The chief object of this thesis is to search abstract function of forms as a basis of product design. This study will be useful in forming the basis of morphology, improving the education of product design, and developing product design. Various products in the vast fieldes of science are divided into three cotegories from the view-point of structure and organization, which is very interesting to me. (1) Function + Form (2) Function + Mechanism + Form (Static Mechanical Function) (3) Function + Mechanism + Form + Electricity (Mobile Mechanical Function) In this study from these functions I extracted basic ones in an abstract manner and classified them. As a result I could classify them as follows : 1) Operative Function Such function as done by "hand", "foot", "body", "mouth", "eye", "ear", etc. 2) Compositive Function Such function as "stand", "join", "strengthen construction", etc. 3) Mechanical Function Such function as "move", "transmit mechanical motion", etc. In addition to this study, a quest for making forms based on carefully chosen abstract functions should be continued.

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The design of interior space is co-ordinates of "interior space" and "man" whose purpose is to live in that interior space. So in the process of planning where various conditions and necessary changes on the drawings are examined and managed, the satisfactory effect cannot be expected without constant imaging the interior space and without prospecting human behavior and life. The aim of this study is, as so to get more effective clue to the design, to grasp the actual conditions of human behavior through experiments and investigation from the view point of psychology, one of sciences of behavior. That is, in considering the relation between man and his (objective) environment, the interior space, I took up the "behavioral environment" formed in his inner life, and examined how he adapts his suitable position of "reading" in the given interior to the environment and what is the pattern of adaptation for the groups as experimental subjects by observing experiments, On the other hand when the same interior is given as a drawing, I investigated by exercises on drawings how the interior was imaged and human behavior was prospected. By comparing these experiments I clarified the actual condition of prospecting the interior space. The result shows that there are some kinds of organic and dynamic patterns in the distribution of positions of subject groups in behavioral experiments and that, in comparison with the behavioral experiments there are inorganic and geometric one in the distribution by investigation on drawings. It was found that, in the design of the interior, the plan of human behavioral life seen through the image of the interior space is formed under the influence of graphical patterns, and inclines to pursue the geometrical human behavior. This seems to be the reason why there is a limit to imaging by drawings and the drawings, when considered as figures, are influenced by "Pragnanz" in the "field" of figures. Therefore, the design of the interior, though proceeded with drawings as means of a plan, should be prepared based on a correct image of the interior space with the full knowledge of the tendency of the distribution of human behaviors.

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1. Noticing the fact that the same design appears quite different to the different persons at different times and places, I searched for the statistical regularity in this phenomenon. 2. Making on purpose six kinds of spoons by combining parts of three kinds of spoons so as to have common characteristics of shape partially, I carried on an experiment in order to test the similarity and difference of those spoons. One hundred subjects were chosen for the experiment from the university students in Tokyo. The result shows that there is much difference in the judgment of similarity and difference of shapes among the subjects and even the same person changed his judgement looking at a pair of design at different times. The average frequency of different judgments comes to 3.1 per 10 times. Though this change of judgements is ordinarily considered as clue to the observation error, when I investigated correlation of each test I found that there were little or no cases where correlation coefficient is 0 or nearly 0. In most cases there were observed positive or negative correlation. The fact shows that each subject does not always judge a form synthetically from a fixed point of view but particular parts or particular characteristics of the form from various view points. 3. In addition to this, I examined the consumers' estimate and recognition of the characteristics of designs by Semantic Differencial method, taking eight kinds of designs of spoons and forks on the market. The subjects consisted of one hundred persons of the Industrial Art Institute and about seventy consumers living in Tokyo. The result shows that there are remarkable differences among the distributions of estimates of designs and the variance of a distributions is large in the case of new and strange design, while the variance of a distribution is small in the case of familiar design. 4. The reason why I put the subtitle "Statistical Approach to Morphology" to this study is that, apart from the traditional morphology based on unchangeable objective forms, I consider this study as an initial step to the attempt to characterize forms with the patterns of distributions of observers' responses to them.

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As in the order of color there are Ostwald Color Solid and Munsell Coor Solid, from which physical and quantitative chromaticity diagram developed, as for form it is necessary to form universally accepted views as to what is form, and for the methods of forming a work of art it is necessary to work out analytic and objective rules with scientific accuracy not the rules of trial and error My researches presented in the first to the eighth Design Society were intended to make an approach to the above mentioned problem. At first I tried to establish order in form, that is to say, to form universally accepted views as to what is form. In the second place the problem of "motion" in form wes discussed and then I studied the problem of analysis of "space". To analyze space, the conception of the coordinates of mathematics and the conception of "Topology" were employed in my study. The coordinates used here are expressed as I c I, distinguished from [c] meaning ordinary coordinates, for the conception of the coordinates are adopted only to serve the purpose of helping the designers to learn how to form. Every form can be found to lie on every kind of |C| and can be moved to other |C| continuously. Every process of design-making an almost infinite variety of shapes, cutting or distorting objects by designers or artists-is involved in |c| and is carried on along the movement of |c|. Some rules are extracted by analyzing these facts closely, putting them in order and classifying them. In the conception of |c| both Euclid's space E^n and all the Non-Euclid spaces are equally supposed to be in 0 dimension, therefore [c] is, of course, included in 0 dimension. |C|^0 becomes |C|^1 when it makes linear groups, |C|^0 becomes |C|^2 when it makes plane groups, |C|^0 becomes |C|^3 when it makes three dimensional groups, and |C|^0 becomes |C|^4, |C|^5…|C|^∞, as the case may be. This is not an abstract conception in mathematics, but the conception related to design directly, from which concrete creation of forms and experiment in design can be extracted.

