The limits of reasoning and the value of knowledge in quantum computing

For the record, this is going to be another post regarding natural philosophy and the limits of reasoning (or, rather, how the limits of knowledge itself thus modifies our reasoning so as to both partially obscure and further reveal its context within temporal and eternal, absolute terms). However, while my previous posts have been enthralled with the logical steps behind delineating between perception (nature as we humans percieve it) and cognition (nature as how humans cognate, or understand, what itself is being percieved), this post is more concerned with the difference between percieved nature (for the sake of argument, let this be defined by a cognitive level of perception, or one which has finalized its journey from the senses to the mind) and ‘true’ nature (nature as it truly exists, or existing independent of any sensory or perceptory constraints, excluding even the context of time). But, as you read forward; “as you shirk it to find it all not too worth it,” please do not let either your genuine interest nor your fathomed level of comprehension be dissuaded by the philosophical rigors which are invoked upon even the slightest mention of the relationship between knowledge and reasoning. The reader should of course go without questioning that, while we can delineate between the two matters using only our requisite lack of knowledge, or the unknowing of what may be reasoned true, it must be stated outright that our perception of nature, lest it be regarded as a less true (though still abstracted) basis for any knowledge to be made absolute, is instead made self-evident by the existence of a prerequisite for any dimensions wherein nature may be percieved by humans, that prequisite being the inter-dimensional tangibility of matter as being neither created nor destroyed (as proven by the hylomorphic framework for change; the existence of matter in any material form thus requires for the (de)privation of said form) but instead existing in a state of uncertainty (chaos, in the sense of uncertainty regarding its dimensional context). In other words, the concept of matter serves scientists to account for how one form of energy is converted into another without seemingly modifying the quantity value of any potential energy as it is realized.

The whole is the sum of its parts, or: Why uniform abstractions of actual quantity fail to encompass uniform values

Indeed, the contentment that matter originates from chaos in turn serves as an unambivolent scientific approval of the reasoning that any perception, when thoroughly scrutinized, may eventually land us back at the invisible wall of perception which stands to limit the extent of any such analysis (in the literal sense of ‘breaking apart’) by drawing a line as to the extent of our reasoning at ‘knowing’ the sum of any individual part (taken from its parts) which are said to comprise its whole. If the whole is truly the sum of its parts, and yet we are left unaware of the number of parts or each their sums, it would therefore be impossible to exactly quantify the sum of the whole, knowing that we are uncertain of the amount of parts which comprise said whole, nor are we seemingly able to figure out the sum of any part. However, we must consider the converse implication of knowing that “the whole is the sum of its parts” (X is Y, Y is Z), which is to say that “the whole” is explicitly being defined as “the sum of [the whole’s parts]” and thus should stand to infer at least the quantity of parts comprising their whole, the sum of which must thereby equate to the combined value of its parts. And so, it would then seem that we can know that value from that of the whole, however, as previously mentioned, there are tangible values within nature (such as those of isotope readings) which may in fact lend to its whole value, except that any such whole value is constrained by the ambiguity of our physical, ‘abstract’ nature, at least in accordance with how it truly exists. Yes, it is indeed possible to obtain quantative values using perception, such as inferring the quantity of trees in a forest using one’s mere eyesight, but there is no quantative basis with which to compute any numerical solution. In other words, the usefulness of quantity and its expression in mathematical terms depends on truly understanding its causality, which requires us to at least know all of the other quantities (or parts) which comprise the sum of the whole.

A brief on Kantian metaphysics

Kant’s philosophy heavily builds upon the metaphysical realism pervaded by Plato using his ‘world of forms.’ However, unlike Plato, Kant makes the distinction between theoretical and practical forms of reason (priori and post knowledge; the principally logical reasoning without empiricism, and the otherwise empirical reasoning using logic, respectively.) In doing so, Kant discusses some of the aforementioned theoretical limitations of metaphysical knowledge, thereby limiting the speculative value of theoretical, post reasoning on its own (reason itself also being an ‘abstract object’) as being unable to surpass the degree of experience afforded to the empirical thinker.

