guyomes

For rotations in 3D space, another nice representation is based on antisymmetric matrices [1]. All rotations can be represented as exp(A), where A has the form:

   0  -z   y
   z   0  -x
  -y   x   0

Moreover, this generalizes to other dimensions. This allows to see that in 2D, rotations have one degree of freedom, in 3D they have three, and in 4D they have six.

[1]: https://en.wikipedia.org/wiki/Rotation_matrix#Exponential_ma...

Some research is actually done in this direction. In 2015, a paper showed how a robot can adapt to injuries like a broken leg [1,2].

[1]: https://www.nature.com/articles/nature14422

[2]: https://hal.science/hal-01158243

Some of this activity was actually documented through the alleged data breach of a hacking company [1].

[1]: https://en.wikipedia.org/wiki/Hacking_Team

In the sector of computer chips manufacturing, ASML [0] is a pretty big European tech company.

Also, if we think in term of people instead of companies, many big tech companies have offices in Europe or buy European companies. They employ European people with tech skills and productivity that seem good enough for those tech companies. So we can say that European people also make products that the average person uses often, even though their company is not labeled as European.

Mostly I think that scientific education level is an important factor for jobs in tech companies, and Europe seems to be ok in this area.

[0]: https://en.wikipedia.org/wiki/ASML_Holding

> The initial point (and randomness) has more influence on the solution time than almost anything else.

On that remark, a theoretical tool to choose the initial point is the Newton Polygon. For univariate polynomials, this leads to some of the fastest solver [1]. The idea to choose the initial point in this case is notably described in Section 6 of this paper [2].

A very rough intuition of the idea is that a polynomial p(z) doesn't vanish if one of its monomials is significantly larger than all the other. Reciprocally, the polynomial has more chances to vanish for values z such that two monomials have the same order of magnitude. Hence this is a good value to choose your initial point. Finally, deciding if two monomials have the same order of magnitude can be done by taking their log, and then it becomes geometry with polygons, hence the name Newton Polygon.

[1]: https://numpi.dm.unipi.it/scientific-computing-libraries/mps...

[2]: https://woelen.homescience.net/science/math/exps/polynomials...

I understand how competition can be seen as variable reward dressed up. On the other hand, in an attempt to classify games, separating the two components competition and chance is still useful. I think that chance is to be understood as a component completely independent of the player's skills. This allows to distinguish competitive games such as chess (competion with skills) and yahtzee (competition with chance) for example.

> I realize that variable reward is a key component of fun

Actually, Roger Caillois wrote a famous book on the different forms of play [1]. He uses four forms of play to classify games, and the one you are referring to is chance (Alea in his book). Another form of play that applies more accurately to chess is competition (Agon in his book). He also emphases two other key components of fun: playing a role (Mimicry) and physical sensations like in a roller coaster (Ilinx).

[1]: https://en.wikipedia.org/wiki/Man,_Play_and_Games

If you like these kind of pictures, you can also find very nice pictures showing the density of the eigenvalues values of integer matrices in the Bohemian matrices gallery [1].

[1]: http://www.bohemianmatrices.com/gallery/

This reminds me of this 1947 documentary [1] in French that imagined smartphones. Many scenes are surprisingly accurate.

[1]: https://youtu.be/ZKfOcR7Qbu4

Note that LIPICs [1] publishes the conference ECOOP chaired by Jonathan Aldrich. It is a very interesting alternative to ACM for conference proceedings: it hosts some great conferences and it has lower APCs. It does not publish journals though.

[1]: https://drops.dagstuhl.de/entities/series/LIPIcs

I found that ipe [1] is a nice alternative to inkscape. It has less features than inkscape, however the latex integration is better for math formula.

[1]: https://en.wikipedia.org/wiki/Ipe_(software)

> My most favoritest feature so far is that it converts tables AND equations to markdown and latex perfectly.

You might be interested in Texmacs [1]. It is has a wysiwyg interface, and it handles nicely tables and mathematical equations. Also you can export documents to the latex format.

[1]: https://www.texmacs.org

> I believe that overpopulation is the root of the sustainability crisis

This has been studied long time ago by scientists such as Alfred Sauvy [1], who concluded that overpopulation is not the cause of sustainability crisis, and that greenhouse gas is the major cause. In particular, limiting the growth of population has few impact on the production of greenhouse gas, whereas changing the means of energy production and consumption is much more impactful.

