The road to technology

Chapter 790 Mathematics
"The invention of numbers saves us from wasting time repeating shouts, 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 appeared later, and people only knew fish at first, so it is important for others to 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 point of view, number is no longer an easy-to-understand concept. Its abstraction adds a layer of mystery to it. The more you think about the concept of number from a philosophical point of view, the more you will feel that it seems like It's an impenetrable fog.

It even makes people wonder: Where did the numbers come from?Did civilized humans invent numbers, or did numbers objectively exist in nature and were only discovered by us humans? "

Speaking of this, Yue Yuanzhou raised his palm, and used holographic materialization technology to materialize a rope above his palm, then tied a knot in the rope, and tied a second knot in a few seconds.

At this time, he looked at Longlin and continued: "If there is no number, then people should initially call the appearance of the first knot and the appearance of the second knot knot, knot. The more knots are tied, the more difficult it is to remember the quantity of the goods, and it is also very difficult to express the quantity of goods. So there is a way to represent the first knot as one and two knots together 'Knot, knot' is also represented by another abstract two."

"And so, addition was born, and one plus one equals two. Of course, people may have used stones in the beginning, but it doesn't make any difference. This is probably the simplest mathematics that humans have learned from nature.

With the addition operation, subtraction came into being as its inverse operation, and 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 who divide from their own way of thinking, and use mathematics as an abstract tool to describe nature, because this kind of abstract number is much simpler than the infinitely lengthy string of "fish, fish, fish" in the human way of thinking . "

Speaking of this, Yue Yuanzhou paused for a moment, then turned the rope back into holographic data, and continued: "Then if it doesn't start from the human way of thinking, then its mathematical system and mathematical operations will be very different. Far Let’s just take this data as an example! A civilization dominated by artificial intelligence, their mathematical system will not have four arithmetic operations, but they can still use the lengthy string of 0 and 1 to express nature”

Indeed it is.

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

Mathematics is not only an intuitive tool, but also 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 application of mathematics is so extensive, the power of mathematics is so great, and the omnipotence and omnipotence of mathematics have surpassed the comprehension of our human wisdom. category.

Having said that, Yue Yuanzhou knows that the category that seems to be beyond the comprehension of wisdom is not mathematics itself, but the ultimate truth of the universe, because it is what human beings most want to describe 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, it should become three.

Because logic is based on reality, especially basic theory, which is the simplest law of reality. 1+1=2 is counted, if it becomes 3, there must be a reason, that is, it must be counted to become three, it 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 still conform to 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 cognition, the direction of mathematical weapons should be divided into two types.

If mathematics or numbers are invented and are just a set of abstract knowledge describing the truth, then the civilization that wants to manufacture the ultimate mathematical weapon should first find a way to link the abstract mathematical axioms with the real world, and then affect the real universe by changing the mathematical kilometers.

On the contrary, if mathematics or numbers exist objectively in nature, then this civilization can directly start with mathematical axioms without considering the issue of linking the two.

Of course, there should be such a situation, which only destroys the inferences and results of abstract propositions such as mathematics.

To put it simply, in the first case, mathematics can be regarded as a painter's pen, and 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 regarded as that the brush of this painter is the brush of Ma Liangzhong, the magic brush.

And people can only understand the objective existence from the painting, so when the pen is tampered with, it is equivalent to closing the door to explore the mystery.

From this point of view, using mathematical weapons is not as good as using physical law weapons, but mathematical weapons have an advantage, and their use is so hidden that the civilizations that have been recruited are almost unaware.

For example, retain the existing axioms and correct logical deduction rules, but modify the reality of the propositional prediction.For example, using geometric axioms to deduce that the three angles of a triangle with two equal sides on a plane must also be equal, but it is possible to make the corresponding angles of such two triangles unequal in reality.The chaos caused by this is more terrible than the chaos caused by modifying the logic.If the logic is modified, new results can be deduced according to the new logic, but if the wrong results are obtained according to the correct logic, it will be irreversible.

Of course, there is also the direct attack on mathematics itself, just like the zero return to the Pangu civilization at that time, in order to achieve the goal of blocking the progress of civilization.

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

(End of this chapter)