~ The Study of Threes ~
http://threesology.org
Visitors as of August 8th, 2022
| Page 1 | Page 2 | Page 3 | Page 4 | Page 5 |
| Page 6 | Page 7 | Page 8 | Page 9 | Page 10 |
| Page 11 | Page 12 | Page 13 | Page 14 | Page 15 |
| Page 16 | Page 17 | Page 18 | Page 19 | Page 20 |
Many of us have encountered one or another phrase representing the idea that Mathematics is Queen of the Sciences. However, I am of the opinion that in order for us to fully appreciate the need to pursue a different model of conceptualization which supersedes present day Mathematics, it is necessary for us to accept the idea that Mathematics is due for a revolution by being revised from its "Queen of all Sciences" status to a position perhaps best described as a pretentious "skilled peasant". It is a peasant who acts much like a person who is fast at reconfiguring a Rubik's Cube to portray a desired portrait of colored squares in a typical arrangement, whereas other configurations (perhaps because they are more difficult), are not being exercised as a sought-after achievement to be accomplished. Alternatively, we might describe it as someone who has a large following of interested practitioners (at different levels and with different interests) who value the game of chess, or poker, or billiards, or martial arts exhibition, or engine tuning, or cooking, etc.., all of which have their own "Axioms" and "Orders of Operation" (rules of play, parameters, and allowances for exploration beyond convention).
Whereas some view Mathematic's as a (or in some cases "THE") backpack of tools essential for exploring into the unknown (if not viewed more specifically as a type of survival kit with or without some St. Bernard's flask and Swiss Army knife); it is not typically viewed in terms of being equated with a leather pouch that some intrepid ancient wanderer may have carried— along with a spear, bow/arrows, flint, etc... In other words it is not thought of in terms of being a collection of crude implements, however skillful the wanderer may be in the usage thereof. While one or another wanderer may think in terms of some imagined improvement for one or another implement thought to be a standard tool of necessity during their era, such considerations are not necessarily commonplace amongst many present day researchers wanting to explore a given subject's boundaries of known considerations, in order to venture into the unknown. They may see Mathematics and its accepted rules as an inviolable standard screw driver ("tweeking" tool) and pair of pliers (like having increased jaw strength and teeth with which to bite and chew on a morsel of thought); but never view their particular usage of this dichotomy in terms of practicing a Functional Fixedness or that it is a set of blinders; and thus metaphorically referring to a person's narrowness of vision, so often seen in religion, but is a cognitive standard amongst many professionals and lay persons in all subjects.
For those of us whose brain is not wired (or let us say born with or taught) to be configured schematically to achieve some appreciable visionary capability to trek along the almost numinous-like vestiges of Pure Mathematic's wanderings into landscapes not realized by those pedestrian common senses primarily interested in the commercialized peculiarities of hand-to-mouth practicalities; it is necessary for us to suggest that in some respects, Mathematicians give the impression of engaging in the exploits of Don Quixote. Yet, Pure Mathematics aside, Mathematics (by way of a trial-and-effort concourse traveled on by multiple people over several centuries), has been proven time and again to provide a means by which to provide assistance in both practical matters and unravel ideas for further consideration that conventional means of experimentation do not offer (perhaps because the general mental framework of most experimenters lack the necessary type of imagination), whereas Mathematics provides the necessary arguments for allowing alternative approaches which current types of experimental equipment act as constraints to excursions into the realms of the once-thought unimaginable, frequently buttressed by a lack of a philosophical basis for being adventuress, and an associated deficiency in theological underpinnings (most often described in dualities such as the common god/no god view). Hence, present theological perspectives can be viewed as a monastery which treats its members as indentured servants forced to abide by an antiquated view of the sacred and reacts to alternative considerations as if they were a threat that the Monastery must protect itself from by shutting its doors and windows, while keeping open its practiced ideology which has conditioned it membership to exercise rituals in which internally owned steps may be taken to gain a proposed greater insight awaiting the worthy in some tower with windows facing the rising and setting Sun to which they are socially expected to pay homage to, and not remember that the practice originated from a distant pagan ceremony. Theology is in crisis because The Axioms of Religion were created by those who expected all future generations to be as dim-witted, dull-minded and delusional as they were.
