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I aim to provide an example of applied category theory in computer science. Your understanding may differ due to the encompassing time frame, however, I ensure that even the most recent findings can rapidly transform into a practical programming concept.

The concept of 'monad' was initially introduced by Roger Godement in 1958, known as the 'standard construction'. The term 'monad' itself came into use later in 1967, credited to Jean Bénabou. The connection between monads and functional programming was first established in 1989 by computer scientist Eugenio Moggi. Moggi implemented monads in semantics to interpret the lambda calculus, a computational model that employs variable binding and substitution for function abstraction and application. The formal incorporation of monads into Haskell occurred in 1992 by Philip Wadler. Since then, monads are increasingly being integrated into mainstream programming languages, including JavaScript. For instance, JavaScript Promises can be viewed as a kind of monad. They encapsulate a value and allow its transformation with the .then method, which can be equated to the 'bind' operation in the realm of monads. Furthermore, a new Promise can be generated from any value using Promise.resolve, an operation analogous to the 'return' operation in monads. Promises have a very practical application and are used in programming by millions of developers every day.

The concept of a monad is one example that is well-understood; however, there are numerous other such ideas. One of these is the Functor, often referred to as "mappable" in mainstream programming languages. Research in this field is ongoing, with concepts like applicative functors, introduced by Conor McBride and Ross Paterson in 2008, already gaining popularity in languages such as Haskell.

Arrows are useful because they provide a computation model that can implicitly make use of state without ever exposing that state to the programmer. The programmer can use arrowized computations and combine them to create sophisticated systems.

A strong arrow is an arrow A having an extra structure known as strength. The strength for A is a natural transformation, generally denoted by t, which consumes a pair of objects (X,Y) and gives back an arrow in the category. In a concrete manner, the strength has this form: t_X,Y: X x AY -> A(X x Y), called tensorial strength. The strength obeys some particular coherence conditions. A deeper explanation involves the monoidal structure of a category and how the 'strength' aids in elaborating the combination of values in the arrow context.

That's not a big issue nowadays since there is univalent foundations, which is based on ∞-groupoids instead of sets.

Visualize the IMDB rating of every episode for any TV series.

450 m/s is 1620 km/h

However, if you experience eye strain after prolonged computer use (as I do), consider a blue light filter glass from Amazon. I recommend the ones with a strong orange tint. They're also available as clip-ons. Give them a shot and see if they alleviate your pain. If they don't help, return them. Essentially, you're making a no-risk investment. In the worst-case scenario, you lose nothing, but in the best-case scenario, it could remedy your eye strain, just as it did for me.

Currently, the random walk hypothesis remains just that - a hypothesis. There is no definitive evidence to confirm that the stock market operates in a random manner.

On the other hand, many believe that there are some long-term patterns and invest huge chunks of money based on that belief. For example, one such belief is that the S&P 500 will continue to have an annual average return of something between 8% - 10% in the decades to come.

If the movements in stock charts, including ETFs like SPY, were truly random, such a pattern could not exist. Consequently, our expected average annual return from the S&P 500 should be 0%. This is because in a genuinely random environment, the likelihood of a rise and a fall would be precisely equal.

The presentation gives us a whole range of views on biodiversity, making it clear that we need to think about both common and rare species when we're figuring out diversity. It hints that this magnitude idea might give us a more detailed picture of diversity by considering how important different species are relative to each other. Then the presentation gets into the weeds of category theory, chatting about enriched categories and size-like invariants. It talks about stuff like monoidal categories, V-enriched categories, and linear categories. These ideas are brought up as tools to help us understand and calculate magnitude.

The presentation also explores how these category theory ideas relate to metric spaces. It suggests that getting a handle on this relationship could give us even more insight into how to max out diversity. Lastly, the presentation brings up the Euler characteristic, which is a concept from algebraic topology. It hints that the Euler characteristic and magnitude are pretty tight, and understanding this connection could give us even more insight into how to max out diversity.

So, to wrap it up, the presentation is a thorough look at how category theory ideas, especially magnitude, can be used to tackle problems in mathematical ecology. It suggests that these ideas can give us a more detailed understanding of diversity and might even help us figure out how to get the most diversity.

References:

https://arxiv.org/abs/2012.02113

https://arxiv.org/abs/1606.00095

Some favorites over the years:

- https://beuke.org/programming-language-popularity/ - GitHub Programming Language Popularity based on BigQuery

- https://beuke.org/arch-linux-archive/ - Arch Linux Date-Based Versioned Upgrades

- https://beuke.org/boltzmann-brains/ - The Ultimate Fate of the Universe

Just order 25x BX41 Boxes with 500 TB for 1015€. They do not support S3 protocol, but have plenty of other protocol options (FTP, SFTP, HTTPS, rsync, mount as network drive, ...).

... model name : Intel(R) Xeon(R) Platinum 8275CL CPU @ 3.00GHz ...

ChatGPT Virtual Machine claims to run on Intel(R) Xeon(R) Platinum 8275CL CPU @ 3.00GHz. Interesting.

But why? A very slow silicion based computer is still a silicon based computer. It doesn't matter how fast, same applies for quantum computers. There is no such definition as IF (> 1000 qubits) THEN "quantum computer" ELSE "nothing".