[Popular Science] & Bald heap paradox paradox

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June 2019 topics

Monet - Haystack

Madeleine Reid

Eubulides, O'Brien Reid, also translated as You Banli hereby. Ancient Greek philosopher, Euclid student, lived in the 4th century BC. The most well-known liar paradox is proposed by him.

Madeleine Reid handed down the paradox raised by seven:

  1. Liar: "I said the sentence is a lie", and that this sentence in the end is not a lie?
  2. Masked men paradox: "? Do you know this masked man you" "do not know" "But he's your father, so you do not know your own father?".
  3. Electra paradox: Electra positive do not know who came from far away to be his brother, but she knew who his brother was, so in the end she was approached know who?
  4. Stranger paradox: you do not pay attention to the people around passing and regard him as a stranger, that person happens to be your father, your father was a stranger you do?
  5. Heap paradox: a heap of grain can not be, but many grains can become a heap; likewise, took a grain, heap or heap from a heap, then repeatedly keep a pieces of a take, whether the last remaining grains still a heap?
  6. Bald paradox: his head covered with hair of people are not bald, pulled out a single hair is not bald, but he kept pulling it can become bald.
  7. Horn paradox: you never lose track horns, so you have horns.

O'Brien Reed paradox Brief

  1. Liar contradiction between the literal and meaningful semantics, abstract symbols from the paradox that means self-produced, which is a logical symbolic language system itself has incompleteness.
  2. Paradox is masked men "know" and "recognize" playing two words, or "you can identify the father" does not mean "you can identify the father wearing a mask."
  3. Electra paradox paradox similar and masked men.
  4. Strangers and masked men paradox paradox similar.
  5. Paradox paradox similar to the heap and bald, together we elaborate below.
  6. Paradox paradox similar to the heap and bald, together we elaborate below.
  7. Horn paradox ignored the premise of the syllogism, that "you have horns" and "had not lost horns" to infer "You still have horns," this conclusion.

Heap paradox

1,000,000 tablets are a bunch.
If a bunch of 1,000,000 tablets, so 999,999 is a pile of grain.
So 999,999 is a pile of grain.
If the grain is a pile of 999,999, then 999,998 is a pile of grain.
So 999,998 is a pile of grain.
If ...
...... is it a bunch.

In-depth understanding of quantifiers

"Bundle of pencils," "snack box", "group of people", "mountain" ... there are a lot of language quantifiers.

But there is no programming language quantifiers.
var a=12
In fact, programming language or mathematics and digital objects are separated, we only deal with the relationship between the digital regardless of the object. 1 + 1 = 2, which is suitable for both two apples, but also for two stars.

Quantifier is essentially a kind of additional things described, it can be regarded as a special adjective .

Quantifiers and natural sciences "unit" is very similar. "Beer" and "1 liter of beer," meaning similar. L describes the volume of these beers, 10 cm x10 cm x10 cm such a standard volume; bottle said to describe the terms of volume, but it is often not a fixed standard, beer bottles of different sizes are not consistent, unless you We saw, otherwise you can not determine "a beer" how much, can be a bottle of 100 ml, 1 liter bottle can be.

Although seemingly are related to the volume, but the "L" is a quantifier, "bottle" is a measure word shape, i.e., from the viewpoint of the shape described. FIG follows from the gas bottle to bottle Fengyoujing, various containers can be called a bottle. "Bottle" shape is an abstract concept.


"Heap" is also a shape quantifier, it is a constraint above the bottom of how small the shape of the structure, rather than quantity, and this solves the problem of heap paradox: "heap" and the number of irrelevant, only the shape and structure of the relevant . As shown below, it can be said that at least four grain could constitute a "stack."



And mathematics and language programs in different languages, there are not a lot of qualitative and quantitative not even semantics in natural language. For example, "How much size" "wealth and poverty", "happy sad" and so on.

This can put a grain of rice into the sand, hair, money, etc., such as:

With 10 million of the rich.
It also has a rich 9.99 million.
It has 9.99 million of the rich.
It also has 9.98 million of the rich.
I have also rich 1 dollar.

Here arises the paradox, the reason is that "the rich." This definition is relative and ambiguous. When we say someone is rich, it is often with a relatively premise, and that is with respect to most people, he is rich.

But more than a dollar than most people considered rich? More than two it? More than 20 million it?

The reason why we say it is vague, that is because they can not determine a clear boundary, daily life can not be said to have a million is rich, but not rich 9,999,999 of .

Another typical case is the color, we used the 400 nm to 760 nm visible range of the human eye is divided into several red orange yellow green blue purple color. But fails to account for everyday life we ​​boundaries between orange and yellow lie, which has brought a lot of scientific interference, so that eventually forced scientists to 600 nm as a dividing line, 599 nm is orange, 600 nano is yellow, it sounds like a paradox, but it is necessary for scientific research.


In fact, on our daily said rich and poor has a similar official statement, the rich standard in the international arena is a personal net worth of 10 million to $ 1 billion.

For many standard has not been or can not be quantified vague content, such as "beauty and ugliness," "good and evil", a temporary alternative is to group voting , that let everyone work together to judge, with the "majority" approach demarcation, that the majority of people say beauty is beautiful.

With the requirements of the development of digital technology and computer science and technology, a lot of fuzzy semantics will gradually be clearly defined, but the process may take decades or even longer, perhaps itself an impossible task, fuzzy extract semantic data and is currently processing a natural language understanding problem.

Quantitative vs qualitative change caused Intelligence Theory

More people are willing to heap paradox interpreted as quantitative lead to qualitative change, although it sounds strange, but also very interesting.

One by one hair-pulling, pulling the trigger quantitative qualitative change, become bald ...

This phenomenon is considered to have emerged more appropriate.

It refers to the emergence of multiple sub-elements common combination of performance out of the new behavior or property .

For example, "not bald" is a hair after tens of thousands demonstrated by the combination of collective property, animal behavior is caused by a combination of body cells after billions out of the collective performance characteristics.

The emergence of the phenomenon can only appear on the cross-level , as for the appearance (how many elements, how the combination), has not, mature scientific theory, we just know when "it appeared that, without knowing the exact how to appear. "

Now known about the emergence of knowledge may be the following:

  • Multiple elements. "Two to five", emerged two elements can be "repeated, consistent, synchronized" These characteristics.
  • Related to each other. All elements must be interrelated acts, "synergistic or antagonistic" can be.
  • Group differentiation. If the group forming module, function between divisive element, then the whole will emerge more efficient, such as group behavior ants and bees swarm formation.
  • Order-related. All are inevitable emergence of order and variation between elements based, such as the fall migratory geese queues emerged in the sky, "the word" or "herringbone" style.

I think, for the emergence of phenomena studied, is likely to be the birth of a new subversive science, it is the science of all sciences, even intelligent science itself, it is the real intelligence theory Intelligence Theory at The .

The core subjects of intelligence theory should at least contain random, repeat, and the law of this factor in the formation of both time and regular basis .


This month's topics mentioned in the previous Flying Arrow immobility paradox can also be from the emergence of the phenomenon be explained, just as movie film, as each frame is static, but the content of these screens distributed throughout the timeline later on, it is the emergence of a complex movement. Flying Arrow is not moving concept reveals the basic principle of the whole universe works.

Welcome attention to my column (tsu • ω •) zu [artificial intelligence] Liberal
June 2019 topics

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Reproduced in: https: //www.jianshu.com/p/466b54f08a7d

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Origin blog.csdn.net/weixin_33958366/article/details/91278631