多重参照框架及数字表述方式对数字加工的影响
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摘要
数字是数学语言的基本单元,离开了数字,人类的数学知识就无法真正建立起来。进行数字加工研究,对探明人类心理的本质,以及人工智能的发展等都具有重要意义。
已有数字认知的研究表明,数字加工特点很大程度上依赖于任务内容,同时,根据不同参照系进行编码的空间信息对数字加工有显著影响。这些参照框架或是以观察者身体的某个部分为中心(自我中心编码),或是以非身体结构为中心(非自我中心编码),而这些参照框架在数字加工任务中无法(至少是很难)与数字表征本身的影响分离。因此,将数字认知加工特点仅仅归结为数字数量表征特点所致,这是不全面,甚至是错误的。
在数量比较或是数字Stroop任务中,同时呈现的两个数字,或是先后呈现的两个数字,它们的数量大小趋势或是字号大小趋势,都有可能产生一种参照框架,从而影响作业表现。数字出现在屏幕不同位置对数字加工的影响,有Simon效应进行了有关描述。数字先后呈现也可能产生“由左到右-由小到大”或是“由远到近-由小到大”的参照框架,影响到作业表现,但没有研究涉及。另外,在实验中要求被试按键作出反应,这种按键的左右布局也会产生一种参照框架的影响。尽管实际工作中人们采用“A-B,B-A”进行了平衡,但是当传递效应的幅度因顺序不同而不同时,平衡会无效,并且把按键布局形成的参照框架效应掩盖在其中。因此,本研究假设,数字加工依据任务性质不同,存在不同的参照框架,有的存在多个参照框架,当这些参照框架与自我中心参照框架一致时,会促进反应;当多个参照框架有的与自我中心参照框架一致,有的不一致时,依据不同参照框架的影响力量可对反应时作出预测。
研究表明,心理数轴的方向与文化因素密切相关,因此,从跨文化视角上的研究可以使我们进一步了解数字加工的特点。由于汉语不同于本文语言系统的特点,以母语为汉语的被试研究数字加工,有着特殊的意义。本研究认为,在没有激活数字语义表征的任务中,各种形式数字(阿拉伯、简体中文、繁体中文和英文数字)的加工不存在显著差异;在激活数字语义表征的任务中,由于各种形式数字间的编码关系影响,四种形式数字的反应时从快到慢依次是阿拉伯数字、简体中文数字、繁体中文数字和英文数字。
综上所述,本研究提出了数字加工多重编码多重参照框架模型。
另外,对数字加工的影响是从刺激呈现开始,到被试反应结束,这个过程的每一环节都可能影响作业表现。许多数字加工研究采用按键反应,却忽略了按键符号即时表征的影响。由于数字激活比字母激活速度快,数字按键的数量表征的干扰,本研究假设在没有激活数字语义表征的任务中,按键为数字键的反应更快;在激活数字语义表征的任务中,按键为字母键的反应更快。
还有,在数量大小与数字呈现知觉大小不同组合的数字Stroop任务中,研究发现了“数量大字号大”与“数量小字号小”的“一致性”效应。根据上述多重参照框架的假设,这种“一致性”效应存在缺陷,因为这里的字号与数量的“一致”有两种情形:先后呈现的两个数字的字号数量都是“前小后大”,或都是“前大后小”。“不一致”也有相应的两种情形。
为了验证数字加工多重编码多重参照框架模型,对上述问题予以探讨,本研究选择了数字Stroop、数字奇偶判断和数字数量比较三个数字加工任务,这三个任务的数量激活程度逐渐加深,并采用数字键(小键盘的“1”和“3”)、字母键(“V”和“N”)两种不同的按键反应,以及语音反应的方式,以大学生和研究生为被试,进行了多个实验,得到了如下结论:
1、数字认知加工任务中,先后呈现的两个数字的字号大小顺序、数量大小顺序,以及按键反应的左右布局,在相应任务中产生了参照框架,影响了被试的操作。这些参照框架具有方向性,当其与“从左到右-从小到大”或是“从远到近-从小到大”的自我中心参照框架方向一致时,促进了被试的反应,反之干扰了被试的反应。当多个参照框架方向不一致时,显示出了不同参照框架对反应的影响力量的强弱,其中按键布局产生的参照框架力量最强。数字加工的多重参照框架假设得到了验证。
2、在未激活数量表征的任务中,不同形式数字之间的反应时不存在显著差异;在激活了数量表征的任务中,四种形式数字的反应时从快到慢依次是阿拉伯数字、简体中文数字、繁体中文数字和英文数字(繁体中文数字和英文数字之间在奇偶判断任务中差异不显著,在数量比较任务中差异显著)。数字加工的多重编码的假设得到了验证。
3、按键符号的即时表征影响了数字加工任务。在没有数量激活的任务中,采用数字键的反应更快;在有数量激活的任务中,采用字母键的反应更快。
4、数字Stroop任务中,字号数量的一致与不一致各有两种情形,四种条件下的反应结果存在差异。字号数量“一致”且与自我中心参照框架一致有最快的反应,字号数量“一致”而与自我中心参照框架不一致并没有促进反应,甚至干扰了反应。
Digit is the basic unit of mathematical language. Without digit, human knowledge on mathematics might not come into being. The research on digit processing is significant in probing into human mental essence and developing human intelligence.
Finished research on digital cognition indicates that characteristics of digital process mostly depend on the content of tasks. Spatial information encoding based on varied reference framework affects digit processing a bit. These reference frameworks are centered on part of an observer’s body (egocentric coding ), or on some non-bodily object (allocentric coding ). These reference frameworks can’t separate from digital representation itself in the task of digit processing. For this, it is quite deficient, even a mistake to attribute the characteristics of digital cognition processing task to those of digital representation.
In the task of digital comparison or digital Stroop, the set of two numbers which occur simultaneously or sequentially, their trends in number volume and letter type size probably result in a reference framework, then affect its performance. Digits occur in different places on the screen, which affects digit processing. The influence is described with Simon effect. Sequential digital occurrence may give rise to a reference framework, from left to right, from small to big, or from far to near, from small to big, which affects its performance, but no research is involved. In addition, in the experiment tested keys are set to response. The keys layout may also give rise to a reference framework. Although in a practical way A-B, B-A Pattern is adopted to balance. Whereas, when the range of transmitting efficiency varies from different order, the balance will be broken, and the reference framework efficiency, resulted from keys layout are concealed. For this reason, it is presumed that digit processing has its varied reference framework because of different nature of tasks. Some have several reference framework. When these reference frameworks coincide with egocentric one, responses are enhanced. When some framework coincide, others don’t, responses can be predicted under the influence of varied reference framework.
It shows that mental axis direction is closely related to cultural elements. From the standpoint of interculture, it helps us to get to know the characteristics of digit processing. As Chinese differs from the language system mentioned here, it’s particularly significant to process controlled digits, taken Chinese as mother tongue. It is supposed that in the task of non-stimulating digital representation,all kinds of digit processing ( Arabic digits, plain Chinese digits, complex Chinese digits and English digits ) have no sharp distinctions. In the task of stimulating digital semantic representation ,the order in which four forms of digits response is Arabic digits, plain Chinese digits, complex Chinese digits and English digits, from the fastest to the least fast.
To sum up, this research put forth a model of digital multi-encoding and multi- reference framework process .
Additionally, the effects on digit processing range from stimulation presentation to finished responses to tests. Each step of the whole process may affect performance. Many researches on digit processing adopt the push-the-button-and-response method, without awareness of the influence of instant representation of keys symbol. Since the speed of digits stimulation is faster than that of letters. And the disturb of numeric representation of numeric key-press. It is presumed that in the task of non-stimulating digital semantic representation,digit keys reacts faster. In the task of stimulating digital semantic representation,letter keys react faster.
Furthermore, in the digital Stroop task of digit volume and digital presentation size, it shows a coincidence reaction that big digit has big letter type, small digit has small letter. Based on the above-mentioned hypothesis of multiplied reference framework, the coincidence reaction has its defects. There are two cases for the coincidence between letter types and digit volume. Two digits presented sequentially are both in increasing or decreasing order. The non-coincidence has its own case.
