The model is extremely simple, but has been proven to be able to solve all the problems that any reasonable computer model can solve, thus its adoption as the "default model".
The smallest known Turing machine that cannot be proven to halt or not as of 2019 is 7,918-states: www.scottaaronson.com/blog/?p=2725. Shtetl-Optimized by Scott Aaronson is just the best website.
A bunch of non-reasonable-looking computers have also been proven to be Turing complete for fun, e.g. Magic: The Gathering.
Turing machine that halts if and only if Collatz conjecture is false Updated 2025-06-17 +Created 1970-01-01
mathoverflow.net/questions/309044/is-there-a-known-turing-machine-which-halts-if-and-only-if-the-collatz-conjectur suggests one does not exist. Amazing.
Intuitively we see that the situation is fundamentally different from the Turing machine that halts if and only if the Goldbach conjecture is false because for Collatz the counter example must go off into infinity, while in Goldbach conjecture we can finitely check any failures.
Amazing.
The third part module, which clutters up any serches you make for the built-in one.
The key question is: why is this not symmetrical?
One answer is: because one of the twin accelerates, and therefore changes inertial frames.
But the better answer is: understand what happens when the stationary twin sends light signals at constant time intervals to each other. When does the travelling twin receives them?
Another way of understanding it is: you have to make all calculations on a single inertial frame for the entire trip.
Supposing the sibling quickly accelerates out (or magically starts moving at constant speed), travels at constant speed, and quickly accelerates back, and travels at constant speed setup, there are three frames that seem reasonable:
- the frame of the non-accelerating sibling
- the outgoing trip of the accelerating sibling
- the return trip of the accelerating sibling
If you do that, all three calculations give the exact same result, which is reassuring.
Another way to understand it is to do explicit integrations of the acceleration: physics.stackexchange.com/questions/242043/what-is-the-proper-way-to-explain-the-twin-paradox/242044#242044 This is the least insightful however :-)
Bibliography:
Please refer to Video "Linus Torvalds saying "Nvidia Fuck You" (2012)".
Does not happen every time, only some times. Can't figure out why. Usually happens when has suspended for a longer time.
bugs.launchpad.net/ubuntu/+source/nvidia-graphics-drivers-470/+bug/1946303 sounds like a likely report, Nvidia driver version 470, but can't find those error messages anywhere. The last line of:once was:which is when sleep starts.
journalctl -o short-precise -k -b -1PM: suspend entry (deep)This suggests that it is not a video bug then, seems that it is not waking up at all? Gotta try to SSH into it. OK. I did SSH into it, and that was fine, so it is just the video that won't start.
PM: suspend exitbugs.launchpad.net/ubuntu/+source/linux/+bug/1949977 is another possible bug, based on kernel version. I'm running 5.13, which is one of the failing versions on the report. Can't find any interesting dmesg though.
In another crash:had the following interesting lines:and there was a corresponding
journalctl -o short-precise -k -b -1nvidia-modeset: WARNING: GPU:0: Lost display notification (0:0x00000000); continuing.
[24307.640014] NVRM: GPU at PCI:0000:01:00: GPU-18af74bb-7c72-ff70-e447-87d48378ea20
[24307.640018] NVRM: Xid (PCI:0000:01:00): 79, pid=8828, GPU has fallen off the bus.
[24307.640021] NVRM: GPU 0000:01:00.0: GPU has fallen off the bus.
[24328.054022] nvidia-modeset: ERROR: GPU:0: The requested configuration of display devices (LGD (DP-4)) is not supported on this GPU.
[repeats several more times]
[24328.056767] nvidia-modeset: ERROR: GPU:0: The requested configuration of display devices (LGD (DP-4)) is not supported on this GPU.
[24328.056951] nvidia-modeset: ERROR: GPU:0: Failed to query display engine channel state: 0x0000927c:0:0:0x0000000f
[24328.056955] nvidia-modeset: ERROR: GPU:0: Failed to query display engine channel state: 0x0000927c:1:0:0x0000000f
[24328.056959] nvidia-modeset: ERROR: GPU:0: Failed to query display engine channel state: 0x0000927c:2:0:0x0000000f
[24328.056962] nvidia-modeset: ERROR: GPU:0: Failed to query display engine channel state: 0x0000927c:3:0:0x0000000f
[24328.056983] nvidia-modeset: ERROR: GPU:0: DP-4: Failed to disable DisplayPort audio stream-0
[24328.056992] nvidia-modeset: ERROR: GPU:0: Failed to query display engine channel state: 0x0000947d:0:0:0x0000000f/var/crash/_usr_sbin_gdm3.0.crash.Related "GPU has fallen off the bus": askubuntu.com/questions/868321/gpu-has-fallen-off-the-bus-nvidia
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