Ciro Santilli @cirosantilli 40

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.

Basically mean that parallel evolution happened. Some cool ones:

This is a porn style defined by Ciro Santilli as:Ciro believes that this is an interesting type of pornography, as it feels more natural and humane than all the horrible trash that comes out of horrendous professional mainstream porn industry.

Yes, it could go down the YouTube/Instagram alley, and lead the vloggers to do things they wouldn't normally do because of the audience. But who is to say that Ciro Santilli doesn't do the same on Stack Overflow to some extent?

That type of porn requires some big courage to make. Or balls if you will. Kudos to those creators, as it is so taboo it could greatly impact their future job prospects.

The travel sex vlog appears to be the most popular way to do it. Presumably the reason being that you would not be able to interact with people in a normal job, so to keep things interesting you need to go to some random places.

Examples:

Bibliography:

One of the main reasons why physicists are obsessed by this topic is that position and momentum are mapped to the phase space coordinates of Hamiltonian mechanics, which appear in the matrix mechanics formulation of quantum mechanics, which offers insight into the theory, particularly when generalizing to relativistic quantum mechanics.

One way to think is: what is the definition of space space? It is a way to write the wave function ${\psi }_x(x)$ such that:And then, what is the definition of momentum space? It is of course a way to write the wave function ${\psi }_p(p)$ such that:

physics.stackexchange.com/questions/39442/intuitive-explanation-of-why-momentum-is-the-fourier-transform-variable-of-posit/39508#39508 gives the best idea intuitive idea: the Fourier transform writes a function as a (continuous) sum of plane waves, and each plane wave has a fixed momentum.

Bibliography:

At the time of the experiment, Illumina equipment was cheaper per base pair and dominates the human genome sequencing market, but it required a much higher initial investment for the equipment (TODO how much).

The reusable Nanopore device costs just about 500 dollars, and about 500 dollars (50 unit volume) for the single usage flow cell which can decode up to 30 billion base pairs, which is about 10 human genomes 1x! Note that 1x is basically useless for one of the most important of all applications of sequencing: detection of single-nucleotide polymorphisms, since the error rate would be too high to base clinical decisions on.

Compare that to Illumina which is currently doing about an 1000 dollar human genome at 30x, and a bit less errors per base pair (TODO how much).

Other advantages of the MinION over Illumina which didn't really matter to this particular experiment are:

Now that's some basal shit! It's basically a fucking blob!!! Except that it is flat. No nervous system. Not even tissues. It is basically a multicellular

Inferior compared to self-directed learning, but better than the traditional "everyone gets the same" approach.

A way to write the wavefunction $\psi (x)$ such that the position operator is:i.e., a function that takes the wavefunction as input, and outputs another function:

If you believe that mathematicians took care of continuous spectrum for us and that everything just works, the most concrete and direct thing that this representation tells us is that:equals:

The opposite of idealism.

In intuitive terms it consists of all integer functions, possibly with multiple input arguments, that can be written only with a sequence of:and such that n does not change inside the loop body, i.e. no while loops with arbitrary conditions.

n does not have to be a constant, it may come from previous calculations. But it must not change inside the loop body.

Primitive recursive functions basically include every integer function that comes up in practice. Primitive recursive functions can have huge complexity, and it strictly contains EXPTIME. As such, they mostly only come up in foundation of mathematics contexts.

The cool thing about primitive recursive functions is that the number of iterations is always bound, so we are certain that they terminate and are therefore computable.

This also means that there are necessarily functions which are not primitive recursive, as we know that there must exist uncomputable functions, e.g. the busy beaver function.

Adding unbounded while loops of course enables us to simulate arbitrary Turing machines, and therefore increases the complexity class.

More finely, there are non-primitive total recursive functions, e.g. most famously the Ackermann function.

Generally, prizes that pay big lumps of money to well established individuals are a bit useless, it would be better to pay smaller sums to struggling beginners in the field, of which there are aplenty.

The most important part about prizes should not be the money, nor the recognition, but rather explaining better what the laureates did. In this, most prizes fail. Thus Ciro Santilli's project idea: Project to explain each Nobel Prize better.

Ah, this list: en.wikipedia.org/wiki/List_of_prizes_known_as_the_Nobel_or_the_highest_honors_of_a_field

Paper by Philip W. Anderson and John M. Rowell that first (?) experimentally observed the Josephson effect.

Paywalled by the American Physical Society as of 2023 at: journals.aps.org/prl/abstract/10.1103/PhysRevLett.10.230

DOI: doi.org/10.1103/PhysRevLett.10.230

TODO understand the graphs in detail.

They used tin-oxide-lead tunnel at 1.5 K. TODO oxide of what? Why two different metals? They say that both films are 200 nm thick, so maybe it is:

A reconstruction of their circuit in Ciro's ASCII art circuit diagram notation TODO:

There are not details of the physical construction of course. Reproducibility lol.

With all this ready, we opened the Nanopore flow cell, which is the 500 dollar consumable piece that goes in the sequencer.

We then had to pipette the final golden Eppendorf into the flow cell. My anxiety levels were going through the roof: Figure 4. "Oxford nanopore MinION flow cell pipette loading.".

At this point bio people start telling lab horror stories of expensive solutions being spilled and people having to recover them from fridge walls, or of how people threw away golden Eppendorfs and had to pick them out of trash bins with hundreds of others looking exactly the same etc. (but also how some discoveries were made like this). This reminded Ciro of: youtu.be/89UNPdNtOoE?t=919 Alfred Maddock's plutonium spill horror story.

Luckily this time, it worked out!

We then just had to connect the MinION to the computer, and wait for 2 days.

During this time, the DNA would be sucked through the pores.

As can be seen from Video 1. "Oxford Nanopore MinION software channels pannel on Mac." the software tells us which pores are still working.

Pores go bad sooner or later randomly, until there are none left, at which point we can stop the process and throw the flow cell away.

48 hours was expected to be a reasonable time until all pores went bad, and so we called it a day, and waited for an email from the PuntSeq team telling us how things went.

We reached a yield of 16 billion base pairs out of the 30Gbp nominal maximum, which the bio people said was not bad.

www.qiagen.com/us/products/discovery-translational-research/dna-rn-a-purification/dna-purification/dna-clean-up/qiaquick-pcr-purification-kit/#orderinginformation (archive)

Manual archive: web.archive.org/web/20190911100243/https://www.qiagen.com/us/resources/download.aspx?id=e0fab087-ea52-4c16-b79f-c224bf760c39&lang=en

Removes PCR byproducts from purified DNA.