The document discusses the evolving nature of dimensions and how our perception and understanding of dimensions is influenced by factors like our minds and scientific/mathematical advances. It provides examples of how dimensions are defined differently in various contexts and disciplines, and how dimensions are not limited to the 3 we can intuitively visualize. The fractal dimensions of the proposed Tower project are meant to separate perception of space from expectations of Euclidean geometry.
Metaphor and Representation in Two Frames: Both Formal and Frame Semantics Vasil Penchev
A formal model of metaphor is introduced. It models metaphor, first, as an interaction of “frames” according to the frame semantics, and then, as a “wave function” in Hilbert space
The practical way for a probability distribution and a corresponding wave function to be assigned to a given metaphor in a given language is considered
A series of formal definitions is deduced from this for: “representation”, “reality”, “language” “ontology”. All are based on Hilbert space
A few statements about a quantum computer are implied:
The so-defined reality is inherent and internal to it
It can report a result only “metaphorically”
It will demolish transmitting the result “literally”, i.e. absolutely exactly
A new and different formal definition is introduced as a few entangled wave functions corresponding to different “signs” in different language formally defined as above
The change of frames as the change from the one to the other formal definition of metaphor is interpreted as a formal definition of thought
Metaphor and Representation in Two Frames: Both Formal and Frame Semantics Vasil Penchev
A formal model of metaphor is introduced. It models metaphor, first, as an interaction of “frames” according to the frame semantics, and then, as a “wave function” in Hilbert space
The practical way for a probability distribution and a corresponding wave function to be assigned to a given metaphor in a given language is considered
A series of formal definitions is deduced from this for: “representation”, “reality”, “language” “ontology”. All are based on Hilbert space
A few statements about a quantum computer are implied:
The so-defined reality is inherent and internal to it
It can report a result only “metaphorically”
It will demolish transmitting the result “literally”, i.e. absolutely exactly
A new and different formal definition is introduced as a few entangled wave functions corresponding to different “signs” in different language formally defined as above
The change of frames as the change from the one to the other formal definition of metaphor is interpreted as a formal definition of thought
Codenamed it as TOAST …stands for The Object And Space state Transform, the expression T in angular bracket indicates generalness as applied to any domains such as scientific, commercial, medical, robotics etc….
The space by itself represents layered structure in term of inner space, micro inner space as well as set of outer spaces lik...e mega, ultra, super….thereby representing subatomic to cosmic [light year] spaces. It is possible to define regions of spaces which in turn are space by them self. The spaces can have vectors operating at space level or at point level as discrete effect.
You can add objects in spaces which are nothing but bound space along with number of properties, behaviors, transforms and tendencies. The objects can interact with other objects and spaces by it. Every object, space, point in space has relative time dimension, thereby enabling “Relativity”. You may also define virtual spaces for business data mining.
Codenamed it as TOAST …stands for The Object And Space state Transform, the expression T in angular bracket indicates generalness as applied to any domains such as scientific, commercial, medical, robotics etc….
The space by itself represents layered structure in term of inner space, micro inner space as well as set of outer spaces lik...e mega, ultra, super….thereby representing subatomic to cosmic [light year] spaces. It is possible to define regions of spaces which in turn are space by them self. The spaces can have vectors operating at space level or at point level as discrete effect.
You can add objects in spaces which are nothing but bound space along with number of properties, behaviors, transforms and tendencies. The objects can interact with other objects and spaces by it. Every object, space, point in space has relative time dimension, thereby enabling “Relativity”. You may also define virtual spaces for business data mining.
Extending the knowledge level of cognitive architectures with Conceptual Spac...Antonio Lieto
Extending the knowledge level of cognitive architectures with Conceptual Spaces (+ a case study with Dual-PECCS: a hybrid knowledge representation system for common sense reasoning). Talk given at Stockholm, September 2016.
Kristiansund Kunsthalle - May 2023 - Neuroscience and Design.pdfMenno Cramer
Everything we interact with impacts us, from nature to non-nature.
Everything which is non-nature is (hu)man-made.
Constructed by a brain, to be consumed by a brain.
So, why do so little people understand how the brain works?
In order to create products, services, spaces which are “healthy” for us/our brains, we need a kind of neuro-ergonomics, understanding of how we are physical, physiological, and psychological beings. Only then will we be able to accurately predict behavioural and mental output/outcomes of the designed stimuli we expose ourselves too.
