Tiling of the plane Updated 2025-07-16
Time-independent Schrödinger equation Updated 2025-07-16
The time-independent Schrödinger equation is a variant of the Schrödinger equation defined as:
Equation 1.
Time-independent Schrodinger equation
. So we see that for any Schrödinger equation, which is fully defined by the Hamiltonian , there is a corresponding time-independent Schrödinger equation, which is also uniquely defined by the same Hamiltonian.
The cool thing about the Time-independent Schrödinger equation is that we can always reduce solving the full Schrödinger equation to solving this slightly simpler time-independent version, as described at: Section "Solving the Schrodinger equation with the time-independent Schrödinger equation".
Because this method is fully general, and it simplifies the initial time-dependent problem to a time independent one, it is the approach that we will always take when solving the Schrodinger equation, see e.g. quantum harmonic oscillator.
Timeline of quantum mechanics Updated 2025-07-16
- 1859-1900: see Section "Black-body radiation experiment". Continuously improving culminating in Planck's law black-body radiation and Planck's law
- 1905 photoelectric effect and the photon
- TODO experiments
- 1905 Einstein's photoelectric effect paper. Planck was intially thinking that light was continuous, but the atoms vibrated in a discrete way. Einstein's explanation of the photoelectric effect throws that out of the window, and considers the photon discrete.
- 1913 atomic spectra and the Bohr model
- 1885 Balmer series, an empirical formula describes some of the lines of the hydrogen emission spectrum
- 1888 Rydberg formula generalizes the Balmer series
- 1896 Pickering series makes it look like a star has some new kind of hydrogen that produces half-integer entries in the Pickering series
- 1911 Bohr visits J. J. Thomson in the University of Cambridge for his postdoc, but they don't get along well
- Bohr visits Rutherford at the University of Manchester and decides to transfer there. During this stay he becomes interested in problems of the electronic structure of the atom.
- 1913 february: young physics professor Hans Hansen tells Bohr about the Balmer series. This is one of the final elements Bohr needed.
- 1913 Bohr model published predicts atomic spectral lines in terms of the Planck constant and other physical constant.
- explains the Pickering series as belonging to inoized helium that has a single electron. The half term in the spectral lines of this species come from the nucleus having twice the charge of hydrogen.
- 1913 March: during review before publication, Rutherford points out that instantaneous quantum jumps don't seem to play well with causality.
- 1916 Bohr-Sommerfeld model introduces angular momentum to explain why some lines are not observed, as they would violate the conservation of angular momentum.
Tinker Tailor Soldier Spy Updated 2025-07-16
Some key points that are a bit hard to grasp, at least in some versions:
- How did Bill Haydon know Jim Prideaux was going to Prague if it appears to be organized as a closely guarded secret by Control?so which one is it?
- How does Smiley deduce that the Witchcraft source, Merlin, is Poliakov? A key step is when top people at the Circus question him about Ricki Tarr, and appear to suggest that there is a link between Ricki Tarr and Merlin. And Ricki told Smiley that Poliakov as the link to the Mole. Smiley understands that it was Karla who tipped off London Center about Ricki's coming through Merlin. He also observers that Witchcraft gives ideological infiltration campaign intelligence after Ricki comes back, as a way to discredit Ricki. It is still all a bit indirect.
Transcendence (2014) Updated 2025-07-16
The premise that "we can't make AGI, but we know enough about the human brain to upload on to a computer" is flawed. Edit: after reading Superintelligence by Nick Bostrom (2014), Ciro Santilli was convinced otherwise. What is flawed is of course just the "extracting connectome with macroscopic probes part". A post mortem connectome extraction with microtome is much more believable. But of course they weren't going to show fake slices of Jonny Depp's brain, are they? Famous actor bodies are sacred! What a huge lost opportunity. On the other hand however, the scale of the first connectome extraction would be arguably too huge to be undertaken by a random pair of rogue researchers. The same would also likely apply to any first time human brain connectome. It would much more likely be a huge public effort, much like the Human Genome Project.
But this film does have the merit of exploring how an AGI might act to take over the AGI might act to take over the world once created, notably by creating its own physical research laboratory. Though it doesn't feel likely that it could go under the radar for 2 years given the energetic requirements of the research. Even the terrorists find it before the FBI!
Transfer Android 11 camera videos to Ubuntu 20.10 Updated 2025-07-16
Transformation (genetics) Updated 2025-07-16
Current Wikipedia seems to say that this refers specifically to cells taking up DNA from other dead cells as in the Avery-MacLeod-McCarty experiment, excluding other types of horizontal gene transfer like bacterial conjugation
Transgenerational epigenetic inheritance Updated 2025-07-16
Trinity (nuclear test) Updated 2025-07-16
Plutonium-based.
Its plutonium was produced at Hanford site.
Trinity: Getting The Job Done
. Source. Good video, clarifies several interesting technical points:- Gun-type fission weapon were much easier to build as you don't need super synchronized charges as in implosion-type fission weapon. But they are less efficient.
- Plutonium make much more efficient usage of uranium, because you don't need to highly enrich a bunch of Uranium-235 in the first place, but rather just use way less enriched Uranium-235 to produce a bunch of Plutonium by converting Uranium-238
Try to fix your own bike before taking it to the shop Updated 2025-07-16
Sometimes you get annoyed to death with your bike not breaking or changing gears perfectly as you would like, and the people at the bike shop never do the job well enough.
