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Faux Outrage

Literally the most important blog in the universe since 2010.

Category Archives: Math!

It was the bottom of the fifth inning in what could only be described in those days as “your standard Rochester RedWings game.”  The score was not close, the customers in the Team Store — unlike the mosquitos outside of it — were not biting, and the weather was as unspectacular as our lead-off man’s batting average.  And yet for some reason, among the fans at the stadium, there was no aura of dread or shame.

Those of us who live “Way Upstate” seem uniquely well-equipped to extract whatever happiness that our sports teams provide us while ignoring the obvious and potentially painful downsides.  Like when we smilingly admire the blinding sunlight that is reflecting off a glistening pile of snow that barricades us into our homes three days before Halloween, we are able to hone in on the goodness in any situation — even if no reasonable person would choose to endure the suffering from which it stems.

We are Buffalo Bills fans, after all.  We live in a perpetual state of standing at the threshold of the Promised Land listening the gods tell us — over and over again — that our people don’t really need to be bothered with all of that milk and honey.  And that’s fine, we guess, so long as housing prices stay low and Wegmans stays open 24 hours.  We get our milk and honey there, anyway.

So it’s no surprise that, given the Rochesterian’s propensity for unapologetic optimism, no one at the stadium that day was interested in buying our novelty rose-colored glasses: Most folks were already wearing a pair.

It was my first summer working at the RedWing’s Team Store, so my responsibilities were (understandably) limited to making change, wiping down the glass countertops, and directing frantic mothers and their potty-dancing kin to the nearest restroom.  However, on this particular day, in the bottom of the fifth inning, I was presented with a completely new, exciting task.  (In retrospect, I realize that my excitement was born entirely out the task’s newness and had nothing to do with any objective scale we use to measure excitation.)

I was instructed to go into the stands (!) and estimate how many people were left in the stadium.  If the crowd had sufficiently dissipated, for score-related and/or weather-related reasons, an employee or two would be sent home (!) a few innings early.  Everyone was counting on me, and all I had to do was count everyone.  Since I managed to get through a year of AP Bio with Mr. Hall, I didn’t see any reason why I wouldn’t be able to handle some large-scale eyeballin’.

I left the store, passed through the main concourse.


I scanned the stands.


I returned to my post.



“That’s it?  Alright, well, I guess I’ll see you tomorrow then.”

Veni, vidi, vici.  

No sweat.

Frontier Field (Rochester, NY)

As planned, I did see my boss the next day.

She told me that there were over 10,000 people in the stadium.


I guess I’m pretty bad at estimating.

For awhile, this fact bothered me.  I don’t seem like the kind of person who would be terrible at estimation.  I’m interested in science, I’ve always had a knack for mathematics and critical thinking.  I can take apart a computer and put it back together.  I can even walk and chew gum at the same time.

So why am I horrendous at estimating?

And just like that, as if I were asking a rhetorical question (and since what I lack in estimation abilities I make up for in misplaced arrogance and self-deception) I realized something:  It is not my fault at all.  Not being able to estimate must be the natural progression of human evolution.  In fact, so far as I can tell, the less able a person is to estimate, the more evolved that person is according to me — errr — to Darwin!

What a relief.

It’s all about self-preservation, a fundamental tenant of natural selection.

Back when we (humans) were without language but overtaken by our primordial will to survive, estimation was fundamental to subsistence.  We had to guess which vegetation was safe to eat, we had to eyeball each type of animal to determine whether their potential deliciousness was outweighed by its possible dangerousness (sorry, cows).  We had to guess at which humans were friendly and which were worthy of our skepticism.  On the whole, it was important — some would say “crazy important” — that we were good guessers.


As time went on, as we gained communicative abilities and moved from a society of hunter-gatherers to a more of a collectivist approach, estimation became less important.  Other skills were favored: language skills, cultivation skills, community skills, nunchuck skills (much later).  The ability to hunt prey and determining which leaves are poisonous (sumac) and which merely taste like poison (also sumac, but still) were still utilized but less important for the survival of the species.  Instead, those that practiced the art of estimation — by attempting to kill dangerous animals with pinpoint accuracy and make educated-but-risky choices  — were less likely to survive in the world of natural selection.

