**2.2.6 Gestalt principles of visual perception**

Gestalt theory was developed by German psychologists Max Wertheimer, Kurt Koffka and Wolfgang Köhler in the early 20th century. The German word *die Gestalt* means "form" or "shape" and Gestalt theory of perception can be summarized as that people tend to perceive things as wholes rather than separate parts. It proposes "laws of organization in perceptual forms" (Wertheimer, 1938) which have been applied by various design disciplines. Basically, people perceive visual stimuli as organized or grouped patterns. Gestalt principles related to spatial design are briefly explained below.

*Figure-ground relationship*: As Köhler (1938) states "*figure perception is represented in the optic field by differences of potential along the entire outline or border of the figure*". Thus, contrast plays an important role in distinguishing figure from the ground. The most famous example that demonstrates figure-ground relationship is probably the Danish psychologist Edgar Rubin's "Rubin's vase" (Figure 2). The figure-ground relationship is related to legibility in spatial design.

Fig. 2. Figure-ground relationship in Rubin's vase (Baluch & Itti, 2011).

Landscape Perception 261

Zube *et al.* (1982) identified four research paradigms on landscape assessment and perception which are; expert, psychophysical, cognitive and experiential paradigms (Taylor *et al.*, 1987). *The expert paradigm*: this paradigm is based on expert judgments of visual quality of landscapes. Evaluation of landscape quality depends on formal characteristics of the landscape such as landform, vegetation, color, texture etc. Another assumption of this paradigm is that natural ecosystems have the greatest aesthetic value. This paradigm is criticized for the lack of user environment and being incompatible with users' perceptions (Lekagul, 2002). Furthermore, S. Kaplan (1988a) points out that experts perceive visual environment different to other people, and expert judgments are "a dubious source of

*The psychophysical paradigm*: In psychophysical paradigm, in contrast to expert paradigm visual quality of the landscape is evaluated by the general public or special interest groups. The main assumption of this paradigm is landscapes have a stimulus property which is external to the observer who perceives the landscape without conscious thinking. Ranking

*The cognitive paradigm*: The cognitive paradigm focuses on why people prefer particular landscapes. The research is directed mostly towards developing a theoretical basis. In contrast to psychophysical paradigm, cognitive paradigm assumes that cognitive processes influence aesthetic judgments. Mostly verbal evaluation techniques, such as semantic differential analysis and adjective checklists, have been used to evaluate preferences and meanings. Most of the evolutionary theories on environmental perception (e.g. prospectrefuge theory and information processing theory) form a basis for this paradigm. However, this paradigm neglects the physical environment and rather focuses on meanings associated

*The experiential paradigm*: This paradigm focuses on human-environment interaction. Human experiences affect the landscape's perceived value. This approach is commonly used in "sense of place" studies and mainly by geographers. However, experiential approach is more subjective than cognitive and psychophysical paradigms; therefore reliability and

Although paradigms explained above may seem completely different from each other, each contributes to overall comprehension of environmental perception. In terms of design and planning, the expert paradigm has been the most used approach in visual landscape assessment. However, there is a certain need for involvement of public or users in order to create enjoyable places for people. Fenton & Reser (1988) criticize that human geographers and landscape architects tend to use *atheoretical* and *apsychological* methods while psychologists use mainly theoretically derived psychometric methods. Professional differences might make it difficult to find a common basis for theoretical and methodological research. Nevertheless, collaboration of disciplines involved in

Assessment of landscape preferences is widely studied in environmental perception research. Landscape preference studies aim to investigate how and why people prefer some

validity of the results are hard to be measured (Taylor *et al.*, 1987).

environmental perception studies is essential to resolve some of the conflicts.

objective judgment" about what other people really care about in the landscape.

and sorting are widely used techniques in visual assessments within this paradigm.

with landscapes (Taylor *et al.*, 1987).

**2.4 Landscape preferences**

*Proximity*: Objects located close to each other tend to be perceived as groups. For example; the number "*3012*" is perceived as two different numbers when a space inserted in the middle: *30 12*.

*Similarity*: Objects that have similar visual characteristics such as color, shape, direction etc. are perceived in groups (Figure 3).

Fig. 3. Gestalt factor of similarity.

*Continuation:* Graham (2008) explains continuation as "*continuation occurs when the eye follows along a line, curve, or a sequence of shapes, even when it crosses over negative and positive shapes*" (Figure 4).

Fig. 4. Factor of continuation (Graham, 2008).

*Closure*: There is a tendency to close and mentally complete the missing parts of an image which is visually incomplete (Figure 5).

Fig. 5. Factor of closure (Graham, 2008).

#### **2.3 Overview of research methodology**

Basically, there are two approaches in visual landscape assessment; objective and subjective. Objective approach to visual landscape assessment assumes that visual quality of the landscape is an inherent characteristic and physical attributes of the environment determine its aesthetic value. On the contrary, subjective approach assumes that visual quality is in the eye of beholder and aesthetic value of an environment can be determined through subjective evaluation. There are also studies which have integrated both objective and subjective approaches.

*Proximity*: Objects located close to each other tend to be perceived as groups. For example; the number "*3012*" is perceived as two different numbers when a space inserted in the middle: *30 12*.

*Similarity*: Objects that have similar visual characteristics such as color, shape, direction etc.

*Continuation:* Graham (2008) explains continuation as "*continuation occurs when the eye follows along a line, curve, or a sequence of shapes, even when it crosses over negative and positive shapes*"

*Closure*: There is a tendency to close and mentally complete the missing parts of an image

Basically, there are two approaches in visual landscape assessment; objective and subjective. Objective approach to visual landscape assessment assumes that visual quality of the landscape is an inherent characteristic and physical attributes of the environment determine its aesthetic value. On the contrary, subjective approach assumes that visual quality is in the eye of beholder and aesthetic value of an environment can be determined through subjective evaluation. There

are also studies which have integrated both objective and subjective approaches.

are perceived in groups (Figure 3).

Fig. 3. Gestalt factor of similarity.

Fig. 4. Factor of continuation (Graham, 2008).

which is visually incomplete (Figure 5).

Fig. 5. Factor of closure (Graham, 2008).

**2.3 Overview of research methodology**

(Figure 4).

Zube *et al.* (1982) identified four research paradigms on landscape assessment and perception which are; expert, psychophysical, cognitive and experiential paradigms (Taylor *et al.*, 1987).

*The expert paradigm*: this paradigm is based on expert judgments of visual quality of landscapes. Evaluation of landscape quality depends on formal characteristics of the landscape such as landform, vegetation, color, texture etc. Another assumption of this paradigm is that natural ecosystems have the greatest aesthetic value. This paradigm is criticized for the lack of user environment and being incompatible with users' perceptions (Lekagul, 2002). Furthermore, S. Kaplan (1988a) points out that experts perceive visual environment different to other people, and expert judgments are "a dubious source of objective judgment" about what other people really care about in the landscape.

*The psychophysical paradigm*: In psychophysical paradigm, in contrast to expert paradigm visual quality of the landscape is evaluated by the general public or special interest groups. The main assumption of this paradigm is landscapes have a stimulus property which is external to the observer who perceives the landscape without conscious thinking. Ranking and sorting are widely used techniques in visual assessments within this paradigm.

*The cognitive paradigm*: The cognitive paradigm focuses on why people prefer particular landscapes. The research is directed mostly towards developing a theoretical basis. In contrast to psychophysical paradigm, cognitive paradigm assumes that cognitive processes influence aesthetic judgments. Mostly verbal evaluation techniques, such as semantic differential analysis and adjective checklists, have been used to evaluate preferences and meanings. Most of the evolutionary theories on environmental perception (e.g. prospectrefuge theory and information processing theory) form a basis for this paradigm. However, this paradigm neglects the physical environment and rather focuses on meanings associated with landscapes (Taylor *et al.*, 1987).

*The experiential paradigm*: This paradigm focuses on human-environment interaction. Human experiences affect the landscape's perceived value. This approach is commonly used in "sense of place" studies and mainly by geographers. However, experiential approach is more subjective than cognitive and psychophysical paradigms; therefore reliability and validity of the results are hard to be measured (Taylor *et al.*, 1987).

Although paradigms explained above may seem completely different from each other, each contributes to overall comprehension of environmental perception. In terms of design and planning, the expert paradigm has been the most used approach in visual landscape assessment. However, there is a certain need for involvement of public or users in order to create enjoyable places for people. Fenton & Reser (1988) criticize that human geographers and landscape architects tend to use *atheoretical* and *apsychological* methods while psychologists use mainly theoretically derived psychometric methods. Professional differences might make it difficult to find a common basis for theoretical and methodological research. Nevertheless, collaboration of disciplines involved in environmental perception studies is essential to resolve some of the conflicts.

