Ciro Santilli @cirosantilli 40

 Articles (13k) Discussions (28) Comments (65) Follows  Received likes Files

New Updated  Top  Announced  A-Z  Liked  Followed

Group of Lie type Updated 2025-07-16

In the classification of finite simple groups, groups of Lie type are a set of infinite families of simple lie groups. These are the other infinite families besides te cyclic groups and alternating groups.

A decent list at: en.wikipedia.org/wiki/List_of_finite_simple_groups, en.wikipedia.org/wiki/Group_of_Lie_type is just too unclear. The groups of Lie type can be subdivided into:

Chevalley groups
TODO the rest

The first in this family discovered were a subset of the Chevalley groups

A_{n} (q)

by Galois:

PS L (2, p)

, so it might be a good first one to try and understand what it looks like.

TODO understand intuitively why they are called of Lie type. Their names

A_{n}

B_{n}

seem to correspond to the members of the classification of simple Lie groups which are also named like that.

But they are of course related to Lie groups, and as suggested at Video "Yang-Mills 1 by David Metzler (2011)" part 2, the continuity actually simplifies things.

 Read the full article

prime-number-theorem Updated 2025-07-16

 View more

Consider this is a study in failed computational number theory.

The

n / l n (n)

approximation converges really slowly, and we can't easy go far enough to see that the ration converges to 1 with only awk and primes:

sudo apt intsall bsdgames
cd prime-number-theorem
./main.py 100000000

Runs in 30 minutes tested on Ubuntu 22.10 and P51, producing:

Figure 1.
Linear $π (n)$ vs $n / l n (n)$ approximation plot
. $f (n) = n$ and $f (n) = l o g (n)$ are added to give a better sense of scale. $l o g (n)$ is too close to 0 and not visible, and the approximation almost overlaps entirely with $p i$ .

Figure 2.
$π (n) - n / l n (n)$
. It is clear that the difference diverges, albeit very slowly.

Figure 3.
$π (n) / (n / l n (n))$
. We just don't have enough points to clearly see that it is converging to 1.0, the convergence truly is very slow. The logarithm integral approximation is much much better, but we can't calculate it in awk, sadface.

But looking at: en.wikipedia.org/wiki/File:Prime_number_theorem_ratio_convergence.svg we see that it takes way longer to get closer to 1, even at

1 0^{24}

it is still not super close. Inspecting the code there we see:

(* Supplement with larger known PrimePi values that are too large for \
Mathematica to compute *)
LargePiPrime = {{10^13, 346065536839}, {10^14, 3204941750802}, {10^15,
     29844570422669}, {10^16, 279238341033925}, {10^17,
    2623557157654233}, {10^18, 24739954287740860}, {10^19,
    234057667276344607}, {10^20, 2220819602560918840}, {10^21,
    21127269486018731928}, {10^22, 201467286689315906290}, {10^23,
    1925320391606803968923}, {10^24, 18435599767349200867866}};

so OK, it is not something doable on a personal computer just like that.

 Read the full article

python/sphinx/virtual_method Updated 2025-07-16

 View more

Polymorphism example:

 Read the full article

python/typing_cheat/hello.py Updated 2025-07-16

 View more

The hello world!

 Read the full article

Finite field Updated 2025-07-16

 View more

A convenient notation for the elements of

GF (n)

of prime order is to use integers, e.g. for

GF (7)

we could write:

GR (7) = {- 3, - 2, - 1, 0, 1, 2, 3}

(1)

which makes it clear what is the additive inverse of each element, although sometimes a notation starting from 0 is also used:

GR (7) = {0, 1, 2, 3, 4, 5, 6}

(2)

For fields of prime order, regular modular arithmetic works as the field operation.

For non-prime order, we see that modular arithmetic does not work because the divisors have no inverse. E.g. at order 6, 2 and 3 have no inverse, e.g. for 2:

0 \times 2 = 01 \times 2 = 22 \times 2 = 43 \times 2 = 04 \times 2 = 25 \times 2 = 4

(3)

we see that things wrap around perfecly, and 1 is never reached.

For non-prime prime power orders however, we can find a way, see finite field of non-prime order.

Video 1.

Finite fields made easy by Randell Heyman (2015)

Source. Good introduction with examples

 Read the full article

Finite general linear group Updated 2025-07-16

 View more

general linear group over a finite field of order

m

. Remember that due to the classification of finite fields, there is one single field for each prime power

m

Exactly as over the real numbers, you just put the finite field elements into a

n \times n

matrix, and then take the invertible ones.

 Read the full article

Flash memory Updated 2025-07-16

 View more

Video 1.

The Engineering Puzzle of Storing Trillions of Bits in your Smartphone / SSD using Quantum Mechanics by Branch Education (2020)

Source. Nice animations show how quantum tunnelling is used to set bits in flash memory.

 Read the full article

Form of government Updated 2025-07-16

 View more

en.wikipedia.org/wiki/List_of_forms_of_government

Rasselas Prince of Abyssinia CHAPTER VIII www.gutenberg.org/cache/epub/652/pg652-images.html:

Oppression is, in the Abyssinian dominions, neither frequent nor tolerated; but no form of government has been yet discovered by which cruelty can be wholly prevented. Subordination supposes power on one part and subjection on the other; and if power be in the hands of men it will sometimes be abused. The vigilance of the supreme magistrate may do much, but much will still remain undone. He can never know all the crimes that are committed, and can seldom punish all that he knows.

 Read the full article

Fourier transform Updated 2025-07-16

 View more

Continuous version of the Fourier series.

Can be used to represent functions that are not periodic: math.stackexchange.com/questions/221137/what-is-the-difference-between-fourier-series-and-fourier-transformation while the Fourier series is only for periodic functions.

Of course, every function defined on a finite line segment (i.e. a compact space).

Therefore, the Fourier transform can be seen as a generalization of the Fourier series that can also decompose functions defined on the entire real line.

As a more concrete example, just like the Fourier series is how you solve the heat equation on a line segment with Dirichlet boundary conditions as shown at: Section "Solving partial differential equations with the Fourier series", the Fourier transform is what you need to solve the problem when the domain is the entire real line.

 Read the full article

Four Treasures of the Study Updated 2025-07-16

 View more

Video 1.

Four Treasures of Chinese Study by a journey of culture (2022)

Source. Over the top and likely without copyright.

Video 2.

Four Treasures of the Study by Li's Ink World (2021)

Source. A more realistic down to Earth one.

 Read the full article

Ciro Santilli's hardware / Motorola Moto G6 Play (2018) Updated 2025-07-16

 View more

Circa 2020, a bowl fell on it from about 25 cm height and broke the screen. £159.99.

www.gsmarena.com/motorola_moto_g6_play-9002.php Upgradable to Android 9.

2023-10: unable to connect to Giffgaff. "Network unavailable". Same SIM works in other phones. So annoying. Update APN to match: www.giffgaff.com/help/articles/internet-apn-settings-guide. Went next to a tower and then got signal. So the receiver is much worse than the pixel one. Vibration appears to be broken.

Authy sync worked: 2023.

 Read the full article

University entry exam Updated 2025-07-16

 View more

These are the most evil examinations society has.

They mean that until you are 18, you have to study a bunch of generic crap you hate just to get into university. Rather than studying whatever it is that you truly love to become a God at it as fast as possible and have any chance of advancing the field.

And then, if you decide that you want to change, which is not unlikely since you haven't really try to study what you signed up for before then, it can be very hard and time consuming, leading to a bunch of adults with useless degress they will never use at work.

With the invention of the Internet, all teaching material can be free and open source. Only laboratory space has any cost (besides the opportunity cost of participation in actual projects in a research team).

Per-country list: en.wikipedia.org/wiki/List_of_admission_tests_to_colleges_and_universities

 Read the full article

Ciro Santilli's hardware / Mechanical and electrical tools Updated 2025-07-16

 View more

2020-01 www.amazon.co.uk/dp/B07D318N7Z

2020-01 "Heat Gun, SEEKONE Professional 2000W 50℃- 600℃ Variable Temperature Control Hot Air Gun Kit with 2 Temperature Modes 7 Accessories for D" www.amazon.com/dp/B078S5QMFG Initially for for cell phone repair, but later learnt they are also useful for heat shrink.

2020-11 BOA 13-2612 Strap Wrench, 6-Inch Capacity 8-Inch Long Lever www.amazon.com/dp/B00096JDKS Official: www.boatoolcorp.com/our-products/boa-constrictor-range/boa-constrictor/

2019-09 "Draper Redline 68001 160 mm Heavy Duty Pliers Set with Soft Grip Handles (3-Piece)" web.archive.org/web/20190903191215/https://www.amazon.co.uk/dp/B071JL6LLL (archive)

2019-08: www.amazon.co.uk/dp/B000LFRYG2 (archive) "Silverline SP1236 Combination Spanner, 8-19 mm - 12 Pieces" 8.48 pounds. Because I needed the 15mm for bike pedal, and the price of 1 and the full set were very close.

6 10/11/12/13/14/17 mm Combination Wrench Set WRENCH SET COMBINATION Open-Ended Spanner/Ring Spanner Set www.amazon.co.uk/dp/B07BZLVGX8 (archive) But they sent one wrong, 8 instead of 11. Chrome Vanadium Steel. Markings: "DROP FORGED A". Quality feels crappy, not very smooth.

2017: Teng 621011 Double Open Ended Spanner 10x11mm www.amazon.co.uk/dp/B0001P0VP8 (archive)

2017: Magnusson AMS49 5M TAPE MEASURE 5m retractable flexible rule. www.screwfix.com/p/magnusson-ams49-5m-tape-measure/5315v (archive)

 Read the full article

University has become a luxury item Updated 2025-07-16

 View more

medium.com/left-right/the-education-system-is-about-to-implode-5c95f774b523 The Education System is About to Implode by Nicholas Budny (2020)

Stanford, MIT, Harvard and Oxford are luxury goods in the same sense that a Mercedes-Benz might be, or the latest iPhone. They sell an aesthetic experience that provides the consumer with social status, similar to acquiring expensive clothes or a fancy house.

Video 1.

Bar scene from Good Will Hunting

. Source. This scene is way way overdone. But:

Hero: You wasted $150,000 on an education you coulda got for $1.50 in late fees at the public library.
Bad guy: Yeah, but I will have a degree. And you'll be serving my kids fries at a drive-through on our way to a skiing trip.

 Read the full article

Ciro Santilli's hardware / ELEGOO Upgraded Electronics Fun Kit Updated 2025-07-27

 View more

2022-10 ELEGOO Upgraded Electronics Fun Kit www.elegoo.com/products/elegoo-electronics-fun-kits-4-versions Manuals:

Elegoo Breadboard power supply module MB‐V2:
- Input voltage: 6.5-9v (DC) via 5.5mm x 2.1mm plug
- Output voltage: 3.3V/5v
- Maximum output current: 700 mA
TODO center positive or center negative?
Does not come with AC adapter, getting this one: www.amazon.co.uk/dp/B08ZN476FW output: DC 9V 1A Power Supply Adapter, Plug 5.5mm x 2.1mm, Center Positive,B rand: Security-01, input: AC 100-240V 50/60 Hz, Cable length: 1.8m
Parts list from the ZIP:
resistors:
- 10x each:
  - 10
  - 100
  - 330
  - 2k
  - 5.1k
  - 10k
  - 100k
  - 1M
- 30x 220
1n4007 General Purpose Rectifier
22pf 104 Ceramic Capacitor
4N35 optocoupler
74HC595 8-bit serial-in, serial or parallel-out shift register with output latches; 3-state
Active buzzer
Buttons
CDS-55 Photoresistor
Electrolytic Capacitor
Focusens MF52D 103f 3950 thermistor. Beta value 25/50 Celcius: 3950. R_25: I measured 9.61 k Ohms. The number 103 they document as:
- digit 1: code of dimension
- digit 2: rated resistance
- digit 3: fills with its precision symbol
These descriptions are weird, but ChatGPT has the theory that the first two digits are actual values, and the last is multiplier, so $10 \times 1 0^{3}$ which makes 10k.
but I have no idea how that maps to 10 k Ohms.
PN2222 General Purpose Transistor
Passive buzzer
3386p Bourns Precision Potentiometer - 1 103T: from 0 to 10k Ohms, measured with multimeter. According to the manual the "103" mean 10 k oms, which is consistent with our measurement. "P 103" is etched into the part.
LEDs:
- White LED 10x
- Kingbright RGB LEDs 10x red, green, yellow, blue:
  maximum Continuous Forward Current: 30 mA for read and blue, 25 mA for green
  303025
  under 20 mA
  Forward Voltage: 2.0 V typical, 2.5 V max
  20 mA appears to be the typical operation. So with the 2.0 V drop on 5 V power we want a resistor such that:
  $(5 - 2) / r = 20 \times 1 0^{- 3} ⟹ r = 150Ω$
  (1)
  for the max 50 mA we would instead have 60 Ohms

 Read the full article

Ciro Santilli's hardware / Bicycle products Updated 2025-07-16

 View more

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.

 Read the full article

University is broken Updated 2025-07-16

 View more

You just have to spend a few minutes with students until they complain about the courses or teachers. And you just have to spend a few hours with teachers until they complain about the students or broader system.

University is broken, and everyone knows it. The only question now is finding a viable, "political cash flow positive" path, into something better.

Bibliography:

academeblog.org/2022/10/05/american-universities-are-going-to-implode/ American Universities Are Going to Implode (2022) by www.linkedin.com/in/jsgabin/
theimaginativeconservative.org/2020/04/higher-education-implode-alexander-zubatov.html Higher Education Is About to Implode by Alexander Zubatov (2020)
2024-05-28 www.theguardian.com/education/article/2024/may/28/i-see-little-point-uk-university-students-on-why-attendance-has-plummeted ‘I see little point’: UK university students on why attendance has plummeted
"There’s a bit of a feeling that there is just box-ticking going on [among students], and getting a degree at the end of it."
Give it to me, baby. OurBigBook incoming.

 Read the full article

Unmigrated sections of the old version of Ciro Santilli's website Updated 2025-07-16

 View more

It is interesting to see how your own ideas shift with time, and Ciro Santilli doesn't think the following are very important anymore, so he was lazy to migrate them.

When he did the original website Ciro was in a "I must show off my skills to get a job mindset", but then after he landed a few jobs he moved to a "CV websites are useless, just do amazing projects and showcase them on your website to help them succeed" mindset.

 Read the full article

Ciro Santilli's hardware / 2023 laptop buy research Updated 2025-07-16

 View more

The P51 is a bit too heavy, and the battery could be better!