Did you go to the Space Exploration Editorial Office? How's it going, are you still mentally normal?
In addition to the leading actors, the "supporting role" with the strongest sense of existence in the film is the "Geiger counter" that the protagonist does not leave behind. But you know what? In addition to "looking for alien traces", it is also closely related to many of the modern technological lives we enjoy.
The story starts with "random numbers" and "rolling dice".
Amazon sells everything weird, including making a book without a word in the body a bestseller.
Million Random Numbers, as the title suggests, is all about 1 million randomly generated numbers. The book was born in 1955, the price is 73 US dollars (about 501 yuan), it has been reprinted three times, has more than 700 reviews on Amazon, and has a rating of 4 stars.
It's hard to imagine anyone needing an all-digital book so that its comment section became an internet spectacle and many buyers began to talk nonsense in a serious way.
"A fascinating book where you can't guess the plot from beginning to end."
"A work of genius, probably used to convey government lies about global warming... I found that the number 23 appears all the time in the book, and as we all know, it means that the New World Order is related to the book. ”
Despite these jokes, Million Random Numbers is actually a rather serious book, one might even call it a book in the field of randomness — the first time in human history that such a large and high-quality random number has been produced.
01 What's so hard about randomization? Roll the dice a few more times
Do the numbers still score by quality? A more accurate statement here might be numbers with greater or weaker randomness.
Dice are the earliest random number generators in humans, but the results of rolling dice seem random, but they may imply patterns. For example, if the mass distribution of a dice is uneven, one side is slightly heavier than the others, which will cause one result to occur slightly more frequently than the others.
Suppose a group of people are betting around this dice, and those who know the secret have a better chance of winning.
Image source: Ancient Rome 12mm dice, 1 to 410 A.D. | British Museum PAS
And even if there is a perfectly balanced dice, to be truly random, all other factors involved in throwing need to be random, hand posture, throwing power, surface friction... This is an almost impossible task.
Believers in quantum mechanics believe that any random produced by classical mechanics is essentially a pseudo-random, a combination of probabilities of deterministic events. They call this randomness "surface randomness."
This makes the dice a seemingly truly random number generator, but in fact pseudo-random. Not to mention the draw of lots and shuffling.
Today, the most exposed pseudo-random in our lives actually comes from computers, but usually they don't say:
As ChatGPT puts it, it seems that it just "casually" gives a number, but in fact follows a whole set of algorithms and formulas, resulting in this result that is not only regular but also predictable.
On this basis, many efforts have been made to generate results that are infinitely close to "true randomness".
In 1951, Alan Turing, the "father of computers", built a random number generator into the Ferranti Mark 1 computer for the first time. His approach is to introduce real-world physical events into the computer's computational process to bring about a random result.
Compared to rolling dice, there are some events that are considered truly random, such as the thermal movement of electrons, the reflection and transmission of light, and nuclear decay. Turing uses thermal noise generated by the thermal oscillation of electrons in a conductor, a process that can generate 20 random bits at a time.
These bits are extremely high-quality random numbers that are used as "seeds" to generate the final random number. The quality of the "seed" directly determines the quality of the final random number.
Turing's ideas brought many inspirations to later generations. For example, there is something called an entropy pool in today's Linux system. Usually, it is kept privately in memory and random numbers are generated when needed.
In order to keep the entropy of the entropy pool from decreasing, the system has been secretly collecting various physical random sources, such as the user's mouse click, the timestamp recorded when using the keyboard - these are considered to be highly random behavior.
However, this process inevitably limits the generation speed, resulting in low efficiency and cannot be widely used; At the same time, this randomly generated instruction is extremely sensitive to interference, and the computer consumes a lot of power to avoid contamination by the outside world.
Thus, another "father of computing" John von Neumann created another random number generator. He used the mathematical method: square an initial value, take the middle number, and then square it and take the middle number. Repeating this process results in a sequence of random numbers with statistically significant properties.
For example, the initial seed is 233, and after the square, you get 54289, where the median value is 428. 428 is our first random number.
The benefits of this approach are obvious, and the speed of producing random numbers is greatly improved. But obviously, this random number is not really random, as long as the seed does not change, the random number will not change.
At this point, the random number generator has a difference between true and false: true random numbers (TRNG) that generate random numbers with the help of physical phenomena, such as the thermal noise mentioned above, nuclear decay, etc.; and von Neumann's creation of the first pseudo-random number generator (PRNG), which is essentially deterministic algorithms, and the generated random numbers are not independent of each other.
02 So tired, why pursue true randomness?
In daily life, we rarely need such a high degree of randomness, and the C that constantly jumps out when using dice to find answers to the exam is also the guide of fate.
It was not until the 1940s that the need for a large number of high-quality random numbers became apparent, which directly led to the creation of the book "Million Random Numbers". The main driving force behind this was the mathematical description of the nuclear fission process, in other words, the nuclear arms race between the United States and the Soviet Union.
The most critical step in designing a nuclear reactor is to predict the distribution of neutrons, but using formulas to derive this process is too complicated. Eventually, a well-known statistical method, the Monte Carlo method, solved this problem. Simply put, people do not know the rate and method of neutrons in the fission process, and after random sampling by the Monte Carlo method, the behavior of neutrons can be simulated, so as to obtain the range of neutron transport.
Use the Monte Carlo method to estimate π values. After placing 30,000 random points, the estimated value of π differs from the true value by 0.07%|Wikipedia
Since the Monte Carlo method is based on random sampling, its operation requires a large number of random numbers to support. Random number tables became a "hot product" in academia for a while, so much so that RAND companies, which served the US military, began to produce such "goods". In 1955, RAND Corporation publicly released the first edition of Million Random Numbers.
Just as a score of 0 is no easier than a score of 100, the urgency of Million Random Numbers comes from the fact that producing high-quality random numbers at scale is actually quite difficult. RAND has made a lot of efforts to do this, and the method is roughly divided into three steps:
- 1 Uses a random frequency pulse source that produces 100,000 pulses per second, connects it to a five-digit binary counter, and outputs the equivalent of turning a 32-grid wheel.
- 2Converts 20 of the 32 bits to decimal (discarding the remaining 12 bits), and finally retains the second digit of the resulting two-digit number and enters it into the IBM punch.
- 3Repeat the above process until 1 million random numbers are generated.
Punch card for creating a table of deviation numbers in 1949|RAND
RAND did not disclose the source of the random pulse, but some speculate that the random pulse came from uranium decay measured by Geiger counters.
A Geiger counter is an instrument used to detect radiation intensity. Uranium releases particles during decay, and the interval between decays is random, so the signal received by the Geiger counter is also random.
Now interested, you can even recreate the process yourself. There is a complete tutorial (https://github.com/nategri/chernobyl_dice) on GitHub, just six uranium glass balls, a Geiger counter, a few glow tubes, and a few brushed metal panels, you can build your own true random number generator.
It was also given a name: Chernobyl dice.
All it takes is a pair of clever hands and a hundred million bits of radioactive material | nategri/chernobyl_dice
The Cold War-era tools bear witness to how humans pursued the ultimate in randomness, and have left a rich legacy of technological development since then. Today, high-quality random number generators have applications in many industries, including cryptography, gambling, statistical sampling, drug experiments, and computer simulations.
The focus on cybersecurity has also inspired this need. In cryptography, the certainty of pseudo-random numbers is a big flaw in the eyes of hackers. Steve Ward, a computer professor at the Massachusetts Institute of Technology, once said, "If you go to an online poker site and you know the algorithm and the seed, you can write a program to predict which cards will be dealt." ”
Von Neumann, who invented the "pseudo-random number generation method", knew this: "Any idea of generating random numbers mathematically is sinful." ”
03 It's not over, quantum mechanics has something to say
So, with the help of random numbers generated by physical phenomena, must they be truly random?
Taking dice rolling as an example, once the angle, speed, wind direction when moving in the air, resistance, and the roughness of the table and other influencing factors are clearly known, then theoretically, the value of the dice when it lands can be fully deduced. The reason why people think of it as "true random" is because the physical environment involves so many variables that the derivation is too complicated.
Is quantum mechanics also considered random only because we can't observe?
In his later years, Einstein was known for his "hatred" of quantum mechanics, questioning that quantum mechanics did not fully describe the state of physical systems. The famous joke "I believe God doesn't roll dice" was born at this time – he didn't believe there was real randomness in the world. His theory was summarized as "hidden variable theory", which believes that behind quantum mechanics, there may be an undiscovered theory hidden that can fully explain the uncertainty of quantum mechanics.
As it turned out, Einstein was wrong, and Bell's inequality in 1964 proved that locality hidden variables do not exist. However, science is the discipline of attributing phenomena through empirical empirical methods. Physical theory is the modeling of reality and is not equivalent to reality. In other words, quantum mechanics can produce true randomness because under existing conditions, we do not have the method of accurate observation.
So, the most rigorous statement is: at the current level of science, we believe that quantum mechanics can produce true randomness.
Some numbers
20,000: Number of IBM punch cards used by RAND Company
23383506944: The number of random bits generated by Mez Halle from 1998-2001. He runs random.org a website that provides random numbers based on radio electrostatic generation
10231: 20,000 heads and ups in a coin toss, from a UC Berkeley student
10014: 20,000 upsides in a coin toss, from another UC Berkeley student
23: UK National Lotto has the most winning numbers in the first 20 years, 266
Author: TTT
Editors: Weng Yao, Biu
bibliography
[1] https://www.rand.org/pubs/monograph_reports/MR1418.html
[2] Timothy Sauer, Numerical Analysis. Translated by Wu Zhaojin, Wang Guoying and Fan Hongjun. People's Posts and Telecommunications Press.2010
[3] No One Lives Left https://igaojin.me/2018/11/23/ Here: Original Sin and Redemption of Blockchain Random Numbers/
[4] https://min.news/en/tech/a3af91fde51e0d335bec92830b9d4237.html
[5] https://www.zhihu.com/question/576761456
[6] https://www.cnblogs.com/sumingk/articles/10092452.html
[7] https://zhuanlan.zhihu.com/p/557583762
[8] https://tashian.com/articles/a-brief-history-of-random-numbers/
[9] https://blog.cloudflare.com/ensuring-randomness-with-linuxs-random-number-generator/#:~:text=On%20Linux%2C%20the%20root%20of%20all%20randomness%20is,can%20contain%20up%20to%204%2C096%20bits%20of%20entropy.