Tom Lehrer is an American singer-songwriter, pianist, and mathematical scientist, known for his satirical and humorous songs. He gained popularity in the 1950s and 1960s for his witty lyrics, which often addressed social and political issues, presenting them in a comedic light.
Physics by Ciro Santilli 37 Updated 2025-07-16
Physics (like all well done science) is the art of predicting the future by modelling the world with mathematics.
And predicting the future is the first step towards controlling it, i.e.: engineering.
Ciro Santilli doesn't know physics. He writes about it partly to start playing with some scientific content for: OurBigBook.com, partly because this stuff is just amazingly beautiful.
Ciro's main intellectual physics fetishes are to learn quantum electrodynamics (understanding the point of Lie groups being a subpart of that) and condensed matter physics.
Every science is Physics in disguise, but the number of objects in the real world is so large that we can't solve the real equations in practice.
Luckily, due to emergence, we can use uglier higher level approximations of the world to solve many problems, with the complex limits of applicability of those approximations.
Therefore, such higher level approximations are highly specialized, and given different names such as:
As of 2019, all known physics can be described by two theories:
Unifying those two into the theory of everything one of the major goals of modern physics.
Figure 1.
xkcd 435: Fields arranged by purity
. Source. Reductionism comes to mind.
Figure 2.
Physically accurate genie by Psychomic
. Source. This sane square composition from: www.reddit.com/r/funny/comments/u08dw3/nice_guy_genie/.
You don't need to understand the from first principles derivation of every single phenomena.
And most important of all: you should not start learning phenomena by reading the from first principles derivation.
Instead, you should see what happens in experiments, and how matches some known formula (which hopefully has been derived from first principles).
Only open the boxes (understand from first principles derivation) if the need is felt!
E.g.:
Physics is all about predicting the future. If you can predict the future with an end result, that's already predicting the future, and valid.
PuntSeq is a side project led by a few University of Cambridge PhDs that aims to determine which bacteria are present in the River Cam.
In July 2019, the PuntSeq team got together with the awesome Cambridge Biomakespace, an awesome biology makerspace open to all, to create a two day science outreach activity showing their procedures.
The data collected in this experiment, together with other collection sessions done by the organizers actually led to a publication on eLife: elifesciences.org/articles/61504 "Freshwater monitoring by nanopore sequencing" by Lara Urban et al. (2021), so it is awesome to see that were are actual being part of "real science".
Ciro knows nothing about biology, but since he is very curious about it, he jumped at this opportunity, and decided to document things as well as his limited knowledge would allow.
All participants chipped in some money to help cover the experiment's costs. Ciro suspects that this activity was done partially to help crowdfund the experiment, but it was a worthy investment!
The impressions you get from the experiment as a software engineer will be:
  • OMG, this is so labour intensive, why haven't they automated this
  • OMG, this is frightening, all the 8 hours of work I've just done are present in that tiny plastic tube
  • Amazing! Look at that apparatus! And the bio people are like: I've used this a million times, it's cheap and every lab has one, just work faster and don't break you piece of junk!
One of the Holiest age old debugging techniques!
The cool thing about bisection is that it is a brainless process: unlike when using a debugger, you don't have to understand anything about the system, and it incredibly narrows down the problem cause for you. Not having to think is great!
Special relativity by Ciro Santilli 37 Updated 2025-07-16
This was first best observed by the Michelson-Morley experiment, which uses the movement of the Earth at different times of the year to try and detect differences in the speed of light.
This leads leads to the following conclusions:
All of this goes of course completely against our daily Physics intuition.
The "special" in the name refers to the fact that it is a superset of general relativity, which also explains gravity in a single framework.
Since time and space get all messed up together, you have to be very careful to understand what it means to say "I observed this to happen over there at that time", otherwise you will go crazy. A good way to think about is this:
  • use Einstein synchronization to setup a bunch of clocks for every position in your frame of reference
  • on every point of space, you put a little detector which records events and the time of the event
  • each detector can only detect events locally, i.e. events that happen very close to the detector
  • then, after the event, the detectors can send a signal to you, who is sitting at the origin, telling you what they detected
Twin paradox by Ciro Santilli 37 Updated 2025-07-16
The key question is: why is this not symmetrical?
One answer is: because one of the twin accelerates, and therefore changes inertial frames.
But the better answer is: understand what happens when the stationary twin sends light signals at constant time intervals to each other. When does the travelling twin receives them?
By doing that, we see that "all the extra aging happens immediately when the twin turns around":
  • on the out trip, both twins receive signals at constant intervals
  • when the moving twin turns around and starts to accelerate through different inertial frames, shit happens:
    • the moving twin suddenly notices that the rate of signals from the stationary twin increased. They are getting older faster than us!
    • the stationary twin suddenly notices that the rate of signals from the moving twin decreased. They are getting older slower than us!
  • then when the moving twin reaches the return velocity, both see constant signal rates once again
Figure 1.
Twin paradox illustration with twins sending light signals at regular intervals
. Source.
Another way of understanding it is: you have to make all calculations on a single inertial frame for the entire trip.
Supposing the sibling quickly accelerates out (or magically starts moving at constant speed), travels at constant speed, and quickly accelerates back, and travels at constant speed setup, there are three frames that seem reasonable:
  • the frame of the non-accelerating sibling
  • the outgoing trip of the accelerating sibling
  • the return trip of the accelerating sibling
If you do that, all three calculations give the exact same result, which is reassuring.
Another way to understand it is to do explicit integrations of the acceleration: physics.stackexchange.com/questions/242043/what-is-the-proper-way-to-explain-the-twin-paradox/242044#242044 This is the least insightful however :-)
Bibliography:
Omniscient debugging by Ciro Santilli 37 Updated 2025-07-16
What it adds on top of reverse debugging: not only can you go back in time, but you can do it instantaneously.
Or in other words, you can access variables from any point in execution.
TODO implementation? Apparently Pernosco is an attempt at it, though proprietary.
Pernosco by Ciro Santilli 37 Updated 2025-07-16
Proprietary extension to Mozilla rr by rr lead coder Robert O'Callahan et. al, started in 2016 after he quit Mozilla.
Middle name by Ciro Santilli 37 Updated 2025-07-16
Middle names are a weird custom.
It's like a semi-secret part of your name that you only randomly use sometimes, and usually only in initials, and which no one else knows except your family.
It is as if the Anglo-Saxons were preparing for a real world Death Note attack I know your true name-style.
SVG 1.2 by Ciro Santilli 37 Updated 2025-07-16
Dropped in favor of SVG 2.
The term "Levi-Civita field" does not correspond to a well-defined concept widely recognized in mathematics or physics. However, it seems like you might be referring to a couple of distinct but related concepts: the Levi-Civita symbol (or tensor) and the Levi-Civita connection in the context of differential geometry.
The Stable Ocean Hypothesis is a scientific concept related to the stability and regulation of Earth's climate through oceanic processes. It posits that during certain geological periods, the ocean's physical and chemical properties, such as temperature, salinity, and circulation patterns, are maintained in a stable state, which in turn has significant implications for global climate, marine ecosystems, and atmospheric conditions.

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