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.

My Stock Market Prediction Using the Pride Cycle

This is a follow-up to my blog on October 10.

I've been watching the Stock Market recently and after looking at historical values for the various stock indices (DJIA, S&P), the GDP (Gross Domestic Product), the CPI (Consumer Price Index), inflation, etc., I have found an interesting pattern that I think can predict what the market will do in the coming years.

Postulate 1:
There is a basic growth rate of the economy of about 3%

Postulate 2:
Stock prices represent an inflation of actual production due to confidence and other emotional factors.

Postulate 3:
The ratio of stock prices to consumption (CPI) should reveal emotional driven cycles.

First, the GDP adjusted for inflation can be predicted very closely by a growth curve, or (principal value) X (1 + % growth rate)^(# of Years). The GDP has been growing at 3%.

Second, the CPI also grows at about 3%, however it fluctuates due to inflation.

The figure below shows a linear plot of the S&P Composite Index, the CPI and a 3% growth curve from 1870 to 2008.


It's hard to tell what is happening in the early years, so here is the same plot with a logarithmic scale. This shows that all 3 lines show about the same growth.


The next plot shows the ratio of the S&P to the CPI. What this shows is how the stock market has deviated from normal economic growth with apparent cycles in the data.


These cycles I compare to "Pride Cycles". Since Stock prices are determined by individuals, there is an emotional and spiritual aspect to price fluctuations. To explain the Pride Cycle, here is a diagram:


Here's a description of the stages in the Pride Cycle

1. Humility - People are humble, willing to do what they are told
   
2. Prosperity - Good leadership arises that leads them to prosperity
   
3. Pride - They get caught up in the prosperity and start getting proud
   
4. Contention - Due to pride, they elevate themselves above others.
   
5. Rebellion - They rebel against their leadership
   
6. War/Captivity - They are invaded, attacked or declare war
   
7. Famine/Disasters - They suffer famine, unemployment, etc (natural or other causes)
   
8. Weakness - They become weak
   
9. Humility - They return to humility and start the cycle all over
   

The most recent, complete cycle was from 1950-1980. Let's see how this compares:

1950-1980

1. Humility - We just finished fighting WWII. We returned home humbled by the traumatic experience.
   
2. Prosperity - Pres. Eisenhower (1953-1961) leads the country to great prosperity which include luxury cars, home comforts like vacuum cleaners, washing machines, toasters, food mixers and electric irons.
   
3. Pride - "Keeping up with the Joneses"
   
4. Contention - The Civil Rights movement (not necessarily bad).
   
5. Rebellion - The "Counterculture" movement in the late 50's to 60's (hippies, drugs, sexual revolution, etc).
   
6. War - Vietnam War from early 60's to early 70's
   
7. Famine - Stagflation and the Oil Crisis in the Early 70's
   

1980-Present

1. Humility - We just finished with Jimmy Carter and the mess the economy was in.
   
2. Prosperity - Pres. Reagan (1980-1988) leads the country to great prosperity.
   
3. Pride - "Yuppies", BMWs, etc.
   
4. Contention - Conservatives vs. Liberals.
   
5. Rebellion - Elect Barrack Obama (Just kidding).
   
6. War/Invasion - The 1990 Gulf War, Sept 11, 2001 Terrorist Attack, Afghanistan War (2001) and Second Iraq War (2002).
   
7. Disasters - Hurricane Katrina, etc.
   
8. Famine - Rising unemployment and falling market.
   

1870-1920
(Added Feb 2, 2009)

1. Humility - We just finished the Civil War.
   
2. Prosperity - Reconstruction Era.
   
3. Pride - Monopolies, Imperialistic foreign policy.
   
4. Contention - Labor Unions, Tariffs, U.S Supreme Court upholds racial segregation (1896).
   
5. Rebellion - Great Railroad Strike (1877), Haymarket Riot (1886), Riots of 1892.
   
6. War/Invasion - Philippine-American War (1898), Spanish-American War (1898), intervention in Nicaragua (1909), occupation of Haiti (1914), World War I (1917), conquered Cuba, annexed Hawaii and Puerto Rico.
   
7. Disasters - San Francisco Earthquake (1906), Wellington Avalanche (1910), The Great Dayton Flood (1913), Hatfield Flood (1916), Spanish Flu Pandemic (1918).
   
