KIM WILLIAMS - Academia.edu (original) (raw)

Papers by KIM WILLIAMS

Humanistic Mathematics Network Journal, 1998

It is often stated that ancient architectural monuments such as the Pantheon were constructed as ... more It is often stated that ancient architectural monuments such as the Pantheon were constructed as models of the Cosmos. An integral part of that interpretation is the notion that the architectural form of the dome represents the heavens. Ancient cultures created two kinds of models for the universe: analogue models represent their objects through physical resemblance;' digital models represent their objects as functions of time. While the idea of roundness appears to be one of the primordial distinctions made with regards to the heavens, round buildings present particular problems that the architect has to solve before he is able to construct a round building as a cosmic model. This paper traces ideas of roundness and the notion of heavenly events as a function of time in ancient culture. It examines the nature of circular and spherical forms as structure. Finally, this information is applied to an analysis of the Pantheon in order to reveal its triumph over of structural problem...

Nexus Network Journal, 2021

Editor-in-Chief Kim Williams examines the way intersections of architecture and mathematics in an... more Editor-in-Chief Kim Williams examines the way intersections of architecture and mathematics in ancient architecture are being brought to light thanks to increased information and new technologies, and introduces the articles in Nexus Network Journal vol. 23 no. 2 (2021). Keywords Nexus Network Journal • Methods of laying out • Methods of analysis Despite centuries of studies and scholars' best efforts at understanding, many mysteries still shroud the fragments of ancient buildings and cities that have come down to us. Today, new light is being shed on artifacts that have eluded earlier attempts at explanation. This is due in part to a new wealth of information placed at our fingertips thanks to advances such as drone photography and satellite observation, made available by sites such as Google Earth and GeoEye. It is also due to new technologies capable of capturing massive data, leading to new means of visualization and analysis such as point clouds. However, most advances in our understanding are due to researchers' persistence in studying, deconstructing, reconstructing and decoding, using whatever means provides them with the most information. This issue of the Nexus Network Journal presents a collection of research on built artifacts of epochs going as far back as 1500 BC, and ranging geographically from Europe to Egypt, from the Middle to the Far East. The topics addressed fall, broadly speaking, into two main groups. The first is concerned with techniques of laying out, that is, how mathematical knowledge was applied in disposing elements into a meaningful patterns of order. The second deals with methods of analysis that allow us to identify and build upon such patterns of order.

It is a great pleasure to write a paper about architecture and mathematics on the occasion of the... more It is a great pleasure to write a paper about architecture and mathematics on the occasion of the conference, Bridges: Mathematical Connections in Art, Music and Science. It is architecture's intimate relationship to mathematics that underscores its ties to art, music and science. The subject is too vast to lie within the range of a single discussion; this paper will look at some facets of these various relationships with the aim of introducing the reader to ideas meriting further study.

Nexus Network Journal, 2017

Nexus Network Journal, 2016

Nexus Network Journal, 2014

Alberti's contribution to the nascent science of fortifications in the 1450s is often ignored, bu... more Alberti's contribution to the nascent science of fortifications in the 1450s is often ignored, but a careful reading of his descriptions of fortifications show that he was the first to describe the elements of fortification formally in the precise mathematical terms of shape, measurements, relationships, proportions. In forming his ideas, Alberti embraced both the old and the new. The old he reelaborated and set in modern terms, and although he cites numerous ancient authors as sources for his information about fortifications, the obvious historical source for Alberti's description of the elements of fortification is Vitruvius. On the other hand, Vitruvius alone cannot account for all of Alberti's knowledge of military architecture. Plans with well-define geometric shapes, solid walls, scarped bases, curtains, towers open to the interior appropriated located on the bases of flanks, loopholes for grazing fire conjoined to systems of defense for dropping stones and other missiles vertically, structures in earth: all of these show that Alberti was in possession of a thorough knowledge of the state of fortifications in his day. All of these features are present in fortresses that had been built some years earlier based on designs attributed to Filippo Brunelleschi. We examine the fortress at Vicopisano to show a built example that Alberti may have seen and drawn on.

