Wednesday, February 15, 2006

Zen Koan Solutions


Koan is a riddle in the form of a paradox used in Zen Buddhism as an aid to meditation and a means of gaining intuitive knowledge, basically a Zen teaching riddle. They are used to break down the barriers to enlightenment. I guess the most famous koan is: "Two hands clap and there is a sound. What is the sound of one hand?". There are many koans like this which keep Zen students busy. Here is a totally scientific and mathematical explanation by me. How to find a solution for these koans:

"Two hands clap and there is a sound. What is the sound of one hand?"

(h) = hand
2(h) = 2 hands
dB = sound (The decibel ( dB ) is used to measure sound level)

from here we can formulate ( x is the sound level of the clap):

2 X (h) = xdB
if 2(h) = xdB
then (h) = xdB / 2

The answer is:

(h) = xdB/2

"Does a dog have Buddha-nature or not?"

We can apply some complex aritmetical rules.
Every complex number has the "Standard Form" : a + bi
So Buddha nature (Bn) as "Standart Form"

Bn = a + bi

for some real a and b

a + bi = 0 if and only a = b = 0

Dog d for some real a and b

if d = a + bi
then d = 0 if and only a = b = 0

d = Bn = 0

"If a tree falls in the forest when there is nobody around, does it make a sound?"

dB = (x) sound level
t = tree
v = velocity of the tree
p = power

t X 1/v . (xdB) (It is the sound that tree makes in certain velocity)
t/v . xdB
t . xdB / v

To measure the two different sound:
P1 = Measured power
P2 = Reference power

The difference in decibels between the two p (powers) is defined to be

10 log (P2/P1)dB where the log is to base 10.

n = nobody
f = forest
if n = 0 then f (n) = P1 [ pmeasured ]
if n > 1 then f (n + 1) = P2 [ preference ]

If the second produces twice as much power than the first, the difference in dB is

10 log (P2/P1) = 10 log 2 = 3 dB
10 log f(n + 1)/ f(n) = 3 dB

Now the power in a sound wave, all else equal, goes as the square of the pressure. (Similarly, electrical power in a resistor goes as the square of the voltage.) The log of the square of x is just 2 log x, so this introduces a factor of 2 when we convert to decibels for pressures. The difference in sound pressure level between two sounds with p1 and p2 is therefore:

20 log (p2/p1) dB = 10 log (p2*2/p1*2) dB = 10 log (P2/P1) dB Where again the log is to base 10.

What does 0 dB mean? This level occurs when the measured intensity is equal to the reference level. i.e., it is the sound level corresponding to 0.02 mPa. In this case we have

sound level = 20 log (pmeasured/preference) = 20 log 1 = 0 dB

So 0 dB does not mean no sound, it means a sound level where the sound pressure is equal to that of the reference level. This is a small pressure, but not zero.

Note: Koans are paradoxical riddles, a problem with no logical solution assigned to students of Zen Buddhism as a subject for meditation. Koans are intended to break through the limitations of ego and intellect and lead to an intuitive flash of enlightenment. There are no logical or arithmetical explanations of these problems because they are meant to break the borders of logical thinking. I am neither a Zen student nor a mathematician and this was just written for fun when I was suffering from a fever and headache.

But Hacker and Artificial Intelligence culture invented some humoristic koans. If you are interested you can check them here and here.

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2 Noises:

At Thursday, March 02, 2006 4:49:00 PM, Anonymous Josh R said...

Seriously, you should sit down and contemplate these without any tools in your hands. Your are cheating yourself if you think these mathematical attempts of solutions are valid.

At Thursday, March 02, 2006 5:08:00 PM, Blogger . nothing . said...

Note to Josh:

Thank you for your comment. But did you read my note at the end of the post clearly? "There are no logical or arithmetical explanations of these problems because they are meant to break the borders of logical thinking." I know what Zen koans are and what they meant for. The only tool you need to solve these koans are yourself, not even your mind!. I know about Zen philosophy and Buddhism more than you think.

And, as the tag of this post explains, it was meant for fun, but not making fun of Zen, there is a difference between. And if you even look at the arithmetical formula's here, some of them are not even scientifically valid, because they are for fun!.

I believe you can have and find humor in everything, even if it's related to something serious.

Thanks again for your comment, cheers.


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