The higgs field and the grid dimensionsEran Sinbar
The Higgs boson (or Higgs particle), that was confirmed on 2012 in the ATLAS detector at CERN is supposed to be a quantum excitation of the condensate field which fills our universe and is responsible for the mass of elementary particles and is named the Higgs field. In this paper I will explain why this Higgs field is part of new dimensions which I refer to as the Grid extra dimensions (or grid dimensions). This paper will explain what are the expected measurements regarding the Higgs boson (particle) based on this assumption. In this paper I will show what will be the future measured evidence that the Higgs particle measured at the particle accelerators is a quantum excitation of the Grid dimensions themselves. This exciting evidence will enable us for the first time to probe new dimensions and open our perspectives to accept the option of extra dimensions and many worlds staggered within our known universe. This understanding might enable future communication through these dimensions between the staggered worlds themselves.
BUS 1 Mini Exam – Chapters 05 – 10 40 Points S.docxhartrobert670
BUS 1
Mini Exam – Chapters 05 – 10
40 Points
Short Answer – Mind your time
Answer four questions from #1 - #6. Must answer #3 and #6. Answer
the XC question for extra credit. Question point count weighted equally.
It is all about business, so make sure to demonstrate / synthesize the bigger picture of business in each and
every answer.
Like all essays, specifying an exacting target word count is rather problematic. I am thinking each answer
would be about 250 - 300 words each, depending upon writing style. If you tend to be descriptive and whatnot,
that number could be 350 - 450 words.
Sidebar: Gauge your knowledge level in this way. This exam should take about 90 – 120 minutes to complete.
Students taking much longer may want to work with me to assess / discuss ways to help master this material in
a future conference session.
1. Although most new firms start out as sole proprietorships, few large firms are organized this way. Why
is the sole proprietorship such a popular form of ownership for new firms? What features of the sole
proprietorship make it unattractive to growing firms?
2. List and discuss at least three causes of small business failure. Workarounds, fixes, or methods to avoid
failure should be discussed.
3. Describe three different leadership styles and give an example of a situation in which each style could be
most used effectively.
4. Discuss Max Weber's views on organization theory. Is there a few principles that particularly resonate
in business today?
5. How has the emphasis of quality control changed in recent years? Describe some of the modern quality
control techniques that illustrate this change in emphasis.
6. Explain how managers could motivate employees by using the principles outlined in expectancy
theory? Create a story/example of expectancy theory at work, incorporating the three questions that
according to expectancy theory employees will ask.
7. XC – What is selective perception? Can you describe a business-centric scenario where selective
perception may hinder a businessperson’s ability to respond to a customer need?
I
Fireworks, Manifesto, 1974.
The Architectural Paradox
1. Most people concerned with architecture feel some sort
of disillusion and dismay. None of the early utopian ideals
of the twentieth century has materialized! none of its social
aims has succeeded. Blurred by reality! the ideals have turned
into redevelopment nightmares and the aims into bureau
cratic policies. The split between social reality and utopian
dream has been total! the gap between economic constraints
and the illusion of all-solving technique absolute. Pointed
Space
out by critics who knew the limits of architectural remedies,
this historical split has now been bypassed by attempts to
reformulate the concepts of architecture. In the process, a
new split appears. More complex, it is not the symptom of
prof ...
Matters of SensationMarcelo Spina and GeorGina HuljicH.docxandreecapon
Matters of
Sensation
Marcelo Spina and
GeorGina HuljicH
ARTISTS SPACE
1110
Marcelo Spina and Georgina Huljich
Matters of Sensation: Materiality in the Sublime
Introduction
MofS focus closely on an evolving materialism in
architecture by a group of emerging contemporary
architects; a “Sensuous Materialism”, an affluent
materialism of sensations rather than an abstract
materialism of pure matter. While materialism implies
a philosophical outlook; a conception of the world
derived from physical phenomena and those relation-
ships which are directly dependant on it; materialism
in its ontology can not be detached from the body. In
fact, as Peter Zellner argues, material bodies can only
be appreciated through sensations. The pursuit of
sensations in these contemporary practices constitutes
a novel form of artistic research that implies “an evolv-
ing materialist/sensualist architecture that gestures
towards a far more negotiable set of relationships
between form, perception and action”1 while still away
from the realm of subjectivity or phenomenology.
To be clear, materialism does not imply here the idea
that material organization at a certain scale will simply
trigger formal organization and structural evolution of
an entire project at another; nor it suggests form find-
ing or form optimization processes as a priori design
criteria. Materialism in these architects has a further
meaning beyond a philosophical one, it indicates a con-
cern with materials as such. In fact the working pro-
cess of this group is rather open. It combines research
and intuition with an obsessive creative surge. This
interest explains not only an experimental approach to
architecture but the will in exploring many different
aspects of architectural form. For these architects, it is
not enough to formulate an idea once; they are inter-
ested in playing through various instantiations of an
idea to demonstrate and rehearse its potential. None-
theless, these architects are not interested in merely
proposing, positioning or illustrating questions, but
they rather choose to produce provisional responses
to them emphasizing in their outcomes the material,
physical and sensorial aspects of form and matter.
Hence the multiplicity of the senses needed to scruti-
nize their work instead of the primacy of the visual.
Grounding Sensation
Sensation is synthetic by definition. Its space is optic
as it is tactile. Bodies are not merely perceived but
they take on a sculptural or tactile quality such as
mass, depth, contour and relief. Deleuze following
Riegl, terms it “haptic space, a space in which there is
no longer a hand-eye subordination in either direction.
It implies a type of seeing distinct from the optical, a
close-up viewing in which “the sense of sight behaves
just like the sense of touch” 2.
In thinking about the exhibition, we wanted to con-
struct an atmospheric ecosystem, a whole ecology of
sensation building ob ...
Course ObjectiveExplore architectural space and form in various.docxmarilucorr
Course Objective:
Explore architectural space and form in various cultures.
15 page paper is due May 4, 2018. The 15 pages should not include cover sheet or citations. Double space, 12 point and number each page. You may choose at two cultures to compare/contrast. You may explore only one. Whatever you do, please use several or one philosophy of architecture. Delve into how a culture define space
Your final research paper is to analyze the importance of architectural space, exploring how at least two cultures express space and the importance of architectural space. I read the wonderful discussions that you all wrote about urban space. Now let us narrow our vision to our immediate space and how we react to space. Try to keep the paper to no more than 15 pages including citations.
OVERALL: Minimum of 15.
Introduction. Identify explain how one culture experience space. Compare to another chore to emphasize. Then tell me how you feel about it. The give summary.
187 | SSpace
soft architecture. Sensors that trigger the opening and closing of doors
and windows, the movement of walls, and even the lowering and raising
of floors and ceilings produce the personalized spaces that characterize
soft architecture. Theatrical stages have had this capability for some
time, and thus have a lot to teach the designer seeking to produce soft
architecture.
Traditional Japanese architecture is an early version of soft architecture.
The ability to change the use and “feel” of a space by simply moving a rice
paper screen and rearranging the mats on the floor is a manual, low-tech
version of soft architecture. A more recent manifestation of softness was
attempted with the Centre Georges Pompidou in Paris (1977) (Figure 93).
It was to have an interior in which many walls and floors were movable.
Unfortunately that degree of flexibility was unjustified. Consequently the
building was renovated in 2000 to increase its capacity and efficiency by
“hardening” it.
In soft architecture each force applied to it creates content that has
form, as “water poured into a vase has form” (Ezra Pound). The water-
generated Blur building by Herzog and Meuron poetically illustrates the
new frontier of soft or reflexive architecture. The term now refers to any
architecture that is not finite or fixed.
See also: Blur • Responsive architecture • Flexibility
Figure 93 Pompidou
Center
Space
The classical questions include: is space real, or is it some kind of
mental construct, or an artifact of our ways of perceiving and thinking?
— Oxford Dictionary of Philosophy
If architecture can be understood as the construction of boundaries in
space, this space must be understood as commonsense space, a space
that possesses meaning and speaks to us long before the architect
goes to work. — Karsten Harries
The ethereal thing about architecture is this thing called “space.” Space, as
a central design concern for architects, has the interesting quality of.
Codenamed it as TOAST …stands for The Object And Space state Transform, the expression T in angular bracket indicates generalness as applied to any domains such as scientific, commercial, medical, robotics etc….
The space by itself represents layered structure in term of inner space, micro inner space as well as set of outer spaces lik...e mega, ultra, super….thereby representing subatomic to cosmic [light year] spaces. It is possible to define regions of spaces which in turn are space by them self. The spaces can have vectors operating at space level or at point level as discrete effect.
