Discussion 1: Thinking about scale

Discussion 1: Thinking about scale#

Introductions#

Each student shares:

  • Name

  • Class year

  • Academic interest and/or major, if declared

  • One fun fact

Fermi Contest#

Break up into groups of 2-3.

For each of the quantities that follow, come up with a ballpark estimate. You’ll have 5 minutes for each.

Then, enter your solutions into the poll:

Afterwards, we will discuss your answers.

For each question, the team whose guess \(B\) is closest to the true answer \(A\) on a logarithmic scale (minimizing \(|\log(A)-\log(B)|\)) wins. (Why a logarithmic scale?)

Fermi Contest Question 1#

How many pet dogs are there in North America?

Fermi Contest Question 2#

How many hours per year does the average American spend sitting in traffic?

  • Is this a large number? Why?

Fermi Contest Question 3#

How much would it cost to pay the tuition, room, and board of all Stanford undergraduates for 1 year?

  • What is this as a fraction of the University endowment?

  • Is this a large fraction of the endowment? What information do you need to know to decide?

Practice Quiz Review#

The following is one of the practice quizzes for the week (three are available on the course webpage).

Ballpark estimates: For each of the quantities below, decide whether the statement is reasonable by coming up with a ballpark estimate. You do not need to compute the final number, instead set up the calculation and be sure to explain your reasoning, and estimate the order of magnitude for comparison. You will be graded on how you broke up the problem and whether your reasoning made sense, rather than the accuracy of your estimate.

Practice quiz 3, question 1#

More than 10 million gallons of milk are consumed in the bay area each year.

Solution

Say there are about 10 million = 10^7 people in the Bay Area. Each probably consumes about 1 cups of milk per week.

There are closer to 100 than 10 weeks per year, and about 10 cups/gallon.

(10^7 people) x (1 cups / week) x (10^2 weeks / year) x (10^{-1} gallons/cup) ≈ 10^8 gallons/year

The statement looks reasonable.

Practice quiz 3, question 2#

I could empty the fountain in white plaza in one day using only a teaspoon.

Solution

The fountain is about 4m x 4m x .5 m, so (4 x 4 x .5 m^3) ~ 10 m^3 of water.

A teaspoon is about 5 mL = 5/(10^2)^3 meters^3 ~ 10^{-6} m^3 of water.

Say I can scoop and dump 1 teaspoon every second, there are 60 x 60 x 24 ~ 10^{5} seconds/day.

(10 m^3 of water) / ((10^{-6} m^3/ teaspoon) x (1 teaspoon / second) x (10^{5} seconds/day)) = 10^2 days.

The statement doesn’t seem plausible, the number of days looks kind of low.

Practice quiz 3, question 3#

Stanford students collectively buy many thousands of textbooks each year.

Solution There are roughly 8,000 undergraduate students, so say there are ~10^4 undergrads + grad students in total.

Say each student takes about 10 courses per year on average, and about 1 in 2 courses requires a textbook, but only 1/10 textbooks cannot be found for free online.

(10^4 students )×(10 courses/student/yr)×(1 books/course) x (10^{-2} books purchased/required) ≈ 10^3 books / year.

The statement seems a bit unreasonable, our estimate makes it seem like there would only be a couple thousand.