Empirical thought, though not necessarily entirely empirical nor pragmatic in its nature, depends upon an ‘empiricism’ which grounds itself in abstractions of perceptory origin. Conversely, it is the practical, priori use of reason which may be used to transcend any such percieved forms of empiricism in order to capture in operative terms the non-abstract nature, or noumenon (Grk. meaning ‘something known,’ used by Kant to describe the form of nature that I termed as ‘perceptory,’ ‘abstract’; e.g. ‘as it truly exists.’) This is an important Kantian distinction between Plato that has become marked by an antithesis between the two forms of knowledge commongly among philosophers to specify the limits of empirical forms of thought.

Praeternaturalis, vel: Non-naturalis silve natura falsa?

Beyond nature, or: non-natural or false nature? This is a problem which occurs from the attempt to use values obtained via perception in their abstract nature and apply them towards computing the quantity of a non-perceptible, though evidently real, metaphysical reality, one in which there is no contextual basis for understanding that which has been described using post knowledge, or an empirical form of thought.

In Platonist philosophy, we are taught that quantity is an abstract object (an object devoid of any contigency upon tangible, material objects) and arguably, at least to some extent within Mathematical Platonism, residing principally within the ‘world of forms.’ However, while mathematical quantity itself may exist in abstract form, it must be expressed in some perceptible manner such as an integer value. In spite of such mathematical constance, this represents an attempt to equivocate a perceptible aspect of our percieved reality with that of another. This is because the quantity itself, while indeed abstract, must be expressed tangibly and therefore must be obtained in a manner that does not rely upon non-abstract constructs such as language-based numerical conventions (1,2,3) while also (most frustratingly) preserving the meanings of the numbers in relation to their quantity values.

Moreover, while mathematics itself exists in the abstract sense, the conventions regarding the formatting of numbers (such as rounding-up practices) are less abstract and instead depend upon perceptible, non-abstract considerations, like how the right-to-left Arabic numeral system may have easily been mutilated by those accustomed to the left-ro-right Roman numerals. While we like to envision mathematics as existing in a perfect state, it may only be percieved in a manner that is devoid of any such abstraction, i.e. printing the integers themselves, with their quantity being abstracted in single-digit or perhaps hexadecimal binary values (binary logic is purely mathematical rather than draped in syntax).

Abstract limitations upon expressing non-abstract metaphysika

The greater problem arises when attempting to find permanence for this information within any metaphysical reality. Without any physical basis for expression (i.e. binary values) or any perceptible reality whatsoever, the value itself remains a valid mathematical expression (e.g. 8) but fails to represent any non-abstract equivalence of its abstract form due to the lack of any perceptible basis with which the quantity itself may be expressed. Moreover, the expression of such a quantity would not guarantee that it is equally relational as an abstraction. The expression of quantity itself is thus transmutable between the real and abstract forms of reality, but completely meaningless in relation to any context originating from within the abstract. The lack of any percieved nature within the metaphysical in turn fails to hand us with a starting point for visualizing ‘1’ of something (you can’t just percieve the pure mathematical quantity of a non-abstract object without the existence of an abstract nature; what is there 1 of?) and, while Platonists hold that mathematics itself is non-abstract, they do not always consider complex maths (such as differentials) to be such.

Metaphysical reality does not contain any of the abstract forms which comprise our own; there is only the matter from which forms take their shape. As such, quantity itself is meaningless unless we are seeking to express the quantity of matter itself, however impossible that may be, due to matter’s indistinguishable state of chaos as it exists non-abstractly/ (The indistinguishable nature of the matter therefore renders it impossible to express its quantity using any numerical sum other than ‘1’; all that we know is that the matter, as a whole, does exist.) (An individual also proposed ‘0’, though I believe this to be incorrect. Metaphysically, matter exists everywhere, though perceptibly, it is made into a non-abstract form.) If we are to stand by the use of mathematics as a non-abstract expression of quantity, then it would indeed be accurate to state that matter can have only a sigular quantity about it.

