advice to myself
I spend a lot of time trying to save time.
Buying nonperishables online, to avoid lugging them around the grocery store. Ordering coffee from an app, so it’s ready when I arrive. Composing blog posts right in WordPress, like some kind of madman, where one stray click could send a half-baked draft to 10,000 subscribers.
I can’t help noticing that this optimization fails to make me any happier or more fulfilled.
No surprise, really. Efficiency saves resources; it doesn’t lend resources meaning. My carefully husbanding time doesn’t make me a better husband — or, for that matter, a better father, friend, writer, brother, pen-pal, or survivor of late-stage capitalism.
Yet it’s hard to turn off. My drive to optimize runs deep.
Maybe I’ve taken one too many economics classes. Or maybe I inherit the legacy of my hominid ancestors, who lived and died by the speed of their grocery checkout line. Or maybe I’m just a broken soul. Whatever the cause, I sometimes despair of turning off my optimizing brain.
So I’m trying to teach myself the next best thing: to treat time not as the objective, but as the constraint.
In any optimization problem, we try to maximize an outcome such as profit (or else minimize an outcome such as cost). This is our objective. While doing so, we must obey certain limitations, perhaps dictated by our budget or available materials. These are called constraints.
The thing is, many optimization scenarios allow multiple formulations.
Here’s one way of optimizing tonight’s dinner: Minimize the time required, as long as the meal meets a certain threshold of tastiness. I.e., what’s the fastest I can make a meal that scores at least a 6 out of 10?
Here’s a second approach: Maximize the tastiness, as long as the meal takes no longer than a certain maximum time. What’s the best meal I can make in the next 40 minutes?
Both seek tasty, fast-to-cook meals. But the difference is vital. Constraints tend to get just barely satisfied. (Optimizers call these “active” or “tight” constraints.) So which do we want: a meal that just barely clears the tastiness threshold, or a meal that just barely fits in the allocated time?
Put that way, the choice seems clear.
When it comes to optimizing one’s life, I’ve come to believe that simple constraints are healthy, but simple objectives are not.
The constraints in my life — time, energy, money — lend themselves to varying degrees of quantification. That’s the nature of being a mortal creature with a finite balance in my savings account. But the objectives I care about — writing with candor, parenting with love, cooking with cardamom — generally do not. That’s the nature of being a complex soul in a universe full of mysteries.
We cannot live by lox alone.
There must also be cream cheese.
And a slice of Bermuda onion.
Ben Orlin:
i have a question regarding your blue covered Math math book, pages 102 and 103 to be specific. Where and how in Excel is this calculation made? i would appreciate some specifics because I’ve been looking at all my Excel references and coming up dry. Very time consuming and wish you had added how to do it in the book itself.
My first program learned was Lotus !-2-3 back in the 80’s under MSDOS. It was for budgeting purposes for New York Tel (old ATT) and had to do it in three parts due to minimal Ram which was caused by evaluating another program called Windows 1 which i declared a joke under the circumstances. Frankly i am tired of all program revisions or should I be calling them apps?
Incidentally your brown covered puzzle book should arrive tomorrow from Amazon and will be passing along the blue book to my Math teaching grandson to give him a few ideas to jazz up his high school classes.
Are you familiar with tau Beta Pi since you made the Spring 2022 Bent mag. with a “drop dead” Brain Tickler.
Bob Schweitzer
Hi Bob, thanks for reading the books! I’m not familiar with Tau Beta Pi but honored to be featured.
I had to look back at that page, and I am embarrassed that I used Excel for this! What I did at the time was write “=RANDBETWEEN(1,6)” in one cell, then use ctrl-R and ctrl-D to copy this across an array 100 cells wide and 10,000 cells tall, for a total of one million cells. Then I used “=COUNTIF(A1:CV100, 4)” to find how many 4’s were included (and similarly for the other numbers). Now that I actually know a bit of programming, this would be just a few lines of code in Python:
from random import randrange
from collections import Counter
dice = [randrange(1,6) for i in range(10**6)]
counts = Counter(dice)
print(counts)
There’s a bug in your code, randrange(1,6) generate numbers from 1 to 5 not 1 to 6
Oops! I guess I’m rolling 5-sided dice today…
Hi Ben. Huge thanks for MwBD.
I see a parallel between your two meal optimising approaches and wages vs constraints. The profit vs cost push paradigm in economics maybe. Is this an appropriate analogy in your opinion?
You say: “Put that way, the choice seems clear.”
To you but not to me.
Your choices text: “Both seek tasty, fast-to-cook meals. But the difference is vital. Constraints tend to get just barely satisfied.”
