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Old 03-25-2005, 06:54 AM   #26
Ecosamurai
 
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Dojo: Takagashira Dojo
Join Date: Jun 2002
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Re: Mathematical treatment of aikido

Quote:
Ben Walter wrote:
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


IMHO.
In modelling, much of what you refer to as the next 'frame' is explainable by the modellers term: uncertainty. Models make the best use they can of underlying scientific knowledge and write this down in a mathematical way using a computer. Such models are called deterministic models. This means that output is determined by input, Newtons descriptions of motion for example are deterministic, they are a set of rules for predicting things. If you put in a very precise number a precise answer follows. Unless the model is non-linear and has certain other properties, in which case it can be chaotic such as Lorenz discovered in a meterological model(help! trying to keep this simple).

In models you can quantify the uncertainty that is given by a range of inputs using monte carlo analysis. To give an example, if I had a Nikyo model and wanted to know what effect the range of possible inputs had on the output I could quantify that using monte carlo methods. This neatly covers the X factor/Ki idea you mentioned of 'something missing'. There would be no missing factor all could be accounted for with a range of inputs.

To give an example that might make things easier.

Roll a die, chances of a given number appearing is 1/6. What about variations in wind, surface structure you rolled the die on, angle of your wrist? In a strictly deterministic model you'd have to account for all that. You could create a complex model to account for all these factors and you could monte carlo it to quantify the uncertainty of output based on range of input.

What you'd find (and there have been investigations into stuff like this) is that your model is waaaay too complex and not as useful as assigning a 1/6 probability to each face of the die. Its predictive power wouldn't be better but worse than the simple 1/6 model.

So to bring it back to Aikido. Yes, you could model Aikido. Yes you could monte carlo it and have it as a more flexible than strictly deterministic model (making use of a quantified range of inputs rather than strict deterministic models).

None of this would give you factor X/Ki/Chi as a variable.

BUT when you've quantified the uncertainty you get to ask where that uncertainty comes from. Could it be Ki? Could it be that our model is inadequate (more likely).
Once again you're back int the realms of the unknown, maybe the unknowable, Godel said that things can be true but never proven....

Sorry about the length of post

Mike Haft
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Old 03-30-2005, 06:31 PM   #27
Tina_Kahina
Join Date: Mar 2005
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Re: Mathematical treatment of aikido

I'm actually doing a project for class over this if anybody has any advice or help i'd greatly appreciate it.
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