One of Satoshi's email addresses, it's how he made the First public announcement of Bitoin on first public announcement of Bitcoin on 2008-10-31.
At some point later on vistomail.com was discontinued and acquired by a super dodgy dude, Alex Elbanna, so it hasn't been Satoshi for a while.
In some systems, e.g. including Metamath, modus ponens alone tends to be enough, everything else can be defined based on it.
www.unilad.com/technology/erik-finman-bitcoin-12-year-old-millionaire-invest-798094-20231207
Shame that he seems to be a American exceptionalism idiot. Perhaps it was inevitable given his circonstances. After a small market crash: x.com/erikfinman/status/1820457023013626322.
Opportunities like this come across only once every few years.This ain’t financial advice…But if you got the cash.Never bet against America
Effect of a change of basis on the matrix of a bilinear form by 
Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16If is the change of basis matrix, then the matrix representation of a bilinear form that looked like:then the matrix in the new basis is:Sylvester's law of inertia then tells us that the number of positive, negative and 0 eigenvalues of both of those matrices is the same.
Proof: the value of a given bilinear form cannot change due to a change of basis, since the bilinear form is just a function, and does not depend on the choice of basis. The only thing that change is the matrix representation of the form. Therefore, we must have:and in the new basis:and so since:
Most definitions tend to be bilinear forms.
We use the unqualified generally refers to the dot product of Real coordinate spaces, which is a positive definite symmetric bilinear form. Other important examples include:The rest of this section is about the case.
- the complex dot product, which is not strictly symmetric nor linear, but it is positive definite
- Minkowski inner product, sometimes called" "Minkowski dot product is not positive definite
The positive definite part of the definition likely comes in because we are so familiar with metric spaces, which requires a positive norm in the norm induced by an inner product.
The default Euclidean space definition, we use the matrix representation of a symmetric bilinear form as the identity matrix, e.g. in :so that:
medium.com/left-right/the-education-system-is-about-to-implode-5c95f774b523 The Education System is About to Implode by Nicholas Budny (2020)
Stanford, MIT, Harvard and Oxford are luxury goods in the same sense that a Mercedes-Benz might be, or the latest iPhone. They sell an aesthetic experience that provides the consumer with social status, similar to acquiring expensive clothes or a fancy house.
Bar scene from Good Will Hunting
. Source. This scene is way way overdone. But:Is it mega fast? Nope
Does it work? Yup.
For positive definite matrices only.
TODO application.
www.studentclustercompetition.us/ comments:
The HPCG benchmark uses a preconditioned conjugate gradient (PCG) algorithm to measure the performance of HPC platforms with respect to frequently observed but challenging patterns of computing, communication, and memory access. While HPL provides an optimistic performance target for applications, HPCG can be considered as a lower bound on performance. Many of the top 500 supercomputers also provide their HPCG performance as a reference.
- math.stackexchange.com/questions/23312/what-is-the-importance-of-eigenvalues-eigenvectors/3503875#3503875
- math.stackexchange.com/questions/1520832/real-life-examples-for-eigenvalues-eigenvectors
- matheducators.stackexchange.com/questions/520/what-is-a-good-motivation-showcase-for-a-student-for-the-study-of-eigenvalues
Every invertible matrix can be written as:where:Note therefore that this decomposition is unique up to swapping the order of eigenvectors. We could fix a canonical form by sorting eigenvectors from smallest to largest in the case of a real number.
- is a diagonal matrix containing the eigenvalues of
- columns of are eigenvectors of
Intuitively, Note that this is just the change of basis formula, and so:
- changes basis to align to the eigenvectors
- multiplies eigenvectors simply by eigenvalues
- changes back to the original basis
ASCII art of a Force of Will, a famous and powerful Magic: The Gathering card first printed in 1996.
This is Ciro Santilli's personal favorite ASCII art he has found in the blockchain so far. Also Ciro could not find any other previous source of this, so there is some chance it is original. One can dream.
The choice of card is probably linked to the function of the card in the game of Magic: The Gathering. This card essentially prevents the opponent from casting a spell they are about to cast. The presumed intended meaning of this art is further accentuated by the old card type term "interrupt" (late renamed to "instant"), which suggests that "this ASCII art is an interruption to the normal monetary transactions of the blockchain".
One of also reminded of the prayer wars interruption attempts. We could not however identify anything specific that this ASCII art might have tried to interrupt besides the normal flow of monetary transactions.