Nowadays, the folks who are the most talented estimators find themselves engaged in unnecessarily risky behaviors.  For example, a person who correctly recognize that there is a 0.001% chance of dying from some dangerous-though-not-necessary action are perfectly reasonable when they engage in that particular behavior.  More often than not, people do not die from driving recklessly, taking illegal drugs, or even going to war.

But what about the person who, because of his/her biological desire to “remain alive,” completely miscalculates and overestimates how dangerous that activity is?  That person does not engage in the behavior at all and, in a world where the activity is not actually a requisite for life, has a 100% chance of survival.  In other words, the person who is less able to estimate the danger associated with a particular activity is more likely to survive given our species’ fear instinct.

Ergo, one’s ability to accurately estimate should be seen as a biological weakness.

So the next time you’re trying to figure out whether potential mate has genes worthy of passing on to future generations, just ask them how many fingers you’re holding up.

If you’re lucky, they’ll estimate somewhere in the neighborhood of 4,000.


Hello, March.  It’s good to see you!

Goodbye, February.  And I don’t mean to offend you, February, but good riddance.

To be honest, February, you frustrate me, and not just because it takes me two or three tries to spell you correctly.  I can even look beyond the unnecessarily cold shoulder you show us on each of your days, or the fact that you are objectively the least interesting month in sports.  I’m not bitter about Valentine’s Day (except for the fact that folks rarely apostrophize [ed. note: actual word!] the holiday), and do not object to your dedication to a better understanding of black history.  I like you, February, but for all of your positive qualities, you will always — at a fundamental level — be one thing to me.

The month when the cost of living in my apartment is about 8% more than normal.

Explanation?  Sure.

(Beware!  Sixth Grade Math lurks!)

Let’s say your rent is $1,000 per month.  (Apparently, you do not live in your own apartment in DC.) This means that you pay $12,000 annually to live in your humble abode.  There are 365 days in a year, so we can determine that it costs you about $32.88 per day to live in your unit.  Also, there are 12 months in a year so we know that there are about 30.42 days in each month.

Depending on the month, your cost per day fluctuates.

January (31 days) / Rent $1,000 / Cost per day: $32.26 / 😀

Average Month (~30.42 days) / Rent $1,000 / Cost per day: $32.88 / 🙂

April (30 days) / Rent $1,000 / Cost per day: $33.33 / 😐

February (28 days) / Rent $1,000 / Cost per day: $35.71 / 😦

This means that it costs you about 9.7% more to live in your apartment in February than it does in January or any of the other months with 31 days (Math alert! [(35.71-32.26)/35.71]*100 = 9.66) and 6.7% more in February than in April or any of the other months with 30 days (More math! [(35.71-33.33)/35.71]*100 = 6.66).

Overall, each day of rent in February costs about 7.9% more than an average day of the year (Still more math! [(35.71-32.88)/35.71*100] = 7.92).

And that sucks.

Ergo, February sucks.

(Even in a leap year.)

Of course, the Heroes of Non-Confrontation among us will sigh and say, “So what, Zach?” And before I am allowed to muster a reply they will abruptly add, “It all evens out in the end, so it’s just a whole lot easier to just have a standard payment every month.  Suck it up.”

Absurd!  I will not ‘suck it up’!


Because it’s stupid, you see.

It doesn’t make any sense to pay for rent on a “monthly” schedule because “a month” is not a standard unit of time!

Months are social constructs that are perfectly useful when specificity is unimportant (e.g., “We went to Costa Rica a few months ago and here is a boring slideshow of our trip and by the way we’re out of beer and there is a rabid raccoon outside our front door.”) but are a special kind of unhelpful when a specific date is central to the statement being made.

For example: Let’s say you have a gambling problem (“My problem is that I lose!”).  And let’s also say that your bookie has a gambling problem (“My problem is that if I don’t collect debts from my family’s mob-connected gambling operation, the don, who is quite powerful and has been known to murder people — even those close to him like myself — for reasons related to uncollected debts, will not be satisfied and thus I have a strong and vested interest in collecting this particular debt that you owe!”).

