“The field that became a black hole”


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(Coming soon)


So, this happened …

Like the others in the room, I also laughed out aloud when the teacher shouted at Denny. None of us were actually mocking him, but when you thought about his answer, it was kinda dumb.

Of course, when the teacher then started shouting at me, it suddenly wasn’t funny anymore. Well, it wasn’t funny to me anymore. My classmates apparently disagreed, and it was now me who was the target of their laughter.

This event took place when I was 14 years old, but it was such an emotionally intense moment that I can still remember it decades later, as if it had happened last week.

We had just started learning calculus at school, and I was lucky to be in Mrs K’s class. She was an excellent maths teacher, although on occasion she would lose her temper with the class. This was one of those days. (And to be fair, I can’t blame her.)

We had all filed into the class and sat in our usual places, ready to begin. The room became silent much quicker than usual, we could sense the stress. Mrs K was standing at the front of class, our assignments from last week in her hands, and she was scowling.

“Question 5 from last week’s homework,” she fumed, “was as easy as they get.” She then reminded us what question 5 was. (You can skip this paragraph if you’re so inclined :)

“You have a field and must build a simple paddock within, by fencing off a rectangular space. The paddock can be a long rectangle, a wide rectangle, or even a square. Calculate the size of the paddock which uses exactly 100 meters of wire around it, but which gives your paddock the greatest area.”

Mrs K was right: in the world of calculus, this really was as easy as it gets. What length of paddock, for a given perimeter, gives the greatest area?

“Let’s see,” Mrs K said while thumbing through the papers in her hands. “And you children, what were the dimensions of your paddocks? The question is asking how long your field is, people!” she shouted out of understandable frustration. “How long is your field?”

“Denny, your answer is 2746 meters. Seriously? Your field is thousands of meters long, but you’ve only got 100 meters of wire. Are you sure about your answer? Did you even think about your answer before you handed your work in?”

People in the class laughed. When you think about it like that, 2746 meters is a ridiculous answer. I laughed too.

“And don’t laugh Greg,” she said shuffling through her papers to find mine. “Your answer was -11 meters. What on earth does a paddock look like if it’s NEGATIVE eleven meters long? Is that like a black hole in the middle of a field?”

Her anger hadn’t started to fade yet. “How will any of you progress at school if you don’t actually stop to think?!”

And she was right. I can only imagine how frustrated she must have felt, wanting so much to teach us, but at the same time being aware of our flippant attitudes to the work.

I clearly hadn’t thought about my answer! I was running on automatic: I did the calculation, I made a dumb mistake along the way, and came up with -11 meters. Even the tiniest bit of attention to the answer would have made me realize I was wrong. But I happily underlined my wrong answer, and moved on to question 6.

That moment, being singled out in front of everyone for my stupid answer, was a powerful lesson for me. I promised myself that I would always think about my answers from then on.

And while I haven’t always got that right, it has mostly become an ingrained habit for me. I’ve never forgotten Mrs K’s lesson.

When this scene originally happened, my default mode was “Doing-without-thinking”. But by now I’ve trained myself to think about my answers, it’s just part of my process. I’m still running on automatic, but at least now it’s “doing-and-thinking” that has become my default.

Have a think about that!

Simple Definition

The field that became a black hole: Think about your answers, so that you spot any holes in your logic (or in your calculations) before committing to your response. Similarly, think about the answers that are given to you, looking for any obvious holes in their message.

Summarizing what it means

The lesson is simple: think about the answer.

If you do, you can have the following:

  • you will produce better quality work
  • people will trust you more
  • you will be less vulnerable to lies and deception
  • you will understand things better
  • you see the simplicity in complexity
  • life becomes less overwhelming.

This is true whether you’re doing assignments for school or university, whether you’re doing calculations for your boss or your client, or whether you’re just responding to someone in conversation. And of course, if someone else is giving you answers, then think about those too!

When you’re solving problems, an answer isn’t just a fact or a number. It’s actually a solution to a problem.

So think about the answer, and judge broadly whether that seems like a reasonable solution.

For example, if I’m making a paddock in a field with 100 meters of wire, does it sound right that the field is 2746 meters long? Does negative 11 meters even make sense?

Remember, I’m not asking you to just do the calculation again. That’s not thinking, that’s doing.

The goal is to actually judge the answer’s reasonableness. If the answer feels right, then move on. If something just isn’t tying together, that’s when you may need to go back to your calculations. Or at least ask more questions.

There are many ways of making sure your field hasn’t turned into a black hole, including comparing to other known knowns, applying rules of thumb, or massively simplifying the problem & solution.

In the chapter below, we explore a series of powerful techniques you could (should?) be using to scan for black holes in your field.

Discussing what it means

PART 1: Thinking about thinking

Let’s begin with a joke

There’s a story about a man and woman talking at a bar, and the woman is being critical about how much the guy drinks. She points out that if he hadn’t been drinking 4 beers a day for the last 20 years, and had instead saved the money and earned compound interest on the cash, he would have enough money now to buy a Ferrari. 

     “Do you drink?” he asks her.

     “No,” she replies.

     “Then where’s your Ferrari?”

This is a great example of someone hearing something, and actually thinking about the answer. He didn’t argue about beer inflation over the last 20 years, or the fact that he gave up drinking for a year, a few years ago. He simply focused on her primary message, and left it in tatters.

So what kind of ‘answers’ can you think about?

You can think about answers that involve calculations – that’s easy.

  • A field can’t have a negative length :)
  • It’s not reasonable to charge $387,399 for a beer at the new bar you’re opening, no matter what your spreadsheet tells you
  • Your estimate that this new sales-tracking app will save you 11 hours of work a day is probably wrong.

Answers can be around facts, and needn’t involve numbers.

  • Can watching TV in a dark room damage your eyes?
  • Instinctively, this doesn’t sound plausible to me, but it’s not my field of expertise so I didn’t know for sure. The good news is that I was at least thinking about the claim.
  • So I took a moment to do a quick search, looking for guidance. The unanimous opinion on the first page of search engine results said that while it can strain the eyes, there is no evidence that it can actually damage the eyes.

You can think about the process, not just the answer

  • If work is being delegated (whether you’re the one giving or receiving) then yes, you should think about what you expect the answer to be, but there’s more …
  • Don’t ONLY think about the answer!
  • Also take time to think about what the process might look like in getting to the answer. This allows you to plan better for the resourcing that will be needed, any additional information (or material) that will be required before beginning, etc.
  • And also think about how long it might take to do the calculation or complete the task. (When I delegate work, I try to give them guidance on how long it should take. Firstly, it helps them know what I expect. Secondly, if they are coming to that target point in time and are still a long way from completing the work, then that gives both of us the chance to talk, to make sure we are both clear on what was needed, and to determine what (if anything) has gone wrong.)

What kind of answers can you NOT think about?

Opinions don’t really fit in here

  • This chapter doesn’t cover the thinking you might go through to determine which political party is ‘better’ – that’s not about truth but about personal values and opinions
  • That said, if truth is core to your value system, and you support a political party that is centred around lies, then that is a black hole.

Choices don’t belong here either

  • You can’t determine which antivirus software is the singular ‘best’, because that very much depends on a person’s individual circumstances, so no amount of “thinking” will produce an absolute truth
  • Again, though, it’s possible to use false logic as you build a case for “the best software for you”, and that’s a black hole to watch out for.

Answers where wrong isn’t wrong enough

  • If someone insists that there is a distance of 100 miles between two cities, and your thinking leads you to a “back of the envelope” estimate of 210 miles, then what should you conclude? Are you wrong, or are they? In theory, either could be right because both numbers could be reasonable estimates of a distance between cities.

