Kind of extends the complex numbers.
Some facts that make them stand out:
- one of the only three real associative division algebras in addition to the real numbers and complex numbers, according to the classification of associative real division algebras
- the simplest non-commutative division algebra. Contrast for example with complex numbers where multiplication is commutative
Output:With our understanding of the discrete Fourier transform we see clearly that:
sin(t)
fft
real 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
imag 0 -10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
rfft
real 0 0 0 0 0 0 0 0 0 0 0
imag 0 -10 0 0 0 0 0 0 0 0 0
sin(t) + sin(4t)
fft
real 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
imag 0 -10 0 0 -10 0 0 0 0 0 0 0 0 0 0 0 10 0 0 10
rfft
real 0 0 0 0 0 0 0 0 0 0 0
imag 0 -10 0 0 -10 0 0 0 0 0 0- the signal is being decomposed into sinusoidal components
- because we are doing the Discrete Fourier transform of a real signal, for the
fft, so there is redundancy in the. We also understand thatrfftsimply cuts off and only keeps half of the coefficients
Sample program output,
counts are randomized each time.First we take the quantum state vector immediately after the input.We understand that the first element of
input:
state:
Statevector([1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],
dims=(2, 2))
probs:
[1. 0. 0. 0.]Statevector is , and has probability of 1.0.Next we take the state after a Hadamard gate on the first qubit:We now understand that the second element of the
h:
state:
Statevector([0.70710678+0.j, 0.70710678+0.j, 0. +0.j,
0. +0.j],
dims=(2, 2))
probs:
[0.5 0.5 0. 0. ]Statevector is , and now we have a 50/50 propabability split for the first bit.Then we apply the CNOT gate:which leaves us with the final .
cx:
state:
Statevector([0.70710678+0.j, 0. +0.j, 0. +0.j,
0.70710678+0.j],
dims=(2, 2))
probs:
[0.5 0. 0. 0.5]Then we print the circuit a bit:
qc without measure:
┌───┐
q_0: ┤ H ├──■──
└───┘┌─┴─┐
q_1: ─────┤ X ├
└───┘
c: 2/══════════
qc with measure:
┌───┐ ┌─┐
q_0: ┤ H ├──■──┤M├───
└───┘┌─┴─┐└╥┘┌─┐
q_1: ─────┤ X ├─╫─┤M├
└───┘ ║ └╥┘
c: 2/═══════════╩══╩═
0 1
qasm:
OPENQASM 2.0;
include "qelib1.inc";
qreg q[2];
creg c[2];
h q[0];
cx q[0],q[1];
measure q[0] -> c[0];
measure q[1] -> c[1];Dummy example of using a React
ref This example is useless and to the end user seems functionally equivalent to react/hello.html.It does however serve as a good example of what react does that is useful: it provides a "clear" separation between state and render code (which becomes once again much less clear in React function components.
Notably, this example is insane because at:we are extracing state from some random HTML string rather than having a clean JavaScript variable containing that value.
<button onClick={() => {
elem.innerHTML = (parseInt(elem.innerHTML) + 1).toString()In this case we managed to get away with it, but this is in general not easy/possible.
And by artificial intelligence, read of course (non-human-identical) artificial general intelligence.
Today-2022, this is placed under the science fiction film category. But maybe this might change during Ciro Santilli's own lifetime?
The basic criteria of "is a film about artificial intelligence good or not" to Ciro Santilli is: does the AI inhabit humanoid, or fully human looking, bodies? Bodies is a bad sign due to:
- the best science fiction works deeply explore the consequences of one single technology: efficient humanoid bodies are a second technological breakthrough besides AI itself. The first AI will obviously be a supercomputer without a body
- it is hard to imagine that the AI wouldn't organize itself as one huge central computer and R&D/command center. Perhaps there will be need for a few separate ones to optimize usage of natural resources, and to have some redundance in case a nuke blows the region, but there would be very very few of the think tanks. But having big centers is fundamental, because you centralize all the flow of ideas and their combination leading to new better outcomes for the AI. The mobile robot actors controlled by this center, if any exist, would then be slaves with some degree of autonomy and infinitely less computational powerful than the think tank.
A convenient notation for the elements of of prime order is to use integers, e.g. for we could write:which makes it clear what is the additive inverse of each element, although sometimes a notation starting from 0 is also used:
For non-prime order, we see that modular arithmetic does not work because the divisors have no inverse. E.g. at order 6, 2 and 3 have no inverse, e.g. for 2:we see that things wrap around perfecly, and 1 is never reached.
