Mathematical treatment of aikido

In the centripedal tenkan argument, i posted that it would be interesting to "model" aikido mathematically i.e. XMA animations.
I mean the whole kit and caboodle, motion sensors, floor pressue sensors etc.
I wonder it the scientists would discover that all aikido movements equations can be reduced to a singular point on each body, and that no-touch/ki throws are just timing or something? Or do they discover that the solutions to the movement equations have a variable in them that they cannot relate to anything physical, and decide to relate it to string theory or something un-ki related?

<XML...>
<Mathematicsedentry>

A computer model is _NOT_ mathematics. Mathematics is built on theorems (and derivatives like collaries and lemmas) not on experimentation.

What you suggest is an experiment. How did that uke and that tori do on that one technique at that one time. It is an isolated incident. You could do some statistical analysis (Bayesian being my favourite and only statistic theory I actually understand) but that still does not give you a proof. Hence it's not mathematics.

String theories (there are five of them!) have nothing to do with motion or body mechanics. String theories are mathematical concepts designed to explain (and predicts) results that standard quantum field theory cannot. Oh, in case you were wondering, quantum field theory and relativity both "work" (IE they predict real live events with great accuracy) but are incompatible. Hence string theories try to bridge that cap. Boy this is off topic.... I suggest that anyone interested refer to Green's book This Elegant Universe.

</Mathematicsedantry>

Yann...

Did you hear that "wooshing" sound as I read your post and it all went clean over my head. LOL

Ben Walter wrote: no-touch/ki throws are just timing or something?

ki : aikido = ether : electromagnetic waves

Dave Humm wrote: Yann... Did you hear that "wooshing" sound as I read your post and it all went clean over my head. LOL

I Just heard it pass my way

Dario Rosati wrote: ki : aikido = ether : electromagnetic waves

Ether (or aether) being a theoretical construct that was later shown not to exist. I like the analogy myself, but it could be a bit contraversial.

Sean
x

I would recomand that anyone who has an interest in moden physical and applied mathematics check out Green The Elegant Universe as it is a great book and will explain a lot in layman terms. Of course, if you want a good grounding in physics, Feyman's lectures are a must. There is NO better text.

Few links The Fabric of the Cosmos by Brian Green, The Elegant Universe also by Brian Green and
Lectures on physics by R. P. Feynman. Enjoy.

Hello all,

The mathematical analysis of aikido would involve nothing more than assigning geometric structure to uke and nage, giving values to the force vectors of attack and response, and then calculating the resulting motion vectors. The motions of aikido are of a purely mechanical nature. Newtonian physics/classical mechanics would be able to handle it, although its treatment would be incredibly difficult due to the complex shape of the human body and the fact that each movable part of the body has six degrees of freedom. (It stinks...I tried to model ikkyo once as a physics project...grrrr)

By the way, wonderful book suggestions...Brian Green is an outstanding author in my opinion. I also suggest "The Emporer's New Mind" and "The Road to Reality" by Roger Penrose for those who want to see how the math fits into all of this.

Man...great thread...aikiphysics =0)
Hope all are well,
Beau Biller
FSU Aikido

Beau Biller wrote: The mathematical analysis of aikido would involve nothing more than assigning geometric structure to uke and nage, giving values to the force vectors of attack and response, and then calculating the resulting motion vectors. The motions of aikido are of a purely mechanical nature. Newtonian physics/classical mechanics would be able to handle it, although its treatment would be incredibly difficult due to the complex shape of the human body and the fact that each movable part of the body has six degrees of freedom. (It stinks...I tried to model ikkyo once as a physics project...grrrr)

I have been attempting to do a statics vector analysis on simply nikkyo showing the effects of uke using a "normal strength" resistance versus a kokyu strength resistance (that gives me the simple equilibrium equation as opposed to dynamics). Reducing the problem to a very simple mode, I still encounter problems due to the shifting rotational stresses involved in the wrist/forearm. The problem is that the resisting force change from "normal" to "kokyu" shifts the incident angle of the applied force on the joint... right at the point where the complicating torsional forces are. Anyone have access to and expertise with a 3D statics modelling software? I don't have expertise with this kind of software and I don't want to fight the learning curve just to satisfy myself on one problem.

