Is it because the mathematics system is different that the information of alien civilization cannot

Is there really no alien civilization in the huge universe? If it exists, why haven't we found it yet? This is the Fermi paradox that most people are familiar with. Scientists have been thinking about this series of questions. They tried to understand the reasons behind this loss of connection. Maybe the aliens can't speak at all? Or maybe the way they communicate is completely different from ours? If aliens really send out a contact signal, is it out of curiosity, pride or loneliness?

　　 When answering the Fermi Paradox(replica hermes), some views believe that alien civilization should have the idea of ​​maintaining its own independence, and this idea is a hypothesis for the motivation of aliens. If such creatures really exist, they are likely to have evolved over hundreds of millions of years in various extreme environments, and therefore have different senses, motivations and emotions from our people on earth. They may be an artificial intelligence that has surpassed the original creature that created them, or they may be a creature that we can't imagine. Perhaps we will never understand the motives of aliens, but it is very interesting to speculate.

　　 No desire to communicate

　　 Someone once suggested that one reason alien civilization chose to remain silent was "fear." Because broadcasting to space will reveal its position and technical level. If we think that our neighbors may be some militants or even worse violent ones, then keeping silent may be the best strategy. Therefore, caution may be a common feature of advanced intelligence.

　　 Some people think that intelligent aliens may lack the curiosity that humans often have. Maybe alien civilizations have no interest in exploring the universe or communicating with other civilizations? There are also people who think that alien civilization is far more intelligent than us, and they are indifferent to our existence. I heard an astronomer say that advanced civilizations “do not want to communicate with us because we can’t teach them anything. After all, we don’t want to communicate with insects.” Is that true? We are unlikely to teach an advanced civilization about "hard" science such as physics. But in fact, physics is relatively easy: the universe is made up of a few basic building blocks, and these basic building blocks interact in a few, appropriate, and definite ways. Therefore, advanced alien civilizations are unlikely to spend a lot of time discussing physics. They all have the same physical theories as ours because we all live in the same universe.

　　 From a more comprehensive point of view, what needs to be studied carefully is those areas that are difficult to master, such as ethics, religion, and art. Advanced alien civilizations do not want to learn anything interesting about electromagnetism from us, but they may be obsessed with understanding and understanding our view of the universe, which may be a challenge to their ideas. Also, saying "we don't want to communicate with insects" is also incorrect. At least, we are very interested in the way of communication between insects: biologists have worked hard to explain the encoded information that may be contained in the dance of bees; the pheromone communication of ants has been studied for many years; the bioluminescence of fireflies, and these creatures The use of light pulses in courtship dialogues has also received long-term attention. These are all part of a broader study of animal communication and animal cognition issues. In fact, the possibility of communicating with "lower" species has attracted humans for thousands of years. Compared with alien intelligent species, Homo sapiens on our planet may be just a "lower" species, but this does not mean that we are born boring. In addition, even if the alien civilization has no interest in primitive life forms like us, it may not necessarily explain why we did not see them and the possible exchanges between them and their own kind.

　　 Another common argument is that the super-intelligent alien civilization is to protect humans from excessive low self-esteem, so they restrain themselves from communicating with us. They have been waiting until we can make a valuable contribution to the dialogue that the Galaxy Club is having. However, as the famous American astronomer Frank Drake pointed out, from a personal standpoint, all of us are accustomed to interacting with individuals with higher intelligence. As children, we will learn from our siblings, parents and teachers; as adults, we will learn from the great writers, scientists and philosophers of the past. This is not a big deal: the worst case is that we may be disappointed when we find that we can never write like Shakespeare or offer insights like Newton - but then we will also shrug and say: We will do our best And OK.

　　 We can think of many other reasons to explain why alien civilizations are so conservative. Maybe they soon found spiritual satisfaction on their planet, and thought there was no need to look for others. Maybe they believe that only those species that are morally advanced enough should try to enter space, and they are also waiting for the day when they can enter that stage. Perhaps the time delay in interstellar communication makes the interaction with other species less attractive, because it seems that communication will become like a one-way transmission of information due to too long time lag. There is also a simple and passive possibility: they don't want to be disturbed at all.

　　The mathematical system is different

　　The problem of mathematics system is another issue worthy of attention. As the famous American physicist Eugene Wigner pointed out, one of the eternal mysteries in science is "the incredible validity of mathematics." Why can mathematics describe nature so appropriately? Whatever the reason, we should all be grateful for being able to understand the universe mathematically. This means that we can assemble airplanes that stay at high altitudes, build upright bridges, and build cars that can drive almost autonomously. Ultimately, all modern technologies have to rely on mathematics.

Perhaps most mathematicians agree, at least tacitly approve of Platonism. Plato's philosophy believes that both mathematics and mathematical laws are some forms of ideas that exist outside of time and space. Therefore, the work of a pure mathematician is similar to that of a gold prospector. What they are looking for is the nugget of absolute mathematical truth that has existed before. Mathematics was discovered, not invented. However, some mathematicians took a strong anti-Plato position.

　　 They claim that mathematics is not an idealized essence independent of human consciousness, but an invention of human thinking. Mathematics is a social phenomenon and part of human culture. Anti-Platonists believe that the objects of mathematics are created by us according to the needs of daily life. Mathematics comes from our brains. Evolution may have connected an "arithmetic module" to our brains. Neuroscientists may even have determined the location of this module: the inferior parietal cortex-a relatively incomprehensible area of ​​the brain. This is not to say that arithmetic is all mathematics. In fact, compared with the huge electronic data exchange system built by mathematicians, it can be regarded as insignificant, so other areas of the brain may also play an important role.

Psychologists once recorded an example: a person with a PhD in chemistry could not solve a basic problem in arithmetic: 5×2-this is beyond his ability, but he can calculate algebraic expressions, such as (x ×y)/(y×x) is simplified to 1. Does this mean that arithmetic and algebra are processed by different areas of the brain? However, it is on the basis of arithmetic that mathematicians all over the world have built such a wonderful temple of abstract thinking.

　　 If the facts show that we do have an arithmetic processing unit in our mind, then we should not be overly surprised. After all, our ancestors lived in a world of discrete objects. In that world, it is very useful to be able to identify the number of predators or the number of prey. In fact, because the ability to make quick judgments based on the number of objects it perceives is so important, we can expect animals to also have a sense of "numbers." There is indeed evidence that rats, raccoons, chickens, and chimpanzees can all make basic judgments about values. Therefore, although the ability to do points is not innate, one might think that the foundation of arithmetic is innate. Integers do not exist independently of human consciousness. Rather, they are the creations of our thinking, an artificial method used by our ancestors’ brains to understand the world around them.

　　Animals cannot be counted in the sense of our understanding. In experiments that claim to prove the ability of animals to count, it is difficult to rule out the possibility that animals use simpler cognitive processes. For example, when there are fewer objects involved, animals may use perception to recognize. We do this ourselves: if there is a plate with 3 biscuits, we don’t need to count to know that there are 3 biscuits, not 2 or 4. Number sense is a process of perception, applicable to up to 6 objects. This process is very effective for 3 objects, probably because there are very few arrangement methods (almost only "∴" and "···" two possibilities). But if there are 23 objects, there are many different arrangements. There is no perceptual clue that allows us to quickly distinguish whether there are 23, 22 or 24 objects in the pile. Similarly, many animals can also judge relative numbers, such as finding the larger of two piles of food. However, animals don’t have to count, after all, 500 bird food always looks bigger than a pile of 300.

　　 If this is correct, then an interesting question will arise: What is the mathematical formula of an alien civilization? Of course, the symbols they use are different, but this is only a trivial difference. We want to know whether they have developed the prime number theorem, the minimum-maximum theorem, and the four-color theorem instead of superficial differences. If their evolutionary history is completely different from ours, then maybe they will not develop the theorems that humans have. Why do you want to do this? If they evolved in a constantly changing, rather than discrete environment, they might not have invented the concept of integers. It may also be possible to develop a mathematical system based on the concepts of shape and size, rather than a system of numbers and sets like humans. Or it is possible that the brains of aliens are much stronger than ours, and they can perform numerical simulations in their brains (or anything that can be their brains). I personally think that it is difficult to imagine this kind of extraterrestrial mathematics. It is almost certain that this is a flawed mathematics, but it is almost impossible to prove that this different mathematical system cannot exist.

