He was at Fairchild. That place was nuts.
In many important applications, what you have to solve is not just a single partial differential equation, but multiple partial differential equations coupled to each other. This is the case for many key PDEs including:
Solving differential equations was apparently Lie's original motivation for developing Lie groups. It is therefore likely one of the most understandable ways to approach it.
It appears that Lie's goal was to understand when can a differential equation have an explicitly written solution, much like Galois theory had done for algebraic equations. Both approaches use symmetry as the key tool.
- www.researchgate.net/profile/Michael_Frewer/publication/269465435_Lie-Groups_as_a_Tool_for_Solving_Differential_Equations/links/548cbf250cf214269f20e267/Lie-Groups-as-a-Tool-for-Solving-Differential-Equations.pdf Lie-Groups as a Tool for Solving Differential Equations by Michael Frewer. Slides with good examples.
It resists to change in electric current. Well seen at: Video "LC circuit by Eugene Khutoryansky (2016)".
Happening multiple times a day on Ubuntu 22.04 for Chromium, even though I turn computer on and off daily, unbearable:
- askubuntu.com/questions/1412575/pending-update-of-snap-store
- askubuntu.com/questions/1412140/pending-update-of-firefox-snap-close-the-app-to-avoid-disruptions
- forum.snapcraft.io/t/how-to-disable-snapd-update-notifications-permanently/31117 Settings > Notifications > Snapd User Session Agent
- www.reddit.com/r/Ubuntu/comments/v1s919/disable_pending_update_of_snap_message_kiosk/
- forum.snapcraft.io/t/refresh-app-awareness-call-for-testing/29123
Very very good. Those nice pre-Dot-com bubble vibes.
Might be freely watchable? Wikipedia links to:
But they do start with an FBI warning about copyright. So... erm.
Part 1 - Networking The Nerds talks about the TCP/IP and early machines implementing it:
- 21:00: shows inside The Pentagon. The way the dude who works there opens a his locked office door with an electric switch is just amazing. Cringely also mentions that there's an actual official speed limit in the corridors as he rides a carrier bike slowly through them.
- 21:45: the universities weren't enthusiastic, because people from other locations would be able to use your precious computer time. But finally ARPA forced the universities' hands, and they joined.
- 24:24 mentions that some of the guys who created ARPANET were actually previously counting cards at Casinos in Las Vegas, just like in the 21 (2008) film
- one of the centerpieces of development was at UCLA. The other was the BBN company. 33:55 shows the first router, then called them Interface Message Processor
- the first message was from UCLA to Stanford University. He was trying to write "Login", and it crashed at the 'g'. Epic. They later debugged it.
- towards the end talks about ALOHAnet, the first wireless computer communication done
Part 2 - Serving the Suits
- Robert Metcalfe. He's nice. Xerox PARC. Ethernet.
- Explains what is a "Workstation", notably showing one by Sun Microsystems. This is now an obscure "passé" thing in 2020 that young people like Ciro Santilli have only heard of in legend (or in outdated university computer labs!). Funny to think that so many people have had this idea before, including e.g. the Chromebook
- 10:46 mentions that all of Cisco, Silicon Graphics and Sun Microsystems and where founded at Margaret Jacks Hall, Building 460, at Stanford University.
- he then talks a lot about Sun. Sun became dominant in Wall Street.
- 19:05: Novell, from Utah. How they almost went bust, but were saved at the last moment by Ray Noorda, who refocused them to their NetWare product which was under recent development. It allowed file and printer sharing in IBM PCs. 22:55 shows how they had a live radio host for people waiting on customer support calls!
- 33:56 mentions how The Grateful Dead had in impact on the Internet, as people wanted computers to be able to access The WELL online forum. They still own the domain as of 2022: www.well.com/. It is interesting how Larry Page also liked The Grateful Dead as mentioned at The Google Story, his dad would take him to shows. Larry is a bit younger of course than the people in this documentary.
- 37 show McAfee
- 43:56: fantastic portrait of Cisco
Part 3 - Wiring the World:
- Berners-Lee at CERN and the invention of the URL.
- 1992: US Government allow commerce on the Internet
- Web browser history, Mosaic and Marc Andresseeen.
- 20:45: America Online
- 23:29: search engines and Excite. Google was a bit too small to be on his radar!
- 25:50: porn
- 27: The Motley Fool and advertising
- 30: Planet U grocery shopping
- 31:50: Amazon
- 33:00: immigrant workers, Indians playing cricket, outsourcing, Wipro Systems
- 41:25: Java
- 46:30: Microsoft joins the Internet. The Internet Tidal Wave Internet memo. Pearl Harbour day talk.
- 56:40: Excite Tour. If they had survived, they would have been Google with their quirky offices.
We don't need to understand a super generalized version of tensor products to know what they mean in basic quantum computing!
Intuitively, taking a tensor product of two qubits simply means putting them together on the same quantum system/computer.
The quantum state is called a separable state, because it can be written as a single product of two different qubits. We have simply brought two qubits together, without making them interact.
If we then add a CNOT gate to make a Bell state:we can now see that the Bell state is non-separable: we've made the two qubits interact, and there is no way to write this state with a single tensor product. The qubits are fundamentally entangled.
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