The problem, or: Mapping between the perceptible (material) and perfected (absolute) forms of existence

If we were to happen upon the unequivocable realization of the sum of the whole, e.g. knowing it to be 1,024, then perhaps our foliage data (let us day, 13 trees) may then be subtracted to leave us with a definitive quantity of every part other than trees in the forest, thus couching our logical propositions in the tangible hands of mathematical expression (and giving some way with which the whole may be specified further). Even without a sum value, we would at least know that the value of our whole should be at least 13, as in the case that said whole consists only of trees within any particular forest. However still, the ‘whole’ we have obtained is then more or less a numerical range of (rather vague) integer values, with those integers representing distinctively perceptable things (like the individual trees). If what appears to be one tree does in fact exist as two separate trees being conjoined as one, then the value becomes false, at no fault of the maths alone, but instead of a faultied perception. In conclusion to this, having a framework for quantifying the whole of nature using the sum of its parts is no use when its perception does not in fact exactly represent its whole. (Why exactly? Well, because exactness itself is absent from chaos, and we cannot derive any exact quantitive value when its degree of accuracy is unknown.)

Even if it were possible to obtain some kind of control whereby quantitive values could be adjusted for their numerical accuracy, tbe representative meanings of said values would, alas, proceed to fall short. Unless we are to know that a singular perceptible ‘part’ of the whole is indeed singular, its value is entirely devoid of any absolute context rather than the context of perception, because it cannot be known that tangible quantities exist in the same quantity as they are percieved. It could just as well be postulated that there also exists something ‘before’ physics other than chaos, maybe even something tagible within that context, but said plane of existence cannot be hold in any quantifiable relation to our own, therefore leaving us without any knowledge to be had. What exists as one part of two halves, or a single pair, is not a “pair” by any measure of its mere existence, but instead its perception in relation to the other half of the pair. The lack of any quantifiable difference between the values of 1 and 2 across both dimensions would render them unequivocable with each other. (In a reality where 1+1=3, one might say that it has a difference to our own reality of exactly 1, however, any world in which two things comprise three may just as well have a difference of 2 or perhaps 42, because there is no form of logical inference spanning both truths. Furthermore, one logical invalidation of this kind would just as well invalidate every mathematical proposition for the same reason; if 2=3 then 2x3 makes 6 into 9, and then 42=43, despite 43-1=42.) And so, it would be a misunderstanding to operate under the impression that we are simply in need of some “magic number” to unlock the secrets of true nature. Instead, one must reckon that the only way to unlock true nature is by employing a sort of perceptible, metaphysical construct, and yet, the chaos from which it originates thus prohibits us from obtaining any order with which it may be distinguished.

It is true indeed that tbe constance of matter can be accounted for during analyses of chemical reactions which, in spite of their seemingly mystical ability to modify their material properties, do not appear to create nor destroy any of their matter, but only to change that matter’s form. However, there are no physical constants which lend to quantifying their matter, nor is there any numerical basis for obtaining its difference from the sum of the whole’s parts. No matter what, you are left with a number that has only any permanence in the same dimension as it was quantified. You are left with a tangible number of arbitrary magnitude that lays in relation only with the other perceptable values found within tangible reality; an integer with a singlular dimensional value. However, this reasoning should not be had without understanding that it too has contraints, even squarely within this dimension. While the value is, at least, a mathematical constant, it is invariably contrained by temporal permanence (the agedness of the information; or, the inability to quantify it at the exact point in which it was true) and even the orders of magnitude that behold microscopic and, eventually, sub-atomic, degrees of perception. In layman’s terms, without knowing the quantity to be currently true whilst cognating its meaning, it may then proceed to have little place amongst the ever-changing forms of matter and their ever-changing values. And, since it is impossible to obtain the value in the same logical step as it is quantified along with any other potential variables, that value stands in relation to an existence which, whether it be as of 1 picosecond (as with figuring particle trajectories) or 1 decade ago (as with estimating climatic and geological trends), or even 10 years ago (the time period between U.S. national censuses), in effect placing at least one degree of separation between past and present.