Nexus Network Journal, 2015

Since its very inception, the Nexus Network Journal has reported on analysis. Analysis at all pha... more Since its very inception, the Nexus Network Journal has reported on analysis. Analysis at all phases of a building's life, from concept to built artefact to ruin, brings to light the many roles that mathematics can play in architecture-symbolic, governing, ordering. This issue of the NNJ is dedicated to a wide range of analytical techniques and results. Of the group of papers presented here, about half were presented during the course of the tenth international, interdisciplinary conference ''Nexus 2014: Relationships Between Architecture and Mathematics'', which took place from 9 to 12 June 2014 in Ankara, Turkey, hosted by the Department of Architecture of Middle Eastern Technical University (METU). All of these articles clearly demonstrate the fundamental importance of analysis for our field. While the researcher can choose among a plethora of techniques for analysis, two approaches can be distinguished. On the one hand, contemporary methods and techniques are able to provide us with information about ancient works of architecture that could never be obtained before, and are thus valuable, even though such methods were unknown (even undreamed of) by the original architects. On the other hand, some researchers prefer to conduct analyses using only the techniques and tools that period architects and artisans might have used, and these can still lead to original results. Both of these approaches are found in this issue, along with a wide variety of tools, methods and techniques. Two papers in this issue exemplify what I mean. In keeping with the venue of the Nexus 2014 conference, two papers presented in Ankara concerned works of Ottoman architecture from the same historic period. At the same time, they are

Crossroads: History of Science, History of Art, 2011

The subject I am going to talk about here belongs, one may say, to the prehistory of descriptive ... more The subject I am going to talk about here belongs, one may say, to the prehistory of descriptive geometry: it is part of our modem discovery of space. Three times a civilization has made such an investigation: in ancient Egypt, in Antiquity, and in modern times, where perhaps we should speak of space-time. And each time, not only science, but the arts participated in this endeavor as well. It is always extremely interesting to compare the progress of the sciences with the evolution of the arts, as well as their histories, their results, and their methods. But it is fair to say that in spite of many valiant pioneering efforts, so far this has not been done systematically enough: think for instance of medieval architecture and its importance for the progress of technology and science.

Religion and the Arts, 1998

Nexus Network Journal, 2013

Nexus Network Journal, 2014

Editor-in-Chief Kim Williams opens volume 16 number 1 (Winter 2014) of the Nexus Network Journal ... more Editor-in-Chief Kim Williams opens volume 16 number 1 (Winter 2014) of the Nexus Network Journal by presenting new developments for this journal, including the introduction of Michael J. Ostwald as co-Editor-in-Chief. Volume 16 (2014) of the Nexus Network Journal ushers in a new phase for our publication, which I am pleased to introduce to our readers. First of all, I am very happy to announce that Michael J. Ostwald of the University of Newcastle is now collaborating with me as Co-Editor-in-Chief of the NNJ. I have been covering this role on my own since the journal's founding in 1999, and welcome not only helping hands and eyes, but a fresh outlook and second perspective on both the journal and the field it serves. When the NNJ was founded the discipline of architecture and mathematics did not even exist as such, and now it is acknowledged and thriving around the globe. Michael began his collaboration with the Nexus conferences and the NNJ in 1998, when he presented a paper at the second Nexus conference, which took place in Mantua,

Nexus Network Journal, 2012

Nexus Network Journal, 2013

Nexus Network Journal, 2002

The fourth conference in the Nexus series for architecture and mathematics shared with its predec... more The fourth conference in the Nexus series for architecture and mathematics shared with its predecessors the cordial, stimulating atmosphere that has characterized Nexus since the beginning, as well as the truly international, interdisciplinary roster of participants and speakers. Participants came from Portugal, Italy,

Nexus Network Journal, 2010

Nexus Network Journal, 2009

Two recent projects for a first-year course in drawing for architecture students have been organi... more Two recent projects for a first-year course in drawing for architecture students have been organized by Sylvie Duvernoy, Michela Rossi and Kay Bea Jones. The first, a four-phase program centering around a tour of the architecture of the Midwest in the United States, was implemented in Spring 2008. The second, a day-long seminar on designs for temporary architecture, took place in December 2008. In both, the use of mathematical concepts to provide an underlying organization for the generation of architectural form was fundamental.

Nexus Network Journal, 2009

The Story of Science is a book series by Joy Hakim of which the first three volumes are now avail... more The Story of Science is a book series by Joy Hakim of which the first three volumes are now available-Aristotle Leads the Way (2004), Newton at the Center (2005) and Einstein Adds a New Dimension (2007)-and three more are planned. The books represent an ongoing project aimed at teaching science in a way that is both specific and interdisciplinary. Kim Williams discussed the project and its goals with author Joy Hakim and art scholar Sabine Russ, who chose the illustrations for the books.

Nexus Network Journal, 2009

Nexus Network Journal, 2012

NNJ editor-in-chief Kim Williams introduces the papers in NNJ vol. 14, no. 2 (Autumn 2012).

Humanistic Mathematics Network Journal, 1998

It is often stated that ancient architectural monuments such as the Pantheon were constructed as ... more It is often stated that ancient architectural monuments such as the Pantheon were constructed as models of the Cosmos. An integral part of that interpretation is the notion that the architectural form of the dome represents the heavens. Ancient cultures created two kinds of models for the universe: analogue models represent their objects through physical resemblance;' digital models represent their objects as functions of time. While the idea of roundness appears to be one of the primordial distinctions made with regards to the heavens, round buildings present particular problems that the architect has to solve before he is able to construct a round building as a cosmic model. This paper traces ideas of roundness and the notion of heavenly events as a function of time in ancient culture. It examines the nature of circular and spherical forms as structure. Finally, this information is applied to an analysis of the Pantheon in order to reveal its triumph over of structural problem...

Nexus Network Journal, 2021

Editor-in-Chief Kim Williams examines the way intersections of architecture and mathematics in an... more Editor-in-Chief Kim Williams examines the way intersections of architecture and mathematics in ancient architecture are being brought to light thanks to increased information and new technologies, and introduces the articles in Nexus Network Journal vol. 23 no. 2 (2021). Keywords Nexus Network Journal • Methods of laying out • Methods of analysis Despite centuries of studies and scholars' best efforts at understanding, many mysteries still shroud the fragments of ancient buildings and cities that have come down to us. Today, new light is being shed on artifacts that have eluded earlier attempts at explanation. This is due in part to a new wealth of information placed at our fingertips thanks to advances such as drone photography and satellite observation, made available by sites such as Google Earth and GeoEye. It is also due to new technologies capable of capturing massive data, leading to new means of visualization and analysis such as point clouds. However, most advances in our understanding are due to researchers' persistence in studying, deconstructing, reconstructing and decoding, using whatever means provides them with the most information. This issue of the Nexus Network Journal presents a collection of research on built artifacts of epochs going as far back as 1500 BC, and ranging geographically from Europe to Egypt, from the Middle to the Far East. The topics addressed fall, broadly speaking, into two main groups. The first is concerned with techniques of laying out, that is, how mathematical knowledge was applied in disposing elements into a meaningful patterns of order. The second deals with methods of analysis that allow us to identify and build upon such patterns of order.

It is a great pleasure to write a paper about architecture and mathematics on the occasion of the... more It is a great pleasure to write a paper about architecture and mathematics on the occasion of the conference, Bridges: Mathematical Connections in Art, Music and Science. It is architecture's intimate relationship to mathematics that underscores its ties to art, music and science. The subject is too vast to lie within the range of a single discussion; this paper will look at some facets of these various relationships with the aim of introducing the reader to ideas meriting further study.

Nexus Network Journal, 2017

Nexus Network Journal, 2016

Nexus Network Journal, 2014

Alberti's contribution to the nascent science of fortifications in the 1450s is often ignored, bu... more Alberti's contribution to the nascent science of fortifications in the 1450s is often ignored, but a careful reading of his descriptions of fortifications show that he was the first to describe the elements of fortification formally in the precise mathematical terms of shape, measurements, relationships, proportions. In forming his ideas, Alberti embraced both the old and the new. The old he reelaborated and set in modern terms, and although he cites numerous ancient authors as sources for his information about fortifications, the obvious historical source for Alberti's description of the elements of fortification is Vitruvius. On the other hand, Vitruvius alone cannot account for all of Alberti's knowledge of military architecture. Plans with well-define geometric shapes, solid walls, scarped bases, curtains, towers open to the interior appropriated located on the bases of flanks, loopholes for grazing fire conjoined to systems of defense for dropping stones and other missiles vertically, structures in earth: all of these show that Alberti was in possession of a thorough knowledge of the state of fortifications in his day. All of these features are present in fortresses that had been built some years earlier based on designs attributed to Filippo Brunelleschi. We examine the fortress at Vicopisano to show a built example that Alberti may have seen and drawn on.

Nexus Network Journal, 2015

Since its very inception, the Nexus Network Journal has reported on analysis. Analysis at all pha... more Since its very inception, the Nexus Network Journal has reported on analysis. Analysis at all phases of a building's life, from concept to built artefact to ruin, brings to light the many roles that mathematics can play in architecture-symbolic, governing, ordering. This issue of the NNJ is dedicated to a wide range of analytical techniques and results. Of the group of papers presented here, about half were presented during the course of the tenth international, interdisciplinary conference ''Nexus 2014: Relationships Between Architecture and Mathematics'', which took place from 9 to 12 June 2014 in Ankara, Turkey, hosted by the Department of Architecture of Middle Eastern Technical University (METU). All of these articles clearly demonstrate the fundamental importance of analysis for our field. While the researcher can choose among a plethora of techniques for analysis, two approaches can be distinguished. On the one hand, contemporary methods and techniques are able to provide us with information about ancient works of architecture that could never be obtained before, and are thus valuable, even though such methods were unknown (even undreamed of) by the original architects. On the other hand, some researchers prefer to conduct analyses using only the techniques and tools that period architects and artisans might have used, and these can still lead to original results. Both of these approaches are found in this issue, along with a wide variety of tools, methods and techniques. Two papers in this issue exemplify what I mean. In keeping with the venue of the Nexus 2014 conference, two papers presented in Ankara concerned works of Ottoman architecture from the same historic period. At the same time, they are

Crossroads: History of Science, History of Art, 2011

The subject I am going to talk about here belongs, one may say, to the prehistory of descriptive ... more The subject I am going to talk about here belongs, one may say, to the prehistory of descriptive geometry: it is part of our modem discovery of space. Three times a civilization has made such an investigation: in ancient Egypt, in Antiquity, and in modern times, where perhaps we should speak of space-time. And each time, not only science, but the arts participated in this endeavor as well. It is always extremely interesting to compare the progress of the sciences with the evolution of the arts, as well as their histories, their results, and their methods. But it is fair to say that in spite of many valiant pioneering efforts, so far this has not been done systematically enough: think for instance of medieval architecture and its importance for the progress of technology and science.

Religion and the Arts, 1998

Nexus Network Journal, 2013

Nexus Network Journal, 2014

Editor-in-Chief Kim Williams opens volume 16 number 1 (Winter 2014) of the Nexus Network Journal ... more Editor-in-Chief Kim Williams opens volume 16 number 1 (Winter 2014) of the Nexus Network Journal by presenting new developments for this journal, including the introduction of Michael J. Ostwald as co-Editor-in-Chief. Volume 16 (2014) of the Nexus Network Journal ushers in a new phase for our publication, which I am pleased to introduce to our readers. First of all, I am very happy to announce that Michael J. Ostwald of the University of Newcastle is now collaborating with me as Co-Editor-in-Chief of the NNJ. I have been covering this role on my own since the journal's founding in 1999, and welcome not only helping hands and eyes, but a fresh outlook and second perspective on both the journal and the field it serves. When the NNJ was founded the discipline of architecture and mathematics did not even exist as such, and now it is acknowledged and thriving around the globe. Michael began his collaboration with the Nexus conferences and the NNJ in 1998, when he presented a paper at the second Nexus conference, which took place in Mantua,

Nexus Network Journal, 2012

Nexus Network Journal, 2013

Nexus Network Journal, 2002

The fourth conference in the Nexus series for architecture and mathematics shared with its predec... more The fourth conference in the Nexus series for architecture and mathematics shared with its predecessors the cordial, stimulating atmosphere that has characterized Nexus since the beginning, as well as the truly international, interdisciplinary roster of participants and speakers. Participants came from Portugal, Italy,

Nexus Network Journal, 2010

Nexus Network Journal, 2009

Two recent projects for a first-year course in drawing for architecture students have been organi... more Two recent projects for a first-year course in drawing for architecture students have been organized by Sylvie Duvernoy, Michela Rossi and Kay Bea Jones. The first, a four-phase program centering around a tour of the architecture of the Midwest in the United States, was implemented in Spring 2008. The second, a day-long seminar on designs for temporary architecture, took place in December 2008. In both, the use of mathematical concepts to provide an underlying organization for the generation of architectural form was fundamental.

Nexus Network Journal, 2009

The Story of Science is a book series by Joy Hakim of which the first three volumes are now avail... more The Story of Science is a book series by Joy Hakim of which the first three volumes are now available-Aristotle Leads the Way (2004), Newton at the Center (2005) and Einstein Adds a New Dimension (2007)-and three more are planned. The books represent an ongoing project aimed at teaching science in a way that is both specific and interdisciplinary. Kim Williams discussed the project and its goals with author Joy Hakim and art scholar Sabine Russ, who chose the illustrations for the books.

Nexus Network Journal, 2009

Nexus Network Journal, 2012

NNJ editor-in-chief Kim Williams introduces the papers in NNJ vol. 14, no. 2 (Autumn 2012).