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수학적 창의성과 개방형 문제(open ended problem)

  • Gwon, O-Nam;Jo, Yeong-Mi;Park, Jeong-Suk;Park, Ji-Hyeon;Kim, Yeong-Sil
    • Communications of Mathematical Education
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    • v.16
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    • pp.217-218
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    • 2003
  • 제7차 교육과정의 기본방향인 '21세기의 세계화 정보화 시대를 주도할 자율적이고 창의적인 한국인 육성'에서 볼 수 있듯이, 새로운 교육과정에서는 학생들의 창의력을 신장시키기 위한 방안으로 교과별 교육과정이나 재량활동 운영 등을 제시한 바 있다. 수학교육에서도 이러한 시대적 흐름에 발맞추어 수학적 창의력의 신장이 강조되고 있는 상황이다. 그동안 이론적인 측면과 실제적인 측면에서 수학적 창의성에 대한 성과가 축적되었다. 이론적인 측면에서 볼 때, Haylock(1987)등에 의해 창의력과 수학적 창의력의 구분되었으며, 특히 '수학적' 창의력에 대한 다양한 정의가 제안되었다. 실제적인 측면에서도 수학적 창의력을 측정하려는 평가 도구들이 그 동안 여러 가지로 개발하였다. 그러나, 이러한 수학적 창의력에 관한 전반적인 연구는 종국적으로 교실 수학수업에 반영되어야 함에도 불구하고, 그리 만족스럽지 못한 상황이다. 특히, 교실에서 수학수업을 실제로 담당하는 교사들이 수학적 창의력을 위한 수업을 하고자 하더라도 당장 가까이에서 구할 수 있는 교수 학습 자료가 여전히 부족한 상황이다. 물론 그 동안 교실 수학수업에서 사용할 수 있는 창의력 개발 프로그램이 전무한 것은 아니다. 그런데 그들 대부분은 게임이나 퍼즐을 이용한 것으로 그 수준이 단순 흥미유발에 그치고 있거나 소수의 영재아를 위한 소재를 중심으로, 특히 수학적 사고 과정을 따르기보다는, 시행착오를 거쳐 원하는 결과를 얻을 가능성이 많으며, 수학과의 연계성이 불분명한 채로 단순놀이에 그치는 경우가 적지 않아, 수업과 연관되어 창의력의 신장이라는 측면에서 볼 때, 적용하기 어려운 사례가 많다. 이러한 상황을 개선하는 데 기여하고자, 현재 교과교육공동연구 지원사업의 하나로 한국 학술 진흥재단의 지원을 받아, '개방형 문제(open-ended problems)'를 중심 소재로 한 '수학적 창의성'을 신장하기 위한 교수학습 프로그램을 개발하여, 중학교 1학년을 대상으로 연구를 진행하고 있다. 개방형 문제라 함은 명백한 정의가 어렵지만 Pehkeon(1995)는 개방형문제의 정의를 명백히 하기위한 시도로서 그 반대로 닫힌 문제에 대한 정의로부터 시작하여, 어떤 문제가 닫혀있다고 하는 것은 그 문제의 출발 상황과 목표 상황이 닫혀 있는 것, 즉 명백히 설명되어있을 때라면 개방형 문제는 이와 반대의 개념임을 시사하였다. Silver(1995)는 개방형 문제를 문제 자체가 다른 해석이 가능하거나 서로 다를 인정할만한 답을 가질 수 있는 문제 또는 풀이과정이 다양한 문제, 자연스럽게 다른 문제들을 제안하거나 일반화를 제시할 수 있는 문제라고 정의하였다. 따라서 개방형 문제란 출발상황이나 목표 상황의 일부가 닫혀있지 않을 때를 말하고 문제의 조건을 만족하는 해답이 여러 가지로 존재하는 문제를 뜻한다. 수학적 창의력을 개발하는 데, 다른 문제 유형보다도, 개방형 문제가 유리하다는 점은 이미 여러 학자들에 의해 주장되어왔다. 미국 국립영재교육센터(NRCG/T)는 기존의 사지선다형이나 단답형 문제와 질문들은 학생들의 사고 능력에 관한 정보를 거의 알려주지 못하기 때문에 한 가지 이상의 답을 요구하는 ‘open-ended' 또는 ’open-response' 문제와 질문을 가지고 수학 분야에서의 창의적 사고 능력과 표현능력을 측정해야 한다고 하였고, 개방형 문제가 일반적으로 정답이 하나인 문제보다 고차원적인 사고를 요구하게 하는 문제 형태라고 하였다. 본 연구에서는 이러한 근거를 바탕으로 개방형 문제의 유형을 다양한 답이 존재하는 문제, 다양한 해결 전략이 가능한 문제, 답이 없는 문제, 문제 만들기, 일반화가 가능한 문제 등으로 보고, 수학적 창의성 중 특히 확산적 사고에 초점을 맞추어 개방형 문제가 확산적 사고의 요소인 유창성, 독창성, 유연성 등에 각각 어떤 영향을 미치는지 20주의 프로그램을 개발, 진행하여 그 효과를 검증하고자 한다. 개방형 문제를 활용한 수학적 창의력 신장 프로그램을 개발하고 현장 학교에 실험 적용하여 그 효과를 분석하고자 하는 본 연구는 창의력 신장에 비중을 두는 수학과 교수-학습 과정에 실제적인 교수 학습 자료를 제공하는 것뿐만 아니라 교사들에게는 수학교실에서 사용 가능한 실제적인 활용방안을, 학생들에게는 주어진 문제를 여러 가지 각도에서 생각하면서 다양한 사고를 경험하는 기회를 가질 수 있어, 수학을 보는 학생들의 태도에도 긍정적인 변화를 가져올 수 있을 것이라 기대한다.

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Downscaling of Sunshine Duration for a Complex Terrain Based on the Shaded Relief Image and the Sky Condition (하늘상태와 음영기복도에 근거한 복잡지형의 일조시간 분포 상세화)

  • Kim, Seung-Ho;Yun, Jin I.
    • Korean Journal of Agricultural and Forest Meteorology
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    • v.18 no.4
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    • pp.233-241
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    • 2016
  • Experiments were carried out to quantify the topographic effects on attenuation of sunshine in complex terrain and the results are expected to help convert the coarse resolution sunshine duration information provided by the Korea Meteorological Administration (KMA) into a detailed map reflecting the terrain characteristics of mountainous watershed. Hourly shaded relief images for one year, each pixel consisting of 0 to 255 brightness value, were constructed by applying techniques of shadow modeling and skyline analysis to the 3m resolution digital elevation model for an experimental watershed on the southern slope of Mt. Jiri in Korea. By using a bimetal sunshine recorder, sunshine duration was measured at three points with different terrain conditions in the watershed from May 15, 2015 to May 14, 2016. The brightness values of the 3 corresponding pixel points on the shaded relief map were extracted and regressed to the measured sunshine duration, resulting in a brightness-sunshine duration response curve for a clear day. We devised a method to calibrate this curve equation according to sky condition categorized by cloud amount and used it to derive an empirical model for estimating sunshine duration over a complex terrain. When the performance of this model was compared with a conventional scheme for estimating sunshine duration over a horizontal plane, the estimation bias was improved remarkably and the root mean square error for daily sunshine hour was 1.7hr, which is a reduction by 37% from the conventional method. In order to apply this model to a given area, the clear-sky sunshine duration of each pixel should be produced on hourly intervals first, by driving the curve equation with the hourly shaded relief image of the area. Next, the cloud effect is corrected by 3-hourly 'sky condition' of the KMA digital forecast products. Finally, daily sunshine hour can be obtained by accumulating the hourly sunshine duration. A detailed sunshine duration distribution of 3m horizontal resolution was obtained by applying this procedure to the experimental watershed.

A Comparative Study on Korean and American High School Home Economics Textbooks Based on Habermas's Three Systems of Action: Focusing on the Learning Objectives and Activities (Habermas의 세 행동체계의 관점에서 본 한국과 미국의 고등학교 가정교과서 식생활 단원의 학습목표와 활동과제 비교 연구)

  • Choi, Seong-Youn;Chae, Jung-Hyun
    • Journal of Korean Home Economics Education Association
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    • v.32 no.1
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    • pp.107-125
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    • 2020
  • The purpose of this study was to analyze the dietary life units of Korean and American high school home economics textbook according to Habermas's three systems of action and to find out how the three systems of action are reflected in the learning objectives and activity tasks of the textbook. To achieve this purpose, this study analyzed the learning objectives and activity tasks of the dietary life units in the textbooks of 'technology & home economics' and 'home economics science' in Korea, and 'succeeding in life and career' in America using a content analysis technique based on Habermas's three systems of action. In analyzing the content, each learning objective or activity was matched with one of the three systems of action by examining the context. In some cases, two or more systems of actions were integrated in one activity. This is a case where a series of learning tasks that involve different action system were grouped into one. The numbers of learning objectives and activities of the units of 'technology & home economics', 'home economics science' textbooks of Korean high schools and 'succeeding in life and career' dietary life of American high schools were 3, 26, and 248, respectively. In Korean textbooks, the percentage of communicative action was highest among the three systems, that is, 66.7% for 'technology & home economics' textbooks and 50% for 'home economics science' textbooks. In comparison technical action was the highest in American textbooks at 66.5%. Activities related to technical action included cooking, conducting research on health and food, or conducting experiments. The activities related to communicative action included role play related to health and table manners, or writing reports after conducting surveys or interviewing professionals. The activities related to emancipative action were to social participation activities such as service project in relation to health and food, or to find problems that occur in dietary life and think about be best solution through practical reasoning.

Implantable Flexible Sensor for Telemetrical Real-Time Blood Pressure Monitoring using Polymer/Metal Multilayer Processing Technique (폴리머/ 금속 다층 공정 기술을 이용한 실시간 혈압 모니터링을 위한 유연한 생체 삽입형 센서)

  • Lim Chang-Hyun;Kim Yong-Jun;Yoon Young-Ro;Yoon Hyoung-Ro;Shin Tae-Min
    • Journal of Biomedical Engineering Research
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    • v.25 no.6
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    • pp.599-604
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    • 2004
  • Implantable flexible sensor using polymer/metal multilayer processing technique for telemetrical real-time blood pressure monitoring is presented. The realized sensor is mechanically flexible, which can be less invasively implanted and attached on the outside of blood vessel to monitor the variation of blood pressure. Therefore, unlike conventional detecting methods which install sensor on the inside of vessel, the suggested monitoring method can monitor the relative blood pressure without injuring blood vessel. The major factor of sudden death of adults is a disease of artery like angina pectoris and myocardial infarction. A disease of circulatory system resulted from vessel occlusion by plaque can be preventable and treatable early through continuous blood pressure monitoring. The procedure of suggested new method for monitoring variation of blood pressure is as follows. First, integrated sensor is attached to the outer wall of blood vessel. Second, it detects mechanical contraction and expansion of blood vessel. And then, reader antenna recognizes it using telemetrical method as the relative variation of blood pressure. There are not any active devices in the sensor system; therefore, the transmission of energy and signal depends on the principle of mutual inductance between internal antenna of LC resonator and external antenna of reader. To confirm the feasibility of the sensing mechanism, in vitro experiment using silicone rubber tubing and blood is practiced. First of all, pressure is applied to the silicone tubing which is filled by blood. Then the shift of resonant frequency with the change of applied pressure is measured. The frequency of 2.4 MHz is varied while the applied pressure is changed from 0 to 213.3 kPa. Therefore, the sensitivity of implantable blood pressure is 11.25 kHz/kPa.

Eye Tracking Analysis for High School Students' Learning Styles in the Process of Solving on Earth Science I (지구과학 I 문제 해결 과정에서 나타난 학습유형에 따른 고등학생의 시선 추적 분석)

  • An, Young-Kyun;Kim, Hyoungbum
    • Journal of the Korean Society of Earth Science Education
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    • v.10 no.1
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    • pp.50-61
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    • 2017
  • The purpose of this study is to analysis eye tracking for high school students' learning styles in the process of solving in the behavioral domains of the College Scholastic Ability Test on Earth Science I. The subjects of this study were 50 students from two classes out of 4 classes in E high school in Chungcheong province. Among them, we conducted experiments by randomly sampling 2 students of each type of learning based on the criteria that they had not encountered the problem of Earth Science I from the past two years. The findings indicate that the item correctness rate of divergers, assimilators, convergers, and accommodators were higher in the knowledge domain, application domain, knowledge-understanding domain, and understanding domain. This confirms that there is a difference among the four learning styles in the level of achievement according to the behavioral areas of the assessment questions. The latter finding was that the high eye-share of AOI 2 appeared higher than AOI 1, 3, 4 in the course of solving the problems. This is because the four types of learners pay more careful attention to the AOI 2 area, which is the cue-or-information area of problem solving, that is, the Table, Figure, and Graph area. Therefore, in order to secure the fairness and objectivity of the selection, it is necessary that an equal number of questions of each behavioral domain be selected on the Earth Science I Test of the College Scholastic Ability Test in general. Besides, it seems to be necessary that the knowledge, understanding, application, and the behavior area of the inquiry be highly correlated with the AOI 2 area in development of test questions.

Simulation platform for living environment to ensure quality life (쾌적한 생활 설계를 위한 주거 및 사무실 시뮬레이터개발)

  • Park, Se-Jin;Kim, Chul-Jung;Kim, Si-Kyung;Mazumder, Mohammad Mynuddin Gani
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.8 no.4
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    • pp.853-860
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    • 2007
  • In this modern era, human beings lead their life in complex environment where there are lots of parameters such as temperature, light, smell, sound, visual stimulus etc. that play important role for quality life. These parameters affect physical and mental behavior of a human being immensely. To ensure quality life the demand for quality products is always associated with human emotion and sensibility. Due to human sensibility and emotion involvement with quality life, the design stages of any kind of product must include some certain features related with emotion and sensibility. The cues for optimizing artificial environment are the physiological responses of human in that environment. The conventional approach of environmental physiology is to measure the relationship between environmental physical parameters and human psychological parameters under artificial conditions. Using that approach we tried to design an artificial environment for our daily lives and activities associated with both physiological and psychological behavior. We developed the technique to present the mock environment and software to measure and evaluate sensibility physiologically or psychologically and a simulator to measure and evaluate sensibility that can be utilized for large scale industrial production and design of environment. Simulator to measure and analyze human sensibility (SMAS) was constructed, which was utilized to estimate human sensibility and to simulate living and office environment.

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Effects of Dietary Taurine on the Lipid Metabolism in Laying Hens (사료내 타우린 첨가가 산란계의 지방대사에 미치는 영향)

  • 박강희
    • Korean Journal of Poultry Science
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    • v.29 no.2
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    • pp.95-100
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    • 2002
  • Two experiments were conducted to investigate the effect of taurine supplementation on lipid metabolism in laying hens. In experiment 1, 19-wk-old laying hens were given one of four taurine supplemented diets (0 (control), 0.4, 0.8, and 1.2% taurine) fur 10 weeks. Abdominal fat weight was lower in the 1.2% diet by 29.2% compared to the control. Serum concentrations of triacylglycerol and HDL-cholesterol were not different among the treatments. However, seam concentration of total cholesterol was higher by 22.4% in the 1.2% diet compared to the control. Concentration of triacylglycerol or total cholesterol in the liver were decreased by 26.1% or 26.4% and 28.2% or 26.4%, respectively in the 0.8% and 1.2% diets compared to the control. The concentration of HDL-cholesterol in liver was also lower by 33.9% in the 1.2% diet compared to the control. In experiment 2, 81-wk-old laying hens were allocated to one of three taurine supplemented diets (0 (control), 1 and 2% taurine) fur 6 weeks. Abdominal fat weight was lower by 25% in 1% taurine supplementation compared to the control. Serum concentrations of triacylglycerol, total cholesterol and HDL-cholesterol of hens fed with 1% diet were not different from those of control group. However, sew concentrations of triacylglycerol and total cholesterol were lower by 44.0% and 19.8%, respectively in the 2% diet compared to the control. Furthermore, serum concentration of HDL -cholesterol in the 2% diet was higher by 75% compared to the control. Concentrations of triacylglycerol and total cholesterol in the liver in the 2% diet were decreased in the 1% diet by 36.8 and 23%, respectively, but increased by 78.4% and 70%, respectively, compared to the control. The concentration of HDL-cholesterol in the liver was not different between the 1% diet and the control, but higher by 62.8% in the 2% diet compared to the control. These results indicated that taurine supplementation decreased the fat storage in abdominal cavity, which was accompanied by the changes in triacylglycerol and cholesterol metabolisms of laying hens.

Debris flow characteristics and sabo dam function in urban steep slopes (도심지 급경사지에서 토석류 범람 특성 및 사방댐 기능)

  • Kim, Yeonjoong;Kim, Taewoo;Kim, Dongkyum;Yoon, Jongsung
    • Journal of Korea Water Resources Association
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    • v.53 no.8
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    • pp.627-636
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    • 2020
  • Debris flow disasters primarily occur in mountainous terrains far from cities. As such, they have been underestimated to cause relatively less damage compared with other natural disasters. However, owing to urbanization, several residential areas and major facilities have been built in mountainous regions, and the frequency of debris flow disasters is steadily increasing owing to the increase in rainfall with environmental and climate changes. Thus, the risk of debris flow is on the rise. However, only a few studies have explored the characteristics of flooding and reduction measures for debris flow in areas designated as steep slopes. In this regard, it is necessary to conduct research on securing independent disaster prevention technology, suitable for the environment in South Korea and reflective of the topographical characteristics thereof, and update and improve disaster prevention information. Accordingly, this study aimed to calculate the amount of debris flow, depending on disaster prevention performance targets for regions designated as steep slopes in South Korea, and develop an independent model to not only evaluate the impact of debris flow but also identify debris barriers that are optimal for mitigating damage. To validate the reliability of the two-dimensional debris flow model developed for the evaluation of debris barriers, the model's performance was compared with that of the hydraulic model. Furthermore, a 2-D debris model was constructed in consideration of the regional characteristics around the steep slopes to analyze the flow characteristics of the debris that directly reaches the damaged area. The flow characteristics of the debris delivered downstream were further analyzed, depending on the specifications (height) and installation locations of the debris barriers employed to reduce the damage. The experimental results showed that the reliability of the developed model is satisfactory; further, this study confirmed significant performance degradation of debris barriers in areas where the barriers were installed at a slope of 20° or more, which is the slope at which debris flows occur.

Removal of Nitrogenous Compounds by Immobilized Mixed Microorganisms Including Photosynthetic Bacteria (광합성 세균을 포함한 고정화 복합미생물에 의한 질소성분 제거)

  • Cho, Kyoung Sook;Kim, Jeong Bo;Jeong, Soo Kyoung;Jeong, Hae Yoon;Cho, Jeong Sub;Kim, Joong Kyun
    • Journal of Marine Bioscience and Biotechnology
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    • v.1 no.2
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    • pp.91-97
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    • 2006
  • For efficient removal of nitrogenous compounds produced in recirculating aquaculture system, the N removal characteristics of immobilized mixed microorganisms were investigated at various mixing ratios of photosynthetic bacteria (PSB) immobilized in PVA beads or CTA cubes and ammonium utilizing bacteria (AUB) immobilized in PVA beads. On the optimal medium of AUB, the maxium gas production rate was obtained at the mixing ratio of 10:40 (PSB:AUB), and the gas production rate increased as the portion of AUB beads in the mixed beads increased. When the mixing ratios of PSB:AUB beads were 50:0, 40:10, 25:25 and 10:40, the final pHs were measured to be 6.29, 6.01, 5.69 and 5.13, respectively. On the optimal medium of PSB, however, the volume and the rate of gas production decreased remarkably as the portion of AUB beads in the mixed beads increased. The final pH was measured to be approximately 6.5, regardless of the mixing ratio. In the reactions by the mixed culture of PSB cubes and AUB beads, all results showed the same tendency of those by the mixed culture of PSB and AUB beads, but the volume and the rate of gas production decreased remarkably, even with 0.2ml of gas production in control. From all the results, the use of mixed PSB and AUB beads at the ratio of 10:40 seems to be efficient to remove nitrogenous compounds in wastewater from recirculating aquaculture system.

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Can We Hear the Shape of a Noise Source\ulcorner (소음원의 모양을 들어서 상상할 수 있을까\ulcorner)

  • Kim, Yang-Hann
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.14 no.7
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    • pp.586-603
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    • 2004
  • One of the subtle problems that make noise control difficult for engineers is “the invisibility of noise or sound.” The visual image of noise often helps to determine an appropriate means for noise control. There have been many attempts to fulfill this rather challenging objective. Theoretical or numerical means to visualize the sound field have been attempted and as a result, a great deal of progress has been accomplished, for example in the field of visualization of turbulent noise. However, most of the numerical methods are not quite ready to be applied practically to noise control issues. In the meantime, fast progress has made it possible instrumentally by using multiple microphones and fast signal processing systems, although these systems are not perfect but are useful. The state of the art system is recently available but still has many problematic issues : for example, how we can implement the visualized noise field. The constructed noise or sound picture always consists of bias and random errors, and consequently it is often difficult to determine the origin of the noise and the spatial shape of noise, as highlighted in the title. The first part of this paper introduces a brief history, which is associated with “sound visualization,” from Leonardo da Vinci's famous drawing on vortex street (Fig. 1) to modern acoustic holography and what has been accomplished by a line or surface array. The second part introduces the difficulties and the recent studies. These include de-Dopplerization and do-reverberation methods. The former is essential for visualizing a moving noise source, such as cars or trains. The latter relates to what produces noise in a room or closed space. Another mar issue associated this sound/noise visualization is whether or not Ivecan distinguish mutual dependence of noise in space : for example, we are asked to answer the question, “Can we see two birds singing or one bird with two beaks?"