Ok. Path of least resistance or 50+1 pass mark.
Then you say: “(Optimizers call these “active” or “tight” constraints.)”?
Which applies to and/or and or which?
I assume perhaps incorrectly;
– optimising option #1
“Minimize the time required, as long as the meal meets a certain threshold of tastiness” … an active constraint?
– optimising option #2
” Maximize the tastiness, as long as the meal takes no longer than a certain maximum time.” … a tight constraint?
Hmmm…
“So which do we want: a meal that just barely clears the tastiness threshold, or a meal that just barely fits in the allocated time?”.
Ahhhh … depends. Love, caring, savings, time constraints etc etc.
And final paragraph makes the distinction between caring vs quantification… ” But the objectives I care about — writing with candor, parenting with love, cooking with cardamom — generally do not. [… lend themselves to varying degrees of quantification.]
The “objectives I care about” not lending themselves to quantification, and “That’s the nature of being a complex soul in a universe full of mysteries.”… again is unclear except in an intuitive understanding which then does not lend itself to realisation of;…
“When it comes to optimizing one’s life, I’ve come to believe that simple constraints are healthy, but simple objectives are not.”
My brain had a hard time parsing text, and seeing choices, and having definitions definite.
I’m hoping for a clarification/s
Maybe it is just me?
And the ping back in economics terms is a free rider. Delete it.
Thanks for your response here.
Very yes. I like your way of framing the constraint vs maximization for time vs taste (or any other target). I would say sometimes optimnizing for time is better, but thinking about this difference is very key. Might I suggest the excellent book “Algorithms to Live By” in case you didn’t devour that yet?
oooooo I love the optimizing time. And I want the up to 40 minute delicious one. I accept your delightful invitation! What time is dinner?
This (and its first “bad drawing” in particular) brings to mind the concept of satisficing (as opposed to optimizing).
In my previous life I was a bond portfolio manager. I had a pretty sophisticated tool to analyze the universe of bonds that fit my investment criteria and analyzed relative value. Could I create a set of constraints and program an optimizer that would select the optimal portfolio?
What did I learn? The optimizer will find problem data and flawed assumptions. The optimizer will maximize error.
After my life in portfolio management, I moved into risk management. What did I learn there? People measure what is easy to measure and obsess over the measurements. They tend to be blind to the risks that are difficult (or impossible) to quantify.
I have spent hours working on optimizing a program just to save a few seconds of runtime… on a program no one but me will ever see.
Hello. Even though I’ve reached the point where, by anyone’s definition, I’m old, I can’t say that life has become a significantly simpler project. No matter what our age, we all need to forge ahead with open hearts and open minds. Neil S.
“Efficiency saves resources; it doesn’t lend resources meaning.” – I am recording this in my journal.I often find myself rushing to be more “efficient” and finding it does not make me feel better at the end of the day. Thank you.
I really like having the extra time to perfect things. And I’m looking for the tasty one that can take up to forty minutes. I gladly accept your kind offer. When do we eat supper?
I just finished reading your Math with Bad Drawings book, which I enjoyed a great deal. However, there is one thing that I think is incorrect in your book. You refer to the “three-fifths” compromise as “pro-slavery”. I think if you read the history of this, you will see that it was an anti-slavery compromise. Those who were pro-slavery wanted to count ALL of the slaves for voting purposes. There would have been no United States of America without this compromise.
Hi Tom, thanks for reading the book, and thanks for the message!
I had to go back and look at that page; indeed, I describe the three-fifths clause as a “proslavery compromise,” which, as you say, isn’t quite accurate. Then again, I don’t think calling it an “anti-slavery” compromise is quite accurate, either. The pro-slavery position was 5/5; the more opposing position was 0/5; so 3/5 was, as the name suggests, a compromise.
In any case, I think it’s fair to say that the importation of the 3/5 clause into the Electoral College really *was* a move that advantaged pro-slavery forces. Indeed, it was discussed in these terms at the constitutional convention, and years later when Andrew Jackson proposed moving to a popular vote, he made sure that his proposal included a re-weighting of the raw vote totals to preserve the South’s hard-won concession in this regard (even though a popular vote where some votes count more would have made for a system both mathematically and democratically awkward).
All that said, the Electoral College has evolved in ways that none of the framers (on either side of the negotiating table) foresaw. In particular, the all-or-nothing way that most states allocate their electors is really the decisive question from a mathematical perspective. (And indeed, the 3/5 clause has not been relevant since 1865!).
It’ so really, but I want to focus on the some targets – job and income, but all other time I spend what I like =) One to to deal, else other to me