
The Brain as Computer: Bad at Math, Good at Everything Else - ohaikbai
http://spectrum.ieee.org/computing/hardware/the-brain-as-computer-bad-at-math-good-at-everything-else
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ineedasername
Think we need to distinguish between math as "performing pre-defined
calculations rapidly", and math as "figuring out solutions to problems, often
novel, sometimes new, that have a mathematical underpining and an ability to
be represented in mathematical terms."

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.

~~~
Waterluvian
My dad always described this as mathematics vs. arithmetic.

Ultimately computers are just doing lots of arithmetic.

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hasenj
The brain is obviously perfectly capable of doing lots arithmetics very
quickly, otherwise it couldn't process vision and audio signals.

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pjc50
Is it? Is there any evidence that it's converting the signals to symbols and
performing arithemtic on the symbols? Or is the signal processing being
performed "directly", through the essentially analogue operation of the
neurons?

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.

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kazinator
An operational amplifier performs arithmetic.

~~~
pjc50
Not _symbolic_ arithmetic though, and the answer is not precise.

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")

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klik99
The brain is actually really good at math - the best example I've heard of
this (I think from the book 'Blink') is catching a flyball - in an instant
someone is able to calculate the trajectory, wind speed, spin and coordinate
with it's own body to run at the right speed to be in the right place when it
lands. Now of course that takes experience but it's not just pattern matching
since training allows people to adapt to new and unseen conditions. But
anytime you have a 'gut' feeling, it's usually because of some behind the
scenes 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.

~~~
kenbellows
I don't agree with that description of what the brain does when you catch a
ball, or with the principle it's proposing. I don't think the brain does any
kind of calculations to figure out how to catch the ball; I think it's
effectively muscle memory. If you've never caught anything before, your brain
will have no clue what to do. As you practice running to catch things, I think
a better description of your subconscious process is something like: "The ball
(or whatever) looks like it's growing bigger in my visual field at a certain
rate. A previous time when it grew bigger at a rate kind of like that, I
applied about _x_ force in the legs, and I didn't get there in time. Another
time when it was growing at about this rate, I put applied a larger amount of
force _y_ , and the ball landed behind me. This time I'll try to apply a
little more than _x_ force, but less than _y_ force, and see how that works."

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.
    

[1]
[https://books.google.com/books?id=fWQhj0HVCbUC&pg=PA37&lpg=P...](https://books.google.com/books?id=fWQhj0HVCbUC&pg=PA37&lpg=PA37&dq=john+searle+dog+catches+ball&source=bl&ots=7M1GnrUP5a&sig=7fNe54CBmwhR2hvnXb-t4f3HWpU&hl=en&sa=X&ved=0ahUKEwjQrJ-w1PLUAhXJHD4KHbhaAHwQ6AEILzAB#v=onepage&q=john%20searle%20if%20my%20dog%20can%20catch%20a%20ball&f=false)

~~~
klik99
Sure, it might not be trig, but in your description there is still calculation
(the ball is growing larger at x rate, so adjust my legs accordingly), just
not of the self-aware conscious variety. There are really two definitions of
'calculation' that are used interchangabley - one is a) the act of
deconstructing into symbols and picking apart, and the other is b) the
execution of algorithm.

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.

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fooker
The brain is incredibly good at math, just the APIs are not exposed.

~~~
vacri
To expand on that point, the brain is not good at simple products of large
numbers, but is fantastic at doing things like triangulation. Or calculating
how much muscle to contract to keep your balance going into a turn whilst
running. Or eyeballing quantities - we notice when we get it wrong, but the
vast majority of the time, we're pretty good at getting estimates correct
about the human-scale world around us.

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TheSpiceIsLife
Have you seen that fellow that calls himself a mathemagician, Arthur Benjamin?

I believe he would argue it's a matter of training.

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vacri
Well, yes, but that's not a very useful distinction. You train computers as
well by programming them. In meatspace, there was a famous experiment in the
'60s where kittens had their heads locked into position so that they only saw
vertical lines - their nascent neuroplastic brains then trained that way, and
as they matured, they simply couldn't see horizontal lines (eg: would walk
into horizontal bars).

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.