You can add objects in spaces which are nothing but bound space along with number of properties, behaviors, transforms and tendencies. The objects can interact with other objects and spaces by it. Every object, space, point in space has relative time dimension, thereby enabling “Relativity”. You may also define virtual spaces for business data mining.
Codenamed it as TOAST …stands for The Object And Space state Transform, the expression T in angular bracket indicates generalness as applied to any domains such as scientific, commercial, medical, robotics etc….
The space by itself represents layered structure in term of inner space, micro inner space as well as set of outer spaces lik...e mega, ultra, super….thereby representing subatomic to cosmic [light year] spaces. It is possible to define regions of spaces which in turn are space by them self. The spaces can have vectors operating at space level or at point level as discrete effect.
You can add objects in spaces which are nothing but bound space along with number of properties, behaviors, transforms and tendencies. The objects can interact with other objects and spaces by it. Every object, space, point in space has relative time dimension, thereby enabling “Relativity”. You may also define virtual spaces for business data mining.
Extending the knowledge level of cognitive architectures with Conceptual Spac...Antonio Lieto
Extending the knowledge level of cognitive architectures with Conceptual Spaces (+ a case study with Dual-PECCS: a hybrid knowledge representation system for common sense reasoning). Talk given at Stockholm, September 2016.
Kristiansund Kunsthalle - May 2023 - Neuroscience and Design.pdfMenno Cramer
Everything we interact with impacts us, from nature to non-nature.
Everything which is non-nature is (hu)man-made.
Constructed by a brain, to be consumed by a brain.
So, why do so little people understand how the brain works?
In order to create products, services, spaces which are “healthy” for us/our brains, we need a kind of neuro-ergonomics, understanding of how we are physical, physiological, and psychological beings. Only then will we be able to accurately predict behavioural and mental output/outcomes of the designed stimuli we expose ourselves too.
The higgs field and the grid dimensionsEran Sinbar
The Higgs boson (or Higgs particle), that was confirmed on 2012 in the ATLAS detector at CERN is supposed to be a quantum excitation of the condensate field which fills our universe and is responsible for the mass of elementary particles and is named the Higgs field. In this paper I will explain why this Higgs field is part of new dimensions which I refer to as the Grid extra dimensions (or grid dimensions). This paper will explain what are the expected measurements regarding the Higgs boson (particle) based on this assumption. In this paper I will show what will be the future measured evidence that the Higgs particle measured at the particle accelerators is a quantum excitation of the Grid dimensions themselves. This exciting evidence will enable us for the first time to probe new dimensions and open our perspectives to accept the option of extra dimensions and many worlds staggered within our known universe. This understanding might enable future communication through these dimensions between the staggered worlds themselves.
BUS 1 Mini Exam – Chapters 05 – 10 40 Points S.docxhartrobert670
BUS 1
Mini Exam – Chapters 05 – 10
40 Points
Short Answer – Mind your time
Answer four questions from #1 - #6. Must answer #3 and #6. Answer
the XC question for extra credit. Question point count weighted equally.
It is all about business, so make sure to demonstrate / synthesize the bigger picture of business in each and
every answer.
Like all essays, specifying an exacting target word count is rather problematic. I am thinking each answer
would be about 250 - 300 words each, depending upon writing style. If you tend to be descriptive and whatnot,
that number could be 350 - 450 words.
Sidebar: Gauge your knowledge level in this way. This exam should take about 90 – 120 minutes to complete.
Students taking much longer may want to work with me to assess / discuss ways to help master this material in
a future conference session.
1. Although most new firms start out as sole proprietorships, few large firms are organized this way. Why
is the sole proprietorship such a popular form of ownership for new firms? What features of the sole
proprietorship make it unattractive to growing firms?
2. List and discuss at least three causes of small business failure. Workarounds, fixes, or methods to avoid
failure should be discussed.
3. Describe three different leadership styles and give an example of a situation in which each style could be
most used effectively.
4. Discuss Max Weber's views on organization theory. Is there a few principles that particularly resonate
in business today?
5. How has the emphasis of quality control changed in recent years? Describe some of the modern quality
control techniques that illustrate this change in emphasis.
