Matrix representation of a positive definite symmetric bilinear form Updated 2024-12-23 +Created 1970-01-01
A positive definite matrix that is also a symmetric matrix.
This theorem roughly states that states that for every quantum algorithm, once we reach a certain level of physical error rate small enough (where small enough is algorithm dependant), then we can perfectly error correct.
This algorithm provides the conceptual division between noisy intermediate-scale quantum era and post-NISQ.
As well put by Wikipedia, a radio receiver has to perform three functions on the signal from the antenna:
- filtering, so you can tune the station you care about. This filters based on the frequency of the carrier wave you want. I.e. you use a bandpass filter.
- amplification: otherwise you won't be able to hear anything if the emitter is too far away
- demodulation: this means decoding the signal based on whatever way it was encoded, notably e.g. AM/FM
It is said that you leave Oxford with either
- a First, i.e. First class, good grades
- a Blue, i.e. a sporting achievement
- a spouse, see also Section "The main function of university is sexual selection"
Surely You're Joking, Mr. Feynman chapter An Offer You Must Refuse (a play on words on The Godfather (1972)) has an interesting historical mention from the early 1950s while at Caltech:
The next day, I had the greatest luck in making a decision. God must have set it up to help me decide. I was walking to my office, and a guy came running up to me and said, "Hey, Feynman! Did you hear what happened? Baade found that there are two different populations of stars! All the measurements we had been making of the distances to the galaxies had been based on Cephid variables of one type, but there's another type, so the universe is twice, or three, or even four times as old as we thought!"I knew the problem. In those days, the earth appeared to be older than the universe. The earth was four and a half billion, and the universe was only a couple, or three billion years old. It was a great puzzle. And this discovery resolved all that: The universe was now demonstrably older than was previously thought. And I got this information right away - the guy came running up to me to tell me all this.
Ciro Santilli very aggressively aggressively people in social media.
There are basically 3 categories:
The fatal flaw of OAuth is that websites have to enable specific providers, they can't just automatically select the correct OAuth for a given email domain. This means that the vast majority of websites will only provide the most widely popular providers such as Google, and the like, which means people won't have decent privacy.
So you are just better off with password logins and a decent password manager.
Number of elements of an elliptic curve over a finite field Updated 2024-12-23 +Created 1970-01-01
Ubuntu 20.10 as per xmrig.com/docs/miner/build/ubuntu:At minexmr.com/#getting_started we see that all you then need is a single CLI command:Seems simple, well done devs!
sudo apt install git build-essential cmake libuv1-dev libssl-dev libhwloc-dev
git clone https://github.com/xmrig/xmrig.git
mkdir xmrig/build && cd xmrig/build
cmake ..
make -j$(nproc)xmrig -o pool.minexmr.com:4444 -u <your-monero-address>Benchmark on Lenovo ThinkPad P51 (2017) as per xmrig.com/docs/miner/benchmark:gives:which according to the minexmr.com mining pool would generate 0.0005 XMR/day, which at the February 2021 rate of 140 USD/XMR is 0.07 USD/day. The minimum payout in that pool is 0.004 XMR so it would take 8 days to reach that.
./xmrig --bench=1M948.1 h/sSo clearly, application-specific integrated circuit mining is the only viable way of doing this.
Some people considering Raspberry Pis also conclude obviously that it is useless at a 10H/s rate:
www.makeuseof.com/cryptos-you-can-mine-at-home/ is a completely full of bullshit article that says otherwise. How can someone publish that!
Really weird and obscure company, good coverage: thequantuminsider.com/2020/02/06/quantum-computing-incorporated-the-first-publicly-traded-quantum-computing-stock/
Publicly traded in 2007, but only pivoted to quantum computing much later.
Strictly speaking, only defined for decision problems: cs.stackexchange.com/questions/9664/is-it-necessary-for-np-problems-to-be-decision-problems/128702#128702
On the Law of Distribution of Energy in the Normal Spectrum Updated 2024-12-23 +Created 1970-01-01
The Planck's law paper.
hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Planck%20(1900),%20Distribution%20Law.pdf contains a replica of the translation present in The Old Quantum Theory by Dirk ter Haar (1967).
Term invented by Ciro Santilli to refer to problems that can only be solved once we have AGI.
It is somewhat of a flawed analogy to NP-complete.
The Kibble balance is so precise and reproducible that it was responsible for the 2019 redefinition of the Kilogram.
It relies rely on not one, but three macroscopic quantum mechanical effects:How cool is that! As usual, the advantage of those effects is that they are discrete, and have very fixed values that don't depend either:One downside of using some quantum mechanical effects is that you have to cool everything down to 5K. But that's OK, we've got liquid helium!
- atomic spectra: basis for the caesium standard which produces precise time and frequency
- Josephson effect: basis for the Josephson voltage standard, which produces precise voltage
- quantum Hall effect: basis for the quantum Hall effect, which produces precise electrical resistance
- on the physical dimensions of any apparatus (otherwise fabrication precision would be an issue)
- small variations of temperature, magnetic field and so on
The operating principle is something along:Then, based on all this, you can determine how much the object weights.
- generate a precise frequency with a signal generator, ultimately calibrated by the Caesium standard
- use that precise frequency to generate a precise voltage with a Josephson voltage standard
- convert that precise voltage into a precise electric current by using the quantum Hall effect, which produces a very precise electrical resistance
- use that precise current to generate a precise force on the object your weighing, pushing it against gravity
- then you precisely measure both:
- local gravity with a gravimeter
- the displacement acceleration of the object with a laser setup
How We're Redefining the kg by Veritasium
. Source. The Kibble Balance, realizing the Kilogram from fundamental constants of nature by Richard Green
. Source. Presented in 2022 for a CENAM seminar, the Mexican metrology institute. The speaker is from the Canadian metrology institute- youtu.be/ZfNygYuuVAE?t=854: they don't actually use the Quantum Hall effect device during operation, they only use it to calibrate other non-quantum resistors
The Watt balance and redefining the kilogram by National Physical Laboratory
. Source. Nothing much, but fun to hear Kibble talking about his balance in beautiful English before he passed.The elliptic curve group of all elliptic curve over the rational numbers is always a finitely generated group.
The number of points may be either finite or infinite. But when infinite, it is still a finitely generated group.
For this reason, the rank of an elliptic curve over the rational numbers is always defined.
TODO example.
From Machine Learning to Autonomous Intelligence by Yann LeCun (2023)
Source. After a bunch of B.S., LeCun goes on to describe his AGI architecture. Nothing ground breaking, but not bad either.We define this category as AI games in which agents are able to produce or consume natural language.
It dawned on Ciro Santilli that it would be very difficult to classify an agent as an AGI if tthat agent can't speak to take orders, read existing human generated documentation, explain what it is doing, or ask for clarification.
Human player test of DMLab-30 Select Described Object task by DeepMind (2018)
Source. This is one of the games from DeepMind Lab. There are unlisted articles, also show them or only show them.