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S2

For the sake of the math I am about to share, the length of the half life doesnt matter-- all that needs to be understood is that there is ametabolic half life-- that is, a period of time at which an original amount of something is reduced by one half. So for this example lets look at the consumption of 10 units (doesnt matter what the unit is) of THC taken at exactly the half life of the previous dose.

first you take 10 (lets assume that 10 is the amount that winds up in your system).

one half life later you take 10 more-- You now have 5 of the original dose in your syatem plus 10 of the new dose-- a cumulative total of 15

one half life later you take 10 more. Now you have 1/4 of the first dose or 2.5, plus half of the second or 5, plus the new dose- 10-- 17.5-- that is also half of the previous total plus the new dose.

The formula going forward is (1/2(CA))+ND
CA= Cumultive amount
ND = New dose

Seems like it will keep going infintely doesnt it?-- well, it wont-- it ramps up fast then levels off Here is the result of the formula over successive doses
10
15
17.5
18.75
19.375
19.6875
19.84375
19.921875
19.9609375
19.98046875
19.99023438
19.99511719
19.99755859
19.9987793
19.99938965
19.99969482
19.99984741
19.99992371
19.99996185
19.99998093
19.99999046
19.99999523
20
20
20

You level off at 20 (well actually very very very close to 20 but never reaches 20). why? Because (1/2(19.999999...))+10 = damn near 20-- as long as your consumption is consistent and you partake on periods of time equal to the half life-- it won't accumulate more than double the dose you are taking-- It wont accumulate infinitely-- even if you take large doses and at rates much less than the half life it will still level off at some point and thats that. this is wher the concept of theraputic doses comes in and why some drugs arent really effective till you have been taking them for a few days-- they need to ramop up to the therapuetic level

doesn't help you pass a drug test but an interesting phnomena none the less

however you could make the following generalization: If you take relatively small amounts and separate them by 3-4 days, you will clean up far faster than daily users, since your plateau will be so much lower than a chronic user.

but you dont need math to know that!

 

Wizard1

A very interesting break down S2....

I understand completely................and that kind of scares me!!!

And you theory of partaking , and letting it go for 3 or 4 days, to keep levels from escalating at a higher rate sound like a cogient hypothisis...

And a much better buzz when you base level is kept
lower at said intervals.

Quite intreging

S2

Thanks, sometimes I get curious about mathematics and try to see if I can come up with formulae to fit varous scenarios -- sort of like doing story probelms on purpose-- the half life issue struck me and when I started playing around with it the plataue caught me off guard-- I had assumed that it would keep going up--once i looked at the formula it made perfect sense to me-- but it seemed counter intuitive when I wasnt thinking about the math

teufelfisch

That's a good description. If your dose stays the same, the mean concentration will approach an upper limit.

However, the general trend among many drug users is to increase the dose over time. The plot no longer approaches a constant, but a line of slope proportional to the amount by which the dose was increased.

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Cassius

It's the same principle as the "go halfway" story problem. You're standing X feet from a door. You take a step equal to half the distance. Then you take another step equal to half THAT distance. Then another, and another. Do you ever reach the door? In actuality yes because it's impossible to take steps so precise, but the math says no. If you can take steps equal to exactly half the distance every time, you'll never reach there.

This half-life problem follows the same form, you just have to look at it from the right perspective. The current dose you took is worth 10. The dose you took the last time is worth 5, because you only take 10-unit doses and you waited exactly 1 half-life. The dose before that is worth exactly 2.5 to your current level, because again you took a 10-unit dose and it was exactly 2 half-lives from the current one.

Therefore, no matter how long you have been doing this (how far back in time you go adding further amounts), you get 10 + 5 + 2.5 + 1.25 + 0.625 + .... = 19.9 repeating, or 20.

Not so counter-intuitive anymore eh? =)

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