Finite fields made easy by Randell Heyman (2015)
Source. Good introduction with examplesFirst They Ignore You, Then They Laugh at You, Then They Attack You, Then You Win
Quora is crap in many, many senses, but in part due to some bad Stack Overflow policies, it is the best crap we've got for certain (mostly useless) subjects. Until OurBigBook.com dominates the world.
The worst thing about quora is that you cannot subscribe only to certain subjects on your feed. Quora just keeps pumping shit you never subscribed to, no matter what. Ciro, for sport, unfollowed every single idiotic subject it was proposing, but it didn't work, sooner or later Quora just keeps pumping more shit back. Mind you, some of that shit is fun. But it's still shit. Though on second thought, YouTube also randomly decides to reset Ciro's humongous "don't recomend this shitty channel" choices from time to time, which is not much different...
Other terrible things, they just seem to have an incredible ability of making the website worse and more annoying over time! Truly amazing:
- around 2022, quora started showing "related" answers to other questions, possibly before actualy answers to the question itself. This, together with an insane number of inline ads that look very similar to answers, makes it very hard to decide what is an actual answer or not!!! E.g.: people complaining:
- around 2021, quora started expanding any link as a huge preview box that completely takes over the answer, and it is very hard to stop it from doing so
- Quora used to show question details beyond the title by default, but stopped: www.reddit.com/r/OutOfTheLoop/comments/uqyvfp/comment/jd6go1b/?utm_source=share&utm_medium=web2x&context=3
Quora is getting so bad that it is basically being killed by Reddit, especially after they lifted the 6-month hard thread lock...
See also: cirosantilli.com/china-dictatorship/quora for a coverage of the intense pro-CCP astroturfing present on the website.
~8GB,
lsblk reports 7796176 * 1KB = 7983284224 bytes.They are shaped like bicornes, which is super cool, but also super impractical!
Markings: "AX ÉCOLE POLYTECHNIQUE PROMOTION X2009"
From Ubuntu 20.04 on an ext4 formatted one:With Linux Unified Key Setup + ext4 the results are similar, maybe hdparam bypasses it?
/dev/sdb:
Timing cached reads: 28656 MB in 1.99 seconds = 14421.31 MB/sec
SG_IO: bad/missing sense data, sb[]: 70 00 05 00 00 00 00 0a 00 00 00 00 20 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
Timing buffered disk reads: 42 MB in 3.03 seconds = 13.88 MB/sec/dev/sdb:
Timing cached reads: 28326 MB in 1.99 seconds = 14251.55 MB/sec
SG_IO: bad/missing sense data, sb[]: 70 00 05 00 00 00 00 0a 00 00 00 00 20 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
Timing buffered disk reads: 38 MB in 3.11 seconds = 12.23 MB/secgnome-disks LUKS + ext4 benchmark with default params also gives about 14 MB/s.In Ciro's ASCII art circuit diagram notation, it is a loop with three Josephson junctions:
+----X-----+
| |
| |
| |
+--X----X--+
Superconducting Qubit by NTT SCL (2015)
Source. Offers an interesting interpretation of superposition in that type of device (TODO precise name, seems to be a flux qubit): current going clockwise or current going counter clockwise at the same time. youtu.be/xjlGL4Mvq7A?t=1348 clarifies that this is just one of the types of qubits, and that it was developed by Hans Mooij et. al., with a proposal in 1999 and experiments in 2000. The other type is dual to this one, and the superposition of the other type is between N and N + 1 copper pairs stored in a box.
Their circuit is a loop with three Josephson junctions, in Ciro's ASCII art circuit diagram notation:
+----X-----+
| |
| |
| |
+--X----X--+When half the magnetic flux quantum is applied as microwaves, this produces the ground state:where and cancel each other out. And the first excited state is:Then he mentions that:
- to go from 0 to 1, they apply the difference in energy
- if the duration is reduced by half, it creates a superposition of .
If you pass parallel light.
This was the first full scale nuclear reactor in the world, and was brought up slowly to test it out.
Hanford B Reactor tour by Studio McGraw
. Source. 2016.- youtu.be/8rlVHEY7BF0?t=335 good description of the fuel element. It uses uranium metal, not Uranium dioxide
- youtu.be/8rlVHEY7BF0?t=652 N Reactor and F Reactor were identical, and came up 2 months later, but much faster because of what they learned on the B
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