March 18, 2010
· Filed under finances, maff
Today, I learned about Benford’s law from Jacob. If you read either of those links, you can see that if you apply Benford’s law to an exponential function you can find the probability distribution of the exponential function. As Jacob’s post mentions, compounding interest is an exponential function.
After I compared time and interest rate dependencies in the exponential function, I started wondering more about relative interest return rates. I believe applying Benford’s law now closes that loop.
The bar plot is the probability distribution of Benford’s law, and the line plot is the cumulative probability distribution of it. Then, you can apply this to principal in a loan, fraction of a desired capital investment goal, and so forth.
Say you take out a loan, and pay 20% down. The loan is free from 48% of the total interest compounding. In other words, the loan is growing at 52% of the total loan potential, as a function of the lending interest rate.
It’s something to think about, and it’s also a tool to use if you apply time to calculations, like if you start to default on payments/investments.
January 30, 2009
· Filed under maff
At some point, I decided I wanted a sweet analog watch. Style, an anti-progressive statement, whatever it may be. Somehow I noticed that a lot of the watch advertisements showed watches at the time 10:10. This observation is still true; a Google Shopping search has a lot of watches at that time.
My current favorite online response is from blogcadre:
. . .
- The hands are nearly symmetrically balanced on [the] face of the dial at 10:08. The minute hand is 48 degrees right of vertical, while the hour hand is 56 degrees left of vertical. Exact symmetry would be achieved at 120/13 minutes past 10:00, approximately 10:08:13.8. Other symmetrical times would not meet the needs above.
. . .
I cut out a lot of the real reasoning: marketing!
My thoughts centered around the symmetry, pun intended. Namely, 10:08:13.8 is NOT symmetrical! Amateurs. The second hand is messing up everything that is good in the world. It’s all or nothing, man.
I thought about this visually, for both the second hand being between the two hands, if you will, and for the second hand being outside the other two hands.
Then, I came up with some killer balances.
Acute: 
Obtuse: 
For the joy of all, I solved those killer formulas. And, I provide you with a nice time table:
Now, you understand what I think of if you hear me say, “Yes, I strive to recognize balance in my life.”
January 25, 2009
· Filed under maff
A well known probability problem is the birthday paradox; if you get over 23 people in a room, the odds are favorable that two people will share the same birthday. I believe this is when the sample distribution moves to a population distribution. That’s not my point. My point is that I wish I had more friends.
Exploding with social popularity, Facebook always lets me know when my friends’ birthdays are. Every few days I have a friend with a birthday, and that person’s received comments greatly increase that day.
Then my curiosity wandered: how many friends do I need to have in order to add a daily task of wishing someone a happy birthday? I used the lazy man’s approach: I avoided theory and just simulated. I used a uniform distribution for birthday odds. I continued the simulation until all of the 365 days were full, which I repeated a thousand times.
The upshot of this: you need 1900 to 2800 friends before you can feel any confidence that you can add the daily task of “wishing happy birthdays” in your virtual community.
Maybe by the time I have that many friends I’ll know a more elegant theoretical solution.