One morning, this bookie says to you, “You know that debt you owe me?  Bring me $5,000 in cash to my front door at sunrise exactly one month from now or I will break your kneecaps — and then I will murder you because of the pressures I feel from my family that are best summarized in the television series The Sopranos. My life is much more complicated than you suspect.  Anyway, as I stated earlier, please bring me the money in exactly one month.”

The current date: January 30th, 2012.

What morning do you show up?

(As it turns out, February can even get you killed.)

We treat “month” to mean something very specific when the reality is that “a month” is about as specific as “a few.”  When someone says “a month,” what they are actually conveying is “an amount of time equal to or greater than 28 days but not greater than 31 days and never 29 days except for once every four years.”

Not very helpful.

Because we often value convenience over logic, as a society, we have all decided to agree to ignore this month-as-fluctuating-variable problem when it comes to payment plans (or anything else that is done “every month” on the same day).  “It probably works out in the end” is a weird response to a math problem with an actual answer that impacts millions of people in our society (renters), right?

Furthermore, it should be noted that in the actual universe, it rarely ever “works out” for renters/landlords. Yearly leases often turn to month-to-month leases that are eventually terminated on a month not matching up with the original “ending” month.  Does the rent change on that last month depending on how many days it has?

Of course not.

Sometimes the renter wins the “average cost per day” battle (such as in the case where the lease operates from December 1, 2009 to February 1, 2011), and sometimes the landlord wins (e.g., February 1, 2011 to March 1, 2012), but in each of the situations the one underlying truth is that the scales of justice are arbitrarily (though not randomly!) tipping back and forth.

Goodbye, February.

And good riddance.

Postscript o’ optimism: Your life just got a little bit cheaper!  Your rental cost per day in March is almost 2% less than average!

(Don’t worry, this isn’t going to be about the DMV.  “It’s so slow — and can you believe those lines!  They’re so long!” You don’t say!)

An activity is said to be efficient when it is performed “in the best possible manner with the least waste of time and effort.”  And while it’s hard to know when a process is as seamless and efficient as it can be, it is not usually very difficult to tell when things are wildly out of control.

I used to believe that I was obsessed with finding the most efficient way to accomplish whatever is on my agenda.  Eventually, I realized that I am not obsessed with hyper-efficiency so much as I am completely awestruck and depressed when I am required to engage in an ungodly and unapologetically inefficient activity.

Because this topic is so important to me, I have decided to find the most horrifying example of inefficiency in action in our daily lives.  Think of this article as a public service that results in your being painfully aware when you are at the pinnacle of time and energy-wasting.

In other words, misery loves company.

After a great deal of deliberation and countless hours of internal (and external!) monologue, I am proud to declare once and for all that the least efficient process in the universe is grocery shopping.

(I believe this is where, if this were a live conversation, at least half of you would loudly declare, “But I like grocery shopping, jerk!”  That’s fine!  Really, it is.  I’m not trying to make a value judgment here, only point out that there’s a lot of wasted energy taking place between the fruits and veggies in the front of the store and the dairy section in back.)

So what makes grocery shopping so groce-ly (!) inefficient?

Why, because of the NUTs, of course!

Number of

For this discussion to work, let’s first assume the following is true (or true enough for these purposes): In an ideal world, the first time we touch a useful object should also be the last time the object remains unused.  At least at the consumer level, this is the most efficient way of operating.


We can calculate the number of unnecessary touches (“NUT”) by adding up the total number of touches and subtracting the last touch (which is the necessary touch, when the item is engaged for its intended purpose).

A classic example of a zero NUT (“no waste ideal”) situation takes place when you purchase a hotdog from a vendor at a baseball stadium.  The transaction is simple: you hand the vendor 300 dollars in cash (inflation!) and they hand you one of the worst hotdogs you have ever eaten (in under five seconds).

Only one touch, one necessary touch.  This means that there are zero unnecessary touches: 1 total touches minus 1 necessary touch equals zero NUT!