~~~
TheSpiceIsLife
In which case, computers, as in microprocessors, are extraordinarily bad at
math.

Without the appropriate programming they can't do anything.

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DonnyV
Maybe math is a less efficient way of describing the world? Maybe the brain
has a better system?

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verinus
Good point- specially when we have holes in our understanding math has its
problems where as humans can come up with a solution...

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okket
"Bad at Calculating, Good at Everything Else" <\- correct title IMHO

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).

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fooker
Btw, automated theorem proving is a thing and many non-trivial results have
come from that field (i.e. theorems humans couldn't prove before).

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okket
If this not only verification but generates genuine new proofs, then I might
be wrong and have to remove one 'long'. Even then, I am convinced, it will
still be a long time until computers can come up with such a complicated
proof, involving so many different fields of mathematics, like Fermat's Last
Theorem.

~~~
mannykannot
Furthermore, math is not just about proving things. Mathematicians invent the
consistent formalisms in which the process of proving takes place, and spot
isomorphisms between apparently different ones. They also have a knack for
choosing to follow paths that will be fruitful, rather than than lose
themselves in a maze of pointless symbol manipulation. AFAIK, no computer has
ever taken it upon itself to find a proof of some nontrivial issue in
mathematics, let alone do any of the less formal things in mathematics.

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manbearpigg
Natural language provides a huge amount of overhead for doing math. If
computers did math in terms of natural language it would be a lot slower for
them too.

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naedish
It'll be interesting to see what changes occur in the human brain as we
develop neural-computer interfaces. The human brain appears to be very good at
performing instantaneous approximate calculations (catching or dodging a
thrown ball). Interestingly, humans don't appear to be as good at memorising
sequences as monkeys (1). It'll be awesome if someday we can see the
difference between how the monkey and human brain behaves while carrying out
this task.

1\.
[https://www.youtube.com/watch?v=aAIGVT3N7B0](https://www.youtube.com/watch?v=aAIGVT3N7B0)

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partycoder
The brain is doing math all the time.

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](https://www.youtube.com/watch?v=Px_hvzYS3_Y)

~~~
goatlover
Does math exist independent of human (and perhaps alien) minds?

What makes a the physical devices we call computers computational, other than
the symbolic meaning we give their behavior?

~~~
partycoder
Since all definitions of mathematics are controversial when subject to
philosophical rigor, and the foundation of mathematics themselves are axioms
(which by definition cannot be proven), and sometimes these axiomatizations
are either incomplete and inconsistent with each other, I will just say it's
an open question.

What we do however know is that mathematical principles so far hold up well
and have been of vital importance to understand nature.

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kazinator
Oh, the brain wetware is good at arithmetic; just unfortunately not in a way
that is available to conscious thought.

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.

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yters
The human mind can grasp platonic/Aristotelian forms, which are at least
potentially infinite in ways of being instantiated. Computers can only deal
with finite things, such as arithmetic. That's the fundamental difference
between the two. Hence Gödel's second theorem that no axiomatic system can
know truth, whereas we can know his theorem is true.

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known
[https://en.wikipedia.org/wiki/Economic_mobility](https://en.wikipedia.org/wiki/Economic_mobility)
!=
[https://en.wikipedia.org/wiki/Social_mobility](https://en.wikipedia.org/wiki/Social_mobility)

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bluetwo
There are ways to solve math problems that don't involve math.

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ankurdhama
Here is a question for all the "brain as computer" proponents. Given the
molecular level activity of a bunch of neurons over time can you figure out
what "maths" happened there? If not, then please stop this "brain as computer"
advertisement and come back when you have the answer to the above question.

~~~
ankurdhama
People who downvote without any comments know how wrong they are and how
easily their arguments can be teared apart.

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djmips
By some pedestrian definition of math.

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adamnemecek
The phrase "bad at math" should be banned.

~~~
HiroshiSan
The phrase "bad at X should be banned " should be banned.

