他承认，练习确实会改变大脑，但值得怀疑的是认定这些改变会影响负责空间推理或数学问题等其他大脑区域的主张。
Practice does change the brain, he allows, but what is questionable is the assertion that these changes affect other brain regions, such as those responsible for spatial reasoning or math problems.
他收集的数据得出了一个关于房间回声持续时间、吸音材料的数量和质量以及空间体积之间关系的数学公式。
The data he compiled yielded a mathematical formula for the relationship between a room's echo duration, its quantity and quality of sound-absorbing materials, and its spatial volume.
研究表明，如果给定15分钟的自由玩耍时间，四到五岁的孩子会将其中三分之一的时间花在有关空间、数学和建筑的活动上。
Research shows that given 15 minutes of free play, four- and five-year-olds will spend a third of this time engaged in spatial, mathematical, and architectural activities.
心理学家苏珊·莱文是芝加哥大学研究幼儿数学发展的专家。她发现，在2岁至4岁之间玩拼图的孩子在后来会发展出更好的空间能力。
Psychologist Susan Levine, an expert on mathematics development in young children the University of Chicago, found children who play with puzzles between the age of 2 and 4 later develop better spatial skills.
现在我们已经知道科学无法尽善尽美，我们无需（像波兰尼那样）那么艰难的斗争以保留逻辑和数学无力施为的概念空间。
Now we know science is not perfectible we do not have to fight so hard to retain a conceptual space for that which cannot be done by logic and mathematics.
这篇文章的作者写道“纵观数学史，数字的概念一直与空间的概念纠缠不清”，现在我们知道它们的联系是由大脑的构造决定的。
The study authors note that "throughout the history of mathematics, concepts of number and space have been tightly intertwined." now we know that the connection even occurs in our brains.
在这个困难的数学阶梯上取得下一个进展之前，得先在四维空间做同样的事情。
On the next rung up the ladder of difficult mathematics comes doing the same thing in four-dimensional space.
但是读懂这种语言，并能够预测出一维元素如何在三维空间当中折叠的，则需要一本数学词典。
But to read this language and predict how the one-dimensional string will fold up in three-dimensional space, you need a mathematical dictionary.
研究一下历史，你就会发现，事实上，在需要空间能力和数学推理的领域——比如国际象棋、作曲和火箭科学——没有出类拔萃的女性。
Look at history and you will see that practically no women have excelled in areas where spatial ability and mathematical reasoning are required, such as chess, composing and rocket science.
数学之所以高于其他领域的学问，是由于其总是能超越时间和空间的禁锢。
More than most other sorts of knowledge, mathematics has always transcended the limits of time and space.
根据社交网络和数学网络分析方法的提示，城市形态研究组项目计算城市空间布局如何影响人们在其中生活的方式。
Taking a cue from social networks and mathematical network analysis methods, the City Form Research Group's program calculates how a cities' spatial layout affects the way people will live in it.
但进入青春期后，由于睾酮增加了男孩的空间能力，他们不但迎头赶上，而且还擅长数学推理。
But after puberty boys catch up and excel in mathematical reasoning as testosterone boosts their spatial ability.
数学研究数和空间的抽象对象。
Mathematics is concerned with the abstractions of time and space.
这个发现有助于解释为何一个人精通数学却不通音律，或者擅长于空间导航技术而不善于学习语言。
This could help explain what makes one person good at math but bad at music, or good at spatial navigation but bad at language
例如在今天，Wolfram Alpha正在发布实时空间气候数据，12组完整的基因数据以及本地地图，以及众多与数学、生物学、物理、地理相关的其他知识领域。
Today, for example, the team is launching real-time space weather data, 12 complete genomes and local maps, as well as other knowledge domains related to math, biology, physics and geography.
从另一方面说，Mann只不过是愿意花一点钱来换取数学多维空间系内的体育方面争执的好结果。
In other words, Mann is more than willing to donate a few pounds to a good cause in order to pursue a sporting spat in mathematical hyperspace.
按照数学家们的分类，三叶形是最简单的纽结。 所谓纽结，它是三维空间中不与自己相交的封闭曲线，或者说是三维空间中与圆周同胚的图形。
The trefoil is the simplest knot in mathematicians' classification.
计算机科学主要建立在数学运算的基础上。它依赖的是空间能力，结果就成了男性领域。
Computer science is built largely on mathematics, which relies on spatial ability and, as a result, it's a male domain.
他的纯数学一塌糊涂，但是他却擅长一切包含空间关系和设计的东西。
He gets thrown off by pure mathematics, but he's good at anything involving spatial relationships and design.
数学家们需要列出三位空间中所有可能的图形方案。
It challenges mathematicians to list the possible shapes into which three-dimensional space can be wrapped up.
而女孩的空间能力位于大脑两侧。测试表明，女性会使用左前脑的语言区域来解决数学问题。
The spatial area for girls is located on both sides of the brain and tests show that many females use the left front verbal side of the brain to attempt to solve mathematical problems.
在信息检索中，向量空间模型是最有效的数学工具之一。
In information retrieval, vector space model is one of significant mathematics tools.
拓扑，数学的一个分支，描述了可能被扭曲，变形，拉伸或以其他方式产生新的形状形状的空间属性。
Topology, a branch of mathematics, describes the spatial properties of shapes that may be twisted, stretched or otherwise deformed to yield new shapes.
大脑的这个部分被认为是控制数学思维、空间关系以及其他类型思维的区域。
This area of the brain is believed to control mathematical thought, spatial relationships and other kinds of thinking.
针对这一问题，建立了以起升机构占用空间最小和行星齿轮减速机构用材最少为目标的多目标最优化数学模型。
Aim at the problem, this paper establishes the mathematical model of multipurpose optimization to made hoisting mechanism to occupy minimum space and planet gear to use minimum material.
大自然之所以如此浪费，是因为对付那些数学家们所说的完全探索的“潜力空间”的最好的办法，就是无目的战略。
Nature is so wasteful because scattershot strategies are the best way to do what mathematicians refer to as fully exploring "the potential space."
数学是研究现实生活中数量关系和空间形式的数学。
Mathematics is the study of quantitative relationship between real life and space form of math.
数学思想是人脑对现实世界的空间形式和数量关系的本质的反映，是思维加工的产物。
Mathematical thought is the reflection of quantitative relations and spatial forms of reality in human brain, and it is the thought processing product.
数学思想是人脑对现实世界的空间形式和数量关系的本质的反映，是思维加工的产物。
Mathematical thought is the reflection of quantitative relations and spatial forms of reality in human brain, and it is the thought processing product.
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