Leaderboard

The other day members of the EDL (English Defence League) came to our city to try and extend their campaign of racial violence and anti-immigrant slander in the wake of the Southport killings ten days ago. You may have read about this recent wave of violence across the UK, including a riot in Liverpool the other night where thugs burnt down a local community hub and library in Liverpool because some posts on social media had spread a lie that all the books in the childrens section of the library had been replaced by copies of the Koran - (they hadn’t). When they arrived in our city however, the EDL supporters got a surprise. They had intended to attack a Mercure Travel Lodge that was allegedly being used to house asylum seekers, but they found themselves outnumbered 4-1 by a well organised protective cordon of counter-protesters and local community leaders who were also protecting our local mosques and LGBT sites, and who successfully held the racists at bay until the police belatedly arrived to stop the EDL from setting fire to the Travel Lodge. https://www.bbc.co.uk/news/articles/cvgrrl0zlg5o The following day I met a female friend and lawyer on our local village green who said “Are you coming to the protest tomorrow ?” When I asked for details, she told me that the EDL were now planning to attack the premises and staff of law firms in our city centre who regularly assist asylum seekers (often on a pro bono basis). There is apparently a hit-list of such law firms circulating on far-right Telegram channels. https://www.bbc.co.uk/news/articles/c624r77gnm2o The Playboy of The Western World (1907) was the title of a play by the Irish playwright John Synge which tells the story of a braggart who falsely claims to have murdered his own father. It came to mind as a suitable epithet for Elon Musk - the CEO of SpaceX, Tesla and X (formerly Twitter) who has recently restored the X accounts of notorious UK hate speech trolls such as Tommy Robinson (EDL co-founder who recently fled the country), Katie Hopkins, and the violent misogynist Andrew Tate. https://www.independent.co.uk/space/elon-musk-tommy-robinson-prime-minister-southport-spacex-b2590114.html Within the last day or so, Elon Musk has put up incendiary posts on his X platform claiming that “Civil War in UK is now inevitable” and has also attacked our new PM Keir Starmer for disputing the accuracy of these irresponsible claims. According to Sky News, Elon Musk is now also planning to sue major companies for “Conspiring to withhold advertising revenue from X/Twitter” and causing it to miss out on billions of advertising revenue. https://news.sky.com/story/its-war-elon-musks-x-sues-companies-for-not-advertising-on-its-platform-13192318 The reality is that many large corporations stopped advertising on X after finding their adverts were being run in tandem with blatantly neo-Nazi and racist content - which happened as a direct result of Elon Musk gutting the staff at X, and removing most of the content moderation procedures that were formerly in place. The Playboy of The Western World” indeed ! - welcome to the land of consequences Elon.

@TheVat extra points for making a clean limerick out of that.

Exchemist has mentioned the most important point, dropping pasta into defined temperature creates the most reproducibility. Now there is quite some chemistry related to pasta cooking and generally speaking, the first process is controlled by water penetration, starch gelatinization and protein coagulation. These steps are all temperature dependent but not all aspects are impacted equally (https://doi.org/10.1016/j.jfoodeng.2007.03.018). For example water penetration occurs at low temperatures, but protein coagulation generally requires higher temperature for homogenous coagulation. Yet, that is also dependent on the way the gluten network is developed during the production of pasta (https://doi.org/10.1080/10408390802437154). Another aspect is the rate of starch gelatinzation to protein coagulation. If coagulation dominates and is done faster than than gelatinzation, starch particles will be trapped in the gluten network resulting in more firm pasta (which is usually desirable). Conversely high starch swelling with an incomplete network allows starch to escape to the surface (and cooking water) which results in soft and sticky pasta (https://digitalcommons.usu.edu/foodmicrostructure/vol2/iss1/2). As gelatinization starts at lower temperatures, cooking from cold will release more starch. That all being said, for dried pasta it generally does not matter unless it has a large surface (e.g. fettucine) where the released starch can make things rather sticky and where cooking in boiling water accelerates protein coagulation. Otherwise, one can do the opposite for example soak pasta at low temps (before starch gelatinization, so <45 ish or so C). This takes care of the water penetration part while gelatinization and coagulation does not occur yet. You can then then just heat it up (e.g cook in sauce) to rapidly induce coagulation without the release of excessive amount of starch.

I hope Saturday Night Live is watching. They need to book the Marsh Family.

Indeed. Something about your title line just said opening line of a limerick. (though I guess the proper meter of a limerick, anapest, would call for an extra syllable, e.g. the indolent apes of old Punt...) I had not heard about using mitochondrial DNA this way, or the precision it might bring. Fascinating stuff.