Regards,

Mike Sigman

Hey Mike,

Mathematically, you could try treating the shifting rotational stresses tensorially so that you don't have to take into acount the rotating coordinate frames. (If your model is completely static, this will work nicely due to no translation.) Pro-E, MD Solids, Algore...are all 3-D programs that could help understand the forces involved. (Algore is an FEA program) However, to examine the stresses in the wrist/forearm you would have to find values for the Elastic moduli of the various components, otherwise whatever values you find would be completely dependent on the cross sectional area of the wrist/arms in question.

Treating a movement like nikyo statically is a great idea. Even if to show the genious in creating that much mechanical advantage.
Hope any of this helps,
Beau Biller
FSU Aikido

Hey, guys -- what about Aikido3D? They've already got the movement modeling down - using animation tools. Make a few improvements to the software to enable the desired analysis, such as calculating for centers of mass and whatnot, and you should have what you are looking for. Note: this is not a trivial problem; but most mathematical simulation programs allow you to import reference images - why not a dynamic image?

"A computer model is _NOT_ mathematics. Mathematics is built on theorems (and derivatives like collaries and lemmas) not on experimentation."

Actually i would argue that a computer model is mathematics, but that is just semantics, and not the point of THIS discussion.

"What you suggest is an experiment. How did that uke and that tori do on that one technique at that one time. It is an isolated incident. You could do some statistical analysis (Bayesian being my favourite and only statistic theory I actually understand) but that still does not give you a proof. Hence it's not mathematics."

Statistics is not mathematics?
I believe that movements of Nage and Uke, are not 100% identical for say Iriminage, but there are general concepts, that could lead to a model. What about the esoteric statement that in aikido there is only one technique. What is the basis for this? I am trying to possibly get a western explanation, for the sake of everybody who does aikido and does not follow the eastern viewpoint. Which is the turn off i think to more people doing aikido.

"String theories (there are five of them!) have nothing to do with motion or body mechanics. String theories are mathematical concepts designed to explain (and predicts) results that standard quantum field theory cannot. Oh, in case you were wondering, quantum field theory and relativity both "work" (IE they predict real live events with great accuracy) but are incompatible. Hence string theories try to bridge that cap. Boy this is off topic.... I suggest that anyone interested refer to Green's book This Elegant Universe."

My understanding of string theory is that theoretically mechanics/QED/"name a branch" can be derived from string theory, so your statement is incorrect, but agreed this is off topic.

Take 2:

The point of this thread was to hopefully stimulate a discussion on what we could learn about aikido, using an analysis technique similar to that used by the XMA - Xtreme martial Arts documentary on Discovery channel in the last 12 months. Throughout this documentary that try to refer everything back to physics, although they do acknowledge Chi/Ki concepts, but again try to explain them. Ki/Chi is not a western concept, and based on the threads contained in this forum, is something we cannot agree on what it is. The best i can make out from everyone's opinion is that it means something different to everybody.

So i propose looking at aikido in a scientific manner. If you sat down and tried to think about what i was proposing, as you are obviously intelligent, as opposed to just nit-picking on attempted humour (string theory comment) to show how much of a smarty-bum you are, we might actually get somewhere? Thank the maker of smilies!

Peter Zalinski wrote: Hey, guys -- what about Aikido3D? They've already got the movement modeling down - using animation tools. Make a few improvements to the software to enable the desired analysis, such as calculating for centers of mass and whatnot, and you should have what you are looking for. Note: this is not a trivial problem; but most mathematical simulation programs allow you to import reference images - why not a dynamic image?

The problem I see with using animation tools (like Poser 5, using perhaps the wire-mesh images) is that the actual force vectors of engagement can't be shown and that's as important as the technique, IMO.

Regards,

Mike Sigman

You guys might find, "Mechanics of Judo" by Robert Blanchard an interesting read for it pertains to the math of a martial art.

Tower, this is ghostrider requesting a fly-by----negative ghostrider, Math 101 has the ball--haha wooooooooooooooooooooooooshh

Ben, what is your problem?... Do not take anything I wrote as a criticism of you. It was not meant as such.

If you want some scientific work on Aikido, I suggest you read some of Tomiki-shihan's works. Sadly, I think they may not be translated. I am not sure. Anyone cares to add anything here?...

Hi Yann;

I don't think you would find much in the way of Tomiki's writing that could be called a scientific treatment - it was more of an educative model in the sense of Kano treating jujutsu in the context of Western Physical Education. Physical education during Kano's time and later when Tomiki was Professor at Waseda was more experience based than experimental. It's still that way (yes even with steroids).

Computer modeling is an interesting concept - all sorts of things you can do there especially the wrist rotations and applied force that characterizes many Shodokan techniques. Modeling "centripetal tenkan" of course would not really have much relevance to us as we tend to draw in with our rotational (tenkan-like) movement - I fear Aikido is far more complex than that.

Peter Rehse wrote: Computer modeling is an interesting concept - all sorts of things you can do there especially the wrist rotations and applied force that characterizes many Shodokan techniques. Modeling "centripetal tenkan" of course would not really have much relevance to us as we tend to draw in with our rotational (tenkan-like) movement - I fear Aikido is far more complex than that.

Hello all,
think I'll jump in here as I'm doing a PhD in computer modelling and environmental science type stuff.
Yann made the point that computer models aren't mathematics. I understand completely where he's coming from but he's wrong. They are not mathematics in the sense that they are not attempts to prove a theorem. But they are collections of mathematical rules which are soundly derived and used to interpret observations and measurements made.

To use the Aikido example, if I had an idea about the motion used in Nikyo and I could write some equations to describe it, I wouldn't be attempting to prove a Nikyo theorem, but I could hope to gain some insight into the nature of Nikyo. I could also use my model (based on mathemtics and translated into computer code) to predict what sort of force would need to be applied to what sort of wrist to make the Nikyo work or to break an attackers arm/wrist.

I could also associate error with that to say that the amount of force is between a and b but most likely to be c.

So in a sense what Yann was saying was right, in response to the original post, you couldn't tinker with the equations and 'model' Aikido and find that there was something within the Aikido theory and not in our more western understanding of the universe. But modelling the movement might prove an interesting excercise in itself in understanding more about the way people bend and respond to forces exerted on them.

Hope this makes sense, I've tried to keep it simple.

Mike Haft

Mike Haft wrote: ...snip.... ...in response to the original post, you couldn't tinker with the equations and 'model' Aikido and find that there was something within the Aikido theory and not in our more western understanding of the universe. But modelling the movement might prove an interesting excercise in itself in understanding more about the way people bend and respond to forces exerted on them.

Just a thought...

If you did model the movements, then applied data gained from actual uke-nage interactions (gained through motion sensors on each joint etc <ref to Xtreme martial arts doco as seen on discovery channel>), and found that your equations did not predict the next "frame" of movement, then you would look at your equations and say "i am missing something here"?
What i am trying to get at is that the "missing something" can only be approximated in western science as factor X, and never actually attributed to a specific physical phenomenon i.e. gravity.
Maybe the factor X is the long lost, unexplainable mythical magical "Ki" that half of the aikido community subscribes to and the other half says is bollocks.
Or maybe your equations model the next "frame" to within a reasonable error, and BINGO, there is no Ki in the movements, they are just simply explainable physical interactions i.e. apparent certipedial/centrifical forces

???

Until western minds do something along these lines, investigate in some way aikido, wushu etc. The discussion of ki/chi is going to be purely conjecture, and most probably end up in a bunch of people diverging away from the topic and basically arguing about something so trivial and unrelated, as so frequently happens forums.

IMHO.

Jeez, you guys are all obviously way smarter than I am... But wouldn't the problem be solved if somebody could teach Aikido to crash test dummies?

Clark Bateman wrote: Jeez, you guys are all obviously way smarter than I am... But wouldn't the problem be solved if somebody could teach Aikido to crash test dummies?

We have those - they are called Uke.

Peter Rehse wrote: We have those - they are called Uke.

Yes, only you can't plug an uke into a computer and get the same readouts...

Ben Walter wrote: Maybe the factor X is the long lost, unexplainable mythical magical "Ki" that half of the aikido community subscribes to and the other half says is bollocks. Or maybe your equations model the next "frame" to within a reasonable error, and BINGO, there is no Ki in the movements, they are just simply explainable physical interactions i.e. apparent certipedial/centrifical forces

Ki is not a factor X, never was. It's not a super natural phenomenon but part of the sum that makes the natural motion happen, that enables you to throw that bigger, stronger person with minimum muscular effort on your part. All motion analysis equipment will do is measure that sum which will obey the physical laws and so won't prove anything.

If you wanted to address the question of whether or not Ki/Chi training of whatever tradition you want to pick was adding something more - a factor X. You would have to take someone who was trained well in the motion mechanics of the techniques. Actually it would be better to have two groups of individuals, one being a control group and first do a bunch of experiments to get handle on the question of what "trained well" means by statistical arguments. You would also need to come up with a sensitive way of measuring caloric usage during every technique performed - how much energy/work nage did per throw. After the preliminary training period and data aquisition, the second phase of the experiment would involve the Ki/Chi training for one group added to the training regimen (so much per day or have several sub groups with a range of amount of training) while the control group would continue the mechanical training (a plateau of skill level ? does the base line change ? etc.). Measurements being taken at a suitable interval - weekly perhaps. You could then ask if there is a significant difference between the groups and if so to what degree and so on. If the Ki/Chi trained group did significantly less work to do the same throw (same being a value judged by the motion analysis data) , then you might have an interesting result but the interpretation of that result would still be tricky.

Probably need to think a lot more on the design of controls for the experiments.

Since it's working with human subjects, project would need a few million dollars to be done right,


write the check to ...

Craig Hocker wrote: Ki is not a factor X, never was. It's not a super natural phenomenon but part of the sum that makes the natural motion happen, that enables you to throw that bigger, stronger person with minimum muscular effort on your part. All motion analysis equipment will do is measure that sum which will obey the physical laws and so won't prove anything. [[snipsky]] You could then ask if there is a significant difference between the groups and if so to what degree and so on. If the Ki/Chi trained group did significantly less work to do the same throw (same being a value judged by the motion analysis data) , then you might have an interesting result but the interpretation of that result would still be tricky.

I dunno. I'm of two minds about this, so I guess my real comment is along the lines of "I think your basic equation might be wrong and needs to have the variables adjusted"... something like that; not a direct disagreement.

Part of the problem is that there are essentially 2 different factors that make up the particular "Ki" involved in throws, etc. For simplicity's sake, I'm going to leave out what is called the "real ki" and focus on the part of movement makes throws more efficient. The essence of the argument will devolve probably to 2 factors: (1.) to an efficient way to move that lets the ground or weight do most of the work and (2.) to ways of manipulating forces against an opponent so that the least amount of effort is needed. Would you agree, generally, that this is where the "significantly less work" part comes in?

It is the utilization of the ground and/or your weight to do a lot of the work that allows a smaller person to be strong in relation to someone of similar size. There is another factor of Ki that actually makes you strong, but I'm going to leave that out of the argument (as in debate) because I don't think it will do anything but complicate the discussion. The manipulation of forces in and against an opponent can be approached on a subtle level or on a grosser level like Shioda does on page 23 of "Total Aikido".... either way takes less work, but can you attribute that savings in work to "ki" or is it mechanics?

If you simply calculate the effort for throws on a caloric basis, using the 2 factors I just mentioned, I think there is obviously a caloric savings. But the factor that bothers me can best be summed up with this simple example: if you shift the load-bearing from the smaller, upper-body muscles to the larger, lower-body muscles, you feel like you're doing work more easily, but since you're using large muscles to do it, don't both essentially require about the same calories?

Anyway, just my 2 cents.

Mike

It seems to me that it would only be the same amount to get things done if you were standing on your hands when doing it from the upper body...

Rob