His father fought a lot with the stupid educational system to try and move his son to his full potential and move to more advanced subjects early.
A crime of society to try and prevent it. They actually moved the family from Singapore to Malaysia for a learning opportunity for the son. Amazing.
This is the perfect illustration of one of Ciro Santilli's most important complaints about the 2020 educational system:and why Ciro created OurBigBook.com to try and help fix the issue.
Bibliography:
Ainan Cawley: Child prodigy (2013)
Source. - youtu.be/Ugi74cwPMSg?t=137 finding the right school
Let's start with the one dimensional case. Let the and a Functional defined by a function of three variables :
Then, the Euler-Lagrange equation gives the maxima and minima of the that type of functional. Note that this type of functional is just one very specific type of functional amongst all possible functionals that one might come up with. However, it turns out to be enough to do most of physics, so we are happy with with it.
Given , the Euler-Lagrange equations are a system of ordinary differential equations constructed from that such that the solutions to that system are the maxima/minima.
By and we simply mean "the partial derivative of with respect to its second and third arguments". The notation is a bit confusing at first, but that's all it means.
Therefore, that expression ends up being at most a second order ordinary differential equation where is the unknown, since:
Now let's think about the multi-dimensional case. Instead of having , we now have . Think about the Lagrangian mechanics motivation of a double pendulum where for a given time we have two angles.
Let's do the 2-dimensional case then. In that case, is going to be a function of 5 variables rather than 3 as in the one dimensional case, and the functional looks like:
This time, the Euler-Lagrange equations are going to be a system of two ordinary differential equations on two unknown functions and of order up to 2 in both variables:At this point, notation is getting a bit clunky, so people will often condense the vectoror just omit the arguments of entirely:
Calculus of Variations ft. Flammable Maths by vcubingx (2020)
Source. What is the Ultraviolet Catastrophe? by Physics Explained (2020)
Source. It is a bit hard to decide if those people are serious or not. Sometimes it feels scammy, but sometimes it feels fun and right!
Particularly concerning is the fact that they are not a not-for-profit entity, and it is hard to understand how they might make money.
Charles Simon, the founder, is pretty focused in how natural neurons work vs artificial neural network models. He has some good explanations of that, and one major focus of the project is their semi open source spiking neuron simulator BrainSimII. While Ciro Santilli believes that there might be insight in that, he also has doubts if certain modules of the brain wouldn't be more suitable coded directly in regular programming languages with greater ease and performance.
FutureAI appears to be Charles' retirement for fun project, he is likely independently wealthy. Well done.
- www.aitimejournal.com/interview-with-charles-simon-ceo-and-founder-futureai
- 2022 raised 2 million USD:
Creativity and AGI by Charles Simon's at AGI-22 (2022)
Source. Sounds OK!- youtu.be/ivbGbSx0K8k?t=856 general structure of the human brain 86B total, matching number of neurons in the human brain, with:
- 14B: brainstem
- 16B: neocortex
- 56B: cerebelum
- www.youtube.com/watch?t=1433 some sequencing ideas/conjectures
Machine Learning Is Not Like Your Brain by Future AI (2022)
Source. Contains some BrainSimII demos.Vimscript unit testing!!!
There are unlisted articles, also show them or only show them.