Lol I think you became too used to Unitary and orthogonal groups. Joigus Would it help to know SO(3.1) and SU(n) are both subgroups of SL(2,c)/Z_2 ? lets start with the following \[sl(2,\mathbb{C})=su(2)\oplus isu(2)\] generators denoted e,f,h [e,f=h] [h,e]=2e [h,f]=-2f the 2C is the linear combination of e,f,h \[\pi (h)=\begin{pmatrix}1&0\\0&-1\end{pmatrix}\] \[\pi( e)=\begin{pmatrix}0&1\\0&0\end{pmatrix}\] \[\pi h=\begin{pmatrix}0&0\\-1&0\end{pmatrix}\] \[f_i,h_i,e_i\] i=1,2,3....r however the set of complex cannot all commute so you need commutations \[[h_ih_j]=0\] \[[h_i,e_j]=A_{ji}e_j\] \[h_i,f_i]=-A_{ji}f_j\] \[[e_i,f_j]=\delta_{ij}h_{ij}\] where \(A_{ij} \) is the Cartan matrix ( I won't go through the ladder operators as they are fairly lengthy) however it can be expressed as \[[h_i,e_i]=\langle\alpha_j\rangle=\frac{2}{\langle\alpha_j,\alpha_j}\langle\alpha_j,\alpha_i\rangle_j=A_{ji}e_j\] \[\begin{pmatrix}2&-1\\-1&2\end{pmatrix}\] the above is for SL(2C) for sl(3,C) the Cartan matrix is an 8 dimensional algebra of rank 2 which means it has a 2 dimensional Cartan sub algebra given as follows \[\pi(t_1)= \begin{pmatrix}0&1&0\\1&0&0\\0&0&0\end{pmatrix}\] \[\pi(t_2)= \begin{pmatrix}0&-i&0\\i&0&0\\0&0&0\end{pmatrix}\] \[\pi(t_3)= \begin{pmatrix}1&0&0\\0&-1&0\\0&0&0\end{pmatrix}\] \[\pi(t_4)= \begin{pmatrix}0&0&1\\0&-1&0\\0&0&0\end{pmatrix}\] \[\pi(t_5) =\begin{pmatrix}0&0&-i\\0&0&0\\i&0&0\end{pmatrix}\] \[\pi(t_6)= \begin{pmatrix}0&0&0\\0&0&1\\0&1&0\end{pmatrix}\] \[\pi(t_7)= \begin{pmatrix}0&0&0\\0&0&-i\\0&i&0\end{pmatrix}\] \[\pi(t_1)=\frac{1}{\sqrt{3}} \begin{pmatrix}0&1&0\\1&0&0\\0&0&-2\end{pmatrix}\] You may note the last is the Gell-Mann matrices if we take the commutator between \(\pi(t_1)\) and \(\pi(t_2)\) we get \([\pi(t_1),\pi(t_2)]=2i\pi(t_3)\) which is familiar in the su(2) algebra. Thus we can define the following \[x_1=\frac{1}{2}t_1\] \[x_2=\frac{1}{2}t_1\] \[x_3=\frac{1}{2}t_3\] \[y_4=\frac{1}{2}t_4\] \[y_5=\frac{1}{2}t_5\] \[z_6=\frac{1}{2}t_6\] \[z_7=\frac{1}{2}t_7\] \[z_8=\frac{1}{\sqrt{3}}t_8\] with change in basis \[e_1=x_1+ix_2\] \[e_2=y_4+iy_5\] \[e_3=z_6+iz_7\] \[f_1=x_1+ix_2\] \[f_2=y_4+iy_5\] \[f_3=z_6+iz_7\] Now I should inform everyone that the basis and coordinates I am describing apply to Dynken diagrams and what I am describing apply to the root diagrams... https://en.wikipedia.org/wiki/Dynkin_diagram the basis above in matrix form is \[\pi(e_1)=\begin{pmatrix}0&1&0\\0&0&0\\0&0&0\end{pmatrix}\] \[\pi(e_2)=\begin{pmatrix}0&0&1\\0&0&0\\0&0&0\end{pmatrix}\] \[\pi(e_1)=\begin{pmatrix}0&0&0\\0&0&1\\0&0&0\end{pmatrix}\] \[\pi(f_1)=\begin{pmatrix}0&0&0\\1&0&0\\0&0&0\end{pmatrix}\] \[\pi(f_2)=\begin{pmatrix}0&0&0\\0&0&0\\1&0&0\end{pmatrix}\] \[\pi(f_3)=\begin{pmatrix}0&0&0\\0&0&0\\0&1&0\end{pmatrix}\] \[\pi(x_3)=\frac{1}{2}\begin{pmatrix}1&1&0\\0&-1&0\\0&0&0\end{pmatrix}\] \[\pi(z_8)=\frac{1}{3}\begin{pmatrix}1&0&0\\0&1&0\\0&0&-2\end{pmatrix}\] @joigus That should help better understand the special linear group of Real as well as complex. Now knowing the above applies to Dynken diagrams will also help better understand the validity of the OPs link as well as the methodology. @TheoM Hope this answers your question as well on the validity behind the LCT's and where they are applied in particle physics so yes the link overall you provided is valid