Yucong Duan

International Standardization Committee of Networked DIKWP for Artificial Intelligence Evaluation(DIKWP-SC)

World Artificial Consciousness CIC(WAC)

World Conference on Artificial Consciousness(WCAC)

(Email: duanyucong@hotmail.com)

Cubism is a revolutionary art movement that emerged in the early 20th century, fundamentally altering the way art represents reality. Pioneered by artists like Pablo Picasso and Georges Braque, Cubism deconstructed traditional perspectives and introduced fragmented forms, multiple viewpoints, and abstract representations. This report applies Prof. Yucong Duan's DIKWP Semantic Mathematics framework to explain Cubism in full detail. By integrating Data, Information, Knowledge, Wisdom, and Purpose (DIKWP) into the analysis, we provide a systematic and comprehensive understanding of Cubism's principles, techniques, and philosophical underpinnings. This approach demonstrates how the DIKWP model can be employed to elucidate complex artistic movements, bridging mathematics, art, and human cognition.

1. Introduction

• 1.1 Background on Cubism

• 1.2 Objectives of the Report

• 1.3 Structure of the Report

2. Overview of DIKWP Semantic Mathematics

• 2.1 Components of the DIKWP Model

• 2.2 Philosophical Foundations

• 2.3 Relevance to Art Movements

3. Understanding Cubism through DIKWP

• 3.5.1 Mathematical Formalism

• 3.5.2 Understanding the Movement's Intentions

• 3.4.1 Mathematical Formalism

• 3.4.2 Ethical and Philosophical Interpretations

• 3.3.1 Mathematical Formalism

• 3.3.2 Constructing the Cubist Knowledge Network

• 3.2.1 Mathematical Formalism

• 3.2.2 Processing Cubist Techniques

• 3.1.1 Mathematical Formalism

• 3.1.2 Identification of Cubist Elements

• 3.1 Data (D) in Cubism

• 3.2 Information (I) in Cubism

• 3.3 Knowledge (K) in Cubism

• 3.4 Wisdom (W) in Cubism

• 3.5 Purpose (P) in Cubism

4. Detailed Analysis of Cubist Artworks

• 4.2.1 Characteristics and Techniques

• 4.2.2 Application of DIKWP Components

• 4.1.1 Characteristics and Techniques

• 4.1.2 Application of DIKWP Components

• 4.1 Analytical Cubism

• 4.2 Synthetic Cubism

5. Validation of the DIKWP Approach to Cubism

• 5.1 Consistency with Cubism's Evolution

• 5.2 Enhancing Interpretative Depth

• 5.3 Bridging Mathematical Formalism and Artistic Expression

6. Implications and Benefits

• 6.1 Improved Understanding of Art Movements

• 6.2 Educational Applications

• 6.3 Cross-Disciplinary Insights

7. Challenges and Considerations

• 7.1 Complexity in Quantifying Artistic Elements

• 7.2 Subjectivity in Interpretation

• 7.3 Need for Interdisciplinary Collaboration

8. Conclusion

9. References

Cubism is an avant-garde art movement that emerged between 1907 and 1914, primarily in France. It is characterized by an emphasis on formal structure, the reduction of natural forms to their geometric equivalents, and the organization of the planes of a represented object independently of representational requirements.

Key figures in Cubism include:

• Pablo Picasso: His work "Les Demoiselles d'Avignon" (1907) is considered a precursor to Cubism.

• Georges Braque: Collaborated closely with Picasso in developing Cubist techniques.

• Juan Gris: Contributed significantly to Synthetic Cubism.

Cubism is generally divided into two phases:

1. Analytical Cubism (1907–1912): Focused on deconstructing objects into basic geometric forms and analyzing them from multiple viewpoints.

2. Synthetic Cubism (1912–1914): Introduced collage elements and simpler shapes, synthesizing objects rather than analyzing them.

This report aims to:

• Apply the DIKWP Semantic Mathematics framework to explain Cubism in full detail.

• Provide a comprehensive analysis of Cubism's principles, techniques, and philosophical underpinnings using DIKWP components.

• Demonstrate how this approach enhances our understanding of Cubism and its impact on art.

The report is structured as follows:

• Section 2: Introduces the DIKWP Semantic Mathematics framework.

• Section 3: Applies each DIKWP component to Cubism.

• Section 4: Provides detailed analyses of Analytical and Synthetic Cubism using the DIKWP model.

• Section 5: Validates the approach and discusses its effectiveness.

• Section 6: Explores implications and benefits.

• Section 7: Addresses challenges and considerations.

• Section 8: Concludes the report.

The DIKWP Semantic Mathematics framework consists of:

1. Data (D): Raw elements with semantic attributes.

2. Information (I): Processed data highlighting meaningful patterns.

3. Knowledge (K): Structured understanding and relationships.

4. Wisdom (W): Integration of ethics, values, and higher-order insights.

5. Purpose (P): Goal-oriented aspects guiding processes.

• Constructivism: Knowledge is actively constructed through cognitive processes.

• Phenomenology: Focuses on human experience and perception.

• Semiotics: Studies signs and symbols as fundamental to meaning.

• Structuralism: Emphasizes relationships within a structure.

Applying DIKWP to art movements like Cubism allows for:

• Systematic Analysis: Dissecting complex artistic concepts.

• Semantic Integration: Embedding meaning into the analysis.

• Multidimensional Understanding: Incorporating visual, cultural, and philosophical dimensions.

In Cubism, Data (D) represents the fundamental visual elements and techniques used by artists.

Let:

• $S$ be the set of semantic attributes relevant to Cubism:

  $$S=\{\text{geometric shapes},\text{multiple perspectives},\text{fragmentation},\text{overlapping planes},\text{monochromatic palette},\text{collage elements},\text{flattened space}\}$$

• $D$ be the set of data elements $d$ in Cubist artworks:

  $$D=\{d\mid \text{Attributes}(d)\supseteq S\}$$

• Geometric Shapes: Simplification of forms into cubes, spheres, cones.

• Multiple Perspectives: Depicting objects from various viewpoints simultaneously.

• Fragmentation: Breaking objects into parts to analyze their structure.

• Overlapping Planes: Intersecting surfaces to create depth and complexity.

• Monochromatic Palette: Limited color range to focus on form and structure.

• Collage Elements (Synthetic Cubism): Incorporating non-traditional materials.

• Flattened Space: Rejecting linear perspective to emphasize two-dimensionality.

Information arises from processing data $D$ with purpose $P$:

FI:D×P→IF_I: D \times P \rightarrow IFI​:D×P→I

Where:

• $D$ is the set of Cubist data elements.

• $P$ represents the artistic purpose of Cubism.

• $I$ is the set of processed artistic expressions highlighting Cubist principles.

• Analyzing Forms: Deconstructing objects to understand their underlying geometry.

• Reconstructing Reality: Reassembling fragmented elements to represent objects innovatively.

• Emphasizing Structure: Focusing on the arrangement of shapes and planes.

• Contextualizing Symbols: Incorporating cultural and symbolic elements.

Knowledge represents the structured understanding of Cubism's concepts and relationships.

Let:

• $K=(N,E)$ be a Cubist knowledge graph.

• $N$ are nodes representing concepts like form, space, perspective, abstraction.

• $E$ are edges representing relationships between these concepts.

An edge $e$ between nodes nin_ini​ and njn_jnj​ with relationship $r$:

e=(ni,nj,r)e = (n_i, n_j, r)e=(ni​,nj​,r)

• Nodes (N): Form, Space, Perspective, Geometry, Abstraction, Collage, Symbolism.

• Edges (E):

• Form $\leftrightarrow$ Geometry (represented by).

• Space $\leftrightarrow$ Flattened Perspective (redefined by).

• Abstraction $\leftrightarrow$ Multiple Perspectives (achieved through).

• Collage $\leftrightarrow$ Synthetic Cubism (characteristic of).

• Symbolism $\leftrightarrow$ Cultural References (incorporated into).

Wisdom integrates ethics, values, and philosophical insights.

