Sunday, April 11, 2010

Calculating the "Cannabis Number"

A classic Gary Larson cartoon depicts the "Libraries of Hell". All the books are labeled "Word Problems". Most people in high school hated word problems. I liked them, was good at turning concepts into math which is probably one reason I was attracted to physics. Carrying out the computations was another matter; I was and still am inept in arithmetic. Let my computer do the computations, I say: doing arithmetic is demeaning to humans. Solving word problems, on the other hand, is a worthwhile pastime.

A few days ago, while soaking in my outdoor tub (like Archimedes who is rumored to have made fundamental physics discoveries in his bath) I was pondering the 4:20 phenomenon in which first the time 4:20 PM and later the date 4/20 became associated with the smoking of marijuana. I was concerned that this number seemed arbitrary and wondered if it might only be an approximation to a more precisely defined "cannabis number" -- a number that is more than a mere human convention but is instead a perfect mathematical concept that dwells not only on Earth but in the eternal world of Platonic Forms. The Cannabis Number CN -- a number that can be calculated mathematically.

So here is my proposal: the exact "cannabis number" is not 4:20 but that time shortly after 4:20 when the Big Hand exactly overtakes the Little Hand. More precisely CN is the number of minutes past 4:20 at which this coincidence occurs.

One might even imagine that 4:20 is the approximate time to start smoking but the veils between worlds actually open at the somewhat later time expressed by the cannabis number.

When the Big Hand overtakes the Little Hand
When the Little Hand lies underneath
When the Big Hand covers up the Little Hand
When the Little Hand's on the bottom
And the Big Hand's on top
That's when the doors must open
That's when we must smoke pot.

That's how Nick defines CN. But what is the numerical value of this "cannabis number"? I leave this calculation as a problem for my readers. Please post your answer in the comments section. Hint: the problem is not as hard as the problem faced by the Russian at the blackboard.


Rudy said...

Ok, start at 4. When does the minute hand catch the hour hand?
Measure progress in minute-tick-marks, with 60in a full circle. At the start, minute hand is at 0, hour hand is at 20 minutes (where the 4 is). When the pass at the X minute tick-mark, the hour hand has moved X-20 ticks and the minute hand has moved X ticks. These represent equal spans of time, and in fact the span is X minutes. So if H is the time in minutes that it takes an hour hand to move one minute-tuck, then H(X-20) = X. We can solve for X if we know H. Well, the hour hand moves five minute ticks per hour, so H takes 12 minutes to move one minute tick. So 12(X-20) = X. So 11 X = 240. So X is 21.8181818... or, if you will, 21 minutes and a bit more than 49 seconds.
4:21:49 and a bit elss than a tenth o f a s e c o n d.
Eureka, I have found it.
per minute speed of the hour hand and M is the degrees per minute speed of the minute hand, then H(X-120) The hour hand moves 30 degrees in sixty minutes or, turning this around, it takes two minutes to move one degree. The minute hand moves 360 1/6 of a minute to move one degree...and it covers 360 ed

Nano said...

the answer is Chokhmah

Anonymous said...

I thought clock time was relative. What I do know is that4:21 is "chronic tardiness".

nick herbert said...

Rudy (Rucker), author of "Postsingular" and "Hylozoic", is a professional mathematician who eats problems like this for breakfast. Rudy sez CN = 1.81818...

I Googled Chokhmah as Kabbalistic "Wisdom"--is this why Rastafarians call cannabis "wisdom weed"?

nick herbert said...

Calculating CN by the "Zeno Technique": The Little Hand always moves at 1/12 the speed of the Big Hand. Thus when the Big Hand moves from 4:00 to 4:20 the Little Hand moves 20/12 minutes. When the Big Hand moves forward this 20/12 distance, the Little Hand has moved 20/12^2. Hence the Little Hand moves a total distance of 20/12 (1 + 1/12 + 1/12^2 + 1/12^3 + ...). This infinite series is easily summed and is equal to 12/11. Therefore the Cannabis Number CN is equal to 20/12 x 12/11 = 20/11. Which is the same as Rudy's calculation CN = 20/11 = 1.8181...

Nano said...

Nick, I shall toke up, and pick a random passage from a holy book and I shall let you know, all in the name of pastafarianism of course.

Long live the noodle.

nick herbert said...

May the Father grant you Wisdom; the Son Courage; and the Holy Spirit the Gift of Tongues.

Teh Tim said...

Chokmah, or Wisdom, is linked with the consumption of Hashish.

The activity of the CB receptors and the resulting alterations to consciousness suggest that the psychoactive cannabinoids hold Tiphareth, or Beauty/Harmony, in potential.

The actual "changes" which occur in one's perception are linked to Netzach (the processes involved in Creativity and Externalization) and Hod (the processes involved in Internalization and the development of Logic).

The overwhelming association between marijuana and "green"-ness suggests, again, a connection with Netzach, the sphere of "Nature", which is linked with Venus -- the Goddess of Love and External Sensory Bliss. Venus is known to carry a mirror which "reflects" the "inner" divine light into material existence. This implies that the experience contained in the marijuana plant is one of introspection powered by an enhancement of one's "surroundings" (or, perhaps, an external intensification powered by a focusing of the "inner Light" -- hell, its probably BOTH at the same time :p). (and as a note: its probably worth mentioning that the first encounters with this "inner Light" (as it has been described here) occur with consciousness in Tiphareth (Beauty/Harmony)).

Just thought I'd share my analysis of the matter =)

(Peace and Love, yo; Love under Will)

Nano said...


my Holy book reading read:

"...just because the whiskey glass is full, don't mean you can get it drunk."