I would bet on Feynman any day of the week. Numerical methods came up in 'Hidden Figures' and her solution was to use Euler to move from a elliptical orbit to a parabolic descent.
Feynman vs. Computer
21–26 of 26 posts
Re: Feynman vs. Computer
#22As a hobbyist, I'm playing with analog computer circuits right now. If you can match your curve with a similar voltage profile, a simple analog integrator (an op-amp with a capacitor connected in feedback) will also give you the area under the curve (also as a voltage of course). Analog circuits (and op-amps just generally) are surprising cool. I know, kind of off on a tangent here but I have integration on the brain…
Speaking of Analog computation:
A single artificial neuron could be implemented as:
Weighted Sum
Using a summing amplifier:
net = Σ_i (Rf/Ri * xi)
Where resistor ratios set the synaptic weights.
Activation Function
Common op-amp activation circuits:
Saturating function: via op-amp with clipping diodes → approximated sigmoid
Hard limiter: comparator behavior for step activation
Tanh-like response: differential pair circuits
Learning
Early analog systems often lacked on-device learning; weights were manually set with potentiometers or stored using:
Memristive elements (recent)
Floating-gate MOSFETs
Programmable resistor networks
Re: Feynman vs. Computer
#23> I hear that in electronics and quantum dynamics, there are sometimes integrals whose value is not a number, but a function, and knowing that function is important in order to know how the thing it’s modeling behaves in interactions with other things. I'd be interested in this. So finding classical closed form solutions is the actual thing desired there?
I haven’t read tfa, so apologies if I’m missing context. But convolution is one example of an integral that outputs a function. Convolution is fundamental for control theory.
Re: Feynman vs. Computer
#24As a hobbyist, I'm playing with analog computer circuits right now. If you can match your curve with a similar voltage profile, a simple analog integrator (an op-amp with a capacitor connected in feedback) will also give you the area under the curve (also as a voltage of course). Analog circuits (and op-amps just generally) are surprising cool. I know, kind of off on a tangent here but I have integration on the brain…
One of my favorite circuits from Korn & Korn [0] is an implementation of an arbitrary function of a single variable. Take an oscilloscope-style display tube. Put your input on the X axis as a deflection voltage. Close a feedback loop on the Y axis with a photodiode, and use the Y axis deflection voltage as your output. Cut your function of one variable out of cardboard and tape to the front of the tube. [0] https://w…
N-SPHERES
N-SPHERES ist the most complex Oscilloscope Music work by Jerobeam Fenderson & Hansi3D and took six years to make.
Since it is almost entirely created with parametric functions, it is possible to store only these functions in an executable program and let the program create the audio and video output on the fly. The storage space required for such a program is just a fraction of an audio or video file, so that it's possible to store the executables for the entire audiovisual EP all on one 3.5" 1.44MB floppy disk.The first 500 orders will receive the initial numbered edition with pen-plotted artwork
Re: Feynman vs. Computer
#25As a hobbyist, I'm playing with analog computer circuits right now. If you can match your curve with a similar voltage profile, a simple analog integrator (an op-amp with a capacitor connected in feedback) will also give you the area under the curve (also as a voltage of course). Analog circuits (and op-amps just generally) are surprising cool. I know, kind of off on a tangent here but I have integration on the brain…
On op-amps I've got a personal theory that the cochlea amplifier in ear is basically an op amp providing negative feedback to prevent excessive amplitudes rather than the positive feedback mentioned in Wikipedia https://en.wikipedia.org/wiki/Cochlear_amplifier
Re: Feynman vs. Computer
#26What is the advantage of this Monte Carlo approach over a typical numerical integration method (like Runge-Kutta)?
I was wondering the same thing, but near the end, the article discusses using statistical techniques to determine the standard error. In other words, you can easily get an idea of the accuracy of the result, which is harder with typical numerical integration techniques.
With many quadrature rules (e.g. trapezoidal rule, Simpson's rule) you have a very cheap error estimator obtained by comparing the results over n and 2n subdivision points.