6. Explain how managers could motivate employees by using the principles outlined in expectancy
theory? Create a story/example of expectancy theory at work, incorporating the three questions that
according to expectancy theory employees will ask.
7. XC – What is selective perception? Can you describe a business-centric scenario where selective
perception may hinder a businessperson’s ability to respond to a customer need?
I
Fireworks, Manifesto, 1974.
The Architectural Paradox
1. Most people concerned with architecture feel some sort
of disillusion and dismay. None of the early utopian ideals
of the twentieth century has materialized! none of its social
aims has succeeded. Blurred by reality! the ideals have turned
into redevelopment nightmares and the aims into bureau
cratic policies. The split between social reality and utopian
dream has been total! the gap between economic constraints
and the illusion of all-solving technique absolute. Pointed
Space
out by critics who knew the limits of architectural remedies,
this historical split has now been bypassed by attempts to
reformulate the concepts of architecture. In the process, a
new split appears. More complex, it is not the symptom of
prof ...
Matters of SensationMarcelo Spina and GeorGina HuljicH.docxandreecapon
Matters of
Sensation
Marcelo Spina and
GeorGina HuljicH
ARTISTS SPACE
1110
Marcelo Spina and Georgina Huljich
Matters of Sensation: Materiality in the Sublime
Introduction
MofS focus closely on an evolving materialism in
architecture by a group of emerging contemporary
architects; a “Sensuous Materialism”, an affluent
materialism of sensations rather than an abstract
materialism of pure matter. While materialism implies
a philosophical outlook; a conception of the world
derived from physical phenomena and those relation-
ships which are directly dependant on it; materialism
in its ontology can not be detached from the body. In
fact, as Peter Zellner argues, material bodies can only
be appreciated through sensations. The pursuit of
sensations in these contemporary practices constitutes
a novel form of artistic research that implies “an evolv-
ing materialist/sensualist architecture that gestures
towards a far more negotiable set of relationships
between form, perception and action”1 while still away
from the realm of subjectivity or phenomenology.
To be clear, materialism does not imply here the idea
that material organization at a certain scale will simply
trigger formal organization and structural evolution of
an entire project at another; nor it suggests form find-
ing or form optimization processes as a priori design
criteria. Materialism in these architects has a further
meaning beyond a philosophical one, it indicates a con-
cern with materials as such. In fact the working pro-
cess of this group is rather open. It combines research
and intuition with an obsessive creative surge. This
interest explains not only an experimental approach to
architecture but the will in exploring many different
aspects of architectural form. For these architects, it is
not enough to formulate an idea once; they are inter-
ested in playing through various instantiations of an
idea to demonstrate and rehearse its potential. None-
theless, these architects are not interested in merely
proposing, positioning or illustrating questions, but
they rather choose to produce provisional responses
to them emphasizing in their outcomes the material,
physical and sensorial aspects of form and matter.
Hence the multiplicity of the senses needed to scruti-
nize their work instead of the primacy of the visual.
Grounding Sensation
Sensation is synthetic by definition. Its space is optic
as it is tactile. Bodies are not merely perceived but
they take on a sculptural or tactile quality such as
mass, depth, contour and relief. Deleuze following
Riegl, terms it “haptic space, a space in which there is
no longer a hand-eye subordination in either direction.
It implies a type of seeing distinct from the optical, a
close-up viewing in which “the sense of sight behaves
just like the sense of touch” 2.
In thinking about the exhibition, we wanted to con-
struct an atmospheric ecosystem, a whole ecology of
sensation building ob ...
Course ObjectiveExplore architectural space and form in various.docxmarilucorr
Course Objective:
Explore architectural space and form in various cultures.
15 page paper is due May 4, 2018. The 15 pages should not include cover sheet or citations. Double space, 12 point and number each page. You may choose at two cultures to compare/contrast. You may explore only one. Whatever you do, please use several or one philosophy of architecture. Delve into how a culture define space
Your final research paper is to analyze the importance of architectural space, exploring how at least two cultures express space and the importance of architectural space. I read the wonderful discussions that you all wrote about urban space. Now let us narrow our vision to our immediate space and how we react to space. Try to keep the paper to no more than 15 pages including citations.
OVERALL: Minimum of 15.
Introduction. Identify explain how one culture experience space. Compare to another chore to emphasize. Then tell me how you feel about it. The give summary.
