Unless you’ve been living under a rock, you’ve by now seen this “meme” and commentary on America’s educational system:
Since I imagine it may be difficult to see, let me enlarge and transcribe it for you:
Reasonableness. Marty ate 4/6 of his pizza and Luis ate 5/6 of his Pizza. Marty ate more pizza than Luis. How is that possible?
In response – the student (whom by the handwriting I’d suggest is probably a 2nd or 3rd-grade student and thus is probably around 7-9 years old) stated:
“Marty’s pizza is bigger then [sic] Luis’s pizza.“
This student’s answer is perhaps inarticulately stated, but nevertheless correct. Not only is the correct answer is the only possible correct answer to the question. What is perhaps ironic (and utterly depressing) is this entire exercise comes under the heading of “Reasonableness,” which this problem was anything but.
So what? Well – for me – this is a symptom of a much bigger problem that I see in business, and in life, and it costs people their lives. The worst part of all, this is learned idiocy in our behaviors.
Did this student win praise for being able to abstractly conceptualize why Marty could eat more pizza than Luis when there is an obvious contradiction in proportionality?
No. He got a fist punch to the face. His teacher writing,
“That is not possible because 5/6 is greater than 4/6 so Luis ate more.”
While I am perhaps not even remotely the first to suggest that school is harmful to our intellect and careers, what is so sad and unfortunate is, this child was developing the very skills necessary to be successful in life. His teacher took those skills, stomped on them, and said, “no, you must be a doltish clod like me and everyone else.”
If we want to wonder why creativity is so lacking in the world – perhaps we should look at how we educate our children.
And as bad as that observation may be – what followed in social media in response to these types of postings is even more depressing. I’ve watched “flame wars” between people saying:
- the teacher was right (which I’ll prove is incorrect in a moment), and the student must abide by authority;
- that it was a trick question (which it wasn’t) and there was no way for a kid to figure this out, therefore, it was an “unfair question,” (which it wasn’t);
- Perhaps most distressingly, that the teacher shouldn’t be punishing people for “thinking outside the box” and that fact is the real problem here.
This last point is perhaps the most commonly argued, and it is by far, the most dangerous. Since when is thinking clearly and being able to conceptualize something properly thinking “outside the box”? The very phrase “outside the box” is thrown around as a buzzword when doltish clod managers have no idea what to do next because they have no ability whatsoever to even understand the facets of the challenges they’re facing.
If you can think clearly about a problem and come up with a solution, that’s not a risky activity. That’s not a gamble. That’s not “thinking outside the box,” that’s called “being clever,” and actually using your brain.
It’s thinking clearly and properly that we should encourage. This student was able to see relationships and ignore erroneous information and provide quickly and simply the answer – the radius of the pizzas are not the same. Considering the kid is probably SEVEN, that’s an amazing achievement. Instead, what this kid got instead of praise was chastisement for not deducing an erroneous result.
Being able to conceptualize what’s going on, and formulate a way of processing the information we’re receiving, is perhaps the greatest life skill. We have to stop telling people to make up lies under the guise of creativity and punish people who can actually see real causal linkages and tell them they’re stupid.
Why? Because it gets people killed. We have to recognize that, just as in some cases “There is no spoon,” in this case…
Marty’s pizza had to be bigger
Any trigonometry student, plumber, pool man, or child filling water balloons can tell you – the bigger the pipe, the more water you’ll move through it. Why?
Well it’s pretty simple. RADIUS matters.
Here’s how the surface area of a circle is calculated:
As you can see, the only variable that increases the surface area of a circle is its radius. If you understand calculus, you know that the rate of change of the area of a circle is given by the first derivative of this equation – 2πr. That means for every unit of change in the radius, the area of the circle changes by twice the constant of π (3.14157….).
The assertion that this kid is wrong, required thinking “outside the box,” magic or anything else is preposterous. The teacher who corrected this kid is incorrect. What this kid saw, perhaps intuitively, is that the radii of the pizzas could not be the same, if in fact, Marty ate more pizza than Luis. That fact is not disputed – it’s given the problem.
