Ciro Santilli @cirosantilli 40

The basic intuition for this is to start from the origin and make small changes to the function based on its known derivative at the origin.

More precisely, we know that for any base b, exponentiation satisfies:And we also know that for $b=e$ in particular that we satisfy the exponential function differential equation and so:One interesting fact is that the only thing we use from the exponential function differential equation is the value around $x=0$, which is quite little information! This idea is basically what is behind the importance of the ralationship between Lie group-Lie algebra correspondence via the exponential map. In the more general settings of groups and manifolds, restricting ourselves to be near the origin is a huge advantage.

Now suppose that we want to calculate $e^1$. The idea is to start from $e^0$ and then then to use the first order of the Taylor series to extend the known value of $e^0$ to $e^1$.

E.g., if we split into 2 parts, we know that:or in three parts:so we can just use arbitrarily many parts $e^{1/n}$ that are arbitrarily close to $x=0$:and more generally for any $x$ we have:

Let's see what happens with the Taylor series. We have near $y=0$ in little-o notation:Therefore, for $y=x/n$, which is near $y=0$ for any fixed $x$:and therefore:which is basically the formula tha we wanted. We just have to convince ourselves that at ${\lim }_{n\to \infty }$, the $o(1/n)$ disappears, i.e.:

To do that, let's multiply $e^y$ by itself once:and multiplying a third time:TODO conclude.

This channel contains several 2D continuous simulations and explains AI techniques used.

The engine appears to be open source: github.com/Primer-Learning/PrimerTools (previously at: github.com/Helpsypoo/primer). Models are closed source however.

They have several interesting multiagent game ideas.

Claims Unity-based, so has the downside of relying on a non-FOSS engine.

Ciro became mildly jealous of this channel when he found out about it, because at 800k subscribers at the time, the creator is likely able to make a living off of it, something which Ciro thought impossible.

As of 2022 he was at 1.6M followers with only 17 videos! Of course, much of those videos is about the software and they require infinite development hours to video time ratios.

Much of this success hinges a large part on the amazing 3D game presentation.

Well done!

Created by Justin Helps. Awesome name.

To make things better, the generically named channel is also the title of one of the best films of al time: Primer (2004).

They seem to be doing hardware acceleration for post-quantum cryptography algorithm.

One has to feel bad for them as they likely threw out entire chip designs over NIST Post-Quantum Cryptography Standardization algorithm breakeges.

This is the mantra of the semiconductor industry:

Encryption algorithms that run on classical computers that are expected to be resistant to quantum computers.

This is notably not the case of the dominant 2020 algorithms, RSA and elliptic curve cryptography, which are provably broken by Grover's algorithm.

However, as of 2020, we don't have any proof that any symmetric or public key algorithm is quantum resistant.

Post-quantum cryptography is the very first quantum computing thing at which people have to put money into.

The reason is that attackers would be able to store captured ciphertext, and then retroactively break them once and if quantum computing power becomes available in the future.

There isn't a shade of a doubt that intelligence agencies are actively doing this as of 2020. They must have a database of how interesting a given source is, and then store as much as they can given some ammount of storage budget they have available.

A good way to explain this to quantum computing skeptics is to ask them:Post-quantum cryptography is simply not a choice. It must be done now. Even if the risk is low, the cost would be way too great.

Vs uranium: uranium vs plutonium Quora answer by Ciro Santilli.

What a material:

You need a secondary password that when used leads to an empty inbox with a setting set where message are deleted after 2 days.

This way, if the attacker sends a test email, it will still show up, but being empty is also plausible.

Of course, this means that any new emails received will be visible by the attacker, so you have to find a way to inform senders that the account has been compromised.

So you have to find a way to inform senders that the account has been compromised, e.g. a secret pre-agreed canary that must be checked each time as part of the contact protocol.

Based on GitHub pull requests: github.com/planetmath

Joe Corneli, of of the contributors, mentions this in a cool-sounding "Peeragogy" context at metameso.org/~joe/:

Some sources say that this is just the part that says that the norm of a $L^2$ function is the same as the norm of its Fourier transform.

Others say that this theorem actually says that the Fourier transform is bijective.

The comment at math.stackexchange.com/questions/446870/bijectiveness-injectiveness-and-surjectiveness-of-fourier-transformation-define/1235725#1235725 may be of interest, it says that the bijection statement is an easy consequence from the norm one, thus the confusion.

TODO does it require it to be in $l^1$ as well? Wikipedia en.wikipedia.org/w/index.php?title=Plancherel_theorem&oldid=987110841 says yes, but courses.maths.ox.ac.uk/node/view_material/53981 does not mention it.

TODO identify better:

This seems to be the "brown Brazilian bean" that many Brazilians eat every day.

Edit: after buying it, not 100% sure. This one felt smaller than what Ciro had in Brazil, borlotti beans might be closer. Pinto beans are smaller, and creamier, and have softer peel, possibly produced less natural gas.

2021-04: second try.

2021-03: did for first time, started with same procedure as borlotti beans 2021-03. Maybe 1h30 is too much. Outcome was still very good.

Proprietary extension to Mozilla rr by rr lead coder Robert O'Callahan et. al, started in 2016 after he quit Mozilla.

TODO what does it add to rr?

Way, way before instant messaging, there was... teletype!

Others: