Which is greater, "infinity" or "infinity+1"?
Which is smarter, an AI model that has absorbed an unknown amount of data, or a model that has learned one more piece of data than it?
I want to talk about this issue out of a chance. When I was testing ChatGPT a long time ago, I suddenly wanted to ask him a tricky question, so I asked it: "Hilbert Hotel Paradox, what impact does it have on the real world?"
To be honest, ChatGPT's donkey lip is not right, and it also insists on a few points, which has his usual characteristics. But one of the answers is worth pondering. He replied: "The Hilbert Hotel is helpful for computer science, because when we deal with infinitely large data sets, the Hilbert Hotel can be our way of thinking."
Infinitely large data sets, this thing obviously does not exist. But when the data parameters used for large model training reach a certain astronomical figure, and when the human feedback mechanism becomes the norm, the model will be exposed to incalculable data during use. Isn't this some kind of infinity?
But can humans control infinity?
Today's topic is actually closer to some kind of science fiction discussion, or some brain holes about the future of AI. You may not know what you are talking about after reading it. But it doesn't matter, let's stretch our brains together and relax the anxiety that has been made by ChatGPT recently.
Let's go to Hilbert's Hotel together and have a vacation.
Welcome to Paradox Hotel
This hotel is located in a tropical resort called "Mathematics".
The Hilbert Hotel is actually a vivid example given by German mathematician David Hilbert when discussing the concept of infinity. It is both a mathematical game and one of several paradoxes that is often known.
It specifically means that, suppose a hotel has an infinite number of rooms, but they are all full. At this time, another passenger comes and wants to book a room. The hotel owner can take it easy and let the guest in room 1 move to room 2, and room 2 to move to room 3... and so on. Anyway, the number of rooms is infinite, so New travelers can live in Room 1.
At this time, another car of passengers came. The owner of the hotel still does the same thing, letting the guests in each room move N rooms backwards, and finally put the new guests in.
And so on, what happens next? If there are infinite new guests. Then the hotel owner just needs to move each guest to an odd-numbered room. For example, if room 2 is moved to room 3, and room 3 is moved to room 5, and all even-numbered rooms are vacated, then infinite guests can still live in them.
Even if there are infinitely many tour groups, and each tour group has infinitely many passengers, the Hilbert Hotel still has a solution, just need to vacate all the non-2n (n∈N+) rooms.
The reason why Hilbert's Hotel is a paradox is that it marks such a thing: Infinity is incomparable.
Infinity + 1 is equal to infinity; infinity + N is equal to infinity, infinity plus infinity, infinity multiplied by infinity, it is still infinity, infinity is immobile, and it changes at any time, and infinity can contain several infinities.
In short, infinity is indescribable.
Infinity is a bit weird
It sounds like the Hilbert Hotel Paradox doesn't work. In fact, it is not the case. Human beings almost inevitably face the problem of "infinity" in many fields. At least in the link of theoretical derivation and concept verification, it is almost inevitable to face infinity. One thing can be more infinite than the other, but they are both infinite. This way of thinking can make many assumptions and explain many problems.
For example, in physics, the Hilbert Hotel Paradox can explain many phenomena in quantum physics, the most typical of which is the assumption about virtual particles in quantum field theory. There are many debates about whether virtual particles really exist, or are they purely hypothetical tools, but they can indeed be used to explain physical definitions such as gravity, photons, and gluons, and then to explain the energy situation in the vacuum, Analyzing cosmic radiation helps. The premise is that we need to use the thinking of the Hilbert Hotel to understand the virtual particles that exist in infinity.
In computer science, data storage is a basic issue. When designing a data structure, it is necessary to consider how to mobilize the structure to ensure the best efficiency and the lowest failure rate if there is a large amount of data to be stored. At this time, it is necessary to assume that the data set is infinite, and the Hilbert Hotel is also used.
Infinity is weird, and the concept is often used in literature, especially science fiction. Science fiction is a deduction of the future, but if something can grow to infinity, it will often appear in a state of anti-common sense. For example, an immortal person may first lose the concept of time, because infinite time is meaningless, and then completely lose all the characteristics of human beings. After all, human beings think and do things in limited time. driven by this premise. Another example is teleportation, will it make space lose its meaning, and then people will lose the need and ability to distinguish space, and then there will be people who never want to stay, and people who are always moving at super high speed, are they still human?
If a thing approaches or even reaches infinity, it will go out of control and appear anti-common sense and anti-logic. This logic seems to apply to AI as well.
Use this logic to explain the emergence of intelligence
In recent years, with the rise of pre-trained large models, more and more people have begun to talk about "intelligent emergence". Generally speaking, the so-called "intelligence emergence" phenomenon refers to the sudden emergence of amazing intelligence when the scale of the model breaks through an unknown limit. For example, the model will express a sense of logic, fluency, and even what humans call emotional intelligence that the trainer did not expect.
In fact, the emergence of intelligence as a goal is not unique today. As early as the 1970s, the theoretical concept of the expert robot was to let the computer show an omniscient and omniscient effect after inputting enough knowledge, so as to help humans solve various problems. It was just that due to the computing power and data carrying capacity at the time, this idea could not be implemented in the end.
Today, under the combination of cloud computing + big data, larger data sets can be applied to AI training, coupled with deep learning algorithms to achieve better data absorption capabilities, and finally produced ChatGPT as a representative The emergence of intelligence.
Just like the black-box nature of deep learning, how the emergence of intelligence is realized, there has never been a particularly reasonable explanation. However, the term "intelligent emergence" is not exclusive to AI. This term was earlier a biological vocabulary used to describe the collective intelligent behavior exhibited by ants and fish schools. An ant is quite stupid, and a fish is not smart, but when a large number of ants gather together, the way of organization and action with a clear division of labor, a strict system, and an exquisite structure is simply amazing. Are Ant Brains Evolving? Probably not, but after the ants gather to a certain scale, they break through some kind of Hilbert Hotel-style intelligence boundary.
From this perspective, perhaps the ultimate goal of the AI road of large models is not to imitate humans. It does not need to evolve intuition, emotion, free consciousness, which are uniquely human things. But it will accumulate infinite amounts of data and knowledge. When we cannot observe and predict how much knowledge is in the large model, then it will have infinite knowledge. The AI model becomes a Hilbert-like hotel, it can swallow more knowledge, swallow more infinity, and finally can show the intelligence that humans want, and it may also show more that humans don’t want, or are not ready want something.
Perhaps we change our thinking, and the final general artificial intelligence AGI and strong artificial intelligence Strong AI may have an internal mechanism not similar to that of humans, but closer to ants, fish schools, and Hilbert Hotel.
We always discuss whether AI is like a human, whether it can do what humans do, what unique abilities humans have, blah blah blah. That's because we don't live in Hilbert's Hotel, we live in a finite world, in short-lived and perishable bodies, in a brain made mostly of water. But AI is not, it is closer to infinity than humans. He can pass the Turing test, he can eventually do everything. But we don't know why, because the AI doesn't want to be human, he just happens to live in the Hilbert Hotel.
"Intelligence emergence" may be a sign. It tells us that the evolutionary goal of AI is not human beings, but the Zerg in "StarCraft".
