Ciro Santilli @cirosantilli 40

A more photon-specific version of the Bloch sphere.

In it, each of the six sides has a clear and simple to understand photon polarization state, either of:

The sphere clearly suggests for example that a rotational or diagonal polarizations are the combination of left/right with the correct phase. This is clearly explained at: Video "Quantum Mechanics 9b - Photon Spin and Schrodinger's Cat II by ViaScience (2013)".

This is an extremely widely used technique as of 2020 and much earlier.

If allows you to amplify "any" sequence of choice (TODO length limitations) between a start and end sequences of interest which you synthesize.

If the sequence of interest is present, it gets amplified exponentially, and you end up with a bunch of DNA at the end.

You can then measure the DNA concentration based on simple light refraction methods to see if there is a lot of DNA or not in the post-processed sample.

Even Ciro Santilli had some contact with it at: Section "How to use an Oxford Nanopore MinION to extract DNA from river water and determine which bacteria live in it", see: PCR!

One common problem that happens with PCR if you don't design your primers right is: en.wikipedia.org/wiki/Primer_dimer

Sometime it fails: www.reddit.com/r/molecularbiology/comments/1kouomw/when_your_pcr_fails_again_and_you_start/and a comment:

For Ciro Santilli's campaign for freedom of speech in China: Section "github.com/cirosantilli/china-dictatorship".

Ciro has the radical opinion that absolute freedom of speech must be guaranteed by law for anyone to talk about absolutely anything, anonymously if they wish, with the exception only of copyright-related infringement.

And Ciro believes that there should be no age restriction of access to any information.

People should be only be punished for actions that they actually do in the real world. Not even purportedly planning those actions must be punished. Access and ability to publish information must be completely and totally free.

If you don't like someone, you should just block them, or start your own campaign to prepare a counter for whatever it is that they are want to do.

This freedom does not need to apply to citizens and organizations of other countries, only to citizens of the country in question, since foreign governments can create influence campaigns to affect the rights of your citizens. More info at: cirosantilli.com/china-dictatorship/mark-government-controlled-social-media

Limiting foreign influence therefore requires some kind of nationality check, which could harm anonymity. But Ciro believes that almost certainly such checks can be carried out in anonymous blockchain consensus based mechanisms. Governments would issues nationality tokens, and tokens are used for anonymous confirmations of rights in a way that only the token owner, not even the government, can determine who used the token. E.g. something a bit like what Monero does. Rights could be checked on a once per account basis, or yearly basis, so transaction costs should not be a big issue. Maybe expensive proof-of-work systems can be completely bypassed to the existence of this central token authority?

Some people believe that freedom of speech means "freedom of speech that I agree with". Those people should move to China or some other dictatorship.

Related: cirosantilli.com/china-dictatorship/hate-speech

There are 3: real numbers, complex numbers and quaternions.

Notably, the octonions are not associative.

Amazing talk by Richard Feynman that describes his experiences at Los Alamos National Laboratory while developing the first nuclear weapons.

Transcript: calteches.library.caltech.edu/34/3/FeynmanLosAlamos.htm Also included full text into Surely You're Joking, Mr. Feynman.

By default, we think of polynomials over the real numbers or complex numbers.

However, a polynomial can be defined over any other field just as well, the most notable example being that of a polynomial over a finite field.

For example, given the finite field of order 9, $GP(3)$ and with elements $\{0,1,2\}$, we can denote polynomials over that ring aswhere $x$ is the variable name.

For example, one such polynomial could be:and another one:Note how all the coefficients are members of the finite field we chose.

Given this, we could evaluate the polynomial for any element of the field, e.g.:and so on.

We can also add polynomials as usual over the field:and multiplication works analogously.

The usual definition of a polynomial is over a field as shown at polynomial over a field.

However, there is nothing in the immediate definition that prevents us from having a ring instead, i.e. a field but without the commutative property and inverse elements.

The only thing is that then we would need to differentiate between different orderings of the terms of multivariate polynomial, e.g. the following would all be potentially different terms:while for a field they would all go into a single term:so when considering a polynomial over a ring we end up with a lot more more possible terms.

If the ring is a commutative ring however, polynomials do look like proper polynomials: Section "Polynomial over a commutative ring".

Based on the Josephson effect. Yet another application of that phenomenal phenomena!

Philosophically, superconducting qubits are good because superconductivity is macroscopic.

It is fun to see that the representation of information in the QC basically uses an LC circuit, which is a very classical resonator circuit.

As mentioned at en.wikipedia.org/wiki/Superconducting_quantum_computing#Qubit_archetypes there are actually a few different types of superconducting qubits:

and hybridizations of those such as:

Input:

Appears to be analogous to the dot product, but also defined for infinite dimensions.

See: internal and spacetime symmetries.