#### **2.4 Landscape preferences**

Assessment of landscape preferences is widely studied in environmental perception research. Landscape preference studies aim to investigate how and why people prefer some

Landscape Perception 263

suggested that moderate novelty, increase diversity, increased contrast among buildings, good maintenance, order, more vegetation and reduced vehicle prominence might produce

According to Bourassa (1990), aesthetic response occurs at both biological and cultural levels. Falk Balling (2010) also state that "*that human landscape preferences is best understood as a continuous progression of aesthetic ideals, tempered by social convention, passed on from one generation to the next through human culture*". But do culture and socio-demographic factors really affect preferences? There are several cross-cultural studies that investigate preferences for landscapes and landscape elements. Generally, the results show that despite cultural differences, people seem to have similar preferences for specific landscapes; however the concepts of novelty and familiarity can affect preferences for people from different cultures. Familiarity plays an important role in feeling secure and safe. People feel comfortable and relaxed in environments which they are familiar to (Kaplan *et al.*, 1998). On the other hand too much familiarity may become boring and people seek for novelty. For instance, Yang & Brown (1992) found that traditional Japanese style landscapes and water presence were highly preferred by people from both Korean and Western cultures. However they also found that while Koreans preferred Western style landscapes, Western tourists preferred Korean style landscapes. A similar result was found by Nasar (1988a). His study results showed that although there were consensus on preferences for ordered, natural, open and well-kept scenes; Japanese subjects highly preferred the American scenes and vice versa. His findings supported Berlyne's assumption that people prefer novelty to familiarity. He also pointed out that the results would have been different if subjects had been chosen from older population since Sonnenfeld (1966) claims that younger people prefer novelty and others familiarity (Nasar, 1988a). In their study Yang &Kaplan (1990) investigated landscape style preferences of Korean and Western individuals. They found a cross-cultural similarity in preferences in favor of landscapes with natural styles. Landscapes with rectangular or

Lyons (1983) showed that there is a strong relationship between age, gender, residential experience and landscape preferences. She found that preference levels changed in different age groups, adolescent male and females had different preferences, urban and rural residents had different preferences, familiar vegetational biomes were preferred highest, and there was no evidence that landscape preferences were shaped by innate or evolutionary factors. Yu (1995) also reported that people from different living environments (rural vs. urban) had different preferences; rural residents had high preference for novelty and modernity. He also indicated that landscape preferences were strongly influenced by education levels. However, his findings did not show any significant relation between

Landscape preference studies are generally based on public or user (non-expert) evaluations. Ranking, rating or sorting of visual stimuli and verbal instruments are popular tools in determination of landscape preferences. Participants are asked to rank, rate or sort visual stimuli according to their preferences. The outcomes can be evaluated in terms of most and least preferred scenes, preference predictors (e.g. coherence, diversity, naturalness etc.), correlations between preference and predictors, content analysis of preferred

environments or comparison of different landscape characteristics.

highly preferred urban environments.

formal designs were less preferred by both groups.

gender and preferences.

environments to others. People judge and interpret their environments and they respond to environments in terms of affective responses. Environmental preference is not luxury for people but essential and tied to basic concerns (R. Kaplan S. Kaplan, 1989). Kaplan sees preference as an indicator of aesthetic judgment (1988b) and as a complex process which involves perception of things and space and reacting to them in terms of their potential usefulness and supportiveness (1988a). According to Charlesworth (1976), species has to be able to both recognize and prefer environments in which it functions well (S. Kaplan, 1988a). Preference for specific landscapes is about the organization of the space, rather than the individual elements (R. Kaplan S. Kaplan, 1989), hence designers should focus on the integrity of different landscape elements.

The bio-evolutionary perspective on landscape preferences were explained in the previous section (Section 2.2): long history of human evolution is believed to be the reason for why we prefer some environments to others. One consistent finding of environmental preference research is that people prefer naturalness or natural environments to human-modified environments (e.g. R. Kaplan S. Kaplan, 1989; van den Berg *et al.*, 2003). Presence of water also increases the preference ratings (Hull & Stewart, 1995; Yang & Brown, 1992). Natural scenes are also assumed to contribute to well-being by reducing stress levels, and to have positive influence on functioning and behavior (Ulrich *et al.*, 1991). It is assumed that preferences for savanna-like landscapes are linked to human evolutionary history, as an adaptation to East Africa savannas for survival (Falk Balling, 2010). Ulrich (1979) found that homogenous ground texture, medium to high levels of depth, presence of a focal point, and moderate levels of mystery leads to high level of preferences in natural scenes (Porteous, 1996).

Complexity has been one of the central concepts in environmental preference research. Although R. Kaplan S. Kaplan (1989) have found that coherence is more significant in explaining preferences, Ode Miller (2011) suggest that landscape preferences have a relationship between measurements of complexity. Their study on rural landscapes showed that "*a landscape with an unequal distribution of land cover, a moderate amount of land cover, and a low level of aggregation is more likely to be preferred over a landscape with many land-cover classes, equal distribution, and strong aggregation*". Complexity is also found to have a positive influence on urban landscape preference (Falk Balling, 2010).

Environmental preference research generally focuses on natural or rural environments and there is little research on urban landscape preferences. This might be due to the fact that urban environments are highly complex structured; there are too many kinds of elements (both natural and cultural) that form urban structure. Moreover, social dynamics have important influence on shaping urban environments. Hence, it is rather difficult to measure and to assess landscape preference determinants in urban landscapes. One of the preference studies in urban environment was conducted by Nasar and his colleagues (1988a). They investigated the visual preferences for urban street scenes. Nasar used bipolar adjectives to describe the environments; closed-open, simple-diverse, chaotic-orderly, dilapidated-wellkept, vehicles prominent-vehicles not in sight, and nature (greenery) not in sight- nature (greenery) prominent. He found (just like he expected) that people preferred ordered, natural, well-kept, and open scenes with vehicles not prominent. However, Nasar was cautious about the interdependence of the variables; he expressed the need for further research for explanation of the relationship between these variables. Nevertheless Nasar

environments to others. People judge and interpret their environments and they respond to environments in terms of affective responses. Environmental preference is not luxury for people but essential and tied to basic concerns (R. Kaplan S. Kaplan, 1989). Kaplan sees preference as an indicator of aesthetic judgment (1988b) and as a complex process which involves perception of things and space and reacting to them in terms of their potential usefulness and supportiveness (1988a). According to Charlesworth (1976), species has to be able to both recognize and prefer environments in which it functions well (S. Kaplan, 1988a). Preference for specific landscapes is about the organization of the space, rather than the individual elements (R. Kaplan S. Kaplan, 1989), hence designers should focus on the

The bio-evolutionary perspective on landscape preferences were explained in the previous section (Section 2.2): long history of human evolution is believed to be the reason for why we prefer some environments to others. One consistent finding of environmental preference research is that people prefer naturalness or natural environments to human-modified environments (e.g. R. Kaplan S. Kaplan, 1989; van den Berg *et al.*, 2003). Presence of water also increases the preference ratings (Hull & Stewart, 1995; Yang & Brown, 1992). Natural scenes are also assumed to contribute to well-being by reducing stress levels, and to have positive influence on functioning and behavior (Ulrich *et al.*, 1991). It is assumed that preferences for savanna-like landscapes are linked to human evolutionary history, as an adaptation to East Africa savannas for survival (Falk Balling, 2010). Ulrich (1979) found that homogenous ground texture, medium to high levels of depth, presence of a focal point, and moderate levels of mystery leads to high level of preferences in natural scenes

Complexity has been one of the central concepts in environmental preference research. Although R. Kaplan S. Kaplan (1989) have found that coherence is more significant in explaining preferences, Ode Miller (2011) suggest that landscape preferences have a relationship between measurements of complexity. Their study on rural landscapes showed that "*a landscape with an unequal distribution of land cover, a moderate amount of land cover, and a low level of aggregation is more likely to be preferred over a landscape with many land-cover classes, equal distribution, and strong aggregation*". Complexity is also found to have a positive

Environmental preference research generally focuses on natural or rural environments and there is little research on urban landscape preferences. This might be due to the fact that urban environments are highly complex structured; there are too many kinds of elements (both natural and cultural) that form urban structure. Moreover, social dynamics have important influence on shaping urban environments. Hence, it is rather difficult to measure and to assess landscape preference determinants in urban landscapes. One of the preference studies in urban environment was conducted by Nasar and his colleagues (1988a). They investigated the visual preferences for urban street scenes. Nasar used bipolar adjectives to describe the environments; closed-open, simple-diverse, chaotic-orderly, dilapidated-wellkept, vehicles prominent-vehicles not in sight, and nature (greenery) not in sight- nature (greenery) prominent. He found (just like he expected) that people preferred ordered, natural, well-kept, and open scenes with vehicles not prominent. However, Nasar was cautious about the interdependence of the variables; he expressed the need for further research for explanation of the relationship between these variables. Nevertheless Nasar

influence on urban landscape preference (Falk Balling, 2010).

integrity of different landscape elements.

(Porteous, 1996).

suggested that moderate novelty, increase diversity, increased contrast among buildings, good maintenance, order, more vegetation and reduced vehicle prominence might produce highly preferred urban environments.

According to Bourassa (1990), aesthetic response occurs at both biological and cultural levels. Falk Balling (2010) also state that "*that human landscape preferences is best understood as a continuous progression of aesthetic ideals, tempered by social convention, passed on from one generation to the next through human culture*". But do culture and socio-demographic factors really affect preferences? There are several cross-cultural studies that investigate preferences for landscapes and landscape elements. Generally, the results show that despite cultural differences, people seem to have similar preferences for specific landscapes; however the concepts of novelty and familiarity can affect preferences for people from different cultures. Familiarity plays an important role in feeling secure and safe. People feel comfortable and relaxed in environments which they are familiar to (Kaplan *et al.*, 1998). On the other hand too much familiarity may become boring and people seek for novelty. For instance, Yang & Brown (1992) found that traditional Japanese style landscapes and water presence were highly preferred by people from both Korean and Western cultures. However they also found that while Koreans preferred Western style landscapes, Western tourists preferred Korean style landscapes. A similar result was found by Nasar (1988a). His study results showed that although there were consensus on preferences for ordered, natural, open and well-kept scenes; Japanese subjects highly preferred the American scenes and vice versa. His findings supported Berlyne's assumption that people prefer novelty to familiarity. He also pointed out that the results would have been different if subjects had been chosen from older population since Sonnenfeld (1966) claims that younger people prefer novelty and others familiarity (Nasar, 1988a). In their study Yang &Kaplan (1990) investigated landscape style preferences of Korean and Western individuals. They found a cross-cultural similarity in preferences in favor of landscapes with natural styles. Landscapes with rectangular or formal designs were less preferred by both groups.