Define the wisdom function $W$:

W:{D,I,K,Wprev,P}→{D′,I′,K′,Wpost,P′}W: \{ D, I, K, W_{\text{prev}}, P \} \rightarrow \{ D', I', K', W_{\text{post}}, P' \}W:{D,I,K,Wprev​,P}→{D′,I′,K′,Wpost​,P′}

• WprevW_{\text{prev}}Wprev​: Prior wisdom or philosophical context.

• WpostW_{\text{post}}Wpost​: Enhanced wisdom after processing.

• Challenging Perception: Questioning how reality is perceived and represented.

• Democratization of Art: Breaking down elitist notions of art by using everyday materials.

• Intellectual Engagement: Encouraging viewers to actively interpret artworks.

• Cultural Reflection: Incorporating elements from different cultures (e.g., African masks).

Purpose provides the guiding intentions of the Cubist movement.

Purpose $P$:

$$P=(\text{Artistic Goals},\text{Constraints},\text{Values})$$

• Artistic Goals: To revolutionize representation in art by depicting multiple perspectives and emphasizing form over content.

• Constraints: Rejection of traditional techniques, societal expectations.

• Values: Innovation, intellectual exploration, challenging conventions.

• Time Frame: Approximately 1907–1912.

• Focus: Deconstructing objects into basic geometric forms.

• Palette: Monochromatic or limited colors to emphasize structure.

• Technique: Fragmentation and overlapping planes.

Data (D):

• Shapes: Cubes, spheres, cones.

• Lines: Intersecting and overlapping to create fragmented images.

• Colors: Earth tones, grays, and browns.

Information (I):

• Form Analysis: Breaking down objects to their geometric constituents.

• Multiple Viewpoints: Simultaneously depicting different angles.

• Spatial Relationships: Exploring the relationship between form and space.

Knowledge (K):

• Nodes (N): Geometry, Perspective, Form, Space.

• Edges (E):

• Form $\leftrightarrow$ Geometry (represented by).

• Perspective $\leftrightarrow$ Multiple Viewpoints (redefined through).

Wisdom (W):

• Philosophical Insight: Reflecting on the nature of perception and reality.

• Ethical Considerations: Challenging established norms to promote intellectual freedom.

• Cultural Impact: Influencing subsequent art movements and modern art.

Purpose (P):

• Goals: To analyze and represent the essence of objects beyond their superficial appearance.

• Constraints: Traditional artistic conventions.

• Values: Intellectual rigor, exploration, and innovation.

Example Artwork:

• "Ma Jolie" (1911–1912) by Pablo Picasso

• Data: Fragmented depiction of a woman with musical elements.

• Information: Merges visual and textual elements; challenges perception.

• Knowledge: Explores the relationship between visual art and language.

• Wisdom: Invites viewers to engage intellectually with the artwork.

• Purpose: To represent complex ideas in a visual form.

• Time Frame: Approximately 1912–1914.

• Focus: Synthesizing objects using simpler shapes and brighter colors.

• Technique: Introduction of collage elements and mixed media.

• Palette: Brighter colors compared to Analytical Cubism.

Data (D):

• Materials: Newspapers, wallpapers, fabrics.

• Shapes: Simpler, more decorative forms.

• Colors: Incorporation of vivid colors.

Information (I):

• Collage Technique: Combining various materials to create new meanings.

• Symbolism: Using found objects to represent ideas.

• Abstraction: Moving away from detailed analysis to synthesis.

Knowledge (K):

• Nodes (N): Collage, Abstraction, Symbolism, Mixed Media.

• Edges (E):

• Collage $\leftrightarrow$ Mixed Media (utilized in).

• Abstraction $\leftrightarrow$ Simplified Forms (achieved through).

Wisdom (W):

• Cultural Commentary: Reflecting on consumerism and mass media.

• Democratization: Making art more accessible by using everyday materials.

• Ethical Insight: Critiquing societal norms and materialism.

Purpose (P):

• Goals: To synthesize new forms and meanings by integrating diverse materials.

• Constraints: Boundaries of traditional art materials and methods.

• Values: Innovation, inclusivity, and exploration of new artistic expressions.

Example Artwork:

• "Still Life with Chair Caning" (1912) by Pablo Picasso

• Data: Oil cloth with chair caning pattern, rope frame.

