We interact with the world. We design our ways of interacting. And some of us find it useful to use mathematics as we design ways of interacting with the world. And that makes mathematics useful in theorizing about our interactions.
That is to say, it has nothing to do with how the world is made, and everything to do with how we have chosen to interact with the world.
I’m not actually seeing any relevance here. Some mathematicians are Platonists, while others aren’t.
But counting itself is surely an invented behavior.
That the universe is literally written in mathematics is an unconventional view, at least amongst contemporary physicists. Of course this is more of a philosophy question than a physics question, and I don’t know if physicists necessarily have the best expertise to answer this question. Nevertheless, I don’t think it is fair to say that
I think there’s a stark difference between naively believing that biology is ultimately reducible (either in a weak, or strong sense) to physics and believing that the universe as a whole is computable a la Tegmark.
Literature cannot be a product of human mind:
At any time T of history there will be literary questions that no human mind can answer with the information available at time T. For example, prior to the writing of The Lord of the Rings, nobody knew whether Frodo would succeed in destroying the One Ring in the fires of Mount Doom. Clearly, all novels must exist in an omniscient mind before we humans write them. Or not.
Mathematics allow us to predict accurately a number of phenomena, the evolution of visible bodies like for instance the Sun’s trajectory in the sky. In cases of chaotic systems, the necessary mathematical equations can reach a high level of complexity .
For quantum phenomena we can only predict distribution of outcomes by using mathematical rules: to single events we can only assign probabilities .
Phenomena like weather or flu virus are a mix of complexity and probability .
Nonetheless, even in case 1 above, there are no “inexorable laws of nature”: Things can happen that do not fit the usual regularities. These are what people of all times call “miracles”, which are beyond our control.
The important point is that what “miracles” actually demonstrate is that even the ordinary visible phenomena are brought about by an omniscient mind . This mind is kind to us, and shapes the world mathematically in order we can calculate and predict it, develop technologies, and live comfortably.
In summary, the “big miracle” is the miracle of the ordinary every daily life: “the appropriateness of mathematics to describe the world is a wonderful gift we should be thankful for”. (Eugene Wigner).
Of course. If there are no inexorable laws of nature, then there are no actual regularities. There is only what we take to be regular. And we take it to be regular for our own benefit. But the world is not obliged to follow what we take to be regular. And that is sometimes expressed in the saying “There’s an exception to every rule.”
Again, if there are no inexorable laws of nature, then there are no actual miracles. There are just cases where we had mistaken expectations.
No, they don’t demonstrate anything of the kind. They demonstrate only that we were mistaken in our expectations. Or, as the saying goes, to err is human.
You may believe that miracles occurred and will occur again. You may wish or pray for miracles but nothing happens outside the natural world. Sure 100 sigma events happen. But when you look deeply at the cause of the 100 sigma event you see what lead up to that event happening. What you realize is that you’re model is wrong, it wasn’t a 100 sigma event. It may have been a discontinuity - a single one time event caused by a confluence of rare events. Look at big storms and mass extinction events.
“What we take to be regular” is always the expression of our belief. For instance, I will not enter a bet with payoff 1 if the Sun dances tomorrow at the sky at 2pm, and payoff 0 otherwise. This is the authentic meaning of the so called “Laws of Nature”.
However, we reach such a belief because actually the Sun ordinarily follows the trajectory described by Newton’s equations and more accurately by General Relativity. And the astonishing thing is, as you very well point out, that this is “for our own benefit”. That is: God shapes the world so that we can calculate it and feel us at home.
Nonetheless, as you point out as well, “the world is not obliged to follow what we take to be regular”. By this you are clearly meaning: “God is not obliged to follow…” because only a person can be said to be not obliged to do something.
Important: we have to distinguish between two types of “exceptions”:
Phenomena we cannot predict because our equations are not yet good enough to describe them, as for instance Mercury’s perihelion before Einstein discovered General Relativity. Such phenomena lead to improve our description.
Phenomena that are unpredictable in principle because they do not fit to any mathematical description, as for instance the Sun dancing in the Sky in Fatima at 2 pm on October 13, 1917, or the precise answer you will give to this post of mine and the time when you will give it.
Phenomena of the second type are those that are freely decided by some author . In case of the dancing Sun, by God; in case of speech or writing, by a human author.
When God freely does things that are beyond our expectation or capability to perform (as for instance to let the Sun dance or a dead resurrect) we call them “miracles”.
@AntoineSuarez I think you could help by acknowledging the seeming contradictions in you own reasoning, some of which have been pointed out to you. That is, if a statement can only be supported by faith, and not math or physics, it is fair to acknowledge that. No one is criticizing you for having faith.
I submit for your consideration; your contention that the existence of a yes or no answer to the largest perfect number implies the mind of God, is itself an un-provable proposition in ANY symbolic system. This follows from the necessity of first defining “the mind of God” in a symbolic system, which ought to be impossible (maybe unknowable) by any logical or theological standard.