Now let’s consider the example of a soup can at a grocery store.  How many times is the can handled before the last, necessary touch (when the soup is opened/consumed)?

Let’s follow journey of a can purchased by an average supermarket shopper:

Touch 1: Pick up can of soup in SOUP AND BAKING GOODS aisle.
Touch 2: Put can of soup in shopping cart.
Touch 3: Put can of soup on conveyor belt for cashier to scan.
Touch 4:
Put can of soup in shopping bag.
Touch 5
: Put can of soup back in shopping cart (bagged).
Touch 6: Place can of soup (bagged) in trunk of car.
Touch 7: Take can of soup (bagged) from trunk of car and place on kitchen counter.
Touch 8: Take can of soup out of bag and place directly on kitchen counter.
Touch 9: Put can of soup in appropriate kitchen storage location.

This means that the average consumer must handle the can of soup a full ten times before actually enjoying any soup-y goodness.  In this case, NUT = 9 (10 total touches minus 1 necessary touch).

One can of soup provides some insight into this inefficiency problem, but now let’s multiply the NUT by the number of items purchased on a given shopping expedition.

On my last “trip” (aren’t trips supposed to be fun?) to the grocery store, I bought about 30 items. Thirty items times nine (the NUT coefficient) equals two hundred and seventy actions over and above ideal efficiency.  That means the total NUT for my trip will be 270, a number signifying a high degree of inefficiency.

How do we know 270 denotes a “high degree of inefficiency”?  Simple.  Imagine your mother calls you up on the phone and asks you to do 270 pointless things.  That seems like a lot, doesn’t it?

Of course, any time you are purchasing goods that you are not immediately consuming, you are going to find yourself with a NUT higher than zero (and thus, not engaged in idealized efficient behavior).  But the grocery store provides a unique opportunity to participate in a spectacularly inefficient process dozens of times in the same location!

And that is why grocery shopping is the least efficient process in the universe.

Thought experiment time!

Let’s say you are hungry.

You are lunch-level hungry.

You are not starving (although you have been known to exclaim, “I’m starving!” in the company of similarly situated folks who have never in their life experienced real poverty).

Let’s also say that three identical, average-sized Styrofoam(R) brand containers have been placed before you.  Each container contains one pound of food fit for human consumption.

The containers are labeled (accurately) as follows:

  1. chicken with brown rice
  2. spicy noodles with vegetables
  3. sushi with seaweed salad

You may select one container.

Which do you choose?

I’ll give you a moment to think about it.

Your container-selection thought process probably went something like this:

  1. Note contents of Container 1 (“C1”)
  2. Note contents of C2, compare to C1
  3. Select more desirable container (C1 vs. C2)
  4. Note contents of C3, compare to more desirable (C1 vs. C2)
  5. Select most desirable container overall (C3 vs. [C1 vs. C2])
  6. “I choose Container [1-3].  That’s my final answer.”

Here’s what your thought process did not look like:

  1. Each container has 1 pound of food
  2. Therefore, no container is superior to the others
  3. “I choose any of the containers.”

I don’t think it’s controversial to point out that we prefer some foods over others.  We are willing to pay a certain price for a particular food item because of what the food is, not simply because it is “food” in the generic sense.

Should “Chinese food” cost the same regardless of whether you’re buying shrimp or noodles or rice or beef or spring rolls?

(Hint: It shouldn’t!)

In other words, since there is no (rational) part of our brain that believes our grocery shopping could be accomplished utilizing this all-food-is-equal theory (“I would like 13 pounds of food at ten dollars per pound, please.”),  why does it make sense to choose our lunch this way?

(Hint: It doesn’t!)

The upshot of this realization is that I am completely paralyzed when I encounter any food-by-the-pound buffet-style “restaurant.”

A pound of tuna may weigh the same as a pound of bok choy, but that is where the similarities end.

