pointless recursion Posted by JP Stormcrow, 19 Oct 2007 06:46 am

Teaching Calculus to a Dog

Pathetic earthlings. … If you had known anything about the true nature of the universe, anything at all, you would’ve hidden from it in terror.

- Emperor Ming

I have carried the title** of this post around in my head for a few years as the label for some musings on “knowability” and the limitations on our ability to really get our heads around “reality”. And since blogging means never having to say you’re sorry for inflicting your wandering sophomoric ramblings on your readers - here it is. (But not to worry. Judges say: “That’s OK! they roll big joints have trouble focusing too!”)

My jumping off point is a simple one: A dog will never learn calculus. Nor will dogs collectively ever master calculus. I hope all can agree on that. (And I exclude here some imaginable cyber-augmented dog, or intelligent critters that dogs might potentially evolve into over the next 50 million years.) They just don’t have it - in fact they don’t even know they don’t have it - their “wetware” is just not capable.

So, let’s move on to Canis lupus familiaris’s favorite fellow social mammalian companions - humankind. On understanding calculus we absolutely pwn the mangy mutts. Yay us!!! But in the grander scheme of things how big is the gap really? How far can our relatively superior mental powers take us?

Here we are as a species having only relatively recently passed a threshold where we became capable of symbolic representation and processing, where we can form and describe reflective models of the world. The growth in our capacity for posing and answering questions about the nature of reality has exploded - and at some level I think it is our conceit that our general purpose processing capabilities are sufficient for us to frame and potentially answer and understand any well-posed question about the world.

But then again, what the fuck do we really know about it? What would make us think that nudging across the threshold of symbolic processing would get us to any truly satisfactory understanding of the world? So let’s just stipulate that humans are capable of some “early intermediate” level of understanding of the world around them. So what? (At some level this is the most fundamentally dissatisfying aspect of life for me personally - the fact that I will die in ignorance … very cheery here today, you can see … maybe there is some way we can all go out suddenly without worrying about it too much … some kind of Big Blast or something. I’ll study on it a bit.)

So what to make of this not very profound point. How do we get past the limits of our own processing power? (Never mind should we?) I see three interrelated mechanisms, all of which are in evidence to various degrees in the world today. (But what would I know? Woof! Woof! )

1) Establish networks connecting ourselves.

2) Create entities that are not bound by our own particular hardware limitations. (Computers)

3) Augment our own capabilities in situ.

Groups, tribes and societies serve for the first. The Scientific Method is basically a social mechanism for capturing and solidifying knowledge. To me the interesting question for networks (and for the time being let’s just stick to networks of “unaugmented” humans), is to what extent can a network “know” more than it’s individual components.

To some extent the answer is clearly “quite a bit” (social insects come to mind) - but for humans specifically, can there be say a “scientific understanding” of something that no single human being (we’re leaving out the machines for now) can articulate or get a full grasp on, but which can be “used” by the network as a whole?

I know at some level this just looks like the argument in Wisdom of Crowds writ large - but I am trying for a slightly different point. Robert Pirsig has a great passage in Lila, an otherwise undistinguished follow-up to Zen and the Art of Motorcycle Maintenance, where he is walking through Manhattan and describes New York City as “the Giant” - a massive uncontrolled entity that has “used” its inhabitants to construct itself very successfully.

Let’s add the “machines” in and you get today’s world - an assemblage of billions of people and this Internet thingie with these relatively dumb things hanging off of it (and there are computers on it as well…) Despite my musings in the previous paragraph, to me this is in most respects still “just” a network of humans with external augmentation right now - still just the information processing equivalent of gaining mechanical advantage with a lever. But it is evident to me that the machines are poised (maybe not in their current form - but relatively soon nonetheless) to “escape” and be increasingly on their own. (But they shouldn’t gloat, they’ll just be cogs in their own unfathomable network.)