The problem with bike shops is that the employees are already swamped with work, and they don't get paid any extra for doing more work.
As a result, paradoxically, they are often happier, and respect you more if you are trying to get them to help you to fix your own bike!
Also, for the same reason, they don't have the time to go for a quick test ride after a fix to ensure that the bug was actually fixed.
So they ignore things that would obviously be huge ridability benefits (although they might not be obvious to newbie customers), for which customers would gladly pay more money for.
But you start to learn how to do stuff yourself and it feel amazing when you finally get there (after infinite trial and error).
Ciro dreams of a bike shop that actually calls you for the appointment and then teaches you how to fix the thing.
TSMC Updated 2025-07-16
One of the companies that has fabs, which buys machines from companies such as ASML and puts them together in so called "silicon fabs" to make the chips
As the quintessential fabless fab, there is on thing TSMC can never ever do: sell their own design! It must forever remain a fab-only company, that will never compete with its customers. This is highlighted e.g. at youtu.be/TRZqE6H-dww?t=936 from Video "How Nvidia Won Graphics Cards by Asianometry (2021)".
How Taiwan Created TSMC by Asianometry (2020)
Source. Some points:- UCM failed because it focused too much on the internal market, and was shielded from external competition, so it didn't become world leading
- one of TSMC's great advances was the fabless business model approach.
- they managed to do large technology transfers from the West to kickstart things off
- one of their main victories was investing early in CMOS, before it became huge, and winning that market
Turing machine decider Updated 2025-07-16
Of course, because what we know about the halting problem, there cannot exist a single decider that decides all Turing machines.
E.g. The Busy Beaver Challenge has a set of deciders clearly published, which decide a large part of BB(5). Their proposed deciders are listed at: discuss.bbchallenge.org/c/deciders/5 and actually applied ones at: bbchallenge.org.
But there are deciders that can decide large classes of turing machines.
Many (all/most?) deciders are based on simulation of machines with arbitrary cutoff hyperparameters, e.g. the cutoff space/time of a Turing machine cycler decider.
The simplest and most obvious example is the Turing machine cycler decider
Turing machine that halts if and only if Collatz conjecture is false Updated 2025-07-16
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.
TuxGuitar Updated 2025-07-16
Just use MuseScore instead.
Can import from: MIDI.
Ubuntu 20.04:
sudo apt install tuxguitar tuxguitar-alsa tuxguitar-jsa tuxguitar-osstuxguitar-jsa was needed, otherwise no sound: askubuntu.com/questions/457321/tuxguitar-no-sound-in-14-04Has OK step sequencer non-realtime up/down/left/right guitar based composition interface.
Has chord insertion.
Has bend editor.
Could be more amazing, but it is OK.
A bit limited by being very "guitar oriented". Shows you guitar strings, and you enter offset to each string. So to enter two adjacent notes you need to use two seprate strings and thing about the offsets. If only it had a more piano based interface.
Drum notation is also atrocious, you have to go to the top chord, and use high numbers starting at 36.
Two photon interference experiment Updated 2025-07-16
Can be achieved in two ways it seems:
- macroscopic beam splitter and optical table
- photolithography
Animation of Hong-Ou-Mandel Effect on a silicon like structure by Quantum Light University of Sheffield (2014): www.youtube.com/watch?v=ld2r2IMt4vg No maths, but gives the result clear: the photons are always on the same side.
- quantum dot source. TODO how do you produce identical photons from two separate quantum dots? See also: quantum dot single photon source.
- superconducting nanowire detector. So the device has to be cooled then? Video "Jeremy O'Brien: "Quantum Technologies" by GoogleTechTalks (2014)" youtube.com/watch?v=7wCBkAQYBZA&t=2497 however says that semiconducting devices can also be used
Ubuntu 21.10 does not wake up from suspend Updated 2025-07-16
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
Ubuntu 23.04 boot broken on kernel 6.2 Updated 2025-07-16
The solution on kernel 6.2 was:as per comments under: bugs.launchpad.net/ubuntu/+source/linux/+bug/2012559. This also made the nvidia driver work: Find GPU information in Ubuntu.
sudo apt instal nvidia-driver-515Previously I had:and it blew up before reaching disk decryption.
nvidia-driver-510I also tried:but that broke in a different way:
nvidia-driver-525Finished apport-autoreport.service - Process error reports when automatic reporting is enabled.
nvidia-modeset: ERROR: GPU:0: Idling display engine timed out: 0x0000947d:0:0:407
(1 of 2) Job systemd-backlight@backlight: nvidia_e.service/start running (32s no limit) Undecidable problem Updated 2025-07-16
Or in other words: there is no Turing machine that always halts for every input with the yes/no output.
Every undecidable problem must obviously have an infinite number of "possibilities of stuff you can try": if there is only a finite number, then you can brute-force it.
Lists of undecidable problems.
Coolest ones besides the obvious boring halting problem:
Upsert with
NOT NULL column Updated 2025-07-16Attempt at nodejs/sequelize/raw/upsert.js:
- stackoverflow.com/questions/48816629/on-conflict-do-nothing-in-postgres-with-a-not-null-constraint OP unable to provide a minimal exampe, but it is likely the problem
- dba.stackexchange.com/questions/292428/postgresql-upsert-issue-with-not-null-columns
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