Tying the price of all goods in your shop to a characteristic unrelated to the essence of the goods (weight as opposed to taste/texture/nutrition) seems contrary to what we know about ourselves (we have varying desires for different goods) and our economy (our level of desire should dictate what we are willing to pay for a particular good).

once wrote of capri pants, “I’m not going to support any article of clothing that is trying to introduce an entirely new class of weather.”  Similarly, I am not going to support any eating establishment that by definition forces me to construct my meal in an entirely foreign way: based not on its inherent deliciousness vs. pricepoint, but rather on some weird hybrid desire-to-weight ratio.

Now before I get too carried away, I should point out that I do understand that it is possible to get “value” at one of these by-the-pound spots.  I know that if you eschew heavy/cheap foods like noodles, cooked rice, and mashed potatoes in favor of airy/costly items, you can “win” the buffet game and victoriously chomp down upon your efficiently-crafted, financially sound lunch.

But you won’t necessarily be eating what you want.

And really, is that any way to live?

(Hint: Nope!)

Quite simply, I refuse to trade the simple “what I want” calculation for the far more complex and less reasonable “what I want given the taste-to-weight ratio.”

“How tasty do I think that chicken is going to be and how much does it cost?”

Suddenly becomes…

“How tasty do I think that chicken is going to be?  How much does that chicken weigh?  Do I know how much ‘a pound’ feels like?  Does it weigh so much that its deliciousness is overcome by the potential cost?  Would I be better served obtaining a less scrumptious item that is lighter per morsel?  Does the chicken seem to be secretly infused with some sort of secret sauce or heft-adding liquid and/or cheese?  Should I be more upset that the guy who just sneezed all over my plate just infected me with Dengue fever or because his snot will actually make my meal cost more?”

That’s no way to live.

Lucky for you, despite the title, this post has nothing to do with Malclom Gladwell.

However, while no intellectual blowhards will be referenced in the paragraphs that follow, there will be references to math, which as many (high) high school students will tell you, “Blows, hard.” In fact, you could even argue that the subject of the post is the opposite of Malcolm Gladwell (though I’m not sure what you’d gain by picking that particular battle).

Let’s begin.

First, I’m going to need you to close your eyes.

Next, I’m going to need you to open your eyes because you won’t be able to read the rest of the instructions unless you do.

(I did not think this through.)

Now, imagine the last time you went to a diner.

Remember your waitress — the one person literally standing between you and pancakes?

I’m going to make a few guesses:

– She was either very old or very young
– She could fake a smile through American History X (title-to-curb-to-bathroom-to-credits)
– She successfully carried more plates at one time than seemed reasonable
– She let you know in the nicest way possible that there is no way on God’s green earth that you can substitute a meat for a non-meat

She also probably puts up with more junk than a urologist and — most crucially — is compensated in a way that suggests her only source of income is the result of her being the sole beneficiary of an “Eat Your Brussels Sprouts and Make Your Bed” allowance policy.

This is our fault.

It is our fault in part because of our willingness to operate in a society where certain food service workers are paid an hourly wage of less than what we are (for some reason) willing to pay for a small — excuse me, tall — frappuccino.

But mostly, it is our fault because we so heavily rely on objective math when we pay our bill at a restaurant rather than objective reality.

I have devised a way of melding these two rational, objective approaches (math and reality) into one SUPERAPPROACH (note: this sounds like, but should not be confused with, the word “SUPERREPROACH”, which is the state of being beyond reproach — in space!) that you may consider utilizing while preparing to tip your local neighborhood waiter or waitress.

In order for the superapproach(tm) to work, we need to first agree that there is some inherent value to the work that a waiter or waitress provides that is completely independent of the cost of the food/drinks purchased.


Okay, good.

There is a reasonable tendency to tip based solely on the total value of the food ordered.  I say “reasonable” because our social rules tell is this is the approach is the way to compensate our server.  But if we think about this norm for over thirteen seconds, we will come to the conclusion that it makes even less sense than that time I tried to write about Planet of the Apes (Warning: I am legally obligated to inform you that you should not even consider clicking on that link).

Here’s why our current tipping culture is not worthy of defense.

SCENARIO #1: You are at a steakhouse.  Your waiter, Jimmothy McNicenberg, approaches.