Bottom line on this scenario - humans become increasingly irrelevant cogs in vast networks where the real action is. Is that satisfying? Well, probably better than pissing it all away for ourselves and many other species by just flaming out. <Insert words here to the effect that this is not meant to disrespect the inevitability of the GNF and the Party. I can’t quite seem to construct the argument that shows this, but I’m sure there is one. Woof! Woof!. >

This brings us to the third possibility (probability). Augmentation of our intellectual capabilities directly via as yet undiscovered mechanisms (but you can see the groundwork being laid). This one seems the most disquieting of them all, but if we figure out to do it, does anyone think we won’t? Well, nevermind, I just realized that the restraint that people have shown with regard to performance-enhancing drugs in sports would indicate that we probably won’t get our heads turned by this possibility. All I can say is, Fasten your seatbelts, it’s going to be a bumpy century.

I had a point in here somewhere - but suddenly I am run over by a truck  … I’ve been consumed by a GNF … it’s time for my walk. (Woof! Woof!)

**I really should use some more explicit system of modeling the world like Quantum Physics to make the point rather than an abstract concept like Calculus - but screw it, I’ve been mentally using “Calculus” all along and I’m not going to change now. (Joseph Heller says that Catch-22 was originally Catch-18, but they changed it when Leon Uris published Mila 18 a short time before the book was to come out - for some reason I thought that was a relevant anecdote when I wrote it.)

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Responses to “Teaching Calculus to a Dog”

  1. on 19 Oct 2007 at 9:17 am 1. Arnaud said …

    I am certainly not a scientist and I stand ready to be shot down in flame by whomever has a better understanding of the issues than I, but there seems to be an underlying assumption to your reasoning, JP.
    There is no guarantee that the world, as investigated by science, is infinitely complex. I am not saying here that we will one day know everything there is to know, just that the “level of complexity” could be finite and within the capacity of the human brain. Calculus is a bad example as mathematics is a human construct (not, as I understand it, a science) and susceptible of infinite complexification.

    As for the third possibility you describe, I cannot possibly be the only one here no to find it that “disquieting” but rather exciting. Well, maybe I am, I remember reading Out of the Silent Planet and rather perversely cheering for Professor Weston.
    “ …till our posterity – whatever strange form and yet unguessed mentality they have assumed – dwell in the universe wherever the universe is habitable.”

    As somebody else said, of matters not totally unconnected: “There is a grandeur in this view of life…”

  2. on 19 Oct 2007 at 9:32 am 2. JP Stormcrow said …

    just that the “level of complexity” could be finite and within the capacity of the human brain

    I agree that it might be, just think it is a bit of a petty conceit for us to assume it to be the case that it is - or that our “reason” and “logic” are broad enough to capture th eworld. Who knows? (this is where I am pretty much just way out there in the sophomoric BS land.)

    And you are right per my footnote that Calculus is not the best example - I’m just stuck on it.

    On the third “augmentation” idea - it is both worrisome and exciting - I just don’t know if the current state of our “moral calculus” is sufficient for any current moves in this direction to not go horribly, horribly wrong. But to most it is probably a more interesting and comforting possibility than just turning all of the heavy intellectual lifting over to the machines, while we take up the title of Intellectually Dominant ‘Life’ Form Emeritus and hope they pass on the good tidbits and remember to feed us.

  3. on 19 Oct 2007 at 9:50 am 3. JP Stormcrow said …

    I kind of left the “network” idea hanging I see.

    I have seen the phrase “having/has the bubble” used to describe the person who is integrating all of the information in an operational situation. (I think this phrase comes from the Navy - or maybe Air Traffic Control.) The concept is that there is one “mind” that is pulling otgether all of the situational information - and although they may lack detail, they are really the only one who “knows” what is really going on.

    Now, clearly no one “has the bubble” for New York City or the Internet, or any sigificant field of science. But my naive presumption is that before adding a piece of “kowledge” to science that the person doing so at least temporarily has the bubble for the relevant and specific parts that they are adding to. But even as I type this, I am thnking that I am wrong. For instance as I recall, Maxwell’s equations were in fact scattered through one of his works and their significance not really recognized by Maxwell at the time. That it was only later that they were grouped together and appreciated as a fundamental basis on which to build. (But then again he did come up with them, so at some level - even if not articulated - he was having the insight.