What if you don’t think about your answers?

Why bother thinking, right? Well, if you think about it (see what I did there?) the real question is, why not bother?

  • When you’re preparing for and then writing exams, if you’re not spotting unreasonable answers, there is a higher risk of failing or not getting as good a grade as you’re capable of. Poor academic results can have a (lifelong?) impact on your career, your options, your earnings.
  • At the office, if you keep making mistakes in the work you hand in, after a while your boss (or your client) will stop trusting you. This will play havoc with your ability to make money, get promoted, or have a positive impact on the people around you. (See #[Sometimes Kitt was sh*t])
  • If you say odd things, or make implausible claims to your prospects – even if you totally believe in what you’re saying because you don’t think hard enough about it – then you will leave them uncomfortable enough that you won’t get any sales. And that will have a significant impact on your earnings. (See #[Eating blue cheese with apple ice-cream])
  • As you know from #[A punch is just a punch], the Learning Circle involves going from naive to overwhelmed to mastery. If you don’t think enough about your subject, then you will remain in the naive phase. And even if you make it into the overwhelming phase 2, your lack of attention to detail means you will never understand the subject well enough to make it to the mastery phase. (As they say, if you can’t explain it simply, then you don’t know it well enough.)
  • And when you delegate work to someone, if you spend a little time thinking about what answer (in broad terms) you’re expecting from them, then when they get back to you, you’ll have a good sense of whether their answers is probably right, or whether they missed the mark and probably have to re-do their work.

The more you think, the better you get at it

Thinking creates understanding, and the better your understand, the more capable you are of spotting problems – either mistakes you make while working in this field, or mistakes made by others.

Ongoing thinking gives you experience against which you can calibrate.

  • The stock exchange fell by 100 points today – is that a lot? Well, if you look at the stock exchange movement every day, it won’t take long before you start to get a feel for what “a lot” would look like.
  • A politician claims in his tax returns to make $100,000 a year from giving speeches at events – does that seem suspicious?
  • These are not difficult answers, but if you haven’t exposed yourself to this information, you won’t have a feel for “normal”.

And through active thinking, you can actually help build an intuition for what seems reasonable or not. The best way I have of describing this is to suggest you read the chapter called #[The sound of hot water pouring].

PART 2: How to think (let’s get practical)

Think before, Think afterwards

I hope from the story of “The field that became a black hole”, it’s obvious that you should think about your answers after you’ve produced them. It’s amazing how often you can avoid a complete mess by just doing this step.

But you should also be thinking before you begin the work. As mentioned earlier in this chapter: think about what the answer might be, think about the process you will have to follow to complete the work, think about how long this will all take.

You can read more about this in #[The red-dot on the wall].

Think before and Think afterwards. How much more clear can I be?

Powerful Techniques you should know

I am not expecting you to memorize these techniques, nor to use every single one of them, every time you are producing some kind of answer.

Instead, I am showing you how broad the range of approaches is, that you can use. Make sure you can apply each one of these. And find other techniques that are suitable to your work that I haven’t mentioned.

Over time you will instinctively know what to do when, but start off with deliberate effort to learn and to apply. (See #[A punch is just a punch].)

