Just Add Water

A Bill Gates Roy Amara quote I encountered last week reminds me strongly of compound interest.

“We always overestimate the change that will occur in the next two years and underestimate the change that will occur in the next ten.”

I hadn’t heard this line before, but based on anecdotal evidence, I think Amara was right to zeroth order, and it is a very smart comment. The question is why this happens. I think the answer is that we are naturally wired for arithmetic, but exponential thinking is unnatural.  But I haven’t quite worked it out yet. We probably use some sort of linear prediction that first over-estimates and then under-estimates the underlying exponential process, but where does that linear prediction come from?

Anyone want to take a crack at an explanation? I could be wrong. Compound interest/exponential thinking might have nothing to do with it.


When I write, I generally start with some sort of interesting motif, like the Gates quote, that catches my eye, which I then proceed to attempt to unravel. Sometimes it turns out there’s nothing there, and sometimes a trivial starting point can fuel several thousand words of exploration.

I call this the “just add attention” model of writing.  It’s like just-add-water concentrates. A rich motif will yield a large volume of mind fuel if you just dissolve it in a few hours of informed attention.

The previous nugget is an example. If I were to let it simmer for a few days and then sat down to do something with the Gates quote, I would probably be able to spin a 4000-word post from it.  I figured I’d let you guys take a crack at this one.

My hit rate has been steadily improving. Nowadays, when I suspect that something will sustain exploration to such and such a depth, I am almost always right.

I prefer the word motif to words like pattern or clue, because it is more general. A motif merely invites attention. By contrast, a pattern attracts a specific kind of analytical attack, and a clue sets up a specific kind of dissonance.


The nature of just-add-attention writing explains why it is hard for me to write short posts. If I wrote short posts, they’d just be too-clever questions with no answers, or worse, cryptic motifs offered with no explanation.

You cannot really compress just-add-attention writing. You can only dehydrate it back into a concentrate. Just-add-attention writing has a generative structure but no clear extensive structure. It is like a tree rather than a human skeleton.

By this I mean that you can take the concentrate — the motif — and repeatedly apply a particular generative process to it to get to what you an extensive form. But this extensive form has no clear structure at the extensive level. At best, it has some sort of fractal structure. A human skeleton is a spine with four limbs, a rib cage and a skull attached. A tree is just repeated tree-iness.

But I hesitate to plunge forward and call all generative-extensive forms fractal, as you might be tempted to do. Fractal structures have more going on.


Just-add-attention writing is partially described well by Paul Graham’s essay about writing essays, which somebody pointed out to me after I posted my dense writing piece a few weeks back. But I don’t think it is the same as the Graham model. I think the Graham model  involves more conscious guidance from a separate idea about the aesthetics of writing, sort of like bonsai.

Just-add-attention writing is driven by its own aesthetic. This can lead to unpredictable results, but you get a more uncensored sense of whether an idea is actually beautiful.

Dense writing is related to just-add-attention in a very simple way: making something dense is a matter of partially dehydrating an extensive form again, or stopping short of full hydration in the first place. Along with pruning of bits that are either hard to dilute or have been irreversibly over-diluted.

Why would you want to do that? Because just-add-attention writing can sort of sprawl untidily all over the place. Partially dehydrating it again makes it more readable, at the cost of making it more cryptic.

This add-attention/dehydrate again process can be iterated with some care and selectivity to create interesting artistic effects. It reminds me of a one-word answer Xianhang Zhang posted on Quora to the question, “how do you chop broccoli?” Answer: “recursively.”

Regular writing can be chopped up like a potato. Just-add-attention writing must be chopped up like a broccoli. It is more time consuming. That’s why I cannot do what some people innocently suggest, simply serializing my longer pieces as a sequence of arbitrarily delineated parts. I have never successfully chopped up a long piece into two shorter pieces. At best, I have been able to chop off a straggling and unfinished tail end into another draft and then work that separately.


Not all generative processes lack extensive structure. The human skeleton is after all, also the product of a generative process (ontogeny). To take a simpler example, the multiplication table for 9 is defined by a generative rule (9 times n), but also has an extensive structure:


In case you didn’t learn this trick in grade school, the extensive structure is that you can generate this table by writing the numerals 0-9 twice in adjacent columns, in ascending and descending order.

If you wanted to blog the multiplication table for 9, and had to keep it to one line. You could use either:

  • The nine times table is generated by multipling 1, 2,…, n  by 9, or
  • Write down 0-9 in ascending order and then in descending order in the next column

Both are good compressions, though the second is more limited. But this is rare. In general a sufficiently complex generative process will produce an extensive-form output that cannot then be compressed by any means other than rewinding the process itself.


