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The Reality And Non-Reality Of Mathematics
There is no doubt that mathematics rules 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 sport be without statistics? However, when it comes down to brass tacks, how much of the real world reality is actually reflected in our math?
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 those 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. Also, our math 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, indeed cannot know, even in principle, exactly where a particle is and at the same time where it is going with 100% accuracy. So we invent a form of probability mathematics like Schrodinger’s equation or the equation that governs Heisenberg’s uncertainty principle. These equations are for our edification, but they do not alter the very 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 only reflections on limits. of the human observer and human instrumentation, not a reflection on the truly real reality of Mother Nature. Our equations of quantum mechanics are approximations imposed on actually real reality, just as Newton’s equation for gravitational attraction was only an approximation in retrospect.
There may be multiple models of reality, each based on mathematics, but not all of them can be correct. Cosmology is an example.
The phrase “but the math works out” means absolutely nothing. Just because mathematics predicts the possibility of some kind of structure and substance, or some law, relationship, or principle that the Cosmos might have, does not necessarily make it so. A good example where the math worked, but the Cosmos didn’t go along for the ride was the ad-hoc stacking of those epicycles upon epicycles in order to explain the motion of the planets. Eventually it became so unwieldy that the baby was thrown out with the bathwater and she conceived a new baby, as Earth was just another planet and not at the center of life, the Universe and all. Once the Earth was postulated to revolve around the Sun, planetary motion fell into place, also mathematically.
Take a more modern example. The math works in string theory, but so far string theory remains a theoretical dream of theorists (accent or emphasis on the word “dream”).
Probability theory is that branch of mathematics that stands between the macro human and human understanding and skills and the micro world of quantum mechanics. This has more to do with the macro than the micro, since the absolutes of the micro are not visible in the scope of the macro; they are beyond the realm of the macro to solve without any fault in the way of human understanding or abilities.
A good example is that there is no probability in quantum mechanics, only probability introduced by the limitations of the conscious mind to get down and dirty to the level of detail necessary 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 (generally), thereby accounting for ETs and perhaps great terrestrial apes; whales and dolphins; and maybe other advanced minds, maybe elephants and some birds.
In the absence of any conscious mind, what use is arithmetic, geometry, trigonometry, calculus, topology, statistics and the many other branches of mathematics to the Universe? Now 1 + 1 = 2 could be universally the case and logically true even in the absence of any conscious mind, or before any life form ever arose, but so what? This cuts no mustard with the Universe! There was no one around to conceive of this or make use of it or equate the manipulation of numbers as a reflection of universal reality (or even non-reality*). There was no conscious or intellectual mind around to appreciate any mathematical utility or utility, beauty or elegance.
Indeed, mathematics is not a reflection on or of reality, only that reality as observed or defined once filtered through the sensory apparatus reflected by the conscious mind. Reality as perceived in the mind is several transitional layers of processing removed from any pure external reality that exists. There’s even an extra layer if the instrumentation is an intermediary. So the conscious mind is limited in its ability to come to terms with the full extent of actually 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 the “why”. For example, there is Newton’s law of gravity, but even he realized that that equation only said “what”, not “how” or “why”.
The non-reality of mathematics.
The following examples are some of what I call the non-realities of mathematics.
* Hypercubes are a nice abstract concept that math/geometry can incorporate. However, while you can play with real cubes, like dice, hypercubes will forever be beyond you.
* Stephen Hawking’s concept of negative time. Since time, in my humble opinion, is only change and change is only motion, then negative time should be negative change and negative motion. This doesn’t make any sense. So while Hawking’s negative time may be useful in a mathematical sense, it bears no relation to our reality and can be safely ignored.
* Many quantum mechanical equations produced infinities, so a sleight of hand concept called renormalization was invented to deal with those cases involving infinities. This sounds to me like dealing cards from under the table or otherwise known as inserting a “fudge factor”. Does renormalization really represent actual reality?
* The mathematics of singularities inherent in the moment of the Big Bang or black holes goes down the rabbit hole, as the laws, principles, and relationships inherent in the physical sciences that are otherwise adequately described mathematically now break down when attempts are made to describe singularities. and so do the accompanying mathematics. So what really is the real reality behind the singularities?
* Mathematics is perfectly capable of dealing with alleged extra dimensions inherent in string theory. However, this 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. Just because 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, but these are just mental concepts that cannot actually be constructed and therefore have no actual reality.
* Space-time: since space is only an immaterial mental concept (that imaginary container in which real physical matter must reside) and since time is also only an immaterial mental concept (our way of accepting change which is only motion – which is also an immaterial mental concept, since motion itself is not composed of anything physical), then space-time must be an immaterial mental concept. Neither space nor time nor space-time is actually composed of any material substance, and the trilogy has no material 3-D structure. However, mathematics involving the concept of space-time is a useful tool for describing reality, but not the actual real reality itself.
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