Connected components of the orthogonal group Updated 2025-07-16
The orthogonal group has 2 connected components:
- one with determinant +1, which is itself a subgroup known as the special orthogonal group. These are pure rotations without a reflection.
- the other with determinant -1. This is not a subgroup as it does not contain the origin. It represents rotations with a reflection.
It is instructive to visualize how the looks like in :
- you take the first basis vector and move it to any other. You have therefore two angular parameters.
- you take the second one, and move it to be orthogonal to the first new vector. (you can choose a circle around the first new vector, and so you have another angular parameter.
- at last, for the last one, there are only two choices that are orthogonal to both previous ones, one in each direction. It is this directio, relative to the others, that determines the "has a reflection or not" thing
As a result it is isomorphic to the direct product of the special orthogonal group by the cyclic group of order 2:
A low dimensional example:because you can only do two things: to flip or not to flip the line around zero.
Note that having the determinant plus or minus 1 is not a definition: there are non-orthogonal groups with determinant plus or minus 1. This is just a property. E.g.:has determinant 1, but:so is not orthogonal.
Endofunction Updated 2025-07-16
ENIAC Updated 2025-07-16
Stack Overflow Updated 2025-07-16
The best place to get answers to programming questions as of 2019. Google into Stack Overflow is always the best bet.
An overview of Ciro Santilli's Stack Overflow contribution can be found at: Ciro Santilli's Stack Overflow contributions.
Stack Overflow in a nutshell
. Source. As the "WTF look at my points" guy, Ciro Santilli approves of this meme. A few more elements could be added, notably deletion of the last link-only answer, but good enough.
By the profile image, the "Grammar Nazi" editor is actually appropriately the notorious serial editor Peter Mortensen. Ciro Santilli welcomes grammar fixes, but more subjective style fixes can be a bit annoying.
Catching mice by Nakanoart
. Possible non-canonical source: twitter.com/nixcraft/status/1376023938749190147
The Social Network Updated 2025-07-16
Thiel Fellowship Updated 2025-07-16
Ciro Santilli approves of this one, related: Section "Free gifted education".
The downside of the Thiel Fellowship is that it is realistically impossible for its fellows to do anything in deep tech, only information science startups would be possible, as they would not have the labs, or lab skills required for any deep tech if they drop out before a PhD. Related: Section "The only reason for universities to exist should be the laboratories".
The only solution is the harder process of actually remodelling our very broken educational system.
Equity (finance) Updated 2025-07-16
Eric W. Weisstein Updated 2025-07-16
Ahh, this dude is just like Ciro Santilli, trying to create the ultimate natural sciences encyclopedia!
Essential fatty acid Updated 2025-07-16
Eta (letter) Updated 2025-07-16
Conservation laws in Schrodinger equations Updated 2025-07-16
TODO is there any good intuitive argument or proof of conservation of energy, momentum, angular momentum?
How to contact Ciro Santilli Updated 2025-07-26
Ciro Santilli is very happy to meet people with related interests, he really loves his like-minded online friends. Even if you don't have something a specific goal in mind for the contact, please just say hi.
To contact Ciro publicly about any general subject that is not covered in a more specific GitHub repository, including saying hi or suggestions about his website either:
- create a GitHub issue at: github.com/cirosantilli/cirosantilli.github.io/issues/new or Giscus thread
- at mention Ciro's main Twitter account
For comments about China, first read:
and then create a GitHub issue at: github.com/cirosantilli/china-dictatorship/issues/new
Publicly viewable contact is preferred if possible to more effectively share Ciro's wisdom with the world.
But if you feel more comfortable with private contact, no problem, either:
- email: username
cirosantilliwith provider ProtonMail which has domain nameproton.me. Note that Ciro also controls the Gmail address with that same username, and keep in mind that dots are ignored in Gmail addresses. But ProtonMail preferred because why should we give our private minds to the CIA by default? Push notifications disabled. - Signal: username
cirosantilli.89signal.me/#eu/BuJjV0enXYTOnFFc1FZV5LFcWodL1a2Oy9VZ5uyQU7xrYxqw+npIcaHBqghWudrI. 89 is a reference to Ciro Santilli's birth year 1989. Push notifications enabled, but treat like email unless we are actively chatting back and forth.
For other less good methods that will also likely work, use direct messages of the following profiles from under Section "Accounts controlled by Ciro Santilli":Ciro's Twitter DMs are also open, but note that Ciro receives endless Chinese language SPAM there which Twitter is doing nothing to combat, so it's not as reliable.
- LinkedIn: www.linkedin.com/in/cirosantilli
- Reddit: www.reddit.com/user/cirosantilli
- Facebook: www.facebook.com/cirosantilli
- Telegram: telegram.me/cirosantilli. Note that end-to-end encryption is present on secret chats only, which don't have device sync. Ridiculous.
If you are a privacy freak or are going to tell Ciro state secrets Ciro has this GNU Privacy Guard public key: pubkey.gpg, but it's not something that he has ever really used.
Disqus comments were removed from his website in 2019-05-04, a manual dump is available here, removal rationale at: why Ciro Santilli removed Disqus comments from his website in 2019-05-04.
Content moderation Updated 2025-07-16
gothinkster/realworld Updated 2025-07-16
Ahh, you can't have new ideas anymore!
Basically puts together every backend with Front-end web framework to create the exact same website.
The reference live demo can be found at: demo.realworld.io/#/ It is based on Angular.js as it links to: github.com/gothinkster/angularjs-realworld-example-app TODO backend?
There are however also live demos of other frontends, e.g.:Note that all those frontends communicate with the same backend.
- React: react-redux.realworld.io. But note that tag addition at post creation is broken there as of March 2021, but not on master: github.com/gothinkster/react-redux-realworld-example-app/issues/151#issuecomment-808417846 so they forgot to update the live server.
- Vue.js: vue-vuex-realworld.netlify.app
As of 2021 Devs are seemed a bit too focused on monetizing the project through their "how to use this project" premium tutorial, and documentation could be better: just getting the hello world of the most popular backend with the most popular frontend is not easy... come on.
github.com/gothinkster/realworld/issues/578 asks for community support, as devs have moved on since unfortunately.
Remember:
- by default, the frontends hardcode the upstream public data API:
https://conduit.productionready.io/apiso you have to hack their code to match the port of the backend. And each backend can have a different port. - when you switch between backends, you must first manually clear client-side storage cookies/local new run will fail due to authentication issues!
Important missing things from the minimum base app:
- server-side rendering:
- github.com/arrlancore/nextjs-ssr-real-world-app-example. As advertised, that global instance does render with JavaScript disabled! Proposed for upstream at: github.com/gothinkster/realworld/issues/423
- github.com/gothinkster/realworld/issues/266
- no javaScript bi-directional communication library built-in... come on: github.com/gothinkster/realworld/issues/107
- email notifications however as tested on the live demo: demo.realworld.io/#/
- error handling is broken/missing/inconsistent across apps
First you should the most popular backend/frontend combination running, which is the most likely to be working. We managed to run on Ubuntu 20.10, React + Node.js Express.js as described at github.com/gothinkster/node-express-realworld-example-app/pull/116:Then just:on both server and client, and then visit the client URL: localhost:4100/
- github.com/cirosantilli/node-express-realworld-example-app/tree/mongo4 which has a simple patch on top of github.com/gothinkster/node-express-realworld-example-app/tree/ba04b70c31af81ca7935096740a6e083563b3a4a for MongoDB 4 supportThis requires you to first install MongoDB on Ubuntu and ensure you can login to it from the command line.
- github.com/gothinkster/react-redux-realworld-example-app/tree/9186292054dc37567e707602a15a0884d6bdae35 patched to use the correct server host/port
localhost:3000:diff --git a/src/agent.js b/src/agent.js index adfbd72..e3cdc7f 100644 --- a/src/agent.js +++ b/src/agent.js @@ -3,7 +3,7 @@ import _superagent from 'superagent'; const superagent = superagentPromise(_superagent, global.Promise); -const API_ROOT = 'https://conduit.productionready.io/api'; +const API_ROOT = 'http://localhost:3030/api'; const encode = encodeURIComponent; const responseBody = res => res.body;
npm install
npm startYou have to hit the Enter key to add tags, it's terrible: github.com/gothinkster/react-redux-realworld-example-app/issues/151#issuecomment-808417846
One cool thing is that the main repo has unified backend API tests:so the per-repository tests are basically useless, and that single test can test everything for any backend! There is no frontend testing however: github.com/gothinkster/realworld/issues/269 so newb.
git clone https://github.com/gothinkster/realworld
cd realworld
git checkout e7adc6b06b459e578d7d4a6738c1c050598ba431
cd api
APIURL=http://localhost:3000/api USERNAME="u$(date +%s)" ./run-api-tests.sh All science is either physics or stamp collecting Updated 2025-07-16
All the financial advice you’ll ever need fits on a single index card Updated 2025-07-16
Continuous spectrum (functional analysis) Updated 2025-07-16
Unlike the simple case of a matrix, in infinite dimensional vector spaces, the spectrum may be continuous.
The quintessential example of that is the spectrum of the position operator in quantum mechanics, in which any real number is a possible eigenvalue, since the particle may be found in any position. The associated eigenvectors are the corresponding Dirac delta functions.
Controlled quantum gate Updated 2025-07-16
Controlled quantum gates are gates that have two types of input qubits:These gates can be understood as doing a certain unitary operation only if the control qubits are enabled or disabled.
- control qubits
- operand qubits (terminology made up by Ciro Santilli just now)
The CSS of Ciro Santilli's website looks broken Updated 2025-07-16
That which does not exist, cannot be broken.
And of course:
Cool data embedded in the Bitcoin blockchain AtomSea & EMBII data format Updated 2025-07-16
Best guess so far, all in ASCII hex of output scripts:
- remove the single output value different from first one from payload, that's the change, and it is randomly placed as far as I see
- 64 bytes: hex address of top level text
- 1 byte: some random punctuation
- decimal number of bytes of some payload
- 1 byte: some random punctuation
- 64 bytes: same as the first address
- CR LF
- ends in NUL
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