Lyons (1983) showed that there is a strong relationship between age, gender, residential experience and landscape preferences. She found that preference levels changed in different age groups, adolescent male and females had different preferences, urban and rural residents had different preferences, familiar vegetational biomes were preferred highest, and there was no evidence that landscape preferences were shaped by innate or evolutionary factors. Yu (1995) also reported that people from different living environments (rural vs. urban) had different preferences; rural residents had high preference for novelty and modernity. He also indicated that landscape preferences were strongly influenced by education levels. However, his findings did not show any significant relation between gender and preferences.

Landscape preference studies are generally based on public or user (non-expert) evaluations. Ranking, rating or sorting of visual stimuli and verbal instruments are popular tools in determination of landscape preferences. Participants are asked to rank, rate or sort visual stimuli according to their preferences. The outcomes can be evaluated in terms of most and least preferred scenes, preference predictors (e.g. coherence, diversity, naturalness etc.), correlations between preference and predictors, content analysis of preferred environments or comparison of different landscape characteristics.

Landscape Perception 265

daily lives. These constructed environmental images form mental representations which are unique to the individual. This process is called cognitive mapping. Memory plays a crucial role in cognitive mapping. As S. Kaplan (1978) states *a cognitive map is based on familiar objects and events*. Hence, cognitive maps can change or improve depending on the individual's

People derive information from their environments through neurophysiological processes, but they also rely on personality and cultural factors to produce cognitive images (Knox & Marston, 2003). Thus, cognitive maps are highly personal constructs. A cognitive map of an individual can be quite different from an actual physical map in terms of accurate distance and structural organization. Simplification and distortion are two most important attributes of cognitive maps (Knox & Marston, 2003). The images might be incomplete or have inaccurate distance estimates. Nevertheless, cognitive images reflect how we see our environments and how we connect places to each other. Consequently, people's orientation and navigation through space can affect their quality of life. Sense of orientation helps people to feel confident and less anxious (Kaplan *et al.*, 1998). Cognitive maps help people to establish their routes and find their way, no matter how incomplete or distorted they are.

The term of "cognitive map" was first introduced by Tolman (1948) in his study where he investigated the spatial behavior of rats in a maze (Göregenli, 2010). However it was Kevin Lynch (1960) who pioneered cognitive mapping studies in urban design and planning with his famous work "The Image of the City". Lynch puts an emphasis on the concept of legibility for structuring and identifying the environment. Legibility plays an important role in way-finding and environmental images are fundamental for way-finding. An environmental image is a product of both immediate sensation and the memory of past experience (Lynch, 1960). Clarity of environmental images, thus the degree of legibility facilitates one's way-finding. Lynch identified five key elements of urban form which determine the legibility of an urban environment; paths, edges, districts, nodes and landmarks. Although paths were found to be the dominant elements of environmental images, Lynch emphasizes that all of the elements operate together and interrelation of

Lynch's work has been mainly criticized for its small sample size and research technique; his five elements of legibility had already been established before interviewing the subjects. Later, he (1984) also criticized his own work for not being practical but being academically interesting (Pacione, 2005). His work also neglected the importance of symbolic meanings associated with places. Lynch was aware of the influence of meaning attached to a place on one's environmental images, however his work focused on urban form and he stated that form should be used to strengthen the meaning in urban design. Still, his legibility framework is still considered as fundamental and influencing in cognitive mapping studies

Today's fast paced urban life-styles urge us doing our daily tasks in a limited time. Hence, difficulties in getting to the desired destination may cause people to feel stressed out. As a primary component of cognitive mapping, legibility should be considered as an essential objective in place-making. Cognitive maps can be used in landscape architecture to investigate the relationship between characteristics of outdoor environments and perceived legibility. Evaluation of existing structure and organization of the environments will

these elements are important in creating legible urban environments.

experiences.

in urban environments.

Although photographs and slides have been widely used as visual stimuli in preference research, there has been a constant debate on the representational validity of them. While some researchers have found that photographs can be adequate and valid resources to use (Dunn, 1976; Shuttleworth, 1980; Stewart *et al.*, 1984), some others do not agree with this idea (Kroh Gimblett, 1992; Scott Canter, 1997). R. Kaplan (1985) points out that use of photographs is less in cost and easy to administer, however sampling of the environments and selection of photographs require careful attention. In-situ assessments are time consuming, expensive and not practical. Besides, other variables of the landscape, (such as air condition and brightness) may vary during assessments and that might affect visual preference judgments of observers. On the other hand, a landscape is definitely more than just a scene and it is dynamic, however photographs and slides reflect landscapes as more static. Sevenant Antrop (2011) state that depending on the character of the landscapes, some vistas are better presented by panoramic photographs, while some by normal photographs; thus, horizontal angle of view should be considered while selecting photographs. Palmer & Hoffman (2001) also support using panoramic images to increase validity. They also suggest that comparing the ratings of representations and actual field conditions from several individuals would help to establish validity of representations.

 However, validity issues remain the same. In their study, Bishop Rohrmann (2003) concluded that "computer simulations do not necessarily generate the same responses as the corresponding real environment". On the other hand, detailing seems to be an important aspect in computer visualizations; higher detail levels are believed to increase the validity (Bishop Rohrmann, 2003; Daniel Meitner, 2001). Nevertheless photographs still seem to be the most popular tools as surrogates for actual landscapes. However as concern about validity increases, researchers will need to prove reliability of their results and we'll see much more debate on this issue.

Alternatively, sometimes verbal instruments such as verbal descriptions and bipolar adjective scales are used for assessment of landscape preferences. People can explain their preferences better by using words rather than rating or ranking visual stimuli. Although verbal assessments are quick and low-cost, analysis of the data may not be easy. Different people may use different adjectives or descriptions for the same preference judgment. Therefore content analysis of verbal descriptions should be done by experts or trained individuals in order to improve accuracy of results. On the other hand bipolar adjective lists, or semantic differentials, have been criticized for presenting adjectives selected by the researcher and therefore limiting people. However, Echelberger (1979) states that semantic differential may contribute to landscape preference assessment. On the contrary R. Kaplan (1985) claims that using adjectives does not tell much about preferences.

#### **2.5 Environmental images and cognitive maps**

Cognition involves perception, thinking, problem solving and organization of information and ideas (Downs Stea, 1973). Hence, environmental cognition can be defined as perception, understanding, organization and retrieval of spatial information. Through cognition, we construct images of our environment which help us to find our way in our

Although photographs and slides have been widely used as visual stimuli in preference research, there has been a constant debate on the representational validity of them. While some researchers have found that photographs can be adequate and valid resources to use (Dunn, 1976; Shuttleworth, 1980; Stewart *et al.*, 1984), some others do not agree with this idea (Kroh Gimblett, 1992; Scott Canter, 1997). R. Kaplan (1985) points out that use of photographs is less in cost and easy to administer, however sampling of the environments and selection of photographs require careful attention. In-situ assessments are time consuming, expensive and not practical. Besides, other variables of the landscape, (such as air condition and brightness) may vary during assessments and that might affect visual preference judgments of observers. On the other hand, a landscape is definitely more than just a scene and it is dynamic, however photographs and slides reflect landscapes as more static. Sevenant Antrop (2011) state that depending on the character of the landscapes, some vistas are better presented by panoramic photographs, while some by normal photographs; thus, horizontal angle of view should be considered while selecting photographs. Palmer & Hoffman (2001) also support using panoramic images to increase validity. They also suggest that comparing the ratings of representations and actual field conditions from several individuals would help to establish validity of representations.

 However, validity issues remain the same. In their study, Bishop Rohrmann (2003) concluded that "computer simulations do not necessarily generate the same responses as the corresponding real environment". On the other hand, detailing seems to be an important aspect in computer visualizations; higher detail levels are believed to increase the validity (Bishop Rohrmann, 2003; Daniel Meitner, 2001). Nevertheless photographs still seem to be the most popular tools as surrogates for actual landscapes. However as concern about validity increases, researchers will need to prove reliability of their results and we'll see

Alternatively, sometimes verbal instruments such as verbal descriptions and bipolar adjective scales are used for assessment of landscape preferences. People can explain their preferences better by using words rather than rating or ranking visual stimuli. Although verbal assessments are quick and low-cost, analysis of the data may not be easy. Different people may use different adjectives or descriptions for the same preference judgment. Therefore content analysis of verbal descriptions should be done by experts or trained individuals in order to improve accuracy of results. On the other hand bipolar adjective lists, or semantic differentials, have been criticized for presenting adjectives selected by the researcher and therefore limiting people. However, Echelberger (1979) states that semantic differential may contribute to landscape preference assessment. On the contrary R. Kaplan

Cognition involves perception, thinking, problem solving and organization of information and ideas (Downs Stea, 1973). Hence, environmental cognition can be defined as perception, understanding, organization and retrieval of spatial information. Through cognition, we construct images of our environment which help us to find our way in our

(1985) claims that using adjectives does not tell much about preferences.

