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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 science in general and physics in particular. Moreover, mathematics plays a major role when it comes to the purely financial aspects of our lives and where would sports be without statistics? However, when it comes down to brass tacks, how much does our math actually reflect actual reality?
The reality of mathematics.
Mathematics is just an abstract mental concept that approximates reality, or reality or possible reality or imaginary/impossible ‘reality’. Mathematics itself is not reality. You can mathematically manipulate the alleged extra dimensions in string theory but that doesn’t mean these extra dimensions actually exist.
Mathematics is a tool that initially attempts to approximate the nature of actual reality. Mathematics itself is not reality. Furthermore, our mathematics is structured to reflect our version of reality based on our observations of what actually happens by necessity. A classic example is quantum mechanics. For example, we don’t know, even in theory, exactly where a particle is and at the same time it goes with 100% precision. So we invent a form of probability mathematics such as the Schrödinger equation or the governing equation of the Heisenberg uncertainty principle. Those equations are for our editing but they don’t change the actual reality that the particle has real coordinates and is moving from A to B. Probability in quantum mechanics, and the mathematical equations associated with it, are only reflections at boundaries. Of human observers and human instruments, not a reflection of the true reality of Mother Nature. Our quantum mechanical equations are actually approximated to actual reality just as Newton’s equation for gravitational attraction was actually only a backward approximation.
There may be many models of reality, each based on mathematics, but they cannot all be correct. Cosmology is a case in point.
The phrase “but the math works” means absolutely nothing. Just because mathematics predicts the possibility of some kind of structure and matter, or the possibility of some law, relationship or principle that the universe might have, does not necessarily mean that it is. A prime example where the math worked but the universe wasn’t along for the ride was the ad-hoc piling on of epicycles to explain the motions of the planets. It eventually got so messed up that the baby was thrown out with the bathwater and a new baby was born, that Earth was just another planet and not the center of life, the universe and everything. Once it was postulated that the Earth went around the Sun, the motions of the planets happened in place – mathematically also in place.
Take a more modern example. The math works on string theory, but to this day string theory remains the theoretical dream of theorists (accent or emphasis on the word “dream”).
Probability theory is the branch of mathematics that deals with the interaction between the macro human and human understanding and capabilities and the micro world of quantum mechanics. It has more to do with macro than with micro because the absolutes of micro do not appear in the scope of macro; They are beyond the scope of macros to resolve without error through human understanding or ability.
A prime example is that there is no possibility in quantum mechanics, only the possibility presented by the limitations of the conscious mind to descend and dirty the level of detail necessary to remove the concept of probability from quantum mechanics.
Mathematics serves no purpose, useful or otherwise, outside the context of the human mind (in particular) or outside the intelligent conscious minds of other sentient species (in general), thus making allowances for ET and perhaps terrestrial great apes; whales and dolphins; And perhaps other advanced minds—perhaps elephants and some birds.
In the absence of any conscious mind, what use is the universe for arithmetic, geometry, trigonometry, calculus, topology, statistics and many other branches of mathematics? Now 1 + 1 = 2 may be universally the case and logically true in the absence of any conscious mind or even before any life forms, but so what? It cuts no mustard with the universe! No one was around to imagine it or use it or equate the manipulation of numbers as a reflection of universal reality (or non-reality*). There was no conscious or intellectual mind around to appreciate any mathematical utility or utility or beauty or elegance.
Mathematics is not really a reflection or reflection of reality, only that reality is observed or defined as thought by the conscious mind once filtered through the sensory apparatus. The reality perceived in the mind is the many transitional layers of processes removed from the pure external reality that occurs there. There is also an additional layer if the device is an intermediary. So the conscious mind is really limited in terms of its ability to deal with the full range of actual reality.
Mathematics is the interaction between man and the human understanding, understanding, etc. of the universe. Mathematics can tell you ‘what’ in reality or theory but never ‘how’ or ‘why’. For example, Newton has his laws of gravity, but he also understood that those equations tell you ‘what’, not ‘how’ or ‘why’.
The non-reality of mathematics.
The following examples are some of what I have termed mathematical non-realities.
* Hyper-cubes are a nice abstract concept that math/geometry can cover. However, while you may be able to play with real cubes, like dice, hyper-cubes will forever be beyond you.
* Stephen Hawking’s concept of negative time. Since IMHO time is only change and change is only motion, then negative time must be negative change and negative motion. That makes no sense. So while Hawking’s negative time may be useful in a mathematical sense, it has no bearing on our reality and can be safely ignored.
* Many quantum mechanical equations yielded infinities so a slit-of-hands concept called renormalization was invented to deal with those cases involving infinities. This strikes me as dealing cards from under the table or otherwise known as inserting the “fuzz factor”. Does renormalization represent actual reality?
* The mathematics of singularities inherent in the moment of the Big Bang or black hole goes down a rabbit hole in that the laws, principles and relationships inherent in physics that are otherwise adequately described mathematically now break down when trying to describe singularities. And therefore includes the mathematics involved. So what exactly is the real reality behind the singularity?
* Mathematics is fully capable of dealing with the alleged extra dimensions inherent in string theory. However, this does not make string theory a reality, nor does it make half a dozen extra and hidden dimensions a reality.
* Mathematics is perfectly capable of dealing with the inverse cubic law, which has no correspondence with our physics. Just because a mathematical equation works doesn’t mean there is a one-to-one correspondence in 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 thus have no real reality.
* Space-time: because space is an immaterial mental concept (the imaginary container in which real physical objects must reside) and time is also only an immaterial mental concept (our way of coming to terms with change which is simply motion – which is also an immaterial mental concept because motion itself is not composed of any material substance), then space-time must be an immaterial mental concept. Neither space, nor time, nor space-time is actually made of any physical matter, and the trinity has no physical 3-D structure. However, mathematics involving the concept of space-time is a useful tool for describing reality, but not really actual reality itself.
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