Logical/Mathematical Intelligence 逻辑 和 数学智能

逻辑/数学智能

Luójí/shùxué zhìnéng

My prayers include the wish to be intelligent.

However, if I have to force myself to learn about ‘being intelligent’ I’ll rather forget about such ‘education’.

I believe that intelligence comes from God and that we should not be making any difference between how we treat intelligent people as opposed to how we are to treat those with what we called “lower IQ’s”.

What then is Logical - Mathematical Intelligence?

Howard Gardner is an American educator and researcher who had studied multiple intelligence for many years. Read about his theory of multiple intelligence at this website: https://infed.org/mobi/howard-gardner-multiple-intelligences-and-education/

• Howard Gardner’s theory of multiple intelligences proposes that people are not born with all of the intelligence they will ever have.
• This theory challenged the traditional notion that there is one single type of intelligence, sometimes known as “g” for general intelligence, that only focuses on cognitive abilities.
• To broaden this notion of intelligence, Gardner introduced eight different types of intelligence consisting of Logical/Mathematical, Linguistic, Musical, Spatial, Bodily-Kinesthetic, Naturalist, Interpersonal, and Intrapersonal.
• Gardner notes that the linguistic and logical-mathematical modalities are most typed valued in school and society.
• Gardner also suggests that there may other “candidate” intelligence—such as spiritual intelligence, existential intelligence, and moral intelligence—but does not believe these meet his original inclusion criteria.

The theory of multiple intelligences was first proposed by Howard Gardner in his 1983 book “Frames of Mind”, where he broadens the definition of intelligence and outlines several distinct types of intellectual competencies.

Read on further after the Chinese translations of the above for our daily dose (for 27 October 2020) of logical and Mathematical intelligence.

我的祈祷包括希望变得更聪明。    Wǒ de qídǎo bāokuò xīwàng biàn dé gèng cōngmíng.
我相信，智力来自上帝，我们不应在对待聪明人的方式与对待所谓“智商较低”的人的方式之间有所区别。
Wǒ xiāngxìn, zhìlì láizì shàngdì, wǒmen bù yìng zài duìdài cōngmíng rén de fāngshì yǔ duìdài suǒwèi “zhìshāng jiào dī” de rén de fāngshì zhī jiān yǒu suǒ qūbié.
霍华德·加德纳（Howard Gardner）的多元智能理论提出，人们并非天生就拥有他们将拥有的所有智能。
Huòhuádé·jiā dé nà (Howard Gardner) de duōyuán zhìnéng lǐlùn tíchū, rénmen bìngfēi tiānshēng jiù yǒngyǒu tāmen jiāng yǒngyǒu de suǒyǒu zhìnéng.
为了扩展这种智力概念，加德纳介绍了八种不同类型的智力，包括逻辑/数学，语言，音乐，空间，身体运动学，自然主义者，人际交往。
Wèile kuòzhǎn zhè zhǒng zhìlì gàiniàn, jiā dé nà jièshàole bā zhǒng bùtóng lèixíng de zhìlì, bāokuò luójí/shùxué, yǔyán, yīnyuè, kōngjiān, shēntǐ yùndòng xué, zìrán zhǔyì zhě, rénjì jiāowǎng.
Back to the practical way in which we can improve and increase our level of logical / mathematical intelligence.  Every day there are puzzles published in our local newspapers.  In Auckland we have the New Zealand Herald.  This newspaper has three puzzles on one page - the WordBuider puzzle, the traditional Sudoku puzzle, and the most interesting one called the "Simon Shuker's Code breaker" which is a test of mathematical logic combined with English vocabulary. 

The WordBuilder looks like it is a test on the English vocabulary. But if we can consider this a little deeper, it is also a test in logic. The reason is that we need to consider where the vowels (that is the ‘a’ , ‘e’, ‘i’, ‘o’, and ‘u’) are placed.

In this example, for instance, there are two vowels - ‘a’ and ‘e’. We also know that logically the vowels usually occur as the second letter in most words. Therefore, we can immediately think of two words - LAKE and BAKE. Then there are BEAK and LEAK. Going further, there are BLEAK, BLAKE, and BALE, ALE, and LAB. How about KALE, a vegetable. Using the starting letter A, we also have ABLE. Finally, there are the words LEK, LEA, KEA, and ELK.

Now try finding words of three letters or more in these groups of five-jumbled-letters:

(GROUP A) G. S. A. I. N. (GROUP B) D. S. A. B. N.

(GROUP C) M. T. E. I. S. (GROUP D) B. W. N. O. R. (GROUP E) R. D. E. L. U.