**2.5 Environmental images and cognitive maps**

much more debate on this issue.

daily lives. These constructed environmental images form mental representations which are unique to the individual. This process is called cognitive mapping. Memory plays a crucial role in cognitive mapping. As S. Kaplan (1978) states *a cognitive map is based on familiar objects and events*. Hence, cognitive maps can change or improve depending on the individual's experiences.

People derive information from their environments through neurophysiological processes, but they also rely on personality and cultural factors to produce cognitive images (Knox & Marston, 2003). Thus, cognitive maps are highly personal constructs. A cognitive map of an individual can be quite different from an actual physical map in terms of accurate distance and structural organization. Simplification and distortion are two most important attributes of cognitive maps (Knox & Marston, 2003). The images might be incomplete or have inaccurate distance estimates. Nevertheless, cognitive images reflect how we see our environments and how we connect places to each other. Consequently, people's orientation and navigation through space can affect their quality of life. Sense of orientation helps people to feel confident and less anxious (Kaplan *et al.*, 1998). Cognitive maps help people to establish their routes and find their way, no matter how incomplete or distorted they are.

The term of "cognitive map" was first introduced by Tolman (1948) in his study where he investigated the spatial behavior of rats in a maze (Göregenli, 2010). However it was Kevin Lynch (1960) who pioneered cognitive mapping studies in urban design and planning with his famous work "The Image of the City". Lynch puts an emphasis on the concept of legibility for structuring and identifying the environment. Legibility plays an important role in way-finding and environmental images are fundamental for way-finding. An environmental image is a product of both immediate sensation and the memory of past experience (Lynch, 1960). Clarity of environmental images, thus the degree of legibility facilitates one's way-finding. Lynch identified five key elements of urban form which determine the legibility of an urban environment; paths, edges, districts, nodes and landmarks. Although paths were found to be the dominant elements of environmental images, Lynch emphasizes that all of the elements operate together and interrelation of these elements are important in creating legible urban environments.

Lynch's work has been mainly criticized for its small sample size and research technique; his five elements of legibility had already been established before interviewing the subjects. Later, he (1984) also criticized his own work for not being practical but being academically interesting (Pacione, 2005). His work also neglected the importance of symbolic meanings associated with places. Lynch was aware of the influence of meaning attached to a place on one's environmental images, however his work focused on urban form and he stated that form should be used to strengthen the meaning in urban design. Still, his legibility framework is still considered as fundamental and influencing in cognitive mapping studies in urban environments.

Today's fast paced urban life-styles urge us doing our daily tasks in a limited time. Hence, difficulties in getting to the desired destination may cause people to feel stressed out. As a primary component of cognitive mapping, legibility should be considered as an essential objective in place-making. Cognitive maps can be used in landscape architecture to investigate the relationship between characteristics of outdoor environments and perceived legibility. Evaluation of existing structure and organization of the environments will

Landscape Perception 267

landscape architects. The model is also grounded on Gestalt figure-background relationship, like Schafer's work. It is based on description of the sounds. In Hedford's model figure-ground relationship is combined with two other dimensions; intensity and clarity (Figure 6). According to Hedford, a soundscape can be described as clear if prominent sounds are strongly experienced against a weak background. However, if prominent sounds are weaker than the background, then the soundscape becomes crowded. If both prominent sounds and the background are experienced equally strong, the soundscape can be described as powerful. On the contrary, if both are experienced

weak, the soundscape becomes mild.

Fig. 6. The model of prominence (Hedfords, 2008).

sound can help people feel relaxed (Carles *et al.*, 1999).

Similar to natural landscapes, natural sounds such as bird sound and water sound are highly preferred by people. This may be explained through evolutionary perspective on landscape perception as well as therapeutic effects of natural landscapes (please refer to section 2.4). In fact, relaxation is found to be an important factor for urban open soundscapes (Yang & Kang, 2005). It is known that natural sounds such as bird and water

provide landscape architects to improve their place-making strategies in terms of design and planning.


State-of-the-Art on the Marine Current Turbine System Faults

*Sana Toumi, Mohamed Benbouzid and Mohamed Faouzi Mimouni*

#### **Abstract**

This chapter deals with the state of the art on the marine current turbine (MCT) system faults. Indeed, the MCT structure consists of a marine turbine, a generator (permanent magnet synchronous generator (PMSG) or doubly fed induction generator (DFIG)), and a PWM power converter. Nevertheless, these systems are exposed to functional and environmental severe conditions. Firstly, the power increase leads to a higher current and/or voltage. Second, the installation of the MCT system under the sea and the existence of the swell and wave imply harmonic current speeds. In fact, several faults (related to the turbine, the generator, the blades, and the converters) can occur in the MCT system. Most of these faults generate the speed and the torque oscillations, which can lead to mechanical vibrations and the rapid destruction of the insulating material generator. Consequently, MCT system performances can be degraded.

**Keywords:** marine current turbine, permanent magnet synchronous generator, doubly fed induction generator, converter, faults

#### **1. Introduction**

Today, the use of the marine current turbine, shown in **Figure 1**, has a great importance in the electrical energy production. Nevertheless, these systems are exposed to functional and environmental severe conditions. Indeed, different faults can exist in these systems, whether on the turbine marine, on the generator, or on the converters [1]. Therefore, the detection of the MCT faults becomes essential in order to minimize the maintenance cost and ensure the continuity of the electricity production.

Moreover, permanent magnet synchronous machines or doubly fed induction generators can be used for MCT systems [2, 3]. Thus, the existence of any fault can lead to an abnormal behavior of the machine and its accelerated aging process [4]. The main faults of permanent magnet synchronous machines can be summarized in two main categories; stator faults (short-circuit between turns, short circuit between phase and neutral, and short-circuit between phases) and rotor faults (magnets (for the PMSG), eccentricity, and rotor windings faults) [5].

**Figure 1.**

*An off-grid marine current turbine structure.*

Furthermore, various studies have presented that 70% of converter faults are related to power switches [6, 7]. Indeed, insulated gate bipolar transistors (IGBTs) are rugged, but, because of electrical stress and excess thermal, they suffer from failure. Converters faults can be, generally, divided into intermittent gate misfiring faults, open-circuit faults, and short-circuit faults. Thus, these faults must be taken into account; otherwise, they can lead to the whole system's performance degradation [8, 9].

This chapter describes the different faults that can be occurring in the marine current turbine system. It is composed as follows; in Section 2, marine turbine faults are described. In Section 3, generator faults and their factors are represented. In Section 4, different types of converter faults are described. The conclusion is given in Section 5.

#### **2. Marine turbine faults**

Marine turbine faults are mainly located at the blades. Indeed, seawater salinity causes the corrosion and the rusting of the blades (**Figure 2**). This requires regular maintenance and the use of a high-performance anti-rust coating. Also, the presence of algae around the blades can also damage the marine turbine.

**Figure 2.** *Marine turbine fault.*

#### **3. Generator faults**

For MCT configuration, both the permanent magnet synchronous generator and the doubly-fed induction generator have been used. **Table 1** gives the advantages and disadvantages of every generator.

#### **3.1 Stator faults**

Stator faults are due to different factors.

• Thermal factors

For a nominal temperature, the insulating material that covers conductors has a well-defined lifespan. Because of a voltage variation or a repetition of starts in a very short time, the temperature can increase and exceed the nominal operating temperature, which leads to the insulating material life reduction [10].

• Electrical factors

The dielectric properties of the insulating material can be contaminated by foreign things (fats, dust, …), which can cause a small current discharge that leads to a short circuit between conductors and magnetic carcasses.

• Mechanical origins

Repetitive starts of the machine cause the temperature rise, which leads to the insulation dilation. This could generate breaks in the insulation that implies a short circuit fault [10].

#### • Environmental origin

In general, humidity and the presence of chemicals in ambient air can degrade the insulating material quality and affect its lifespan [11].

The main faults of the stator are given by (**Figure 3**); short-circuit between turns (a), short circuit between phase and neutral (b), and short-circuit between phases (c) [12]. These faults generate a disturbance in the spatial distribution of the rotating

**Table 1.** *Generator topologies comparison.*

**Figure 3.** *Different short-circuit faults in the stator.*

**Figure 4.** *Speed curve before and after fault.*

**Figure 5.** *Torque curve before and after fault.*

field. This causes, first of all, the electromagnetic torque and the speed oscillations (**Figures 4** and **5**, respectively), which lead to mechanical vibrations. Moreover, the short-circuit current with important values can lead to the rapid destruction of the insulating material (**Figure 6**) [13, 14].

**Figure 6.** *Insulating material destruction.*

#### **3.2 Rotor faults**

• Rotor winding faults

These faults present between 42 and 50% of all rotor failures in electrical machines. It can generate noise, mechanical vibrations, and the bearing wear rise. Moreover, winding faults are 12 times more frequent in inverter-powered machines than in those powered directly by the grid [14].

• Eccentricity

The stator and the rotor, for an electrical machine in healthy conditions, have the same rotation axis (same center) (**Figure 7**). Eccentricity is defined as an unsymmetrical air gap between the rotor and the stator. It can be static or dynamic.

For the static eccentricity, the stator and the rotor centers are different (**Figure 8**), however, the rotor always turns around its axis. The main cause of static eccentricity is the incorrect position of the stator and the rotor [15].

In the case of dynamic eccentricity, the rotor does not turn around its axis of rotation where there is an unbalance as shown in **Figure 9**. The main cause of the dynamic eccentricity is the mechanical resonances at critical speed [16] that leads to the electromagnetic forces increase.

**Figure 7.** *Stator and rotor in healthy conditions.*

#### **4. Converter faults**

As shown in **Figure 10**, the MCT converter consists of three legs. Each leg is composed of two semiconductor switches (*T*k, *Tk*+3 *k* = 1, 2, 3) and two freewheeling diodes (*D*k, *Dk*+3). For the switches control, a PWM bloc based on logic control signals *S*k (*k* = 1, 2, 3) is used, and it is expressed by:

$$S\_k = \begin{cases} \mathbf{1} \circ T\_k \, on \, and \, T\_{k+3} \, off \\ \mathbf{0} \circ T\_{k+3} \, on \, and \, T\_k \, off \end{cases} \tag{1}$$

Most converter faults are short-circuit and open-circuit faults.

#### **4.1 Open-circuit fault**

IGBT's open-circuit faults are, generally, caused by the loss of bonding wires of the control signal or the transistor rupture by a short-circuit [17]. Furthermore, this fault can occur when the switches are destructed by an accidental overcurrent or a fuse connected with series for short protection is blown out. It can arise on the upper switch (**Figure 11a**), the lower switch (**Figure 11b**), or even the two switches at the same time (**Figure 11c**).

Following this fault, the converter cannot synthesize balanced output voltages, thus providing large torque ripple (**Figure 12**) and increasing speed harmonics distortion (**Figure 13**) [18].

*State-of-the-Art on the Marine Current Turbine System Faults DOI: http://dx.doi.org/10.5772/intechopen.109517*

**Figure 10.**

**Figure 11.** *Open-circuit fault.*

**Figure 12.** *Torque curve.*

*Short-circuit fault.*

#### **4.2 Short-circuit fault**

In this case, the fault transistor current increases. When this fault is applied to the whole leg, this latter becomes definitively short-circuited (**Figure 14**). The phase currents become strongly unbalanced and their amplitudes can reach several times that of the currents in normal operation. This not only causes very high torque ripples but can also damage other converter components. In addition, the short-circuit current can result in significant amplitudes.

#### **5. Conclusion**

This chapter presents the different faults that can occur in the marine current turbine system, either on the turbine, the machine, or the converter. In this contest, these faults have been analyzed and described by giving each one its impact on the MCT behavior. In fact, Currents, voltages, torque, and speed have been attacked by strong ripples, which lead to the degradation of the MCT performances. Thus, the abovepresented study should be useful for the design of advanced robust control techniques in order to correct the effects of the faults and improve the MCT performances.

*State-of-the-Art on the Marine Current Turbine System Faults DOI: http://dx.doi.org/10.5772/intechopen.109517*

#### **Author details**

Sana Toumi1,2\*, Mohamed Benbouzid2,3 and Mohamed Faouzi Mimouni1

1 Laboratory of Automation, Electrical Systems and Environment (LASEE), University of Monastir, Monastir, Tunisia

2 University of Brest, Brest, France

3 Shanghai Maritime University, Shanghai, China

\*Address all correspondence to<EMAIL_ADDRESS>
© 2023 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

## **References**

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[2] Zhou Z, Scuiller F, Charpentier JF, Benbouzid MEH, Tang T. Grid-connected marine current generation system power smoothing control using supercapacitors. In: Proceedings of the IEEE Annual Conference on IEEE Industrial Electronics Society (IECON'38); 25-28 October 2012. Montreal, Canada: IEEE; 2012. pp. 1-6

[3] Bachir S, Tnani S, Trigeassou JC, Champenois G. Diagnosis by parameter estimation of stator and rotor faults occurring in induction machines. IEEE Transactions on Industrial Electronics. 2006;**53**:963-973

[4] Awadallah MA, Morcos MM, Gopalakrishnan S, Nehl TW. Detection of stator short circuits in VSI-Fed Brushless DC motors using wavelet transform. IEEE Transactions on Energy Conversion. 2006;**21**:1-8

[5] Toumi S, Amirat Y, Elbouchikhi E, Trabelsi M, Benbouzid MEH, Mimouni MF. A simplified mathematical approach for magnet defects modeling in PMSGbased marine current turbine. In: Proceedings of the IEEE International Conference on Sciences and Techniques of Automatic Control and and Computer Engineering (STA'17); 19-21 December 2016. Sousse, Tunisia: IEEE; 2016. pp. 552-557

[6] Toumi S, Amirat Y, Elbouchikhi E, Trabelsi M, Benbouzid MEH, Mimouni MF. A comparison of fault-tolerant control strategies for a PMSG-based marine current turbine system under converter faulty conditions. Journal of Electrical Systems. 2017;**13**:472-488

[7] Toumi S, Amirat Y, Trabelsi M, Elbouchikhi E, Mimouni MF, Benbouzid MEH. Backstepping control of a PMSG-based marine current turbine system under faulty conditions. In: Proceedings of the IEEE International Renewable Energy Congres (IREC'09); 20-22 March 2018. Hammamet, Tunisia: IEEE; 2018. pp. 1-6

[8] Amirat Y, Benbouzid MEH, AlAhmer E, Bensaker B, Turri S. A brief status on condition monitoring and fault diagnosis in wind energy conversion systems. Renewable and Sustainable Energy Reviews. 2009;**3**:2629-2636

[9] Parker MA, Ran L, Finney SJ. Distributed control of a fault-tolerant modular multilevel inverter for directdrive wind turbine grid interfacing. IEEE Transactions on Industrial Electronics. 2013;**2013**:60

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[11] Thomson JS, Kallesoe CS. Stator fault modelling of induction motors. In: Proceedings of the IEEE International Symposium on Power Electronics, Electrical Drives, Automation and Motion (SPEEDAM); 23-26 2006. Taormina, Italy: IEEE; 2006

[12] Toumi S, Benelghali S, Trabelsi M, Elbouchikhi E, Amirat Y, Benbouzid MEH, et al. Modeling and simulation of a PMSG-based marine current turbine system under faulty rectifier conditions. Electric Power Components & Systems. 2017;**45**:715-725

[13] Tallam RM, Lee SB, Stone G, Kliman GB, Yoo J, Habetler TG, et al. *State-of-the-Art on the Marine Current Turbine System Faults DOI: http://dx.doi.org/10.5772/intechopen.109517*

A survey of methods for detection of stator-related faults in induction machines. IEEE Transactions on Indudtry Applications. 2007;**43**:920-933

[14] Kliman GB, Lee SB, Shah MR, Lusted RM, Nair NK. New method for synchronous generator core quality evaluation. IEEE Transactions on Energy Conversion. 2004;**19**:576-582

[15] Devanneaux V, Kabbaj H, Dagues B, Faucher J. An accurate model of squirrel cage induction machines under static, dynamic or mixed eccentricity. In: Proceedings of the IEEE International Symposium on Diagnostics for Electrical Machine, Power Electronics and Drives (SDEMPED); 01-03 September 2001. Grado, Italy: IEEE; 2001. pp. 121-126

[16] Andriamalala RN, Razik H, Baghli L, Sargos FM. Eccentricity fault diagnosis of a dual-stator winding induction machine drive considering the slotting effects. IEEE Transactions on Industrial Electronics. 2008;**55**:4238-4251

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[18] Toumi S, Benelghali S, Trabelsi M, Elbouchikhi E, Benbouzid MEH, Mimouni MF. Robustness analysis and evaluation of a PMSG-based marine current turbine system under faulty conditions. In: Proceedings of the IEEE International Conference on Sciences and Techniques of Automatic Control and Computer Engineering (STA'15); 21-23 December 2014. Hammamet, Tunisia: IEEE; 2014. pp. 631-636

#### **Chapter 8**


*Article* **Linear Superposition as a Core Theorem of Quantum Empiricism**

**Yurii V. Brezhnev**

> Department of Quantum Field Theory, Tomsk State University, 634050 Tomsk, Russia<EMAIL_ADDRESS>
**Abstract:** Clarifying the nature of the quantum state |**Ψ** is at the root of the problems with insight into counter-intuitive quantum postulates. We provide a direct—and math-axiom free—empirical derivation of this object as an element of a vector space. Establishing the linearity of this structure—quantum superposition—is based on a set-theoretic creation of ensemble formations and invokes the following three principia: (I) quantum statics, (II) doctrine of the number in the physical theory, and (III) mathematization of matching the two observations with each other (quantum covariance). All of the constructs rest upon a formalization of the minimal experimental entity—the registered micro-event, detector click. This is sufficient for producing the C -numbers, axioms of linear vector space (superposition principle), statistical mixtures of states, eigenstates and their spectra, and non-commutativity of observables. No use is required of the spatio-temporal concepts. As a result, the foundations of theory are liberated to a significant extent from the issues associated with physical interpretations, philosophical exegeses, and mathematical reconstruction of the entire quantum edifice.