• Information: Blurs the line between reality and representation.

• Knowledge: Introduces the concept of mixed media in fine art.

• Wisdom: Challenges the notion of what constitutes art.

• Purpose: To disrupt conventional perceptions and expand artistic possibilities.

• Adaptive Framework: DIKWP accommodates the transition from Analytical to Synthetic Cubism.

• Holistic Analysis: Captures the movement's development and diversification.

• Reflective of Intentions: Aligns with the artists' evolving goals and techniques.

• Structural Understanding: Provides a clear framework to dissect complex techniques.

• Philosophical Integration: Incorporates the movement's underlying philosophical inquiries.

• Interconnected Concepts: Highlights the relationships between techniques, purposes, and cultural impacts.

• Quantitative and Qualitative Fusion: Combines mathematical rigor with artistic analysis.

• Semantic Enrichment: Embeds meaning into formal structures.

• Interdisciplinary Approach: Demonstrates the applicability of mathematical frameworks to art movements.

• Systematic Analysis: Offers a structured method to study complex art movements.

• Deeper Insights: Unveils layers of meaning and intention.

• Comparative Studies: Facilitates comparisons between different movements.

• Curriculum Development: Integrates DIKWP into art education.

• Student Engagement: Encourages active participation in art analysis.

• Critical Thinking: Enhances analytical skills through structured frameworks.

• Interdisciplinary Collaboration: Bridges art, mathematics, philosophy, and cognitive science.

• Innovative Research: Opens new avenues for studying art through mathematical models.

• Cultural Appreciation: Enhances understanding of cultural and historical contexts.

• Subjectivity of Art: Difficulties in standardizing artistic elements.

• Nuanced Interpretation: Quantitative models may not capture all artistic nuances.

• Personal Biases: Analysts' interpretations may vary.

• Cultural Differences: Meanings may differ across cultures and contexts.

• Expertise Integration: Requires knowledge from multiple disciplines.

• Resource Allocation: May need significant time and resources for comprehensive analysis.

The application of the DIKWP Semantic Mathematics framework to Cubism provides a comprehensive and systematic approach to understanding this complex art movement. By dissecting Cubism through Data, Information, Knowledge, Wisdom, and Purpose, we gain profound insights into its principles, techniques, and philosophical foundations.

This approach not only validates the DIKWP model but also demonstrates its effectiveness in explaining artistic movements. It bridges the gap between mathematical formalism and artistic expression, offering valuable tools for education, research, and cross-disciplinary collaboration.

The DIKWP framework enhances our appreciation of Cubism, highlighting its innovative contributions to art and its enduring impact on how we perceive and represent reality.

1. Antliff, M., & Leighten, P. Cubism and Culture. Thames & Hudson, 2001.

2. Chipp, H. B. Theories of Modern Art. University of California Press, 1968.

3. Duan, Y. Proposals on DIKWP Semantic Mathematics. [Online resource].

4. Golding, J. Cubism: A History and an Analysis, 1907–1914. Belknap Press, 1988.

5. Harrison, C., & Wood, P. Art in Theory 1900–2000: An Anthology of Changing Ideas. Wiley-Blackwell, 2003.

6. Léal, B., Piot, C., & Bernadac, M.-L. The Ultimate Picasso. Harry N. Abrams, 2000.

7. Richardson, J. A Life of Picasso. Random House, multiple volumes, 1991–2007.

8. Rubin, W. S. Picasso and Braque: Pioneering Cubism. The Museum of Modern Art, 1989.

9. Stepanova, T. Mathematics and Art: A Cultural History. Princeton University Press, 2015.

10. Additional scholarly articles on Cubism and the application of mathematical models in art analysis.

Final Remarks:

The comprehensive analysis of Cubism using the DIKWP Semantic Mathematics framework illustrates the model's versatility and depth. By methodically applying each component—Data, Information, Knowledge, Wisdom, and Purpose—we have unpacked the complexities of Cubism, providing clarity and insight into its revolutionary approach to art. This methodology not only enhances our understanding of Cubism but also sets a precedent for analyzing other art movements, fostering a richer dialogue between art, mathematics, and human cognition.