One parameter subgroup Updated 2025-07-16
The one parameter subgroup of a Lie group for a given element of its Lie algebra is a subgroup of given by:
Intuitively, is a direction, and is how far we move along a given direction. This intuition is especially vivid in for example in the case of the Lie algebra of , the rotation group.
One parameter subgroups can be seen as the continuous analogue to the cycle of an element of a group.
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Wikipedia mentions quoting his Nobel Prize biography:
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Nice, nice place. Natural sciences only, no bullshit.
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The Questioning City by British Pathé (1963)
Source. Located in Cambridge, United Kingdom.
Second largest number of Nobel Prize as of 2019, need on say more? en.wikipedia.org/w/index.php?title=List_of_Nobel_laureates_by_university_affiliation&oldid=934987075
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Lie Groups, Physics, and Geometry by Robert Gilmore (2008) 7.2 "The covering problem" gives some amazing intuition on the subject as usual.
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Animal rights Updated 2025-07-16
Ciro Santilli has mixed feelings about animal rights.
On one hand, his irrational side wants of course all animals to be happy.
On the other, he does not care about this enough to not kill and eat them, even though he believes that you could live off plants relatively well.
His more rational side says: humans are sacred. Either because you believe in the soul, or because your built-in empathy behaviours. If it is not a human, do whatever you want to it. Killing is already undoubtedly the greatest sin. It is not OK to kill a human painlessly is it? So if torturing it brings humans good, then do it.
Of course, this does get use close and closer to "the what is a human" question, which is more relevant than ever in the awakening of genetics: all species are after all a continuum right?
And Ciro does not have a simple solution to this problem, besides that in 99.9999% the answer is obvious to 99.9999% of the people, and for the others cases, we have to do it like the law and make flawed rules to cover the remaining 0.000099999% cases and let juries decide the rest.
The only other sensible sacredness barrier is the common vegetarian "nervous systems are sacred" one. But how can you believe that if you also follow the religion of physics, where everything is just made of atoms?
Is it evil to take one neuron and torture it? What does that even mean? It will be fun when pain and pleasure are fully understood.
And you are going to have a really hard time when mosquitoes start transmitting deadly diseases that kill your family.
Laws in most 2020 Western modern societies have converged to a hypocritical balance between not offending people too much by hiding the killing and minimizing the pain when possible at low cost. Killing animals painlessly is basically always fine if it brings any "non sadistic" pleasure to humans. And torturing animals is fine with approval e.g. to make medicines.
This has the downside of increasing costs for society. Maybe there are practical benefits besides people feeling bad about animals? Maybe we would have more serial killers if people were free to torture animals? Maybe people in butcher shops would become depressive if their bosses weren't forced to use more expensive painless killing methods? Neither of those seems like huge arguments though.
It eventually comes down to: "how much more is a human life worth than that of an animal" which brings Jesus's Matthew 6:25-34 "Do Not Worry" (archive) quote to mind:
Therefore I tell you, do not worry about your life, what you will eat or drink; or about your body, what you will wear. Is not life more than food, and the body more than clothes? Look at the birds of the air; they do not sow or reap or store away in barns, and yet your heavenly Father feeds them. Are you not much more valuable than they?
Non-vegetarian pets owners also baffle Ciro, as most of them basically extend the sacred human line further arbitrarily to certain other cute looking animals like dogs, cats or rabbits, but will gladly kill a cow indirectly by paying someone to pay someone to pay someone to cut it into small pieces. Or they believe that certain specific individuals are sacred. Admittedly, the latter is more rational, and looks a lot of how we treat our own families well, and can accept that other families are not doing so well.
Ciro's even more rational evil side says: the real reason why humans are sacred is a practical one: people have families that love them, and they come to kill you if you kill them, and this starts endless chains of violence that make society unbearable.
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Their only undergraduate courses that matter:
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