Detail from an Impression Figure by Margaret Watts Hughes, pigment on glass, date unknown (recolored). Courtesy of Cyfarthfa Castle Museum and Art Gallery via

Intelligence & Representation:

Models of the world in natural and artificial systems


Program OverviewDates & TimesTuition & FeesProgram GoalsVenueFacultyAudienceApplication Requirements


Program Overview

How do living systems encode reality?

The study of the representation of the world in the service of strategic goals using mechanisms of inference has been the subject of intelligence research for several centuries.

When George Romanes wrote his foundational monograph on Animal Intelligence in 1884 he sought to place intelligence squarely in a comparative Darwinian framework, concluding that “Wherever we find an animal able to do this, we have the same right to predicate mind as existing in such an animal that we have to predicate it as existing in any human being other than ourselves”.

In the twentieth century the study of intelligence was dominated by consideration of the special character of the human species. Binet’s research on the IQ, Cattell’s investigations of ability, and the growing dependence on analytical tasks to include language, mathematics and puzzles – from  Chomsky to Simon -  moved the study of intelligence away from the larger questions of strategic representation towards rather small corners of  human activity. 

Moreover the field has contracted into an almost exclusive emphasis on inference, to include reinforcement learning, Bayesian updating, and most recently, a veritable zoo of gradient-based approaches to training classifiers and neural networks. Questions of collective intelligence, how the brain-mind-culture nexus is developed, and the larger domain of inquiries into the nature of representation have been relatively neglected. 

In parallel to developments in the mind and brain sciences, historians,  philosophers, humanists and artists have explored turning points and revolutions in our representation of reality. From our formal representation of form in art from perspective to iconology (e.g Panofsky), the representations of time in mechanics (e.g Galison) and narrative (e.g. Jakobson), and  the question of realism and abstraction in art (e.g. Miller).

This school seeks to place the study of representation at the center of questions of intelligence. Analyzing and extending modern empirical and mathematical theories of representation are at its core. Profound work in the humanities will also be included to both inform and extend the analysis. 

There are also social and ethical implications of this inquiry into the representational dimensions of intelligence. 

As human society becomes increasingly reliant on AI to augment our cognitive capacities and simultaneously attentive to identifying intelligence in other species or lifeforms, progress in these areas requires a consilient definition of intelligence. At the center of this challenge is the special role that understanding plays in human intelligence and the role that it will play in larger collective and hybrid settings. How can we speak of fairness and justice without an understanding of what this means in a hybrid intelligence?

We need to move beyond human-centric qualifications toward a more nuanced and pluralistic understanding of how diverse systems represent and select among the breadth of possible rules by which to solve problems. An understanding of intelligence should be able to extend across scales – from neural circuits underlying sensory encodings in the brain to the psychology of learning and memory – and across domains – from AI forms of representation to philosophical and artistic facets of knowledge. The challenge is considerable, but without including diverse communities it is bound to become too narrow and parochial. 

Ph.D. students are invited to spend two weeks, among an international cohort of students and faculty, addressing key open questions and challenges in understanding intelligence and the nature of representation. A broad historical context will frame the inquiry within humanistic and quantitative perspectives. A key element of this school is to give the same weight to the origin or creation of representations and coding as is given to matters of inference.

The curriculum will combine lectures, workshops, reading groups, and formal and informal discussion. Bringing together perspectives from neuroscience, mathematics, computation, arts, and philosophy, among others, students and faculty will explore natural and artificial intelligences. Specific topics to be covered include: brain and cognition, definitions of intelligence, and knowledge systems. Workshops and group work will provide deeper experience with key questions and challenges and a range of approaches by which to address these. In addition to acquiring skills to use in their own research, students will grow their global scientific network and experience the research culture of the EU-UK.

This program is a partnership between the Santa Fe Institute and the Max Planck Institute for Mathematics in the Sciences and Hamburg University of Technology (Germany), Complexity Science Hub Vienna (Austria), Quantitative Life Sciences, International Center for Theoretical Physics (Italy), and Institute for Advanced Studies, University of Amsterdam (Netherlands). In 2023, the program is generously hosted by the Isaac Newton Institute for Mathematical Sciences.

Dates & Times

August 13 – August 25, 2023, plus travel days.

The institute is a full-time (all-day) commitment. Participants are expected to attend the entire program.

Tuition & Fees

There is no tuition for this program.

Students eligible for NSF support – US citizens or permanent residents – will receive an allowance to cover their travel, housing and meals throughout the program, i.e. there is no cost for these students. All other students will be eligible for travel/housing awards made possible through Complexity-GAINs partners; campus accommodations are available at approximately £85 per night.

Program Support   This program is made possible, in part, through the support of the National Science Foundation under Grant No. 2106013 (PI David Krakauer), IRES Track II: Complexity advanced studies institute - Germany, Austria, Italy, Netherlands (Complexity-GAINs). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the investigator(s) and do not necessarily reflect the views of the National Science Foundation.

Program Goals
  • Assess current and future research directions in intelligent systems
  • Understand the research process by which to integrate theory, modeling and empirical analyses
  • Enhance mathematical and computational modeling capacity
  • Establish international collaborations and connections
  • Enrich the diversity of the complex systems research community

The summer school takes place in Cambridge UK, an exceptional scholarly center with a long history of fundamental contributions to the sciences and arts. Sessions are held at the Isaac Newton Institute, convenient to the city center. Participants are accommodated in guest lodgings within easy reach of the institute and Cambridge's numerous historical, cultural and entertainment amenities.


David Krakauer portrait by Kate Joyce

The summer school Director for 2023 is:
David Krakauer, President and William H. Miller Professor of Complex Systems at the Santa Fe Institute. David's research explores the evolution of intelligence and stupidity on Earth. This includes studying the evolution of genetic, neural, linguistic, social, and cultural mechanisms supporting memory and information processing, and exploring their shared properties.

Faculty include: 


Nihat Ay, SFI professor and Head of the Institute for Data Science Foundations at Hamburg University of Technology (DE). Nihat is a mathematician with particular expertise in information geometry. His work centers on theories of learning and embodied intelligence.

portrait of Erica

Erica Cartmill, professor of anthropology and developmental psychology at University of California, Los Angeles (US). Erica studies the acquisition and evolution of human language and in particular how the multimodal aspects of communication contribute and constrain the construction of meaning.


Jessica Flack, SFI professor and director of the Collective Computation group at SFI. Jessica's work aims to understand how nature collectively computes solutions to problems and how these solutions are refined in evolutionary and learning time.

portrait of Jacob

Jacob Foster, professor of sociology at University of California, Los Angeles (US). Jacob's interests lie in the social production of collective intelligence, evolutionary dynamics of ideas, and the co-construction of culture and cognition.


John Krakauer, SFI external professor, professor of neurology at Johns Hopkins School of Medicine (US), and director of the BLAM Lab. John has particular expertise in sensori- and visuo-motor learning and memory representations.


Melanie Mitchell, the Davis Professor of Complexity at SFI. Melanie's current research focuses on conceptual abstraction, analogy-making, and visual recognition in artificial intelligence systems.

Orit Orit Peleg, SFI external professor and professor of computer science and in the BioFrontiers Institute at University of Colorado, Boulder (US). Orit is a biophysist interested in collective behaviors and sensing in living systems.

with others to be announced.


The summer school welcomes Ph.D. students from the physical, natural, and quantitative social sciences, mathematics, philosophy, and adjacent domains. Prior experience with computational or mathematical modeling is not required. A serious interest in the topic of intelligence and representation is essential. Students are expected to be full contributors to the school and engage actively in discussion and debate. The program is limited to no more than 26 students.


  • Students must be enrolled in an accredited, degree-granting Ph.D. program.
  • Students should have completed at least one year of Ph.D. coursework and have defined and be pursuing their thesis research, or have completed a substantial independent research project as part of their degree.
  • Students should not yet be in the final stages of their dissertation, e.g. should not be scheduled to defend.
  • SFI policy requires participants to provide proof of COVID-19 vaccination prior to beginning the program.

The Complexity-GAINs team is committed to offering inclusive educational programs in which all participants feel valued and supported in their learning journey. We believe that human diversity in all of its dimensions is essential to meaningful scientific progress. We believe that open discourse and respectful sharing of broad perspectives is essential for understanding our world and worlds beyond. We work to ensure our educational programs reflect and encourage this diversity and inclusivity, and we welcome you to join us.

Application Requirements

During the application period, access the application through the "Apply now" button.

Applicants should provide:

  • Biographical information (filled out directly in the application portal)
  • Current academic cv, including list of publications, if any
  • Two letters of recommendation, including at least one from your thesis advisor or a member of your thesis committee.
  • Research statement, describing your thesis research and how the theme of the school intersects with your current work or future research directions you might undertake. (max. 1 page)
  • Personal statement, describing your motivation for participation in the Complexity-GAINs program. The statement should specifically address the international aspect of the program and how this relates to your broader professional/career goals. (max. 1 page)

Complexity-GAINs International Summer School takes place in:

  • 2022 – socio-behavioral systems
  • 2023 – intelligent systems
  • 2024 – ecosystems