Summed up, the old analogies of using the terms "father" and "mother" and "children" when referring to God, a given Religious figure, and the general public, (superseding the old analogies of Shepard and flock); are mental conventions of an out-dated intellectual era in which there was widespread illiteracy (notwithstanding current views that the public remains highly ignorant, irrational and predisposed to illogicalities), along with poor nutrition and medical treatment (despite current costs and the many obstacles to nutritious food and good medical care). For example, the old reference of "Mother Earth" and its associated philosophies which support views looking towards way of protecting it, has become replaced with the idea that such beliefs are to be addressed with the view that the umbilical cord between Earth and Humanity needs to be severed, because like all human mothers, the Earth too is on an incremental path of deterioration and death. Humanity must kick itself out of the nest, den and troop, to begin life anew. Similarly, humanity must seek to severe its dependency on the present models of mathematics in order to remove its imperialist-like occupations throughout the world's subjects.
Interestingly, the idea about a subject holding the rank of "Queen" differs amongst respective partitioners. In other words, partitioners of other subjects have also referred to their preference as Queen. If the title of "Queen" is not used, then one might find the word "mother" such as in the notion of "Motherland" or "Mother Earth", though others prefer to say "Fatherland". It should be of interest to note we don't have titles like "brotherland, sisterland, uncleland, auntland", etc... However, instead of referring to a large spaceship as the "mother ship", it is not altogether uncommon for the occasional usage of the term "granddaddy". But it may be uncommon for some to equate "supreme commander" with "god commander" or "king commander". In other words, such phrases and the lack of other phrases provides a tell-tale sign of human cognitive parameters for certain contexts. Although the "axioms" for one context may be transferable to other subjects if one would take the time to think about it and make allowances for differences in terminology, the fact that such a consideration is not a common activity may suggest an impediment to the present model of conceptualization humanity is using due to the overlapping traits of activity required by a global economy of interaction.
- Mathematics is Queen: Carl Friedrich Gauss ("Mathematics is the queen of the sciences and number theory is the queen of mathematics.") He Gauss has been referred to as the Prince of Mathematics.
- Theology is Queen: Thomas Aquinas Thomas Aquinas described theology as the queen of science in his great work Summa Theologica written between 1265 and 1274.
- Philosophy is Queen:
Immanuel Kant
Philosophy (actually, metaphysics), declared Immanuel Kant, is “the Queen of the Sciences.” And, indeed, for many centuries philosophy was the mother of virtually all disciplines. There was little distinction between philosophy and psychology, and even the “hard” sciences of physics and chemistry were part of “natural philosophy.” René Descartes wrote authoritatively about the neuroscience of his time, and John Locke was one among many philosophers who explored the anatomy and physiology of the sense organs. The idea of “bridge building” back then would have been all but unintelligible. There were no islands, no disciplines, and there was little “specialization” where the study of human nature was concerned.
Curiously, we don't routinely come across the idea that Chess is the Queen of all board games. Or perhaps you might prefer some other board game is Chess based on some other value such as number of players in the word, how many board games are sold, world recognition suggesting importance, etc... And if someone should ask you to name the Queen of sports, which one would you be inclined to consider as deserving of such a title? Or transfer the title of "King of Rock and Roll" from Elvis Presley to some singer and/or musical performer living today? Or how about the Queen of Rock and Roll, or the Queen of Opera, or the Queen of Jazz, etc... It all depends on which performer is either seen as a preacher or god-like figure, and to which (religion-like) music a person prefers to attend at concerts and pay tithing in the form of music and memorabilia sales.
Those in religion may seek to argue that all subjects are a representation of their beliefs which are routinely attached with a Universal tag called "god". Likewise, those who favour mathematics may seek to argue that all subjects are a representation of their views which are routinely attached with a Universal tag called "number". Similarly, we may well find instances in which a person defines all subjects in accord with their philosophy which is routinely attached with a Universal tag such as "singularity", "duality", "triplicity", quadrilicity, quinticity, etc... Singular items are said to have a dual state and triplistic (or more) groups are said to be elaborations, complements, confluences, or other fused conditions of the dual state. Some arguments have a much better representation than others, and those less versed in different topics may well find themselves succumbing to another's persuasiveness. Others come to believe in their own rationalizations and support any subject that has a large following.
Before the plane was developed, the idea that many might be able to fly like a bird or some insect... or even some cloud had to be generated as a consideration of possibility before such an ability became a reality. The same goes for the development of a new type of Mathematics exceeding our present standards, no matter how different ideas have become attached with the symbols and Wikipedia: Language of Mathematics, as if in so doing one's ideas are automatically endowed with a reputation of uniqueness and sophistication. Take an idea and attach to it the presumed logic of some mathematical genre of exploration and one's subject of interest becomes automatically transformed from an ugly duckling to a beautiful art piece which requires a particular ability of appreciation in order to fully grasp its true essence of cognitive entanglements previously described as weird, nonsense, or some other tagged disparagement before being associated with mathematics. Indeed, when one reaches a supposed philosophical dead end in their contemplations of a particular subject, they need only begin to adopt an association with mathematics to re-inflame embers thought to be dying out.
Like any language, the so-called language of Mathematics is very much context dependent aligned with a person's vocabulary. The language of Mathematics is not concise, precise nor unambiguous in contrast to the opening definition in the foregoing Wikipedia link: "The language of mathematics or mathematical language is an extension of the natural language (for example English) that is used in mathematics and in science for expressing results (scientific laws, theorems, proofs, logical deductions, etc) with concision, precision and unambiguity." Often times, just like in any language, expressions in Mathematics can be viewed as both specific and general. Just because there is a similar meaning derived amongst several context applications does not make a given Mathematical statement concise, precise and unambiguous. Like the idea that one picture is worth a thousand words, so too can this be flipped around to say that one word is worth a thousand pictures... depending on person and context. Just because a Mathematician focuses on the statement 1 + 1 = 2 and proposes it as a Universal concept, does not mean that everyone should or must adopt this perspective as an immutable idea since it has been transformed to be read as 1 + 1 = 3 when a pregnant woman is counted along with her mate. In other words, there is some ambiguity in the basic equation when one detaches it from the human ego's insistence of declaring an absolute for the purposes of projecting some purity... some truth.
A context dependency with respect to language investigated by linguistics— which does not... or at least has not shown itself to take an extended look at Mathematics with the same level of scrutiny it has participated in when analyzing the world's languages and unveiling basic patterns such as the dualities of noun/pronouns, verb/adverb, Antonyms/Synonyms, periods/question marks (viewing exclamations as emphasized periods), consonants/vowels, as well as three-patterned indices such as SOV (Subject- Object- Verb) word order, tenses (ring-rang-rung), genders (masculine- feminine- neuter), etc...
The Wikipedia article on the Language of Mathematics is hilariously naive, particularly noted in the list of features (which to me) exemplifies multiple aspects of ambiguity... but if your favor mathematics or have bought into the rhetoric of how Mathematics is portrayed as having some universal unimpeachable character; this view of ambiguity becomes erroneous since a person's personal involvement requires them to embrace Mathematics like some religious belief that demands its disciples a disciplined regime for practicing a faith where non-believers are referentially viewed in terms of being a heretic, infidel, ignoramus, blasphemer... or worse. The Mathematical Education process is like a step-wise initiation taking multiple years, with levels of accomplishing given tasks defined in terms of a Mathematics curriculum, with its own variety of golden fleece hunting, crusade involvement, and of course killing some dragon to win the fair maiden and become a knight/dame, prince/princess or king/queen in one's own right (even though the realm of Mathematics is frequently referred to as a "Queen-dom"). Instead of being called a Newbie, Neophyte, Novice or Apprentice, all are called students, with three later defining degreed entitlements called the Bachelor's, Master's, PhD. Take a look at the rather laughable list of so-called unambiguous, precise and concise definitions for defining the language of Mathematics:
- Use of common words with a derived meaning, generally more specific and more precise. For example, "or" means "one, the other or both", while, in common language, "both" is sometimes included and sometimes not. Also, a "line" is straight and has zero width.
