Why Math?
Many people ask, "Why do I need math?
I know how to add, how to subtract, divide, and multiply."
But tell me this, what do you know about probability?
Do you know what expected value is?
Or combination or permutation?
We lose when we play the lottery, we lose at roulette.
We lose at blackjack, slots, and craps.
Doctors make mistakes conveying probabilities
Of sickness or infection to patients.
Courtroom testimonies that are full of crap,
Are accepted as reality.
CEOs are worth billions of dollars,
After a single year of good performance.
But in the next years they aren't worth half that much.
But we can stop wasting our time and money,
If we take the time to learn more about stats,
And probability.
There are mountains of data that surround us,
And processing it is difficult.
Learning stats and probability,
Let us make better life choices.
But for now they don't understand.
They don’t understand
The principles of randomness.
Something Needs to Be Done
Dear Mr. Neil DeGrasse Tyson,
I have heard a lot about your activities in promoting the STEM sector of education and economy. You give me hope for a better future for the STEM sector in the U.S. by championing STEM education. Student these days in the U.S. do not receive enough training on probability, statistics, and other real-world applications of math that is more advanced than arithmetic. Every year, people as a whole lose millions on lottery tickets, hoping for that slight chance to win big. Many others go broke trying to gamble their way back from debt in a casino or other setting, a statistical improbability. People do not understand that in a casino, the house always wins in the long run, so playing more loses more money, and playing three other people in poker, even if you are twice as good as any of them, there is still a negative expected value. Students no longer know what nCr is, or what the Monte Hall problem is. In fact, very few of them can even solve a probability problem using a simple, case-by-case basis to decide whether or not a decision is beneficial.
The lack of mathematical understanding of real-world situations is hindering our children substantially on the world stage, especially against countries like China, who are in close competition with the U.S. Despite being the most powerful and technologically advanced nation on the face of the planet, our students' average mathematical capabilities rank 25th in the world. In fact, this mathematical deficiency even extends to doctors, who have a responsibility to inform you of the results of your tests. I myself have been subjected to this lack of understanding.
My doctor told me that there was a 99.9% chance I was going to die within 10 years. I had tested positive for AIDS. However, after a little research I discovered that the doctor had reported the probability that I had tested positive for AIDS given that I had AIDS, instead of the probability that I had AIDS, given that I had tested positive. In reality, I did not have AIDS, and the true probability my doctor should have reported was 1 out of 11. Even professionals who should be trained against making such mistakes are showing holes in their learning. This is a clear indicator that skills related to analyzing data and calculating probability is severely lacking here in the US, and something needs to be done.
Since you are so well liked and well known, I hope that you will champion the improvement of mathematics classes throughout the nation as you do with science education. The children of America and its future depends on the realization of this problem and on how the administration deals with it. If we hope to continue producing the world's top scientists and engineers, as well as overall, educated populace, I am sure you'll agree with me that this problem must be addressed, because right now, they don’t understand. They don’t understand the principles of randomness.
Sincerely,
A Concerned Mathematician
If Probability Was Person
Probability is not very popular. He doesn't have many friends, and the only ones he has think he is annoying. Probability is a very complex person, which only a few can figure out. He feels lonely sometimes, and often quite useless, despite his great potential. The only true friend to Probability is Statistics, who needs Probability for much of his job. Probability and Statistics get along well, but there are days when Probability feels that Statistics doesn't need him anymore.
Not so long ago, Probability was diagnosed with attachment disorders and given medication. However, his medication doesn't always work well and some days he feels particularly bad. Statistics often tries to comfort Probability, who desperately clings on to his only true friend. One day, Probability is feeling especially down, and Statistics is away on a business trip, one that does not require help from Probability. It was then that Probability decided that if no one wanted him or needed him, he might as well just end it all. So, he went to the top of the tallest building in his city, and as he was standing at the edge of the roof, he told himself, “No one cares about what I can do. No one cares about my factorials, or my permutations. No one cares about how I could contribute to society.” And so, Probability jumped off the building, and died.
The next day, Statistics returned from his business trip to find that everyone had gone crazy. Without probability, people could not make good life choices. Some were jumping off rooftops, believing they could fly. Others were gambling away millions on ridiculous bets. A select few even played Russian Roulette with five bullets. Statistics, after spending so much time with probability, understood some basic principles, and was not vulnerable to stupid decisions. As for everyone else, they don’t understand. They don’t understand the principles of randomness, they don’t understand probability.
A Mathematical Day in the Life of Bob
7:30 a.m. Bob wakes up, showers, brushes his teeth, eats breakfast, and watches the news. The weather comes on every 10 minutes for 2 minutes, breakfast takes 10 minutes, so there is an 83% chance of Bob catching the entirety of the weather while he is eating.
8:30 a.m. Bob shows up at the train station. The train arrives every 10 minutes, stops for 20 seconds, so only a 3.3% chance a train is stopped at the station when Bob reaches the top of the platform.
8:45 a.m. Bob gets of the train and walks two blocks to his office. The two traffic lights are green for 30 seconds, flashing for 15 seconds, and red for 45 seconds. There is a 11% chance that Bob is able to walk to the office without having to stop at a traffic light.
8:55 a.m. Bob arrives at the office building. The elevator is constantly going from floor to floor, but consistently returning to the first floor, since people are always waiting for the elevator before work. Average time between the elevator arriving is 45 seconds, standard deviation is 20 seconds, so the probability of an elevator arriving within 15 seconds of Bob arriving is 7%.
8:56 a.m. Bob arrives at his floor, but doesn’t want his boss to see him, because his boss is always asking Bob to fetch coffee for him. The boss looks out his door for 10 seconds every 30 seconds. It takes Bob 15 seconds to walk to his desk. Probability of not being spotted by his boss is 16%.
11:17 a.m. Bob is getting bored, so decides to go on Facebook. Bob switches between his work and Facebook every 30 seconds, and his boss, while walking around, can only see his screen for 10 seconds, but will see his screen 3 times. Probability of not being caught is 11%.
1:00 p.m. Bob is going out to lunch, but doesn’t want to run into a co-worker he got into a fight with yesterday. They are both going to the same restaurant and ordering out. Bob will be there for 7 minutes, and his co-worker, being indecisive, will be there for 8 minutes, both between 1:00 and 1:30. The probability of them not running into each other is 44%.
1:50 p.m. Bob is heading back to the office. However, he knows that there is a planned protest that will be on a street he needs to pass by, but he doesn’t remember whether it is at 1:45 or 2:45. It will slow him down 10 minutes, but taking an alternate route guarantees an extra 4 minutes. The best decision is to take the extra route, which has expected value of 4 extra minutes as opposed to gambling, which has expected value of 5 extra minutes.
4:00 p.m. Bob has a presentation to make, but he is unprepared. There are five people going before him, and Bob thinks that they’ll take an average of eleven minutes, with a standard deviation of 3 minutes. There is a 23% chance he will escape without having to present.
6:05 p.m. Bob is going to dinner with a few of his co-workers later, and stops by a convenience store to buy a lottery ticket. He pays one dollar for it, which is more than it is worth. Taking into account all of the other prizes than can be won, as well as the probability of someone else guessing the same numbers as him, the expected value of the ticket should be 97 cents.
9:17 p.m. Bob is at the bar with his co-workers. One of them bets him $100 that the Blackhawks will lose the series against the Ducks, but if he is right, Bob will have to pay him $115. The series hasn’t begun yet, and the Hawks are considered better than the Ducks, with the Hawks projected to win 55% of the games. If these projections are correct, Bob should take the bet, which has an expected value of gaining him $15.
11:00 p.m. Bob is drunk, arrives at home. Across the street, a neighbor and his wife see Bob, and try to guess where he’ll step next. But a drunkard’s walk is almost completely random, and they don’t understand. They don’t understand the principles of randomness.