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"Martial Arts is the Maths of the Human Body"

  • 25-07-2005 4:47pm
    #1
    Registered Users, Registered Users 2 Posts: 673 ✭✭✭


    This is a quote i got from a general MA book and i thought it was very true. It was from a Chinese MA master, i cant remember who.

    What do you guys think?

    I think it can be called the "maths" rather than the "mechanics" or "physics" or other things because maths is purer and, a mathematician will tell you, nobler and more beautifull - like a good well-rounded MA. There is certainly an artistic beauty in many mathematical studies.

    All other sciences are dervived form maths and you could say that all other human physical interaction can be dreived form how Ma-ists study the human body. Movement, dexterity, the effect of the sub-concience, physiological health, aggression, timing, intuitive kinetics, phsucal skill etc etc. (Lets seperate the application of MA from MA just as a mathematician would seperate maths form the application - physics, chemistry, accounting, economics etc)

    So self-defence is just one application of MA, as is battle-field tactics, sports MA, aggression awareness, street-savvy etc. Does this ring true for any of you folks? I think its nice analogy.


Comments

  • Closed Accounts Posts: 334 ✭✭TwoKingMick


    It would be, but then an awful lot of MA logic equates to 1 + 1 = 3.


  • Closed Accounts Posts: 1,639 ✭✭✭john kavanagh


    a long long time ago we used to be a lot more active as a species...

    now we're not...

    which leads to unused adrenaline/energy

    which results in

    STRESS

    the healthiest way to deal with this imo is good healthy sport whether that be 'sport' martial arts, tennis, rugby etc etc

    healthy Physical Exercise keeps you in shape physically and mentally (as it requires you to constantly face your ego). i would have PE as analogous to Math in your example and then its different manifestations would be 'sport' martial arts, tennis, rugby etc etc as the applications


  • Registered Users, Registered Users 2 Posts: 5,335 ✭✭✭Cake Fiend


    It would be, but then an awful lot of MA logic equates to 1 + 1 = 3.

    And often the square root of -4.36.


  • Closed Accounts Posts: 4,487 ✭✭✭Kevin_rc_ie


    i think this martial arts is anything other than hitting people is rubbish. everybody that get's mad into something says what they do is the matematics of something. piano players say piano music is the mathematics of the soul or some rubbish.


  • Posts: 0 ✭✭✭ [Deleted User]


    Following the analogy...

    If mathematics is not used in the form of integral or differential calculus to calculate velocities or measure areas...

    If mathematics is not used as arithmetic to solve simple human addition/subtraction problems...

    If mathematics is not used as algebra to solve simple efficiency problems...

    etc. etc. etc.


    ...then the mathematics becomes an esoteric work in itself only existing to exist, serving no functional purpose. Not unjustifiable to study but the student must be clear that they are studying for reasons other than functionality.

    Carrying the analogy over to MA...

    If the MA cannot be applied functionally in a proven way then it is merely an isoteric activity with no basis in the functional "real" world.


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  • Closed Accounts Posts: 4,487 ✭✭✭Kevin_rc_ie


    Swoosh.


  • Registered Users, Registered Users 2 Posts: 23,246 ✭✭✭✭Dyr


    martial arts=maths because maths sucks :mad:


  • Closed Accounts Posts: 4,487 ✭✭✭Kevin_rc_ie


    Bambi wrote:
    martial arts=maths because maths sucks :mad:

    therefore MAs suck?

    Did you mean MA>Maths?


  • Registered Users, Registered Users 2 Posts: 23,246 ✭✭✭✭Dyr


    No, MA's by and large are teh suck

    this may seem like a controversial theory to put forward on a MA board but deep down we all know its true :eek:


  • Closed Accounts Posts: 4,487 ✭✭✭Kevin_rc_ie


    oh. i can't say i understand what you're saying. Martial Arts in general, are stupid "things"?


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  • Registered Users, Registered Users 2 Posts: 23,246 ✭✭✭✭Dyr


    in general, yes. They cause bad karma in our collective unconsciousness and are alleged to have made the little baby jesus cry :mad:


  • Closed Accounts Posts: 4,487 ✭✭✭Kevin_rc_ie


    Goodbye.


