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This point is beautifully argued in lots of different sources, and is clearly a pillar of AGI.
Perhaps one may argue that our deep learning layers do form some kind of hierarchy, e.g. this is very clear in certain models such as convolutional neural network. But many of those models cannot have arbitrarily deep hierarchies, which appears to be a fundamental aspect of intelligence.
How to Create a Mind:
The lists of steps in my mind are organized in hierarchies. I follow a routine procedure before going to sleep. The first step is to brush my teeth. But this action is in turn broken into a smaller series of steps, the first of which is to put toothpaste on the toothbrush. That step in turn is made up of yet smaller steps, such as finding the toothpaste, removing the cap, and so on. The step of finding the toothpaste also has steps, the first of which is to open the bathroom cabinet. That step in turn requires steps, the first of which is to grab the outside of the cabinet door. This nesting actually continues down to a very fine grain of movements, so that there are literally thousands of little actions constituting my nighttime routine. Although I may have difficulty remembering details of a walk I took just a few hours ago, I have no difficulty recalling all of these many steps in preparing for bed - so much so that I am able to think about other things while I go through these procedures. It is important to point out that this list is not stored as one long list of thousands of steps - rather, each of our routine procedures is remembered as an elaborate hierarchy of nested activities.
Human Compatible: TODO get exact quote. It was something along: life goal: save world from hunger. Subgoal: apply for some grant. Sub-sub-goal: eat, sleep, take shower. Sub-sub-sub-goal: move muscles to get me to table and open a can.
This just works, but it is also so incredibly slow that it is useless (or at least the quality it reaches in the time we have patience to wait from), at least on any setup we've managed to try, including e.g. on an Nvidia A10G on a g5.xlarge. Running:would likely take hours to complete.
time imagine "a house in the forest"As highlighted e.g. at Human Compatible by Stuart J. Russell (2019), this AI alignment intrinsically linked to the idea of utility in economy.
- From Motor Control to Team Play in Simulated Humanoid Football
From Motor Control to Team Play in Simulated Humanoid Football by Ali Eslami (2023)
Source. Likely a reupload by DeepMind employee: www.linkedin.com/in/smalieslami.DeepMind’s AI Trained For 5 Years by Two Minute Papers (2023)
Source. The 5 years bullshit is of course in-game time clickbait, they simulate 1000x faster than realtime.This section is about the definition of the dot product over , which extends the definition of the dot product over .
Some motivation is discussed at: math.stackexchange.com/questions/2459814/what-is-the-dot-product-of-complex-vectors/4300169#4300169
The complex dot product is defined as:
E.g. in :
Just like the usual dot product, this will be a positive definite symmetric bilinear form by definition.
There's no point.
The question remains there, but people lose the ability to help the asker.
Reputation is meaningless regardless, since JavaScript gurus will always have 1000x more readers than low level junkies.
The deeper problem: the existence of multiple separate websites instead of just using the tags on a single website.
Examples:
Discrete Fourier transform of a real signal by 
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01See sections: "Example 1 - N even", "Example 2 - N odd" and "Representation in terms of sines and cosines" of www.statlect.com/matrix-algebra/discrete-Fourier-transform-of-a-real-signal
The transform still has complex numbers.
Summary:Therefore, we only need about half of to represent the signal, as the other half can be derived by conjugation.
- is real
"Representation in terms of sines and cosines" from www.statlect.com/matrix-algebra/discrete-Fourier-transform-of-a-real-signal then gives explicit formulas in terms of .
NumPy for example has "Real FFTs" for this: numpy.org/doc/1.24/reference/routines.fft.html#real-ffts
DFT of with 25 points
. Source at: numpy/fft_plot.py. This plot illustrates how the DFT of a real signal is symmetric around the middle point, and so only half of the transform points are needed to reconstruct the original signal. We also see how the phase of the sinusoids determines if their DFT components are real or imaginary.It is a shame that they refocused to more applied courses. This also highlights their highly "managed" approach to content creation. Their 2022 pitch on front page says it all:they are focused on the highly paid character of many software engineering jobs.
for as few as 10 hours a week, you can get the in-demand skills you need to help land a high-paying tech job
But one cool point of this website is how they hire tutors to help on the courses. This is a very good thing. It is a fair way of monetizing: e-learning websites must keep content free, only charge for certification.
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!
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/derivative - 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 4. Visual Studio Code extension tree navigation.
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.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. - Internal cross file references done right:
- Infinitely deep tables of contents:
Figure 6. Dynamic article tree with infinitely deep table of contents.Live URL: ourbigbook.com/cirosantilli/chordateDescendant 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