187 | SSpace
soft architecture. Sensors that trigger the opening and closing of doors
and windows, the movement of walls, and even the lowering and raising
of floors and ceilings produce the personalized spaces that characterize
soft architecture. Theatrical stages have had this capability for some
time, and thus have a lot to teach the designer seeking to produce soft
architecture.
Traditional Japanese architecture is an early version of soft architecture.
The ability to change the use and “feel” of a space by simply moving a rice
paper screen and rearranging the mats on the floor is a manual, low-tech
version of soft architecture. A more recent manifestation of softness was
attempted with the Centre Georges Pompidou in Paris (1977) (Figure 93).
It was to have an interior in which many walls and floors were movable.
Unfortunately that degree of flexibility was unjustified. Consequently the
building was renovated in 2000 to increase its capacity and efficiency by
“hardening” it.
In soft architecture each force applied to it creates content that has
form, as “water poured into a vase has form” (Ezra Pound). The water-
generated Blur building by Herzog and Meuron poetically illustrates the
new frontier of soft or reflexive architecture. The term now refers to any
architecture that is not finite or fixed.
See also: Blur • Responsive architecture • Flexibility
Figure 93 Pompidou
Center
Space
The classical questions include: is space real, or is it some kind of
mental construct, or an artifact of our ways of perceiving and thinking?
— Oxford Dictionary of Philosophy
If architecture can be understood as the construction of boundaries in
space, this space must be understood as commonsense space, a space
that possesses meaning and speaks to us long before the architect
goes to work. — Karsten Harries
The ethereal thing about architecture is this thing called “space.” Space, as
a central design concern for architects, has the interesting quality of.
1. Visualizing complex geometries and their dimensions within an ever-expanding reality The methods used to communicate our perception of objects are influenced by the human mind engaging with an ever expanding objective world (constantly redefined through research). This provides a systematic structure and representation with which to experience that world whilst questioning the responsive ,manner in which dimensions evolve alongside our consciousness. For objects and concepts to be considered real, the mind, which has an active role in the construction of their reality, provides the framework into which perception and thought are choreographed in order to be represented. This structure includes space, time and causation, space being a precondition of perception rather than an idea formed in the mind because we are capable of perceiving objects in three dimensions. In order to understand the changing definition of dimensions , we must ask "What can we know?" Our knowledge is constrained to mathematics and the science of the natural, empirical world. The reason that knowledge has these constraints, Immanuel Kant argues, is that the mind plays an active role in constituting the features of experience and limiting the mind's access to the empirical realm of space and time. The rational order of the world as known by science could never be accounted for merely by the chance accumulation of sense perceptions. The mind contributes to assessing and describing objects and the world around us, but just because we do not experience all realities does not mean they are not present. Kant justifies this by arguing that perception is based both upon experience of external objects and a priori knowledge. The external world provides those things that we sense; it is our mind that processes this information about the world, giving it order and allowing us to comprehend and appropriate it. Things that we perceive are apparently unknowable, as they themselves are mere concepts; yet without concept, intuition is nondescript; without intuition, concept is meaningless. If this is to be reasoned, then the identity of dimension needs to be addressed. One explanation of space is that it is part of the fundamental structure of the universe, a set of dimensions in which objects are separated and located, have size and shape, and through which they can move. Faith dimensions/divination and dimension: Virtual space, on the other hand, is not based upon architectural forms or landscapes but is concerned with the notion of information and cognitive space. Conceptual space is the virtual space with which we are most familiar, hence the term "cyberspace". This virtual space may be the clouds of data that travel and reside on the network or the interface-space. Though there may be a lack of buildings or doors in conceptual space, we are nevertheless encountering space (Second Life further pushes the boundaries of conceptual virtual space, events and dimensions). The interface acts as a locale at which further experiences and dimensions of virtual space are revealed. We have a hard time visualizing fractional dimensions or more than three, because our imagination limits us, even though many of our speculated theories can be formulated in any number of them. Some theories are only mathematically consistent if space has a certain number of dimensions. For example, super-string theory needs nine spatial dimensions. Judging from this, it seems plausible that there are extra dimensions of space – we simply do not observe them in everyday life because they are small – which brings me to the fractal dimension and its part in the design criteria for the Tower project in Manhattan .