**Keywords:** quantum foundations; non-axiomaticity; detector clicks; ensembles; superposition principle; arithmetic; numbers; vector space; abstracting; interpretations; self-referentiality

#### **1. Introduction and Summary**

. . . somewhat curious that, even after nearly a full century, physicists still do not quite agree on what the theory tells us . . .—G. 't Hooft ([1], p. 5)

It is almost a crying shame that we are nowhere close to that with quantum mechanics, given that it is over 70 years old now—C. Fuchs ([2], p. 32)

The contradiction between the fundamental nature of quantum theory (QT) and the phenomenological feature of its mathematics [3] is likely to never cease instigating the attempts to overcome it. As H. Putnam had said, "Human curiosity will not rest until . . . questions [of the nature of the QT-formalism] are answered".

The subject-matter and leitmotiv of what follows is that the linear superposition and theory's axioms have an origin—they are derivable, and it is entirely empirical. The theory is thereby demystified, and the interpretative challenges that accompany the exegeses of QT are a *nonexistent* problem coming from "a confusion of categories" ([4], p. 89), i.e., from the "semantic confusion" ([5], p. 10). A direct outgrowth of this ideology is not only a derivation of the superposition principle (page 35) but also the axiom-free production of the "chief" quantum formula—the Born rule *p* = |a|2 [6].

#### *1.1. On the Foundations of Quantum Theory*

The debates concerning the foundations of quantum mechanics (QM) hitherto "show no sign of abating" ([7], p. 222, [8,9]), and despite widespread scepticism [10–15], it is generally acknowledged that the problem is a real one [9,16–19]; it is not something made up or "just a dispute over words" ([20], p. 5) and sometimes "has been regarded as a very serious one" ([15], p. 418, [21,22]). Say, R. Penrose has expressed (2004) an even more radical "conviction that present-day quantum mechanics has no credible ontology, so that it *must* be seriously modified".

**Citation:** Brezhnev, Y.V. Linear Superposition as a Core Theorem of Quantum Empiricism. *Universe* **2022**, *8*, 217. https://doi.org/10.3390/ universe8040217

Academic Editors: Steven Duplij and Michael L. Walker

Received: 8 February 2022 Accepted: 21 March 2022 Published: 28 March 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

In recent decades, the discussions have even worsened [2,23], and current research has intensified due to the tremendously increased and formerly inconceivable technological possibilities of operating with individual micro-objects and the urge to implement the idea of quantum computing [20,24].

The reason for this state of affairs remains the same as it was before. Unlike the classical theories, e.g., thermodynamics or relativity theory, "Ma di assiomatizzazioni della teoria quantistica ce ne sono moltissime" ([17], p. 30) and the QM-axiomatics itself seems wholly divorced from human language [5,8,9,15,17,25–32]. Quantum postulates are not merely formal. They are phrased in terms of linear operators on a complex Hilbert space H [4,10,13,25,33–37] and, with that, literally not a single word here can be brought into conjunction with reality by means that have *at least some kind* of relationship with the classical description. What is more, it is very well known that the abstract character of these terms is required by the essence of the point (covariance) and, at the same time, that the attempt to link them with physical images is imposed by a decree and results in the famous paradoxes associated with concepts, such as causality, (non)locality, and realism [9,27,28,38–45]. All of that causes a problem with interpretations of QM.

It is well known that the theory has steadfastly resisted any unique ontological reading and, in particular, reconciliation between interpretations. This is reflected not only in the voluminousness of the literature. The differences in viewpoint are often based on points of principle [3,8,14,15,46–51], and even highly qualified publications face criticism [52–55]. Among other things, we encounter appeals [3,12,16,17,43,56–58] (there is even a manifesto(s) [50], (p. 990), [59], ), striking titles such as "scandal of quantum mechanics" [60,61], "QUANTUM OUTCOME: ALLAH WILLED IT?" ([62], p. 188; Wheeler), "the Oxford Questions . . . to two clouds" ([63], p. 6), "The Canon for Most of the Quantum Churches" ([50], p. 988), "Quantum mechanics for the Soviet naval officers" ([64], p. 161), "the patron saint of heretics in the One True Church of Copenhagen" (about D. Bohm), "A Feminist Approach to Teaching Quantum Physics" ([2], p. 182), "Church of the Larger Hilbert Space" (J. Smolin) [2,12], and also April Fools' [65] and the medical jokes about "the "state of health of the quantum patient'" ([66], p. vii), political parallels with "Marxism . . . [and] the Cold War" [67], and many more [3,9,27,68–71].

An interesting fact is that Cambridge University Press has published a 500-page-long book [2] containing an arresting electronic correspondence—D. Mermin called it "samizdat" (self-published)—between C. Fuchs and modern researchers and philosophers in the field of quantum foundations. This correspondence has continued ([23], over 2300 pages) and now covers 1995–2011. It characterizes the state of affairs in the field, and does not merely add to one's impression of the unending discussions about quantum matters (see introductory sections in [50] (!) and in [64]), it also represents, due to the lack of formality, a plentiful source of ideas and of valuable thoughts. Schlosshauer's very informative "quantum interviews" [16] pursue the same goals.

It is worth mentioning that the quantum challenges had led, quite a while ago, to attempts to revise, even formalizing, the logic of our thinking [72,73]—a very nice mathematical theory dating back to von Neuman in the 1930s ([25], Section III.5) termed quantum logic [74]. There are handbooks on that subject [75], and this topic is still under intensive investigation now. See also the last paragraph in Section 6.3.1.

The lack of transparent motivations for mathematics—a pressing requirement of physics—means that QM-formalism is hard to distinguish from a "cook book of procedures and rituals" (J. Nash), a "user-manual" ([32], p. 1690), [76], ([27], p. xiii), or from "a library of . . . tricks and intuitions" [21]. Therefore, the "dissatisfaction regarding comprehension" and the "need for interpretation that is alien to an exact science" ([77], pp. 7–8) lead to the fact that "we admit, be it willingly or not, that quantum mechanics is not a physical theory but a mathematical model" ([32], p. 1701) or that "nature imitates a mathematical scheme" ([78], p. 347; Heisenberg). De facto, QT "is in a sense like a traditional herbal medicine used by "witch doctors". We do not REALLY understand what is happening" (J. Nash) and "we have essentially *no* grasp on why the theory takes the precise structure that it does" ([2],

p. 32), which raises the suspicion that "something is wrong with the theory" (H. Putnam) and that "this quantum skyscraper is built on very shaky ground" ([64], p. 8). (Throughout the text, the *italic* and *slanted* type in "quotations" is original, unless otherwise indicated.)

At the same time, well-founded opinions have long been known to the effect that "quantum theory needs no "interpretation'" [43], in refs. [3,12,60] or that "only consequences of the basic tenets of quantum mechanics can be verified by experiment, and not its basic laws" ([11], p. 16). In other words, the discrepancies between opinions are significant and often radical: from epithets such as "schizoid, . . . situation is desperate" ([15], p. 420), ([79], p. 424) to supporting the rationale for quantum computations [24] and whole books written on the subject [8]. Concerning the "schizoid", the case in point is the many-world conception by Everett–DeWitt. See also pages 158, 161, 176–179 in [80] regarding the "state of schizophrenia" and "explanations" as to why "schizophrenia cannot be blamed on quantum mechanics" ([80], p. 182).

In any case, the controversy between "the warring factions, ..., many [quantum] faiths, . . . and instrumentalist camps" ([16], pp. 60–61), ([81], Section 5.5), [30,33]—"[t]hey all declare to see the light, the ultimate light" ([50], p. 987)—cannot be considered as an acceptable state of affairs (see also Section 11.1) for the simple reason that the quantum philosophy issues turn into an "industry"of interpretations—an unhealthy state of affairs— while, at the same time, the very same philosophers call for its denial: "interpretation of QM emerged as a growth industry" ([82], p. 92).

#### *1.2. Formula of Superposition*

Conversely, the "dominant role of mathematics in constructing quantum mechanics" has led to the conclusion that mathematical "assumptions are usually considered to be physical" ([32], p. 1691). That is to say, "there has been a substitution of concepts" ([76], p. 295) and "one of the consequences of quantum revolution was the replacement of explanations of physical phenomena by their mathematical description" ([76], p. 296). These characteristics convey, in the best possible way, the dissatisfaction with the fact that quantum physics "was actually reduced to a physical interpretation of the Hilbert space theory" ([32], p. 1690). The H-space in itself is a fairly cumbersome mathematical structure and even determines a crucial principle: the superposition of states [26]. It is thus not surprising that this principle becomes "one of the vague points . . . the [Dirac] argument is difficult to consider as rational . . . the physical principle simply fits underneath it" (excerpt from the preface to the Russian edition of [83]).

The mathematics of the H-space contains three constituents: a vector space, the innerproduct add-on over it, and topology. The two latter ones invoke the first one, which is completely independent (algebra) and begins with the formula

$$
\langle \Psi \rangle = \mathfrak{a} \cdot |\mathfrak{q}\rangle + \mathfrak{b} \cdot |\mathfrak{x}\rangle \,. \tag{1}
$$

This is the pivotal expression of quantum theory. Comprehending its genesis is tantamount to comprehending the nature of the *linearity* of QM.