Moreover the world population is expected to be less than 12 billions in 2100 [2], which is plainly sustainable. This is mostly due to the demographic transition, a pattern observed in most countries, where the fertility rates decrease over time. More specifically I recommend the excellent book of Emmanuel Todd and Youssef Courbage on this subject [3]. The authors argue that in most countries throughout history, when both the majority of men and the majority of women know how to read and write, then the fertility rate decreases, and a revolution becomes imminent.

[1]: https://en.wikipedia.org/wiki/Alfred_Sauvy

[2]: https://www.un.org/en/desa/world-population-projected-reach-...

[3]: https://cup.columbia.edu/book/a-convergence-of-civilizations...

One interesting application of taking the value appearing in majority, or more generally taking the median, is to remove noise or people from a sequence of several photos taken from the same point of view. This idea is to superimpose all the photos, and for each pixel, you simply keep the median [1].

[1]: https://patdavid.net/2013/05/noise-removal-in-photos-with-me...

> That seems like almost fundamental emergent idea that is behind all the intelligence in the World.

That is indeed quite nice, yet intelligence seems much more diverse in biological organisms and not always reduced to nodes and edge strengths. The nodes and edges are a way to store data and to modify it that seems particularly well adapted mechanisms based on electricity.

On the other hand, there exists other very different (and slower) biological intelligent mechanisms that are not based on electricity. For example, a tree is perfectly adapted to its environment, capable of taking energy from the sun, materials from the ground, transform it, and so on. Yet the intelligent mechanism that created trees is not based on neural networks as far as I understand it. In this mechanism, the data is stored in DNA, and DNA can be rewriten at each new generation. It is a completely different (and slower) approach.

Finally I agree that the emergence of fast intelligence through neural network is incredible, although for me the first impressive advance is the use of the electricity to speed up the information exchange. The arrangements in nodes and edges could follow naturally from the fact that the transmission of electric signals works better through 1D circuits. The second impressive advance is the way the networks are layered. This is critical and very difficult to have an arrangement of edges and nodes that can both be trained and inferred efficiently. Without the proper arrangement, a biological neural network or a computer circuit is much less intelligent.

Finally in the future we could imagine intelligent mechanisms based on quantum mechanics for example. In this case, it would probably be vastly different from nodes and edges, due to the underlying physical constraints that are different in electricity and in quantum mechanics.

tldr: yes nodes and edges seem fundamental in fast intelligence based on electricity, but other very different intelligent mechanism exist in biological organisms, and other very different intelligent mechanisms could still be invented in the future.

From what I understand, Gene Regulatory Network [1] works very differently from Biological Neural Circuits [2]. Finally, Perceptron used in computers [3] is based on arithmetic operations and is again different from any of those two biological mechanisms. However, perceptron appears to be a good tool to model functions that depends on a large number of parameters.

What we may infer from that is that after a lot of time of evolution, functions depending on a lot of parameters appear. Yet Biological Neural Circuits seem quite bad at approximating simple continuous functions such as the multiplication between two numbers.

Gene Neural Network and Biological Neural Circuit are quite impressive structures considering their size, materials, and energy constraints. However if you allow bigger size, more energy, and faster conducting materials, it should be possible to do have faster modeling tools.

Moreover, to better take into account non-linear functions, my two cents is that Perceptrons could be further enhanced using piecewise polynomial functions instead of piecewise linear functions [4,5].

[1]: https://en.wikipedia.org/wiki/Gene_regulatory_network

[2]: https://en.wikipedia.org/wiki/Neural_circuit

[3]: https://en.wikipedia.org/wiki/Perceptron

[4]: https://doi.org/10.1109/TPAMI.2021.3058891

[5]: https://doi.org/10.1109/TPAMI.2022.3231971

Not sure if that counts, there is also the lua game engine Moai [1].

[1]: https://en.wikipedia.org/wiki/Moai_(software)

Writing square root of two as a continuous fraction leads to a periodic sequence of coefficients. More generally, a continuous fraction is periodic if and only if the number it represents is a quadratic number, that is, a linear combination of a rational number and the square root of a rational number [1]. It does not exactly answer your question, yet in the sense of continuous fraction at least, square root of two is more structured than pi, and less random.

Edit: the golden ratio is also a quadratic number, so this intuition is wrong in the end!

[1]: https://en.m.wikipedia.org/wiki/Periodic_continued_fraction#...

The Association for Professional Observers maintains a list of observer deaths and disappearances [1] that is also disturbing.

[1]: https://www.apo-observers.org/observer-safety/misses/

> you don't learn any transferable skills

Actually, playing video games is an activity that let you practice real-time thinking. Other activities with real-time thinking include music instruments, sports and social interactions. By real-time thinking, I mean an activity that requires you to think and act within short timelapses. It appears also that activities involving real-time thinking can be quite fun, and few course in schools involve real-time thinking.

