The Brain as Computer: Bad at Math, Good at Everything Else
spectrum.ieee.org
spectrum.ieee.org
In short, computers are good at rapidly performing the calculations of a solved problem, or implementation of the algorithm. Humans are good at coming up with the algorithm. A good, general purpose algorithm generator is probably ai-complete, although i could see "evolution" as a plausible answer to such an algorithm generator too, though maybe only in its capacity to generate beter generators. Or maybe I'm talking out my excretorial orifice, I'm often not sure.
Ultimately computers are just doing lots of arithmetic.
I think ultimately it means that "doing arithmetic / doing math" are defined by the observer rather than the doer. True for any abstraction - the brain does exactly what it does, then to ask if its doing "abstracted task X" is not really meaningful from the perspective of brain, the abstraction in the first place is a mental construct we create.
Otherwise you're asserting "doing arithmetic" as a property of any analogue system, and would say that a falling ball needs to understand calculus in order to make an arc.
The brain is doing purposeful data processing. Yes it's just signals doing their thing following the laws of physics but that's also what computers do.
Arithmetics in a CPU are just electrical signals passing through wires. If you were to look at these signals without any awareness of why they are flowing this way here and there, you wouldn't be able to tell that these signals are an encoding of some arithmetic operations.
If processing audio and visual signals does not involve doing arithmetics, then what does it involve?
If people are going to argue that inanimate objects perform arithmetic, they will need to define arithmetic. Digital or analog calculators do it symbolically, subject to interpretation of the symbols by a human.
If a human is using a calculator or an abacus or blackboard to perform arithmetic, would we also say that the abacus or blackboard performs arithmetic? (Great, now we have to define "performs")
The way I see it, an operational amplifier, or a person catching a ball (to take an example from another post here) is performing a task that can be analyzed mathematically and modeled arithmetically, which is not the same as doing the analysis or setting up the model and performing the calculations.
Translating maths into a mess of symbols and deconstructing it consciously is of course a laborious process - but AFAIK no computer is good at that either.
My own personal metaphor is the conscious mind as programmer and the unconscious mind as computer. If I correctly program my unconscious mind I can spontaneously realize the right answer far faster than I can understand why.
The result is the similar if one was to calculate such trajectories, but I am not sure what happens in the mind can be called calculation. How can it be properly tested that brain indeed calculates trajectories when catching a ball? Would practicing catching ball improve their relevant mathematical abilities demonstrable on paper?
This is a substantial oversimplification of course (there are many more factors involved than how fast the ball is growing in the visual field), but I think the point is clear enough. I doubt there's any trigonometry happening in the brain's circuitry; it seems much more plausible to me that the brain is really good at remembering how it felt in previous circumstances, recognizing how those remembered circumstances relate to the current one, and trying to adjust.
As I understand it, this is actually a significant debate in cognitive science, philosophy of mind, and related fields. One prominent proponent of a view like the one I've expressed here, that the brain doesn't require or use heavy math to do things like catch flying objects but rather acquires the ability over time through experience, is John Searle. He is known for using the example of his dog's ability to catch a ball that's bounced off a wall when discussing and arguing against theories of mind that propose that all unconscious processes must be following algorithms or rules (like running through computations to figure out how to catch a ball). Here's a quote of his from the BBC program Horizons (quote found in "New Technologies in Language Learning and Teaching", issue 532, on page 37 [1]):
If my dog can catch a ball that's bounced off the wall, that may be
just a skill he's acquired. The alternative view (the pro-AI view)
would say: "Look, if the dog can catch the ball it can only be
because he knows the rule: go to the point where the angle of
incidence equals equals the angle of reflection in a plane where the
flatness of the trajectory is a function of the impact velocity
divided by the coefficient of friction" - or something like that.
Now, it seems to me unreasonable to think that my dog really *knows*
that. It seems to me more reasonable to suppose he just learns how
to look for where the ball is going and jumps *there*. And a lot of
our behavior is like that as well. We've acquired a lot of skills,
but we don't have to suppose that, in order to acquire these skills,
the skills have got to be based on our mastery of some complex
intellectual structure. For an awful lot of things, we just *do* it.
My point is that 'feeling' or 'muscle memory' is the execution of (super hacky, ad hoc and efficient) algorithm, the big difference between computer calculation and brain calculation being that the brain is far more plastic than the computer. Presumably in an insects mind the 'muscle memory' is hardcoded (deliberately reductionist here), whereas we have a conscious mind that can train and 'program' our unconscious mind.
In your quote, 'we just do it' is ignoring the great complexity of the human mind that can perform complex interconnected tasks with seemingly no effort at all, if it has been trained properly. Replace training with programming, and the parallels are there - graphics programming for instance is a huge collection of hacks and rules of thumb to get something that looks like perspective and light. Like our brain, it's results orientated so it truly doesn't matter if it's not 'correct'.
Now of course the brain and computers are different, but it's incorrect to say the brain doesn't calculate - it just is a lot more unwieldy to program than a computer.
Just look at machines that don't do precalculated movements (ASIMO, but even many of its patterns are prepared; Boston Dynamics robots, etc) versus those that do (industrial assembly line robots) and it gap is insanely wide. And even then, the dynamic bots are doing maybe one or two things at a time (walk, stop, pickup, walk, drop) nothing complex or integrated.
Otherwise you're asserting "doing arithmetic" as a property of any analogue system, and would say that a falling ball needs to understand calculus in order to make an arc. Downthread someone is saying that crystal formation is "doing arithmetic". While there may be a philosophical sense in saying that all actions of the universe are in some sense arithmetical as they obey physical laws, this is not a useful way to talk.
(Repost of my comment above)
You almost described a transistor. :)
The physical world, at our scale in inherently analogue.
(Might be digital at a quantum level, but we don't know that yet.)
Inside neuronal systems there doesn't seem to be a direct symbolic representation - and if there is, the neuronal patterns of somebody doing calculus on paper versus e.g. catching a ball are entirely different.
It is not very meaningful from an information theoretic pov to debate whether the results come from the multiplication algorithms computers follow or via some trained analog network; the result is the same.
I believe he would argue it's a matter of training.
In the Nature vs Nurture debate, the purists on either side tend to use tortured, hair-splitting definitions to make their arguments, and it's usually those somewhere in the middle that sound the sanest.
Without the appropriate programming they can't do anything.
I agree (though probably not in the sense you intended) - in fact, the human brain is the only thing we know of in the universe that can do math.
I do not hold the apparently widespread view that anything performing an action that can be modeled mathematically is doing mathematics, but it is clear by now the two sides on this issue are not going to reach an agreement.
At least in so far as living macroscopic beings are concerned, they're all doing computation of some sort by processing environmental information and using the results to produce behavior. They're about as good at math as any other computer programmed to reproduce those algorithms.
So long as "processing" information isn't the same as actually producing that behavior, as in the case of crystal growth, they're doing something besides what they're doing.
Though I'd prefer to think that crystals are actually doing math too, but they're so good they don't even need to think about it.
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>Therefore the sage goes about doing nothing, teaching no-talking.
>The ten thousand things rise and fall without cease,
>Creating, yet not possessing.
>Working, yet not taking credit.
>Work is done, then forgotten.
>Therefore it lasts forever.
Neither is an issue that some way of thinking might raise more questions than it answers. Actually, if any of those questions is both interesting and solvable, that is a virtue.
In sum, I was just trying to see through what angle OP was framing their point.
[1] You don't really need to understand _how_ you're moving your arm. You just do it -- it's on autopilot.
Highly recommended if you're interested in philosophical discussions about this sort of stuff. I'm finding it highly entertaining and deliciously provocative.
You can also claim that Google is a giant lookup table. They should stop hiring computer scientists and start repurposing brains!
Saying the brain literally computes is making a philosophical claim as to what exists, as opposed to a useful metaphor.
-- Mother Nature
It will be a long, long time until computers spit out something like the prove of Fermat's Last Theorem (which requires being good at math and not calculating).
Just making your eyes converge at a focal point so you can read this involves math, and that's probably some of the most trivial stuff. The inverse kinematics involved in moving your limbs also do involve plenty of math, try to do it in a robot arm and see what I am talking about.
The problem is that our way of doing arithmetic has a lot of overhead. The algorithm we learn in school is not that good in terms of efficiency. However imagining an abacus (not a 10 bead one) and exploiting muscle memory seems to be probably faster: https://www.youtube.com/watch?v=Px_hvzYS3_Y
What makes a the physical devices we call computers computational, other than the symbolic meaning we give their behavior?
What we do however know is that mathematical principles so far hold up well and have been of vital importance to understand nature.
Just like there are computer languages in which there is little or no arithmetic support, even though the machine does nothing but arithmetic when evoking their meaning.
Just like we can apply silly abstraction inversions to bring about arithmetic in a system that doesn't expose it (e.g. Church numerals in a lambda calculus), the brain implements conscious arithmetic in a very inefficient way.