Eubulides, Aubrede, is also translated into Euban Leeds. Ancient Greek philosopher, a student of Euclid, lived in the 4th century BC. The most famous liar paradox was put forward by him.

Aubrey put forward seven paradoxes handed down from generation to generation:

1, 000,000 is a pile.

If 1 000,000 tablets are a pile, then 999,999 tablets are also a pile.

So 999,999 pills are a pile.

If 999,999 tablets are a pile, then 999,998 tablets are also a pile.

So 999,998 pills are a pile.

if ...

..... so 1 is a pile.

A bundle of pencils, a box of fast food, a group of people, a mountain ... there are quantifiers in many languages.

But there are no quantifiers in the programming language.

var a= 12

In fact, in programming language or mathematics, numbers and objects are separated, and we only deal with the relationship between numbers, regardless of objects. 1+ 1=2, suitable for two apples and two stars.

The essence of quantifiers is an additional description of things, which can be regarded as special adjectives.

Quantifiers are very similar to "units" in natural science. "A bottle of beer" is similar to "1 liter of beer". L describes the volume of these beers, and the standard volume is10cm x10cm x10cm; Bottle is also described by volume, but it is often not a fixed standard. The beer bottles are not the same size. You can't be sure what a bottle of beer is unless you see it with your own eyes. 100 ml can be a bottle, and 1 liter can also be a bottle.

Although it seems to be related to volume, "Sheng" is a quantifier and "Bottle" is a shape quantifier, both of which are described from the perspective of shape. As shown in the figure below, all kinds of containers can be called bottles, from refined bottles of wind oil to liquefied gas bottles. "Bottle" is an abstract concept of shape.

"Dui" is also a shape quantifier, which constrains the shape structure of a multi-bottom and small-top, rather than quantity, and solves the paradox problem of "Dui": "Dui" has nothing to do with quantity, but only with shape structure. As shown below, it can be said that at least four grains can form a "heap".

Different from mathematical languages and programming languages, there are many semantics in natural languages that cannot be quantified or even qualitative. Such as "size", "poverty and wealth", "happiness and sadness" and so on.

This can turn rice grains into sand, hair, money and so on. , such as:

Those who have 654.38+million are rich.

Then 9.99 million people also have money.

There are 9.99 million rich people.

Then 9.98 million people also have money.

...

People who have 1 yuan are also rich.

There is a paradox here because the definition of "wealth" is relative and vague. When we say that someone is rich, we often have a relative premise that he is richer than most people.

But is 1 yuan richer than most people? How about two dollars more? What about 20 million more?

The reason why it is vague is that we can't determine a clear boundary. In daily life, we can't say that people with10 million yuan are rich, while people with 9.99999999 yuan are not rich.

Another typical example is color. We are used to dividing the visible light range of human eyes from 400 nm to 760 nm into red, orange, yellow, green, blue, blue and purple. But in daily life, we can't tell exactly where the boundary between orange and yellow is, which interferes with many scientific researches, so that in the end, scientists forced 600 nanometers as the dividing line, 599 nanometers as orange and 600 nanometers as yellow. This sounds like a paradox, but it is necessary for scientific research.

In fact, there are similar official statements about the so-called rich and poor in our daily life. The international standard of the rich is that the personal net worth is between 654.38+0 billion and 654.38+0 billion dollars.

For many vague contents such as "beauty and ugliness" and "good and evil" that are not standardized or quantifiable, a temporary alternative is to vote in groups, that is, let everyone judge together and divide the boundaries by "the minority is subordinate to the majority", that is, most people think that beauty is beauty.

With the development of science and technology and the requirements of digital computer technology, many fuzzy semantics will be clearly defined gradually, but this process may take decades or even longer, which may be an impossible task in itself. The extraction and processing of fuzzy semantic data is also a difficult problem in natural language understanding.

More people are willing to interpret the paradox of grain pile as quantitative change leading to qualitative change. Although it sounds strange, it is also very interesting.

Pull out your hair one by one, and quantitative change will lead to qualitative change and baldness. ...

It is more appropriate for us to regard this phenomenon as emergence.

Emergence refers to a brand-new behavior or attribute expressed by the combination of multiple sub-elements.

For example, "not balding" is an attribute collectively expressed by tens of thousands of hairs, and animal behavior is a feature collectively expressed by billions of cells in the whole body.

Emergence can only occur at the cross-level level. As for when it appears (how many elements are there and how to combine them), there is no relatively formed scientific theory at present. We only know that "it just appeared, but we don't know how it appeared."

At present, the knowledge about emergence may only be as follows:

I think the study of emerging phenomena is likely to give birth to a new subversive science, which will be the science of all sciences, even the science of intelligence itself, and a real intelligence theory.

The core research objects of intelligence theory should at least include randomness, repeatability and the law and time factors based on them.

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