So for, “ Uncertainty Principle is one of the foundational rules of modern physics”.

First thing, As Richard Feynman said, “The problems inherent to the Uncertainly Principle lay in the measuring not in the Uncertainty of Physics”

What is Uncertainty Principle ?

Uncertainty Principle

It is ∆ X ∆ P ≥ h/2∏, means Momentum and position of an electron, both cannot be measured at the same time. You can either tell momentum or position of an electron in a little tiny fraction of time but not the both. It’s because when you measure the velocity of an electron in a quantum system you need its exact position and vice versa. And because,

“The Compton effect cannot be ignored: the interaction of the electron and the illuminating light should then be considered as a collision of at least one photon with the electron. In such a collision, the electron suffers recoil which disturbs its momentum. Moreover, the shorter the wave length, the larger is this change in momentum. Thus, at the moment when the position of the particle is accurately known, Heisenberg argued, its momentum cannot be accurately known”. (The Stanford Encyclopedia of Philosophy)

It’s all about the future behavior of an electron in coming instants of time but what about the past?

In the Chicago Lectures, Heisenberg admits that position and momentum can be known exactly for the past. He writes:

“If the velocity of the electron is at first known, and the position then exactly measured, the position of the electron for times previous to the position measurement may be calculated. For these past times, δpδq is smaller than the usual bound. (Heisenberg 1930, p. 15)

Indeed, Heisenberg says: “the uncertainty relation does not hold for the past”.

Now what left with uncertainty? It is only the problem of prediction on basis of past events. Why it is not the same as we usually do within classical physics. That is the question,

Thus, Uncertainty Principle appears as “The Theory of Probabilities” and what then? Central Limit Theorem kills its uncertainty with huge mathematics of probabilities.

Central Limit Theorem considers the randomness in a single sample as a single unit. It suggests creating, as many probability samples as possible, give us the approximately absolute value. The more sample you add the more accurate you become.

In certain conditions a number of arbitrary variables each with a distinct value and inconsistency will be something like normally distributed. Specifically, guess! that a sample is taken holding a big number of examinations, each examination being arbitrarily produced in a way that does not rely on the values of the other examinations, and that the arithmetic average of the examined values is calculated. If this practice is acted upon repeatedly, the Central Limit Theorem asserts that the calculated values of the average will be distributed consistent with the normal distribution, which gives you a “Curve Bell” for at least more than 30 of sample size. As you increase the sample size you get closer to the normal value. With highest size of samples you can get as normal value as the absolute one.

However, uncertainty appeared and brought chaos with it. Physics was dead almost if mathematics did not rescue it immediately (personal point of view).

I thought this clarification was for the phrase,

“Uncertainty Principle is one of the foundational rules of modern physics”

And I commented on that, “It’s a bit like what we call “hasty generalization” or quick assumption in logic. Anyhow!

Second thing,

Unfortunately I don’t properly remember whether Iqbal used or not, the phrase, “God does not change His habits”, as you stated,

“Such an uncertain Nature may definitely not be equated with that God who does not change His habits!”

However, no matter, Iqbal quoted it or not, it’s a Quranic verse and maybe you took it from Quran. But by all means it does not imply that Uncertainty is necessarily not the habit of God, logically. On the contrary Iqbal emphasizes passionately in his lectures and poetry everywhere that the only absolute attribute that nature possesses is “Continuous Change”. He even goes further and says,

“It is the lot of man to share in the deeper aspirations of the universe around him and to shape his own destiny as well as that of the universe, now by adjusting himself to its forces, now by putting the whole of his energy to mould its forces to his own ends and purposes. And in this process of progressive change God becomes a co-worker with him, provided man takes the initiative”

Iqbal quotes verses in favor of his arguments as he has the habit of quoting verses from Quran, such as,

“Verily God will not change the condition of men, till they change what is in themselves” (13:11).

So all Iqbal said was,

“Nature as we have seen is not a mass of pure materiality occupying a void. It is a structure of events, a systematic mode of behavior, and as such organic to the Ultimate Self. In the picturesque phrase of Qur’an it is the habit of Allah”

How you can support your argument by providing a different version of the definition of God’s habit………. with the habit of God, which is ever-growing nature as Iqbal, sees it, It is the behavior of God, if you intended to say. You see! Latter is the practical meaning of the Former.

You built up a hypothetical syllogism between the unchanging habits of God and uncertainty in nature. If God has unchanging habits then the Nature must not be one of his habits at all because nature is uncertain. Totally opposite to the argument, Sayyid Ahmad Khan usually used and you mentioned it in the beginning.

A few paragraphs latter you asserted the otherwise,

“Their position is clearly ambivalent which at times becomes openly hostile. The answer is that to accommodate freedom of will, human volition, mysticism and intuition they need a non-mechanistic explanation of the universe. They desire a world free from the categories of space, time and causality wherein human individuality may grow without any restriction.”

Now we know that Iqbal (plus Bergson) believes that only absolute attribute of nature is “Continuous Change”. In other words he means that the behavior of nature, the uncertainty which is the behavior God actually is a wonderful habit of God that never changes. The law of Continuous Change never changes because it is absolute. I think all this happened because of two almost vague terms, the behavior and the habit of God.

Also you said,

“To accommodate freedom of will, human volition, mysticism and intuition they need a non-mechanistic explanation of the universe”,

……..Which is obviously an uncertain world,

According to Quranic verse the habit of God is unchangeable which is, latter understood by Iqbal that “Continuous Change” is the habit of God. Definitely Iqbal sees freewill as an attribute of uncertain world, as Continuous Change, because according to Iqbal God has a dynamic world as his static habit.

So when you put your remarks there,

“The study of God or His behavior does not make the subject-matter of Science at all. This is the purview of Theology, and Science is verily not Theology. No scientist, no matter how devout believer he is, has ever claimed that he was studying either God or His behavior. This is basically a category mistake, mixing two separate areas of inquiry which are mutually exclusive”

What two separate areas of inquiry?

1. Study of nature?
2. Study of God?

Or

1. A posteriori
2. A priori

Now we know a posteriori is limited to the frames of references. It could be an a priori for someone else. Illusions are always a posteriori experiences for their observers. So when all humans are agreed with some a posteriori inference it means the observation of one has made so many witnesses who used their own frames of references for deciding the truth. This is how common intellect grows. The fact that the planet earth rounds around the sun is still a priori knowledge for billions of the people. All they saw images and calculations and nothing else but they still believe that Earth rounds around the sun.

That is the same case with your argument. What part of the mysterious nature has been studied properly and if it has got good logic and best explanations, no matter by only a few members of the human tribe, that part (while being a priori still) has become a posteriori for everyone. This will never stop ever. So the study of nature which is a posteriori is still a priori for someone else. Study of God will remain in the same sphere until it remains a priori knowledge in the world.

…..

I passionately want to talk about the “Instinct on Matter of Religion” but it is not related with the topic. My review is to be continued with your comparative study of Hanafi and Iqbal. I am sure, you never mind discussions. They are always delicious.

Best Regards
Idrees