“Oh, but technology and computers and AI…”

(Too) many acolytic children of the ‘new world’ are keen on attempting to shut down this entire discourse with so-called assurances, ones which are lacking in their veracity; assurances that modern technology will solve the problem of the limits of perception upon one lucky compute cycle, or perhaps in response to a thought-provoking AI prompt which, despite all odds, proclaims to have thoroughly unstrung the proverbial Gordian’s knot lying somewhere in between ‘all’ and ‘nothing.’ Foremost, it needs to be said that, once humans begin to rely upon LLMs (large language models) for finding guidance towards eudaimonia must also be when the pursuit of wisdom might just as well be pronounced dead. (Employing an intelligence to supplant humans in their foremost purpose as tools–contemplative reasoning–seems like it would be no less wasteful than tasking middle-schoolers with performing the maths operations needed to manage an Excel spreadsheet; it runs contrary to our intended purpose, as I’m sure any peripetitic thinker would agree.) (Grk. peripatetikos means ‘to walk around,’ from peri (around) + patein (walk); a name used in reference to Aristotle’s school of thought. It is thought to be named after Aristotle himself, who was known to pace around whilst lecturing.)

In the defense of our physical inability to “seize the moment,” as afforded by the linear passage of time, there exists truly nothing which may be percieved in the very same moment as it is brought to form. The very instance of the ‘privation’ of that exact form is what then instigates the chemical reactions that materialize the change, which itself is delayed in terms of its perception on behalf of the senses, and then the transmission of neurons firing in the human brain (which itself is distanced by the travel of neurons from the brainstem all the way to the prefontal cortex). And though material phenomena are not quite sporadic enough to completely evade this sequence, but still unruly enough to continue changing anyway, their values can hardly be used to compute its portion amongst all of perceptable nature as it existed then. Instead, they would merely simulate a non-existant material change occurring within the current state of perceptable nature, which itself may have been affected by the last change so as to skew the accuracy of any such analysis, all due to even the slighest of variation to the control (that being the otherwise-percieved variables of the change’s surrounding nature). You would have to know all of the variables which exist so as to obtain them at once (for the sake of argument we will ignore the time spent between each operation of a computer processor per compute cycle), and since that, as previously stated, there is no such ‘magic number,’ even your efficient computing routine becomes tainted by time passages.

So, computers are simply not physically capable of using all of their mathematical ingenuity in order to beat time passages, but they are at least capable of periodically recording the same value over time in order to reflect its change. This is fine and well for most statistical analyses, in which the numerical values are more used to present observable trends in graph form, and the values may very well be useful in relation to such an endeavor, however they may still not be equivocated with any individual values that exist as true only within its extant variables, because of the lack of any standard logical process, or a way to absolutely transform the whole logic of its own dimension into that of the perceptable one. Regardless, the limits of perception, contrary to widely-held beliefs, are not inherently determined by an animal’s sensory configuration or capacity for perception, nor are they confined to the laws of electricity. It is still purported that quantum computing may one day be capable of using superposition (with a multi-qubit system) and this could in fact solve the matter of operations being displaced by their processed sequence, but is definitely incapable of obtaining values using non-existant variables or otherwise plugging in said difference without employing a complex algorithm which, once again, must be able to communicate the entirety of its logical constructs using a non-abstract vehicle (one that, unlike the syntaxes of complex maths, is entirely devoid of any real-world permanence) for there to even be a chance at disproving Kant and his Critique of Metaphysics.