  • Think about who is giving you the answer.
    • Someone who has been in corporate their whole career may have lots of advice for entrepreneurs, but it might be better to listen to people who have succeeded as entrepreneurs.
  • Test people’s wider knowledge on the subject.
    • A colleague was giving me advice about vaccines, but when I asked, they didn’t know the difference between a coronavirus and a retrovirus, which made their comparison of Covid19 vaccines and Aids vaccines a little “iffy”.
  • Think about the order-of-magnitude of the answer.
    • Someone once told me that masks can’t stop viruses, because people can still smell things with a mask on. It only took a few seconds of searching to show that (depending on which smell and which virus) smell molecules are dozens or hundreds of times smaller than viruses. So their conclusion that if smells get through then viruses can, is not logical.
    • Just to be clear, I’m not saying you can conclude that virus can or can’t go through masks, I’m just saying that knowing that smells get through doesn’t tell you whether or not viruses can.
  • Consider the chain of logic.
    • People – including you! – sometimes use non-sequiturs, where they state something that is definitely true, and then say “therefore”, and then they state some incorrect conclusion.
    • In the above example: “You can smell with a mask on”+”therefore”+”masks can’t stop a virus” is an example of a non-sensical chain of logic, since the one definitely doesn’t prove the other.
  • Allow for the fact that possibility doesn’t mean actuality.
    • Just because you can come up with something might be true, doesn’t mean it is true. In this case, your challenge is not to try find a problem with their facts (which could be correct) but in recognising that they are what they are, without meaning anything else.
    • See #[The pharmaceutical company that invented headaches] for a deeper discussion of this.
  • Find at least one counter-example.
    • Like in the joke at the start of this section about beers & Ferraris, he didn’t have to debate compound interest, it was enough to point out that her ‘rule’ isn’t always true.
    • Or when products on Instagram claim you can lose lots of weight walking just 10 minutes a day, but you know many overweight people who walk a lot more than that daily!
  • Do some basic maths.
    • I remember having a drink with some friends, when a know-it-all was claiming that at university, his IQ was so high that it increased the class average by 10 points, for a class of about 30 people. It took less than 1 minute of mental arithmetic for me to work out his IQ would have to be more than 400 (!) in order for that to be true. I called bullshit.
  • Apply any rules-of-thumb you know on the topic.
    • You might know from using the treadmill that a reasonable walking speed is about 4km/h (about 3mph), so you can ‘test’ a restaurant’s claim that it’s only 15 minute walk from the station.
    • Or there is the Rule Of Nines in burn injuries, or the Rule of 78 for loan interest, or sound takes 3 seconds a travel 1km. Or anything else that you’ve learned in your job that let’s you ‘test’ an answer.
  • Think about “so what?” regarding their claim.
    • A new credit card claims that normally when you spend 100 dollars you get 100 points, but they have a loyalty scheme where you get 1000 points when you spend 100 dollars. So what? What you then need to know is how many of their points you have to redeem to get anything out. If it’s also 10x higher, then there really is no difference between the schemes.
  • Be aware of cognitive biases, and don’t let them taint your thinking.
    • Deals where you might lose something feel worse than deals where you might gain something, even if the expected outcome is the same.
    • We kill so many sharks every year to protect ourselves from fear, not from actual sharks, who hardly kill anyone.
    • Events seem more likely when we hear about them from many people.
    • Restaurants often sound worse than they are, because unhappy customers are more likely to complain to lots of people, than happy customers are to share their joy with people.
  • Do a quick search.
    • If someone claims that eyes get damaged by watching TV in low light, you might not know enough to challenge that claim. But a quick search shows (according to pretty much all the links on the first page of search results) that it’s not true.
    • A quick search is not proof, but it at least gives you some direction in your thinking.
  • Do a BETTER search.
    • NASA did not invent Velcro – which was actually patented a few years before NASA was founded. But depending on how you word your search, you will find sites that make that claim strongly.
    • Similarly, if you’re a vegetarian and Google has started personalizing your search results accordingly, then a further search about whether it’s healthy to eat meat or not will produce results which are biased in one direction.
    • Get good at searching.

Don’t overthink

Firstly, remember that it’s OK not to analyse everything. Don’t sit with your friends over a delicious meal, and challenge every single statement they make. It’s fine to go with the flow sometimes, either by not thinking, or by accepting that what they say sounds odd but you’ll just let it slide.

You can read #[The Pepsi & Pie deal] for another chapter that explains how easy it is to become that annoying friend that others dislike :)

Secondly, thinking about the answer doesn’t mean redoing all the calculations yourself. It doesn’t mean doing a detailed research project to test the facts. Sometimes it’s enough to know that – roughly – it sounds OK, and you can proceed on this basis.

The process of making sure your field doesn’t turn into a black hole isn’t about accuracy, it’s about the big picture.

It’s about direction. It’s about a decision on whether you can move forwards, or whether you need to go back a few steps (or even back to the beginning).

Please treat it as such.

#[Three drops of blood in your bath] teaches you a lot more about orders-of-magnitude, so read that next.

Just for fun: movie goofs

In line with the theme of not overthinking things, when you’re watching a movie, try to let go and lose yourself in the story.

I’m proud to say that I’ve come out of movies that had so many plot holes, and I didn’t even notice one of them. I also watched that episode of “Game of Thrones” where there was a Starbucks coffee cup on the table, and I didn’t see it.

On the other hand, when watching “Star Wars: The Phantom Menace”, I do remember thinking that if Tatooine was orbiting a binary star system, how come we only ever see single shadows in those scenes?!

And if you noticed any of the following goofs when watching these movies, you are definitely overthinking! That’s not a black hole in your field, that’s a needle in a haystack that you’re spotting!

  • “The Hurt Locker,” was set in 2004, but the one character referenced YouTube, which was only created in 2005. There is also an iPod, which was only introduced in 2007.
  • In “Raiders of the Lost Ark” they mention Thailand, which was called Siam for three more years after the movie was set.
  • “Forrest Gump” invested in Apple in 1975, although Apple didn’t go public until 1980. Whoops.

Think about this …

  • Think about the answer.
  • Think about the big picture, not the detail.
  • And think just the right amount.

Making it personal

Get your #HashtagYourLife journal out and get ready to start scribbling …

In terms of your personal style …

  • On a scale of 1 to 10, how good are you at thinking about answers that you come up with, to decide if they’re reasonable?
  • On a scale of 1 to 10, how good are you at thinking about what answer you expect to get, before you set about doing the calculations?
  • In terms of delegating work to people, do you think about what they’ll have to do, how long it should take, and broadly what the answer should be … and then communicate that to them as part of the delegation? If not, why not?
  • Knowing the kind of work you do, out of the twelve Powerful Techniques I describe above, which is the one that you can see will give you “most bang for your buck” if you start using it regularly in your thinking-and-doing?

In terms of having a feel for numbers …

  • What does a teacher earn? What does a lawyer earn?
  • Out of the 100 people who graduated from high school with you, how many will have died by the time you all turn 60?
  • What is the distance between New York and London? What is the distance between Cape Town and Moscow? What is the distance between Moscow (west Russia) and Vladivostok (east Russia)?
    • (I think the answers to this one will surprise you.)
  • What does a loaf of bread cost? What does a kitchen-size fire extinguisher cost? How much would it cost to fumigate a three bedroom house?
  • How tall is an average flagpole? How tall is a 10 story building?
  • What does a large dog weigh? What does a medium size family sedan weigh?
  • Can you calculate, using mental arithmetic only, the square root of 2 times 8 times 100 times 10,000? (It’s not as difficult as it seems, don’t give up too quickly!)

Of course you don’t need to know any of these numbers. My point is that the more ‘benchmarks’ you have like this, the easier it is to call bullshit when someone tells you something that isn’t quite true.

Finally, take a guess at how many words there are in this article. Quickly page-up and try come up with a number. Don’t take more than 30 seconds. You can check your answer by doing the square-root calculation I’ve given above. Were you right?

OK, you can relax now. Go do something that doesn’t involve thinking.

But just for a short time :)

Related Stories

#[Sometimes Kitt was sh*t]

#[Eating blue cheese with apple ice-cream]

#[A punch is just a punch]

#[The sound of hot water pouring]

#[The pharmaceutical company that invented headaches]

#[The Pepsi & Pie deal]

#[The red-dot on the wall]

#[Three drops of blood in your bath]

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