  • Registered Users, Registered Users 2 Posts: 23,246 ✭✭✭✭Dyr


    oh im going nowhere, i like things that are sucky... im listening to whitesnake right now :D


  • Closed Accounts Posts: 3,964 ✭✭✭memphis


    This logic could be applied to TKD couldn't it, and possible other MA's? I mean the number 3 appears to frequent clearly in TKD. Take a look at many of the Tuls. Alot of the motions are done in blocks of threes, and then 3*3=9, hence the reason for 9th Dan being the highest ranking. Also 9 is the highest 1 digit number before you start using double numbers.

    So yes, MA = mathamatics!!


  • Registered Users, Registered Users 2 Posts: 23,246 ✭✭✭✭Dyr


    tkd=bingo by the sound of that :confused:

    escrima has 12 angles, multiple 3 count, 5 count, 6 count, and god knows what else because i stopped listening by then. i need a calulator just to train :(


  • Closed Accounts Posts: 334 ✭✭TwoKingMick


    columok wrote:
    Following the analogy...

    If mathematics is not used in the form of integral or differential calculus to calculate velocities or measure areas...

    If mathematics is not used as arithmetic to solve simple human addition/subtraction problems...

    If mathematics is not used as algebra to solve simple efficiency problems...

    etc. etc. etc.


    ...then the mathematics becomes an esoteric work in itself only existing to exist, serving no functional purpose. Not unjustifiable to study but the student must be clear that they are studying for reasons other than functionality.

    Carrying the analogy over to MA...

    If the MA cannot be applied functionally in a proven way then it is merely an isoteric activity with no basis in the functional "real" world.


    O'queef, thats about the most insightful thing you've ever said. Kudos.


  • Posts: 0 ✭✭✭ [Deleted User]


    Thank you


  • Registered Users, Registered Users 2 Posts: 1,368 ✭✭✭king_of_inismac


    I don't know if I should reply to this, as some of the replies are simply ridiculous.

    MA's in general would be based much more on the physics of the human body, rather than on any kind of mathematics.

    Take for example a simple karate punch. The objective (from my perspective) is to channel as much energy from the ground into the punch. Using your body as a medium to channel the force. The lines of the body will dictate the strength of the punch, along with technique. Straight lines will allow the power to flow directly from the floor to the target, other lines will not. (this is just one example, and probably the easier to explain)

    The more I study Martial Arts, the more I realise it is the application of the basic laws of physics (This fact does not make the perfection of a technique any way easier!)

    Martin


  • Registered Users, Registered Users 2 Posts: 673 ✭✭✭pearsquasher


    Hmm. the usual mixture of excellent replies and plain daft ones. As with any analogy, anyone can use it to denegrate or promote their vested interest. Because i posted it, i'm going to be a bit more positive (geddit?) about it. :D

    I made the point that MA is more than the "physics" of the human body because there's more going on than the mechanical (vectors, force, momentum etc). Theres also the human mind driving it all. Just as the human mind has come up with amazingly clever ways of manipulating numbers to describe the world... form the time "0" was invented, to actually coming up with a counting system, to the complex mathemtaical equations that drive chaos theory and quantum mechanics.

    There's this thing with MA where people have fought life-or-death battles and afterwards discovered the essence of what helped them survive and, with TMA's, created kata to describe or encapsulate this essence in order to pass it on. This, i think, is equivalent to a mathamtician gaining insight into some process, be it purely isoteric or functional and developing a formula with many variables to decribe it. Isnt the formula usually elegant in the way its simple but encapusualtes a million possibilities - by changing variables and testing it? I'm not going to harp on about kata but just gave this as a facet of what i'm talking about.

    Also, on the point of an MA being functional vs isoteric. Well, lets not forget the "art" part. (not so necessary for you sportsters perhaps). The "art" part implies a higher order of thinking rather than just functionality, as in other art forms. How is my sculpted piece of lava-rock "functional". Does it serve a purpose?

    Put it this way, most people would not consider mathematics to be "artstic" in any way, just like most folks fail to see the "art" of MA's and simply strive for some sort of practical use... despite the fact most people don't get into fights. But, ask a qualified matematician, someone who's imersed themselves in their field, who's sought out deep meaning and understanding in their study, and i pretty much guarantee you they'd say their was art in it and would agree that, yes, there are practicxal applications of math, but isn't the artistic and isoteric nature of it all, far more stimulating? Just like a good MA. The real trick is to integrate it all together (no pun intended). This is proffesor level thinking rather than leaving-cert level and it's definitely where i want to be.


