How to avoid insanely high times in "post to add time"-threads

[Fiona]

This may be less of a regular dare and more of a howto, but hopefully it will motivate some of you to create that kind of thread since you can be positive that it will remain somewhat sane.

Also: I'm daring you to read through a mathematical text and trying to understand it, certainly for some of you that has to be torture. ;-)

-----------------------------------

I often see people create threads along the lines of “every post adds one day/week/whatever to my time in denial/chastity/...” which then blow up resulting in very high results. The issue here is the mostly linear growth of the time with the posts: On the one hand, nobody is going to post if the initial time is over before the first post or if it is very short, on the other hand high times tend to blow up.

The correct solution is to remember your math-lessons: There are many more functions than just boring linear ones. One post that is currently running had the right idea in that sense, except that the picked function was that the n'th post would add n hours; the function that results from that can alternatively be written as follows:

n → (n² + n) / 2

This is a quadratic function and it soon resulted in very high times that seem to have surprised the poster. Don't use something like that. unless you want to get a permanent time.

Though if you really want to get a permanent time, you can also say that every post adds twice the time that the previous one added. This is what is known as an exponential function, it is defined as such:

n → 2^n

Almost all laypeople underestimate how fast this function grows because it seems to start out rather innocent: 1, 2, 4, 8, 16, 32. But let's look just a bit further: if n=10, you get a still somewhat manageable 1024, for n=20 you get 1048576 and for n=30 you get a staggering 1073741824. Long story short: Don't use exponential functions or anything like it.

Of course I'm not posting here to give you bad ideas with functions that go through the roof, but instead to provide you with functions that limit the maximum time.

The simplest function for that may be the one that always reduces the added time by a constant factor (for example every post adds halve of what the previous one added). This may sound like a solution but has the undesirable property that this function is what mathematicians would call convergent and in fact converges very fast: If you divide by two, the maximum time that you can ever get is twice the time of the initial post. I call that boring.

Another solution that has a maximum time would be to start with the first post being able to add a large amount of time (let's call that k units of time) and subtract one from that with every following post until no more new time is added. (So the second one adds k-1, the third k-2 and so on.) Obviously this also results in a maximum time, namely (k²+k)/2. (If this sounds familiar, that is because it is exactly the same formula as the one where we add one unit of time per added post in the beginning, except we do it backwards.) I would say that this is better, but still not fully convincing.

What I would consider desirable would be a formula that adds a decent amount of time rather quickly in the beginning but that reduces the added time to prevent insanely high values, without there being a hard maximum time. The great thing is that there are indeed such functions, the most popular one being the so called harmonic series where the n'th post adds 1/n units of time. That sum grows to infinity but will after a certain amount of time grow increasingly slowly. The issue if you use it like that is of course that the first handful of posts will still have a very high effect compared to everything that follows.

The solution to this is to not start at zero: Instead act as if the first 20 posts had already been made and discarded and multiply the the added time be 20: That way the first post adds 20/20=1 units of time, the second one 20/21, the third 20/22 and so on. The resulting development looks like this:

1: 1.0
2: 2.0
3: 2.9
4: 3.7
5: 4.6
6: 5.4
7: 6.1
8: 6.9
9: 7.6
10: 8.3
11: 8.9
12: 9.6
13: 10.2
14: 10.8
15: 11.4
16: 12.0
17: 12.5
18: 13.1
19: 13.6
20: 14.1
21: 14.6
22: 15.1
23: 15.6
24: 16.0

OTOH, if you get 300 posts you will still be 56 units. It's of course your choice what the time-units are and also to change the starting-point. If you choose 50 for example, the values change like this:

1: 1.0
2: 2.0
3: 2.9
4: 3.9
5: 4.8
6: 5.7
7: 6.6
8: 7.5
9: 8.4
10: 9.2
11: 10.0
12: 10.9
13: 11.7
14: 12.5
15: 13.2
16: 14.0
17: 14.8
18: 15.5
19: 16.2
20: 17.0

yet, even after 300 posts, you would still be at 97.7

It's of course up to you whether these are days, hours, weeks, whatever.

Anyways: My personal conclusion is that versions of the harmonic series are the most sensible thing to use for almost all of the “post to add time”-threads.

[Butterfly]

I have moved this to the getdare.com section as it is not a dare.