There is no doubt that mathematics rules the root of reality when it comes to laws, principles and relationships within the sciences in general and the physical sciences in particular. Furthermore, 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 of the really real reality is actually reflected in our mathematics?
The Reality of Mathematics.
Mathematics is just a shorthand mental concept that simulates reality, or approximates reality or a possible reality or even an imaginary/impossible ‘reality’. Mathematics is NOT reality itself. You can mathematically manipulate the supposed extra dimensions in string theory, but that doesn’t necessarily mean that these extra dimensions actually exist.
Mathematics is a tool that in a first approximation tries to reflect on the nature of the really real reality. Mathematics is not reality itself. Furthermore, our mathematics is structured to reflect our version of reality based on our observations, not necessarily what actually happens. The perfect example is Quantum Mechanics. For example, we may not know, or even be able to know even in principle, exactly where a particle is and, 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. Those equations are for our edification, but they don’t alter the really real fact that the particle has real coordinates and goes from A to B. Probability in Quantum Mechanics, and the mathematical equations associated with it, are just reflections on limits. of the human observer and human instrumentation, not a reflection of the actual reality of Mother Nature. Our Quantum Mechanics equations are forced approximations to the really real reality, just as Newton’s equation for gravitational attraction was really only a hindsight approximation.
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. The fact that mathematics predicts the possibility of some kind of structure and substance, or some law, relationship or principle that the Cosmos may have, does not necessarily mean that it is so. An excellent example where the math worked but the Cosmos didn’t go the way was the ad-hoc piling up of those epicycles upon epicycles to explain the motion of the planets. Eventually it became so unwieldy that they threw the baby out with the bath water and conceived a new baby, with Earth being just another planet and not at the center of life, the Universe and everything. Once it was postulated that the Earth revolved around the Sun, planetary motion fell into place, mathematically also into place.
Let’s take a more modern example. The math works in String Theory, but to this day String Theory remains the theoretical dream of theorists (accent or emphasis on the word “dream”).
Probability theory is that branch of mathematics that stands between macrohuman and human understanding and abilities and the microworld of quantum mechanics. This has much more to do with the macro than with the micro since the absolutes of the micro are not visible in the realm of the macro; they are beyond the realm of the macro to resolve through no fault of human understanding or skill.
A good example is that there is no probability in quantum mechanics, only probability introduced by the limitations of the conscious mind in getting to the level of detail required to remove the concept of probability from quantum mechanics.
Mathematics serves no purpose, useful or not, outside the context of the human mind (specifically) or outside the intellectual conscious minds of other sentient species (in general), thus taking into account ET and perhaps the great terrestrial apes; whales and dolphins; and maybe other advanced minds, maybe elephants and some birds.
In the absence of conscious minds, what use is the Universe to arithmetic, geometry, trigonometry, calculus, topology, statistics, and the many branches of mathematics? Now 1 + 1 = 2 might be universally the case and logically true even in the absence of a conscious mind, or before any form of life came into existence, but so what? That doesn’t cut the mustard with the Universe! There was no one around to conceive of it or make use of it or equate number manipulation as a reflection of universal reality (or even unreality*). There was no conscious or intellectual mind around to appreciate any usefulness or mathematical usefulness or beauty or elegance.
In fact, mathematics is not a reflection on or of reality, only that reality as it is observed or defined once it has been filtered through the sensory apparatus, thus weighed by the conscious mind. Reality as perceived in the mind is several layers of transition processing removed from whatever pure external reality there is. There is even an additional layer if the instrumentation is an intermediary. So the conscious mind is limited in terms of its ability to come to terms with the full scope of really real reality.
Mathematics is the interface between humans and human understanding, understanding, etc. of the Cosmos in general. Mathematics can actually or theoretically tell you the ‘what’ but never the ‘how’ or ‘why’. For example, there is Newton’s Law of Gravity, but even he realized that that equation only told you ‘what’, not ‘how’ or ‘why’.
The non-reality of mathematics.
The following examples are some of what I call the unrealities of mathematics.
*Hypercubes are a good abstract concept that math and geometry can incorporate. However, while you may be able to play with real cubes, like dice, hypercubes will always be beyond you.
*Stephen Hawking’s concept of negative time. Since IMHO time is just change and change is just motion, then negative time would have to be negative change and negative motion. That doesn’t make any sense at all. So while negative Hawking time may be useful in a mathematical sense, it has no bearing on our reality and can be safely ignored.
* Many quantum mechanical equations returned infinities, so a sleight-of-hand concept called renormalization was invented to deal with cases involving infinities. That seems to me to be dealing cards under the table or otherwise known as inserting a “cheating factor”. Does renormalization represent a really real reality?
* The mathematics of singularities inherent in the time of the Big Bang or in Black Holes goes down the rabbit hole in that laws, principles, and relationships inherent in the physical sciences that are otherwise described mathematically so adequately they now fall apart when it comes to describing the singularities. and so does the adjoining mathematics that is also involved. So what is actually the actual reality behind singularities?
* Mathematics is perfectly capable of dealing with alleged extra dimensions inherent in String Theory. However, that does not make string theory a reality, nor does it make half a dozen extra, hidden dimensions a reality.
* Mathematics is perfectly capable of dealing with an inverse cube law that has no correspondence with our physics. The fact that a mathematical equation works does not mean that there is a one-to-one correspondence with the real physical world.
* Mathematics is perfectly capable of dealing with zero, one and two dimensions, however these are just mental concepts that cannot actually be constructed and therefore have no real reality.
* Space-Time: Since space is just an immaterial mental concept (that imaginary container in which real physical matter must reside) and since time is also just an immaterial mental concept (our way of accepting change that is just motion – which is also an immaterial mental concept since motion itself is not composed of anything physical), then space-time has to be an immaterial mental concept. Neither space nor time nor space-time is actually composed of any material substance and the trilogy does not have a material three-dimensional structure. However, mathematics involving the concept of space-time is a useful tool for describing reality, but not actual reality itself.