Is human thinking algorithmic?

Prerequisite for this article- precise definition of a Turing machine, or in other word, what an algorithm is. 

People are divided on this question.

People who say that human thinking is algorithmic, rightly point out how the physics relevant to describe the human brain (and also all of known physics, for that matter) is essentially algorithmic, and saying that human brain is anything but algorithmic would be living in denial of the extraordinary evidence present that physics works.

People who say that human thinking cannot be algorithmic, rightly point out how they just 'feel' a sense of autonomy that a Turing Machine cannot have. Often, this group cannot put a finger on why they feel that their thinking is not algorithmic.

In this article, we will not go into the first possibility simply because the evidence in its favor is overwhelming. The evidence available from physics plus the capabilities of the present day AI is an enormous amount of evidence in its own right.

We will instead try to go into the other possibility, that the human thinking is not algorithmic. We will investigate into two aspects.

First, why should we even consider this idea?

Second, given the evidence otherwise, is it even possible to make a logical case for the possibility that human thinking is not algorithmic?

If human thinking is not algorithmic, then this directly means that the world is not described well by a Turing Machine. That is, finite sets of laws cannot describe the world.

So, why are we even asking this question?

Short answer- the hard problem of consciousness.

The hard problem of consciousness is a philosophical 'why' question about the existence of the observer. Why is there an observer?

But how do we know that there is an observer. Each of us knows for sure about one case, from their own first person experience.

Is it even possible to make a logical case for the possibility that human thinking is not algorithmic?

The possibility that the Universe is not well described by an algorithm is such radical an idea that it is only paralleled by Newton's own radical discovery, that the Universe is well described by an algorithm.

This would mean that it is not just that the Universe is capable of generating complex behavior arising from simple laws, which, although can in principle be studied in terms of the simple laws, would instead require new emergent laws to be studied efficiently.

Philosophers call this weak emergence.

Weak emergence is a great idea in its own right, but here we are interested in something stronger- strong emergence.

Strong emergence means that it is not just that you cannot efficiently study complex phenomenon from fundamental laws, you cannot even it do it in principle. That is, truly new laws may emerge as the complexity of the system increases.

Where are we going with this?

If we are going to assume that human thinking is not algorithmic, then we should also recognize how radically it is going to shift our fundamental view of the laws of physics. Of many other things, it would mean the breakdown of the pursuit of finding a theory of everything.