Ciro Santilli's preferred visualization of the real projective plane is a small variant of the standard "lines through origin in ".
For those sphere points in the circle on the x-y plane, you should think of them as magic poins that are identified with the corresponding antipodal point, also on the x-y, but on the other side of the origin. So basically you you can teleport from one of those to the other side, and you are still in the same point.
Ciro likes this model because then all the magic is confined just to the part of the model, and everything else looks exactly like the sphere.
It is useful to contrast this with the sphere itself. In the sphere, all points in the circle are the same point. But this is not the case for the projective plane. You cannot instantly go to any other point on the by just moving a little bit, you have to walk around that circle.
Spherical cap model of the real projective plane
. On the x-y plane, you can magically travel immediately between antipodal points such as A/A', B/B' and C/C'. Or equivalently, those pairs are the same point. Every other point outside the x-y plane is just a regular point like a normal sphere.It is unbelievable that you can't find easily on YouTube recreations of many of the key physics/chemistry experiments and of common laboratory techniques.
Experiments, the techniques required to to them, and the history of how they were first achieved, are the heart of the natural sciences. Without them, there is no motivation, no beauty, no nothing.
School gives too much emphasis on the formulas. This is bad. Much more important is to understand how the experiments are done in greater detail.
The videos must be completely reproducible, indicating the exact model of every experimental element used, and how the experiment is setup.
A bit like what Ciro Santilli does in his Stack Overflow contributions but with computers, by indicating precise versions of his operating system, software stack, and hardware whenever they may matter.
It is understandable that some experiments are just to complex and expensive to re-create. As an extreme example, say, a precise description of the Large Hadron Collider anyone? But experiments up to the mid-20th century before "big science"? We should have all of those nailed down.
We should strive to achieve the cheapest most reproducible setup possible with currently available materials: recreating the original historic setup is cute, but not a priority.
Furthermore, it is also desirable to reproduce the original setups whenever possible in addition to having the most convenient modern setup.
Someone with enough access to labs has to step up and make a name for themselves through the huge effort of creating a baseline of amazing content without yet being famous.
Until it reaches a point that this person is actively sought to create new material for others, and things snowball out of control. Maybe, if the Gods allow it, that person could be Ciro.
Tutorials with a gazillion photos and short videos are also equally good or even better than videos, see for example Ciro's How to use an Oxford Nanopore MinION to extract DNA from river water and determine which bacteria live in bacteria for an example that goes toward that level of perfection.
The Applied Science does well in that direction.
This project is one step that could be taken towards improving the replication crisis of science. It's a bit what Hackster.io wants to do really. But that website is useless, just use OurBigBook.com and create videos instead :-)
We're maintaining a list of experiments for which we could not find decent videos at: Section "Physics experiment without a decent modern video".
Ciro Santilli visited the teaching labs of a large European university in the early 2020's. They had a few large rooms filled with mostly ready to run versions of several key experiments, many/most from "modern physics", e.g. Stern-Gerlach experiment, Quantum Hall effect, etc.. These included booklets with detailed descriptions of how to operate the apparatus, what you'd expect to see, and the theory behind them. With a fat copyright notice at the bottom. If only such universities aimed to actually serve the public for free rather than hoarding resources to get more tuition fees, university level education would already have been solved a long time ago!
One thing we can more or less easily do is to search for existing freely licensed videos and add them to the corresponding Wikipedia page where missing. This requires knowing how to search for freely licensed videos:
- Wikimedia Commons video search, e.g.: commons.wikimedia.org/w/index.php?search=spectophotometry&title=Special:MediaSearch&go=Go&type=video
- YouTube creative commons video search
Related:
- relevant University YouTube channels:
- K-12 demo projects:
- books:
- Practical approach series by Oxford University Press: global.oup.com/academic/content/series/p/practical-approach-series-pas
See: exam.
Spin is one of the defining properties of elementary particles, i.e. number that describes how an elementary particle behaves, much like electric charge and mass.
The approach shown in this section: Section "Spin comes naturally when adding relativity to quantum mechanics" shows what the spin number actually means in general. As shown there, the spin number it is a direct consequence of having the laws of nature be Lorentz invariant. Different spin numbers are just different ways in which this can be achieved as per different Representation of the Lorentz group.
Video 1. "Quantum Mechanics 9a - Photon Spin and Schrodinger's Cat I by ViaScience (2013)" explains nicely how:
- incorporated into the Dirac equation as a natural consequence of special relativity corrections, but not naturally present in the Schrödinger equation, see also: the Dirac equation predicts spin
- photon spin can be either linear or circular
- the linear one can be made from a superposition of circular ones
- straight antennas produce linearly polarized photos, and Helical antennas circularly polarized ones
- a jump between 2s and 2p in an atom changes angular momentum. Therefore, the photon must carry angular momentum as well as energy.
- cannot be classically explained, because even for a very large estimate of the electron size, its surface would have to spin faster than light to achieve that magnetic momentum with the known electron charge
- as shown at Video "Quantum Mechanics 12b - Dirac Equation II by ViaScience (2015)", observers in different frames of reference see different spin states
Quantum Spin - Visualizing the physics and mathematics by Physics Videos by Eugene Khutoryansky (2016)
Source. web.archive.org/web/20181119214326/https://www.bipm.org/utils/common/pdf/CGPM-2018/26th-CGPM-Resolutions.pdf gives it in raw:The breakdown is:
- the unperturbed ground state hyperfine transition frequency of the caesium-133 atom is 9 192 631 770 Hz
- the speed of light in vacuum c is 299 792 458 m/s
- the Planck constant h is 6.626 070 15 × J s
- the elementary charge e is 1.602 176 634 × C
- the Boltzmann constant k is 1.380 649 × J/K
- the Avogadro constant NA is 6.022 140 76 × mol
- the luminous efficacy of monochromatic radiation of frequency 540 × 1012 Hz, Kcd, is 683 lm/W,
- actually use some physical constant:
the unperturbed ground state hyperfine transition frequency of the caesium-133 atom is 9 192 631 770 Hz
Defines the second in terms of caesium-133 experiments. The beauty of this definition is that we only have to count an integer number of discrete events, which is what allows us to make things precise.the speed of light in vacuum c is 299 792 458 m/s
Defines the meter in terms of speed of light experiments. We already had the second from the previous definition.the Planck constant h is 6.626 070 15 × J s
the elementary charge e is 1.602 176 634 × C
- arbitrary definitions based on the above just to match historical values as well as possible:
the Boltzmann constant k is 1.380 649 × J/K
the Avogadro constant NA is 6.022 140 76 × mol
the luminous efficacy of monochromatic radiation of frequency 540 × 1012 Hz, Kcd, is 683 lm/W
Five votes:
All but president are per state. Official list seems to be e.g. for Sao Paulo: divulgacandcontas.tse.jus.br/divulga/#/estados/2022/2040602022/SP/candidatos
The Google Story suggests that this practice existed in academia, where it was brought from. But I can't find external references to it easily:
At Google, the preference is for working in small teams of three, with individual employees expected to allot 20 percent of their time to exploring whatever ideas interest them most. The notion of "20 percent time" is borrowed from the academic world, where professors are given one day a week to pursue private interests.
3ad6677303fb6f700a4f2f977fe86e5324e0ddb0d3b33a649e513d7e88904e85 Updated 2025-07-11 +Created 1970-01-01
This contains various outputs that seem trivially spendable in a made up of two non-zero constants, e.g.:Or are we missing something? The values are quite small and wouldn't be worth it the miner fees most likely. But is there a fundamental reason why this couldn't be spent by a non-standard miner?
{
"value": 0.00002000,
"n": 9,
"scriptPubKey": {
"asm": "1 8fe61f026c7545a99c6e0f37a5a7eceee5fdf6723c1994ccbfb740556632e9fe",
"desc": "rawtr(8fe61f026c7545a99c6e0f37a5a7eceee5fdf6723c1994ccbfb740556632e9fe)#lxgt8lak",
"hex": "51208fe61f026c7545a99c6e0f37a5a7eceee5fdf6723c1994ccbfb740556632e9fe",
"address": "bc1p3lnp7qnvw4z6n8rwpum6tflvamjlmanj8svefn9lkaq92e3ja8lqcc8mcx",
"type": "witness_v1_taproot"
}
}, Sponsor Ciro Santilli's work on OurBigBook.com Financial crime preventive measures Updated 2025-07-11 +Created 1970-01-01
Crazy shady crypto people seem to like Ciro Santilli, so this is in order.
Giving to Ciro Santilli is the worst possible way to launder your money, as donations amounts are clearly publicly disclosed (though not donor identities if they with to remain anonymous), and clear records kept of every donation made (including private note of donor identities if known). Also suspicious donations are promptly reported to the authorities.
Donation refunds upon donor's requests are only made at our discretion, and may be declined, unless required by law of course. This is to reduce the risks of us unknowingly serving as money mules or aiding money laundering.
Ciro Santilli believes that he is not require to report large donations to either:But note that Ciro will preventively report if there are any further suspicious aspects to any donations received.
- charities have to report anonymous donations of £25,000 or more as "serious incident", but Ciro Santilli does not have a registered charity: www.gov.uk/guidance/how-to-report-a-serious-incident-in-your-charity, related: docs.ourbigbook.com/project-governance
- dealers selling goods over 10,000 euros for cash must make a Suspicious Activity Report (SAR) www.gov.uk/guidance/money-laundering-regulations-high-value-dealer-registration. However Ciro Santilli does not sell any goods, only provides services, and services are excluded from the report requirements
Where blog is taken in a wide sense, including e.g. Medium, WordPress, Facebook, Twitter, etc., etc.
The main shortcoming of blogs is the lack of topic convergence across blogs. Each blog is a moderated castle. So who is the best user for a given topic, or the best content for a given tag, across the entire website?
The only reasonable free material we have for advanced subjects nowadays are university lecture notes.
While some of those are awesome, when writing a large content, no one can keep quality high across all sections, there will always be knowledge that you don't have which is enlightening. And Googlers are more often than not interested only in specific sections of your content.
Our website aims to make smaller subjects vertically curated across horizontal single author tutorials.
MIT calculus course UCLA calculus course
* Calculus <---> * Calculus
* Limit <---> * Limit
* Limit of a function
* Limit of a series <---> * Limit of a series
* Derivative <---> * Derivative
* L'Hôpital's rule
* Integral <---> * IntegralSome more links:
- prose.sh/ multiblog, the only feature is easy of publishing from CLI
There are unlisted articles, also show them or only show them.