if it’s equal on both sides. I see a theoretical problem in this that needs to be addressed.

Let’s take a simple equation:

2+2=4

And let’s say theoretically we want to know what happens to the 2s that we have used to make 4. We dissect that 4 and find our 2s. Problem solved ? Yes on a practical level but No on a deeper level. That I would try to explain.

How do we know that these are the same 2s that were combined previously? What if we divide each 2 into two 1s. We will use letters a,b,c and d just to identify each. Now let us rewrite the equation like this:

(1a+1b) + (1c+1d)=4

2ab+2cd=4

And after dissection we get the equation like this :

4= (1a+1c) + (1b + 1d)

4=2ac+2bd

(It is assumed that 2 was only made of two 1s but we know that if we go into decimals then there can be infinite options. )

Therefore , we can say that certainty of our assumption to reach reality(truth) depends on:

1- Information that we are provided with about the components that made that reality in first place. i.e. regarding constituents of 2s whether these are made of two 1s or twenty 0.1s?

2- How much are we interested to know the reality? i.e. does it serve any purpose to know if we get 2ab and 2cd back ?

Yes it seems meaningless to know if we are able to get the same 2 or not. But let’s say we do want to know. Then if we know that each 2 had only two components then we can calculate that our probability of acquiring the one of the same 2s is 1/3 (unordered) or 1/6 (if we artificially label output order).

So if we do this mental exercise then we can answer how were we able to get that real truth of whether those were same 2s or not! And that is our theoretically ability to see through the core of each 2. That is our access to information that is not readily available.

Here I believe is the answer to some of our quantum mechanics questions. Whether the Schrödinger Cat is alive or dead, is not the matter of Superposition where it’s both (which ofcourse can not be true ) rather it’s our limitation on information due to barrier of the box within which the cat is. A 4-dimensional entity will not face that barrier and would be able to answer this question right away.

Similarly collapse of wave function is same as dissection of the 4 into 2s and not worrying the true nature of those 2s. And If we do decide on the true reality of 2s then wave function won’t collapse and all possible outcome will become visible.

Is it possible to take mathematics deeper into the reality of matter itself and suggest that hydrogen atom is equivalent to 1 in language of math and while going into subatomic world we are actually getting into the decimal realm of mathematics? And is there possibility of discovering a new world of Quantum Mathematics? And to add more to this idea , Can we argue that consciousness is the ability of a unit to have this innate understanding that it is made up multiple ingredients and where magnitude of consciousness is directly proportional to the number of ingredients it possesses? Those ingredients are atoms and cells but also thoughts, learnings from experimentation and history and interactions with other units of existence.

This concept of “mathematical barrier to unmask reality” provides mathematical foundations to quantum mechanics and has the power to inspire us to dig more into true nature of reality and see beyond what it seems and meanwhile keeps us humble on our inability to cross certain barriers.

And may be this is the barrier what Albert Einstein was referring to when he said, “As far as laws of mathematics refer to reality, they are not certain. And as far as they are certain, they do not refer to reality.”

Muhammad Waqas