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I Identification of Problem People live in the world filled with infinite variety of forms. How do they perceive these forms? What images of those forms do they throw on their minds? Through formative and experimental study of "images of forms and their estimate" we wanted to improve our study on forms for design. The object of this study of forms is to throw light on the relation between forms and human beings. II Research Method The materials for forming a work of art (solid plaster material) which are to be used in our experiment are as follows: (a) a_1, a_2, a_3 … g_1, g_2, g_3 series-a fixed volume of 1000 cc, having geometric, organic and automatic forms (b) A_1, A_2, A_3 … G_1, G_2, G_3 series-a rotating substance with the longest diameter of 85 mm (fixed) and the height of 225 mm (fixed) (as large as a beer bottle) (c) P_1〜P_<20>, Q_1〜Q_<20>, R_1〜R_<20>-a rotating substance (free-form) Putting these three series of materials on the table, the subjects whose eyes are bandaged are made to enter the room and to touch them at first, and to look at them later. The differences of their tactual evaluation of those materials and visual evaluation of them are closely analyzed according to those different forms. III Results and their analysis 1) Making a list of those evaluations of forms by the subjects consisting of twenty men and twenty women, we performed a test of significance, examining significant differences in sampling. 2) To make clear the relation between the differences of visual and tactual recognition, the difference of sex and each series of forms. IV Conclusion 1) As visual sense perceives a form as a whole, while tactual sense perceives a form partially, there arise differences in evaluation of forms. 2) To analyze the difference of sex and the difference of visual and tactual perception it is necessary that there should he least differences between forms of each material. 3) There is a tendency that males perceive an object with its entire form, while females perceive an object partially.

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Paul Klee, in his bulky note concerning the theory of art, refers to perspective and explains one-point perspective. Klee seems to have considered perspective as one of the basic principles or rules of design. But Klee was not content with so-called traditional perspective drawing, but he, trying to deviate from it, introduced "shifting viewpoint". Of his works drawn in one-point perspective there are many in which he placed several vanishing points to which parallel horizontal lines that recede from the observer appear to converge, but not to one vanishing point only. It seems to me that Klee first accepted the system of Renaissance perspective, from which he contrived to deviate afterwards. Klee also made such an expression as included in the same canvas several objects seen from bifferent view-points. This is composed multiple perspective. He gave expression to a complicated mixture of front and back spaces by means of variations of the line of locus which moves according to different viewpoints. This is an expression beyond general perspective drawing, and is considered as an expression of his own original space-floating space.

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The value of industrial design, if it is to be recognized objectively and quantitatively, should be grasped from such three different points of view as follows: (1) product value: time-cost-price studies (2) sales value: price-occasion-quantity studies (3) use value: beauty-function-life studies The fact that industrial design has not become a vital factor of business management is due to the lack of sufficient recognition of industrial design, which prevents industries from reconstructing and reorganizing their system based on industrial design. In this treatise I studied how much industrial design, if well administered, contributes to the development of enterprises. I compared and examined the relation between the working hours required for design and workmanship of finished products, and also the relation between the cost price determined by design and workmanship of the products. To make such a comparative study it is necessary to have the whole business company reorganized as industrial design centered system. In order to administrate cost I set up a standard model necessary for control and dealt with the problem of cost exchange table. To estimate workmanship of products I advised to concentrate all the faculties of a sales department to make a standard for judging the sales value which is necessary to decide the market price of the products. Taking these results into consideration, I worked out TCP Administration Table in which the estimate of product value of design, grasped on the basis of an estimated retail price of workmanship of the product, is expressed graphically in quantity by the length and position of a line, which will be useful to decide whether the products bring some benefits to the company or not, and will be found useful as basic materials for making plans for the future.

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To find basic factors for the recognition and lettering of alpha-numerical characters (alphabet and numbers), Fourier analyses were applied on the orthogonal components (X and Y components) involved in the drawing motion to reproduce some samples of lettering as line figures. Relative contributions of harmonics in the X and Y components were examined by the following ways: 1) Harmonics in each of the X and Y Fourier series were eliminated one by one in the order of their frequencies, and 2) the compositions of thus reduced functions were reproduced as typed lines composed of 1 with the aid of Computer HIPAC 103, and 3) these reproductions of characters were visually evaluated. The results of these analyses showed that the reproductions of characters become gradually worse as the number of harmonics used for reproduction decreases, but the basic feature of the character is always kept as far as the first three harmonics, which have usually large amplitudes, are remained, except that H, K and R need four to six harmonics. In this sense, the invariant feature of an alpha-numerical character depends upon these small number of harmonic combinations. From the founding that some alpha-numerical characters, such as S, Z and 8, have almost the same harmonic combinations as the essential factor to keep their basic features, the phase differences between the X and Y component series were considered as the second important factor for the discrimination among such characters. It is also found that the part, where the drawing line of an alpha-numerical character is discontinued, will be the third important factor for discrimination among the characters.

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