WordBuilder看起来像是对英语词汇的测试。但是，如果我们可以更深入地考虑这一点，那么它也是逻辑上的检验。原因是我们需要考虑元音（即“ a”，“ e”，“ i”，“ o”和“ u”）的放置位置。
WordBuilder kàn qǐlái xiàng shì duì yīngyǔ cíhuì de cèshì. Dànshì, rúguǒ wǒmen kěyǐ gēng shēnrù dì kǎolǜ zhè yīdiǎn, nàme tā yěshì luójí shàng de jiǎnyàn. Yuányīn shì wǒmen xūyào kǎolǜ yuán yīn (jí “a”,“e”,“i”,“o” hé “u”) dì fàngzhì wèizhì.

The next puzzle, Sudoku, is already familiar to most readers. Read more on how to solve SODUKU challenges in the article found earlier on this website. http://www.u-write-read.com/2020/03/07/sudoku-for-seniors-老年人要玩数独/

Read also “Sudoku is Fun taking the Francis Run” at http://www.u-write-read.com/2019/10/04/solving-hard-sudokus-解决困难的数独/

There is also “Francis’s Rules for Sudoku” at http://www.u-write-read.com/2019/03/29/francis-rules-for-sudoku/

And also “Try Solving this Sudoku Challenge” at http://www.u-write-read.com/2017/03/10/try-solving-this-sudoku-challenge-尝试解决这个数独挑战-whakamatauria-rapanga-teen-sudoku/

Two more websites to follow on: http://www.u-write-read.com/2017/01/10/sudoku-puzzle-10-jan-2017/. and http://www.u-write-read.com/2016/12/31/sudoku-is-easy/

数独是一种有趣的逻辑游戏。它不需要英语。它只是将数字放入框中，以便每一行，每一列和每个正方形包含从1到9的数字，且没有重复。
Shù dú shì yī zhǒng yǒuqù de luójí yóuxì. Tā bù xūyào yīngyǔ. Tā zhǐshì jiāng shùzì fàng rù kuāng zhōng, yǐbiàn měi yīxíng, měi yīliè hé měi gè zhèngfāngxíng bāohán cóng 1 dào 9 de shùzì, qiě méiyǒu chóngfù.
Now try to complete the Sudoku Challenge shown here.  We know that cell h4 = 3; cell e5 = 8;  What other numbers between 1 and 9 can be placed into the other sells? 

The next and last puzzle is known as the “Simon Shuker’s Code Breaker’. It has the appearance of a crossword puzzle but it is not. The cells in a 13 x 13 grid are numbered such that each number represents a different letter in the alphabet. Every puzzle has an initial clue, and most of the time, there are usually two clues. In the puzzle here, the two clues are N for number 15 and T for number 16.

If we then replace all the cells numbered 15 to N and all the cells numbered 16 to T, we then start looking at the grid logically and try to complete the entire grid.

下一个也是最后一个逻辑游戏，被称为“西蒙·舒克的密码破译者”。它看起来像填字游戏，但这不是文字游戏。它是逻辑游戏。在13 x 13网格中的单元是编号，以便每个数字代表字母表中的不同字母。每个谜题都有一个初始线索，并且在大多数情况下，通常有两个线索。在这里，这两个线索分别是数字15的N和数字16的T 。
Xià yīgè yěshì zuìhòu yīgè luójí yóuxì, bèi chēng wèi “xīméng·shū kè de mìmǎ pòyì zhě”. Tā kàn qǐlái xiàng tián zì yóuxì, dàn zhè bùshì wénzì yóuxì. Tā shì luójí yóuxì. Zài 13 x 13 wǎng gé zhōng de dānyuán shì biānhào, yǐbiàn měi gè shùzì dàibiǎo zìmǔ biǎo zhōng de bùtóng zìmǔ. Měi gè mí tí dōu yǒu yīgè chūshǐ xiànsuǒ, bìngqiě zài dà duōshù qíngkuàng xià, tōngcháng yǒu liǎng gè xiànsuǒ. Zài zhèlǐ, zhè liǎng gè xiànsuǒ fēnbié shì shùzì 15 de N hé shùzì 16 de T.

Let us consider another example.

Here the clues are 12 = R and 13 = C.

We find the number 12 in cell c7 and the number 13 in cell c9. There is another 13 in cell i10.

让我们考虑另一个例子。  这里的线索是12 = R和13 =C。 
Ràng wǒmen kǎolǜ lìng yīgè lìzi.  Zhèlǐ de xiànsuǒ shì 12 = R hé 13 = C.

