What was the universe like before the Big Bang? How does our brain work? Can we predict the future? After thousands of years of civilization development, mankind's understanding of the universe and everything in the world has reached astonishing heights, but there are still many problems that exceed the limits of our current understanding.
In the unknown world, some can be gradually explored and understood by humans, some may be something we can never know, and some may not even be imagined. So, where are the limits of human exploration of the unknown? If you want to push the limits, you have to know it. Epoch-making technological change and disruptive innovation often come from breaking through the limits of cognition.
—Editor
Discover the limits of truth
Constantly breaking the "forbidden zone" that cannot be measured
For something that cannot be measured, we cannot know its true nature. For example, the inability to measure the real quantum world hinders our understanding of it, but it does not prevent scientists from thinking about and exploring it
Most people believe that even if we don't look, reality remains. This idea seems correct, but it is a tricky proposition that needs to be proved - how can we know the truth when something seems supposed to exist, but can never be observed?
The laws of nature have led to the formation of forbidden areas that cannot be accessed by human intelligence. For example, nothing is faster than the speed of light, so the farthest light that can reach a telescope determines the boundaries of the universe we can observe, which means that we can never observe the world beyond that boundary. For example, according to general relativity, nothing in a black hole can escape, so the inside of the black hole has become another forbidden area that human beings cannot measure.
The laws of quantum mechanics, unlike Newton's laws of motion, cannot give definitive predictions. According to the quantum uncertainty principle, which uses the same device to measure certain properties of quanta, it is impossible to know whether the results measured today will be the same as tomorrow's.
Classical quantum theory explains this by the fact that in the quantum world, the state of particles exists in a "fog" of many possibilities, which can be described by a mathematical equation called the "wave function"—quantum particles collapse into a single definite state only when they are measured.
However, not everyone agrees on this. Flatko Vedral, a physicist at the University of Oxford in the United Kingdom, believes that it is wrong to oppose a certain particle that follows quantum theory to the results of observers and instruments that follow the laws of classical physics, and "reality should be seen as a whole, a huge wave function".
If this statement is accepted, it will give mankind a new understanding of quantum physics. Because this means that the measurement of one object also has an impact on other objects, and the measuring instrument and the observed object are always interacting - that is, the reality we see is the product of the observer and the observed object.
Carlo Rovelli of the University of Aix-Marseille in France believes that everything that exists is related to other things, including yourself. When you measure a particle, it's there, but it's not always in that state.
Maybe we'll never be able to prove which explanation is correct, and maybe we'll find a way to see through "quantum fog" without collapsing the wave function. This could then give birth to a deeper quantum theory that would make this otherwise unmeasurable part of the world "perceptible." Védral said: "It's probably going to be a much weirder world. ”
Predict the limits of the future
Can AI conquer complexity and chaos?
From weather forecasts to protein structures, some things are theoretically predictable, but too complex to be practical. Artificial intelligence (AI) is changing the cognitive limits of complexity and helping humans push those limits
Although everyone knows that "the future is unknowable", people will always have a strong curiosity about what will happen in the future. Human pursuit of science is, to a large extent, the pursuit of certainty in predicting the future. Because once you have a large number of rules like Newton's laws of motion, you can make the future as certain as the past.
However, there will always be many "surprises" in everything, because there is a gap between what is "predictable" in theory and what is "measurable" in practice. Whether it's the limitations of technology or the incredible complexity of the natural world, it means that some things are actually unpredictable.
What's more, the things that human beings want to explore are often composed of many objects that interact with each other, and their complexity is unimaginable. For example, we can accurately predict the flight path of a soccer ball, but we can't make the same prediction for particles, because so many particles in flight are influencing each other, and existing computing power can't simulate all of these interactions at the same time—more than 10 particles, you can't.
Complexity exists in many areas of science. In the life sciences, for example, a protein is a long list of amino acid molecules folded into complex shapes that perform various tasks in the living body.
Understanding the precise structure of proteins can aid in new drug design. In theory alone, even though we already know what determines the function and folding shape of each protein, because each protein has so many atoms interacting with each protein, one can't calculate it perfectly. This is a frustrating cognitive limit.
Chaos is also an important contributor to complexity, referring to seemingly random and unpredictable irregular movements that occur in deterministic systems. Some system behaviors are very sensitive to small differences in initial conditions, and weather is a prime example. Small changes in temperature or humidity in a certain weather can lead to unpredictable storms the next day. For another example, the Moon's orbital period around the Earth is about 27 days, but the maximum error of each month can be up to 15 hours, which is caused by the gravitational changes of the Moon by the Earth and the Sun.
Chaos makes things more complex, which limits our perception of things. Everything in the world, from weather forecasts to financial markets to disease transmission patterns, is affected by chaotic phenomena, but there are a few tricks we can use to better understand them. Tim Palmer, a physicist at the University of Oxford in the United Kingdom, says a practical strategy is "ensemble simulations." For example, weather forecasts often come with a probability of rainfall, and the results obtained through this strategy allow people to judge with relative confidence whether they should bring an umbrella when going out.
Today, AI has revolutionized the ability to calculate protein structures. After being trained on thousands of known protein structures, AI models can use this knowledge to predict new protein structures. This is another new way to instantly push the limits of human knowledge.
The limits of mathematical reliability
The basis for "self-evident" is not perfect
Mathematics is the best tool for human beings to describe the universe, and many of the laws of nature are written in mathematical language. But it can also go wrong, because the reliability of mathematics itself depends on the axioms it is based on, and we must first assume that these axioms are correct
Mathematics, considered the most trusted subject ever undertaken by mankind, is the foundation of scientific rigor and the cornerstone of much other knowledge. This may be true, but Penelope Maddy, a philosopher of mathematics at the University of California, Irvine, points out that there are limits to the credibility of mathematics.
"Mathematics is built on axioms that cannot be proved." Vera Fisher, a mathematician at the University of Vienna in Austria, said that scientists observe natural phenomena, summarize laws, and then derive universally applicable mathematical axioms. For example , assuming that " there is and only one line between two points " is universally true, this constitutes one of the rules of Euclidean geometry. Another example is the assumption that " 1+2 " equals " 2 + 1 " , which establishes the basis for arithmetic operations.
These axioms are self-evident, but mathematics is much more esoteric than arithmetic. The goal of mathematicians is to reveal the properties of numbers, their relationships to each other, and to build models of the real world through mathematics. These more complex tasks are still solved by theorems and proofs based on axioms, but the related axioms may change. For example, a straight line between two points has different properties on a surface than on a plane, which means that the basic axioms are necessarily different in different geometric systems.
The gold standard for mathematical reliability is set theory. As one of the most primitive concepts in mathematics, sets usually refer to the totality of things combined according to some characteristic or law and the properties of their neighbors. Since the beginning of the 20th century, mathematicians have established the set theory system of ZFC axioms that is common to mathematics.
The ZFC axiom set theory system enables mathematicians to create endless interesting results and even develop precise mathematical methods to measure our trust in ZFC-derived theories. Mathematicians may provide the basis for the establishment of much scientific knowledge, but they cannot guarantee that it will never change or change.
The Austrian-American mathematician, logician and philosopher Kurt Gödel proposed the "Gödel incompleteness theorem" in the 30s of the 20th century, making mathematicians fully aware of the futility of pursuing perfection. David Aspero of the University of East Anglia in the UK said: "Mathematicians have learned to accept this reality. ”
In fact, the imperfections of mathematics somehow make mathematics more interesting. The possibility of becoming more perfect is one of the charms of the mathematical discipline.
Perceive the limits of the world
"The joy of knowing the fish"
We can never fully perceive the pain of others, nor can we express the experience of color and love in words, let alone understand the experience of other animals. This means that we may never know if sentient AI has been created
Imagine a woman who grew up in a black-white-gray room from birth, and everything she sees is monochromatic. Maybe she's been studying color science all her life, but she's never seen anything other than black and white. And when she left the room for the first time and saw the colorful real world, what new knowledge about colors she learned...
This thought experiment was proposed by Australian philosopher Frank Jackson in 1982. Experiments have shown that some types of knowledge cannot be acquired by reading, measuring or deriving, and must be learned through direct experience.
The theory of the impossibility of sharing the subjective experience of others has had a great impact on the medical community. For example, when a person hallucinates, it is difficult for others to know his state of mind. Similarly, it is difficult to appreciate how painful a patient is, and doctors can only rely on their descriptions, but they cannot know whether one person's "pain" is the same as another's "pain."
Stephen Law, a philosopher at the University of Oxford in the United Kingdom, believes that man's inner world is a private realm, hidden behind some kind of super barrier. This is very different from physical barriers such as the skull, and even if we can enter the physical brain of a person, we cannot enter the mental world.
This cognitive limit leads us to never know if we perceive the world the same way as everyone else. Much experimental evidence suggests that everyone experiences and feels differently about a particular color, sound, and smell. This is not only because of slight differences in the physical form of sensory organs, but also because each person's brain cells process foreign information differently.
Anil Seth, a neuroscientist at the University of Sussex in the United Kingdom, and his colleagues investigated the diversity of human sensory experiences through a "perceptual census". This is an online survey of how people experience games, hallucinations, and other visual and auditory stimuli. Surveys have shown that it is difficult to truly understand the inner world of other people, and even more difficult to understand the perception of other species that have completely different sensory inputs from us, such as the world perceived by bats using "echolocation."
This means that no matter how we understand reality through science, equations, theory, and experimental measurements, there is always a private realm that belongs entirely to the individual, and that is also an unknowable limit realm. And it will lead to a serious question: How do we know if we've created an AI that is sentient, even conscious, emotional?
Describe the limits of the world
Does logic exist above the comprehension of the human brain?
Logic is the basis of knowledge, and we use logic to construct facts into systems of thought, but paradoxes force us to question what is known. But what if the logic itself is flawed?
A man with black hair, who is plucked out one by one, will eventually become bald. But how many hairs do you need to pull out to be bald during this process? It's hard to say.
This is a thought experiment that philosophers love, and another version of the "sand pile paradox" proposed by the ancient Greek philosopher Eubreid. It is often used to prove that classical logic is not enough to describe the world around us.
Logic runs through human knowledge, and paradoxes often start with seemingly correct premises, use seemingly valid reasoning, and eventually lead to erroneous or contradictory conclusions. Many paradoxes force us to question what we think we know.
Some philosophers believe that the concept of logic itself needs to be re-recognized. Take the hair plucking process as an example, half of the hair is plucked, still not bald, but not as "bald" as at the beginning. To this end, computer scientist Lotfi Zadeh proposed the concept of "fuzzy logic" in 1965. However, there is a deeper question here: Can we be sure that logic—even reformed logic—is sufficient to understand the universe in its entirety?
David Wolpert of the Santa Fe Institute in New Mexico has been thinking about this for decades. Recently, he suggested that there might be some higher-level logical model that could be used to understand the universe, but that might not be comprehensible to the human brain.
Using the simple word "problem," Walpert says, some organisms, such as single-celled paramecium, simply can't imagine what "problem" is. In fact, according to our intellectual standards, all other species on Earth have certain limitations in the way they understand the world around them, and humans will obviously have limitations.
"If we are paramecium, what is above us?" Walpert believes that it is possible for us to somehow acquire a higher-level system of thinking, perhaps it will be a super Turing machine that transcends the normal rules of computation, or an alien life form that shares intelligence with us, or maybe something completely different. What would this new way of understanding look like? "I can't imagine it." "And that's the key. ”
◆ Is there an engine faster than the speed of light?
In addition to the propulsion systems of traditional spacecraft, there may be a way to move quickly through space: twisting the surrounding space. We can think of it as a breaststroke, piling up the water in front of us and then pushing the water back. Based on this principle, can we make engines that move quickly in space?
Anything with mass distorts space-time to some extent. The appeal of a warp engine is that, in theory, it is faster than the speed of light. But if it goes faster than the speed of light, it will be massive enough to form a black hole. The solution proposed by physicists is to use negative matter, which can warp space-time without creating a black hole. There is good reason to think that negative matter cannot exist, but the laws of nature do not rule out this possibility.
◆What's inside a black hole?
If you fall into a black hole, you will definitely not come back. Not only people, including instruments sent to measure or anything else, as long as it is swallowed up by this space, no one can be spared.
Beyond the black hole's event horizon, the strong gravitational pull compresses everything into a "spaghetti." Still, it's possible for something to leak out of the black hole.
The famous British physicist Stephen Hawking discovered that due to quantum effects, black holes release a type of radiation, which is called "Hawking radiation". This is an extremely slow process. If the black hole evaporates completely, then the information it has absorbed over countless years will disappear, but there is a very important natural law that "information will not be destroyed", which is the black hole information paradox.
By photographing and modeling black holes, scientists can theoretically explore what is inside black holes, and at the same time get closer to solving the mystery of black holes step by step by understanding what happens at the edge of the event horizon. Many hope that this process will confirm a new theory of quantum gravity—a theory that goes beyond quantum mechanics and general relativity.
◆What is it like to be a bat?
In the 70s of the 20th century, the philosopher Thomas Nagel proposed through research that it is impossible to understand conscious experience based on our physical perception of the world. Some studies have found that humans experience the world differently than other animals. For example, we can dissect a bat and see its physical structure, even down to the atom, but we can't enter its hidden inner world and know how it feels to "see" the world through "echolocation." "We may be able to imagine the inner world of monkeys more than octopuses. But we may still be mistaken about the monkey's idea. Anil Seth of the University of Sussex in the UK said.
◆Is infinity infinity?
It's not that simple. The 19th-century mathematician George Cantor proved two types of infinity. "Natural numbers" (1, 2, 3...) ) is countable infinity, a continuous real number between every two natural numbers (e.g. 1.234566...). is uncountable infinity.
In daily life, we generally do not deal with the problem of infinity, but "infinity" is an important concept. It always comes up in physical equations, especially those describing the Big Bang and black holes.
Mathematicians have a better understanding of this tricky concept. Cantor proposed the continuum hypothesis that there could be another "infinity" between two types of "infinity". Traditional mathematics can't determine whether this assumption is correct, but the latest mathematical research shows that there is hope that the answer to this question will eventually be found.
Author: Fang Lingsheng/Compiler
Image: Visual China
Editor: Xu Qimin