  • Registered Users, Registered Users 2 Posts: 33,518 ✭✭✭✭dudara


    Mathematics is a rigourous system for describing a science based upon axioms or accepted facts. it is a universal language in which we describe the world.

    I might just be having a more obtuse than normal morning, given that I've only had two coffees so far, but describing MA as the mathematics of the human body just seems a bit too airy-fairy for me.

    Any sport that tests the human body and requires concentration can fall into that category. Why is there this continuous effort to give a mysticism to MAs? I love TKD, it does allow me to focus my thoughts and clear my head, but I don't see it as anymore than a sport.


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  • Registered Users, Registered Users 2 Posts: 23,246 ✭✭✭✭Dyr


    I hereby apologise for all daft replies, Maths brings out the worst in me :(


  • Posts: 0 ✭✭✭ [Deleted User]


    Personally I dont think the maths analogy works. Maths is a science with proofs required before something is accepted and taught to others as fact. Many MAs dont use this methodology. Here is where your analogy falls down. To over complicate it is kinda muddying the waters.
    be it purely isoteric or functional
    Isoteric is either a kind of stretching/weight lifting or some kind of sports drink... :p. I think esoteric is the word you're looking for.
    The "art" part implies a higher order of thinking rather than just functionality, as in other art forms. How is my sculpted piece of lava-rock "functional". Does it serve a purpose?
    You cant reach a higher plane of consciousness by telling yourself how artful, philosophical, serious and enlightened your way of thinking is. How many religious people really think? How many challenge themselves and really challenge their belief structures pushing their understanding of the universe? Spirituality isnt dogma. Spirituality isnt obeying canon or chanting or bowing or doing things a certain "spiritual" way. Art isnt strictly higher than function.

    Martial arts have their "art" rooted in science. A comparison might be architecture. Architecture being the optimal compromise of form and function. A structure must have a basis in function before it can transend function and appeal due to its form. Some structures are appealing because of the purity of their form, their efficiency etc. If you try and have a beautiful structure forgetting all of the function all of the reality you lose it all. Muhammed Ali had all the function but transcended it all by having beautiful form. Amazing to watch. It needed the fundamentals of being a good boxer, athlete, having sparred all day/all night before he could really become an artist.
    This is proffesor level thinking rather than leaving-cert level and it's definitely where i want to be.
    Dude you cant just tell yourself that you want high level thinking rather than the idiotic MA proletariat. It doesnt work that way.


  • Registered Users, Registered Users 2 Posts: 673 ✭✭✭pearsquasher


    Well lucky for me that I don't have to tell myself these things but simpley experience them in the art that i've been studying for 10 years - the analogy fits into recent insights i've had into my chosen art, thats all.

    I do like the architecture analogy - form and function. But architecure has styles whereas maths is pure an goes beyond a style. There are simple truths in it that are played with in infinite combinations that lead to greater understandings of our world. A well-rounded martial art has this too, i feel.


  • Posts: 0 ✭✭✭ [Deleted User]


    Well lucky for me that I don't have to tell myself these things but simpley experience them in the art that i've been studying for 10 years - the analogy fits into recent insights i've had into my chosen art, thats all.
    No need to qualify yourself. Not to me anyway. If you want to be thinking a certain way you're missing the point. Its not about saying that you want to mentally be somewhere. If youre trying to grasp at philosophy like that you'll never catch it. Let go of trying to have complex understanding and then you'll get further towards understanding complex things.
    But architecure has styles whereas maths is pure an goes beyond a style.
    Maths is limited. Its far from pure. Its not universal. Architecture may have gothic, romanesque, georgian etc but the concept of functional and beautiful spaces is universal.


  • Registered Users, Registered Users 2 Posts: 673 ✭✭✭pearsquasher


    Hmm. .. i'm not so much grasping at complex ideas as you say, but rather, from training with people who have gained insight into Martial Artistry, finding that ideas emerge, which are actually simple rather than complex. They transform from mere ideas into defnite feelings and intuitive instincts - becoming subconcious and intuitive and therefore of practical use, perhaps.

    I'm not coming at this from a "i read about this and want to achieve it", but its more like "these are the esoteric things we read about and what our teachers tell us, but now they're starting to be absorbed and make tangible sence through my own experience". I'm well aware of the folly of trying to force these things unnaturally and ahead of time. This is not the case here.