Now, learning new languages like html or how to fine-tune LLM can be quite fun. Learning how to draw nice pictures, or how to write nice books can be quite fun too. It's nice to let children explore different activities (or free internet CD if we speak about 1996) so that they can find the ones that resonate with their inner motivations.

Slight correction, Mistral.AI was funded by two people from Meta (Guillaume Lample, Timothée Lacroix) and one from Deepmind (Arthur Mensch).

For new technologies, what matters most might be the universities where people are from, rather than the companies. The founders of Google graduated from Stanford. The founders of Mistra AI graduated from École Polytechnique and École Normale Supérieure, that are renowned in France, notably for their scientific formations.

That makes sense. I did observe significant speed up using this technic for evaluating a polynomial on several values. I used Hörner algorithm and indeed the number of registers is very small in this case.

If the lack of registers is really the bottleneck, a variant might to use both zmm registers for some cumulative sums and ymm registers for some others. In this case the speed up might be less spectacular though.

Edit: actually, I just discovered that zmm registers overlap the ymm registers, so the only registers left are the ones from the FPU.

I wonder if this code could be even further speed up, by taking into account the througput versus the latency of the FMA operator. If the latency is 4 cycles and the througput is 0.5 cycle for example, that means that doing n dependent operation will cost 4n cycles, and n independent operations will cost 0.5 cycles, that is an 8x speed up. By dependent operation, I mean that the input of an operation depends on the output the previous operation.

In the current final code, each loop has 3 independent FMAs. And in each loop iteration, the 3 FMAs are dependent on the FMAs from the previous iteration.

So one thing that could speed up the computation is to do 6 independent FMAs per loop iteration instead of 3. This can be done as follow. Instead of doing cumulative sums from 0 to n-1, one could split the computation of the cumulative sums from 0 to n/2-1 and from n/2 to n-1. So the main loop goes only from 0 to n/2-1, and at the k-th loop iteration, we do the 2x3 FMAs corresponding the entries of indices k and n/2+k. And at the end we add the cumulative sums.

Another indicator is the rate of citizen un prisons. The laws on gun ownership doesn't prevent the US government to have high rate of citizens incarcerated [1]. On the other hand, US is a state of law, and in theory, US incarceration does not come from oppression but from justice and written laws [2]. Now even though gun ownership might be one way to garanty that US remains a state of law, it is not obvious that it is the only way. If US was not a state of law, I would not be comfortable that GAFAM companies gets their own armies, as in the funny dystopian novel Jenifer Government [3].

[1]: https://en.wikipedia.org/wiki/List_of_countries_by_incarcera...

[2]: https://en.wikipedia.org/wiki/Rechtsstaat

[3]: https://en.wikipedia.org/wiki/Jennifer_Government

Olvid [0,1] seems interesting too.

[0]: https://olvid.io

[1]: https://github.com/olvid-io/olvid-android

The smart approach in 1975 was to use Parsons code, which was also turning songs into hashes, computable in your head. You could then find your song back as simply as looking a word in a dictionary. Hopefully this idea won't die any time soon.

[1]: https://en.wikipedia.org/wiki/Parsons_code

Actually the link between economy and neural network is quite strong historically. Friedrich Hayek is an economist who invented the word catallaxy to describe "the order brought about by the mutual adjustment of many individual economies in a market" [2]. Then he went on to work on a global theory of the brain, and was cited by Frank Rosenblatt in 1958 as an inspiration for the model of the perceptron [3].

[1]: https://en.wikipedia.org/wiki/Friedrich_Hayek#Economic_calcu...

[2]: https://en.wikipedia.org/wiki/Catallaxy

[3]: https://citeseerx.ist.psu.edu/doc_view/pid/2688969848b753368...

Another derivation-free optimization algorithm is the Cross-Entropy Method [1].

The main idea is to use a random generator to sample 100 points for example. Then take the 20 points with maximal evaluations. Finally adapt your random generator to maximize the chances of sampling those 20 points, and start again.

When used for continuous functions, you can use Gaussian random generator, and this becomes similar to the CMA-ES algorithm [2].

[1]: https://en.wikipedia.org/wiki/Cross-entropy_method [2]: https://en.wikipedia.org/wiki/CMA-ES

Marc Laidlaw, who worked on the game's story of Half-life and Half-life 2, published a script online [1] that could have been the outline of the plot of Episode 3. That could be sufficient for a serie.

[1]: https://combineoverwiki.net/wiki/Epistle_3

Voxel files could be a simpler step for 3D images.