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I’m fairly certain there aren’t any matrix multiplications happening in my brain right now

by klysm 3y ago

mitthrowaway2 3y ago
If it can be said that a lens can perform a Fourier transform, then it can certainly also be said that the brain can perform matrix multiplications. Both might not do the computation using sequential IEEE 754 floating point operations, but they perform the computation nonetheless.
- klysm 3y ago
  A lens and the Fourier transform are directly related because the underlying physical process is being modeled. Matrix multiplication and the way our brain works are not close in the same way. The result is similar enough, but there’s no reason (that I know of) to believe that the underlying mechanism in our brains is matrix multiplication
  - mitthrowaway2 3y ago
    A lens performs a Fourier transform just because any process that groups light waves by spatial frequency is necessarily performing a Fourier transform. That's because a Fourier transform is defined by how it relates input and output, not by whether it happens via a piece of glass, or a pen and paper, or a FFT software routine. So this might be just a philosophical matter, but as far as I am concerned, there is no distinction between "performing a matrix multiplication" and "performing the operation that a matrix multiplication performs", such as projection, mapping, rotation, scaling. If you can mentally picture a plane being stretched, skewed, or spun, along with all the points on that plane, then you are mentally executing (in that case) 2x2 matrix operations. But we do this so effortlessly that we don't notice it. As a kid learning to read, you might start by recognizing individual letters and sounding out the words. But at some point in fluency, you hardly even notice the letters anymore -- recognizing them disappears into an effortless task that is executed so quickly you might not even notice it's happening. That doesn't mean that your nervous system is no longer performing some kind of best-fit-comparison between an optical image on your retina and a set of learned characters; it certainly must be, but it's just happening (basically) with hardware acceleration. You might think you aren't doing matrix multiplication because you aren't consciously iterating through [A1B1 + A2B1 + ...] like a child sounding out vowels, but the operation is necessarily happening somewhere along the line; it's just happening at the hardware level below your conscious perception. I can do digital matrix multiplication with Numpy, but I can also make a circuit that does analog matrix multiplication using op-amps, where the addition and multiplication happens in voltages; I can make a mechanical device that does matrix multiplication using gears and levers, and I can certainly coax neurons to multiply matrices. It's hard to imagine a better structure to implement a matrix multiplication than the dendrites of a neuron.

I’m fairly certain there aren’t any matrix multiplications happening in my brain right now

by klysm 3y ago

I’m fairly certain there aren’t any matrix multiplications happening in my brain right now

If it can be said that a lens can perform a Fourier transform, then it can certainly also be said that the brain can perform matrix multiplications. Both might not do the computation using sequential IEEE 754 floating point operations, but they perform the computation nonetheless.

klysm 3y ago
A lens and the Fourier transform are directly related because the underlying physical process is being modeled. Matrix multiplication and the way our brain works are not close in the same way. The result is similar enough, but there’s no reason (that I know of) to believe that the underlying mechanism in our brains is matrix multiplication
- mitthrowaway2 3y ago
  A lens performs a Fourier transform just because any process that groups light waves by spatial frequency is necessarily performing a Fourier transform. That's because a Fourier transform is defined by how it relates input and output, not by whether it happens via a piece of glass, or a pen and paper, or a FFT software routine. So this might be just a philosophical matter, but as far as I am concerned, there is no distinction between "performing a matrix multiplication" and "performing the operation that a matrix multiplication performs", such as projection, mapping, rotation, scaling. If you can mentally picture a plane being stretched, skewed, or spun, along with all the points on that plane, then you are mentally executing (in that case) 2x2 matrix operations. But we do this so effortlessly that we don't notice it. As a kid learning to read, you might start by recognizing individual letters and sounding out the words. But at some point in fluency, you hardly even notice the letters anymore -- recognizing them disappears into an effortless task that is executed so quickly you might not even notice it's happening. That doesn't mean that your nervous system is no longer performing some kind of best-fit-comparison between an optical image on your retina and a set of learned characters; it certainly must be, but it's just happening (basically) with hardware acceleration. You might think you aren't doing matrix multiplication because you aren't consciously iterating through [A1B1 + A2B1 + ...] like a child sounding out vowels, but the operation is necessarily happening somewhere along the line; it's just happening at the hardware level below your conscious perception. I can do digital matrix multiplication with Numpy, but I can also make a circuit that does analog matrix multiplication using op-amps, where the addition and multiplication happens in voltages; I can make a mechanical device that does matrix multiplication using gears and levers, and I can certainly coax neurons to multiply matrices. It's hard to imagine a better structure to implement a matrix multiplication than the dendrites of a neuron.