Friday, December 31, 2010

Extract #2 from "Essential Jo"


Here is the second extract from my forthcoming book "Essential Jo".

Informal grip

As with golf, tennis, or any other activity which requires using a stick-like object, your grip is one of the most important features.

The “informal grip” is one you adopt when you are not actively engaged in training. We use the traditional method also seen in other Japanese and Chinese weapons arts: the weapon is held palm down and behind your shoulder. This is not only subtle and non-confrontational; it also provides an element of concealment and surprise, should you need it against would-be assailants.

Surprisingly, the hold is also quite effective in allowing a “quick draw” for defence.

The key to this “quick draw” is to hold the jo slighly off-centre, palm closer to the end facing downwards. I’ve found that the ideal point is approximately one palm width from the centre (or slightly less than that).

What this means is that when you drop the jo naturally it slopes upwards at a gradual incline – an incline that permits you, where necessary, to jab the jo forwards at an attacker so that it follows a straight line directly to your opponent’s eye (or face generally).

In other words, if you have the correct bias to your grip, your relaxed thrust will not have any “upwards scoop”. All this can be achieved without any effort or muscular exertion – merely by having the right grip.

The “rule of quarters”

I have a rule that I follow in terms of handling the jo – a rule which I call “the rule of quarters”. This is because, apart from the informal grip referred to above, I believe that the jo should principally be held with one hand at the end, and the other at the quarter marker closest to that end.

When you slide the jo through your hands you generally move one hand up to the ¾ mark, then swap ends.

I’ll detail this further on in relation to the hand changes. It is sufficient for the present purposes to note that the quarter markers are significant. In order to isolate these, grab the jo exactly in the middle, then find the midway point from the middle to the end. This will be where one of your hands should grip, while the other goes to the end.

The thrusting grip

The basic grip at the conclusion of a thrust is performed in accordance with the “rule of quarters”: your right hand is at the butt, while your left hand is at the nearest quarter point.

Both hands grip the jo naturally and in a relaxed fashion. In this respect it is important to note that except at the point of impact the jo is never gripped too tightly.

The “slide then jab” principle

In the coming Chapters, I will frequently make reference to something I call “slide, then jab”. This is the central principle for thrusting with the jo as it ensures the appropriate staged activation which in turn delivers optimum transfer of momentum and accordingly maximum application of force to your target.

Under this principle you must thrust in exactly this sequence:
  1. Slide your jo to the ¼ position (ie. to the thrusting grip); then
  2. Jab the remainder of the movement (ie. thrust your jo without any sliding).
It is important to remember that in the first part of the movement (the slide) you are not moving your front arm forward – all that is happening is that you are sliding your jo through your front hand to the ¼ position (in accordance with the “rule of quarters” as described above).

After you have finished sliding to the ¼ position you should throw your front arm into your thrust (keeping your thrusting grip at the ¼ mark firm).

The striking grip

The basic grip at the conclusion of a strike is also performed in accordance with the “rule of quarters”. However in this case your left hand is at the butt of the jo while your right hand is at the nearest quarter point (with a slightly different grip – more on that in a moment).

The left/right difference is quite critical to the theory behind the jo. From the outset it should be observed that jo techniques are not to be applied ambidextrously. Note that the jo is “right side biased”. It is merely that the right and left are employed quite differently. Thrusts lead with the left hand, while strikes lead with the right.

I used to think that this was a mere oddity. For a time I strenuously trained each technique equally with both hands. Or at least I tried to. No matter how hard I tried, the result was never satisfactory. Lately I’ve had a sort of epiphany: the right and left sides are not “unequal”. They are just different. Just as the left and right hemispheres of your brain have slightly different functions and perceive/approach the world in slightly different ways, so your left and right hands should follow suit.

With a predominantly 2-handed weapon like the jo, your hands need to work in concert. But they must be allowed to work in their natural way. You could spend your life trying to write well with your non-preferred hand, but it would produce uncertain (and pointless) results. I have a “leftie” friend who was forced to use his right hand as a child. His handwriting (with either hand) is a disaster, and he attributes this (probably with good reason) to the forced attempts to get him to write with his right hand.

“So,” I hear you ask, “where does this place left-handed jo users?” I suppose in the ideal world they would use the jo in the reverse to the “usual” manner. However because both hands are used equally (if differently) and because jo skills are not “intuitive” – they have to be learned over a lengthy period just as any fine motor skill – “lefties” don’t tend to experience any real difficulty in using the jo the “standard” way. That’s my experience anyway. And good thing too: it would be challenging, if not impossible, for left and right-handed students to train together using standard drills such as the kumijo.

So I’m afraid that, as with students of the katana, left-handed jo users need to accept the “injustice” of living in a right-handed world!

Details of the striking grip

I mentioned above that the right hand grip for striking is very particular. You will note from the above picture that the hand is turned over – specifically it is turned over to the point that the base knuckle of your index finger rests on the jo. This means that when the force of the strike is transmitted through your knuckle and into your hand giving your jo a solid support base. At the same time the knuckle can act to steady your jo and “guide” it along the correct path. Conversely, an “under hand” grip provides none of that “guiding” and is, moreover, weak: on heavy impact your jo is liable to slip out of your hand.

Copyright © 2010 Dejan Djurdjevic

Saturday, December 11, 2010

Crescent stepping


A colleague at the Traditional Fighting Arts Forums recently posed this question:
    The only explanation i've ever heard for the crescent stepping (other than just being able to generally move in various ways) comes from George Mattson's "The Way of Karate" where he states that it represents protecting the groin as you move into the opponent's range.

    Any other explanations? Surely there's more to it than that..?
My answer is: not really.

To my mind, the crescent step is the way one should perform basic ayumi ashi (natural stepping) when there is no initial lunge with the front foot (more on this in a minute). This is primarily so as to protect your groin (which the crescent step achieves by bringing your knees together during the step).

There is very little "time loss" because the arc drawn by your knee inwards does not significantly alter the path taken by your hip. So crescent stepping is quite useful for general movement because it is inherently protective of your most delicate regions without overly compromising speed and mobility.


Basic "ayumi ashi" (natural stepping) as practised in many karate schools. Note the crescent stepping (ie. the knees coming together).

Now it is true that the crescent step is slightly slower than a straight step.

But if speed in stepping is imperative, you should be utlising a lunge (hence my original point) - not a natural step. In other words, you should either lunge (oi ashi) or lunge and step (suri ashi or yori ashi).

Why?

Because, as I've pointed out before, when you move your front leg (as opposed to your back leg) you instantly exert pressure on your opponent. In other words, the moment you raise your front leg, you are exerting pressure. However when you move your back leg, you only exert pressure on your opponent when your back leg crosses the mid-line of your body.

When you lunge, then step so that your back leg moves to the front (suri ashi), you are generally closing the gap. This in turn means that the point at which you might have done a crescent step would have been well out of range. Accordingly there is no need to do a crescent step when you are performing the initial lunge or the follow-up step.


Suri ashi - a kind of stepping where you lunge, then step, with your back leg passing the front.

When you are simply lunging (oi ashi) or lunge stepping so that back leg never passes (yori ashi), crescent stepping is not really possible and it is therefore not an issue.


Oi ashi - lunging


Yori ashi - a kind of stepping where you lunge, then bring your back leg up without it passing the front.

Otherwise, in normal stepping (ayumi ashi) you should always do a crescent step (unless you want to invite a kick to the groin!).

Now just because an art might require the practice of crescent stepping doesn't imply that the art's tactics centre on that kind of stepping.

In any art, correct positioning and timing can (and should) negate the need for a crescent step in combat. After all, this is precisely why such a step is unnecessary with a lunging step - the positioning and timing make it a non-issue.

The lunge example relates primarily to range. But clearly angle can also negate the need for crescent stepping. The Chinese internal art of baguazhang uses this principle and avoids any need for crescent steps.

This just highlights that crescent stepping is very much part of kihon (basics): it assumes linear, natural stepping (ayumi ashi) that is in line with your opponent's centre.

While it might be tactically inadvisable to be in line with your opponent's centre, kihon is often about what to do when things go wrong or don't go exactly to plan. It is for this reason that karate systems like goju (and shotokan) use crescent stepping in their basic training. In other words, they don't rely on (or even envisage) the tactic of being lined up with the opponent's centre, but rather they teach certain basic movements as skills for coping with being in an "unforgiving" position (to which beginners are somewhat prone). Otherwise, standard goju tactics involve being to the side of your opponent's centre, while shotokan tactics often involve being well out of danger in a linear sense.

Can crescent stepping be useful for other purposes or fulfill other objectives? Sure.

For one thing, it helps avoid the clashing of knees when moving into an opponent.

It is also possible to use crescent stepping to unbalance your opponent (eg. by applying pressure to the side of your opponent's thigh - either on the inside or outside). However I don't think these are the reasons behind the use of crescent stepping in karate and some other arts. They are just side-benefits and possible applications.

Nor do I think crescent stepping is some kind of "code" to preserve the "five feet" (ie. a means of indicating 5 different optional movements when stepping, namely: moving forward, backward, sideways, around and lifting the knee). In my view you don't need a "code" for such things in kata and even if you did the crescent step isn't a particularly representative of the various options (any more than a normal step would be).

So in the end, I think crescent stepping is primarily a means to avoid exposing your groin in natural stepping. It's that simple.

Copyright © 2010 Dejan Djurdjevic

Monday, December 6, 2010

Mathematical dimensions and martial arts analysis


Introduction

The other night I dreamt I was back at university, in a mathematics lecture. The lecturer writes up Pierre de Fermat's last theorem1 on the board as follows:

cn = an + bn, where n = 3 or greater, has no possible solution.

Instead of asking us to prove the theorem, he simply says: "How many variables are there?"

I woke up and wondered about that piece of cheese I'd eaten the night before. Then I started thinking about the substance of the dream: How many "variables" are there in, say, c3 = a3 + b3? And how does this compare with the number of "variables" in Pythagoras' theorem c2 = a2 + b2?

Pure mathematics relating to number theory arguably has no practical application. Yet I realised that maybe, just maybe, my subconscious was telling me something "useful" in martial terms.

Flawed dimensional analysis

It seems to me that when marital artists analyse techniques, they often do so in either 2 dimensions without considering the 3rd, or in 3 dimensions without considering the 4th (ie. time). Such analysis is necessarily fundamentally flawed; “rules” applicable in one dimension do not translate equally to another. This is why Fermat’s last theorem makes intuitive sense. You can’t expect Pythagoras’ theorem, which works in 2 dimensions, to “survive” the transition to 3 dimensions, or 4 and so on.

Yet I've often noticed that when demonstrating or teaching, martial arts instructors will ask a student to launch an attack when both parties are stationary. Furthermore, the instructor might pause the attack or defence at a particular point to consider the angles and positioning. To make matters worse, sometimes the only angle considered by the instructor is that on one plane (usually the horizontal) - reducing the analysis from 4 dimensions to 3 dimensions to 2. Youtube is full of such demonstrations.

The same martial arts instructors might then go on to build an entire theory of martial technique and training on the basis of this flawed analysis. I shall give some examples in due course. But first, let us examine the common flaws in dimensional analysis:

2D analysis

I have mentioned already that instructors will, when analysing techniques, sometimes look at angles and vectors from a 2 dimensional perspective only.

So for example, they might look from above at the angle of a hook/cross/haymaker and wonder what angle of evasion/deflection/interception will negate it. But they might not look at the angle from the side. In other words, they will examine the angles and vectors on a horizontal plane without considering the vertical plane.

Using this flawed analysis, it is commonly regarded that a deflection of a curved punch from the outside is impossible. Since most “power punches” have some element of curve,2 the conclusion is made that it is impractical to attempt to deflect punches on the outside. Rather, if one is going to “block” the punch (ie. deflect or parry it) one is going to be forced to move on the inside.

This is conclusion is at odds with the generally accepted theory in traditional martial arts that you should, where possible, move to the outside of your attacker. Opponents of this traditional paradigm cite the general “improbability” of using a “block” (ie. a deflection or parry) on the outside against “punches used in the street”2 (ie. punches commonly occurring in civilian defence situations - ie. part of what Patrick McCarthy calls "Habitual Acts of Physical Violence") as a reason why the traditional paradigm is wrong: If one is forced to move on the inside, the whole “block/punch” approach becomes problematic, because one is very likely going to walk into a second punch and a third, etc.

Leaving aside the issue of whether moving on the inside is necessarily “fatal”,3 let us examine whether it really is impossible to deflect a curved punch on the outside.


A video in which I discuss common flaws in dimensional analysis of martial arts technique

As I discuss in the video above, when you consider a curved punch in 3 dimensions, you get a very different picture. All of a sudden you realise that the curve of a punch on a horizontal plane is largely irrelevant to the question of whether or not it can be deflected along another plane.

In this case, we don’t have to confine ourselves to the horizontal plane when considering how to deflect the punch. Rather, we can utilise the vertical plane (or an angled plane somewhere in between). The exact plane we might have to use depends on the circumstances.

Regardless, as I demonstrate in the above video, the deflection on the outside is not substantially more difficult because of the fact that a punch is curved – it is just that we are accustomed to thinking that it will be.

Accordingly, coming back to Fermat, we shouldn’t be surprised that Pythagoras’ theorem doesn’t translate to 3 dimensions.




If you recall, Pythagoras’ theorem states that in any right-angled triangle with the sides a, b and c (c being the hypotenuse) the following equation applies:
c2 = a2 + b2

This can be represented graphically as shown on the right.

You will note that a square built on the hypotenuse will have an area equal to the sum of the squares built on sides a and b.

But if what if we built cubes on each of the sides of the triangle? Would the volume of the cube on the hypotenuse be equal to the sum of the cubes built on sides a and b?

Intuition should tell you that the premise is fundamentally flawed because it attempts to translate a theorem applicable in 2 dimensions (squares) to 3 dimensions (cubes). If such a translation were possible, it would imply a fixed ratio of area to volume. Yet we know from the square cube law that this is not the case.

Accordingly it should come as no surprise that it is fairly easy to prove Fermat’s last theorem for the special case of right-angled triangles4 – without recourse to any of the difficult ellipsis mathematics utilised by Andrew Wiles1 in his general proof. In fact, I have done just so for the purposes of this article: I invite you to read my paper: “Fermat’s last theorem: a proof for right angled triangles”.

3D analysis

Considering the above discussion, one might be forgiven for thinking that an analysis of martial technique in 3 dimensions is going to be complete. However such an analysis denies the all-important 4th dimension – time.

In this regard, martial arts instructors will commonly discuss a particular response to a particular attack without necessarily considering that both parties are moving when the attack is launched, and how this movement relative to each other will affect the outcome. This is what I have often described as the "dynamic context" – and hence my (oft-made) argument that techniques need to be practised in such a dynamic context, rather than from a "standing start".

It is for this reason that “ippon kumite” (one step sparring) is necessarily flawed, and useful only as a tool for teaching beginners basic biomechanical and kinaesthetic skills. It cannot serve as a tool for teaching “reality-based” self-defence, because it is always predicated on the attacker and defender starting from stationary positions. This might be valid for the first attack (and I would argue that it often isn’t – first attacks can be, and are, launched when both defender and attacker are in motion) but it says nothing of what happens once the fight has begun and entered the “melee phase”.

4D analysis: placing your techniques into a dynamic context

So in order to truly understand how to apply martial techniques in a dynamic environment it is evident that one needs to practise them there.

One way to do this is in a context where your own counter attack has just been thwarted or has otherwise failed.

So, for example, there is a move at the end of the kata gekisai dai ichi where one deflects downwards and follows with a double punch. As I have discuss in the video embedded earlier in this article, this technique comes into its own when you’ve executed a kick, only to find that your kick has been deflected and you are about to fall into your opponent’s punch. In that case, the downward depressing deflection of the punch as per the gekisai movement is very effective. But unless you practice this in a dynamic context (an example being our “embu”5 or 2 person forms), you won’t ever get the chance to see how the technique might really be applied in a dynamic setting.

Another example of this is to be found in the naihanchi/naifunchin/tekki series of kata: Those kata feature a downward block followed by a hook punch. What the kata implies (but does not show) is that the kiba dachi stance must be used along the lines of evasion (tenshin) for this technique to work.6

This evasion might be angled backwards, or it might be angled forwards. As with the gekisai technique discussed above, the naihanchi movement is particularly applicable using the forward evasion when your own attack has been thwarted: With your momentum moving forward, you have little choice but to sustain that forward momentum so as to avoid falling into the line of your attacker’s counter. However this realisation will never come to light if we only ever examine the kata move with both parties starting from a stationary position…

4D analysis: avoiding the “attacker who pauses”

There is another problem with ippon kumite (one step sparring) training paradigms and it is this: the drills used often assume that the attacker will remain stationary after the attack is completed. This assumption is fundamentally flawed and is almost single-handedly responsible for the failure of many traditional martial artists to apply their techniques in a dynamic setting.

A classic example of this is to be found in the case of the kote gaeshi: most traditional schools continue to teach this technique in a manner that relies (unconsciously) on the assumption that after an attack is launched, the attacker will remain stationary. This assumption leads to some fairly fundamental errors in footwork.

Yet if one takes into account the 4th dimension (time) and factors in the continuing movement of the attacker (in particular the withdrawal of the punching arm), kote gaeshi suddenly “comes to life” as a supremely useful technique. I discuss this at length in my article “Kote gaeshi: how to apply it against resistant partners”.

In the video embedded earlier I have included some more examples of throwing methods where the 4th dimension (time) should be (but often isn’t) factored in. The images to the left illustrate one such throw. However there are many more examples one could give along the same lines – too many to recount here.

4D analysis: avoiding the “posture” premise

I have previously discussed how a martial art like taijiquan is nothing like yoga: the former deals with movement, the latter with “postures” (see my article “Taiji and yoga: poles apart?”). The same distinction can be made of any martial art vs. yoga.

However tempting it is to take “snapshots” of martial arts techniques and consider those snapshots as “postures”, this must be avoided. That is because martial arts is not about postures. And those snapshots are just that - transient points in the context of continuous movement.

In the video embedded earlier in this article I have alluded to one obvious example of the pitfalls of “snapshot analysis”, namely the sukui uke (scooping deflection) used in jodo (the art of the 4 foot staff).

The sukui uke can (and often is) “frozen” for analysis at the point where the jo would intercept the attack. When analysed in this frozen context, the angle of deflection appears manifestly inadequate: While one might argue that the angle (which is directed downward and away from the defender’s head) might well allow the attacker’s stick to slide away harmlessly, even a cursory examination will show you that the stick might just as easily slide up towards the defender’s hands.

But this whole “frozen” analysis is predicated on the basis that the technique will be employed statically as kind of “raised shield”. It is nothing of the sort. The word “sukui” (scoop) should give some clue as to how the technique is really used.

Rather than be used as a kind of “shield”, the sukui uke relies on the scooping, circular action to slide the attacker’s stick to the side and away. Simultaneously, the defender’s jo will rotate around and come down sharply onto the attacker’s head. There simply is no finer, no more poetic, technique in the whole of the martial arts: the harder the attack, the more the defender’s jo is propelled around and downwards onto the attacker. None of this is apparent if one “freezes” the movement and attempts to analyse it from there.

Conclusion

Martial arts are about movement – or, to use the baguazhang concept, change. They are concerned with understanding and mastering a dynamic, shifting world.

Attacks in civilian defence situations will necessarily take place in such a dynamic setting. They generally won’t take the form of one-step sparring, where your attacker (who has been stationary) launches an attack and remains stationary from then onwards.

So in order to correctly analyse and understand martial techniques, one needs to take into account all the dimensions of an attack and defence. Analyses that are static (3 dimensional) or limited to one plane (2 dimensional) will be fundamentally flawed, since the analyses in those dimensions won’t transfer to higher dimensions.

Mathematically, this concept is echoed in Fermat’s last theorem namely:
    No three positive integers a, b, and c can satisfy the equation:
    an + bn = cn
    for any integer value of n > 2.
Perhaps pure mathematics does have some practical application after all - if only to remind us of what is relevant (and what is not) when formulating theories upon which we base physical pedagogics.

Footnotes

1. Pierre de Fermat famously proposed his “last theorem” in around 1637 when he wrote in the margin of a copy of Diophantus' Arithmetica:
    "I have discovered a truly marvelous proof that it is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second into two like powers. This margin is too narrow to contain it."
The theorem was finally proved in 1995 by Andrew Wiles - 358 years after it was first proposed. However, Wiles used 20th century mathematics relating to elliptic curves - a methodology that would have been unknown to Fermat. If Fermat did indeed have a proof (and most mathematicians appear to believe that he did not), it would have relied upon fairly elementary mathematics (eg. algebra and geometry).

Curiously, Fermat wasn't a mathematician by profession: he was a lawyer at the Parlament of Toulouse. Despite his amateur status, he is ranked with Rene Descartes as one of the two leading mathematicians of the first half of the 17th century. Fermat's influence was such that Isaac Newton credited his method of calculus to "Monsieur Fermat's method of drawing tangents."

2. While it is true that “power punches” tend have some element of curve, it is worth noting that other punches, notably jabs, follow a straight path.

3. I propose to deal with the questions of moving on the inside vs. moving on the outside and the “impossibility” of using “block/punch” in separate articles in the near future.

4. In writing this article, I decided it would be useful to prove Fermat’s last theorem for the special case of right-angled triangles.

I then thought it would be interesting to attempt what so many have foolishly attempted, and that is to solve the theorem generally.

So, in contrast to Fermat’s comment in the margin of Arithmetica, I shall include a (purported) general proof for his theorem in this note (since there is sufficient space to contain it!):

    The assumption

    Assume:
    an + bn = cn
    where a, b and c are real, whole integers and n > 2.

    Known value of c

    For any values of a, b and c the following equation is true:
    a2 + b2 - 2abV = c2
    where V either:
    • = cos θ (a value > - 1 and < 1), if a, b and c are capable of forming the sides of a triangle and where cos θ is the angle opposite the hypotenuse; or
    • ≤ - 1 or ≥ 1, if a, b and c are not capable of forming the sides of a triangle,
    and where 2abV produces a whole integer.

    Accordingly c = √(a2 + b2 - 2abV)

    If n = an odd integer

    cn = √(a2 + b2 - 2abV) (a2 + b2 - 2abV)n-p = an + bn
    where p = the place of n in the sequence of odd integers.

    [For example, if n = 3, 3 is the second odd integer, hence p = 2
    and the following equation applies:
    c3 = √(a2 + b2 - 2abV) (a2 + b2 - 2abV) = a3 + b3.]


    If we square both sides, we get:
    (a2 + b2 - 2abV)n = (an + bn)2

    (an + bn)2 can be factored as follows:
    • (a + b)2 (an-1 - an-2b + an-3b2........ + a2bn-3 - abn-2 + bn-1)2
      or
    • (a2 + b2 + 2ab) (an-1 - an-2b + an-3b2........ + a2bn-3 - abn-2 + bn-1)2
    However (an + bn)2 cannot be factored as (a2 + b2 - 2abV)n regardless of the value of V.

    It follows that:
    (a2 + b2 - 2abV)n ≠ (an + bn)2
    if n = an odd integer.

    If n = an even integer

    cn = (a2 + b2 - 2abV)n-2 = an + bn

    [For example, if n = 4 the following equation applies:
    c4 = (a2 + b2 - 2abV)2 = a4 + b4.]


    However an + bn cannot be factored as (a2 + b2 - 2abV)n-2 regardless of the value of V.

    It follows that:
    (a2 + b2 - 2abV)n-2 ≠ an + bn
    if n = an even integer.

    Conclusion

    cn ≠ an + bn if n = an odd integer
    and
    cn ≠ an + bn if n = an even integer

    QED ;)

    Footnotes

    † It is evident that if n = an odd integer an + bn can be factored over a and b as: (a + b) (n variables of a, b) and not otherwise. So for example:
    a3 + b3 = (a + b) (a2 + b2 - ab) [3 variables of a, b]
    a5 + b5 = (a + b) (a4 + b4 + a2b2 - a3b - ab3) [5 variables of a, b]
    a7 + b7 = (a + b) (a6 + b6 - a3b3 – a5b – ab5 + a2b4 + a4b2) [7 variables of a, b)]
    etc.

    ‡ The sum of 2 integers to an even power cannot be factored over real numbers. However the equation can, in some cases, be rewritten as the sum of 2 powers whose degree is an odd positive integer, eg:
    a6 + b6
    = (a2)3 + (b2)3
    = (a2 + b2)(a4 - a2b2 + b4).
    However this still does not enable an + bn to be factored as (a2 + b2 - 2abV)n.


5. Consider my articles “Really USING your kata” and “The ‘Oh sh*t!’ moment: more about 2 person forms” and “Muidokan embu: 2 person form for karate”.

6. Consider my articles “Taisabaki and tenshin – evasion in karate: Part 1 and Part 2” and “Evasion vs. blocking with evasion”.

Copyright © 2010 Dejan Djurdjevic

Wednesday, December 1, 2010

Another award for The Way of Least Resistance!


I just received word that this blog has received the honour of another award - this time selected by Home Alarm Monitoring as one of the "Top 40 Tae Kwon Do Re Mi Blogs".

This is especially an honour since I don't practise taekwondo. I'm glad it has been of some use and interest to those who practice this fine art.

I'd like to thank Allen Wright and Home Alarm Monitoring for this honour.

Copyright © 2010 Dejan Djurdjevic