2. In order to understand the changing definition of dimensions , we must ask "What can we know?“ Each separate discipline defines space using it’s own relevant dimensions, whereby specific contexts in which dimensions as descriptive paramters are addressed. Kant believed space and time exist at one level of reality but not at another, whereby axioms of geometry are not self-evident or true in any logically necessary way but thought of as “synthetic”, claiming that consistent non-Euclidean geometries are possible. If Euclidean axioms depend on our “pure intuition” of space, namely actual space, and because we are able to visualise imaginatively then there is a possibility that we may also visualise non Euclidean geometry.
3. There is no model or projection of curved space that does not distort shapes and sizes. The best model of a curved Riemannian space (the two-dimensional surface of a sphere) only has lines that are intuitively curved in the third dimension. The Surface cannot be visualised without that third geometry .This is why spherical trigonometry existed for centuries without anyone thinking of it as a non-Euclidean geometry. The fascination with complex geometry highlights the awarenss that dimension is limited through our perception of Euclidean geometry because the possibilities are confined to our ability to envisage these complex geometries or to justify their precedence within the real world. Examples of Riemannian symmetric spaces are the with their natural Riemannian metric actual space, because we are able to visualize imaginatively. Only if non-Euclidean space could be visualized would Kant be wrong. A fractal geometry configuration displays self-similarity through scale invariance The knowledge that we are able to hold expands with our relationship to the real world.
4. Intuitive dimensions influence predictable appropriation While parametric design can involve light-level adaptation, structural load resistance and aesthetic principles, its main references are to Cartesian geometry. Because of its ability to modify by means other than erasure and recomposition, parametric design is known as associative geometry . This complexity of proportionate dimensions and their continuous cross-model amendments are specific auxiliary tools to design processes: the antithesis of intuitive, accidental and adaptive design criteria.
5. The reflecting surfaces have a Hausdorff dimension greater than its topological dimension with the aim of presenting An infinite number of geometric iterations of an infinite length while the area remains finite. Fractal Tower plan River Hudson Hudson Pier 32 Surface detail The Tower sits on the edge of a pier in Manhattan's Battery Park. It screens, reflects and alters the urban fabric. Employing time-sequence simulation and metamorphosis to describe and evolve physical space, we can bring the concept of dimension into the intuitive realm, whereby the ever changing framework with which our mind identities and relates to also contributes to the changing dimensions in an attempt to make parametric design less formulaic and more intuitive. Using perception and the mind’s eye to re-appropriate the individual’s relationship to space and its appropriation.
6. Viewing pod surface distorts, reflects and collages immediate context Dimensions describe the physical world, and parameters within those dimensions, such as light levels, alter our perceptions and in turn our relationship with these descriptions. This allows for an adaptation of Cartesian geometry and Gestalt psychology to address the non-Euclidean within our surroundings. With regard to the Tower, the imagined/subjectively perceived space is translated and continually morphed as a result of the surface renderings and reflections, whose boundaries and physical transitions are non-static, thus creating a dynamic series of dimensions. The reflecting surfaces have a Hausdorff dimension greater than its topological dimension, with the aim of presenting an infinite number of geometric iterations of an infinite length while the area remains finite. The Hausdorff dimension is one measure of the dimension of an arbitrary metric space; this includes complicated spaces such as fractals.
7.
8. The surface reflections, however, are too irregular to be easily described using a traditional Euclidean geometric language. Both these criteria are characteristics of fractal as a geometric object.
9. Fractals epitomised complex dimensions before the invention of computers. A fractal is neither one or two-dimensional; rather it is of a fractional dimension, because its complex geometry suggests its surface. No single, small piece of it is line-like, but neither does it describe a plane. It is too big to be thought of as a one-dimensional object, but too thin to be of two dimensions. Its dimension is most accurately described by a number between one and two. Fractal dimensions reserve self-similarity across scales, only being restricted through context. Scale invariance is an exact form of self-similarity where at any magnification there is a smaller piece of the object that is similar to the whole. The reason I use this as a tool for the Tower's design criteria is to separate the perception and appropriation of Euclidean geometry and space from the constraints of expectation and as an analogy to its vertical gallery and exhibition typology. Julia fractal configuration, non-specific scale Hyperbolic geometry distorts surface iterations
10. Looking up at fractal tower surface viewing pod The Tower project therefore attempts to present a projected physicality, reiterating that the tangibility of architectural dimension is expanding along with our objective world. What can be imagined can be communicated using a lexicon of dimension.