One theoretical motivation for its existence is that it has the fundamental property that we are immediately certain it will terminate, unlike while loops with arbitrary conditions.
Primitive recursive functions are the complexity class that divides those two.
Continuous version of the Fourier series.
Can be used to represent functions that are not periodic: math.stackexchange.com/questions/221137/what-is-the-difference-between-fourier-series-and-fourier-transformation while the Fourier series is only for periodic functions.
Therefore, the Fourier transform can be seen as a generalization of the Fourier series that can also decompose functions defined on the entire real line.
As a more concrete example, just like the Fourier series is how you solve the heat equation on a line segment with Dirichlet boundary conditions as shown at: Section "Solving partial differential equations with the Fourier series", the Fourier transform is what you need to solve the problem when the domain is the entire real line.
People love green on black mostly.
www.reddit.com/r/Monero/comments/1brryao/ciro_santilli_received_a_1000_xmr_donation_to/ from 1000 Monero donation:
- user
-TrustyDwarf-: - user
rbrunner7: automobi1e
Also known as: Quantitative PCR (qPCR).
This describes one possible concentration detection method with fluorescent molecules that only become fluorescent when the DNA is double stranded (SYBR Green)
Polymerase Chain Reaction (PCR) - Quantitative PCR (qPCR) by Applied Biological Materials (2016)
Source. This allows you to predict the exact initial concentration by extrapolating the exponential curve backwards.
OK, can someone please just stop the philosophy and give numerical predictions of how entropy helps you predict the future?
The Unexpected Side of Entropy by Daan Frenkel
. Source. 2021.The Biggest Ideas in the Universe | 20. Entropy and Information by Sean Carroll (2020)
Source. In usual Sean Carroll fashion, it glosses over the subject. This one might be worth watching. It mentions 4 possible definitions of entropy: Boltzmann, Gibbs, Shannon (information theory) and John von Neumann (quantum mechanics).- www.quantamagazine.org/what-is-entropy-a-measure-of-just-how-little-we-really-know-20241213/ What Is Entropy? A Measure of Just How Little We Really Know. on Quanta Magazine attempts to make the point that entropy is observer dependant. TODO details on that.
Atoms exist and last for a long time, while in classical electromagnetic theory punctual orbiting electrons should emit radiation quickly and fall into the nucleus: physics.stackexchange.com/questions/20003/why-dont-electrons-crash-into-the-nuclei-they-orbit
In other sections:
Bibliography:
It should be illegal to give someone money to advertise your product.
We should just use tags and upvote-based algorithms.
TODO find Sergey Brin quote bout advertising being a form of perverting search engine ranking neutrality. In other words, there are neutral metrics to what people find good, like links and upvotes. And then advertising is a way to pervert that to someone's profit.
Sometimes Ciro Santilli thinks advertising should be on-subscription only, but that is too restrictive, e.g. imagine the local business owner who wears a t-shirt of their business.
Replacement of master and slave terminology from technology Updated 2025-05-23 +Created 1970-01-01
The IETF was a notable one: www.nytimes.com/2021/04/13/technology/racist-computer-engineering-terms-ietf.html
- developers.google.com/style/word-list (archive) Google's avoid word list is a masterclass in 2020's political correctness
Simulates vintage hardware synthesizers, and includes some pretty complex ones!
Aims to show an UI that looks exactly like the synthesizers in question.
Submit a new job. The most important command!
Examples:
- mechanical resonance, notably:
- pipe instruments
- electronic oscillators, notably:
- LC oscillator, and notably the lossy version RLC circuit
Perhaps a key insight of resonance is that the reonant any lossy system tends to look like the resonance frequency quite quickly even if the initial condition is not the resonant condition itself, because everything that is not the resonant frequency interferes destructively and becomes noise. Some examples of that:
- striking a bell or drum can be modelled by applying an impuse to the system
- playing a pipe instrument comes down to blowing a piece that vibrates randomly, and then leads the pipe to vibrate mostly in the resonant frequency. Likely the same applies to bowed string instruments, the bow must be creating a random vibration.
- playing a plucked string instrument comes down to initializing the system to an triangular wave form and then letting it evolve. TODO find a simulation of that!
Another cool aspect of resonance is that it was kind of the motivation for de Broglie hypothesis, as de Broglie was kind of thinking that electroncs might show discrete jumps on atomic spectra because of constructive interference.
Converts RNA to DNA, i.e. the inverse of transcription. Found in viruses such as Retrovirus, which includes e.g. HIV.
- Stack Exchange's censorship of "I think Trump is disgusting as a person" from Ciro Santilli's profile: cirosantilli.com/china-dictatorship/sstack-overflow-forbids-criticizing-the-character-of-genocidal-political-leaders-like-xi-jinping
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