Discounts that happen more often than not by 
Ciro Santilli 37 Updated 2025-05-09 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-05-09 +Created 1970-01-01 There is value in tutorials written by beginners by Ciro Santilli 37 Updated 2025-05-09 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-05-09 +Created 1970-01-01Ciro Santilli is a big believer that there is value in tutorials written by beginners, because beginners are more likely to explain things in a way that other beginners can understand.
Even though they make more mistakes, this more approachable point of view can be very valuable.
And mistakes/omissions can be corrected on comments by people with more knowledge, so that the writer also ends up learning something new.
By other people:
- jakobschwichtenberg.com/about/ from Jakob Schwichtenberg mentions quotes C. S. Lewis book "Reflections on the Psalms"[ref]:
It often happens that two schoolboys can solve difficulties in their work for one another better than the master can. [...] The fellow-pupil can help more than the master because he knows less. The difficulty we want him to explain is one he has recently met. The expert met it so long ago he has forgotten. He sees the whole subject, by now, in a different light that he cannot conceive what is really troubling the pupil; he sees a dozen other difficulties which ought to be troubling him but aren't.
Knock knock.
As of 2019, the silicon industry is ending, and molecular biology technology is one of the most promising and growing field of engineering.
Ciro Santilli is especially excited about DNA-related technologies, because DNA is the centerpiece of biology, and it is programmable.
First, during the 2000's, the cost of DNA sequencing fell to about 1000 USD per genome in the end of the 2010's: Figure 2. "Cost per genome vs Moore's law from 2000 to 2019", largely due to "Illumina's" technology.
The medical consequences of this revolution are still trickling down towards medical applications of 2019, inevitably, but somewhat slowly due to tight privacy control of medical records.
Ciro Santilli predicts that when the 100 dollar mark is reached, every person of the First world will have their genome sequenced, and then medical applications will be closer at hand than ever.
But even 100 dollars is not enough. Sequencing power is like computing power: humankind can never have enough. Sequencing is not a one per person thing. For example, as of 2019 tumors are already being sequenced to help understand and treat them, and scientists/doctors will sequence as many tumor cells as budget allows.
Then, in the 2010's, CRISPR/Cas9 gene editing started opening up the way to actually modifying the genome that we could now see through sequencing.
What's next?
Ciro believes that the next step in the revolution could be could be: de novo DNA synthesis.
This technology could be the key to the one of the ultimate dream of biologists: cheap programmable biology with push-button organism bootstrap!
Just imagine this: at the comfort of your own garage, you take some model organism of interest, maybe start humble with Escherichia coli. Then you modify its DNA to your liking, and upload it to a 3D printer sized machine on your workbench, which automatically synthesizes the DNA, and injects into a bootstrapped cell.
You then make experiments to check if the modified cell achieves your desired new properties, e.g. production of some protein, and if not reiterate, just like a software engineer.
Of course, even if we were able to do the bootstrap, the debugging process then becomes key, as visibility is the key limitation of biology, maybe we need other cheap technologies to come in at that point.
This a place point we see the beauty of evolution the brightest: evolution does not require observability. But it also implies that if your changes to the organism make it less fit, then your mutation will also likely be lost. This has to be one of the considerations done when designing your organism.
Other cool topic include:
- computational biology: simulations of cell metabolism, protein and small molecule, including computational protein folding and chemical reactions. This is basically the simulation part of omics.If we could only simulate those, we would basically "solve molecular biology". Just imagine, instead of experimenting for a hole year, the 2021 Nobel Prize in Physiology and Medicine could have been won from a few hours on a supercomputer to determine which protein had the desired properties, using just DNA sequencing as a starting point!
- microscopy: crystallography, cryoEM
- analytical chemistry: mass spectroscopy, single cell analysis (Single-cell RNA sequencing)
Ciro is sad that by the time he dies, humanity won't have understood the human brain, maybe not even a measly Escherichia coli... Heck, even key molecular biology events are not yet fully understood, see e.g. transcription regulation.
One of the most exciting aspects of molecular biology technologies is their relatively low entry cost, compared for example to other areas such as fusion energy and quantum computing.
If you are going to live, you might as well chase one of them.
You might not achieve them in your lifetime, but you never know. At some point, the pieces just "fall into place", and they happen.
And they will all come from deep tech.
Ciro Santilli would like to contribute to them. but this is a bit less realistic than software projects.
And one can at least have some fun by learning deeply about those subjects.
The most important projects done by Ciro Santilli by Ciro Santilli 37 Updated 2025-05-09 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-05-09 +Created 1970-01-01Ciro Santilli has sometimes wasted time with low impact projects such as those listed at Ciro Santilli's minor projects instead of doing higher impact projects such as those mentioned at: Section "The most important projects Ciro Santilli wants to do".
But maybe "Everything you did brought you where you are now." applies, maybe it is during the "low impact activities" that one gets the inspiration and experience required for the "high impact ones".
Kavli Institute for Theoretical Physics by Ciro Santilli 37 Updated 2025-05-09 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-05-09 +Created 1970-01-01Furthermore, TODO confirm it is possible that a solution does not exist at all if and aren't sufficiently small.
This formula is likely the basis for the Lie group-Lie algebra correspondence. With it, we express the actual group operation in terms of the Lie algebra operations.
Notably, remember that a algebra over a field is just a vector space with one extra product operation defined.
Vector spaces are simple because all vector spaces of the same dimension on a given field are isomorphic, so besides the dimension, once we define a Lie bracket, we also define the corresponding Lie group.
Since a group is basically defined by what the group operation does to two arbitrary elements, once we have that defined via the Baker-Campbell-Hausdorff formula, we are basically done defining the group in terms of the algebra.
Relational database management system by Ciro Santilli 37 Updated 2025-05-09 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-05-09 +Created 1970-01-01Per language:
Like everything else in Lie groups, first start with the matrix as discussed at Section "Lie algebra of a matrix Lie group".
Intuitively, a Lie algebra is a simpler object than a Lie group. Without any extra structure, groups can be very complicated non-linear objects. But a Lie algebra is just an algebra over a field, and one with a restricted bilinear map called the Lie bracket, that has to also be alternating and satisfy the Jacobi identity.
Because of the Lie group-Lie algebra correspondence, we know that there is almost a bijection between each Lie group and the corresponding Lie algebra. So it makes sense to try and study the algebra instead of the group itself whenever possible, to try and get insight and proofs in that simpler framework. This is the key reason why people study Lie algebras. One is philosophically reminded of how normal subgroups are a simpler representation of group homomorphisms.
To make things even simpler, because all vector spaces of the same dimension on a given field are isomorphic, the only things we need to specify a Lie group through a Lie algebra are:Note that the Lie bracket can look different under different basis of the Lie algebra however. This is shown for example at Physics from Symmetry by Jakob Schwichtenberg (2015) page 71 for the Lorentz group.
- the dimension
- the Lie bracket
As mentioned at Lie Groups, Physics, and Geometry by Robert Gilmore (2008) Chapter 4 "Lie Algebras", taking the Lie algebra around the identity is mostly a convention, we could treat any other point, and things are more or less equivalent.
Sponsor Ciro Santilli's work on OurBigBook.com 1000 Monero donation Careful what you wish for by Ciro Santilli 37 Updated 2025-05-09 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-05-09 +Created 1970-01-01 Pinned article: ourbigbook/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 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.
Figure 3. Visual Studio Code extension installation.
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. 
- 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