    My analogy to maths was simply something i found rang true for me this week and was wondering what others though. Of course it can fall down if you anaylse every aspect of it negatively. How about pondering the positive behind it. If it doens't speak to you, fair enough, it might to someone else.


  • Posts: 0 ✭✭✭ [Deleted User]


    Well many of your posts on the topic are sidestepping between various vagaries without saying anything particularily concrete.

    You think martial arts are like maths. Maths in my eyes is a science that taken to its highest level becomes an art (like most things). But the TMA training method uses a religious rather than a scientific testing method. It involves believing anecdotes, unchallengeable authority figures and cult like behaviour. So I'm sorry but I have to trash your analogy. It doesnt work.

    I would say that an amazing realisation that has hit me after many years of martial arts training is how sad the human mind can be. The human mind will find excuses to shy away from hard work and pain. The human mind will cling to delusion, to superhero dreams rather than face reality. The human mind will allow people play around with "lethality" as though it were a toy or triviality to indulge violent fantasy. We all do this. Anyone who says they dont is a liar.

    Martial arts has led me to people, with lots of years training who seem to have taken evolutionary steps back. I think a martial arts world where such incredible power of life or death over your fellow human being is believed to be passed on through secret training exposes the worst of humanity. Many MAs showcase the worst traits of humanity- delusion, ego, passive-aggresiveness, paranoia...

    The question is can the martial arts world transend all this crap and become better people? Not until they stop deluding themselves with pseudo religious psycho-babble. Its a sport you do in a hall two or three times a week. Its not a lifestyle.

    If you want to learn about the battlefield join the army! Surely thats the ultimate means of personal evolution if thats your thing?


  • Registered Users, Registered Users 2 Posts: 1,604 ✭✭✭blondie83


    columok wrote:
    Personally I dont think the maths analogy works. Maths is a science with proofs required before something is accepted and taught to others as fact. Many MAs dont use this methodology.
    Yes but you have to understand the proofs ;)

    On a completly unrelated note, I heard lately that the equals sign was only invented about 250 years ago, so people beforehand had to do a lot of their proofs completly in essay form! Anyone know if this is true?

    Oh and Colum congrats on the BEuntitled1.jpg


  • Posts: 0 ✭✭✭ [Deleted User]


    Cheers Sinead,

    You too- well done.

    Heading off to edinburgh in September to do an Masters in Landscape Architecture.

    As for the proofs thing. Absolutely. You need to understand the theory but the theory must make sense to begin with.


  • Closed Accounts Posts: 20,759 ✭✭✭✭dlofnep


    Colum is a genius, let's steal his lunch money. He'll be loaded!!


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  • Posts: 0 ✭✭✭ [Deleted User]


    Colum is a genius, let's steal his lunch money. He'll be loaded!!

    Thats it now I'm dropping to 60. I figure if I use an angle grinder I can lose at least two limbs and cruise under that weight limit. ;)


  • Closed Accounts Posts: 20,759 ✭✭✭✭dlofnep


    Hah, you and Mick are going to drop to 60 and I'm going to eat like 9 pizza's and climb to 70. I win!!


  • Posts: 0 ✭✭✭ [Deleted User]


    I'll cut off the necessary amount of limbs at the weigh in.

    Note to John: Dont reveal your cunning plan on the interweb to you enemy.


  • Closed Accounts Posts: 20,759 ✭✭✭✭dlofnep


    columok wrote:
    I'll cut off the necessary amount of limbs at the weigh in.

    Note to John: Dont reveal your cunning plan on the interweb to you enemy.

    Blast it, foiled again!


  • Closed Accounts Posts: 4,487 ✭✭✭Kevin_rc_ie


    lol he's just like a james bond bad guy


  • Registered Users, Registered Users 2 Posts: 23,246 ✭✭✭✭Dyr


    One of the guys i train with is an architect and he does tai chi so i dunno what to think now :confused:


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  • Closed Accounts Posts: 4,487 ✭✭✭Kevin_rc_ie


    he's gay?


  • Posts: 0 ✭✭✭ [Deleted User]


    Sure TwoKingMick aka Michael "King of the Slam" Leonard runs a kitten sanctuary in Firhouse.


