Results 1 to 10 of 10

Thread: Why is Mathematics So Successful?

  1. #1
    Funding Member
    "Friend of Germanics"
    Skadi Funding Member

    Nachtengel's Avatar
    Join Date
    Jul 2008
    Last Online
    @
    Ethnicity
    German
    Gender
    Posts
    5,904
    Thanks Thanks Given 
    94
    Thanks Thanks Received 
    751
    Thanked in
    414 Posts

    Why is Mathematics So Successful?

    Sam Vaknin, Ph.D. - 4/16/2010

    In earlier epochs, people used myths and religious narratives to encode all knowledge, even of a scientific and technological character. Words and sentences are still widely deployed in many branches of the Humanities, the encroachment of mathematical modeling and statistics notwithstanding. Yet, mathematics reigns supreme and unchallenged in the natural sciences. Why is that? What has catapulted mathematics (as distinct from traditional logic) to this august position within three centuries?

    Mathematics is a language like no other. Still, it suffers from the drawbacks that afflict other languages. The structure of our language, its inter-relatedness with the world, and its inherent limitations dictate our worldview and determine how we understand, describe and explain Nature and our place in it. Granted, languages are living things and develop constantly (consider slang, or the emergence of infinite numbers theories in mathematics). But, they evolve within a formal grammar and syntax, a logic, a straitjacket that inhibits thinking "outside the box" and renders impossible the faithful perception of "objective" reality.

    So, what made mathematics so different and so triumphant?

    1. It is a universal, portable, immediately accessible language that requires no translation. Idealists would say that it is intersubjectively shared. This may be because, as Kant and others have suggested, mathematics somehow relates to or is derived from a-priori structures embedded in the human mind.

    2. It provides high information density, akin to stenography. Just a few symbols arranged in formulas and equations account for a wealth of experiences and encapsulate numerous observations. Mathematical concepts and symbols do not correspond to material objects or cause them, nor do they alter reality or affect it in any way, shape, or form. One cannot map a mathematical structure or construct or number or concept into the observed universe. This is because mathematics is not confined to describing what is, or what is necessarily so - it also limns what is possible, or provable.

    3. Mathematics deals with patterns and laws. It can, therefore, yield predictions. Mathematics deals with forms and structures: some of these are in the material world, others merely in the mind of the mathematician.

    4. Mathematics is a flexible, "open-source", responsive, and expandable language. Consider, for instance, how the introduction of the concept of the infinite and of infinite numbers was accommodated with relative ease despite the controversy and the threat this posed to the very foundations of traditional mathematics - or how mathematics ably progressed to deal with fuzziness and uncertainty.

    5. Despite its aforementioned transigence, mathematics is invariant. A mathematical advance, regardless of how arcane or revolutionary, is instantly recognizable as such and can be flawlessly incorporated in the extant body of knowledge. Thus, the fluidity of mathematics does not come at the expense of its coherence and nature.

    6. There is a widespread intuition or perception that mathematics is certain because it deals with a-priori knowledge and necessary truths (either objective and "out there", or mental, in the mind) and because it is aesthetic (like the mind of the Creator, the religious would add).

    7. Finally, mathematics is useful: it works. It underlies modern science and technology unerringly and unfailingly. In time, all branches of mathematics, however obscure, prove to possess practical applications.

    Still, the conundrum remains: what are mathematical objects? Do they "really" exist (the Platonic view), or are they mental figments?
    Knives and forks are objects external to us. They have an objective - or at least an intersubjective - existence. Presumably, they will be there even if no one watches or uses them ever again. We can safely call them "Objective Entities".

    Our emotions and thoughts can be communicated - but they are NOT the communication itself or its contents. They are "Subjective Entities", internal, dependent upon our existence as observers.

    But what about numbers? The number one, for instance, has no objective, observer-independent status. I am not referring to the number one as adjective, as in "one apple". I am referring to it as a stand-alone entity. As an entity it seems to stand alone in some way (it's out there), yet be subjective in other ways (dependent upon observers). Numbers belong to a third category: "Bestowed Entities". These are entities whose existence is bestowed upon them by social agreement between conscious agents.

    But this definition is so wide that it might well be useless. Religion and money are two examples of entities which owe their existence to a social agreement between conscious entities - yet they don't strike us as universal and out there (objective) as numbers do.

    Indeed, this distinction is pertinent and our definition should be refined accordingly.

    We must distinguish "Social Entities" (like money or religion) from "Bestowed Entities". Social Entities are not universal, they are dependent on the society, culture and period that gave them birth. In contrast, numbers are Platonic ideas which come into existence through an act of conscious agreement between ALL the agents capable of reaching such an accord. While conscious agents can argue about the value of money (i.e., about its attributes) and about the existence of God - no rational, conscious agent can have an argument regarding the number one.

