If everyone spends there 1 random hour, how many people do we need so that each hour with probability 90% (or at least 80%) at least 2 people are there?
First, let's assume that everyone logs on and off at the hour, then there are 24 windows a day. Let's also assume that everyone chooses to work each hour with probability 1/24, rather than working one hour a day for certain. We then have a binomial distribution with parameters num and 1/24, and can increment the number of people until we get less than 20% of the probability in 0 and 1, and it turns out we cross that barrier at 71 people.
This is an underestimate because we assumed that the start/end times are synchronized.
We can also enforce the "always work exactly one hour a day" rule by seeing this as a combinatorial problem, where we have num people and 23 clock bells which are permuted randomly, and we want to know the percentage of clock bells that have at most one person in between them.
To estimate how much of an underestimate that was, I wrote a very short program to simulate this scenario. From my model, we cross over to 80% at about 85 people. Incorporating a random spread in how long people are logged in, from 0.5 to 1.5 hours, doesn't change anything.
I am not sure how many people you could get to sign up, but the fewer you get, the more hours they'd have to commit. From my model, if you can only get 60 people, they'll need to work on average 1.5 hours; for 45 people, you'd need them to commit to 2 hours.
The numbers don't look too good. Even 60 people, with an average commitment of 1.5 hours, seems like a challenge. Maybe the LW community could meet it?
Before I was very involved in the Less Wrong community, I heard that Eliezer was looking for people to sit with him while he worked, to increase writing productivity. I knew that he was doing important work in the world, and figured that this was the sort of contribution to improving humanity that I would like to make, which was within the set of things that would be easy and enjoyable for me.
So I got a hold of him and offered to come and sit with him, and did that once/week for about a year. As anticipated, it worked marvelously. I found it easy to sit and not talk, just getting my own work done. Eventually I became a beta reader for his "Bayes for Everyone Else" which is really great and helped me in my ability to estimate probabilities a ton. (Eliezer is still perfecting this work and has not yet released it, but you can find the older version here.)
In addition to learning the basics of Bayes from doing this, I also learned how powerful it is to have someone just to sit quietly with you to co-work on a regular schedule.
I’ve experimented with similar things since then, such as making skype dates with a friend to watch informational videos together. This worked for awhile until my friend got busy. I have two other recurring chat dates with friends to do dual n-back together, and those have worked quite well and are still going.
A client of mine, Mqrius, is working on his Master’s thesis and has found that the only way he has been able to overcome his akrasia so far is by co-working with a friend. Unfortunately, his friend does not have as much time to co-work as he’d like, so we decided to spend Mqrius’s counseling session today writing this Less Wrong post to see if we can help him and other people in the community who want to co-work over skype connect, since this will probably be much higher value to him as well as others with similar difficulties than the next best thing we could do with the time.
I encourage anyone who is interested in co-working, watching informational videos together, or any other social productivity experiments that can be done over skype or chat, to coordinate in the comments. For this to work best, I recommend being as specific as possible about the ideal co-working partner for you, in addition to noting if you are open to general co-working.
If you are specific, you are much more likely to succeed in finding a good co-working partner for you. While its possible you might screen someone out, its more likely that you will get the attention of your ideal co-working partner who otherwise would have glossed over your comment.
Here is my specific pitch for Mqrius:
[edit]
An virtual co-working space has been created and is currently live, discussion and link to the room here.