Ciro Santilli @cirosantilli 35

Converts DNA to RNA.

This is a way to host a server that actually hide the IP of the server from the client, just like Tor hides the IP of the client from the server. Amazing tecnology!

This is why it enables hosting illegal things like the Silk Road: law enforcement is not able find where the server is hosted, and take it down or identify the owner.

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I guess you also have to change the sign of the gravitational constant?

We looking at the definition the orthogonal group is the group of all matrices that preserve the dot product, we notice that the dot product is one example of positive definite symmetric bilinear form, which in turn can also be represented by a matrix as shown at: Section "Matrix representation of a symmetric bilinear form".

By looking at this more general point of view, we could ask ourselves what happens to the group if instead of the dot product we took a more general bilinear form, e.g.:The answers to those questions are given by the Sylvester's law of inertia at Section "All indefinite orthogonal groups of matrices of equal metric signature are isomorphic".

The only perfect cryptosystem!

The problem is that you need a shared key as large as the message.

Systems like advanced Encryption Standard allow us to encrypt things larger than the key, but the tradeoff is that they could be possibly broken, as don't have any provably secure symmetric-key algorithms as of 2020.

OMG, the second half of the game where the world becomes quite open and all backstories are revealed, is one of the best gaming moments ever.

Two parallel Josephson junctions.

In Ciro's ASCII art circuit diagram notation:

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Man-made virus!

TODO: if we had cheap de novo DNA synthesis, how hard would it be to bootstrap a virus culture from that? github.com/cirosantilli/cirosantilli.github.io/issues/60

Is it easy to transfect a cell with the synthesized DNA, and get it to generate full infectious viral particles?

If so, then de novo DNA synthesis would be very similar to 3D printed guns: en.wikipedia.org/wiki/3D_printed_firearms.

It might already be possible to order dissimulated sequences online:

This equation is a subcase of Equation "Schrödinger equation for a one dimensional particle" with $V(x)=x^2$.

We get the time-independent Schrödinger equation by substituting this $V$ into Equation "time-independent Schrödinger equation for a one dimensional particle":

Now, there are two ways to go about this.

The first is the stupid "here's a guess" + "hey this family of solutions forms a complete basis"! This is exactly how we solved the problem at Section "Solving partial differential equations with the Fourier series", except that now the complete basis are the Hermite functions.

The second is the much celebrated ladder operator method.

Predicts fine structure.

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Following the definition of the indefinite orthogonal group, we want to show that only the metric signature matters.

First we can observe that the exact matrices are different. For example, taking the standard matrix of $O(2)$:and:both have the same metric signature. However, we notice that a rotation of 90 degrees, which preserves the first form, does not preserve the second one! E.g. consider the vector $x=(1,0)$, then $x\cdot x=1$. But after a rotation of 90 degrees, it becomes $x_2=(0,1)$, and now $x_2\cdot x_2=2$! Therefore, we have to search for an isomorphism between the two sets of matrices.

For example, consider the orthogonal group, which can be defined as shown at the orthogonal group is the group of all matrices that preserve the dot product can be defined as:

Some sources distinguish "invariant" from "covariant" such that under some transformation (typically Lie group):TODO examples.

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