963 karma · joined February 20, 2007
let f(ax, ay) = a^k f(x,y) be a homogeneous function in the plane x,y for a scalar a, then f can also be written as:
f(x,y) = f(y*x/y, y) = y^k f(x/y,1)
and the symmetry by a matrix transformation in the plane
x-> ax + by and y-> cx+dy then transforms the function f as:
f(ax+by, cx+dy) = (cx+dy)^k f((ax+by)/(cx+dy),1)
now introduce z=x/y and f(x/y,1)=F(z) then
F((az+b)/(cz+d)) = (cz+d)^k F(z)
Projective spaces are cool ;-)
just my 2 ct
log(a*b) = log(a) + log(b)
Also the log function comes very natural from the human senses, e.g. exponential scale of the musical tones, sound amplitude measured logarithmically, the eye works logarithmically too.
just my 2 ct
Nowadays there are many monitors available with a much better frequency response for less money, e.g. KRK or Behringer. But still many studios have NS-10 just for compatibility.
An example: Of course GPT can at some point make better music than me, but I am playing an instrument not because I want to sell the recordings, but because it is a lot of fun for me.
Let GPT do my taxes, then I have more time for playing. (can it do taxes finally?)
* Athletes and Sports Competitors * Motorcycle Mechanics * Stonemasons
only to give some examples, where roboters are almost impossible.
I do about half of my searches now in perplexity because you get really relevant links. I use google only for trivial searches.
Maybe that is one of the Great Filters of the Fermi paradox.
https://en.wikipedia.org/wiki/Cancer_epigenetics
"As Vogelstein et al. point out, in a colorectal cancer there are usually about 3 to 6 driver mutations and 33 to 66 hitchhiker or passenger mutations.[2] However, in colon tumors compared to adjacent normal-appearing colonic mucosa, there are about 600 to 800 heavily methylated CpG islands in promoters of genes in the tumors while these CpG islands are not methylated in the adjacent mucosa."
It would be great if I could use it as a kernel in JupyterLite!
If you even want to get rid of MS windows or MacOS, then reaper is the right tool for the job. Together with the zynthian synths you have a (semi) open source production environment.
I think the problem is that many electronic musicians these days do not have the knowledge how to program a synth. They just use the pre-canned sounds that come with NI.
https://techcrunch.com/2021/10/10/tesla-hosts-festival-at-be...
"Tesla submitted plans to invest around $5.8 billion in a battery plant with a capacity of 50 GWh next to the 300-hectare site, and Musk promised volume production of battery cells by the end of the year. Volkswagen’s planned factory in Salzgitter is expected to produce 40 GWh."
https://shop.m5stack.com/products/m5paper-esp32-development-...
This solution has many unusual properties—in particular, the existence of closed timelike curves that would allow time travel in a universe described by the solution. Its definition is somewhat artificial in that the value of the cosmological constant must be carefully chosen to match the density of the dust grains, but this spacetime is an important pedagogical example.
The solution was found in 1949 by Kurt Gödel.
The Gödel metric is an exact solution of the Einstein field equations in which the stress–energy tensor contains two terms, the first representing the matter density of a homogeneous distribution of swirling dust particles (dust solution), and the second associated with a nonzero cosmological constant (see lambdavacuum solution). It is also known as the Gödel solution or Gödel universe.
Following Gödel, we can interpret the dust particles as galaxies, so that the Gödel solution becomes a cosmological model of a rotating universe. Besides rotating, this model exhibits no Hubble expansion, so it is not a realistic model of the universe in which we live, but can be taken as illustrating an alternative universe, which would in principle be allowed by general relativity (if one admits the legitimacy of a nonzero cosmological constant). Less well known solutions of Gödel's exhibit both rotation and Hubble expansion and have other qualities of his first model, but travelling into the past is not possible. According to S. W. Hawking, these models could well be a reasonable description of the universe that we observe, however observational data are compatible only with a very low rate of rotation.[4] The quality of these observations improved continually up until Gödel's death, and he would always ask "is the universe rotating yet?" and be told "no, it isn't".[5]
Many other exact solutions that can be interpreted as cosmological models of rotating universes are known. See the book Homogeneous Relativistic Cosmologies (1975) by Ryan and Shepley for some of these generalizations.