Just-add-attention writing is easy for those who can do it, but not everybody can do it. More to the point, of the people who can do it, a significant majority seem to find it boring to do. It feels a little bit like folding laundry. It is either a chore, or a relaxing experience.

What sort of people can do it?

On the nature front, I believe you need a certain innate capacity for free association. Some people cannot free associate at all. Others free associate wildly and end up with noise. The sweet spot is being able to free associate with a subconscious sense of the quality of each association moderating the chain reaction. You then weave a narrative through what you’ve generated. The higher the initial quality of the free association, the easier the narrative weaving becomes.

On the nurture front, this capacity for high-initial-quality free association cannot operate in a vacuum. It needs data. A lot of data, usually accumulated over a long period of time. What you take in needs to age and mature first into stable memories before free association can work well on this foundation. The layers have to settle. By my estimate, you have to read a lot for about 10 years before you are ready to do just-add-water writing effectively.

Unfortunately, initial conditions matter a lot in this process, because our n+1 reading choice tends to depend on choices n and n-1.  The reading path itself is guided by free association. But since item n isn’t usable for fertile free association until, say, you’ve read item n+385, there is a time lag. So your reading choices are driven by partly digested reading choices in the immediate past.

So if you make the wrong choices early on, your “fill the hopper” phase of about 10 years could go horribly wrong and fill your mind with crap. Then you get messed-up effects rather than interesting ones.

So there is a lot of luck involved initially, but the process becomes a lot more controlled as your memories age, adding inertia.


This idea that just-add-attention writing is driven by aged memories of around 10 years of reading suggests that the process works as follows.

When you recognize a motif as potentially interesting, it is your stored memories sort of getting excited about company. “Interesting” is a lot of existing ideas in your head clamoring to meet a new idea. That’s why you are sometimes captivated by an evocative motif but cannot say why. You won’t know until your old ideas have interviewed the new idea and hired it. Motif recognition is a screening interview conducted by the ideas already resident in your brain.

Or to put it in a less overwrought way, old ideas act as a filter for new ones. Badly tuned filters lead to too-open or too-closed brains. Well-tuned ones are open just the right amount, and in the right ways.

Recognition must be followed by pursuit. This is the tedious-to-some laundry-folding process of moderated free association. It is all the ideas in your head interrogating the new one and forming connections with it.

Finally, the test of whether something interesting has happened is whether you can extract a narrative out of the whole thing, once the interviewing dies down.

A good free association phase will both make and break connections. If your brain only makes connections, it will slowly freeze up because everything will be connected to everything else. This is as bad as nothing being connected, because you have no way to assess importance.

The pattern of broken and new connections (including those formed/broken in distant areas) guides your narrative spinning.

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About Venkatesh Rao

Venkat is the founder and editor-in-chief of ribbonfarm. Follow him on Twitter


  1. Yes, you need to balance Sensing with iNtuiting (and vice versa).

  2. Roy Amara, not Bill Gates: http://en.wikipedia.org/wiki/Roy_Amara

  3. According to Wikipedia — http://en.wikipedia.org/wiki/Romanesco_broccoli — romanesco broccoli is also called “roman cauliflower” and is a member of the cauliflower family, while broccoli is in the cabbage family.

    I had never heard of romanesco until I read this, so I’m taking on faith that Wikipedia knows more about it than I do.

    • They are all members of the brassica genus. They are further broken down into cruciferous vegetables. Broccoli, cauliflower and cabbage are all members of the oleracea branch.

  4. > We probably use some sort of linear prediction that first over-estimates and then under-estimates the underlying exponential process, but where does that linear prediction come from?

    Who says it’s linear? It looks hyperbolic to me. (Where does hyperbolic discounting come from in humans and animals? Dunno, but one plausible explanation is unreliable internal or circadian clocks.)

    • Hyperbolic in what sense precisely?

      • Discounting.

        • Hmm… Not sure if discounting is the right model here. This is more prediction error than NPV. We may care less than we should about returns in Year 10, but predicting it ought to be an independent thought process.

          • You asked why is it that we can easily predict a result in five years but less easily predict in ten years. I think the reason is that we know that variabilities increase as time passes. New information can dramatically alter circumstances – so much so that predicting beyond a certain point is going to be less and less accurate. Learning over a ten year period adds so much new information that we become aware of that process more and more. I find that the perspective of time on the planet has dramatically altered my planning. There are so many variables to consider. For example, the stock market crash dramatically altered retirement plans for many people. If things continue as they are then predictions for ten years can be accurate, but in the real world the chance of factors staying as they are is less and less certain. Whenever our plans start out with : “If all things remain as they are, then . . . (fill in the blank with a ten year result)” we have to know that we are entering much chancier territory. I would say that this area enters a fantasy world where science fiction can predict trends, but not specifics. Therefore, a ten year plan has to have a more general focus than a five year one. Nowdays I would shorten even that to two years. I feel very confident that I can carry out a two year plan and have the result very near predictions. I feel a five year plan has less accuracy as far as outcomes and a ten year plan is nearly unknowable. Still, I think that one needs a ten year plkan and even a life-long goal of some sort, or stagnancy sets in. Like plants, we have to keep growing or die.

