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Recapturing the Magic of Math, Clear Versus Clever, General & Surprising (Reading/Study Notes 5.30.18)

Resource: More better math


“Math’s important. It’s elegant. It’s a magical way to deal with abstract concepts on your way to finding out the provable truth. There’s not enough math in the world. Math isn’t the same as arithmetic. Basic arithmetic is necessary, but everything beyond that is simply easily-graded compliance disguised as busy-work.”

“What would a year of hands-on truth-finding do for a class of freshman? What mathematical and vocational doors would it open? Every day we spend teaching hand factoring of binomials to non-math majors is another day we raise mathematically illiterate kids. What are we waiting for?”


Math and arithmetic are not the same. Math, truly understood and rightly taught, has a musical and mystical dimension that makes it feel exciting and relevant to the student. But this is not what most school students learn because the focus is on giving them busy work in the name of teaching them the “right” things without regard for their interests. What if we were more flexible and intuitive in our approach to teaching a subject like math? How much better would we do at generating interest? Seth Godin doesn’t say it explicitly here, but I think the key is to start with the student instead of the subject. Instead of trying to make something interesting, it’s more effective to understand where the interests are already live.

The full possibilities of learning will never be explored until we find a way to integrate study and reflection with hands-on participation.

Resource: Clear vs Clever Copywriting is a Big, Fat, Bloated Myth (And a Scapegoat for Subpar Writers)

“If your process is tame, commonplace, average, pedestrian…then the output of your efforts will reflect that. If your process is uninteresting, dreary, unimaginative and lazy, then your writing will reflect that, too.”

“Every single word carries its own private nuance, spin, shadow of suggestion. Every single word walks around cloaked in a veil. Nothing is on its face. Everything means something. Even the plainest of language is communicating a sneaky little message. There’s no escaping it.”

“So it should follow that when you sit down to write the copy for your business, the words for a promotion, the name for a company, or something equally as important for your career, it becomes difficult to get people excited about what you do, if what you say isn’t exciting. By exciting, I don’t mean exclamation points or bold claims. I mean purposefully selected to convey the exact emotion that the reader wants (and needs) to feel.”

“It takes the writer who is willing to throw all preconceived notions to the wind; who is willing to finger paint with ideas. Brilliant writing is never clean writing. There’s nothing clean about it. It’s messy. It’s savage. It’s dirty. Which is why I always say that the writing process is truly an editing process–and it is. Because the real genius of editing is not in adding a comma, or correcting a run on sentence–it’s about running each word through a specific filter, and making sure that when it comes out on the other side? It conveys exactly what you want it to. That’s writing.”

“Real clever writing is, by nature, clear to the person buying it. That’s what makes it clever. And if you’re selling something? That’s the only person who matters.”

“Clever writing is sharp. It is bright. It is skillful. Precisely why the clear brigade hates it. Approaching clear/clever from an either/or perspective is for subpar writers who aren’t talented enough to merge science and art. Clever does not have to be unclear, and clear does not have to be unclever. When you’re doing it right.”

“Precisely why your words need to brilliantly reflect you & your brand’s personality–and everything it stands for. If your company is really as innovative as you say it is, then your words need to mirror that same level of innovation. If you’re really as unconventional as you say you are, then your words cannot fall flat. If you’re really starting some kind of revolution, then your words cannot be yesterday’s.”


Make your words reflection your message.

Good writing is the kind that gets the reader to buy what you’re selling. The questions you have to ask are: “Who are you writing for? What are you selling? Are your words speaking to the “why” that makes them want to buy?

Clear versus Clever is a false dichotomy. If it’s not clear, it’s not truly clever. If it’s not clever, it’s not truly clear. Be clear by saying what you mean and be clever by saying it in a way that reveals the distinctiveness of your personality.

All of your competitors have fancy websites, professional business cards, and a standard list of benefits listed on their homepage. You can separate from the crowd anymore just by looking clean, crisp, and professional. You have to use your voice in a way that shouts out the difference.

Resources: General and Surprising


“The most valuable insights are both general and surprising. F = ma for example. But general and surprising is a hard combination to achieve. That territory tends to be picked clean, precisely because those insights are so valuable. Ordinarily, the best that people can do is one without the other: either surprising without being general (e.g. gossip), or general without being surprising (e.g. platitudes).”

“Where things get interesting is the moderately valuable insights. You get those from small additions of whichever quality was missing. The more common case is a small addition of generality: a piece of gossip that’s more than just gossip, because it teaches something interesting about the world. But another less common approach is to focus on the most general ideas and see if you can find something new to say about them. Because these start out so general, you only need a small delta of novelty to produce a useful insight.”

“A small delta of novelty is all you’ll be able to get most of the time. Which means if you take this route your ideas will seem a lot like ones that already exist. Sometimes you’ll find you’ve merely rediscovered an idea that did already exist. But don’t be discouraged. Remember the huge multiplier that kicks in when you do manage to think of something even a little new.”

“Corollary: the more general the ideas you’re talking about, the less you should worry about repeating yourself. If you write enough, it’s inevitable you will. Your brain is much the same from year to year and so are the stimuli that hit it. I feel slightly bad when I find I’ve said something close to what I’ve said before, as if I were plagiarizing myself. But rationally one shouldn’t. You won’t say something exactly the same way the second time, and that variation increases the chance you’ll get that tiny but critical delta of novelty.”

“And of course, ideas beget ideas. (That sounds familiar.) An idea with a small amount of novelty could lead to one with more. But only if you keep going. So it’s doubly important not to let yourself be discouraged by people who say there’s not much new about something you’ve discovered. “Not much new” is a real achievement when you’re talking about the most general ideas. Maybe if you keep going, you’ll discover more.”

“It’s not true that there’s nothing new under the sun. There are some domains where there’s almost nothing new. But there’s a big difference between nothing and almost nothing, when it’s multiplied by the area under the sun.”


Most good insights come in the following form: they are both general (applying to many things) and surprising (unanticipated).

Universal and surprising is a difficult combination to find. Paul Graham defines “small deltas of novelty” as little increases in one of those areas. These small deltas have a significant impact. Graham argues that it’s false to say “there’s nothing new under the sun.” He contends that it would be more accurate to say “there’s almost nothing new under the sun.” And “almost nothing new” is not only the best we can do, but it’s a lot more than we think.

Don’t be afraid to repeat yourself. Technically, it’s a very difficult thing to do anyway. When you write about things you’ve already written about before, you tend to say it differently. These tiny variations can gradually add up to become small deltas of novelty where you say something old in a very powerful or interesting or novel way.

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