Scalar (mathematics) by Ciro Santilli 40 Updated 2025-07-16
A member of the underlying field of a vector space. E.g. in , the underlying field is , and a scalar is a member of , i.e. a real number.
The ideal university by Ciro Santilli 40 Updated 2025-07-16
This is a version of free gifted education but more focused on university.
This is Ciro Santilli's ideal university system. It is a system that actually lives up to the name "Open University":
Related:
So far as of the early 2020's, the university that comes closest to some but not all of these principles is the University of the People. It's sad that it's such a crappy unknown thing, but it is what it is.
Besides of course sexual selection, considering in this section only "formal learning" activities.
Consider e.g. the 2020 University of Oxford, where many many people are taking courses without any laboratory work (and also without much use at all) like literature and history, and they are paying about 9k pounds/year for it: how much it costs to study at the University of Oxford?.
Basically all of this could be done online from books.
Laboratories are impossible however, because expendables of every experiment you do cost from hundreds to thousands of dollars, not to mention crazy upfront equipment costs.
For this reason, the brick and mortar aspect universities should focus exclusively on laboratories, and ensuring that the students with the most relevant knowledge (which can be readily obtained online) get access to those laboratories. Students should of course fully master every aspect of theory pertinent to their experiments. principal investigators should hand pick whichever criteria they want to select their students, possibly based partly on exam as a service if they find it a useful metric.
Furthermore, the use of laboratories should put great focus on novel research. A lot of laboratory instruction could be done from video of an experiments. As much as possible, we should use laboratories for novel research. Related: Section "Videos of all key physics experiments".
This is the actual main function of university for many people as of the 2020s. And it fulfills it quite well. A breeding ground.
In a closely related sense, university is simply a symbol of personal status. Not a place where you go to learn. And especially in the Anglophone world of fancy colleges, university also doubles down as a form of long term luxury hotel. Even if it ends up meaning debt.
There's nothing wrong with sexual selection. This type of natural eugenics is an important part of humankind. It is however just sad that any type of learning falls so much behind. A close second would be fine. But as it stands, it is just too far off.
Ciro Santilli's general feeling is that university should not own IP, it should belong to the researchers. Instead, university should help researchers make their startups, so they can become big, and then we can tax them and reinvest in the universities.
Of course, this goes through the nonprofit impact measurement difficulty. Maybe we could instead limit the IP to some reasonably small percentage, like 10%?
But still, as of 2020, if feels like universities are way too greedy.
University entry exam by Ciro Santilli 40 Updated 2025-07-16
These are the most evil examinations society has.
They mean that until you are 18, you have to study a bunch of generic crap you hate just to get into university. Rather than studying whatever it is that you truly love to become a God at it as fast as possible and have any chance of advancing the field.
And then, if you decide that you want to change, which is not unlikely since you haven't really try to study what you signed up for before then, it can be very hard and time consuming, leading to a bunch of adults with useless degress they will never use at work.
With the invention of the Internet, all teaching material can be free and open source. Only laboratory space has any cost (besides the opportunity cost of participation in actual projects in a research team).
Per-country list: en.wikipedia.org/wiki/List_of_admission_tests_to_colleges_and_universities

Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 5. . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact