Sexual reproduction is context-clearing and starting over from ROM.
Sure, you could be cloned, but that wouldn't be you. The process of accumulating memories is also the process of aging with death being an inevitability.
Software is sort of like this too, hence rewrites.
That's not quite clear philosophically. I like the thought experiment of them migrating each of your neurons one at a time from the biological into a computerized emulation (each emulated neuron having a physical mechanism to send proper electrical/chemical signals to those that are still biological, while doing software message passing with the digital ones) - do you at any point stop being you? Once the migration is complete and you're being fully emulated in silicon, is it still you? If they then restart the computer, is it still you after it's resumed? If they duplicate the code/weights onto two computers, are both you? And if they then reassemble your biological body with the neural connectivity based on that in the emulation - is it still you? And what if they clone the two digital "yous" into two separate bodies?
I personally don't have a clear answer to any of these, not more than I would in the plain Ship of Theseus thought experiment.
Interesting, and I used to think that math and sciences were invented by humans to model the world in a manner to avoid errors due to chains of fuzzy thinking. Also, formal languages allowed large buildings to be constructued on strong foundations.
From your anecdote it appears that the calculations in the paper were numerical ? but I suppose a similar argument applies to symbolic calculations.
https://inspirehep.net/files/20b84db59eace6a7f90fc38516f530e...
using integration over phase space instead of position or momentum space. Most people think you need an orthogonal basis set to do quantum mechanical calculation but it turns that "resolution of unity is all you need", that is, if you integrate |x><x| over all x you get 1. If you believe resolution of unity applies in quantum gravity, then Hawking was wrong about black hole information. In my case we were hoping we could apply the trace formula and make similar derivations to systems with unusual coordinates, such as spin systems.
There are quite a few calculations in physics that involve perturbation theory, for instance, people used to try to calculate the motion of the moon by expanding out thousands of terms that look like (112345/552) sin(32 θ-75 ϕ) and still not getting terribly good results. It turns out classic perturbation theory is pathological around popular cases such as the harmonic oscillator (frequency doesn't vary with amplitude) and celestial mechanics (the frequency to go around the sun, to get closer or further from sun, or to go above or below the plane of the plane of the ecliptic are all the same.) In quantum mechanic these are not pathological, notably perturbation theory works great for an electron going around an atom which is basically the same problem as the Earth going around the Sun.
I have a lot of skepticism about things like
https://en.wikipedia.org/wiki/Anomalous_magnetic_dipole_mome...
in high energy physics because frequently they're comparing a difficult experiment to an expansion of thousands of Feynman diagrams and between computational errors and the fact that perturbation theory often doesn't converge very well I don't get excited when they don't agree.
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Note that I used numerical calculations for "unit and integration testing", so if I derived an identity I could test that the identity was true for different inputs. As for formal systems, they only go so far. See
https://en.wikipedia.org/wiki/Principia_Mathematica#Consiste...
It affects people too. Something I learned halfway through a theoretical physics PhD in the 1990s was that a 50-page paper with a complex calculation almost certainly had a serious mistake in it that you'd find if you went over it line-by-line.
I thought I could counter that by building a set of unit tests and integration tests around the calculation and on one level that worked, but in the end my calculation never got published outside my thesis because our formulation of the problem turned a topological circle into a helix and we had no idea how to compute the associated topological factor.