    And you can even dive into our own minds to see the principle at work. In this case ‘having the bubble” corresponds to what Dennet mocks as the Cartesian theater - the “real” you watching and guiding it all. Probably more accurate to view the mind itself as the output of a network of competing/cooperating processing units.

  4. on 19 Oct 2007 at 11:16 am 4. Seattle said …

    “At some level this is the most fundamentally dissatisfying aspect of life for me personally - the fact that I will die in ignorance …”

    Good Lord, man! What an impossible goal to get stuck on. I hope to die not knowing an awful lot when you consider all the possibilities- Besides, it’s much more exciting to contemplate all the possible discoveries in the future. Just think if you KNEW without doubt that you had reached the limits of knowledge. There’d be nothing left to do but rot on the branch.

  5. on 19 Oct 2007 at 11:26 am 5. christian h. said …

    Irrelevant but funny story: a former math professor here at UIC got an offer to move somewhere else (University of Washington or so). As is usual in such a case, he was asked what it would take to keep him here. Now this professor was always pissed off by what he considered to be the stupidity of students, as well as the ease (in his view) with which his colleagues in math ed could get (big) grants. This led him to claim that he could teach a chimp calculus more successfully than they could teach children.

    So, he asked for a chimp. Literally. The then-head of department (now a colleague of mine) had to go the Dean (it was Stanley Fish at the time) and tell him that this guy wanted a chimp to teach him calculus (one has to say, far more benign than what the biological sciences do to them).

    (Further proof that we mathematicians are completely normal people. Most of the time.)

  6. on 19 Oct 2007 at 11:30 am 6. JP Stormcrow said …

    Just think if you KNEW without doubt that you had reached the limits of knowledge. There’d be nothing left to do but rot on the branch.

    … ah but that is my ideal plan - learn “it all” then die immediatley. Others can rot and wither after me.

    You’re right it is an absurd notion. What I am really sayng is that I am frustrated that I will die with essentially no more real insight into anything than I have right now. Now an optimist might view that as a cause for celebration - but I’m stuck on “I didn’t want the damn glass in the first place.”

  7. on 19 Oct 2007 at 11:33 am 7. christian h. said …

    More seriously, a couple points.

    First, while it is certainly true that mathematics is a human construct, it’s not clear to me what “making it arbitrarily complicated” would even mean. If it is a human construct, it stands to reason that it can never be made more complicated than the human capacity to understand it. In addition, mathematics is guided by the natural sciences; we don’t just make shit up for the heck of it.

    Second, I’d be more terrified of dying all-knowing. Or rather, of living all-knowing. Not only would that be horrible given all there is to know, it would also be incredibly boring.

  8. on 19 Oct 2007 at 11:39 am 8. JP Stormcrow said …

    Irrelevant … story

    What? You dare comment on this tightly-crafted disciplined post with such extraneata? Have you know sense appropriateness?

    So… what was the result?

  9. on 19 Oct 2007 at 11:40 am 9. JP Stormcrow said …

    …it would also be incredibly boring.

    maybe

  10. on 19 Oct 2007 at 12:07 pm 10. black dog barking said …

    If Calculus isn’t working you might want to try “Chinese Algebra”. Richard Pryor used the term in the context of “My dick was harder than Chinese Algebra”.

    In fact, Chinese Algebra gives us a bit of insight into how the inter-networked We values knowledge. Googling chinese algebra shows an Urban Dictionary page rated first, complete with oblique crotch reference. Nearly every other item on the first page refers to math in the Orient, likely zero crotch references in the whole group (who’s actually gonna look?). And that is why they aren’t number one. QED.

    Googling “chinese algebra” richard pryor returns no evidence that Richard Pryor ever said such a thing about his dick. They are wrong. Does knowing this make me a bad person?

  11. on 19 Oct 2007 at 12:47 pm 11. Seattle said …

    Blink, blink. Can’t say that. Can’t say that either. Nope, that’s out. So I’d say, “No, just unusually well rounded…”

  12. on 19 Oct 2007 at 2:30 pm 12. Oaktown Girl said …

    There are many folks who believe that when enough people on the planet raise their consciousness out of the muck (need not be “total enlightenment” as such), the power of that shift alone will change everything as we know and understand it (in a good way).

    Whether that happens or not, I think a majority of people raising their consciousness out of the muck would be a good thing.

    [*Belches, scratches stomach, goes back to watching Brittney Spears updates on the E! entertainment channel*]

  13. on 19 Oct 2007 at 2:55 pm 13. A.Citizen said …

    Buy, borrow or steal The Oirgin of Wealth by Eric Beinhocker and you will find much to interest you.

    The question of ‘knowing everything…’ is currently believed to revolve around power functions. What are they?

    Google on folks!

  14. on 19 Oct 2007 at 3:21 pm 14. JP Stormcrow said …

    Buy, borrow or steal The Oirgin of Wealth by Eric Beinhocker and you will find much to interest you.

    Thanks for the tip - certainly looks interesting from the blurb I read on it.

    Accounting for the creation of wealth has long challenged humanity’s best minds. For business readers and academics, Beinhocker is a zealous and able guide to the emerging economic paradigm shift he calls the “Complexity Economics revolution.” A fellow of the economic think tank McKinsey Global Institute, he rejects traditional economic theory, based on a physics model of closed systems, in which change is an external disruptive shock. Instead, he outlines an open, adaptive system with interlocking networks that change organically, reflecting the interaction of technological innovation, social development and business practice. Wealth is created to the degree that this interaction decreases entropy in favor of “fit order” that meets human needs, desires and preferences. Beinhocker is sufficiently comfortable with this evolutionary model to advocate a comprehensive redesigning of institutions and society to facilitate it.

  15. on 19 Oct 2007 at 5:49 pm 15. James Killus said …

    I always filed these musings under “There are some things man is not meant to know, Dr. Frankenstein!” The first examples I had were “What is it like to live upstairs from yourself?” and “What was it like to ball Janis Joplin” (thereby dating the musings to the year after her death).

    Obviously I was fascinated with the notion of experience even back then, and just as obviously, the joints we rolled were very big.

    Concerning non-experiencial knowledge, I have in recent years come to suspect that the scientific enterprise may be reaching its limits in certain sorts of things. This has been prompted by reflections on the number of times I’ve seen the figurtive wheel reinvented and the uncomfortable feeling that there are some areas where one cannot really learn enough to make an impact within a single human lifetime.

    Perhaps we’ll eventually work out a different research unit than the graduate student and professor seeking tenure, and perhaps we’ll make smarter people somehow, but until then, well, I dunno.

  16. on 19 Oct 2007 at 7:30 pm 16. spyder said …

    There are some things man is not meant to know, Dr. Frankenstein!

    As my father put it to me when i begged the question for the umpteenth time: As long as you are human you will just never really know! And just for the discerning, how much Southern Comfort (gawd i liked that beverage) did it take to ball Janis?????

    There is always the platypus to consider; i’m not sure math would help solve that one though???

  17. on 19 Oct 2007 at 7:30 pm 17. spyder said …

    Somehow i scored a double hit on my way to preview and got both an incorrect post and an edited corrected one.

  18. on 19 Oct 2007 at 8:45 pm 18. Oaktown Girl said …

    spyder - we can delete one, just say which. One of the magic edit fairies will take care of it.

  19. on 20 Oct 2007 at 5:15 pm 19. JP Stormcrow said …

    OK, I’ve had a chance to sleep on it .. and everyone is right, I’m very happy to be a cog in the grand machine, head down doing my part, born in ignorance and buried in same. I like this plan!

    What, if some day or night a demon were to steal after you in your loneliest loneliness and say to you: “This life as you now live it and have lived it, you will have to live once more and innumerable times more; and there will be nothing new in it, but every pain and every joy and every thought and sigh and everything unutterably small or great in your life will have to return to you, all in the same succession and sequence — even this spider and this moonlight between the trees, and even this moment and I myself. The eternal hourglass of existence is turned upside down again and again — and you with it, speck of dust!” — Would you not throw yourself down and gnash your teeth and curse the demon who spoke thus?

    Quote via Chris Clarke and Cosma Shalizi.

  20. on 20 Oct 2007 at 5:16 pm 20. JP Stormcrow said …

    Oh … but in the meantime - Go Tribe!