  • Registered Users, Registered Users 2 Posts: 23,246 ✭✭✭✭Dyr


    and on that bombshell we say goodnight...


  • Closed Accounts Posts: 20,759 ✭✭✭✭dlofnep


    columok wrote:
    Sure TwoKingMick aka Michael "King of the Slam" Leonard runs a kitten sanctuary in Firhouse.

    I'll have you know that his new nickname is Mick "The Potato Famine Slammin'" Leonard and anyone who calls him otherwise has me to deal with (at 60kg).


  • Registered Users, Registered Users 2 Posts: 673 ✭✭✭pearsquasher


    Well many of your posts on the topic are sidestepping between various vagaries without saying anything particularily concrete.

    Funny how my posts reflect my inclination towards MA. I'm vague because real conflict is vague. Its within the mist of this chaos that one must find things that work for you - here i'm talking about fighting AND my style of posting - hows that for "vague"? We are using a written format to dscuss something that inherently cannot be discussed to any great meaning with exact wording. No amount of clarity in writing can convey the concepts Martial Artists are studying - all we can do is throw a spot light on the flickering candle of MA and give a feeling of what we're talking about. This applies to all arts of course. Is it hard to see why i'm vague? Its not to be all mystic for the sake of it, but i find it hard to talk concrete about something that is completely not so. Get it? So i use analogies a bit more than if i was talking about type of trees. It works for me and i enjoy similar discussions on other mb's, books and conversations.
    But the TMA training method uses a religious rather than a scientific testing method. It involves believing anecdotes, unchallengeable authority figures and cult like behaviour.

    You are completely incorrect there. Maybe the TMA you studied was like this, and you got burned and seem to be on an anti-TMA drive since. It's fine to watch out for people falling into the same trap as yourself but you;re displaying a classic case of painting everything with the same brush. Admittedly though, most TMA's i've experienced outside my current one have some of the traits you are talking about, but not all of them have. I would say the average TMA in Ireland is what you describe - that is why one must search for the above-average MA, to learn from mistakes made, to have a critcal eye, like you seem to think you have, and to seek the highest art possible.

    There is absolutely no religious aspect to the TMA i study outside of the individuals own belief system. There is absolutely zero refusal by any teacher in the Bujinkan system to answer any question on anything we do and they accept all challenges to any query that is thrown at them. Cult-like behaviour is a cheap way of comparing a TMA that you have no idea how it internally functions, to a group of zeolots that blindly follow a destructive meglomaniacal individual. The Grandmater of the Bujinkan is admired and sought out the world over because of his skill. He doesn't issue doctines, give orders or control anyone but merely shows martial artists what is possible.
    I would say that an amazing realisation that has hit me after many years of martial arts training is how sad the human mind can be. The human mind will find excuses to shy away from hard work and pain. The human mind will cling to delusion, to superhero dreams rather than face reality. The human mind will allow people play around with "lethality" as though it were a toy or triviality to indulge violent fantasy. We all do this. Anyone wh says they dont is a liar.

    This is true but i try to see what the human mind is capable of for the benefit of the individual and society. The martial arts i study gives me the lens to increase my world view, make me think about my own falicies and correct them, challenge my preconceptions and lead me down a road away from fantasy and ideas that could get me injured. We play with ther truth in the TMA that i do and scrutinise everything.
    Martial arts has led me to people, with lots of years training who seem to have taken evolutionary steps back. I think a martial arts world where such incredible power of life or death over your fellow human being is believed to be passed on through secret training exposes the worst of humanity. Many MAs showcase the worst traits of humanity- delusion, ego, passive-aggresiveness, paranoia...

    But a few, and guess what, i study one of them, showcase the potential of the human mind and body, the power of benvolance and love and the richness of human intellect and ingenuity. Ignore tha bad ones, theyre necessary for attracting the bad people... and seek the ones that attract the good.

    Its a sport you do in a hall two or three times a week. Its not a lifestyle.

    You see, you consider your art a sport so have immediately set up this condition that its a twice a week physical activity that doesn't effect your life outside of the hall you train in. MA's aren't lifestyles, i agree, (what is?) but they should damn well inform your moral character which does effect your lifestyle.
    If you want to learn about the battlefield join the army! Surely thats the ultimate means of personal evolution if thats your thing?

    But why join the army to study interesting battlefield concepts when you can seek out a school of martial arts that convey the same things without the added dangers of actually ending your life?


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  • Posts: 0 ✭✭✭ [Deleted User]


    Martial arts are completely concrete. They are training systems that emphasise different methods of unarmed or armed combat in different ways. Some work, some don't. Some have tradition some dont. You can attach deep significance to some that are no more that modern dance. This doesnt make it significant.
    You are completely incorrect there. Maybe the TMA you studied was like this, and you got burned and seem to be on an anti-TMA drive since. It's fine to watch out for people falling into the same trap as yourself but you;re displaying a classic case of painting everything with the same brush. Admittedly though, most TMA's i've experienced outside my current one have some of the traits you are talking about, but not all of them have. I would say the average TMA in Ireland is what you describe - that is why one must search for the above-average MA, to learn from mistakes made, to have a critcal eye, like you seem to think you have, and to seek the highest art possible.
    I've seen the religious mentality in Kung Fu, TKD, Shotokan and Wado Ryu Karate, Lau Gar and Bujinkan (and probably more). The fact that you use anecdotal evidence to support your theories says it all. "Well I know my sensei once used this move to beat up four scumbags" etc. etc.
    We play with ther truth in the TMA that i do and scrutinise everything.
    Maybe you should scrutinise some of your training with a bit of sparring? Come along to the Boards Meet and Fight and see for yourself! ;)
    But a few, and guess what, i study one of them, showcase the potential of the human mind and body, the power of benvolance and love and the richness of human intellect and ingenuity. Ignore tha bad ones, theyre necessary for attracting the bad people... and seek the ones that attract the good.
    Bujinkan has far too much nad punching to be considered a force to ignite benevolence and goodness throughout the universe.
    but they should damn well inform your moral character which does effect your lifestyle.
    Dont agree.
    But why join the army to study interesting battlefield concepts when you can seek out a school of martial arts that convey the same things without the added dangers of actually ending your life?
    Training in Bujinkan and going to war are worlds apart. They convey none of the same things.


  • Registered Users, Registered Users 2 Posts: 1,799 ✭✭✭Clive


    columok wrote:
    I've seen the religious mentality in Kung Fu, TKD, Shotokan and Wado Ryu Karate, Lau Gar and Bujinkan (and probably more).

    BJJ, MMA etc.


  • Closed Accounts Posts: 334 ✭✭TwoKingMick


    Clive i dont get your point? Everyone knows the Gracies, Machados and Matt Thornton are infallable! I read it on their web sites. Are you telling me i bought their t-shirts for nothing?


  • Registered Users, Registered Users 2 Posts: 1,799 ✭✭✭Clive


    I once heard that Rickson was attacked by a bear, then realised that it´s front legs looked similar to it´s back legs, and that´s when he invented leg locks. That and question marks.


  • Closed Accounts Posts: 334 ✭✭TwoKingMick


    Well then obviously i should let that man define my lifestyle!


  • Registered Users, Registered Users 2 Posts: 1,799 ✭✭✭Clive


    Well that´s up to the promoters...


  • Registered Users, Registered Users 2 Posts: 1,604 ✭✭✭blondie83


    columok wrote:
    Cheers Sinead,

    You too- well done.

    Heading off to edinburgh in September to do an Masters in Landscape Architecture.

    As for the proofs thing. Absolutely. You need to understand the theory but the theory must make sense to begin with.
    Very true, but the theory can make sense without you understanding it! When I think back to the proofs I did/learnt off by heart last year...they made no sense to me whatsoever, yet they were obviously sound theories - I just didn't have the mental capacity to understand them :)

    I don't actually know what my point is here btw, so dont all be looking for one!


  • Closed Accounts Posts: 15 BlackBeltDave


    I dont think that maths and martial arts are teh same at al, Maths is something that is done in a class room or studied in a book by people while martial arts are trained by masters who are masters in the arts of war and combat and killing and healing.

    I think martial arts are like a race to the finish line. You have to go very far before you are nearly finished and before you get there it gets very hard to get to the end when you get there you are then a master and can show other people how to run the race but they may not finish.


  • Registered Users, Registered Users 2 Posts: 3,577 ✭✭✭Colm_OReilly


    To paraphrase AJ Ayers, logic and mathematics are true only because we don't allow them to be anything else.

    AJ Ayers Language, Truth, and Logic


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