          • Glee:

            That’s not what I asked. I asked why we might systematically overestimate in the short term and underestimate in the long term. See. The opening Amara quote.

            Simple prediction uncertainty over longer terms is well-understood and modeled.

  5. Venkat, are you implying or insisting that there is only one good, or “right” way to creatively engage in self-learning and subsequent follow-on instruction of others?

    I ask because your process as recounted, requires a lot more then just a motivated individual. Your uptake period of about 10 years of serious reading seemingly implicates those able to afford the time. School costs money and what of those of us who are both somewhat younger, and also of much lesser finacial means?

    I find the ideas here somewhat useful to someone in my position, but I balk at the idea that you have to be a bon vivant, or a Master/ Ph.d holder to engage creative and free associative facilties.

    Your allusion to 10 plus years of solid reading to a working man like myself seems a not so subtle reference to the time one spends in the Acadamy. So what of us in the unwashed masses, unable to pay for such a privledge?

    • I don’t know if you live in the U.S. but if you do there are free lending libraries all over the place. Even if your town’s isn’t very good it’s probably part of a consortium with neighboring towns. Worse come to worse, you obviously have internet access which means you can read tons of stuff for free. The Browser is a great way to find good long-form journalism and Project Gutenburg has piles of public domain books for free.

      If you don’t have time to read because you’re working 72 hour weeks then you’ve either already made your choice not to engage in a program like Venkat’s or you will need to find a job with fewer hours. Not really anyone else’s responsibility to buy books for you or find time for you to read them.

      • Dan, I’m not sure how to respond to something like that. Maybe you are in a position to “Make a Choice” but that’s not something we all are blessed with. Time is money and even with my stong reading habits I would never be able to acheive the density required, not with my obligations to my family and their wellbeing.

        I am getting at the fact that you need the skill of free association in order to be a good mechanic, and the model as presented by Venkat offers no such allowance for “correct” free-associative creativity outside of education in the Acadamy.

        In a way the beginning of his post pre-empts this, as brings up the concept of linear overreach. I think here he is improperly using this platitude as a crutch to prop up the specific case study he uses below. I might have been less concerned if Venkat had simply acknowledged that he was only engaging in an anecdotal case study, rather then what appears to be an attempt at universalization.

        I am less preturbed by your prideful, if impractical, naivete with regards to the current economy, and the subsequent effects of that poor economy on those of us who are both college educated, yet unemployed or currently retraining at a Technical College. More power to you Dan.

        • I am getting at the fact that you need the skill of free association in order to be a good mechanic, and the model as presented by Venkat offers no such allowance for “correct” free-associative creativity outside of education in the Acadamy.

          Your interpretation. My interpretation, confirmed by Venkat’s reply to you, was that directed learning as in “the Academy” actually inhibits the slow-cooked model of thinking presented by Venkat in the post. Also not seeing where Venkat claimed to have the correct method of free-association.

          I am less preturbed by your prideful, if impractical, naivete with regards to the current economy, and the subsequent effects of that poor economy on those of us who are both college educated, yet unemployed or currently retraining at a Technical College.

          See, I interpreted your contribution as being prideful, impractical, and naive — hence my response. I don’t see any contradiction between working 40-50 hour weeks and reading voluminously in one’s spare time. If you work more hours than that then you have less time to read (obviously). If you’re changing dirty diapers you have less time to read (again, obviously). These are just facts about the world. I don’t see that there’s any naivte involved in pointing out facts about the world.

          When you choose to have a family with children and all the rest you have less time for other stuff. This is a choice you’ve apparently already made. In other words, at one point you WERE in a position to make a choice and you made it. You can’t blame (or credit) anyone else for making that choice and you’re the one who has to live with the consequences. Again, I don’t see where pointing this stuff out is in any way “naive.”

          • Look, I’m not in the mood for a flame war.

            If you thought my posts were prideful then why didn’t you say so the first time?

            I’m sorry I ruffled your feathers. Now can we please just agree to disagree?

    • Formal learning actually impedes this sort of thing. Time and access to books is really all you need. But you do need the books. Trying this sort of thing without books is like trying to learn swimming without getting into water.

      But yeah, access to opportunity is always an issue in every worthwhile pursuit.

      • I can work along those lines. Let me take a crack at clarification.

        I’m trying to get at the insistantance on “book” or in your model here we could sub “knowledge”. Is it somehow not appropriate within your model to substitute another source of, “knowledge”? Namely, “practical experiance?” Looking only to books as a source of, “knowledge” is the classic, “Academy mistake”

        All my comments revolving around, “The Academy ” revolve on this point. Your model skews towards “reading”, and “books” when it in fact it might also be correct to skew inverse towards more ” practical experiance” and less reading.

        Of course you can’t have one without the other, all I’m concerned about is that you model though implicit with “experiance” doesn’t seem to think experiance warrants enough, (or really any!) consideration of its own. That’s what I’m taking issue with. The fact you seemingly ignore the learning and knowledge that practical experiance brings to an individual along with his/her readings.

        The goal and process are inherently human, yet there are different intensities, paths, methods, and schedules to the same mountian. Your writting has a spirtual dimension of introversion, so it is subsequently more prone to fundamental adjustment with seemingly small-frame changes, one tweak in a fractal changes the whole picture.

        I’m asking the master to either accept one of these “minor tweaks” or else double down. either way, it should be fun to watch. Hope this doesn’t seem to rantish, thanks for your response.

        • Experience knowledge and book knowledge work differently in some ways and are similar in others. I was talking purely about a variety of the latter. I am focusing on reading and writing, not knowledge in general terms.

          I am not sure why you would expect effort in one domain to lead to deliver rewards in another. It’s like complaining that years spent practicing carpentry cannot make you a great cook, and that that’s unfair.

          I might write about experience-based knowledge another time, but it is notin-scope for this post.

          • >>I am not sure why you would expect effort in one domain to lead to deliver rewards in another<<

            That wasn't exactly what I was saying. I'm not quite sure what you are getting at here.

            Still I find it odd an claim that you somehow don't make use of "experiance" while writing. I feel your post sort of begs the question.

            You can't learn eloquence from a book, even as that is what you seem to be addressing as a matter of knowledge.

            I guess I misunderstood you that you were only writing about this knowledge side of eloquence and not the experiance side?

            Eloquence, to me, is a practice, and thus a matter of experiance, books obviously help develop the skill but this free asssociativeness arises from ones experiances with the books, not just the knowledge gained from them.

            You talk of "pruning" mal-formed writing like bonsai, but how does one learn what is and isn't mal-formed writing?

            Surely that is also matter of experiance?

            I see knowledge and experiance as inseperable the two are not able to be fully seperated no matter how hard you might try, kind of like the yin/yang. No matter how much yang there is always a tiny bit of yin.

  6. We also tend to overestimate the duration of simple tasks (how long does it really take to empty the dishwasher?) and underestimate the duration of complex ones (we should clean out the garage this afternoon!).

    I think it’s because of an inability to cope with uncertainty. The complex project or longer horizon has more uncertainty, more variables, more interactions. We’re less able to understand the scope and ramifications and possible outcomes, so we simplify in our heads and therefore underestimate. The simple project or short time frame is much more knowable, so because we can see all of it, it looks bigger.

    I’m not sure how to mitigate this effect except by deliberately adjusting your estimates in the other direction. Short-term bias is easier to correct. I know that it only takes a couple of minutes to put away the dishes, despite by bias toward thinking it’ll take FOREVER. Long term bias is harder to deal with, but may be much more critical. I don’t know of any research to prove it, but if complexity is the cause of this tendency, then we have to be much more prone to underestimating at ever shorter time-frames as our world gets more complex.

    Please insert Black Swan reference here.

  7. Not really related to the subject of your post, but some things in human perception are, in fact, exponential. In music, octaves are perceived as equal intervals apart, but they are a doubling of frequency. Loudness is measured in decibels largely because linear increments on the (logarithmic) decibel scale are perceived as linear increments in loudness. I’m sure there are similar characteristics in how we process vision, touch, etc. And I believe this is mostly because our senses can handle a very wide range of intensities, and you really need a logarithmic scale to make sense of it all.

  8. I read through the Boyd biography based on your recommendation and interest in Boyd’s work, and I was reminded of a portion of this post about the Destruction and Creation essay that I think was in the appendix of that book. Boyd discusses analysis and synthesis, and their role in creating new models to orient ourselves with. Full reading here: http://goalsys.com/books/documents/DESTRUCTION_AND_CREATION.pdf

  9. Prowling Feline says

    My old boss used to say (based on his long experience in ibanking and private equity) something similar to your first point – people over-estimate what they can achieve in the short term, and under-estimate what they can achieve in the long term; thus, we should budget our time accordingly.

  10. Things on the ten year horizon appear to fall off the end of the earth. A mist of overwhelming current life moments cloud the opposite way- as if we can accomplish dowsing from an iphone. Add water and we plan to float, and feed that tree you gave so little importance.