JMcN: May I take your order?
You: Where would you like to take it?
JMcN: …
You: Ho ho, actually, yes, I would like the New York Strip steak with a side of mashed potatoes.  And an oatmeal stout.
JMcN: How would you like your steak?
You: ASAP!
JMcN: …
You: Medium.
JMcN: And for the lady?
You: She will have the chicken salad and a glass of pinot noir.
The Lady: I can order for myself, you know.
You: Make that two glasses.
JMcN: …

Jimmothy serves you two plates, a few drinks, and according to standard tipping rules, makes $15-20.

SCENARIO #2: You are at a diner for brunch.  Your waitress, Lorainedrop Snugglefish, approaches.

LS: May I take your order?
LS: …

[five minutes pass]

LS: Uhh, are you ready to order now?
You: Yeah, sorry about that.  I haven’t eaten yet!  You know how it is!
LS: Right, shug.  What can I get you?
You: Well, first, a question: the menu here says the Mexican omelet comes with red onions, green peppers and cheddar cheese.  Can I get it with green onions, red peppers, and substitute bacon for the cheese?
LS: Yes, yes, and no.
You: Okay, well, then just get me four eggs, one poached, one sunny-side up, one over-easy, and one over-medium.  With home fries, well done, of course — can you make sure the edges are crispy? — and a raisin bagel scooped out — Atkins, ha! — with light cream cheese on the side.  And half-caf-decaf and a medium orange juice.
LS: And for you, ma’am?
You: She’ll have the…
The Lady: I will take care of this.
You: Women!  Can’t live with ’em, can’t calculate my self-worth without ’em!
LS: …
The Lady: Do you have soy milk?
LS: No, we only have whole milk.
The Lady: [sighs] Okay, well, can I have the tomato basil and mozzarella sandwich, on wheat, lightly toasted?  And on the side, can I have a half grapefruit — pink and pre-sliced, please — with some cane sugar sprinkled on the top — but not too much, and make sure it’s all natural not Splenda, you know — and an iced tea, with no ice.  And some water, with a little ice.  Crushed ice, please, thanks.  Oh, and I need a new fork.  Mine fell on the floor.
: Is that all?
: We’re kind of in a hurry, too.  We have to be somewhere in a half hour.
LS: I’ll see what I can do. [she leaves]
You: Man, what was her problem?

Lorainedrop Snugglefish (not pictured above), who just wrote enough on her waitress pad to qualify for a Regents diploma, serves you four plates, four drinks, and “earns” from you about $3-4 based on standard tipping practices (STP).  And maybe you’re saying, “Zach, you are misrepresenting my hypothetical self!  I would tip way more than that for a $17 brunch!  I’d tip like $10!” Well, if that’s the case, please kindly send me a copy of the New York Daily News article praising your boundless generosity.

Whether we’re talking about the waiter at the steakhouse or diner waitress, we ought to first recognize that a similar service is being offered, i.e., carrying out — literally and otherwise — an order.  And again, to the extent that this task has a specific value independent of whether you’ve ordered $100 or $20 worth of food, we should treat these two situations similarly to the extent that it is reasonable to do so.

Here is what I propose.


By default, tip 15% of your bill, just like society tells you.

Tip 20% if you are trying to impress a date.

Tip 50% if you are trying to impress the waitress.

At a diner or otherwise uber-cheap restaurant, never tip less than $5 on a full meal.

Additionally, add a percentage point — or dollar, whichever is more reasonable based on the total billed amount — for any of the following:

  1. Any order consisting of more than one complex sentence or three commas.
  2. Any question that could have been answered by reading the menu.
  3. Any instruction that the waitress will have to verbalize to kitchen.
  4. Each time the waitress shakes out her writing hand during the ordering process.
  5. Each time the waitress alerts you that what you’ve ordered “actually isn’t very good.”  (This is the easiest way into my wallet.)
  6. Each three minute increment lounging at the table after bill could have been paid.

You might think this is a lot to memorize, but to remember these rules, just keep in mind this simple mnemonic:


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