Hardcoded and unique network addresses for every single device on Earth.
Started with 48 bits (6 bytes), usually given as 01:23:45:67:89:AB but people now encouraged to use 64-bit ones.
How they are assigned: www.quora.com/How-are-MAC-addresses-assigned Basically IEEE gives out the 3 first bytes to device manufacturers that register, this is called the organizationally unique identifier, and then each manufacturer keeps their own devices unique.
Like PCR, but does not require thermal cycling. Thus the "isothermal" in the name: iso means same, so "same temperature".
Not needing the thermo cycling means that the equipment needed is much smaller and cheaper it seems.
Published by Werner Heisenberg in 1925-07-25 as quantum mechanical re-interpretation of kinematic and mechanical relations by Heisenberg (1925), it offered the first general formulation of quantum mechanics.
It is apparently more closely related to the ladder operator method, which is a more algebraic than the more analytical Schrödinger equation.
It appears that this formulation makes the importance of the Poisson bracket clear, and explains why physicists are so obsessed with talking about position and momentum space. This point of view also apparently makes it clearer that quantum mechanics can be seen as a generalization of classical mechanics through the Hamiltonian.
QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga by Silvan Schweber (1994) mentions however that relativistic quantum mechanics broke that analogy, because some 2x2 matrix had a different form, TODO find that again.
Inward Bound by Abraham Pais (1988) chapter 12 "Quantum mechanics, an essay" part (c) "A chronology" has some ultra brief, but worthwhile mentions of matrix mechanics and the commutator.
You need separate accounts for different countries: money.stackexchange.com/questions/73361/two-banks-in-two-countries-is-it-possible-to-have-a-unique-paypal-account it's a pain.
This was the original name of Google Search.
One wonders if this name has some influence from the LGBT culture in San Francisco! The sexual innuendo is palpable.
"Back" is of course a reference to "backlinks", since Google Search relies on incoming links (AKA backlinks) to a webpage to determine its importance.
Bibliography: discuss.bbchallenge.org/t/decider-cyclers/33
Example: bbchallenge.org/279081.
These are very simple, they just check for exact state repetitions, which obviously imply that they will run forever.
Unfortunately, cyclers may need to run through an initial setup phase before reaching the initial cycle point, which is not very elegant.
Top one: OurBigBook.com.
The wave equation contains the entire state of a particle.
From mathematical formulation of quantum mechanics remember that the wave equation is a vector in Hilbert space.
And a single vector can be represented in many different ways in different basis, and two of those ways happen to be the position and the momentum representations.
More importantly, position and momentum are first and foremost operators associated with observables: the position operator and the momentum operator. And both of their eigenvalue sets form a basis of the Hilbert space according to the spectral theorem.
When you represent a wave equation as a function, you have to say what the variable of the function means. And depending on weather you say "it means position" or "it means momentum", the position and momentum operators will be written differently.
This is well shown at: Video "Visualization of Quantum Physics (Quantum Mechanics) by udiprod (2017)".
Furthermore, the position and momentum representations are equivalent: one is the Fourier transform of the other: position and momentum space. Remember that notably we can always take the Fourier transform of a function in due to Carleson's theorem.
Then the uncertainty principle follows immediately from a general property of the Fourier transform: en.wikipedia.org/w/index.php?title=Fourier_transform&oldid=961707157#Uncertainty_principle
In precise terms, the uncertainty principle talks about the standard deviation of two measures.
We can visualize the uncertainty principle more intuitively by thinking of a wave function that is a real flat top bump function with a flat top in 1D. We can then change the width of the support, but when we do that, the top goes higher to keep probability equal to 1. The momentum is 0 everywhere, except in the edges of the support. Then:
- to localize the wave in space at position 0 to reduce the space uncertainty, we have to reduce the support. However, doing so makes the momentum variation on the edges more and more important, as the slope will go up and down faster (higher top, and less x space for descent), leading to a larger variance (note that average momentum is still 0, due to to symmetry of the bump function)
- to localize the momentum as much as possible at 0, we can make the support wider and wider. This makes the bumps at the edges smaller and smaller. However, this also obviously delocalises the wave function more and more, increasing the variance of x
Bibliography:
- www.youtube.com/watch?v=bIIjIZBKgtI&list=PL54DF0652B30D99A4&index=59 "K2. Heisenberg Uncertainty Relation" by doctorphys (2011)
- physics.stackexchange.com/questions/132111/uncertainty-principle-intuition Uncertainty Principle Intuition on Physics Stack Exchange
Like all poor countries, Brazil's lack of money and scientific culture severely limit its ability to make technological and scientific advances.
While this sounds obvious, Ciro Santilli has felt it first hand since he moved from Brazil to Europe, and it is just shocking.
Physics education needs more focus on understanding experiments and their history by 
Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16This is the only way to truly understand and appreciate the subject.
Understanding the experiments gets intimately entangled with basically learning the history of physics, which is extremely beneficial as also highlighted by Ron Maimon, related: there is value in tutorials written by early pioneers of the field.
In the Surely You're Joking, Mr. Feynman chapter O Americano, Outra Vez! Richard Feynman describes his experience teaching in Brazil in the early 1950s, and how everything was memorized, without any explanation of the experiments or that the theory has some relationship to the real world!
Although things have improved considerably since in Brazil, Ciro still feels that some areas of physics are still taught without enough experiments described upfront. Notably, ironically, quantum field theory, which is where Feynman himself worked.
Feynman gave huge importance to understanding and explaining experiments, as can also be seen on Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979).
'Making' - the best way of learning science and technology by Manish Jain (2018)
Source. Uses the frequency of the hyperfine structure of caesium-133 ground state, i.e spin up vs spin down of its valence electron , to define the second.
International System of Units definition of the second since 1967, because this is what atomic clocks use.
TODO why does this have more energy than the hyperfine split of the hydrogen line given that it is further from the nucleus?
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