There is no doubt that mathematics rules reality when it comes to laws, principles, and relationships within science in general and physical science in particular. Moreover, mathematics plays a dominant role when it comes to the purely economic aspects of our lives and where would sports be without statistics? However, when it comes to brass tacks, how much real reality is actually reflected in our mathematics?
Mathematics fact.
Mathematics is just a reductive mental concept that simulates reality, approximates reality, potential reality, or even imaginary/impossible “reality”. Mathematics is not a reality in and of itself. You can mathematically manipulate the alleged extra dimensions in string theory but that doesn’t necessarily mean that these extra dimensions actually exist.
Mathematics is a tool that, at its approximate beginning, attempts to reflect what real life really is. Mathematics is not a reality in and of itself. Furthermore, our mathematics is designed to reflect our version of reality based on our observations and not necessarily what is actually happening. The perfect example is quantum mechanics. For example, we may not even know, even in principle, exactly where a particle is and also at the same time where it is going with 100% accuracy. So we invented a form of probability mathematics like the Schrödinger equation or the equation that governs the Heisenberg uncertainty principle. These equations are meant for our enlightenment but they don’t really change the real fact that a particle has actual coordinates and goes from A to B. Our quantum mechanics equations dictate approximations to real reality just like Newton’s equation for gravity was really only approximations in hindsight.
There can be multiple models of reality, each based on mathematics, but not all of them can be correct. Cosmology is an example of this.
The phrase “but the math works” means absolutely nothing. Just because mathematics predicts the possibility of some kind of structure and substance, or some laws, relationships, or principles the universe might have, doesn’t necessarily make it so. A prime example where the mathematics worked but the cosmos did not progress in flight is the custom stacking of these rotations upon rotations in order to explain the motion of the planets. Finally, it got so hard that the baby threw up the bathwater and conceived a new baby, since the Earth was just another planet and not at the center of life, the universe and everything. Once it was assumed that the Earth revolved around the Sun, the motion of the planets fell into place—mathematically, into place, too.
Take a more recent example. Mathematics works in string theory, but so far string theory remains a theoretical dream for theorists (emphasis or emphasis on the word “dream”).
Probability theory is the branch of mathematics that intersects human cognition and capabilities, the macro-human and the micro-world of quantum mechanics. This has more to do with the macro than with the micro because the absolute of the macro is not visible in the macro world; They are beyond the scope of the macro to be resolved without error by human understanding or capabilities.
The prime example is that there is no probability in quantum mechanics, only probability introduced by the limitations of the conscious mind getting down and dirty to the level of detail required to remove the concept of probability from quantum mechanics.
Mathematics serves no purpose, useful or otherwise, outside the context of the human mind (specifically) or outside the intellectual conscious minds of other sentient species (in general), allowing permission for ET and possibly terrestrial great apes; Whales and dolphins. And maybe other advanced brains – maybe elephants as well as some birds.
In the absence of any conscious minds, what good is the universe for arithmetic, geometry, trigonometry, calculus, topology, statistics, and the many other branches of mathematics? Now 1 + 1 = 2 may be the case universally and logically true even in the absence of any conscious mind, or before the emergence of any form of life, but what then? This does not cut the mustard with the universe! No one was around to conceive of it, capitalize on it, or equate the manipulation of numbers as a reflection of global reality (or even non-reality*). There was no conscious or intellectual mind about appreciating any usefulness, mathematical utility, beauty or elegance.
Mathematics is really not a reflection of reality or reality, only that reality as it is observed or defined once filtered through a sensory apparatus contemplated by the conscious mind. Reality as perceived in the mind is several transitional layers of processing removed from whatever pure external reality is occurring. There’s even an extra layer if the hardware is a middleman. Thus the conscious mind is limited in its ability to come to terms with the full scope of truly real reality.
Mathematics is the interface between humans and understanding, comprehension, etc. of the universe as a whole. Mathematics can actually or in theory tell you “what” but never “how” or “why”. For example, there is Newton’s law of gravity, but he also realized that this equation only told you the “what”, not the “how” or “why”.
The unreality of mathematics.
The following examples are some of what I call the unrealism of mathematics.
* Super cubes are a nice abstract concept in which you can incorporate math/geometry. However, while you may be able to play with real cubes, such as dice, hyper cubes will bypass you forever.
* Stephen Hawking’s concept of negative time. Since IMHO time is just change and change is just movement, negative time has to be negative change and negative movement. This makes absolutely no sense. So while Hawking’s negative time may be useful in a mathematical sense, it does not affect our reality and can be safely ignored.
* A lot of quantum mechanical equations yielded infinities, so a sleight of hand concept called renormalization was invented to deal with those cases involving infinities. Dealing under the table seems to me to be the “fudge factor” input. Is re-normalization a real reality?
* The mathematics of singularities inherent at the moment of the Big Bang or in black holes collapses down the rabbit hole as laws, principles, and relationships inherent in the physical sciences that are adequately described mathematically now collapse when trying to describe singularities, as well as the accompanying mathematics that is also involved. So what is the really real reality behind the singularities?
* Mathematics is fully capable of dealing with the so-called extra dimensions inherent in string theory. However, that doesn’t make string theory a reality, nor does it make the half-dozen extra, hidden dimensions a reality.
* Mathematics is fully capable of dealing with the inverse cube law which is not compatible with our physics. Just because a mathematical equation works does not mean that there is a one-to-one correspondence to the real physical world.
* Mathematics is fully capable of dealing with zero, one dimension, and two dimensions, however these are just mental concepts that cannot be physically constructed and therefore have no truly real reality.
*Time and Space: Since space is just an immaterial mental concept (that imaginary container in which actual physical things must exist) and since time is also just an immaterial mental concept (our way of dealing with change which is just motion – also an immaterial mental concept since motion itself does not consist of anything physical), then spacetime must be an immaterial mental concept. Neither space nor time nor space-time is composed of any physical substance and the triad does not contain a three-dimensional physical structure. However, mathematics involving the concept of space-time is a useful tool in describing reality, but it is not, in fact, real reality itself.