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>the new proof is so simple that one researcher summed it up in a single tweet. Didn't look that simple to me! Reminds me of Andrew Ng showing his students the simple one liner to solve the cocktail party problem in Octave. There's a lot represented in that one line of code!
>the new proof is so simple that one researcher summed it up in a single tweet. Didn't look that simple to me! Reminds me of Andrew Ng showing his students the simple one liner to solve the cocktail party problem in Octave. There's a lot represented in that one line of code!
Where is the tweet?
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I read that, but I believe that's describing the problem. Anyone care to explain the answer in a similar simple way? Actually one thing weird wiht that explanation is they call sensitive bits the ones that don't change the output? You'd think it would be the red ones
That is the solution! See? It's so simple it seems like a formulation of the problem itself! The solution is to think of the input ('001') in terms of an n-dimensional cube, where n is the length of the input. So for example, a binary logic with 5 bits ('01010') would require a 5-dimensional cube. From there, you check whether moving from one input ('00001') to an adjacent input ('00011') causes a flip in the output.…
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That is the solution! See? It's so simple it seems like a formulation of the problem itself! The solution is to think of the input ('001') in terms of an n-dimensional cube, where n is the length of the input. So for example, a binary logic with 5 bits ('01010') would require a 5-dimensional cube. From there, you check whether moving from one input ('00001') to an adjacent input ('00011') causes a flip in the output.…
Interesting... so what does a "5 dimensional" cube look like? I am having difficulty visualizing that
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That is the solution! See? It's so simple it seems like a formulation of the problem itself! The solution is to think of the input ('001') in terms of an n-dimensional cube, where n is the length of the input. So for example, a binary logic with 5 bits ('01010') would require a 5-dimensional cube. From there, you check whether moving from one input ('00001') to an adjacent input ('00011') causes a flip in the output.…
Interesting... so what does a "5 dimensional" cube look like? I am having difficulty visualizing that
This[0] article might help though.
Surprisingly good for a Quanta Magazine article.
It's an important and interesting but unusually simple mathematical topic that can be explained quite well without dumbing it down, leading to a "surprisingly good" article compared to scientific divulgation in general.
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Interesting... so what does a "5 dimensional" cube look like? I am having difficulty visualizing that
An easier way to think of it is just as a matrix where each vertex is connected to n other vertices. The reason an n-cube is used specifically is because the bits correspond to spatial coordinates, which obviously require a uniform structure (like a cube if we're talking 3D) in order to make sense. This[0] article might help though. [0] https://en.wikipedia.org/wiki/5-cube
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From the article: > Other measures involve looking for the simplest way to write the Boolean function as a mathematical expression, or calculating how many answers the banker would have to show a boss to prove they had made the right loan decision. There’s even a quantum physics version of query complexity in which the banker can ask a “superposition” of several questions at the same time. Figuring out how this measu…
I'm not seeing the connection between this research and fixed-point arithmetic.
A good primer on the history of CS is probably Code, The Hidden Language of Computer Hardware and Software, by Charles Pretzold. I've put together some notes on it here: http://alvaroduran.com/code.
Any feedback is much appreciated!