Ciro Santilli @cirosantilli 40

One major difference between the elliptic curve over a finite field or the elliptic curve over the rational numbers the elliptic curve over the real numbers is that not every possible $x$ generates a member of the curve.

This is because on the Equation "Definition of the elliptic curves" we see that given an $x$, we calculate $x^3+ax+b$, which always produces an element $y^2$.

But then we are not necessarily able to find an $y$ for the $y^2$, because not all fields are not quadratically closed fields.

For example: with $a=1$ and $b=1$, taking $x=1$ gives:and therefore there is no $y\in \mathbb{Q}$ that satisfies the equation. So $x=1$ is not on the curve if we consider this elliptic curve over the rational numbers.

That $x$ would also not belong to Elliptic curve over the finite field ${\mathbb{F}}_4$, because doing everything $\mathrm{mod}4$ we have:Therefore, there is no element $y\in {\mathbb{F}}_4$ such that $y\times y=2$ or $y\times y=3$, i.e. $2$ and $3$ don't have a multiplicative inverse.

For the real numbers, it would work however, because the real numbers are a quadratically closed field, and $\sqrt{3}\in \mathbb{R}$.

For this reason, it is not necessarily trivial to determine the number of elements of an elliptic curve.

Given:the norm ends up being:

E.g. in ${\mathbb{C}}^2$:

Ultimate explanation: math.stackexchange.com/questions/776039/intuition-behind-normal-subgroups/3732426#3732426

Only normal subgroups can be used to form quotient groups: their key definition is that they plus their cosets form a group.

Intuition:

One key intuition is that "a normal subgroup is the kernel" of a group homomorphism, and the normal subgroup plus cosets are isomorphic to the image of the isomorphism, which is what the fundamental theorem on homomorphisms says.

Therefore "there aren't that many group homomorphism", and a normal subgroup it is a concrete and natural way to uniquely represent that homomorphism.

The best way to think about the, is to always think first: what is the homomorphism? And then work out everything else from there.

Era of quantum computing before we reach physical errors small enough to do perfect quantum error correction as demonstrated by the quantum threshold theorem.

Setting: you are sending bits through a communication channel, each bit has a random probability of getting flipped, and so you use some error correction code to achieve some minimal error, at the expense of longer messages.

This theorem sets an upper bound on how efficient you can be in your encoding, for any encoding.

The next big question, which the theorem does not cover is how to construct codes that reach or approach the limit. Important such codes include:

But besides this, there is also the practical consideration of if you can encode/decode fast enough to keep up with the coded bandwidth given your hardware capabilities.

news.mit.edu/2010/gallager-codes-0121 explains how turbo codes were first reached without a very good mathematical proof behind them, but were still revolutionary in experimental performance, e.g. turbo codes were used in 3G/4G.

But this motivated researchers to find other such algorithms that they would be able to prove things about, and so they rediscovered the much earlier low-density parity-check code, which had been published in the 60's but was forgotten, partially because it was computationally expensive.

www.knfusa.com/en/laboport/ (archive).

It runs one instance of the Linux kernel and has one IP address. Each node is therefore a complete computer. As such is must also contain RAM memory, disk storage and a network interface controller.

And the articles that really matter:

Web of Stories contains amazing interviews with many (mostly American) winners.

See Surely You're Joking, Mr. Feynman chapter Alfred Nobel's Other Mistake's amazing comments about the Nobel Prize.

TODO who is the digital switch person he mentions?

NIST database for spectral line: physics.nist.gov/PhysRefData/ASD/lines_form.html

Let's do a sanity check.

Searching for "H" for hydrogen leads to: physics.nist.gov/cgi-bin/ASD/lines1.pl?spectra=H&limits_type=0&low_w=&upp_w=&unit=1&submit=Retrieve+Data&de=0&format=0&line_out=0&en_unit=0&output=0&bibrefs=1&page_size=15&show_obs_wl=1&show_calc_wl=1&unc_out=1&order_out=0&max_low_enrg=&show_av=2&max_upp_enrg=&tsb_value=0&min_str=&A_out=0&intens_out=on&max_str=&allowed_out=1&forbid_out=1&min_accur=&min_intens=&conf_out=on&term_out=on&enrg_out=on&J_out=on

From there we can see for example the 1 to 2 lines:

We see that the table is sorted from lower from level first and then by upper level second.

So it is good to see that we are in the same 121nm ballpark as mentioned at hydrogen spectral line.

TODO why I can't see 2s to 2p transitions there to get the fine structure?

This is the one that hit Ciro Santilli the hardest, coming in at the point in which he started to discern between games and the real world a little better. His parents bought it for him during a trip to Disney World in Florida in 1996 (?), since electronics were much cheaper in the USA.

So as Ciro became older, and turned into a software engineer, he started to become more and more morbidly curious about "N64 internals": tool-assisted speedrun, how the devkit looks like, how games were developed for it, hardware leaks, etc.