- It isn’t possible for the teacher and the student to be “right” at the same time.
- It’s not a case of “the kid didn’t understand the problem” or the facts were incomplete, inconsistent, or ambiguous
- It’s not a case of “it depends on what point of view” you’re looking at the problem from.
- It’s not a case that magical thinking was required.
- It does not require some mumbo-jumbo equivocation, Common Core stupidity, or anything of the sort.
What was required was creating an explanation that was reasonable to explain what was being observed as the outcome. This kid did this, and he explains it as best as he can saying “Marty’s pizza was bigger.”
And, again, he’s absolutely right.
Moreover, it’s the only possible explanation.
Just so we’re all on the same page, we could both eat 1/4th of a pizza… and depending upon the radius length… the amount of pizza eaten may not be constant.
This is your pizza… there are many like it but this one is yours.
This is my pizza – hear me roar – my one slice has a greater a surface area than your entire pizza.
(Take that Luis!)
This silliness of not being able to think clearly, and the maelstrom of idiocy that has since erupted across the internet, should concern everyone. The thinking that results in this student being chastised ultimately leads to people being killed, companies being destroyed, and egregious avoidable errors being committed. We should have given this kid a pat on the back and commended him for being able to see the “right” answer in a highly complex and ambiguous situation under stress.
How does a third-grade math problem wind up getting everyone killed? It doesn’t. But that student 40 years from now winds up in a situation where his ability to think clearly, and see the radius and not the pizza slice count, matters. Two examples to compare and understand – Air France flight 447 and Quantas Air Flight 32.
AIR FRANCE 447
The final words of from the cockpit seconds before the Airbus 330 of Air France flight 447 smashed into the Atlantic ocean were as simple as they were haunting:
Air France flight 447 had been in the air for three hours and 40 minutes since taking off from Rio de Janeiro for Paris on the evening of May 31, 2009. Strong turbulence had been shaking the plane for half an hour and they continued to fly into bad weather. The route between Rio and Paris would take the plane through what is known as the ITCZ, the Inter-tropical convergence zone, and it is an area of the ocean that routinely sees unstable weather and storms. Pilots flying this route routinely must deal with the weather of the ITCZ, as well as other phenomenon such as “St. Elmo’s Fire” (where ice crystals that are electrically polarized strike the hull of the airplane and discharge), and the fact that often the storms are so large and so tall, navigating around them is not always feasible.
On this flight, the crew maintained its flight heading and speed, and the computers of the gigantic Airbus were constantly measuring the environment, the plane’s systems, and the plane’s performance, and making millions of calculations and adjustments. The plane was level, flying straight and normal, at 38,000 feet.
Without warning, the gauge indicating the external temperature rose by several degrees, even though the plane was flying at 38,000 feet (where the average temperature should be a balmy -65 degrees F). The false reading was caused by ice crystals from the storm clouds coating the sensors on the outside of the plane. These crystals insulated the sensor and thus made the sensors think it was warmer out than it actually was – much like farmers coating oranges with ice to insulate them from dangerous frost conditions.
As a result of the ice buildup, the computers which were piloting the Airbus 330 suddenly could not determine pressure and temperature conditions outside the aircraft; sensors critical to determine altitude. As Air France 447 continued through thunderclouds over the Atlantic, more and more ice clogged the plane’s sensors, including the pitot tubes that were instrumental in determining the plane’s airspeed.
The computers unable to make sense of both altitude and airspeed did exactly what they were programmed to do.
2:09 AM, the Airbus 330, unable to make sense of the inaccurate information and readings it was receiving, disengaged the main autopilot and an alarm sounded in the cockpit.
If you’ve ever wondered why pilots get paid a six-figure salary even though they fly only on average about 15 minutes of flying time – this is why.
Alarms and caution and warning indicators lit up on the cockpit monitors. The Airbus 330’s systems began diagnosing what was wrong and what to do, feeding the pilots information, not all of it being relevant or even accurate. One after another, the autopilot, the automatic engine control system, and the flight computers shut themselves off.