8. Famine - I think the disasters took care of any need for famine.
   

My Prediction (Revised Nov. 20, 2008)
The stock market needs to drop to the level of the relative CPI again. Depending on where the bottom is, these are the values for the growth curve for the next few decades.

Date	DJI Average Baseline
12/1/2008	1660
1/1/2010	1717
1/1/2015	2007
1/1/2020	2343
1/1/2025	2734
1/1/2030	3188

It is possible that our economy is growing faster due to technical innovations, however the CPI and GDP don't necessarily show it.

Today, the Dow dropped below 8000 (7552 on Nov 20th). This seems alarming, but I think it still has a ways to go. My prediction is the DJIA will drop below 2500 within 10 years. While this is about an 80% drop, there was a bigger drop from 1929 to 1932 when it fell 90%.

Of course this is my opinion based on limited analysis and I do not recommend making any decisions based on this related to stocks. I do recommend staying out of debt, making purchases with cash, and working towards reaching "Humility" as soon as possible.

Made in the USA: Spoiled brats

I got this in an email. I couldn't have written this better. The email said that David Letterman wrote it. I checked it on snopes.com and it was actually written by Craig R. Smith

The other day I was reading Newsweek magazine and came across some poll data I found rather hard to believe. It must be true given the source, right? The same magazine that employs Michael (Qurans in the toilets at Gitmo) Isikoff. Here I promised myself this week I would be nice and I start off in this way. Oh what a mean man I am.

The Newsweek poll alleges that 67 percent of Americans are unhappy with the direction the country is headed and 69 percent of the country is unhappy with the performance of the president. In essence 2/3s of the citizenry just ain't happy and want a change.

So being the knuckle dragger I am, I starting thinking, ''What we are so unhappy about?''

Is it that we have electricity and running water 24 hours a day, 7 days a week? Is our unhappiness the result of having air conditioning in the summer and heating in the winter? Could it be that 95.4 percent of these unhappy folks have a job? Maybe it is the ability to walk into a grocery store at any time and see more food in moments than Darfur has seen in the last year?

Maybe it is the ability to drive from the Pacific Ocean to the Atlantic Ocean without having to present identification papers as we move through each state? Or possibly the hundreds of clean and safe motels we would find along the way that can provide temporary shelter? I guess having thousands of restaurants with varying cuisine from around the world is just not good enough. Or could it be that when we wreck our car, emergency workers show up and provide services to help all involved. Whether you are rich or poor they treat your wounds and even, if necessary, send a helicopter to take you to the hospital.

Perhaps you are one of the 70 percent of Americans who own a home, you may be upset with knowing that in the unfortunate case of having a fire, a group of trained firefighters will appear in moments and use top notch equipment to extinguish the flames thus saving you, your family and your belongings. Or if, while at home watching one of your many flat screen TVs, a burglar or prowler intrudes; an officer equipped with a gun and a bullet-proof vest will come to defend you and your family against attack or loss. This all in the backdrop of a neighborhood free of bombs or militias raping and pillaging the residents. Neighborhoods where 90 percent of teenagers own cell phones and computers.

How about the complete religious, social and political freedoms we enjoy that are the envy of everyone in the world? Maybe that is what has 67 percent of you folks unhappy.

Fact is, we are the largest group of ungrateful, spoiled brats the world has ever seen. No wonder the world loves the U.S. yet has a great disdain for its citizens. They see us for what we are. The most blessed people in the world who do nothing but complain about what we don't have and what we hate about the country instead of thanking the good Lord we live here.

I know, I know. What about the president who took us into war and has no plan to get us out? The president who has a measly 31 percent approval rating? Is this the same president who guided the nation in the dark days after 9/11? The president that cut taxes to bring an economy out of recession? Could this be the same guy who has been called every name in the book for succeeding in keeping all the spoiled brats safe from terrorist attacks? The commander in chief of an all-volunteer army that is out there defending you and me?

Make no mistake about it. The troops in Iraq and Afghanistan have volunteered to serve, and in many cases have died for your freedom. There is currently no draft in this country. They didn't have to go. They are able to refuse to go and end up with either a ''general'' discharge, an ''other than honorable'' discharge or, worst case scenario, a ''dishonorable'' discharge after a few days in the brig.

So why then the flat out discontentment in the minds of 69 percent of Americans? Say what you want but I blame it on the media. If it bleeds it leads and they specialize in bad news. Everybody will watch a car crash with blood and guts. How many will watch kids selling lemonade at the corner? The media knows this and media outlets are for-profit corporations. They offer what sells. Just ask why they are going to allow a murderer like O.J. Simpson to write a book and do a TV special about how he didn't kill his wife but if he did … insane!

Stop buying the negative venom you are fed everyday by the media. Shut off the TV, burn Newsweek, and use the New York Times for the bottom of your bird cage. Then start being grateful for all we have as a country. There is exponentially more good than bad.

I close with one of my favorite quotes from B.C. Forbes in 1953:

''What have Americans to be thankful for? More than any other people on the earth, we enjoy complete religious freedom, political freedom, social freedom. Our liberties are sacredly safeguarded by the Constitution of the United States, 'the most wonderful work ever struck off at a given time by the brain and purpose of man.' Yes, we Americans of today have been bequeathed a noble heritage. Let us pray that we may hand it down unsullied to our children and theirs.''

I suggest this Thanksgiving we sit back and count our blessings for all we have. If we don't, what we have will be taken away. Then we will have to explain to future generations why we squandered such blessing and abundance. If we are not careful this generation will be known as the ''greediest and most ungrateful generation.'' A far cry from the proud Americans of the ''greatest generation'' who left us an untarnished legacy.

Historic Election

I voted for McCain, and tonight he showed true class in his concession speech. We now have a black man as president. I personally think this is amazing. It shows how our country can overlook its racist history. I have to admit that I have been in fear of Obama becoming president (based solely on many of his ideologies). As a Christian, I am willing to forgive and forget his questionable past. Now that he has been elected president, I will be praying for him every night. I hope that when the mantle of authority rests on his shoulders, that he realizes the significance and importance of his position. My prayers will be to bless him with discernment, truth, wisdom and strength.

Tonight I was a poll watcher for the "Yes on Prop 8" campaign. As I made my very last phone call as part of this effort, I thought "finally its over". While it has taken much energy, I know that I don't have as much at stake near term as many others. I'm reminded of comments I read recently. Basically, I feel sympathy for those who had hoped for so long to have a marriage and then legally have it taken away. No matter who is right or wrong, I know that thousands of people will be suffering deep emotional pain. I will also be praying for them. I still feel that passing prop 8 was and is important, but I also recognize all people as children of God. I hope to understand how to love others better.

I will also repenting of any heated emotions that I felt or words that I uttered in this battle.

Finally, I am glad to live in California and the United States. I have found raising children among opposition to our beliefs and values to be beneficial. There have been examples and counter examples all around us of why we live the way we do.

For it must needs be, that there is an opposition in all things. If not so...righteousness could not be brought to pass, neither wickedness, neither holiness nor misery, neither good nor bad.

1929 to 2008 Stock Market Crash Comparison

Click Here for an updated version of this blog

It seems everyone is comparing our current financial crisis to the Great Depression. I thought I would compare this stock market "crash" to the one in 1929. Basically I found the day that stocks (Dow Jones Industrial) dropped to 80% of a recent high (October 24, 1929 and Oct 7, 2008). These are day 0. The bottom axis is relative to these days so that we get a good overlay.

The 100 day view shows that the two track closely. The 3 year view shows that this might take a while. (Click on images to see larger graph).

Updated December 5, 2008. Now using two axes to display actual dollar values.
An alternate viewpoint here

Thanks Mom and Dad

Financial crisis and uncertain political future have been on my mind recently. After the stock market dropped further today, I was noticing that I actually felt a calm about the upcoming challenges facing our nation and world. I thank my mom and dad for this for two reasons.

First: Tonight I was looking for my brown lunch bag. I've been using it for two weeks, even though it is slightly torn and wrinkled. I decided to start bringing lunch to work like I used to do. In school, I remember saving lunch sacks as encouraged by my mother. I always liked the pharmacy bags; they lasted the longest.