Luckily Ciro's mind is not interested enough by that useless shit for Ciro to seriously study it himself. But that's what YouTube is for, right? Why do useless stuff when other more useless people can do it for you?

The console has only 4 MB of RAM memory. It is quite incredible what can be done with 8 MB, from the point of view of a 2020 worls where 16 GB laptops are the norm.

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.

The 2020 one on official website: www.trekbikes.com/gb/en_GB/bikes/hybrid-bikes/fitness-bikes/fx/fx-3-disc/p/28474/ archive.ph/wip/jMDdw TODO find 2021.

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:

2026-04-15: was hearing back wheel hit something periodically. First I separated the disk breaks with the tool but didn't solve. Then I noticed broken spoke, 9th clockwise from tube valve. I replaced it, but unfortunately spreading the disk break made me lose back breaks so I had to go into break fluid territory. Some conclusions: you can't do break fluid without the break pads and disk break in the break. This opens it up for contamination. The correct thing to do is to put a plastic protection on top of them. I spilled fluid on break at one point, it was horrible, I ended up changing the break pad which improved things a bit. Overall break felt slightly worse than before but passable.

2026-02-13: chain reched .7, changed it to new KMC X9. x9 9 speed chain 114 links. www.amazon.co.uk/dp/B07J38GX7L Started slipping like crazy on cassette when I pedaled hard, changed it to www.amazon.co.uk/dp/B073H3DST7 SHIMANO CS-HG400 9-speed cassette (11-36 teeth) which internet said was compatible and it seems to be. Didn't manage to remove it and needed help from bike shop as usual. After that it stopped slipping.

2025-09-30: kickstand broken while taking it on car. Proceeding to buy Bontrager Rear Mount Adjustable Kickstand www.trekbikes.com/gb/en_GB/equipment/bike-accessories/bike-kickstands/bontrager-rear-mount-adjustable-kickstand/p/36015/ 20 pounds + 4 delivery. The new kickstand is slightly different from the previous one, it is less slick looking, but perhaps a bit more sturdy, notably the little arm is shorter which might help prevent the previous failure mode. It came with 3 types of screws, but the two of correct diameter were a bit shorter or longer than the old ones so I just kept the old ones.

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: buying another pair of Shimano 324 combination pedals for it: www.wiggle.com/p/shimano-m324-combination-pedals

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 hand pump, I think Sport Drive HP? ride.lezyne.com/collections/hand-pumps/products/sport-drive-hp

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)

2026-04: finally lost the second Cateye Viz450, the attachment is just too crap

2026-03-23: old Cateye Viz450 not charing anymore, it seems that the usb charging port disconnected from the PCB, if I bend it a bit it charges, but it is hard. Tried to prope it open with flat screwdriver but failed, shame, not very repairable, I'd be able to solder if if I could open it. So that's the failure mode. Rebuying.

2025-11-06: bought another Cateye Viz450 for baby trailer.

2022-02: lost my Karrimor REFLEKT, must have fallen off from trouses somewhere.

2022-02: bought Burg Wachter Sold Secure Bike Chain, Lock and Ground Anchor Kit 1m, 10mm chain width: www.amazon.co.uk/Burg-Wachter-Sold-Secure-Gold-Chain/dp/B09MMGL9B7

2022-02 bought Kryptonite Kryptoflex double loop cable 1.2m length 10mm diameter braided steel cable: www.kryptonitelock.com/en/products/product-information/current-key/210818.html

2022-02: bought a Trelock BC 115/110/4 chain white for my saddle after Liv Flourish 2 (2018) the saddle of was stolen at home. Same as this but white: www.trelock.com/en/lock/locks/chain-locks/bc-115-110-4-green. The keys are a bit larger than I'd like.

2021-11: buying a Cateye ViZ450 www.cateye.com/intl/products/safety_lights/TL-LD820/ 51 dollars after CatEye RAPID X2 was stolen. Unfortunately, it is not very compatible with my Topeak saddle bag... the attachment is to wide to fit the saddble bag, and even if it did it is slanted to account for seat tube slant so it would not be very verfical. Arghh, they have futher options on the website: www.cateye.com/intl/products/parts/5342460/ that is the one I need, Clip C-2 or Clip C-1N. On Amazon it didn't have clear choices for that... mine came with the BracketSP-15. Ah, can buy on Amazon for 3 dollars, OK then.

2021-11: COZYROOMY multitool broke apart already, like before, but much sooner this time. What a piece of junk!!! Buying the Topeak Mini 18+ Bike Multitool www.topeak.com/global/en/products/75-Mini-Tools/173-mini-18+ Has a spoke wrench.

2021-09: COZYROOMY multitool stolen, even though it was completely in pieces already. 2021-09-21 12:30PM discovered, seat bag open, one tool on floor, and some leftovers inside, but black bag gone. Bicycle last seen 2021-09-20 6PM. Would likely have spotted it if it had happened before. Bicycle last used: 2021-09-19 6PM. Would almost for sure have seen it if it had happened by then. Rebought it.