　　 This is not to say that our own math is wrong. The relationship of eπi=-1 is undoubtedly true, and it is inevitable anywhere in the universe. However, other intelligent species with different evolutionary histories may not see the relevance of concepts such as e, π, i, = or -1 at all. Similarly, they may also have concepts that are important in their own environment-concepts that we cannot invent.

　　The key here is that human mathematics enables us to develop airplanes, bridges and cars. Perhaps this type of mathematics is necessary for technological development. For a civilization to build a radio transmitter that can broadcast at interstellar distances, it must understand the inverse square law and many other "earth" mathematics. One answer to Fermi's paradox is that other civilizations have developed other mathematical systems, which are suitable for the conditions of the invention, but not for the construction of interstellar communications or propulsion devices.

As this solution to the paradox, similar to the other solutions, there are also considerable difficulties: even if it is applicable to some civilizations (many civilizations will even deny this possibility), it is certainly not applicable to all civilizations. . I can imagine a super-intelligent race of marine organisms developing a mathematical system (right angle system) without Pythagoras' theorem, but not all species will live in the ocean. Some will be terrestrial creatures like us, and it seems reasonable to assume that at least some of them have developed mathematics that we are familiar with.

　　 The last thought, the core of mathematics is the problem of patterns. Even though mathematics itself is universal, perhaps different intelligent species will appreciate and study different types of patterns. For mathematicians, nothing is more interesting than learning different mathematical systems. For me, this provides another reason why intelligent species will choose to try and communicate.

　　The information is hidden in the bottle?

　　 There is also a relatively new point of view. Perhaps the information has been sent out, but they are all hidden in the bottle, and we cannot open it yet.

　　 We know that it is possible to use electromagnetic broadcasting to transmit information over interstellar distances. In addition, the advantage of using this system for communication is that it can travel in a straight line at the fastest speed-the speed of light. But as we have seen, electromagnetic broadcasting also has some problems. An all-round broadcast can cover many stars, but the cost is extremely high. The cost of sending a targeted message is much lower, but the size of the potential audience is also reduced. Another problem is that this requires listeners to listen at the right time. If an alien civilization proudly broadcasts one of its greatest movie scripts to the universe, but all the audience hears is "Forget it, Jack. This is Chinatown." Then a large part of the script is wasted. Of course, as long as the listener hears the ending message of a long broadcast, he can infer the civilization that broadcasts the message, which is already very important in itself. But the same result can be achieved by sending a cheaper and more reliable beacon—"we are here". If you want to spread a lot of information and let the extraterrestrial wisdom community share your cultural highlights, scientific knowledge and accumulated wisdom, is it the best way to send it by electromagnetic broadcasting?

　　 About the cheapest, most accurate, and most effective method of information transmission, perhaps communication theorists have the most say. After all, it was these people who developed theories that made the Internet and wireless Internet work effectively. In 2004, Christopher Rose (Christopher Rose, a professor of electrical engineering at Rutgers University) and Gregory Wright (Gregory Wright, an astrophysicist) used the communication theory method to analyze the interstellar communication problem. They abandoned the requirement that information must be sent as fast as possible, and instead investigated how much energy is required to send the information. Their conclusion is surprisingly clear, but counterintuitive: from an energy point of view, writing a message on some material and throwing it into space is much more meaningful than broadcasting the message. Sending a physical message has an additional advantage: if the message is intercepted and decoded, then the entire message can be accepted without duplication: you can guarantee that the recipient has the opportunity to watch the entire Chinatown movie instead of Let them take a risk to see only the last few seconds.

　　 Therefore, Ross and Wright made a compelling point that alien civilizations are more likely to use bottles instead of electromagnetic broadcasts to send information. The starting point of their discussion is based on some daily insights: If you need to transfer large amounts of data from one end of the town to the other, then a reliable way is to fill a truck with Blu-ray discs and drive to your destination. In addition, simple physical exchange usually has a faster data transfer rate than radiation. Consider this example: theoretically the maximum information rate for optical fiber transmission is about 100 megabits per second, but you can easily exceed this rate by pushing a box full of 5TB hard drives across the desktop.

