This is a section about Linear algebra!

Linear algebra is a very important subject about which there is a lot to say.

For example, this sentence. And then another one.

This is a section about Fundamental theorem of calculus!

Fundamental theorem of calculus is a very important subject about which there is a lot to say.

For example, this sentence. And then another one.

Check out: OurBigBook.com, the best way to publish your scientific knowledge. It's an open source note taking system that can publish from lightweight markup files in your computer both to a multi-user mind melding dynamic website, or as a static website. It's like Wikipedia + GitHub + Stack Overflow + Obsidian mashed up. Source code: github.com/ourbigbook/ourbigbook.

Sponsor me to work on this project. For 200k USD I will quit my job or not get a new job and work on OurBigBook full time for a second year to try and kickstart The Higher Education Revolution. Status: ~44k / 200k USD. At 2M USD I retire and work on open STEM forever. How to donate: Section "Sponsor Ciro Santilli's work on OurBigBook.com".

I first quit my job 1st June 2024 to work on the project for 1 year after I reached my initial 100k goal mostly via a 1000 Monero donation. For a second follow up year, I increased my requirement to 200k USD to give me more peace of mind. So the total donation so far is 144k, and if I reach a total of 300k USD, then I'll work on the project for a second year. A second year greatly improve chances of success: year one I improved my tech, year two I come guns blazing to solve courses and expand further.

Mission: to live in a world where you can learn university-level mathematics, physics, chemistry, biology and engineering from perfect free open source books that anyone can write to get famous. More rationale: Section "OurBigBook.com"

Explaining things is my superpower, e.g. I was top user #39 on Stack Overflow in 2023^[ref][ref] and I have a few 1k+ star educational GitHub repositories^{[ref][ref][ref][ref]}. Now I want to bring that level of awesomeness to masters level Mathematics and Physics. But I can't do it alone! So I created OurBigBook.com to allow everyone to work together towards the perfect book of everything.

My life's goal is to bring hardcore university-level STEM open educational content to all ages. Sponsor me at github.com/sponsors/cirosantilli starting from 1$/month so I can work full time on it. Further information: Section "Sponsor Ciro Santilli's work on OurBigBook.com". Achieving what I call "free gifted education" is my Nirvana.

This website is written in OurBigBook Markup, and it is published on both cirosantilli.com (static website) and outbigbook.om/cirosantilli (multi-user OurBigBook Web instance). Its source code is located at: github.com/cirosantilli/cirosantilli.github.io and also at cirosantilli.com/_dir and it is licensed under CC BY-SA 4.0 unless otherwise noted.

To contact Ciro, see: Section "How to contact Ciro Santilli". He likes to talk with random people of the Internet.

GitHub | Stack Overflow | LinkedIn | YouTube | Twitter | Wikipedia | Zhihu 知乎 | Weibo 微博 | Other accounts

Besides that, I'm also a freedom of speech slacktivist and recreational cyclist. I like Chinese traditional music and classic Brazilian pop. Opinions are my own, but they could be yours too. Tax the rich.

Let's create an educational system with:

I offer:

My approach is to:For minors, parents are welcome to join video calls, and all interactions with the student will be recorded and made available to parents.

I have a proven track of explaining complex concepts in an interesting and useful way. I work for the learner. Teaching statement at: Section "How to teach". Pricing to be discussed. Contact details at: Section "How to contact Ciro Santilli".

I am particularly excited about pointing people to the potential next big things, my top picks these days are:I am also generally interested in:

 -------------------------------------
|  Force of Will               3 U U  |
|  ---------------------------------  |
| |                  ////////////   | |
| |                ////() ()\////\  | |
| |               ///_\ (--) \///\  | |
| |        )      ////  \_____///\\ | |
| |       ) \      /   /   /    /   | |
| |    ) /   \     |   |  /   _/    | |
| |   ) \  (  (   /   / /   / \     | |
| |  / ) ( )  / (    )/(    )  \    | |
| |  \(_)/(_)/  /UUUU \  \\\/   |   | |
| .---------------------------------. |
| Interrupt                           |
| ,---------------------------------, |
| | You may pay 1 life and remove a | |
| | blue card in your hand from the | |
| | game instead of paying Force of | |
| | Will's casting cost.  Effects   | |
| | that prevent or redirect damage | |
| | cannot be used to counter this  | |
| | loss of life.                   | |
| | Counter target spell.           | |
| `---------------------------------` |
|                                     l
| Illus.  Terese Nelsen               |
 -------------------------------------

A quick 2D continuous AI game prototype for reinforcement learning written in Matter.js, you can view it on a separate page at cirosantilli.com/_raw/js/matterjs/examples.html#top-down-asdw-fixed-viewport. This is a for-fun-only prototype for Ciro's 2D reinforcement learning games, C++ or maybe Python (for the deep learning ecosystem) seems inevitable for a serious version of such a project. But it is cute how much you can do with a few lines of Matter.js!

<iframe src="_raw/js/matterjs/examples.html#top-down-asdw-fixed-viewport" width="1000" height="850"></iframe>

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In physics, measurements help to understand the physical world. Two fundamental quantities we often measure are length and time. Length is defined as the distance between two points. It helps us quantify how far apart objects are, whether that’s measuring the size of a classroom, the height of a building, or the distance between two cities. On the other hand, time refers to the continuous progression of events, allowing us to determine how long a process takes. Time is essential for understanding motion, cycles, and changes in the physical world.

Units of Measurement
To ensure consistency in scientific communication, standardized units of measurement are used. The International System of Units (SI) provides the framework for this.
For measuring length, the SI unit is the metre (m). Smaller lengths can be expressed in millimetres (mm) or centimetres (cm), while larger distances, such as the space between cities or countries, are measured in kilometres (km). For instance, the length of a pencil may be 18 cm, while the distance between London and Manchester is approximately 260 km. Knowing how to convert between these units is important: for example, 1 kilometre is equal to 1,000 metres, and 1 metre is equivalent to 100 centimetres.

When measuring time, the SI unit is the second (s). This unit is widely used in science, particularly for measuring short intervals. For longer durations, minutes (min) and hours (h) are commonly used. For example, it may take you 5 minutes to walk to school, while a football match lasts 90 minutes, which is equal to 1 hour and 30 minutes. In scientific experiments, time intervals are often much shorter, measured in seconds or even fractions of a second. The relationship between units of time is straightforward: 60 seconds make up 1 minute, and 60 minutes make up 1 hour.

Measuring Length
Various tools are used to measure length, depending on the precision required. For everyday measurements, a ruler or tape measure is sufficient. For more precise scientific measurements, devices such as vernier calipers or micrometers are used. These tools allow us to measure length down to fractions of a millimetre. For example, a ruler may tell us that a piece of string is 12 cm long, but a vernier caliper could measure it more precisely, to the nearest tenth of a millimetre, like 12.3 cm.
In physics experiments, it’s crucial to ensure accuracy and precision when measuring length. This can involve repeated measurements and careful observation to minimize errors.

Measuring Time
To measure time intervals, we often use stopwatches or clocks. A stopwatch is particularly useful in experiments where we need to record the exact time something takes to occur, such as the duration of a pendulum’s swing or the time it takes for an object to fall. For instance, if you want to measure how long it takes for a ball to drop from a certain height, you could use a stopwatch to record the fall in seconds.
In modern physics, extremely precise instruments like atomic clocks are used to measure time with remarkable accuracy. These clocks can measure time intervals to a fraction of a second, and they are used for highly sensitive experiments, such as those involving the speed of light or synchronization in satellite systems.

Practical Applications of Length and Time
For instance, when studying the motion of objects, knowing how far something has moved (length) and how long it took (time) is fundamental to calculating speed. In technology, precise time measurements are important for synchronization in communication systems, while accurate length measurements are key in construction, engineering, and manufacturing processes.

Example Questions

1. Convert 5.5 kilometres into metres.

2. How many seconds are there in 2 hours?

3. You have a ruler marked in centimetres. If a pencil measures 14.5 cm, how long is it in millimetres?
4. Using a stopwatch, you record the time it takes for a marble to roll down a ramp as 3.2 seconds. How would you express this time in milliseconds?

5. A cyclist travels 24 kilometres in 2 hours. What is the cyclist’s average speed in kilometres per hour (km/h)?

6. If a pendulum takes 2.5 seconds to complete one swing, how many swings will it complete in 1 minute?

Up March 2023 web.archive.org/web/20230306090740/https://pypi.org/project/china-dictatorship/

Down November 2023 web.archive.org/web/20231110041847/https://pypi.org/project/china-dictatorship/

In the context of an A* search, a heuristic function is said to be admissible if it does not overestimate the cost to reach the goal. Such functions can also be viewed as being "optimistic".

When using an admissible heuristic, A* is guaranteed to return a cost-optimal solution, i.e. the best path. Let's prove it by contradiction:

Assume that the algorithm returned a path, the cost of which is greater than that of the optimal path $P$. Let's call $C$ the cost of the path that was followed, and $C^{\ast }$ the cost of $P$, noting that $C^{\ast }<C$. First, we can safely assume that at least one node in $P$ was not expanded during the algorithm's execution (if all nodes of $P$ were expanded, then $P$ would have been chosen instead since that would lead to a lower path cost${}^{[1]}$). Without loss of generallity, let's take the first occurance of such unexpanded node and name it "n". Let's call the actual cost from n to the destination $h^{\ast }(n)$ and define $g^{\ast }(n)$ as the cost of the optimal path starting from the origin all the way to n. Remember that A* is a best-first search on the value of $f$, so $f(x)\ge C$ for all unexpanded nodes. Here's what we've got:

Now note that $g^{\ast }(n)+h^{\ast }(n)$ is equal to "the cost to reach n following the optimal path" + "the cost to reach the goal starting from n, following the optimal path". That's just equal to the total cost of the optimal path! So, both $f(n)>C^{\ast }$ and $f(n)\le C^{\ast }$ hold simultaneously which obviously constitutes a contradiction. $\square$

[1]: Remember than $h(n)$ (our heuristic) is just a hint to prioritize certain expansions over others. When everything is expanded however, $g(n)$ is the sole metric that will be considered, which will always lead to the optimal path being selected, that being $P$.

A common misconsception suggests that glass is a liquid of high viscosity. This not the case. Glass is its own distinct state of matter that doesn't coincide with any other classical one. Every liquid (except Helium) can be turned into glass, if a sufficiently rapid cooling takes place. This process is called vitrification. When a liquid is cooled (water for example) it normally goes through the process of crystallization. We say that the water is frozen as ice forms which has a very specific structure that is characterized by its stability (crystalline solid). If the cooling happens quickly enough, the water molecules don't have the opportunity to occupy the lowest energy sites and this is how the amorphous solids forms.

Annealing illustrates this phenomenon. When glass is cooled down in order to solidify, this process must be done during a specific time interval in order for the molecules to have enough time to position themselves in a more stable manner. If during the glass making process, the produced glass has been solidified too rapidly, then the stress present in the solid makes it too fragile to the point where it can rupture/shatter even during handling. By reheating the glass and slowly droping the temperature again, we ensure that the glass object has gained a much more stable structure.

As crystalline solids have a melting point, amorphous ones have a glass transition temperature which surprisingly depends on thermal history (how rapidly was the former liquid made into glass?). Around this temperature point, the viscosity of the glass increases rapidly and can be classified as a solid (under classical terms). It should be noted that the viscosity as well as other properties of the substance made into glass, present a continuous change as the temperature changes. This is not the case with "ordinary" freezing as liquid water turns spontaneously into a solid in a discontinuous manner (during the freezing process the temperature stays constant. Immediately below $0^{o}C$ all the water has turned into ice).

The glass state is metastable and its transition to a crystalline solid is thermodynamically favoured although kinetically inert.

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Created by the german chemist Carl Friedrich Claus, it makes it possible to convert hydrogen sulfide (from natural gas) to elemental sulfur.
The overall reaction can be descibed as follows:

The Claus' process served as a better replacement of the Frasch process, which obtained elemental sulfur from naturally found deposits underground.

Welcome to my home page!

A scribe is a person who serves a professional copyist. The work of scribes can involve copying manuscripts and other texts as well as secretarial and administrative duties such as the taking of dictation and keeping of business, judicial and historical records for kings, nobles, temples and cities. The profession has developed into public servants, journalists, accountants, bookkeepers, typists, and lawyers.

One of the most important professionals in ancient Egypt was a person educated in the arts of writing and arithmetic. Scribes were considered part of the royal court, were not conscripted into the army, did not have to pay taxes and were exempt from the heavy manual labor required of the lower classes. Sons of scribes were brought up in the same scribal tradition, sent to school and inherited their fathers' positions upon entering the civil service. Much of what is known about ancient Egypt is due to the activities of its scribes and the officials. Monumental buildings were erected under their supervision, administrative and economic activities were documented by them, and stories from Egypt's lower classes and foreign lands survive due to scribes putting them in writing.

In addition to accountancy and governmental politicking, the scribal professions branched out into literature. The first storeis were probably religious text. Other genres evolved, such as wisdom literature, which were collections of the philosophical sayings from wise men. These contain the earliest recordings of societal thought and exploration of ideas in some length and detail.

In the Middle Ages, every book was made by hand. Specially trained scribes had to carefully cut sheets of parchment, make the ink, write the script, bind the pages and create a cover to protect the script. This was all accomplished in a writing room called a scriptorium which was kept very quiet so scribes could maintain concentration. A large scriptorium may have up to 40 scribes working. Scribes woke to morning bells before dawn and worked until the evening bells, with a lunch break in between. They worked every day except for the Sabbath. Scribes were only able to work in daylight, due to the expense of candles.

The scribe was a common job in medieval European towns during the 10th and 11th centuries. Many were employed at scriptoria owned by local schoolmasters or lords. These scribes worked under deadlines to complete commissioned works such as historic chronicles or poetry.

These scribes would meticulously record the information presented in the texts, but not mindlessly. In the case of herbals, for instance, there is evidence that the monks improved upon some texts, retracted textual errors, and made the text particularly relevant to the area in which they lived. Some scribes even went so far as to grow some of the plants included in the texts. They had little room or patience to disseminate the imaginary plants. The writers truly restricted themselves to only include practical information.

Meanwhile, in the case of bestiaries, the scribes generally copied and cited previous texts to pass them on. Unlike the herbals, the scribes could not grow an animal in their garden, so largely the information taken from the bestiaries was taken at face value.


In the 13th century, Paris was the first city to have a large commercial trade of manuscripts, with book producers being commissioned to make specific books for specific people. Paris had a large enough population of wealthy literate persons to support the livelihood of people producing manuscripts.



Wait, why the paragraph break doesnt work at all?

I can not join your movement because I really have more reasons than other ones. For privacy, I can't explain that. And, For me, I know that for the current situations in China, I can't do anything. For China, I think only solution is revolution not reform. The protesters will die with nobody know that without tech. People could try, but it is a Way of Sacrifice.


space.bilibili.com/355027238/dynamic
chinadigitaltimes.net/chinese/667881.html

According the report, this organization help programthink arrested. I research that for some days, and the evidences express its correctness.


净网志愿者协会, may one day you will be captured by them. But you are foreigner, they don't have a way to do that.


净网志愿者协会, it is a semi-official organization but with high-tech hacker technology. You know, in China, high-tech hackers will not be an offical. Because it is a semi-official organization with many young little-pink engineer, the tracking for programthink, it could be done.


They are actually not wumao, but they may be more formidable opponent. But you live aboard, they can't do anything and officals will not always listen their views.


Why do I think its claim for programthink's arrest is credible? Because some inference.
The organization says programthink is 马勇康.
github.com/programthink/zhao/issues/418


one year passed, 2022/05, offical media(only media) say 马某某，煽动分裂国家、煽动颠覆国家政权
baijiahao.baidu.com/s?id=1731886110528251526&wfr=spider&for=pc


the 马 first name only has 1% population in China. Coincidence? And according the report's keyword: 浙江温州, 科技有限公司，“洗脑”，“人生导师”，顽固


just like a copycat keyword for programthink blog and it conforms characteristics.


and the organization say 马勇康 is 山东人, the offical media say he is 浙江人


According the data in the website or anywhere:
www.23mofang.com/ancestry/library-surname/5f34ee9eff5a3344d6a8aabe


浙江(ZheJiang province) have less 马 than 山东.
And programthink family's post say programthink lastly has a business travel to a city in eastern China, you see 温州，浙江，上海，all keyword is about the eastern China. 温州 is a interesting keyword, if you search programthink's issues, it has a strange 温州 people, but no other Zhejiang province's county.


And other crime such as 政治纲领, as I know for CCP cop, they need some more outstanding achievement. 继续调查中，because the CCP cop needs more news by the mouth even it is not neutral. And, it is possible that programthink think he could take the all blames on his shoulder maybe.


These inference may is only inference by brain ———— we never know what is a truth.


www.bilibili.com/video/BV14S4y1T7RT/?spm_id_from=333.999.0.0
净网志愿者协会 mentions programthink in the video.


I only know that they may be the not many real high-tech little-pink and hackers and really can do that. They are more terrible cop, even sometimes, gov will not listen them. I don't know in 2022 the organizations like it will do what.


Sometimes I think what is better? For my reasons I know I couldn't join yours. And I can't keep "doublethink"(ps: I'm not an official, official never doublethink). The only difference between China and 1984 may is the war is peace. China gov officials say China love peace, and in fact, CCP indeed take less war than other countries. But it is Chinese nature, may CCP also keep something.


CCP is not worse like Russia, so it is more difficult, for any reform. And reform may not work too fast or really work, only revolution.

This is a section about Vector space!

Vector space is a very important subject about which there is a lot to say.

For example, this sentence. And then another one.

This is a section about Abstract algebra!

Abstract algebra is a very important subject about which there is a lot to say.

For example, this sentence. And then another one.

This is a section about Algebra!

Algebra is a very important subject about which there is a lot to say.

For example, this sentence. And then another one.