- Use of common words with a meaning that is completely different from their common meaning. For example, a mathematical ring is not related to any other meaning of "ring". Real numbers and imaginary numbers are two sorts of numbers, none being more real or more imaginary than the others.
- Use of neologisms. For example polynomial, homomorphism.
- Use of symbols as words or phrases. For example, A = B and ∀x are respectively read as "A equals B" and "for all x".
- Use of formulas as part of sentences. For example: "e=Mc2 represents quantitatively the mass–energy equivalence." A formula that is not included in a sentence is generally meaningless, since the meaning of the symbols may depend on the context: in "e=Mc2", this is the context that specifies that e is the energy of a physical body, m is its mass, and c is the speed of light.
- Use of mathematical jargon that consists of phrases that are used for informal explanations or shorthands. For example, "killing" is often used in place of "replacing with zero", and this led to the use of assassinator and annihilator as technical words.
Since Mathematics is ambiguous at times, and no one yet has described which language is best for Mathematics (such as Japanese, Chinese, English, Latin, Italian, etc...), it is of value to note that the discussion of which language might be better for the development of mathematics. For example, this article touches upon this consideration: The New Language of Mathematics by Daniel S. Silver. Clearly, while the language of Mathematics may at times be described as a perfect language, the problem(s) lay in how the so-called perfect language is interpreted and retranslated.
The brain makes sense of math and language in different ways
Imagining some other possibility than the contemporary is an activity very often seen in the expressions of some journalists, movie producers, science fiction writers, politicians, advertisers, inventors, philosophers, career counselors, trainers, stock market speculators, lottery ticket buyers, sculptors, etc... Children and day-dreamers are sometimes cited as having this capacity, though few pursue some dream to create the non-ordinary, unless it is to project themselves into a social position of power, fortune, or fame. What they achieve in terms of their social position of accomplishments is the extent of their capacity to create something new, and not some new technology, medicine, or tool. Their vision is limited to some personal acquisition for themselves and perhaps their family, friends and colleagues, and not to create that which is focused on benefiting all of humanity. Their vision is one of selfishness and self-centeredness. However, history clearly reveals that the human mind is capable of novel ideas. A reference such as: How does our brain produce creative ideas? by Pronita Mehrotra, August 15, 2018, can be viewed as a generality, and is not meant to be a discussion about whether or not different subjects requires specific types of brain processing (other than respective symbols and vernacular) of a given topic such as mathematics. Is there a fundamental, underlying (universal) brain activity applicable to all subjects and can therefore be processed in a given subject area's corral of considerations from which a newer idea arises? Or do different original ideas have their own underlying fundamental patterning? Is it possible for a non-mathematician to create a novel form of mathematics, or even be able to provide a direction where such a creature may exist? It is truly unfortunate that when speaking of a transcendent model of Mathematics the trend is to latch onto ideas revolving around transcendental numbers and not such ideas as transcendental Calculus, transcendental Algebra, transcendental Trigonometry, etc... Since the word "transcendental" has become most frequently attached to the word "number", it advances the position much like religion which attaches to itself words like god, morality, heaven, etc., whereby the common inclination is for considerations not to traverse beyond such notions. A type of functional fixedness takes place in terms of cognitive biases. Mathematics reeks of cognitive biases... despite working quite well with such biases.
It should go without saying that all novel ideas are born out of some philosophy, but that philosophical inquiry which remains in the arena of philosophy is not helpful. Everyday ideas can be used to transform a subject only if the ideas are mixed and matched in the barnyard of creatures which a creative thinker may frequently tinker with experimental cognitive overlays. While the novel word "mathematics" is said to be derived from the ancient Greeks (What is mathematics? by Elaine J. Hom & Jonathan Gordon, November 11, 2021), knowing what other ancient cultures called their mathematics (however crude or applied), would be helpful in deciphering cognitive processing for the rudimentary beginnings of the craft. Using the phrase "that which is learnt" to define the word "mathematics" may seem silly by today's interpretation of the phrase since so many non-mathematical subjects are learned. Either the translation of the word "mathematics" is wrong or how we of today would decipher the meaning of the phrase meant to be interpreted differently in an ancient context, or the mathematicians of the past were not particularly bright in the coining of a word for their number-related activities.
Let us take a look at how a few words related to Mathematics are defined in terms of origination:
- Mathematics: (Greek) "that which is learnt"
- Algebra: (Arabic) "reunion of broken parts"
- Calculus (Latin) "small pebble"
- Geometry (Greek) "to measure earth"
- Trigonometry (Greek) "triangle a- measure"
- Arithmetic (Greek) "number"
- Algorithm: (Arabic) (derived from a mathematician's name: Muhammad ibn Musa al-Khwarizmi)
- Logarithm: Formed from New Latin, logarithm adds to the Greek noun arithmos the prefix log- ("word, thought, speech, discourse"), from the Greek noun logos.)
- Number: c. 1300, "sum, aggregate of a collection," from Anglo-French noumbre, Old French nombre and directly from Latin numerus "a number, quantity," from PIE root *nem- "assign, allot; take."
- Addition: comes from the Old French word addition, meaning "that which is added."
- Multiply: mid-12c., multeplien, "to cause to become many, cause to increase in number or quantity," from Old French multiplier, mouteplier (12c.) "increase, get bigger; flourish; breed; extend, enrich," from Latin multiplicare "to increase," from multiplex (genitive multiplicis) "having many folds, many times as great in number," from combining form of multus "much, many" (see multi-) + -plex "-fold," from PIE root *plek- "to plait."
It would be interesting to know what word or phrase (or gesture) early humans in their rudimentary attempts to develop a number system came to call their activity. Describing a word for a number is one thing, but describing what the word means in general terms is another. It is also of some interest to the study of cognitive development to make a reference to the origin of symbols, for example those of division and multiplication: (Discover the Origins of Division and Multiplication. If one was not familiar with the use of symbols for mathematics and saw them individually or collectively laying about such as on a telephone doodling pad, an artist viewing them might use them as a design for pottery. And just like artistic symbols used on arts and crafts, we see similar patterning of repetition in Mathematics, as if a chalk board or piece of paper (or ancient clay tablet) were the side of a pottery bowl being ingrained (from one side to the other) with repetition, as if "to balance an equation" for the sake of some unrecognized attempt to create symmetry.
But the question about whether a new Mathematics can be created is not a new one. Here is one example:
How do scientists and mathematicians create new mathematics for describing concepts? What is new mathematics? Is it necessarily in format of previous mathematics? Can one person make (invent or discover) a mathematics such that it isn't in format of geometry or algebra or analysis that we know?
Of course I know we can define a new meter and have a new geometry, or define a new n-ary operation and have a new algebra, etc. But can we create a new mathematics that is not like that?
In fact my question is this: when a scientist (in particular, a physicist), tries to create a mathematical theory for a concept, how does he/she do it? May he/she invent a new mathematics that is not in format of previous available mathematics at all? (i.e it wasn't geometry or algebra or analysis, etc.)
I think the answer is absolutely! Of course it depends who you ask. But, I definitely believe a new type of maths can be created in a format not previously available. – MathGuy; May 9, 2017 at 19:27
@TyeCampbell Thanks. But how? I think when a person would to create a mathematical theory for a concept, he see the previous mathematics and modeling the concept. May he define a new meter or operation. But all of this works is in format of previous mathematics. Is there an example such that one person create a new mathematics? – S Ali Mousavi; May 9, 2017 at 19:36
It really depends what you define by new mathematics,one could argue that no new math was born after ancient Greeks or babylonians etc. Do you consider complex analysis new? How about topology? Those are all new concepts. – kingW3; May 9, 2017 at 19:39
Sometimes, new mathematics is made for a tool to solve an existing problem, like for example the Grothendieck ring of varieties. – Simon Marynissen; May 9, 2017 at 19:39
@SAliMousavi it certainly takes some creativity, but I believe it can be done. How do you believe that the maths we all know and love today came to be? Some very creative minds! As for how... if I knew the answer to that question, I would have a lot more money and be a lot more famous!! – MathGuy; May 9, 2017 at 19:48
I've never heard of a new field of mathematics being created with no connections to known fields. Sometimes very innovative concepts arise that might at first seem to have very little to do with previous work - graph theory or group theory, for example. But it soon becomes apparent that there are many deep connections between the new fields and the old. – Jair Taylor; May 9, 2017 at 20:25
As an illustrative example, Leonhard Euler created graph theory by trying to solve a puzzle about the seven bridges of Königsberg. As he said, "This question is so banal, but seemed to me worthy of attention in that [neither] geometry, nor algebra, nor even the art of counting was sufficient to solve it." – user856: May 9, 2017 at 20:33
The old saying "Those who cannot remember the past are condemned to repeat it." by George Santayana, The Life of Reason, 1905., might well be applied to mathematics and not just sociological or political themes. It is therefore more troublesome to consider whether or not repetition of the old math ideas is made due to the position in which the past of Mathematics is not well known or not known correctly, or not know at all. Advancing Mathematics might require some type of mutagenic biological development or punctuated equilibrium process (in the brain) because a conscious intent is kept enslaved to repeating past activities due to the institutionalization of Mathematics. While some say that we know the past of Mathematics well, I think we have remembered it wrongly... such as over-looking at how much dichotomization plays a role.
But how do we define a progressive idea if it is like viewing it as an ant colony whose "progress" is defined in terms of increased size and a multiplication of the same activities taking place on a smaller scale?
It is necessary for us to imagine the existence of a super-normal type of mathematics whatever it may eventually be called (I have playfully labeled as an "Accordian (Dynamic) Calculus"); in order for us to focus our cognitive attention(s) in such a direction; either part-time, half-time or full-time. We humans need to be able to acknowledge that such a creature exists before we can begin thinking about undertaking further observations and possible entrapment for the sake of study and some margin of domestication; though some minds may have already been contemplating some sort of related hint, but do not have a distinction of what it is or what it can be— as one scrambles to displace some of the junk in our thoughts which have come attached to it in our mental excursions executed from one day or moment to the next. There may be many who see such a territory of cognitive ability unfolding within themselves, but do not have a coherent box in which to place it because of the words being employed or the context to which the ideas may arise... most of which may not be related to Mathematics because it is a subject not familiarly being practiced. However, if one lets a given subject restrict one's thoughts within the parameters of a subject whose culturally embedded ideas act as a constraint or distraction, then regards of one's ability to achieve a possible clarity beyond the customary; they are limited towards developing such a perceptual cognitivity into complying with accepted parameters of thought governed by the vocabulary of a subject whose standard usage is a repetition of a reduced coherence... a reduced sobriety, a reduced sanity of the possible.
I frequently encounter ideas which may speak of a dominant duality concept, yet imply the existence of a developed or deve-loping triplicity... which is reminiscent of ancient peoples in their cognitive development of enumeration getting hung up on a "2 versus 3" or a "2 becoming 3", where anything beyond a two is plural or many... etc., Whereas they acknowledge the distinction, the distinction becomes become reflected on with such frequency, the mirror-imaging effect is the practice of yet another duality having become embellished. Here is one such example: Laws of Form by George Spencer Brown, Cognizerco. 1994
Date of Origination: 30th August 2022... 5:01 AM
Date of Initial Posting: 10th September 2022... 5:56 AM
Updated Posting: 2nd January 2023... 11:08 AM