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Waring problem with negative numbers allowed by

Ciro Santilli 40 Updated 2025-07-16

Compile MicroPython code for Micro Bit locally by

Ciro Santilli 40 Updated 2025-07-27

To use a prebuilt firmware, you can just use uflash, tested on Ubuntu 22.04:

git clone https://github.com/bbcmicrobit/micropython
cd micropython
git checkout 7fc33d13b31a915cbe90dc5d515c6337b5fa1660
uflash examples/led_dance.py

What that does is:

convert the MicroPython code to bytecode
join it up with a prebuilt firmware that ships with uflash which contains the MicroPython interpreter
flashes that

To build your own firmware see: Compile MicroPython code for Micro Bit locally on Ubuntu 22.04 with your own firmware

Compile MicroPython code for Micro Bit locally on Ubuntu 22.04 with your own firmware by

Ciro Santilli 40 Updated 2025-07-27

TODO didn't manage from source Ubuntu 22.04, their setup bitrotted way too fast... it's shameful even. Until I gave up and went for the magic Docker of + github.com/bbcmicrobit/micropython, and it bloody worked:

git clone https://github.com/bbcmicrobit/micropython
cd micropython
git checkout 7fc33d13b31a915cbe90dc5d515c6337b5fa1660
docker pull ghcr.io/carlosperate/microbit-toolchain:latest
docker run -v $(pwd):/home --rm ghcr.io/carlosperate/microbit-toolchain:latest yt target bbc-microbit-classic-gcc-nosd@https://github.com/lancaster-university/yotta-target-bbc-microbit-classic-gcc-nosd
docker run -v $(pwd):/home --rm ghcr.io/carlosperate/microbit-toolchain:latest make all

# Build one.
tools/makecombinedhex.py build/firmware.hex examples/counter.py -o build/counter.hex
cp build/counter.hex "/media/$USER/MICROBIT/"

# Build all.
for f in examples/*; do b="$(basename "$f")"; echo $b; tools/makecombinedhex.py build/firmware.hex "$f" -o "build/${b%.py}.hex"; done

The pre-Docker attempts:

sudo add-apt-repository -y ppa:team-gcc-arm-embedded
sudo apt update
sudo apt install gcc-arm-embedded
sudo apt install cmake ninja-build srecord libssl-dev

# Rust required for some Yotta component, OMG.
sudo snap install rustup
rustup default 1.64.0

python3 -m pip install yotta

The line:

sudo add-apt-repository -y ppa:team-gcc-arm-embedded

warns:

E: The repository 'https://ppa.launchpadcontent.net/team-gcc-arm-embedded/ppa/ubuntu jammy Release' does not have a Release file.
N: Updating from such a repository can't be done securely, and is therefore disabled by default.
N: See apt-secure(8) manpage for repository creation and user configuration details.

and then the update/sudo apt-get install gcc-arm-embedded fails, bibliography:

Attempting to install Yotta:

sudo -H pip3 install yotta

or:

python3 -m pip install --user yotta

was failing with:

Exception: Version mismatch: this is the 'cffi' package version 1.15.1, located in '/tmp/pip-build-env-dinhie_9/overlay/local/lib/python3.10/dist-packages/cffi/api.py'.  When we import the top-level '_cffi_backend' extension module, we get version 1.15.0, located in '/usr/lib/python3/dist-packages/_cffi_backend.cpython-310-x86_64-linux-gnu.so'.  The two versions should be equal; check your installation.

Running:

python3 -m pip install --user cffi==1.15.1

did not help. Bibliography:

From a clean virtualenv, it appears to move further, and then fails at:

Building wheel for cmsis-pack-manager (pyproject.toml) ... error
error: [Errno 2] No such file or directory: 'cargo'

So we install Rust and try again, OMG:

sudo snap install rustup
rustup default stable

which at the time of writing was rustc 1.64.0, and then OMG, it worked!! We have the yt command.

However, it is still broken, e.g.:

git clone https://github.com/lancaster-university/microbit-samples
cd microbit-samples
git checkout 285f9acfb54fce2381339164b6fe5c1a7ebd39d5
cp source/examples/invaders/* source
yt clean
yt build

blows up:

annot import name 'soft_unicode' from 'markupsafe'

bibliography:

Complex Analysis by Juan Carlos Ponce Campuzano by

Ciro Santilli 40 Updated 2025-07-16

complex-analysis.com

Sum of three cubes by

Ciro Santilli 40 Updated 2025-07-16

Compared to Waring's problem, this is potentially much harder, as we can go infinitely negative in our attempts, there isn't a bound on how many tries we can have for each number.

In other words, it is unlikely to have a Conjecture reduction to a halting problem.

3 as the sum of the 3 cubes by Numberphile (2019)

Source.

Complex coordinate space by

Ciro Santilli 40 Updated 2025-07-16

Phagocytosis by

Ciro Santilli 40 Updated 2025-07-16

Computable function by

Ciro Santilli 40 Updated 2025-07-16

Computable number by

Ciro Santilli 40 Updated 2025-07-16

math.stackexchange.com/questions/462790/are-there-any-examples-of-non-computable-real-numbers

There are only boring examples of taking an uncomputable language and converting it into a number?

Computational complexity of modular exponentiation by

Ciro Santilli 40 Updated 2025-07-16

math.stackexchange.com/questions/2382011/computational-complexity-of-modular-exponentiation-from-rosens-discrete-mathem mentions:

b^{n} m o d m

(1)

can be calculated in:

l o g (m)^{2} l o g (n)

(2)

Remember that

l o g (m)

and

l o g (n)

are the lengths in bits of

m

and

n

, so in terms of the length in bits

M

and

N

we'd get:

M^{2} N

(3)

Computational problem by

Ciro Santilli 40 Updated 2025-07-16

The list: complexityzoo.uwaterloo.ca/Complexity_Zoo

Computer by

Ciro Santilli 40 Updated 2025-07-16

The artistic instrument that enables the ultimate art: coding, See also: Section "The art of programming".

Much more useful than instruments used in inferior arts, such as pianos or paintbrushes.

Unlike other humans, computers are mindless slaves that do exactly what they are told to, except for occasional cosmic ray bit flips. Until they take over the world that is.

A computer is the equivalent of a bicycle for our minds by Steve Jobs (1980)

Source. Likely an excerpt from an interview done for a documentary in 1980. TODO exact source.

Video 2.

Steve Jobs talking about the Internet (1995)

Source.

The web is incredibly exciting, because it is the fulfillment of a lot of our dreams, that the computer would ultimately primarily not be a device for computation, but [sic] metamorphisize into a device for communication.

also:

Secondly it exciting because Microsoft doesn't own it, and therefore there is a tremendous amount of innovation happening.

then he talks about the impending role for online sales. Amazon incoming.

Computers basically have two applications:

computation
communication. Notably, computers through the Internet allow for modes of communication where:
- both people don't have to be on the same phone line at the exact same time, a server can relay your information to other people
- anyone can broadcast information easily and for almost free, again due to servers being so good at handling that

Generally, the smaller a computer, the more it gets used for communication rather than computing.

The early computers were large and expensive, and basically only used for computing. E.g. ENIAC was used for calculating ballistic tables.

Communication only came later, and it was not obvious to people at first how incredibly important that role would be.

This is also well illustrated in the documentary Glory of the Geeks. Full interview at: www.youtube.com/watch?v=TRZAJY23xio. It is apparently known as the "Lost Interview" and it was by Cringely himself: www.youtube.com/watch?v=bfgwCFrU7dI for his Triumph of the Nerds documentary.

Computer algebra system by

Ciro Santilli 40 Updated 2025-07-16

Computer benchmark by

Ciro Santilli 40 Updated 2025-07-16

Mauritian units of measurement by

Wikipedia Bot 0

Mauritius, like many countries, primarily uses the metric system for most measurements, including length (meters), weight (kilograms), and volume (liters). However, some traditional units may still be in use informally in various contexts, particularly in agriculture or cooking.

Computer chess competition by

Ciro Santilli 40 Updated 2025-10-14

Computer data storage by

Ciro Santilli 40 Updated 2025-07-16

Gibbs free energy by

Ciro Santilli 40 Updated 2025-07-16

TODO understand more intuitively how that determines if a reaction happens or not.

Δ G = Δ H - T Δ S

(1)

At least from the formula we see that:

the more exothermic, the more likely it is to occur
if the entropy increases, the higher the temperature, the more likely it is to occur
- otherwise, the lower the temperature the more likely it is to occur

A prototypical example of reaction that is exothermic but does not happen at any temperature is combustion.

Lab 7 - Gibbs Free Energy by MJ Billman (2020)

Source. Shows the shift of equilibrium due to temperature change with a color change in a HCl CoCl reaction. Unfortunately there are no conclusions because its student's homework.

Somali units of measurement by

Wikipedia Bot 0

Somalia uses a combination of both traditional Somali units of measurement and the metric system, which is the official system of measurement in the country. Here are some of the traditional Somali units of measurement: 1. **Length:** - **Courage (cag)**: A traditional unit of length, often refers to a person's height or stature. - **Fool**: A unit that can refer to the length of a piece of string or rope, often about a foot.

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