　　 In modern communication networks, we often do not use "physical" technology. We usually hope that information can be transmitted quickly. In most cases in daily life, the propagation of electromagnetic signals is basically instantaneous. However, when we send radio information to stars, the information will continue to travel for hundreds or thousands of years. In this case, urgency does not seem to be an important factor, and we can reasonably tolerate the delay. Ross and Wright applied this idea to the case of interstellar communication. In this context, they asked: "When is it better to write, and when is it better to transmit information?"

　　 A key point of their argument is the fact that we are using smaller and smaller materials to store more and more data. When I was young, my music collection included some black plastic shelves. When I moved the CD, the volume of the physical collection shrank, but the amount of music I owned increased.

For many years to come, this trend seems to be unsustainable for no reason, and it should eventually be possible to store all written and electronic library materials in the world, for example, 1020 bits of information in a single grain of no more than quality 1 gram of material. How much energy is needed to burn this information on a substrate with a mass of 1 gram, and then send it into space at a speed of, say, one thousandth of the speed of light? And how much energy does it take to broadcast so many digits of information? Rose and Wright calculated the numbers and compared them. They pointed out that there is always a two-phase balance distance, beyond this distance, it is better to use the method of burning information. The distance between gain and loss depends on several factors, but on an astronomical scale, it has never been particularly large. Their general conclusion is that in terms of the energy required for each bit of information, burning is definitely more effective than emission. Depending on details such as the distance and speed of information dissemination, the difference in efficiency may be astronomical.

　　 People can reasonably question that any information recorded on 1 gram of matter will not survive interstellar travel: cosmic rays and various other factors will reduce the quality of information. In addition, during the thousands of years when the information block is transmitted, the position of the target star will drift. Therefore, some kind of propulsion system is needed to push the information block back to the orbit of the star. Once the "information bottle" reaches its destination, a dismantling system needs to be deployed. Ok. You can provide 10 tons of fuel and shielding device for every 1 gram of burning material, which is still more advantageous than broadcast information. You can send all these particles that contain rich information, at least from the perspective of energy use and information persistence, it is more meaningful than broadcasting this information.

　　Of course, we only have a vague understanding of the economic operation mode of the earth, so we have no idea how the economy of an alien civilization will operate. For technologically advanced civilizations, perhaps the amount of energy used to transmit each bit of information is no longer an important factor to consider, and they can afford this cost-for the issue of interstellar communication, they can adopt a A goalless approach. However, it is difficult for us to know exactly how many bottles they threw.

　　 Therefore, here is an answer to Fermi's paradox: We have been looking for a kind of broadcast, but what we are looking for should be the information in the bottle. We might argue that if alien civilizations think it's easy to send physical information, then why haven't we seen it yet? Since it is meaningless to throw a small bottle into space, they will definitely attach a clear, obvious and long-lasting beacon to the bottle. So where is the beacon?

　　 Ross-Wright's point of view raises some interesting questions. For example, suppose a piece of information has arrived in the solar system, and some kind of beacon is really attached to the information bottle, then where should we search? Since RNA molecules can store a lot of information in a small mass, maybe life itself is information? In summary, should we shift the focus of SETI's search from radio telescopes and optical telescopes to directly searching for those recorded materials? However, even if the answer to this question is "yes", it is difficult for the participants to accept it. Traditional SETI can use mainstream astronomical research: for example, if the radio telescope has been aimed at Vega, searching for alien signals in the direction of Vega will not cost too much extra. However, how to obtain funds to search for an object of unknown shape, unclear properties, or even where it is (at the Earth-Moon Lagrangian point? Asteroid belt? Oort cloud?)?

　　No organization will approve such a task. So, just like the drunk at night looking for the lost key under a street light pole, it’s not because there is where he lost his keys, but because it’s where he can see, so we might be warned, Look for electromagnetic broadcast signals, because this is what we can do.