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Its such an odd question. Almost as bad as the one about monkeys and Shakespeare's Hamlet. But its not that hard. Its a bit mathematical, though.

First we must start with the basic premise that time flies when you (the metaphorical you, not you personally) are having fun. Then we extrapolate it to say that the more fun you have, the faster time flies.

This obviously means that:

Actual Time - Perceived Time = Fun (measured in seconds lost)

The next step in this experiment (it's the best part) is to play with one monkey as a friend uses a stopwatch to time you. When you are finished, you tell him your Perceived Time and he records the Actual time. Then you use the above equation to find out how much fun your monkey is.

Now comes the sad part. Put the monkey in a measured amount of water. You'll have to drown the bugger because he'll thrash too hard for you to tell how much water he displaces. I know, I know, but they're MONKEYS, the FDA hasn't approved this procedure for human trials. Once this is done you'll know two things: How much fun is 1 monkey, and what volume is 1 monkey.

Now, when your barrel of monkeys arrives, you must find its volume. best to use the formula for cylindric volume; barrels float, and if you think one monkey thrashing is hard to drown...

Now some math:

Volume of Barrel / Volume of 1 Monkey = No. of Monkeys in the Barrel

and then:

How Much Fun Is 1 Monkey x No. of Monkeys in Barrel = How Much Fun is a Barrel of Monkeys

Easy, no?

I can't help but notice the extreme flaws in the above theory. How is recrezoobarrelology (the study of fun animals in barrels) supposed to be taken as a serious field of study with inconsistent theories such as this being published? In fact, every single equation cited is flawed.

First Flaw:
Actual Time - Perceived Time = Fun (measured in seconds lost)
However, as was stated quite clearly as the foundation of this entire theory, time flies when you're having fun. In other words, the more fun you are having, the faster time flies, which as an equation can be expressed as:
Actual Time / Fun quotient = Perceived Time
Or, to make fun the subject of the equation:
Fun quotient = Actual Time / Perceived Time
This results in time flying by a factor dependent upon the determined fun quotient. At a fun quotient of 2, time flies twice as fast. This theory is also extendable to cover tedium, in which case the fun quotient is less than 1.

If the original equation of actual time - perceived time determining fun was accepted, then it would suggest that a monkey is very little fun when encountered for a small actual time, but a lot more fun when you are with it for a larger amount of time. While to be fair this may accurately state the "total fun benefit obtained" from the monkey in the amount of time, it does not give an accurate quantification of how much fun a particuar monkey is (though if carried to the extreme, with the monkey played with until it is no longer fun, then the total fun content of a single monkey could be ascertained).

Second Flaw:
Volume of Barrel / Volume of 1 Monkey = No. of Monkeys in the Barrel
I'm particularly surprised this mistake made it through, since it does not consider the packing density of Monkeys in transit. Keep in mind there must be at least some quantity of oxygen in the monkey barrel, unless you have ordered a barrel of bonsai monkeys. Also consider that in transit, at least some of the barrel will have filled with monkey poo (which is *definitely* not fun, unless being thrown by the monkeys at people you dislike).

In order to use cylindric volume to calculate the actual volume taken up by the monkeys, it is first necessary to remove any gaps between the monkeys, so you are measuring their volume alone, and not that of any air between them. To do this, you feed the monkeys into a large blender, blending until completely liquified, then feed them into an empty cylinder (preferably transparent and labelled with appropriate measurement markings in advance, but keep in mind to measure from the bottom of the liquified monkey meniscus!). Once this is done, ensuring that all the monkeys have been completely liquified, and no longer have any gaps between them, the number of monkeys can be calculated as follows:
(Depth of Liquified Monkeys * pi * (radius of cylinder)^2) / Volume of one monkey = Number of monkeys
Of course, you could always just count the monkeys in the barrel, removing the need to liquify them, but where's the fun in that?

Third Flaw:
How Much Fun Is 1 Monkey x No. of Monkeys in Barrel = How Much Fun is a Barrel of Monkeys
The main flaw in this equation arrives as a result of the first flaw mentioned above. Since fun is not an actual integer value, but rather a quotient, this formula will no longer work, since it would most likely vastly overstate the amount of fun a barrel of monkeys are. For example, if a single monkey makes time fly 20% faster, giving a fun quotient of 1.2, the above equation would say two monkeys make time fly 140% faster! While I don't doubt two monkeys may be fun, that may be a bit of an overstatement. A more accurate estimate would be:
Fun Quotient of a Barrel of Monkeys = ((Fun Quotient of 1 Monkey - 1) * Number of Monkeys) + 1

However, even then, one must consider the law of diminishing returns. I'd suspect that once you start passing 100 monkeys or so, it's pretty hard to get too much more fun out of them. All your primate fun potential will have been exhausted, in a kind of Amdahl's Law sort of way. In order to determine this, further experiments should be carried out to determine at what rate additional monkeys truly do increase fun levels, by performing experiments to determine the fun quotients of varying numbers of monkeys, and comparing it to the graph produced by the function stated above. In fact, I'll order my lab assistant to start research on that immediately once he's back from his latest tetanus and rabies injections...

Well, now that those problems have been addressed, you budding recrezoobarrelologists can get back to your monkey drowning, safe in the knowledge that your findings will be properly calculated. Now all I need to do is figure out how to get this published in a scientific journal....

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