Stabilizer (group) Updated 2025-07-16
Suppose we have a given permutation group that acts on a set of n elements.
If we pick k elements of the set, the stabilizer subgroup of those k elements is a subgroup of the given permutation group that keeps those elements unchanged.
Note that an analogous definition can be given for non-finite groups. Also note that the case for all finite groups is covered by the permutation definition since all groups are isomorphic to a subgroup of the symmetric group
TODO existence and uniqueness. Existence is obvious for the identity permutation, but proper subgroup likely does not exist in general.
Ciro Santilli's energy throughout the day varies as follows:
  • morning: highest
  • 11AM: peak exercise performance
  • after lunch: brain death. Possibly due to Ciro's partial Spanish descent?
  • late afternoon and evening: can do some stuff
Ciro has low tolerance to sleep deprivation which makes him very irritable, and low ability to sleep if there is any light. It must have to do with those damned ganglion cell photoreceptors. On the other hand, Ciro Santilli's wife can sleep without any problems with some morning light! It is definitely genetic. Ciro conjectures that people from very Northern parts of the world must have a gene that allows them to sleep even if there is some light, while more equatorial people don't. Maybe: pubmed.ncbi.nlm.nih.gov/33049062/
Ciro has mild olfactory synesthesia for star anise (八角, bajiao), which is widely used in Chinese cuisine and makes Ciro think uncontrollably of the color blue. Ciro does not have any other known synesthesias. He is also prone to nerd sniping form time to time.
Ciro is a reptilian-like being with cold hands and feet and low blood pressure. For this reason he believes that he will die of cancer or some respiratory problem. If the Chinese government doesn't get him first that is. This also partly explains why Ciro is not a big fan of swimming.
Besides Chinese food, Ciro really likes eating fruits and roasted nuts, maybe partly because he was born in Brazil, and partly because of monkey nature, see his Chinese name. At home he is known as "水果大王" (the big king of the fruits). Ciro is also a sucker for yoghurt (natural without added sugars and full fat, fat-tree yoghurt is terrible, often eaten with fruits). Ciro's "favorite drink" could be tonic water with freshly squeezed lemon. Tied with fresh fruit juices. Chocolate-wise, although not a huge fanatic, a Lindt dark chocolate with whole hazelnut pieces bar will do the job.
Ciro does not like receiving or giving gifts on expected social situations like birthdays or Christmas. Ciro believes that every day is equally precious, and can be a day to give, be it through awesome open source software contributions, or if you find something that your friend will like
Ciro has some respiratory allergies. When he was around 5, he had relatively serious asthma crisis which scared his parents to death. Throughout his life, he appears to be allergic at an intermediate level to: mold or dust mites (or whatever it is that old books/pillows have), cats (itching on touch), hay fever (in May in the UK, likely grass pollen). But even outside of hayfever season, Ciro's nose is constantly either running in the cold, or often partially blocked while sleeping throughout the year. Ciro believes however that this also gives him higher resistance to viral infections, since it has been many many years since he had a cold/flu, and when everyone in the office is going down with it, he's just fine. Ciro wonders if his active immune system will actually kill off cancers early, which he ranks as his most likely causes of death, along with respiratory and gastro-intestinal problems. Ciro has low blood pressure and cannot get fat, so cardio vascular problems seem much less likely.
Ciro is generally democrat due to his high compassion level. He believes that politics is highly genetically determined, and that just like you enter a room full of people and immediately like some and dislike others, the same goes for politics. People just vote for whoever they want to see more of because their way of speaking makes them feel good. There is not rationality involved in it at all.
Ciro self diagnoses a slight graphomania in the early 2020's. This is largely what led him to create OurBigBook.com, and contribute to Stack Overflow. Literature Nobel Prize laureate Naguib Mahfouz also suffers from the condition however, so maybe good can also come out of it:
If the urge to write should ever leave me, I want that day to be my last.
When Ciro was quite young, maybe around 7-10, when he got very angry or sad for some stupid reason (bullying perhaps? Ciro forgot), he would have a psychosomatic manifestation: his spine would become visibly curved sideways (scoliosis). While writing this paragraph, Ciro Googled it, and found e.g. medium.com/@michaelrosen_94192/the-root-cause-of-scoliosis-5c461002b634 that describes:
The Root Cause of Idiopathic Scoliosis
It is proposed that Adolescent Idiopathic Scoliosis (AIS) is a condition created by emotional stress. Evidence is presented that unresolved emotional stress can cause unbalanced tensions in the fascia and growing muscles that gradually deform the spinal column.
so it is a somewhat well known thing! Incredible. Can you imagine the level of the passions that lead to such physical deformations? But of course, it was all for nothing.
Espionage Updated 2025-07-16
Stack Overflow content deletion Updated 2025-07-16
Stack overflow allows deleting content/making it visible only to 10k rep users.
Ciro Santilli is strictly against this, and this is an intended core policy of OurBigBook.com.
If you delete people's content randomly, they will be much less likely to write anything.
Getting downvoted to oblivion is one thing, but data loss? Unacceptable.
Only illegal content must ever be deleted. Or extremely obvious spam. But anything in a gray area should never be removed.
Deletion can be done by either:
Euclid's postulates Updated 2025-07-16
Postulates are what we now call axioms.
The amount of detail in which he remembers all that happened is astounding. Not too different from the Murray Gell-Mann interview in that aspect.
Marked read speeds up to 150 MB/s
Write speed burning 5 GB Ubuntu ISO from Dell Inspiron 15: 5.4 MB/s
For clean Dell Inspiron 15 3520 cryptocurrenty laptop bootstrap and backup.
The only thing that matters is that students aim towards the goals described at explain how to make money with the lesson.
Any "homework for which the student cannot use existing resources available online" is a waste of time.
The ideal way to go about it is to reach some intermediate milestone, and then document it. You don't have to do the hole thing! Just go until your patience with it runs out. But while you are doing it, go as deep and wide as you possibly can, without mercy.
The Moonshots in Education project also has a fantastic related quote:
Real World Work. Students must produce learning projects with real world applications and an authentic audience.
It's great right? You can't link to your other answer alone: Stack Overflow link-only answer policy, but you can't copy the other answer either.
And because not all duplicate close votes succeed, see e.g. stackoverflow.com/questions/59649238/how-to-use-the-m5ops-in-gem5-such-m5-exit-and-m5-dump-stats-in-se-mode/63955139#63955139 the result is that someone else will come and answer the same thing in a different wording.
And some answers answer two questions that are not duplicates, e.g. superset/subset questions.
So just do a slight variation wording yourself and get all the reputation.
www.tritoncycles.co.uk/urban-bikes-c4/hybrid-c30/trek-fx-3-equipped-urban-bike-2021-p39860/s102315 XL color Dnister Black. £675.00 plus £35.00 delivery. Disc breaks, 2x9 gears. Bought 2023 on a bit of a sale.
Specs upon buying:
Weight after bought measured differentially on bathroom scale: 13.5 kg
Gears: 11-36T on back, 46-30T on front. So min speed is 30/36 = 0.83 and max is 46/11 = 4.18, so range is 4.18 / 0.83 ~= 5. Compared to Kross which was 11-32 on back vs 48-28 on front, so min 28/32 = 0.875 and max 48/11 = 4.36. So the ranges are very comparable! This confirms Ciro's suspicion that 3 speeds on cranckset is just useless.
I was sized just at the lower limit of XL, but decided to go for it. The seatpost goes all the way into the tube, which is a good thing, might help with noises?
Frame serial under bottom bracket: WTU173C0374S. Registered at: www.bikeregister.com/
Initial impressions:
I'm unable to place a U-lock carrier on this bike in a way that doesn't block one of the two bottles inside frame, or hits leg on if on side. Tried both Kryptonite and Abus ones I have lying around. Shame. Also the Topeak MTS Trunkbag does not fit well on the pannier rack, it is not wide enough to strap: 11cm outer width, 9cm inner width, same geometry as that of the Liv bike.
Log:
2025-09-13: chain reached 0.75, rebuying KMC X9. x9 9 speed chain 114 links. www.amazon.co.uk/dp/B07J38GX7L
2025-08: rear mudgard broke in the exact same way as last time, so I'm saying fuck this bullshit and I just fixed it up with some wire which will likely be more resistant than the shitty metal thing they had.
2025-06-26: I suddenly lost the ability to shift the front gear, cable seemed fine, upon inspection I noticed that the pedal could move sideways. Maybe linked to screeching sound that has been coming from that area for a while. As per www.youtube.com/watch?v=cPQyQnNdews leading to www.youtube.com/watch?v=QqBtB8Kyl2U this is a different system from the Kross one, two piece compression slotted rather than 3 piece. The side to side issue is mentioned precisely at: youtu.be/QqBtB8Kyl2U?t=357 Buying the standalone removal tool: www.amazon.co.uk/Professional-Extracto-Compatible-Hollowtech-Maintenance/dp/B0DP6QF11X Fixing it fixed the shift issue, but I noticed that the little plastic piece was broken. Also a few days later it became loose again during a ride, but thankfully I had the tool and put it back mid rid. TODO wanted to rebuy it but it's really hard to find... Going to try this one: www.bikeparts.co.uk/products/shimano-altus-fc-mt210-chainset-46-30-9-speed-black-170-mm-w-o-chainguard 175 mm and see if it comes with both arms. Bought it. has both arms. But I can't fit it, appears to be 1 or 2 mm short compared to the other cranck, the new arm does go on the old crank. There is a small rubber seal that is perhaps not too well inserted which might be to blame? Fuck my life! On the old one, it seems to be fully inserted into a tight hole. I didn't manage to insert the new one enough to make it fit, but if I remove it then it fits... just removing it for now then, how important could that be? Famous last words. Web says 12-14 nM torque on holding screws.
2025-06: rebuying 2x Shimano B05S brake pads, breaking is not too great and I don't want to repeat last year's episode of on-road failure. Will also be bleeding for the second time, God help me. The old pads weren't too bad, but I replaced them anyways. The bleeding was a failure and the brakes were too soft to be useful at the end, fuck. Went to two bike shops, both said bleeding not too bad, one said likely problem was contamination/friction issues. Tried cleaning rotors further, improved. Buying sandpaper and new rotors as well 2x SHIMANO SM-RT26 6-Bolt Disc Rotor and also got two more brake pads, totalling 3 new before I start putting them in with new rotor.
2025-04: rear shift cable snapped near shifter when going over a cattle grid, was already a bit off in the previous days after last adjust I then noticed. I'll buy a SHIMANO Gear Inner Wire Y60098070 on Amazon and might pass by bike shop as well I'll see.
2025-03: rear middle metal connection broke off read mudguard. Rebuying £21.04 from: www.tritoncycles.co.uk/frames-forks-c6/frame-fork-spares-c152/eurofender-snello-700c-fenders-46mm-rear-p33330/s93941 Quite disappointed with that, didn't come with any screws, though perhaps these are frame dependant. And the drilling was a bit different, this model seems to be intended to have some wiring passing inside via some rubber tubes that I removed, and unfortunately the hole on front was too high up and didn't match up with the screw hole on frame. I just removed the broken metal piece from it and put it on the old mudguard.
2024-09: buying CHUMXINY Brake Bleed Kit: www.amazon.co.uk/dp/B0CXDQ2S1S I hope I don't regret this. But I can't find an original one on Amazon either so... £12.74. Quality is a bit crap but seems to work. The 7mm wrench however is so bad that it can't unscrew a 7mm nut.
2024-09: chain reached 0.75, rebuying KMC X9. x9 9 speed chain 114 links: www.amazon.co.uk/dp/B07J38GX7L
2024-09: when going down a hill in intense breaking, noise started coming from back disk brake. Tried to adjust, but made it worse, had to bail out on nearby bike shop. Readjusted, told me to replace back pads and likely bleed. Bought two Shimano B05S brake pads to replace the B01S that came with the bike, Internet says compatible. Brake maintenance finally caught up with me, it was a great summer and I kept putting it off. Changed just the back one for now, front still has life it seems.
2024-06: noticed a sideways lump on back tyre between spoke 23 and 24 when washing. The only sign of damage was internal near grip part, I could see some clear shearing... God those tyres are crap, or at least crap to what I've subjected them. Inner tube and outside seem perfect, so weird. If only the Schawlbe had worked! But OK now I'm forced to get something new and better, thinking:They had a Schwalbe Marathon Plus 700x35c (non-Tour, as that one didn't fit as per previous experiment) on the shop and I went for it. They said 35c was the maximum recommended for that mudgard which is a bit of a shame, but good to know. Also getting one from Amazon to match on front as shop only had one.
2024-04: micropuncture on front tube? Could not identify during ride, refilled and was OK to get home. Almost no pressure in middle of ride. Passed through some deep water which may have made things worse? Had a small pice of glass-like material stuck in tyre, but didn't seem to penetrate? One day and a half later, was full empty again after full fill without riding, so confirming micropuncture theory. Buying 2x Conti Tube Cross 28 (700C) presta inner tubes.
Tried to put a spare Schwalbe Men's Marathon Plus Tour 700x40C on the bike to get better stability. It seemed to fit the wheel quite well, but unfortunately failed to go well in the fork because it was too tall and hit the mudgard. Without mudgard it might work. Measured height was 6cm for Schwalbe vs 5.3cm for the stock one.
2024-02: another broken spoke... what crappy weak wheels!!! Bought Bavel 290 mm spokes 36pcs 14G J Bend Silver. Broken position was 22nd clockwise from inner tube valve hole.
2023-12: chain reached 0.75, rebuying KMC X9. x9 9 speed chain 114 links.
2023-12: broken spoke! Also had to replace nipple because broke inside nipple. At least learned how to change tire at last.
2023-05: rebuying another Topeak Aero Wedge saddle bag for this new bike
2023-05: 2x Elite custom race cage water bottle frame cages, felt great, much better than those on the Kross! www.elite-it.com/en/products/bottle-cages/fibre-reinforced-material-frp/custom-race
2023-05: ParkTool TR1 tyre levers + GP-2 super patch kit
2023-05: Kask Rapido Medium Black/Yellow fluo helmet, got a more racy helmet too! 69 pounds, way more any previous helmet I've owned: www.kask.com/en/cycling/helmets/rapido_24_2.htm
2023-05: Lezyne V-Pro 10 multi-tool ride.lezyne.com/products/v-pro-tool No spoke wrench unfortunately.
Initial equipment:
Annotated copypasta:
Weight limit: This bike has a maximum total weight limit (combined weight of bicycle, rider and cargo) of 136 kg (300 lb)
General relativity Updated 2025-07-16
Unifies both special relativity and gravity.
Not compatible with the Standard Model, and the 2020 unification attempts are called theory of everything.
One of the main motivations for it was likely having forces not be instantaneous, but rather mediated by field to maintain the principle of locality, just like electromagnetism did earlier.

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