2021-07 Topeak MTS Trunkbag EX Strap Type www.topeak.com/global/en/products/192-Rear-Rack-Bags/859-MTX-TRUNKBAG-EX Fit nicely on the back of the Kross bicycle (2017). 8L. Originally to carry some extra food and water on a long summer trip. 36 pounds.

2020-11-30: Bought more "Finish Line DRY Teflon Bicycle Chain Lube" 8oz/240ml www.amazon.com/dp/B00Z779GMO/ after previous disaster with the bottle because lock is a bit hard to open.

2020-11-30 WD-40 Bike, All Conditions Lube Bicycle Lubricant, 250ml. Markings: "Contains PTFE". www.amazon.com/dp/B00O8QF3PY Sprays out of bottle, so very thin.

2020-11: Park Tool CC-2 Chain Checker Tool www.amazon.co.uk/dp/B000OZFILW 24 pounds www.parktool.com/product/chain-checker-cc-2

2020-04: www.amazon.co.uk/gp/product/B014LC7HS0 "Park Tool HPG-1 High Performance Grease", 113 g, blue. www.parktool.com/product/high-performance-grease-hpg-1#tabbed-section | www.parktool.com/assets/doc/product/HPG-1_SDS.pdf

2020-02: CatEye AMPP500 45 pounds www.cateye.com/intl/products/headlights/HL-EL085RC/ High mode 500 lumens: 1.5hrs, Daytime HyperConstant mode 500/250 lumens： 5hrs. 2020-11: noticed it was cracked on top front between button and light, I think I dropped it the other day from waist height.

2020-02: Karrimor REFLEKT Band 2 pounds from Sports Direct to replace old that I destroyed by playing with it with hands on work desk www.karrimor.com/karrimor-reflect-band-765007

2020-01: Muc-Off Drivetrain Cleaner - 500ml www.halfords.com/cycling/bike-maintenance/bike-cleaning/muc-off-drivetrain-cleaner-500ml

2020-01: Halfords Microfibre Heavy Duty Cloths www.halfords.com/motoring/car-cleaning/sponges-brushes-buckets/halfords-microfibre-heavy-duty-cloths (archive) 87% polyester, 13% polyamide.

2019-12: www.amazon.co.uk/gp/product/B07GQSXN8B SENZEAL Bicycle Spoke Wrench Tool Spoke Key Spanner 6 in 1 for Bike Wheel Cycle Wrench 10-15 Gauge. TODO 2024: can't find those for the life in me.

2019-12: Halford's Bike Hut Chain Cleaning Kit: www.halfords.com/cycling/bike-maintenance/bike-cleaning/bikehut-chain-cleaning-kit 18 pounds. GCN video using it: www.youtube.com/watch?v=KM6mzE5lQ0w Review video saying it is useless: www.youtube.com/watch?v=rCo41pftAjU

2019-11: Multitool: www.amazon.co.uk/dp/B07MW3K2GK "COZYROOMY Bike Repair Kits - Bicycle tool kit with 10 in 1 Multi-Function Bike Tool, multi-purpose bone wrench And related spare tools, 1 Portable tool bag, 6 Month Warranty". No spoke wrench unfortunately. But does have 15mm bone wrench, which opens Kross front wheel. Some months later, the thing came apart, quality was a bit shit. But I kept it in the saddle bag anyways for a long time, and just used it by putting part of it manually together.

2019-11: "CatEye RAPID X2" real lights, 40 dollars. Hopefully to increase side visibility at night, and day visibility on fast roads when cycling further on weekends. www.cateye.com/intl/products/safety_lights/TL-LD710-R/ (archive) USB rechargeable. 80 lumens in high mode lasting 1 hour, 5 hours in low mode, 30 hours flashing, 16 hours rapid/pulse. Lost 2021-11 in a big city, didn't know the path well, had to cross a bunch of streets, was on back of back bag, likely stolen.

2019-10 WD-40 Smart Straw 450ml www.amazon.com/dp/B01MEHN4VC (archive)

2019-10 Finish Line Dry Teflon Tube www.amazon.com/dp/B00B704LZW (archive) Tube broke while opening the first day. I glued it with some superglue, but two months later found it leaked into my "oils bag", so I threw it away... it must have penetrated through the super glue.

2019-08: "CatEye CA475RAPMIN Rapid Mini Rear Lights and Reflectors, Black" stolen: www.amazon.co.uk/dp/B01I4193PY (archive). Very good quality. Those USB rechargeable lights you just have got to take off with you whenever parked in town or else drug addicts will steal them because they are easy to remove for recharging. Tempted to just stick to dynamo ones that are screwed in. Re-bought original back light: AXA Basta, was a bit different from previous one, cannot take in lamps anymore, even though there is the plastic casing for them! Just not metal / wires.

Nuclear magnetic resonance work: