Unthinkable Thoughts

‘‘There are wavelengths that people cannot see, there are sounds that people cannot hear, and maybe computers have thoughts that people cannot think.’’

Richard Wesley Hamming

Something that is simultaneously trivial and fascinating (to me) is that the deeds of some other person my age will be very different, and sometimes far greater, than my own. Trivial because it’s so obviously true, for all of us. But fascinating because this person has had the same period of time and an almost identical human body to work with, so their accomplishments must have stemmed from differences in their environment and/or thoughts they had that I did not. No doubt the former plays a role, but if we confine our analysis to a college classmate I think we can establish a role for the latter as well: Sitting in the same auditoriums, coming from a similar background, this person somehow achieves a different understanding of the subject matter (and the world).

We apply the term “genius” to those who make important realizations that escaped everyone else, and try hard to explain what made these people special. Why didn’t the Theory of Relativity occur to everyone? While such explanations often emphasize a special combination of talent and opportunity, it also appears that simple birth defects and accidents can produce genius-level ability in the otherwise unremarkable. Based on this, one might propose that our brains normally have barriers which block many thoughts from appearing. But what is the system that determines which thoughts we have? And as a natural extension of this, how do we set ourselves up to have the widest/wisest range of thoughts?

Your thought-subset

As so often happens, Paul Graham has an interesting comment on this: he argues that we’re unable to think clearly about things that are part of our identity (e.g. religion, ancestry, preference for Apple products), and so to expand the range of topics you can productively think about you need to minimize your identity. Thought provoking (*cough*), and a seemingly perfect philosophy if you’re a Buddhist inventor. But it does seem more like a surgeon than a full-on savior: even if true, it only tells us how to remove certain specific blocks from our thinking.

Another proposition comes from an instruction that I wish someone had given my undergraduate self. We students were frustrated with having to cram huge curricula in some courses, and often vented about the folly of closed book exams. The important thing was being able to find information on demand, not memorizing tons of facts you might never need, right? Well, kind of… Now that I’ve spent some time thinking for a living, it’s clear that most of our progress comes from connecting dots. That is, coming up with solutions based on multiple pieces of information. Sure, you could easily look up those same pieces of information, but if they’re not already in your head when you encounter the problem you miss out on the solution. Based on this, a big limitation to what we’re able to think would simply be the quality and quantity of dots already in our heads; the more you already know about, the wider range of thoughts you can have.

To me this seems quite in line with empirical evidence, although it’s also obvious that other factors play a role. For instance, there’s the person who knows a lot of facts but somehow can’t venture into uncertain territory. To quote Hamming again:

If you read all the time what other people have done you will think the way they thought. If you want to think new thoughts that are different, then do what a lot of creative people do − get the problem reasonably clear and then refuse to look at any answers until you’ve thought the problem through carefully how you would do it, how you could slightly change the problem to be the correct one.


So your ability to think clearly plays into it, as does the amount of knowledge you have to draw on. It seems to me that there’s also a huge amount filtering that occurs before thoughts even enter your consciousness. That is, your brain actually processes a multitude of thoughts for every one that you’re aware of, but most of them are discarded almost immediately. Whatever governs this filtering process must have a profound effect on at least our subjective experience on thinking. I don’t know enough neuroscience to say anything really rigorous on this subject, but intuitively it seems possible that the filter is simply synaptic patterns formed by your past experiences. On a side note, maybe that’s where déjà vus come from: subconscious processing leaking slightly into the conscious domain, so that when the thought is presented to consciousness proper it seems to have (indeed has) happened before.

Such a filtering mechanism would certainly constitute a type of biological limit to what thoughts you are able to think. But one could easily imagine more profound limits based on the physiological wiring of our brains. It would naturally follow that different wiring would allow different thoughts. Returning to the original quote from Hamming, I’m sure most would agree that our deterministically programmed computers can’t think human thoughts. But perhaps they (or future versions of them) can think a different type of thoughts, which we in turn aren’t able to.

In other words, the Venn diagram might look like this:

Your thought-subset,  advanced

You might find it difficult to imagine the types of thoughts a computer would have; I certainly do. In order to come up with a decent answer we would need to examine what constitutes a thought, which I’ll leave for another post. But lest we let the barriers in our brains censor the very idea of inhuman thoughts, I’ll end with this reminder from Schopenhauer:

“Every man takes the limits of his own field of vision for the limits of the world.”

A paradigm of possibilities

When I was a teenager I adopted the basic stance that I wanted to try everything at least once. I quickly realized that this wasn’t really feasible, since some things would probably end up with me dead and thus unable to try more things. But it worked fairly well as a rule of thumb.

Don't die

Then I matured a bit, made a few realizations. That time isn’t a limitless resource. That certain things require opportunity or skills that can’t be instantly conjured; that you’ll never step into the same river twice. While none of this argues against trying new things, it does shift your perspective a bit: If doing one thing can prevent you from doing another, if you can’t try literally everything, then you need to start making choices.

But which choices? Can we recreate the essence of ‘try everything’ within the confines of practical reality? If we only get a certain number of picks from the buffet of experiences, it would stand to reason that we should maximize the novelty of each choice. But does this extend to trying something new over repeating a great experience of the past? For example, do we order our favorite meal at a restaurant, or one that we’ve never tried before? The latter choice will in all likelihood be less enjoyable, taste-wise, but if we ever want to try something better than what we already know we’ll have to take that risk1.

An interesting choice

Such a choice might be controversial, but not very complicated. It gets trickier when we recognize that our pool of options does not remain constant over time. In other words, some of your actions will expand your opportunities (making money, for example) while others limit you (becoming addicted to heroin, say). With this in mind, I would propose the following as a basic stance for experiencing life:

A paradigm of possibilities    Follow whichever course of action seems likely to allow the greatest number of novel experiences henceforth2.

To illustrate this, let’s imagine that a (superior) foreign power invades your country. Do you resist, or surrender? Dying is pretty much the ultimate loss of options, so if the only way to avoid this is surrender then that’s what our paradigm would propose. On the other hand, joining a totalitarian regime (or the Borg) might represent such a loss of options that guerrilla resistance would offer a life richer in opportunities (albeit endangered). This deliberation may seem Machiavellian and/or cowardly compared to say “make a stand for liberty”, but I wonder if it’s really any different than the underlying motivation of this nobler sounding rationale.

Before anybody brings up Barry Schwartz, let me emphasize that these possibilities are not the same thing as choices. They’re not options that we necessarily have to choose between, but rather potentialities that may unfold during your lifetime. Let’s take a concrete example: if I choose to set aside money in a retirement fund, I might end up spending my sixties traveling or writing, or working regardless. More possibilities than if I had no savings, but my default state would be to continue whatever I was doing as long as I was financially above water. Thus the added possibilities would rather manifest as the absence of forced choices than as a choice of actions suddenly forced upon me.

One final point I’d like to make is that while at first glance it would seem that never making choices would allow the most possibilities, this is not the case in practice. Sure, if you never get around to choosing a major you have every field open to you. But on the other hand you won’t have access to jobs that require specialized skills, nor to graduate studies or indeed to any of the intellectual experiences that require understanding of a specific subject. Similarly, if you never marry you may have “access” to every member of the opposite sex, but perhaps not to being a parent (not to mention that your pool of potential partners will shrink over time regardless). Your actions unlock new possibilities, and while you’re postponing a choice others pass you by. Of all the thoughts I’ve shared here, this might also be the most useful regardless of whether you buy into the unconditional commitment to curiosity or not: Remember that life is not a fixed pie of opportunities. The options you have today might not be available tomorrow, and what is available tomorrow depends in large part on your actions today.

[1] Of course not everyone would prefer this ideology, just as not everyone would prefer entrepreneurship over a stable job. But if we ascribe to the idea of ‘try everything’ then the choice seems fairly obvious.

[2] Correspondingly, Paul Graham talks about staying upwind of promising opportunities.

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