In Formula (1), there occur the complex numbers a, b ∈ C, symbols of operations · and +, and also vectors |*ψ* , |*ϕ* , |*χ* ∈ H. It is clear that until an empirical basis for all these devices is found, the interpretation of Abstraction (1) and questions of the kind "Quantum States: What the Hell Are They?" (55 times in [23]) will remain a problem. To all appearances, the problem is considered so difficult—"quantum states . . . cannot be "found out'" ([8], p. 428)—that the non-axiomatic meaning of these symbols was not even discussed in the literature. In the meantime, not only is the situation far from hopeless, but it also admits a solution. The present work is devoted to gradual progress towards an understanding of Formula (1). Stated differently, Equality (1) becomes an empirical "theorem" (p. 56).

• The main part of the challenge is not only to ascertain what is being added/multiplied in Formula (1), but also to realize primarily *what "to add/multiply" is*, and "Where Mathematics Comes from" [84] at all.

"What does it mean, physically, to "add" things?" [2], (p. 178; D. Darling). More than that, aside from the symbols {a, b, |*ψ* , |*ϕ* , |*χ* , ·, +}, Expression (1) contains the sign of equality = (see also [85] (pp. 29, 30 (!), [86]), and, surprising as it may seem, it conceals one of the key points—the third principium of quantum theory (III, p. 29).

The guiding observation is based on the fact that the only thing that we have access to are the microscopic events, and therefore, "we have little to begin with other than what an experimental physicist would call experiments with a single microsystem" ([87], p. 5).

"[W]e must recognize that the focusing on individual elements whatever these may be is absolutely indispensable for all our thinking. . . . What may be regarded as an individual event?"

#### R. Haag ([88], p. 302)

Consequently, we must begin from individual events and from collecting them into ensemble formations. It is precisely in this context that we will use the word empiricism— quantum empiricism of micro-acts of perception—and it is in this respect that QT has a statistical nature. As Einstein put it, "It may be a correct theory of statistical laws, but an inadequate conception of individual elementary processes" ([30], p. 156; Einstein); see also ([25], ([30], Chs. 7–8), [70], [89], pp. 38–40), ([89], p. 40). Such a viewpoint has been long championed by L. Ballentine [90] and H. Groenewold ([91], p. 468) and justified in detail by G. Ludwig [87,92–94]. A. Leggett proposes accordingly "extreme statistical interpretation"[16] (p. 79) , [95], in the sense that "to seek any further "meaning" in the formalism is pointless and can only generate pseudoquestions". With that, he overtly applies such characteristics as "complete gibberish" ([95], p. 70) and "verbal window dressing" ([16], p. 79).

The difficulty is, of course, in creating the object |*ψ* itself. A step-by-step characterization of this procedure (Sections 3–8) and key words to what follows have been reflected in the (sub)section titles listed in the Contents.

#### *1.3. Physics Mathematics; Doctrine of Numbers*

Thus, the situation appears to be one whereby the physics itself faces inconsistencies in its foundations and the mathematical superstructures are difficult to reconcile with its motivations (physical principles) [96]. However, on the other hand, attempts to axiomatize an interface between them [97] only conceal a deeper insight [22]. M. Born had called attention to the fact that "probable refinements of mathematical methods will not suffice to produce a satisfactory theory, but that somewhere in our doctrine is hidden a concept" and T. Maudlin was more definite: "physicists have been misled by the mathematical language they use to represent the physical world".

In other words, we observe an overemphasis on the role of the ready-made mathstructures—algebras, spaces, and the like—and an under-evaluation of "seemingly naïve" empirical aspects voiced in the ordinary language [98]. The situation is no different from that which H. Weil had characterized in the introductory section to ([99], p. 10) as follows.

"All beginnings are obscure. Inasmuch as the mathematician operates with their conceptions along strict and formal lines, he, above all, must be reminded from time to time that the origins of things lie in greater depths than those to which their methods enable them to descend".

The "origins" are expressible of course only in the natural language; Section 2 is devoted to this.

What we propose below is an implementation of the idea that the postulational view must be abandoned and replaced by a negation of the prior existence of both the physical "preconceived notions" [92] (p. 328) and the mathematical structures. Physics and mathematics should be created "from scratch". Paul Benioff calls this idea "a coherent theory of physics and mathematics" [2] (p. 33; P. Benioff), [96] (p. 639), Then, due to the initial absence of mathematics, introducing mathematical structures is almost ruled out, proofs must be replaced by an empirical inference, and semantics of physics—the language of physical reasoning—is initially under a linguistic ban. It cannot exist a priori. That is to say, even the natural-language conjunction of mathematical terms with physical adjectives (and verbs [100] (p. 3102; "to happen, to be, to exist")) becomes far from being free, as with the classical description's language (Sections 2.1, 5.4, 6.4 and 6.5). R. Haag, on the first page of the work [101], emphasizes:

•"we should not consider ["vocabulary of Quantum Theory"] as sacrosanct. . . . every word in the vocabulary is subject to criticism".

Returning to the ensemble formations, it is only they that have to come to the fore, and argumentation should be subordinated only to the low-level microscopic empiricism. The predominance of the empirical over the theoretical will then immediately touch on the closest creature of the latter—the notion of a number—since numbers do not come "from the sky", and the theory will have to be a quantitative one.

Despite the overflow of abstracta in QT, the *doctrine of number* —,number × unit-, to be precise (Sections 7 and 9)—has, it seems, not yet entered foundational discussions [102]. Consequently, the numbers turn into a kind of "problem of numbers" (principium II), and we are thus led to the necessity of revising the take on the foundations themselves:

,quantum fundamentals- ,the problem/doctrine of the number- .

This paradigm shift is a unique trait of the quantal (not the classical) view of things and a substantial part of the following is devoted specifically to that.

In the outline of the present work, the workflow will constitute re-creating the structure of a linear vector space. More precisely, producing an *a priori unknown* mathematics, which *will be* an algebra of such a space with a complex conjugation. As a matter of fact, we provide an answer to Haag's question "How do we translate the description of an experimental arrangement into mathematical symbols?" in the context of their own "idea of basing the interpretation of quantum theory on the concept of "events" which may be considered as facts independent of the consciousness of an observer" ([88], p. 295).

The main point to be immediately emphasized is that the mathematization of the discrete micro-acts of observations is quite a nontrivial procedure (105), and further, the strategy, along with the structure of this article, can be schematized as follows.

This box-diagram cannot be reduced or restructured. For example,

•*Superposition foregoes numbers*, and measurement and physical properties follow *strictly after* the |ket -vectors have been created.

By and large, the aforesaid ideology is supported by the common belief—often certainty even [12]—that QM is *not* perturbative, its linearity is *not* associated with linear approximation of something else, and, in general, it is *not* extensible (ultimate [103] and non-deformable) and must be free of interpretations [12,43]. All of these concerns, in one way or another, are directly related to the derivation of Formula (1).

#### **2. Points of Departure**

In the Beginning was the Word—A. Zeilinger ([39], 01:0547)

Most of the time the apparatus is empty and sometimes you have a photon coming through—A. Zeilinger ([39], 1239)

Since empiricism is in essence supra-mathematical [104], i.e., it is concerned with *meta*mathematics [105,106], its mathematization, i.e., theory construction, should begin not with postulates and definitions, but rather with the semantic formation of an object language (of "the Quanta") of vocabulary that "may only be described by "words" and not by a theory" [58], [87] ( p. 106), [93]. As A. Peterson and K. Popper had observed, "Math can never be used in phys until have words" ([107], p. 209), i.e., "we cannot construct theories without using words" ([108], p. 12). Therefore, relying on the established understanding of the underlying causes for the quantum eye on physics [13,25,27,33], up until the end of this section, we will adopt the natural-language meaning of the words observation, system, state, numbers (!), plus and to divide, physical influence, transition, large/small, micro/macro, etc. Their contents will later be defined more precisely or entirely changed. For instance, the sense of the word "state" will be drastically transformed, to which we are drawing attention in advance. Accordingly, a degree of informality—it has been clarified in Remark 10—is inevitable here, but "the lack of precision . . . is a necessity" ([109], p. 48) at the moment.

#### *2.1. Variations as Micro-Level Transitions*

We will (and "must" [105] (Ch. 3)) first view the concept of a system at an intuitive level ([110], Section 1.1)—there is what is referred to as an isolated system S.

S Let us tentatively (a priori) relate the concept of a *state* to the associated context describable by the words "the system S can *vary*, *be different*, or *in different states*". That is to say, system S is always in a certain state Ψ belonging to the set T = {Ψ, Φ, ...}, each element of which is admissible for S, and all of them are different from each other: Ψ = Φ.

In other words, the concept of a quantum system may not have a precise/axiomatical definition at the moment. Otherwise, if it comes to that, the system is what is being constantly varied when observed, and "varied" is the key word here.

The statement "states are different" does not require a consideration when Ψ and Φ, referred to as state, are the abstract elements of an abstract set {Ψ, Φ, ...}. However, in order to tie its elements to reality, we have to introduce the criteria of coincidence/distinguishability of one from the other. Criteria may not come from observational procedures, without which it is impossible to either detect states or claim that they differ, coincide, or that they are, if any.

On the other hand, the nature of micro-phenomena shows that observations are always associated with an irreducible intervention in the system, manifesting in what is known as *transition* Ψ Ψ (or destruction). As an example, observations at accelerators are literally the destructions, and bulk at that. Due to a lack of criteria, there is no sense in attributing to this concept the adjectives small/large, (in)significant/partial, or collocations such as "comparison of destructions at instants *t*1, *t*2". Let us proceed from the idea that initially there is nothing but the transition. Transitions may actually occur without destruction Ψ Ψ, however.