The computers switched off because they knew they were being fed faulty data and needed humans to fly the plane.
Unbeknownst to the pilots… the clock started ticking. In 242 seconds, they would be dead.
Let me say that what follows next is painful. I have no doubt that Bonin, his co-pilot David Robert, and the captain of the aircraft (who was in crew rest at the beginning of the crisis), Marc Dubois, did everything they believed to be correct. They bet their lives against their judgment. These were not three men who acted negligently, in my view. The unfortunate sad fact of the evidence we know is, however, that they failed to understand what was going on around them and they compounded incorrect thinking upon itself until they drove the Airbus into the ocean.
I do not mean to impugn their character. I have no doubt they were honourable men.
The error that was made was Bonin, having been jolted perhaps by the series of failures and warnings, pulled up on the stick of the aircraft and the aircraft began to climb. The aircraft climbed at such a fast rate that eventually the air outside the aircraft could not generate sufficient lift, and it began to stall. The flight crew ignored all of the warnings the computers were telling them. Bonin at one point believed the aircraft was overspeeding, saying, “I think we’re going crazy fast!”
In fact, they had deprived the plane of any hope of resuming normal flight. A stall, once it takes hold, is exceptionally serious and can be unrecoverable. A stall does not mean that the engine(s) have stopped working, or that the aircraft has stopped moving. What it does mean, however, is that the plane has stopped flying.
In the dark, at 38,000 feet, in a thunderstorm, with their instruments no longer deemed reliable, attempting to climb even at max power (at one point Bonin and Roberts believed they were in TOGO – which is the setting for “Take off and Go Around” – which is the maximum thrust and lift settings), was the opposite of what needed to occur. Overwhelmed by the information they were receiving, their inability to focus on what was the correct information, and perhaps most critically, Bonin’s inability to think clearly about what happened next, combined with Dubois’ inability to understand what was happening with the flight deck when he returned, was judged to have been the cause of the crash that would kill everyone onboard. The Airbus was going “crazy fast” over 500 mph straight toward the water.
Over the next four minutes, Air France 447 fell into a stall, despite the pilots doing everything they could to increase thrust and altitude. The flight deck persisted in attempting to raise the nose and increase the pitch, thereby compounding the stall, to the very end. Flight data from the crash indicates that at the final point, the plane was falling out of the sky like a rock that was thrown off a bridge. The last command of Captain Dubois was to increase the pitch of the aircraft by ten degrees.
Then the Airbus impacted with the water, going as fast as a freight train, and shredded itself into pieces not much bigger than a yard, over half a mile of ocean, before sinking below the waves.
Smart men. Honourable men. Fathers. Husbands. Friends. Because they couldn’t see clearly when it mattered most and instead attempted to assume the opposite of what was going on killed everyone on the flight, and themselves.
The BEA, the French Civilian Air authority, had concluded the following:
The STALL 2 warning triggered at 2 h 10 min 51 but did not elicit any response from the crew. Even though the stall warning had been sounding for 9 seconds, the
aeroplane climbed above the propulsion ceiling with the vertical speed still high, and with a flight path speed that was dropping as a result of this vertical speed. At
this point, only descent of the aeroplane through a nose-down input on the sidestick would have made it possible to bring the aeroplane back within the flight envelope.The rapid reduction in speed was accompanied by an increase in the angle of attack.
The lift ceiling, at the Mach at which the aeroplane was flying at that time, was broken a few seconds after breaking through the propulsion ceiling. Due to its momentum, the aeroplane continued to climb: the aeroplane’s kinetic energy was converted
into potential energy until the point was reached when the aeroplane unavoidably started to descend. The PF was still applying nose-up inputs and the angle of attack
continued to increase. Even with the engines at the TOGA thrust setting, the drag generated by this high angle of attack was so high as to prevent the aeroplane
from accelerating.Subsequently, the position of the sidestick, maintained in its nose-up or neutral
position, continued to exacerbate the situation and made the recovery uncertain, even impossible.
It’s heartbreaking. There was no emergency warning from the crew. There was no mechanical failure. The inability to think clearly and deal with what was happening made it impossible to avoid crashing into the ocean.
The Miracle – Quantas Flight 32
Imagine you’re flying a plane the size of the Empire State Building and the engine explodes.
On November 4th, 2010, Quantas Air flight 32 departed Singapore to Sydney. At 7,400 feet during its “climb-out,” there was a catastrophic failure of an inboard Rolls-Royce engine resulting in an “uncontained engine failure.” Shrapnel flew out of the engine that destroyed itself at supersonic speed, crippling control systems running along the Q380’s left wing leading edge, peppering the fuselage, invading the underbelly, puncturing two fuel tanks in at least ten locations, and damaging or disabling 21 of the 22 aircraft’s systems.
It is the most damaged aircraft that has landed safely in aviation history.
Amazingly enough, we have actual footage of this crisis. Just for a moment, imagine you look out the window and see this:
Now realizing that most of you aren’t aviation experts, the little thing “sticking out of the wing” is actually a chunk of the jet’s housing rammed through the wing and next to it is a hole roughly the size of a watermelon.
At one point in the crisis – the engine was on fire, the fuel system was on fire, all four engines were damaged, and the hydraulics of the aircraft were either partially functional or completely non-functional.
(Another view of the hole in the wing that the engine explosion created)
The Pilot In Command of the aircraft, Captain Richard Champion de Crespigny, has been credited in the media as “having guided a heavily damaged double-decker jet to the safety of Singapore Airport and averting what could have been a catastrophe”.
What de Crespigny told investigators and the media was:
The sound of the engine failure was really like a backfire in a car – like a boom – so that is something we just react to instinctively with procedures that we learn in the simulator. So that is not a surprise, it’s not shocking. It doesn’t cause a panic reaction at all.
A second boom, however, about half a second later, shook the entire aircraft and was highly unusual. The flight crew wondered immediately how damaged the plane was, and if other engines were about to fail, on fire, or might also explode. When questioned, de Crespigny said,
But it really doesn’t matter about those thoughts. What you have to do is fly the aeroplane; you have to aviate.
The difference between Quantas 32 and Air France 447 can be traced to one exceptionally important thing:
The ability to think clearly, focus, and understand what’s actually going on.
De Crespigny had surmised that the engine explosion had knocked out the aircraft’s ability to function as an integrated system. Thus, while the crew determined what was wrong with the aircraft (which was extensive) de Crespigny concluded that they would need to land the plane as if it was no more sophisticated than a simple single engine aircraft. Above all else, we have to aviate. Given the extent of the damage to the plane, that intuition turned out to be “the right call,” and is largely responsible for turning what could have been one of the worst disasters in aviation into a miracle. That said, De Crespigny had to fight his instincts and instead remained clearly focused:
We were going to be coming in too fast and landing an aircraft that was way too heavy, out of balance, with damaged wings, little rolling capacity and broken wheel brakes, speed brakes and an inoperative engine reverser. Perhaps all these failures would add up to be an impossible mix.
To top it all off, the runway was barely long enough to land the plane under ideal conditions, let alone while it was overweight, with chunks missing out of the plane, every control surface damaged, no ability to stop, barely any control of the engines, and massive fuel leaks. What was worse, the broken anti-locking for the landing gear meant that the wheels would likely seize upon landing and reach levels of heat that could cause the wheels to burst, the brakes to fuse, and with jet fuel leaking everywhere, the plane bursting into flames as it ran down the runway was a real possibility.
When the plane was landing, every caution and warning indicator was sounding. Later the pilots would recount how they were receiving stall warnings just before they landed. De Crespigny saw in his head that single engine plane that he needed to lightly touch down ont he runway and was focused on attempting to land the plane as “softly” and as “slowly” as possible.
In the end, that’s what they did.
