Ciro Santilli @cirosantilli 37

This is not bad, but some divergences to the better BBC miniseries, which presumably sticks more closely to the novel:

Related:

Answers suggest hat you basically pick a random large odd number, and add 2 to it until your selected primality test passes.

The prime number theorem tells us that the probability that a number between 1 and $N$ is a prime number is $1/log(N)$.

Therefore, for an N-bit integer, we only have to run the test N times on average to find a prime.

Since say, A 512-bit integer is already humongous and sufficiently large, we would only need to search 512 times on average even for such sizes, and therefore the procedure scales well.

The key takeaway is that setting an explicit value function to an AGI entity is a good way to destroy the world due to poor AI alignment. We are more likely to not destroy by creating an AI whose goals is to "do want humans what it to do", but in a way that it does not know before hand what it is that humans want, and it has to learn from them. This approach appears to be known as reward modeling.

Some other cool ideas:

A parameter that you choose which determines how the algorithm will perform.

In the case of machine learning in particular, it is not part of the training data set.

Hyperparameters can also be considered in domains outside of machine learning however, e.g. the step size in partial differential equation solver is entirely independent from the problem itself and could be considered a hyperparamter. One difference from machine learning however is that step size hyperparameters in numerical analysis are clearly better if smaller at a higher computational cost. In machine learning however, there is often an optimum somewhere, beyond which overfitting becomes excessive.

The total derivative of a function assigns for every point of the domain a linear map with same domain, which is the best linear approximation to the function value around this point, i.e. the tangent plane.

E.g. in 1D:and in 2D:

Every vector space is defined over a field.

E.g. in ${\mathbb{R}}^3$, the underlying field is $\mathbb{R}$, the real numbers. And in ${\mathbb{C}}^2$ the underlying field is $\mathbb{C}$, the complex numbers.

Any field can be used, including finite field. But the underlying thing has to be a field, because the definitions of a vector need all field properties to hold to make sense.

Elements of the underlying field of a vector space are known as scalar.

For an example with context, have a look at E. Coli K-12 MG1655 and the second protein of the genome, e. Coli K-12 MG1655 gene thrA.

Group of the unitary matrices.

Complex analogue of the orthogonal group.

One notable difference from the orthogonal group however is that the unitary group is connected "because" its determinant is not fixed to two disconnected values 1/-1, but rather goes around in a continuous unit circle. $U(1)$ is the unit circle.

2013 notes: www-thphys.physics.ox.ac.uk/people/AlexanderSchekochihin/A1/A1MT13.html

Created by Dr. Rod Nave from Georgia State University, where he worked from 1968 after his post-doc in North Wales on molecular spectroscopy.

While there is value to that website, it always feels like it falls a bit too short as too "encyclopedic" and too little "tutorial-like". Most notably, it has very little on the history of physics/experiments.

Ciro Santilli likes this Rod, he really practices some good braindumping, just look at how he documented his life in the pre-social media Internet dark ages: hyperphysics.phy-astr.gsu.edu/Nave-html/nave.html

The website evolved from a HyperCard stack, as suggested by the website name, mentioned at: hyperphysics.phy-astr.gsu.edu/hbase/index.html.

Shame he was too old for CC BY-SA, see "Please respect the Copyright" at hyperphysics.phy-astr.gsu.edu/hbase/index.html.

exhibits.library.gsu.edu/kell/exhibits/show/nave-kell-hall/capturing-a-career has some good photo selection focused on showing the department, and has an interview.

Kell hall is a building of GSU that was demolished in 2019: atlanta.curbed.com/2020/1/31/21115980/gsu-georgia-state-atlanta-kell-hall-demolition-park-library-north