For the letter along cell c6 therefore we find the following series of numbers - 6, 12, 2, 13, 2, 1, 2, 1 - an 8-lettered word. The logic here is to find a word where the third, fifth, and seventh letters are similar and that the sixth and eighth letters are similar. Logic also dictates that the number 2 has to be a vowel. Trying a, e, i, o, and u into the third, fifth, and seventh letters gives us just one logical answer and that is the word ” PRECEDED”. So now we got 6 = P; 2 = E; and 1 = D. 12 of course is given as R and 13 is given as C.

因此，对于单元格c6上的字母，我们发现以下数字系列-6，12，2，13，13，2，1，2，1-一个8字母的单词。此处的逻辑是找到第三个，第五个和第七个字母相似且第六个和第八个字母相似的单词。逻辑还规定数字2必须是元音。尝试在第三个字母，第五个字母和第七个字母中输入a，e，i，o和u只会给我们一个合乎逻辑的答案，那就是单词“ PRECEDED”。所以现在我们得到6 = P; 2 = E;和1 =D。当然12表示为R，13表示为C。
Yīncǐ, duìyú dānyuán gé c6 shàng de zìmǔ, wǒmen fāxiàn yǐxià shùzì xìliè-6,12,2,13,13,2,1,2,1-yīgè 8 zìmǔ de dāncí. Cǐ chǔ de luójí shì zhǎodào dì sān gè, dì wǔ gè hé dì qī gè zìmǔ xiāngsì qiě dì liù gè hé dì bā gè zìmǔ xiāngsì de dāncí. Luójí hái guīdìng shùzì 2 bìxū shì yuán yīn. Chángshì zài dì sān gè zìmǔ, dì wǔ gè zìmǔ hé dì qī gè zìmǔ zhōng shūrù a,e,i,o hé u zhǐ huì gěi wǒmen yīgè héhū luójí de dá'àn, nà jiùshì dāncí “PRECEDED”. Suǒyǐ xiànzài wǒmen dédào 6 = P; 2 = E; hé 1 =D. Dāngrán 12 biǎoshì wèi R,13 biǎoshì wèi C.

The grid now looks like this:

We find that in column 9, there is a word with only one letter missing - P ? C. E. D. The ? has to be a vowel, and therefore this number 7 is the letter “a” for the word “paced.” For the word P. A. ? D. A. at cell a9, across, we can now see that the only possible word is P. A. N. D. A. So, the number 8 = N.

We now have a four-lettered word N. ? D. E. at cell a11 down. The only word that fits is N. U. D. E. So, 9 = U.

The long ten-lettered word starting from cell i4 has an interesting profile. the first and the sixth letters are similar and the third and the tenth letters are also similar. This is unique. There is only one word that matches these requirements. That word is “I N. T. O. X. I. C. A. N. T”. So we have a great logical find - 16 = I; 14 = T; 5 = O; and 23 = X.

Then the four-lettered word at cell d5 (down) is ” ? E T O.” The only word that fits here is VETO. Therefore, 3 = V.

At cell a1, the word with one letter missing is ” D. E. V. E. ? O. P. ” We can conclude here that number 4 is L and the letter is “Develop.” At cell a1 (down), the letter here is “D. E. P. T. H. ” with number 17 equal to the letter ‘H.’

At cell f11 down the only word there is “unmanned” as the letter “t” has gone to number 14. Therefore, 19 = M.

For the letter in cell a13 down, the word is ABDOMEN with number 10 = B.

At cell e1, across, the only letter that makes sense for number 18 is an “s”.

At cell 3a down, the letter Q for number 15 makes good sense. VANQUISH.

There are very few letters left.

We have numbers 11, 20, 21, 22, 24, 25, and 26 left.

For letters we have F, G, J, K, W, Y, and Z.

For cell g1 across, the word WISDOM comes to mind. If 20 = W then the cell g1 down becomes WISHFUL, 24 = F. Then cell k1 across becomes FEELINGS, number 11 becomes G. Cell h7 down becomes JOGGED or 21 = J.

It is the final lap now. Only numbers 20, 22, 25 and 26 are left. Cell m1 across, we can tick away K and Y for LANKY. The letter K in cell h9 is also correct for the letter AKIN.

The last letter Z must be number 26 to make the word DAZEDLY for cell m7 across.

That’s it, Folks.

Google “Simon Shuker’s Code Cracker” for more.

在逻辑上找到每个单词时，我们发现字母与数字的匹配。将这样的字母存入网格将使我们慢慢地为整个网格提供完整的解决方案。

Zài luójí shàng zhǎodào měi gè dāncí shí, wǒmen fāxiàn zìmǔ yǔ shùzì de pǐpèi. Jiāng zhèyàng de zìmǔ cún rù wǎng gé jiāng shǐ wǒmen màn man dì wéi zhěnggè wǎng gé tígōng wánzhěng de jiějué fāng'àn.