Two different Ψ, Φ may be destroyed into new Ψ , Φ, as well as into the combinations of the old/new. Thus, strictly speaking, the sense of words "different, new, ..." eludes us in this case, which is why even the identification of Ψ-elements and the T itself, as a set, becomes questionable. Therefore, besides the formal writings Ψ = Φ and Ψ = Φ for Ψ, Φ ∈ T, the *physical* distinguishability/equivalence (recognizability ≈/≈) needs to be established. As to the identification (and to the identity) in this regard, see von Neumann's reasoning: "One might object against II . . . " on page 302 of their book [25]. The sole thing that distinguishability may rely on is the transition acts. In turn, variation is a key element in transitions, which is why we will begin constructing with distinguishability.

Let us take the still virtually unlimited way A of intervening A in S and attempt to introduce distinguishability Ψ ≈ Φ as A -distinguishability. Due to the fact that microtransition Ψ A Ψ is not pre-determined, initial states Ψ undergo arbitrarily free changes. Next time, the results will be different and absolutely arbitrary (the term "different" is understood to mean =), and each act is indiscernible from a case in which it contains ones similar to itself within itself. It would be natural to associate such a case to the absurd, which is unrelated to the meaning of the words "physical observation", and to discard the given A .

Non-meaninglessness arises only if we impose the negation of random combinations of = and = in transitions, at least for a part of T, i.e., introduce the preservation acts Ψ A Ψ. The "preservation" should be read here as indestructibility of state, i.e., as a (=)-coincidence under the secondary act Ψ Ψ Ψ. Otherwise, the vanishing difference between "preservation" and "variation" leads to linguistic chaos ([111], p. 232). This means that the destruction Ψ Ψ may not be considered as a one-fold one. State Ψ on the right should be examined for changeability and transform into the left part of the subsequent transition: Ψ Ψ Ψ. Thereby, the structure Ψ Ψ with the *binate* entity "before/after" or "on the left/right" becomes the key one, and we consider it an initial object in subsequent constructs. The preserved states are, by definition, those that pass the reproducibility test.

 The terminology *α*-event [12] could be used instead.

Freedom of elements in Sequence (4), including the choice of *α*-states, is not limited by anything besides the ban on Equation (2). Therefore, this arbitrariness, which is physically never recognizable, curtails the generic chain from Sequence (4) into the shortened one

$$
\overline{\Psi} \dashv \stackrel{\scriptstyle}{\dashv} \sim \overline{\lnot \, \overline{\llcorner} \, \overline{\llcorner} \, \cdots \sim \overline{\ll'} \, \overline{\ll'}} \stackrel{\scriptstyle}{\dashv} \sim \overline{\ll'} \stackrel{\scriptstyle}{\dashv} \cdots \stackrel{\scriptstyle}{\dashv} \stackrel{\scriptstyle}{\dashv} \tag{5}
$$

which is identical to the scheme

$$\overbrace{\overline{\cdots \cdots \overline{\overline{\mathbf{h}} \cdots \cdots}}}^{\overline{\cdots}} \cdots \overbrace{\overline{\cdots} \overbrace{\cdots}}^{\overline{\cdots} \overbrace{\overline{\mathbf{h}}}^{\overline{\mathbf{h}}}} \tag{6}$$

with certain *α* ∈ T.

Discussions on "what happens . . . [and] "how" ([25], p. 217) at the very microscopic level are extremely widespread in the literature [18,41,44,45,53,56,77] (see [19,33,40,112] for the exhaustive references), although it is not difficult to predict the fact that the attempts to understand the inner structure of Box (6) will only lead back to an identical box; so, the "turtles all the way down" (ascribed to W. James), followed by the great Wheeler's slogan "No tower of turtles" (1989).

Indeed, the uncontrollability of micro-changes is universally known, yet describing them as a process in time *t* %→ *t* + *ε* will start employing language terminology—functions, arithmetic operations, the physical words, etc.—that has not yet been created even for the fixed instants *t*1, *t*2. However, what may be associated with fixed time are only nontemporal entities, for which we have nothing but transitions (Equation (5)). The attempt to manage them, i.e., to control intervention in S, results in looping or "measuring the measurement", in addition to the ambiguity of this term itself.

"[I]t is not meaningful to speak of a measurement "at time ˜*t*." . . . the real physical meaning of the time parameter . . . has nothing to do with the notion "time of measurement"". "[T]he description of the measurement process in quantum mechanics in terms of "pre-theories" is not possible"

> G. Ludwig ([87], p. 288), ([92], p. 340)

See also [58] (p. 100), [92] (p. 365), [94] (p. 150), [113] (pp. 644–646), and [114]. Just as before, the physical assessments such as "abrupt", "(ir)reversible", "(non)simultaneous", "immediately following ..." [25] (pp. 231, 410), or the "weak/nondemolishing" (measurements [53]), etc.are unacceptable here. No temporal process may be present in the foundations of the theory (([87], Sections VII.4, 6), ([92], Chs. III, XVII), [93]) since it is immediately not clear: "Furthermore, what exactly are we having at instants *t*1 or *t*2?". In the reverse direction—,time measurement-—the situation is also rather indefinite since the ""Time" is not an entity to which the operations of measurement, direct or indirect, apply" ([114], p. 5).

**Remark 1.** *All the information stated above means that attempts to deduce QM dynamically ([16], 10 · Reconstructions) are beforehand doomed to vicious circles "round the boxes" and time t, such as attempts to dynamically "vindicate" Lorenz's contraction instead of kinematic postulates of the relativity theory [69]. A consistent theory must rest either on "irreducible" elements* (6) *or upon "boxes" of a different kind. In the latter case, the theory becomes a particular* model with interpretation*; e.g., the Lindblad equations [115,116], decoherence [112,117–119], stochastic dynamics,*

*and other statistic-dynamical models [40,77]. Anyway, an ability to model and understanding are not the same thing, and this point was repeatedly emphasized in the literature ( [16], ([17], Section I.2), [32]) with regard to QT.*

That said, if theory is built *as a fundamental one rather than as a model* ([16], p. 144), with a primary entity *changeability* A , Box (6) may only be involved in it as the initial starting point and as an *indescribable* object with the absolute rather than with a relative sense. Elements of reality, in whatever understanding—say, Bell's "*be*ables" [28]—may not exist before/after/inside/outside of the box. It can only be the *structureless abstractio*. Accordingly, the notions of preparation, of measurement, of "interaction with", and of a physical process are meaningless without the construction of Box (6).

These statements are clearly in agreement with the fact that any reasoning must not contradict the formal logical rules [105]; hence, there must exist [96,106,120] the empirically undefinable logical atoms. A. Peres writes ([121], p. 173): "While quantum theory can in principle describe *anything*, a quantum description cannot include *everything*. In every physical situation *something* must remain unanalyzed". Moreover, as Pauli put it, "Like the ultimate fact without any cause, the individual outcome of a measurement is . . . not comprehended by laws". Specifically, the set T and transitions arrows A are also the atoms. It is a ". . . preexisting concept . . . We cannot formulate the theory without this concept", concludes B. Englert ([12], p. 2). From the aforesaid, we may formulate the following tenet.

IQuantum statics should forego quantum dynamics.

#### (*The first principium of quantum theory*)

The rationales do not end here and will be later amplified once we begin to exploit the terminology that is usually taken for granted from the outset, viz., the quantitative descriptions ([2], p. 178). If they arise not as numerical interpretations of something but out of an experiment, then observation should be the beginning, and the "manufacture of numbers'—the end. In other words, the model "theory with boxes" other than Boxes (5) and (6) implicitly implies the logical sequence ,model of process- ,numerical interpretation-, in which empiricism holds a role other than primary. It is clear that, regardless of the model, such a situation will always remain unsatisfactory in the physical respect.


**2. Definition of anemia and epidemiology**

The definition of anemia in the elderly in the literature is controversial. The WHO criteria were established in the 1960s in a cohort lacking individuals >65 years of age [14]. According to WHO criteria anemia was defined as hemoglobin <12 g/dL in women and <13 g/dL in men and absolute iron deficiency was defined as a serum ferritin <30 ng/mL [15, 16]. The National Health and Nutrition Examination Survey

III classifies anemia into four categories as per underlying cause such as anemia from nutritional deficiency, anemia due to renal diseases, anemia of chronic disease and unexplained anemia, in the absence of other specific causes. Worldwide both the number and ratio of older adults growing and there are nearly 500 million (7%) adults, 65 years and older in the world and by 2030 will double to 1 billion (12%). It was predicted that 164 million elderly people who constitute 23.9% of geriatric population were suffering from anemia globally and death risk was elevated to 49% [3, 17]. As per a systematic review the prevalence of anemia was found to be 3–50%. Out of that 3–25% constituted from community-based studies, 31–50% from nursing homes studies and 40–72% hospital admissions [18]. The prevalence of anemia in the institutional studies was observed to be 24%, 31.4%, 46.8%, 54.5%, 66.3%, 67% and 74% in Belgium, Israel, Pakistan, Ethiopia, German, China and US Arespectively [1, 19–23]. Whereas the prevalence of anemia was observed to be 7.3%, 17.7%, 19% and 38% in Turkey, rural India, Iran and urban India respectively in population-based studies [24–27].