Road to science and technology

“The invention of numbers saves us from wasting time shouting repeatedly, but numbers also have a big disadvantage, that is, their abstraction.

For example, '6 fish' is more abstract than 'fish, fish, fish, fish, fish, fish' because the number 6 only appeared later. At first, people only knew about fish, so we have to help others understand that 6 fish is What does it mean? Both parties must know the meaning of the number 6. "Yue Yuanzhou continued to tell,

"From this perspective, numbers are no longer an easy-to-understand concept. Its abstractness adds a layer of mystery to it. The more you think about the concept of numbers from a philosophical perspective, the more it seems like It's an incomprehensible fog.

It even makes you wonder: where did the numbers come from? Did civilized humans invent numbers, or do numbers objectively exist in nature and were just discovered by us humans? "

Having said this, Yue Yuanzhou raised his palm, used holographic materialization technology to materialize a rope on the top of his palm, then tied a knot on the rope, and then tied a second knot a few seconds apart.

At this time, he looked at Dragon Scale and continued: "If there are no numbers, then people should initially call the first knot and the second knot as knots. But when people find that with the goods that need to be recorded The more knots there are, the more knots are tied, and it becomes more and more difficult to remember the amount of goods, and it is also very difficult to express the amount of goods. So there is a method of expressing the first knot as one and two knots together. 'Knot, knot' is also represented by another abstract two."

"So, the addition operation was born, one plus one equals two. Of course, people may have used stones at the beginning, but it makes no difference. This may be the simplest mathematics that humans have learned from nature.

With the addition operation, subtraction as its inverse operation comes into being. Then what is multiplication? In fact, the essence is also addition. The same is true for division as the inverse operation of multiplication. So what is the essence of the four arithmetic operations?

In fact, it is human beings' division from their own way of thinking, using abstract tools like mathematics to describe nature, because this kind of abstract number is much simpler than the infinitely lengthy string of 'fish, fish, fish' in human thinking. . "

Having said this, Yue Yuanzhou paused, then turned his hand to turn the rope into holographic data, and then continued: "If it were not based on the human way of thinking, then its mathematical system and mathematical operations would be completely different. Far from it. If not, let’s take this data as an example! A civilization dominated by artificial intelligence will not have four arithmetic operations in their mathematical system, but they can still use that lengthy string of 0s and 1s to express nature.”

That's true.

The true meaning of the universe is there, and different races just use different mathematical systems to explain it.

Mathematics is both an intuitive tool and an abstract concept in the Utopia. Perhaps it is this wonderful property that makes it one of the most useful tools in human history.

The famous physicist Eugene Wigner once wrote: In the field of natural science, the applications of mathematics are so extensive, the power of mathematics is so great, and the vastness and omnipresence of mathematics have exceeded our human wisdom. category.

Having said that, Yue Yuanzhou knows that in fact, the category that seems to be beyond the understanding of wisdom is not mathematics itself, but the ultimate truth of the universe, because it is what humans want to describe most with mathematics!

By the same token, if in a certain universe, its macroscopic underlying rule is that one plus one equals three, then when a person puts two stones together, they should become three.

Because logic is based on reality, especially basic theories, which are the simplest laws of reality. 1+1=2 is calculated. If it becomes 3, there must be a reason, that is, it must be counted as three. This is not as simple as replacing the symbol 2 with 3. So it must have a mechanism to change this state. Any two things put together will automatically become three.

This would cause the universe to collapse.

Of course, the stone at this time cannot be the stone in our concept, but a "thing" based on that law.

Moreover, if such rules really exist, then such mathematical operations are still in line with the laws of nature, and such mathematical tools can still be used to describe and explore the phenomena 'seen' in that world, because this mathematical system was born in In such an environment.

Therefore, based on this understanding, the directions of mathematical weapons should be divided into two types.

If mathematics or numbers were invented as just a set of abstract knowledge that describes truth, then a civilization that wants to create the ultimate mathematical weapon should first find a way to link abstract mathematical axioms to the real world, and then affect the real universe by changing mathematical kilometer.

On the contrary, if mathematics or numbers exist objectively in nature, then this civilization can directly deal with the axioms of mathematics without having to consider the connection between the two.

Of course, there should be a situation that only destroys the inferences and results of abstract propositions like mathematics.

To put it simply, in the first case, mathematics can actually be regarded as the painter's pen, and the mathematical formulas are the painter's paintings. Of course, what the painter draws is a description of the real world.

Then the second situation can be seen as the painter's pen is the pen of the magic pen Ma Liangzhong.

People can only understand objective existence from paintings, so when the pen is tampered with, it is equivalent to closing the door to explore the mysteries.

From this perspective, using mathematical weapons is not as good as using physical laws. However, mathematical weapons have an advantage. Its use is so subtle that the civilization that is attacked is almost unaware of it.

For example, retain the existing axioms and correct logical deduction rules, but modify the reality of propositional predictions. For example, using geometric axioms, it can be deduced that the three angles of two triangles with equal sides on the plane must also be equal, but in reality, the corresponding angles of such two triangles can be unequal. The confusion caused by this is more terrible than the confusion caused by changing the logic. If the logic is modified, new results can be deduced according to the new logic. However, if all correct logic is followed but the wrong result is obtained, it will be irreversible.

Of course, there is also the possibility of directly attacking the mathematics itself, just as the Nullifiers did to the Pangu civilization at that time, in order to block the progress of civilization.

When a civilization wants to explore the nature of mathematics, it will inevitably think about these issues. Just like today's Shenzhou civilization, if you want to complete the ultimate computer, you must explore the essence of mathematics and the origin of computing.