Why can't nine women have a baby in one month?

In this posting I plan on answering the famous question:

If it takes 9 months for a woman to have a baby, why can't 9 woman have a baby in one month?

If you don't like math, then you probably won't like my explanation.

So let's look at the general idea of splitting up a job. There are lovely quotes like

• "helping hands make light work"
• "the more the merrier"

The premise is that it takes 1/2 as long to do a job if 2 people are involved, 1/3 as long for 3 people, etc. The reality is that there is another factor called the "partitionability" or the ease with which a job can be split up.

There is another component to splitting up a job. It's the "communicability". In other words, how easy is it for everyone to communicate together when trying to get the job done. Get a scratch piece of paper and draw two dots. There is one line between the dots. For 3 dots, there are 3 lines. For 4 dots, 6 lines. For 5 dots, 10 lines. The equation for how many lines connect n dots is n(n-1)/2. Each dot represents a person and each line represents interaction between people in performing the job. Depending on the job, the "communicability" may be easier or more difficult.

When combining the partitioning with the communicability, we get the equation:



A plot of this equation looks like:



As you move from left to right, you are adding more people to help. At first you get the "helping hands" effect, and the time to do the job decreases. Then, you start running into the problem of having everyone know what everyone else is doing. That is where you start losing benefits from the "helping hands" effect. How many times have you worked on a project and somebody (maybe yourself) ended up frustrated and made one of these comments:

• I don't know what is going on.


• What am I supposed to be doing?


• I thought that was my job!


• As soon as I do something I find out someone else already did it.

For the specific case in the plot, there is actually a sweet spot where best size of a group to do the job is 5 to 8 people. This size depends on p and c.

It's also interesting to note that you are better off with one person doing the job than having 18 or more people. Of course there are other concerns here, like having the one person get hit by a bus. There is also another plot related to costs (I'll have to look it up later.)

Now we should be ready to apply this equation to a woman having a baby. Once again the question:

If it takes 9 months for a woman to have a baby, why can't 9 woman have a baby in one month?

First, if we look at the equation, the "partitionability" factor "p" is zero since you can't split up a baby between several women's wombs.

Second, the cost of communication factor "c" is infinite for the same reason. The resulting plot is here (c=0.1 instead of infinity):



The sweet spot is of course, one woman having a baby taking nine months.

The main message of this blog is to show how a scientist can use math to oversimplify reality and explain something that is already obvious. In reality it's very difficult to know the validity of assumptions when the scientific explanation is used for something less intuitive or obvious.

Desert Snow

A friend sent me this picture taken in Adelanto (in the desert near Victorville, California). It shows snow on a Joshua Tree. They had a foot of snow.

I'm a Victim ;-)

Some of us love to play the victim. We haven't been treated fairly. We've been oppressed by an evil, powerful person or organization. We can even be victims of second hand smoking.

For a while, I've been telling people that I'm a victim of "second hand dieting". My wife has been on and off diets for much of our marriage. I'd open the refrigerator, ready with my manly appetite only to find "lite" mayonnaise, low fat ice cream, and a variety of other diet foods. Once she made brownies. The smelled good! The looked good! Yuck!! What did she put in them??? A diet book said that you could use apple sauce instead of the oil. Yes, it is lower in fat and calories. No, it is not a brownie.

I guess with enough of my complaining, I am no longer a victim of second had dieting. We've compromised with 2% Milk and have plenty of other good foods.

So my latest victimization happened last week. I was walking our dog "Bo" and a car was driving by. It started to slow, so I was careful to pay attention. Whenever a car slows, there is always a chance it is turning into a nearby driveway and I have to be careful not to get hit. Especially when I'm breaking the law and letting Bo walk off his leash. This car was full of young people and had no intentions of pulling into a driveway. They were stalking ME! They rolled down their windows and I became a victim of a drive by caroling! It was the young women from church coming home from an activity. They saw me and decided to sing Christmas Carols.

I guess I'm a pathetic victimization addict if these are the worst cases of victimization I have experienced.

1929 to 2008 Stock Market Crash Comparison - Using Google Spreadsheet

This is the same as a previous posting, but instead I'm using Google Spreadsheets to see if it will be easier to update the data.

The Dow Jones Industrial average (^DJI) is scaled from 1929 by 14000/400. Day "zero" corresponds to October 24, 1929 and Oct 7, 2008.

Update: August. 1, 2015:  I learned an important lesson from this post.  I can't and shouldn't try to predict the future.

Update: Feb. 12, 2010: Scale Time Axis for 1929 (see Market Oscillations)


Added Sept. 23, 2010, 100-day moving average and 1987 Crash data.
Update May 3, 2013, New chart type

The Financial Crisis - An Epiphany

I have been asking myself as I read the continuing stream of terrible news about the financial crisis, how bad is it really? Everyday there are announcements of thousands of jobs being eliminated. The stock market and other financial markets have taken a terrible beating. The Federal government and just about every state are in deep deficits.

My chest tightens. I start gritting my teeth. I feel anxious. But then I remember something...

Just a few months ago, the news was reporting that proposition 8 was behind in the polls. The newspapers had editorials and news stories against prop 8. The media showed countless demonstrators against it. Every famous person that expressed an opinion was against proposition. Even our government officials were against it. I heard one story on the radio about the 100,000 volunteers that would be out on election day. Yet a majority of people I spoke with supported prop 8. I saw far more "Yes on 8" demonstrations in person, but very few on the news. It's no wonder that there is such a backlash after prop 8 passing. People were relying on the news for information and were mislead about what the truth was.

Another example of misleading news: I live in California and have experienced several earthquakes. While there is often severe damage near the epicenter, we usually feel mild shaking. Of course the news shows the worst footage available and we immediately get concerned phone calls from out of state relatives.

So, back to the financial crisis. Yes people are losing jobs. Yes the stock market is down and the financial world is unstable. I have asked many people, "How has the financial crisis affected you?" expecting sad stories. I have been surprised that a majority of people that I have asked have been unaffected. I spoke with my brother and his business has been booming. My company currently has too much work. I still sit in traffic everyday because thousands of people are still going to work. I do have friends that have been hit hard. Other friends have survived recent layoffs.

Is the current crisis better or worse because of the news media? I would guess worse off. So what value is the media as a source of information? One of the strongest opponents to prop 8 was the LA Times. Now their parent company has filed for bankruptcy. No matter what side of the issues you are on, the LA Times failed you. We need to continually ask ourselves when listening, watching, and reading the news: "is this accurate?".

We can also ask why we don't get more news like this.