My mom and dad always taught me to make due with what I have. That's one of the reasons I started playing tennis around the age of 12. I could ride my bike with my cheap racket to a public court, and I could entertain myself and a friend at no cost. We would find balls in the bushes and make them last. I've started playing tennis again (like I've started bringing lunch and saving the bag). With Tennis, I'm more extravagant than when I was 12. I have tennis shoes I bought for $29 (on sale), my racket from Costco ($39) and I now buy my balls ($1.99 a can).

My dad made all kinds of cool stuff and could repair just about anything to extend its life. My mom was just as thrifty, sewing amazing things, cooking, etc. Recently I was in a group and the question was asked "what is your family heritage?". I drew a blank at the time, but since I've realized the part of my heritage is to be thrifty; finding value in and appreciating all resources.

Second reason I am feeling calm is the eternal perspective my parents taught me. I feel that this is in complete harmony with my parents thriftiness. There is a greater purpose that extends beyond life's obstacles and set backs. Actually, these challenges make life more valuable. While going through a challenging period a few years ago, I remember praying and my thoughts were drawn to my father. The details are very private, but I realized that his life was an example of integrity and consistent with the principles he taught. I realize the same is true with my mother.

In the Doctrine and Covenants, section 38 verse30 it reads: "if ye are prepared, ye shall not fear".

Thanks Mom and Dad for preparing me.

The real cause of the financial crisis

I'm departing from my usual defense of marriage blogging to focus on the current financial crisis.

While this article primarily blames the financial crisis on the demise of the 1933 Glass-Steagall Act in 1999 and tries to blame the Democrats and Bill Clinton, the truth is it was primarily a 1999 Republican bill and vote that repealed the act (even though Bill Clinton did sign the bill). The data presented, however show that the rise in subprime mortgage lending started 2 years earlier in 1997.

The best information that I could find related to this was in a PBS Article. Basically Federal Reserve policies and Republicans opened the door to bad lending.

The real financial crisis is the Community Reinvestment Act. The article in wikipedia states:

Clinton's HUD secretary, Andrew Cuomo, "made a series of decisions between 1997 and 2001 that gave birth to the country's current crisis," the liberal Village Voice noted. Among those decisions were changes that let Fannie and Freddie get into subprime loan markets in a big way. [2] Other rule changes gave Fannie and Freddie extraordinary leverage, allowing them to hold just 2.5% of capital to back their investments, vs. 10% for banks.

In 2003, Bush attempted to overhaul the finance industry but his proposal was rejected along party lines. Ron Paul introduced "FREE HOUSING MARKET ENHANCEMENT ACT".

In a related New York Times article on Sept. 11, 2003, there is a quote from Representative Barney Frank of Massachusetts, the ranking Democrat on the Financial Services Committee

''These two entities -- Fannie Mae and Freddie Mac -- are not facing any kind of financial crisis. The more people exaggerate these problems, the more pressure there is on these companies, the less we will see in terms of affordable housing.''

Gandhi Quote

"I like your Christ, I do not like your Christians. Your Christians are so unlike your Christ."
-- Mahatma Gandhi

I'm currently analyzing Christ's words in the four gospels. As a result, I'm seeing some interesting patterns. I'll be posting more about this later. Gandhi is right; we all fall short of being what Christ asks of us.

My most recent favorite:
Matthew 25:31 ¶ When the Son of man shall come in his glory, and all the holy angels with him, then shall he sit upon the throne of his glory:
32 And before him shall be gathered all nations: and he shall separate them one from another, as a shepherd divideth his sheep from the goats:
33 And he shall set the sheep on his right hand, but the goats on the left.
34 Then shall the King say unto them on his right hand, Come, ye blessed of my Father, inherit the kingdom prepared for you from the foundation of the world:
35 For I was an hungred, and ye gave me meat: I was thirsty, and ye gave me drink: I was a stranger, and ye took me in:
36 Naked, and ye clothed me: I was sick, and ye visited me: I was in prison, and ye came unto me.
37 Then shall the righteous answer him, saying, Lord, when saw we thee an hungred, and fed thee? or thirsty, and gave thee drink?
38 When saw we thee a stranger, and took thee in? or naked, and clothed thee?
39 Or when saw we thee sick, or in prison, and came unto thee?
40 And the King shall answer and say unto them, Verily I say unto you, Inasmuch as ye have done it unto one of the least of these my brethren, ye have done it unto me.