Special Numbers
Do you know what a googol is? A googol is a very, very large number. 1.0 * 10100. Or, in long-hand…
10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
I remember googol from some trivial bit of knowledge in my “math geek” high school days. I just stumbled across it again in my reading and it’s fascinating me. I’m reading all about natural numbers which are normal numbers like 0, 1, 2, 3 and so on. Not the supposedly unnatural numbers like 3.14159265. Decimals and fractions are straight out. The most natural are the prime numbers. Once you are a prime you are in a class of your own, however, there is even a pecking order in there with a variety of special types of primes. While it’s not a prime hunt, Sierpinski numbers are one example of this that I’m currently helping hunt for.
After stumbling on googol I had to try my favorite Google function ever, the Google Calculator. There is no connection between Google and googol other than sharing the same letters and both sounding like something a 8 month old baby may emit during feeding. I was not disappointed, Google Calculator let me know exactly what a googol is. The calculator even defies the 32-bit (or even 64-bit) world and at least pretends to tell me things like googol mod 154351. However, it has yet to give me a number that doesn’t evenly divide into a googol so I’m tempted to test it to see if it’s really doing it right. Maybe a prime number generator built off of Google? Would probably be really slow but could make a great article for Wired magazine. 🙂
I now have a new favorite Google Calculator query (replacing the answer to life the universe and everything):
mass of the earth * (googol * speed of light) / pi
which it effortlessly tells me is
(mass of Earth * (googol * the speed of light)) / pi = 5.70099405 × 10132 m kg / s
which is completely meaningless and entirely useless, but very fun.
Prime Number Hunt
I’m reading a book on math (specifically cryptography). I was doing some searching online about prime numbers and ran across the project Seventeen or Bust. It’s interesting and you can participate by running the client.
Oceans Twelve
Tammy and I along with her two sisters and their significant others went to see Oceans Twelve today. I thought Oceans Eleven was great so I was eagerly looking forward to Oceans Twelve. It was a fine movie, but didn’t live up to the previous one. For some reason the soundtrack and cinematography impressed me more than the actual story. Will have to check out the soundtrack when it is available.
The Da Vinci Code
The last time I read a book as aggressively as I read The Da Vinci Code had to be the Dune series. I don’t intend to elevate this book to that level, after all, Dune is one of my favorite stories ever. However, this book is an absolute page turner. Usually books take about 50 to 100 pages to get me really interested. This one took the first 2!
I thoroughly enjoyed this book. A very fun read. I’m not going to say anything about the story – I want you to be as surprised as I was while reading it.
What's the Matter With Kansas?
I heard about Thomas Frank’s book What’s the Matter With Kansas? on The Daily Show shortly after the presidential election. The author caught my interest and I picked up a copy of the book. I found this book to be a great read. He does a good job of looking at historical precedent and taking apart what has changed.
From the book:
A while back the Wall Street Journal ran an essay about a place where hatred trumps bread,? where a manipulative ruling class has for decades exploited an impoverished people while simultaneously fostering in them a culture of victimization that steers this people’s fury back persistently toward a shadowy, cosmopolitan Other. In this tragic land unassuageable cultural grievances are elevated inexplicably over solid material ones, and basic economic self-interest is eclipsed by juicy myths of national authenticity and righteousness wronged.
The essay was supposed to be a description of the Arab states in their conflict with Israel, but when I read it I thought immediately of my dear old Kansas…
Frank does not write from the center. He clearly is pro-liberal, pro-union and pro-choice. However, the text does not turn into self-righteous drivel. In fact, he takes issue with the lack of liberal attitudes in the democratic party – pointing out the weakness that now dominates it.
Finding Neverland
Finding Neverland is a really great movie. We went to see it today during a matinee and it seems others had this idea as well. The movie was in one of the smaller theatres and it was packed for a 2:00pm matinee. Johnny Depp is great in this story about the making of Peter Pan.
I will not try to summarize the story only to tell you that there were very few dry eyes leaving the theater. The story takes a sad and heartfelt turn at the end.
You will not regret parting with your $8 for this one.
iMac G5
Those of you that have had to endure me rambling on and on about
computers at some time probably know that I cut my teeth in the world of
Apple. Actually, my computer lineage is like this:
- TI-99/4A
- Apple //c
- Fat Mac
- Macintosh IIc
- “the wonderful world of Unix”
- Windows NT
- on and on…
I was a huge Mac fan (err, zealot?) when that wondrous thing called multi-finder was released. I was eager to see the first color Mac. I really like these machines, but I got so frustrated with the sad excuse for an operating system that I had to bail. Additionally, they just don’t carry any weight in the business world.
I’ve been excited about Mac OS X for a while now and I finally took the plunge. They had a one day sale and I decided it was time to get an iMac. I got the 20" iMac G5. It’s the most visible computer in our house so I appreciate the aesthetics. Plus, it’s just a lot of fun.
I just got it set up tonight. It’ll take a while to stop fumbling around in this thing. I’ll share my re-acquaintance experiences as it goes.
Thingelstads Announce Pregnancy
MINNETONKA, Nov 25, 2004 (BABYWIRE) – Jamie and Tammy Thingelstad took a moment out of their Thanksgiving day activities to announce they are pregnant with their first child. The couple are ecstatic with the news and eager to let friends and family know.
The Thingelstads had decided that it was time to start a family shortly after getting married in 2002. After an unsuccesful attempt last year they were eager to try again. Tammy suspected that she was pregnant after having continual cravings for Lion’s Tap cheeseburgers. She took a home pregnancy test and was excited to see the good news. It was very early though and the couple kept the news close.
After passing the first trimester the couple made a trip to get an ultrasound as initial tests for the heartbeat were not successful. The ultrasound showed a healthy, early stage baby with two legs, two arms, a huge head and a quickly beating heart. While conducting the ultrasound it kicked a few times and spun around. Fetal movement is a great sign of a healthy baby.
This is the first grandchild for both sets of grandparents. Upon reaching them they were overjoyed. Kaye Olson, mother of Tammy, simply shrieked after hearing the news! Rosalin Chrest, mother to Jamie, was excited to hear the news and started sewing baby clothes immediately. Meanwhile Don Olson, famed softball coach and father to Tammy, immediately renewed his contract with the local girl’s softball league and quickly joined Tammy in hoping for a daughter. The numerous aunt’s of the future child were all delighted as well.
The Thingelstads are looking forward to a smooth pregnancy and a new member to the family in June of 2005. Tammy is hopeful the child will not take after her husband’s 9 lbs 8 oz birth.
About the Thingelstads
Jamie and Tammy Thingelstad reside in Minnetonka, Minnesota with their cats Logan and Gypsie. They have been married since July, 2002. The couple enjoys outdoor activities and decorating a very colorful house.
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SOURCE: Thingelstad’s
Jamie and Tammy Thingelstad
Change Game
Introduction
When my wife and I decided to get married and start living together she found one of my habits to be a little annoying. It’s a habit that most guys have regarding change. Most guys probably have a jar, shoebox, or some other type of container that is filled with spare change. At the end of the day, you simply empty your pockets of change and put it in there. I had, over the years filled various containers full of change and every few years would lug it to the bank to be counted.
She didn’t think much of the boxes of change sitting around, so she tried to convince me to make a game out of using my change. Instead of thinking of all that spare change as a nuisance, it was a challenge to figure out how to use it in the right combinations. The goal of the game? To complete a cash transaction and have no change left in your pocket.
My slightly obsessive nature took this game and just ran with it of course! If you wish to play along, continue reading.
Recommended Equipment
The change game requires no equipment at all, but even intermediate players will find that their game play is improved with a simple coin purse. Here is an example of a leather coin purse that is ideal for the change game. Buy one here!
Coin purses can also be found in plastic, however they do not wear as well as the genuine leather type. This coin purse will allow you to keep your change organized, and by simply squeezing it’s sides the change game enthusiast can determine their change situation.
Rules
There are only a few rules to the change game.
- The ‘Give a penny, take a penny’ tray is completely out-of-bounds for the change game. You may not deposit a penny, or any other coin, into it or use a coin from it in your transaction. Ever!
- You cannot tip your way to a win. Simply taking the change you have and putting it in a tip jar disqualifies a win.
- The value of the coin is irrelevent for the change game, you only care about the number of coins. Having three quarters is as close to winning as three pennies.
- You win when you have no coins left!
Basic Strategy
When playing the change game you need to keep an eye on your current status. Strategically, certain combinations of coins are more likely to yield a win or be used quickly. Also, remember that small coins can be moved quickly.
For example, while 5 pennies are a lot of coins, you can use them very quickly as a nickel substitute.
 
A great tip while playing the change game is to combine nickels and dimes in place of quarters.
Advanced Strategy
To the uninitiated the change game can be a simple game of luck. It seems straightforward that you will have a set amount of change, hopefully less than $0.99, and the transaction will require change between $0.01 and $0.99. You have a 1 in 99 chance of winning. However, this assumes that the change required for transactions is evenly distributed.
To test wether this is indeed the case we analyzed 2,886 transactions over a 7 year period. These 2,886 transactions excluded restuarant bills (since they are typically rounded with a tip) and recurring payments or utility bills that would bias a specific cent value. We also excluded all transactions over $1,000 since it would be unlikely that cash would be used in such a transaction. The average transaction was $61.15 and the median was $35.29, with 1,850 of the samples being below $50, a very reasonable amount for a cash transaction. We then plotted the distribution of the change required for these transactions.
The distribution is not even. Nine values appear over 40 times in this analysis: $0.02, 0.04, 0.50, 0.80, 0.90, 0.94, 0.95, 0.98 and 0.99. While these 9 numbers only represent 9.1% of the possible winners, they are 15.8% of the transactions. In fact, if you just focus on the values above $0.90, those four values which only represent 4.0% of the possible outcomes are 7.8% of the actuals.
It is also clear that certain ranges or values should be avoided. There are nine more values that appear fewer than 20 times: $0.12, 0.27, 0.31, 0.33, 0.41, 0.58, 0.62, 0.66 and 0.74. While these should represent 9.1% of the winners, they actually are only 5.3%. Clearly combinations that should be avoided.
In general you can observe in the pattern that the range above $0.50 has a slightly higher likelihood of winning than the range below it.
Winning
You win the change game when you have depleted all of your coins. The coin purse on the left is an example of an ‘in play’ player and the coin purse on the right is after winning (the safety pin is not relevant to the change game).