In order to test the model of digital multi-encoding process and multiplied reference framework, to explore above-mentioned issues, three tasks, digital Stroop, digital judgment between odd numbers and even numbers, digital volume comparison, are chosen. In these three tasks, digital stimulation procedure of volumes is increasingly enforced. Digit keys ( 1 and 3 on the small keyboard ), letter keys ( V and N) are used to test two different kinds of keys responses and phonetic responses are adopted. Controlled group includes graduates and postgraduates. After dozens of experiments, conclusions are made as follows:
1. In the task of digital cognition process, the sequential occurrence order of two digit types, digit order, then layout of key responses give rise to reference framework in their own course, and even affect the performance of the tested. These reference framework has its direction. When it keeps accompany with the direction of egocentric reference framework, from left to right, from small to big, or from far to near, from small to big, it may enhance the response of the tested, Conversely,prohibit the response. When the directions of many reference framework do not coincide, it shows different reaction forces to different reference framework. Among them, the strongest power results from keys layout. The hypothesis of digital process and multiplied reference framework is to be proved.
2. In the task of non-stimulating quantity representation ,digital reactions in any form has striking distinctions. In the task of stimulating quantity representation,the order of four forms of digital reactions, from the fastest to the least fast, is Arabic digits, plain Chinese digits, complex Chinese digits and English digits. ( The differences between complex Chinese digits and English digits are not striking in the task of judging odd and even numbers. The differences are striking in the task of quantity comparison. ) The multi-encoding hypothesis on digital process is proved.
3. Instant representation of key symbols affects the task of digital process. In the digital non-stimulating task, the responses to digit keys are faster; while the responses to letter keys are faster.
4. In the digital Stroop task, there are two cases for coincidence and non-coincidence between letter types. There exist reaction differences under four kinds of conditions. The coincidence between letter types and digits keep pace with egocentric reference framework, which enhances the fastest response. The coincidence between letter types and digits doesn’t keep pace with egocentric reference framework, which doesn’t enhance the response but prohibit the response.
已有数字认知的研究表明,数字加工特点很大程度上依赖于任务内容,同时,根据不同参照系进行编码的空间信息对数字加工有显著影响。这些参照框架或是以观察者身体的某个部分为中心(自我中心编码),或是以非身体结构为中心(非自我中心编码),而这些参照框架在数字加工任务中无法(至少是很难)与数字表征本身的影响分离。因此,将数字认知加工特点仅仅归结为数字数量表征特点所致,这是不全面,甚至是错误的。
在数量比较或是数字Stroop任务中,同时呈现的两个数字,或是先后呈现的两个数字,它们的数量大小趋势或是字号大小趋势,都有可能产生一种参照框架,从而影响作业表现。数字出现在屏幕不同位置对数字加工的影响,有Simon效应进行了有关描述。数字先后呈现也可能产生“由左到右-由小到大”或是“由远到近-由小到大”的参照框架,影响到作业表现,但没有研究涉及。另外,在实验中要求被试按键作出反应,这种按键的左右布局也会产生一种参照框架的影响。尽管实际工作中人们采用“A-B,B-A”进行了平衡,但是当传递效应的幅度因顺序不同而不同时,平衡会无效,并且把按键布局形成的参照框架效应掩盖在其中。因此,本研究假设,数字加工依据任务性质不同,存在不同的参照框架,有的存在多个参照框架,当这些参照框架与自我中心参照框架一致时,会促进反应;当多个参照框架有的与自我中心参照框架一致,有的不一致时,依据不同参照框架的影响力量可对反应时作出预测。
研究表明,心理数轴的方向与文化因素密切相关,因此,从跨文化视角上的研究可以使我们进一步了解数字加工的特点。由于汉语不同于本文语言系统的特点,以母语为汉语的被试研究数字加工,有着特殊的意义。本研究认为,在没有激活数字语义表征的任务中,各种形式数字(阿拉伯、简体中文、繁体中文和英文数字)的加工不存在显著差异;在激活数字语义表征的任务中,由于各种形式数字间的编码关系影响,四种形式数字的反应时从快到慢依次是阿拉伯数字、简体中文数字、繁体中文数字和英文数字。
综上所述,本研究提出了数字加工多重编码多重参照框架模型。
另外,对数字加工的影响是从刺激呈现开始,到被试反应结束,这个过程的每一环节都可能影响作业表现。许多数字加工研究采用按键反应,却忽略了按键符号即时表征的影响。由于数字激活比字母激活速度快,数字按键的数量表征的干扰,本研究假设在没有激活数字语义表征的任务中,按键为数字键的反应更快;在激活数字语义表征的任务中,按键为字母键的反应更快。
还有,在数量大小与数字呈现知觉大小不同组合的数字Stroop任务中,研究发现了“数量大字号大”与“数量小字号小”的“一致性”效应。根据上述多重参照框架的假设,这种“一致性”效应存在缺陷,因为这里的字号与数量的“一致”有两种情形:先后呈现的两个数字的字号数量都是“前小后大”,或都是“前大后小”。“不一致”也有相应的两种情形。
为了验证数字加工多重编码多重参照框架模型,对上述问题予以探讨,本研究选择了数字Stroop、数字奇偶判断和数字数量比较三个数字加工任务,这三个任务的数量激活程度逐渐加深,并采用数字键(小键盘的“1”和“3”)、字母键(“V”和“N”)两种不同的按键反应,以及语音反应的方式,以大学生和研究生为被试,进行了多个实验,得到了如下结论:
1、数字认知加工任务中,先后呈现的两个数字的字号大小顺序、数量大小顺序,以及按键反应的左右布局,在相应任务中产生了参照框架,影响了被试的操作。这些参照框架具有方向性,当其与“从左到右-从小到大”或是“从远到近-从小到大”的自我中心参照框架方向一致时,促进了被试的反应,反之干扰了被试的反应。当多个参照框架方向不一致时,显示出了不同参照框架对反应的影响力量的强弱,其中按键布局产生的参照框架力量最强。数字加工的多重参照框架假设得到了验证。
2、在未激活数量表征的任务中,不同形式数字之间的反应时不存在显著差异;在激活了数量表征的任务中,四种形式数字的反应时从快到慢依次是阿拉伯数字、简体中文数字、繁体中文数字和英文数字(繁体中文数字和英文数字之间在奇偶判断任务中差异不显著,在数量比较任务中差异显著)。数字加工的多重编码的假设得到了验证。
3、按键符号的即时表征影响了数字加工任务。在没有数量激活的任务中,采用数字键的反应更快;在有数量激活的任务中,采用字母键的反应更快。
4、数字Stroop任务中,字号数量的一致与不一致各有两种情形,四种条件下的反应结果存在差异。字号数量“一致”且与自我中心参照框架一致有最快的反应,字号数量“一致”而与自我中心参照框架不一致并没有促进反应,甚至干扰了反应。
Digit is the basic unit of mathematical language. Without digit, human knowledge on mathematics might not come into being. The research on digit processing is significant in probing into human mental essence and developing human intelligence.
Finished research on digital cognition indicates that characteristics of digital process mostly depend on the content of tasks. Spatial information encoding based on varied reference framework affects digit processing a bit. These reference frameworks are centered on part of an observer’s body (egocentric coding ), or on some non-bodily object (allocentric coding ). These reference frameworks can’t separate from digital representation itself in the task of digit processing. For this, it is quite deficient, even a mistake to attribute the characteristics of digital cognition processing task to those of digital representation.
In the task of digital comparison or digital Stroop, the set of two numbers which occur simultaneously or sequentially, their trends in number volume and letter type size probably result in a reference framework, then affect its performance. Digits occur in different places on the screen, which affects digit processing. The influence is described with Simon effect. Sequential digital occurrence may give rise to a reference framework, from left to right, from small to big, or from far to near, from small to big, which affects its performance, but no research is involved. In addition, in the experiment tested keys are set to response. The keys layout may also give rise to a reference framework. Although in a practical way A-B, B-A Pattern is adopted to balance. Whereas, when the range of transmitting efficiency varies from different order, the balance will be broken, and the reference framework efficiency, resulted from keys layout are concealed. For this reason, it is presumed that digit processing has its varied reference framework because of different nature of tasks. Some have several reference framework. When these reference frameworks coincide with egocentric one, responses are enhanced. When some framework coincide, others don’t, responses can be predicted under the influence of varied reference framework.
It shows that mental axis direction is closely related to cultural elements. From the standpoint of interculture, it helps us to get to know the characteristics of digit processing. As Chinese differs from the language system mentioned here, it’s particularly significant to process controlled digits, taken Chinese as mother tongue. It is supposed that in the task of non-stimulating digital representation,all kinds of digit processing ( Arabic digits, plain Chinese digits, complex Chinese digits and English digits ) have no sharp distinctions. In the task of stimulating digital semantic representation ,the order in which four forms of digits response is Arabic digits, plain Chinese digits, complex Chinese digits and English digits, from the fastest to the least fast.
To sum up, this research put forth a model of digital multi-encoding and multi- reference framework process .
Additionally, the effects on digit processing range from stimulation presentation to finished responses to tests. Each step of the whole process may affect performance. Many researches on digit processing adopt the push-the-button-and-response method, without awareness of the influence of instant representation of keys symbol. Since the speed of digits stimulation is faster than that of letters. And the disturb of numeric representation of numeric key-press. It is presumed that in the task of non-stimulating digital semantic representation,digit keys reacts faster. In the task of stimulating digital semantic representation,letter keys react faster.
Furthermore, in the digital Stroop task of digit volume and digital presentation size, it shows a coincidence reaction that big digit has big letter type, small digit has small letter. Based on the above-mentioned hypothesis of multiplied reference framework, the coincidence reaction has its defects. There are two cases for the coincidence between letter types and digit volume. Two digits presented sequentially are both in increasing or decreasing order. The non-coincidence has its own case.
In order to test the model of digital multi-encoding process and multiplied reference framework, to explore above-mentioned issues, three tasks, digital Stroop, digital judgment between odd numbers and even numbers, digital volume comparison, are chosen. In these three tasks, digital stimulation procedure of volumes is increasingly enforced. Digit keys ( 1 and 3 on the small keyboard ), letter keys ( V and N) are used to test two different kinds of keys responses and phonetic responses are adopted. Controlled group includes graduates and postgraduates. After dozens of experiments, conclusions are made as follows:
1. In the task of digital cognition process, the sequential occurrence order of two digit types, digit order, then layout of key responses give rise to reference framework in their own course, and even affect the performance of the tested. These reference framework has its direction. When it keeps accompany with the direction of egocentric reference framework, from left to right, from small to big, or from far to near, from small to big, it may enhance the response of the tested, Conversely,prohibit the response. When the directions of many reference framework do not coincide, it shows different reaction forces to different reference framework. Among them, the strongest power results from keys layout. The hypothesis of digital process and multiplied reference framework is to be proved.
2. In the task of non-stimulating quantity representation ,digital reactions in any form has striking distinctions. In the task of stimulating quantity representation,the order of four forms of digital reactions, from the fastest to the least fast, is Arabic digits, plain Chinese digits, complex Chinese digits and English digits. ( The differences between complex Chinese digits and English digits are not striking in the task of judging odd and even numbers. The differences are striking in the task of quantity comparison. ) The multi-encoding hypothesis on digital process is proved.
3. Instant representation of key symbols affects the task of digital process. In the digital non-stimulating task, the responses to digit keys are faster; while the responses to letter keys are faster.
4. In the digital Stroop task, there are two cases for coincidence and non-coincidence between letter types. There exist reaction differences under four kinds of conditions. The coincidence between letter types and digits keep pace with egocentric reference framework, which enhances the fastest response. The coincidence between letter types and digits doesn’t keep pace with egocentric reference framework, which doesn’t enhance the response but prohibit the response.
引文
2 [美]莎伦·布雷姆等著,郭辉,肖斌译,亲密关系,人民邮电出版社,2005年10月第1版,P41
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