Sometimes you get annoyed to death with your bike not breaking or changing gears perfectly as you would like, and the people at the bike shop never do the job well enough.
The problem with bike shops is that the employees are already swamped with work, and they don't get paid any extra for doing more work.
As a result, paradoxically, they are often happier, and respect you more if you are trying to get them to help you to fix your own bike!
Also, for the same reason, they don't have the time to go for a quick test ride after a fix to ensure that the bug was actually fixed.
So they ignore things that would obviously be huge ridability benefits (although they might not be obvious to newbie customers), for which customers would gladly pay more money for.
But you start to learn how to do stuff yourself and it feel amazing when you finally get there (after infinite trial and error).
Ciro dreams of a bike shop that actually calls you for the appointment and then teaches you how to fix the thing.
What poor countries have to do to get richer Teach everyone English by 
Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16This is obviously the most efficient investment any non-English speaking country must do, because you need to know English to be able to learn from rich countries and innovate.
Further discussion at: Section "Having more than one natural language is bad for the world".
In this section we will gather some more advanced ideas besides the basic features described at how the website works.
The projects you do must always aim to achieving some novel result.
You don't have to necessarily reach it. But you must aim for it.
Novel result can be taken broadly.
But there must be something to your project that has never been done before.
You can start by reproducing other's work.
Ciro Santilli's hardware Panasonic NN-SF464M microwave (2017) by Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16As of 2018-12, I believe that I might have fried the UART on this board when I burnt my last UART to USB converter by connecting ground to 5V.
Linux kernel logs don't show, but do show with the exact same components on the Pi 3 (SD card with
enable_uart=1 + image Raspbian Lite 2018-11-03 and UART cables).Serial from
cat /proc/cpuinfo: 00000000a50c1f69Datasheets: Raspberry Pi 2.
It does not matter how, if it is exact, or numerical, or a message from God: a number has to come out of the formulas in the end, and you have to compare it with the experimental data.
Many theoretical physicists seem to forget this in their lectures, see also: Section "How to teach and learn physics".
Unit of mass.
Defined in the 2019 redefinition of the SI base units via the Planck constant. This was possible due to the development of the Kibble balance.
A suggested at Physics from Symmetry by Jakob Schwichtenberg (2015) chapter 3.9 "Elementary particles", it appears that in the Standard Model, the behaviour of each particle can be uniquely defined by the following five numbers:
Once you specify these properties, you could in theory just pluck them into the Standard Model Lagrangian and you could simulate what happens.
Setting new random values for those properties would also allow us to create new particles. It appears unknown why we only see the particles that we do, and why they have the values of properties they have.
Funding:
- 2023: 1.1m pounds www.uktech.news/deep-tech/lumai-grant-20230215
Solving the Schrodinger equation with the time-independent Schrödinger equation by Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16Before reading any further, you must understand heat equation solution with Fourier series, which uses separation of variables.
Once that example is clear, we see that the exact same separation of variables can be done to the Schrödinger equation. If we name the constant of the separation of variables for energy, we get:
- a time-only part that does not depend on space and does not depend on the Hamiltonian at all. The solution for this part is therefore always the same exponentials for any problem, and this part is therefore "boring":
- a space-only part that does not depend on time, bud does depend on the Hamiltonian:Since this is the only non-trivial part, unlike the time part which is trivial, this spacial part is just called "the time-independent Schrodinger equation".Note that the here is not the same as the in the time-dependent Schrodinger equation of course, as that psi is the result of the multiplication of the time and space parts. This is a bit of imprecise terminology, but hey, physics.
Because the time part of the equation is always the same and always trivial to solve, all we have to do to actually solve the Schrodinger equation is to solve the time independent one, and then we can construct the full solution trivially.
Once we've solved the time-independent part for each possible , we can construct a solution exactly as we did in heat equation solution with Fourier series: we make a weighted sum over all possible to match the initial condition, which is analogous to the Fourier series in the case of the heat equation to reach a final full solution:
- if there are only discretely many possible values of , each possible energy . we proceed and this is a solution by selecting such that at time we match the initial condition:A finite spectrum shows up in many incredibly important cases:Equation 3.Solution of the Schrodinger equation in terms of the time-independent and time dependent parts.
- if there are infinitely many values of E, we do something analogous but with an integral instead of a sum. This is called the continuous spectrum. One notable
The fact that this approximation of the initial condition is always possible from is mathematically proven by some version of the spectral theorem based on the fact that The Schrodinger equation Hamiltonian has to be Hermitian and therefore behaves nicely.
It is interesting to note that solving the time-independent Schrodinger equation can also be seen exactly as an eigenvalue equation where:The only difference from usual matrix eigenvectors is that we are now dealing with an infinite dimensional vector space.
- the Hamiltonian is a linear operator
- the value of the energy
Eis an eigenvalue
Furthermore:
- we immediately see from the equation that the time-independent solutions are states of deterministic energy because the energy is an eigenvalue of the Hamiltonian operator
- by looking at Equation 3. "Solution of the Schrodinger equation in terms of the time-independent and time dependent parts", it is obvious that if we take an energy measurement, the probability of each result never changes with time, because it is only multiplied by a constant
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!
Intro to OurBigBook
. Source. We have two killer features:
- 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-calculusArticles 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/derivativeVideo 2. OurBigBook Web topics demo. Source. - 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.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 3. Visual Studio Code extension installation.
Figure 4. Visual Studio Code extension tree navigation.
Figure 5. Web editor. 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.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. 
- Infinitely deep tables of contents:
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