    Apparently, the category of bestowed entities is free from the eternal dichotomy of internal versus external. It is both and comfortably so. But this is only an illusion. The dichotomy does persist. The bestowed entity is internal to the group of consenting conscious-rational agents - but it is external to any single agent (individual).

    In other words, a group of rational conscious agents is certain to bestow existence on the number one. But to each and every member in the group the number one is external. It is through the power of the GROUP that existence is bestowed. From the individual's point of view, this existence emanates from outside him (from the group) and, therefore, is external. Existence is bestowed by changing the frame of reference (from individual to group).

    But this is precisely how we attribute meaning to something!!! We change our frame of reference and meaning emerges. The death of the soldier is meaningful from the point of view of the state and the rituals of the church are meaningful from the point of view of God. By shifting among frames of reference, we elicit and extract and derive meaning.

    If we bestow existence and derive meaning using the same mental (cognitive) mechanism, does this mean that the two processes are one and the same? Perhaps bestowing existence is a fancy term for the more prosaic attribution of meaning? Perhaps we give meaning to a number and thereby bestow existence upon it? Perhaps the number's existence is only its meaning and no more?

    If so, all bestowed entities must be meaning-full. In other words: all of them must depend for their existence on observers (rational-conscious agents). In such a scenario, if all humans were to disappear (as well as all other intelligent observers), numbers would cease to exist.

    Intuitively, we know this is not true. To prove that it is untrue is, however, difficult. Still, numbers are acknowledged to have an independent, universal quality. Their existence does depend on intelligent observers in agreement. But they exist as potentialities, as Platonic ideas, as tendencies. They materialize through the agreement of intelligent agents rather the same way that ectoplasm was supposed to have materialized through spiritualist mediums. The agreement of the group is the CHANNEL through which numbers (and other bestowed entities, such as the laws of physics) are materialized, come into being.

    We are creators. In creation, one derives the new from the old. There are laws of conservation that all entities, no matter how supreme, are subject to. We can rearrange, redefine, recombine physical and other substrates. But we cannot create substrates ex nihilo. Thus, everything MUST exist one way or another before we allow it existence as we define it. This rule equally applies bestowed entities.

    BUT

    Wherever humans are involved, springs the eternal dichotomy of internal and external. Art makes use of a physical substrate but it succumbs to external laws of interpretation and thus derives its meaning (its existence as ART). The physical world, in contrast (similar to computer programmes) contains both the substrate and the operational procedures to be applied, also known as the laws of nature.

    This is the source of the conceptual confusion. In creating, we materialize that which is already there, we give it venue and allow it expression. But we are also forever bound to the dichotomy of internal and external: a HUMAN dichotomy which has to do with our false position as observers and with our ability to introspect. So, we mistakenly confuse the two issues by applying this dichotomy where it does not belong.

    When we bestow existence upon a number it is not that the number is external to us and we internalize it or that it is internal and we merely externalize it. It is both external and internal. By bestowing existence upon it, we merely recognize it. In other words, it cannot be that, through interaction with us, the number changes its nature (from external to internal or the converse).

    By merely realizing something and acknowledging this newfound knowledge, we do not change its nature. This is why meaning has nothing to do with existence, bestowed or not. Meaning is a human category. It is the name we give to the cognitive experience of shifting frames of reference. It has nothing to do with entities, only with us.

    The world has no internal and external to it. Only we do. And when we bestow existence upon a number we only acknowledge its existence. It exists either as neural networks in our brains, or as some other entity (Platonic Idea). But, it exists and no amount of interactions with us, humans, is ever going to change this.
    http://www.globalpolitician.com/2636...c-science-mind

  2. The Following User Says Thank You to Nachtengel For This Useful Post:


  3. #2
    Senior Member
    Join Date
    Jul 2018
    Last Online
    8 Hours Ago @ 10:23 PM
    Ethnicity
    Celto-Germanic
    Ancestry
    Irish, Scottish
    Country
    United Kingdom United Kingdom
    Location
    North Ireland
    Gender
    Family
    Married
    Politics
    National Socialist
    Religion
    Ethnic Catholic
    Posts
    1,306
    Thanks Thanks Given 
    1,476
    Thanks Thanks Received 
    1,577
    Thanked in
    851 Posts

    Names of Polygons.


    Naming POLYGONS - 2 D closed shapes - they don't have to be regular.

    The word polygon comes from Late Latin polygōnum (a noun), from Greek πολύγωνον (polygōnon/polugōnon), noun use of neuter of πολύγωνος (polygōnos/polugōnos, the masculine adjective), meaning "many-angled". Individual polygons are named (and sometimes classified) according to the number of sides, combining a Greek-derived numerical prefix with the suffix -gon, e.g. pentagon, dodecagon. The triangle, quadrilateral and nonagon are exceptions.


    Beyond decagons (10-sided) and dodecagons (12-sided), mathematicians generally use numerical notation, for example 17-gon and 257-gon.[12]
    Exceptions exist for side counts that are more easily expressed in verbal form (e.g. 20 and 30), or are used by non-mathematicians. Some special polygons also have their own names; for example the regularstarpentagon is also known as the pentagram.

    Name Edges Properties
    monogon 1 Not generally recognised as a polygon,[13] although some disciplines such as graph theory sometimes use the term.[14]
    digon 2 Not generally recognised as a polygon in the Euclidean plane, although it can exist as a spherical polygon.[15]
    triangle (or trigon) 3 The simplest polygon which can exist in the Euclidean plane. Can tile the plane.
    quadrilateral (or tetragon) 4 The simplest polygon which can cross itself; the simplest polygon which can be concave; the simplest polygon which can be non-cyclic. Can tile the plane.
    pentagon 5 [16] The simplest polygon which can exist as a regular star. A star pentagon is known as a pentagram or pentacle.
    hexagon 6 [16] Can tile the plane.
    heptagon (or septagon) 7 [16] The simplest polygon such that the regular form is not constructible with compass and straightedge. However, it can be constructed using a Neusis construction.
    octagon 8 [16]
    nonagon (or enneagon) 9 [16]"Nonagon" mixes Latin [novem = 9] with Greek, "enneagon" is pure Greek.
    decagon 10 [16]
    hendecagon (or undecagon) 11 [16] The simplest polygon such that the regular form cannot be constructed with compass, straightedge, and angle trisector.
    dodecagon (or duodecagon) 12 [16]
    tridecagon (or triskaidecagon) 13 [16]
    tetradecagon (or tetrakaidecagon) 14 [16]
    pentadecagon (or pentakaidecagon) 15 [16]
    hexadecagon (or hexakaidecagon) 16 [16]
    heptadecagon (or heptakaidecagon) 17 Constructible polygon[12]
    octadecagon (or octakaidecagon) 18 [16]
    enneadecagon (or enneakaidecagon) 19 [16]
    icosagon 20 [16]
    icositetragon (or icosikaitetragon) 24 [16]
    triacontagon 30 [16]
    tetracontagon (or tessaracontagon) 40 [16][17]
    pentacontagon (or pentecontagon) 50 [16][17]
    hexacontagon (or hexecontagon) 60 [16][17]
    heptacontagon (or hebdomecontagon) 70 [16][17]
    octacontagon (or ogdoëcontagon) 80 [16][17]
    enneacontagon(or enenecontagon) 90 [16][17]
    hectogon (or hecatontagon)[18] 100 [16]
    257-gon 257 Constructible polygon[12]
    chiliagon 1000 Philosophers including René Descartes,[19] Immanuel Kant,[20] David Hume,[21] have used the chiliagon as an example in discussions.
    myriagon 10,000 Used as an example in some philosophical discussions, for example in Descartes' Meditations on First Philosophy
    65537-gon 65,537 Constructible polygon[12]
    megagon[22][23][24] 1,000,000 As with René Descartes' example of the chiliagon, the million-sided polygon has been used as an illustration of a well-defined concept that cannot be visualised.[25][26][27][28][29][30][31] The megagon is also used as an illustration of the convergence of regular polygons to a circle.[32]
    apeirogon A degenerate polygon of infinitely many sides.



    Constructing higher names


    To construct the name of a polygon with more than 20 and less than 100 edges, combine the prefixes as follows.[16] The "kai" term applies to 13-gons and higher and was used by Kepler, and advocated by John H. Conway for clarity to concatenated prefix numbers in the naming of quasiregular polyhedra.[18]


    Tens and Ones final suffix
    -kai- 1 -hena- -gon
    20 icosi- (icosa- when alone) 2 -di-
    30 triaconta- (or triconta-) 3 -tri-
    40 tetraconta- (or tessaraconta-) 4 -tetra-
    50 pentaconta- (or penteconta-) 5 -penta-
    60 hexaconta- (or hexeconta-) 6 -hexa-
    70 heptaconta- (or hebdomeconta-) 7 -hepta-
    80 octaconta- (or ogdoëconta-) 8 -octa-
    90 enneaconta- (or eneneconta-) 9 -ennea-


    History


    Historical image of polygons (1699)

    Polygons have been known since ancient times. The regular polygons were known to the ancient Greeks, with the pentagram, a non-convex regular polygon (star polygon), appearing as early as the 7th century B.C. on a krater by Aristophanes, found at Caere and now in the Capitoline Museum.[33][34]




    In nature


    Polygons appear in rock formations, most commonly as the flat facets of crystals, where the angles between the sides depend on the type of mineral from which the crystal is made.


    Regular hexagons can occur when the cooling of lava forms areas of tightly packed columns of basalt, which may be seen at the Giant's Causeway in Northern Ireland, or at the Devil's Postpile in California.


    In biology, the surface of the wax honeycomb made by bees is an array of hexagons, and the sides and base of each cell are also polygons.




    Polygon - Wikipedia 06 May 2019.





  4. The Following User Says Thank You to jagdmesser For This Useful Post:


  5. #3
    Senior Member
    Join Date
    Jul 2018
    Last Online
    8 Hours Ago @ 10:23 PM
    Ethnicity
    Celto-Germanic
    Ancestry
    Irish, Scottish
    Country
    United Kingdom United Kingdom
    Location
    North Ireland
    Gender
    Family
    Married
    Politics
    National Socialist
    Religion
    Ethnic Catholic
    Posts
    1,306
    Thanks Thanks Given 
    1,476
    Thanks Thanks Received 
    1,577
    Thanked in
    851 Posts
    Problem 8÷2(2+2) = ?



    It’s 1,” wrote one person.

    Another insisted: 16.


    There is also something called the BODMAS method, which stands for: “Brackets, Orders, Division, Multiplication, Addition, Subtraction.” Both explain the order of operations when trying to solve a math equation.

  6. #4
    Senior Member Mööv's Avatar
    Join Date
    Mar 2011
    Last Online
    2 Weeks Ago @ 04:34 PM
    Status
    Available
    Ethnicity
    German
    Ancestry
    Donauschwaben
    Subrace
    Keltic nordid/Alpinid
    State
    Danube Swabian Community Danube Swabian Community
    Location
    Wigrid
    Gender
    Age
    37
    Zodiac Sign
    Aquarius
    Family
    Single parent
    Occupation
    Mad scientist
    Politics
    Politically incorrect
    Religion
    Heathen
    Posts
    1,393
    Thanks Thanks Given 
    666
    Thanks Thanks Received 
    183
    Thanked in
    114 Posts
    Well, when given two consecutive operations of the same order one should evaluate them as they appear from left to right. So 16.
    Lieber tot als Sklave!

  7. #5
    Funding Member
    "Friend of Germanics"
    Skadi Funding Member

    Finnish Swede's Avatar
    Join Date
    Nov 2017
    Last Online
    @
    Ethnicity
    Finnish Swede
    Ancestry
    Father: Swedish, Mother Finnish Swede
    Subrace
    Sub-Nordid - Nordid - Baltid mix
    Country
    Other Other
    State
    Finland Swede Community Finland Swede Community
    Location
    Ostrobothnia
    Gender
    Age
    21
    Zodiac Sign
    Pisces
    Occupation
    Student
    Politics
    No specific ideology
    Religion
    Lutheran
    Posts
    1,738
    Thanks Thanks Given 
    374
    Thanks Thanks Received 
    2,433
    Thanked in
    1,339 Posts
    Quote Originally Posted by Mööv View Post
    Well, when given two consecutive operations of the same order one should evaluate them as they appear from left to right. So 16.
    Correct.

    Old times .... * and / have not always been equal operations => and the result would have been different.

  8. The Following 2 Users Say Thank You to Finnish Swede For This Useful Post:


  9. #6
    Senior Member Ravenrune's Avatar
    Join Date
    Sep 2018
    Last Online
    1 Week Ago @ 07:30 AM
    Ethnicity
    Anglo-Saxon-Celt
    Ancestry
    Irish, English, Scottish, German, French, Mi'kmaq
    Country
    Canada Canada
    Gender
    Zodiac Sign
    Scorpio
    Family
    Single adult
    Occupation
    maker of things
    Politics
    non-corruption for the people
    Religion
    Pantheism / Norse pagan / Taoism
    Posts
    535
    Thanks Thanks Given 
    76
    Thanks Thanks Received 
    587
    Thanked in
    295 Posts
    Mathematics is used in everything from all the sciences to carpentry, cooking, and every other kind of construction. Even when shopping for groceries I use math if I have a certain amount or can't go over a certain amount.

