bg2b.bsky.social
Wanderer in the cosmic outback
17 posts
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Someone told me the ending was a bit subtle. I thought I remembered it and had no idea what they meant. But when I went back and read the *whole* book, I understood.
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Right up there with the alien face hugger
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But if I knew a spatial slice at x0 for all times with the same amount of info (number of rhs), I think I could solve for all other x in an analogous manner. That's probably clear as mud, but that's my current intuition.
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In that form, the distinction seems irrelevant. It appears you'd need exactly the same amount of info no matter what. So while we do perceive time as special, I suspect it doesn't carry more info. We think about time slices because we usually specify "now" and want to know what will happen. 3/
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But if I expand the linear system to include trivial equations for the boundary conditions, I could instead write the problem as finding a unique u such that Au = 0. The u has everything related to both boundary conditions and "outputs". 2/
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I agree that causality makes time special, but thinking more I suspect time slices don't carry more info. An EM simulator makes internally a finite dimensional system of linear equations. To solve, the boundary conditions have to give as many right hand sides as there are equations. 1/
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But is it the case that a time slice determines things but a space slice doesn't? E.g. if I took Maxwell's equations with sufficient boundary conditions for uniqueness, would I need more boundary conditions when thinking about a space slice than a time slice? Does time somehow carry more info?
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Take a 1D vibrating string. Make a 2D plot of displacement u as a function of (x, t). The interior satisfies the equation
\frac{\partial^2 u}{\partial t^2} = c^2 \frac{\partial^2 u}{\partial x^2}. Where's the distinguished nature of time? Is 3 (or 4) D somehow different? Asking seriously, IDK.
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apps.apple.com/us/app/rock-...
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I'm not as surprised by A Tale of Two Cities as I am by The Little Prince. I love that book but wouldn't have guessed it had those sorts of numbers.
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Seems like I'm consistently using my left eye with my right hand, but with my left hand I don't find either eye standing out. 🤷
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The Polgar sisters come to mind as an interesting case. en.m.wikipedia.org/wiki/L%C3%A1....
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TIL
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Was listening to Bat Out of Hell earlier
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If you're ever in central NJ with some time to kill, check out Northlandz. It's seen better days (the thing is pretty much uncleanable), but is still amazing.