If one goes full art critic mode, it is also tempting to draw a parallel between the card's "You may pay 1 life" alternative casting cost (as opposed to 5 mana, 3 and two blue, which is a very large cost for most games) as being a reference to the money spent by the uploader of the art to upload it.
TODO understand exactly how it was encoded and why it is so weird. The
UUUU has a slightly weird encoding which we fixed by hand here TODO understand. -------------------------------------
| Force of Will 3 U U |
| --------------------------------- |
| | //////////// | |
| | ////() ()\////\ | |
| | ///_\ (--) \///\ | |
| | ) //// \_____///\\ | |
| | ) \ / / / / | |
| | ) / \ | | / _/ | |
| | ) \ ( ( / / / / \ | |
| | / ) ( ) / ( )/( ) \ | |
| | \(_)/(_)/ /UUUU \ \\\/ | | |
| .---------------------------------. |
| Interrupt |
| ,---------------------------------, |
| | You may pay 1 life and remove a | |
| | blue card in your hand from the | |
| | game instead of paying Force of | |
| | Will's casting cost. Effects | |
| | that prevent or redirect damage | |
| | cannot be used to counter this | |
| | loss of life. | |
| | Counter target spell. | |
| `---------------------------------` |
| l
| Illus. Terese Nelsen |
-------------------------------------
Force of Will Magic: The Gathering card (Alliances)
Source. A high resolution scan of the original card depicted in the ASCII art for comparison.The following two ASCII transactions:suggest this ASCII art might have been uploaded by Figure "Erich Erstu", AKA Hyena, creator of cryptograffiti.info, a service which would have allowed uploading ASCII content to the blockchain.
tx 0f05c47a8caafadecc10d70ba3bf010eaf6bb416b5e1ad7b01cf3445f5fb7a1c
I am. Therefore, I have come to be.
-- Hyena
tx e6d48f6912929a58a2ee30c13768058777d8547215c27109b5cb0724e7abaaba
Erich,
Bro, this looks excellent!!
-DurielThe only other mention of "Duriel" in the blockchain is tx 140562ceb42fc8943fa52ccc0ddbb11ca2d88dae9b5240d7a4b46864538c515a which has some freedom of speech comments and gives the email:paystamper.com was some other blockchain service from circa 2015:
Duriel@paystamper.com = 1HcuhfTAiQCt6KdMG2rZLXsTcKYj9nLDhSAll found so far are also reproduced at: asciiart.website/index.php?art=people/naked%20ladies therefore not blockchain original.
- tx 9206ec2a41846709a59cafb406dd7b07082bfc27664bbc5c6d4df310c1e1b91f block 290848 (2014-03-16) via cryptograffiti.info: sexually aroused naked woman sitting looking forward with legs open showing her vagina. Vagina row as an identifier for Ctrl + F:A bit bellow tx 8367a48e4a863e37b3749bc9c111327b07a7c383ec9b3e7ce8d41949e71e1c10 has a large hand showing the middle finger and wearing a watch:
. `. .\x./-`--...../' ; :Reproduced e.g. at: www.textartcopy.com/ascii-middle-finger.html/"\ |\./| | | | | |>~<| | | /'\| |/'\.. /~\| | | | \ [ | | | | \ | | | | | \ | ~ ~ ~ ~ |` ) | / \ / \ / \ / |--//''`\--| | (( +==)) | |--\_|_//--| - tx 0aab36554c2ac5ec23747e7f21f75dbe3f16739134cf44953ad7ac98927146d6 block 322920 (2014-09-28) via cryptograffiti.info: naked woman laying on her side showing her vagina from under her legs, signed
fsc. Vagina row:Fully reproduced e.g. at www.asciiart.eu/people/sexual/women which credits the art to a "Marcin Glinski" (Polish: Marcin Gliński), possibly this dude github.com/silentlamb/ASCII-Arts | www.linkedin.com/in/marcinglinski)The signature is also listed at www.asciiart.eu/ascii-artists/who-is-who for example.`-:/"-7.--"" _::.-'P::.. \} - tx 66826fccef3e3ebb34abce25bfeff8f9dcaaf88e4707a5576c494d8a1cf1681a block 388714 (2015-12-16) has a one liner penis and breasts:soon followed by more breasts at 37c1e90c6ce3e648c51bfa38cbb43e996cd46e038517596d4c90ca2a6425a701:
jEW B====D ( . Y . )Found by Messages from the mines.jEW ( . Y . )TIDDIES( . Y . )
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