  10. The Following User Says Thank You to Ravenrune For This Useful Post:


  11. #7
    Grand Member
    Join Date
    Oct 2009
    Last Online
    1 Week Ago @ 04:26 AM
    Ethnicity
    English
    Ancestry
    English, Anglo-Saxon
    Country
    England England
    Location
    South Coast
    Gender
    Zodiac Sign
    Aries
    Family
    Married
    Occupation
    Self Employed
    Politics
    Free Speech / Anti-EU
    Religion
    Pagan
    Posts
    5,040
    Thanks Thanks Given 
    1,584
    Thanks Thanks Received 
    2,589
    Thanked in
    1,392 Posts
    I was once reading a book, I think it was about quantum physics, and the author claimed that there could be parts of the Universe where the laws of mathematics break down.

    I can't imagine how absurd existence would be, at least on a human level, in a place such as this.

  12. The Following User Says Thank You to SaxonPagan For This Useful Post:


  13. #8
    Senior Member Ravenrune's Avatar
    Join Date
    Sep 2018
    Last Online
    1 Week Ago @ 07:30 AM
    Ethnicity
    Anglo-Saxon-Celt
    Ancestry
    Irish, English, Scottish, German, French, Mi'kmaq
    Country
    Canada Canada
    Gender
    Zodiac Sign
    Scorpio
    Family
    Single adult
    Occupation
    maker of things
    Politics
    non-corruption for the people
    Religion
    Pantheism / Norse pagan / Taoism
    Posts
    535
    Thanks Thanks Given 
    76
    Thanks Thanks Received 
    587
    Thanked in
    295 Posts
    Quote Originally Posted by SaxonPagan View Post
    I was once reading a book, I think it was about quantum physics, and the author claimed that there could be parts of the Universe where the laws of mathematics break down.

    I can't imagine how absurd existence would be, at least on a human level, in a place such as this.

    Sometimes I find statements like that sound profound but really may be just someone making up some kind of vague statement to sound profound (I maybe I'm just dumb lol).


    There are supposedly some complex ideas in physics which only a few people even understand and so we mere mortals (including all the physicists who don't understand it) just have to take their word for it (like believing the priest astronomers of old ;-) ).

  14. The Following User Says Thank You to Ravenrune For This Useful Post:


  15. #9
    Grand Member
    Join Date
    Oct 2009
    Last Online
    1 Week Ago @ 04:26 AM
    Ethnicity
    English
    Ancestry
    English, Anglo-Saxon
    Country
    England England
    Location
    South Coast
    Gender
    Zodiac Sign
    Aries
    Family
    Married
    Occupation
    Self Employed
    Politics
    Free Speech / Anti-EU
    Religion
    Pagan
    Posts
    5,040
    Thanks Thanks Given 
    1,584
    Thanks Thanks Received 
    2,589
    Thanked in
    1,392 Posts
    I also came around to this view in the end.

    For us mere mortals, quantum physics (in its current state) leads nowhere but I do enjoy reading some of its philosophical implications.

    For example, who invented the laws of the Universe and why should time flow in a past --> present --> future direction? Is there a reason for this or is it just arbitrary, and if so are there places where the opposite is true

  16. The Following User Says Thank You to SaxonPagan For This Useful Post:


  17. #10
    aka Johan the Blind Goodman John's Avatar
    Join Date
    Jun 2019
    Last Online
    Friday, September 13th, 2019 @ 04:52 PM
    Status
    Available
    Ethnicity
    German
    Ancestry
    Germany, Scotland
    Country
    United States United States
    Gender
    Age
    56
    Family
    Married
    Occupation
    Hospital Administration
    Politics
    Generally Conservative
    Religion
    Cathar
    Posts
    147
    Thanks Thanks Given 
    31
    Thanks Thanks Received 
    92
    Thanked in
    62 Posts
    To paraphrase Richard Dawkins, "[Mathematics] is successful because it works, bitches"

Similar Threads

  1. Mathematics Is Essentially A European Accomplishment
    By Nachtengel in forum Research & Technology
    Replies: 0
    Last Post: Monday, October 2nd, 2017, 01:50 PM
  2. Replies: 10
    Last Post: Friday, December 19th, 2008, 11:32 AM
  3. Mathematics Is Racist!
    By Blutwölfin in forum Immigration & Multiculturalism
    Replies: 4
    Last Post: Thursday, March 16th, 2006, 04:26 PM
  4. Crowds and Mathematics
    By infoterror in forum Psychology, Behavior, & Neuroscience
    Replies: 4
    Last Post: Wednesday, January 26th, 2005, 02:50 AM

Bookmarks

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •