The Math You Wish You Took
As you read the draft, there are a few times when we insert a QR code bringing you here. Just to give you a sense of the specific complementary content we’ll offer in the final manuscript (with unique QR code for each pointer), you’ll find below draft versions for:
Life Impact Curve
Population Dynamics Systems Model
Confidence Intervals
Causation versus Correlation Challenge
Life Impact Curve
Start with this blank Life Impact graph:
[here, we have a graph with the vertical axis being “Life Impact” and the horizontal axis being “Financial Shifts”]
Let’s translate shifts in your financial status into some qualitative measure of the Life Impact (LI) of these shifts. We start by arbitrarily assigning the 1.0 to a +$10,000 Financial Shift.
Now, the most you would risk for a 50/50 chance of winning $10,000 is _____ . [J.T., we map this to -1.0 on the LI graph]. Keep in mind that you’d certainly jump at this proposition if the downside risk were $500. And it’s unlikely you’d risk more than $5,000 for a 50/50 chance to win $10,000.
Next, the most you’d risk for a 90% chance of winning $10,000 is ______ .” Note that this response helps us sketch out your LI Curve using this equation:
90%*(1.0) = 10%*(-9.0)
Ping-ponging ahead, what gain would barely entice you to make a 50/50 bet with a loss that corresponds to the financial shift you came up with in Step 3 for your -9 LI value?
Calibrate your curve by considering how much you’d pay to insure against a .1% chance of losing $1,000,000.
Let’s say you’d pay $2,000 to insure against a .1% chance of a million-dollar loss. Say your QL curve maps a $2,000 decrease in your financial status to a -.3 QL value. Then we know that a loss of $1,000,000 maps to -300 on your LI Curve. This trade-off is invaluable in analyzing insurance policies that protect you from low-risk high-consequence catastrophes.
Population Dynamics Systems Model
A very simple model starts by assuming there are three population segments:
C = Number of Age 0-20 Children
P = Number of Age 21-40 Adults
E = Number of Age 41+ Adults
We make some crude assumptions. With each passing year, some 5% of the current year’s C leave the cohort – mostly the 20-year-olds who age into the P group. The P population produces babies, and we’ll assume that the number of new additions to the C cohort is about 15% of the current P population. We estimate that 6% of the P group leave the cohort each year – mostly 40-year-olds aging into the E group, with some dying. The P group get replenished by the 5% of the C’s who turn 21. Finally, about 2.5% of the E’s pass away each year. The dynamic equations governing this simple system are:
C (N +1) = .95*C(N) + 1.15*P(N)
P (N + 1) = .94*P(N) + .05*C(N)
E (N + 1) = .975*E(N) + .05*P(N)
Confidence Intervals
Phenomena Actual
# of American casualties in the Revolutionary War 6,800
# of U.S. labor strikes during World War II 14,000
# of stars in the Milky Way 100 billion
# of lakes (2+ acres of water surface) in Canada 880,000
# of ants on earth 20 quadrillion
# of U.S. schoolkids eligible for free or reduced lunch in 2019 29.6 million
# of U.S. Children Age 3-10 experiencing homelessness in 2017 600,000
Monthly wage (in U.S. $’s) of garment workers in Ethiopia $26/month
# of Instagram followers of Selena Gomez 396 million
Average # of standardized tests taken by a U.S. kid during their K12 years 112
# of Americans relying on food banks in 2021 53 million
# of Abortions performed in the U.S. in 2020 930,000
% of Princeton students from families in the bottom 20% of Income 2.2%
# of U.S. adults who believe the earth is flat 25.8 million
The # of active websites globally 200 million
# of U.S. citizens age 62 and older w/ outstanding student loan debt 1.4 million
# of millionaires in the U.S. in 2020 22 million
Money made in 2022 by nine-year-old Ryan Kajifrom his kids’ toys YouTube channel $29.5 million
Cost of the USS Gerald Ford aircraft carrier $13 billion
# of assault weapons in the U.S. 20 million
# of civilian-owned firearms in the U.S. 393 million