“Ladies and gentlemen,” De Crespigny said, “welcome to Singapore. The local time is five minutes to midday on Thursday 4 November, and I think you’ll agree that was one of the nicest landings we have experienced for a while.” De Crespigny returned home a hero.
There were no injuries reported among the 440 passengers and 29 crew on board the plane. However, when the engine exploded, it spread shrapnel and debris over residential areas destroying several cars and damaging houses. Luckily, no one was injured.
Unlearning Bad Habits
You see, the third-grade student understood the problem not as “well how can four be bigger than five?” which of course it never can be. Instead, that student saw the problem correctly as, “how can Marty’s pizza be bigger than Luis’, even when Luis seems to have eaten more pieces?”
Given what was asked – how can this be possible – this student actually saw the problem clearly and gave the only correct answer.
The difference between Bonin and de Crespigny’s reactions are unfortunately similar. Bonin, suffering from cognitive tunneling, attempted to reconcile all the data he was receiving and that lead to the entire flight crew going down the wrong path. De Crespigny, who was contending with an airplane that was substantially physically damaged, cut through all the noise and asked the question that would keep them alive – how the hell do we keep flying and not fall out of the sky until we can land safely.
The teacher’s answer, and all those defending the teacher, are suffering from cognitive tunneling or perhaps charitably, cognitive dissonance. Instead of focusing on what the question asked, everyone is focused on facts, analysis, and events, that don’t matter. We’re asking questions such as who’s right and who’s wrong.
The teacher is wrong. CLEARLY wrong. I’ve demonstrated how the teacher is CLEARLY wrong. It’s not even up for debate!
It’s not a trick question. It’s a simple question. And it’s amazing a kid who is seven, who hasn’t had trigonometry, and who probably doesn’t know what the area of a circle is, could intuitively figure out that Marty’s pizza was bigger. Instead of praising that and saying, “we need to teach students how to think clearly,” we’re arguing over lots of stuff that quite frankly just doesn’t matter and is going to train people to get other people killed one day.
The lesson that kid will remember his whole life is – 5 is always bigger than 4. Luis actually ate more pizza.
The lesson he should have learned was, “That’s not the answer I was anticipating, but you’re right, that is the answer. Good job!”
The people who can do this without prompting, who can see connections and understand the “real problem” are often known by a single word – creatives.
In the end, creative people aren’t necessarily smarter than everyone else (although many of us are), but what we can do is we can actually see the problems and challenges that, if fixed, will make a difference.
For Bonin, Roberts, and Dubois, they took a perfectly functional airplane and through a series of missteps, drove it into the ocean and maximum speed. For de Crespigny and his team, they took a plane with the engine and wings literally falling off and managed to land it on the tarmac without a single injury.
On December 7th, 1941 – we said that it was a lack of ability to “put the pieces together” that lead to the sneak attack on Pearl Harbor. We scapegoated two senior flag officers for their inability to see the “big picture”: Admiral Husband E. Kimmel and General Walter C. Short. The inquiries into Pearl Harbor accused them of not being able to see “the big picture” and recognize the Japanese were about to attack the United States. Putting aside whether or not you agree with that accusation (which for the record I do not), we paid a hefty price.
On September 11, 2001 – we said that the inability of the United States government to prevent the deaths of over 3,000 people was due to a “lack of imagination”. In other words, we couldn’t see the problem clearly, focused instead on tactical issues and bureaucratic fighting. We paid a hefty price.
The CEO of K-Mart couldn’t see how Target and Wal*Mart would erode their business. Now they’re out of business.
Kodak, a company that invented photography, would ultimately collapse because it couldn’t see how digital cameras would replace film.
And I’m pretty sure, the company that made the last buggy whip, made the best goddamned buggy whip you ever saw.
The car came anyways.
We need to encourage children, we need to encourage everyone to see clearly about problems and challenges. If we’re lucky, all that happens is a few points off on a math test.
If we’re unlucky… well… that’s another story, isn’t it?