*Alex Preda*

- Published in print:
- 2009
- Published Online:
- February 2013
- ISBN:
- 9780226679310
- eISBN:
- 9780226679334
- Item type:
- chapter

- Publisher:
- University of Chicago Press
- DOI:
- 10.7208/chicago/9780226679334.003.0004
- Subject:
- Sociology, Culture

This chapter examines the emergence and consequences of a vernacular “science of financial investments.” While many eighteenth-century writers saw financial knowledge as devilish and destructive ...
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This chapter examines the emergence and consequences of a vernacular “science of financial investments.” While many eighteenth-century writers saw financial knowledge as devilish and destructive (centered upon the bodily and verbal skills required by street transactions), these new authors set out to build a science of investments grounded in observation and calculation. Among the main outcomes of this process are the rationalization of investor behavior and the representation of financial markets as supra-individual, quasi-natural entities, which cannot be controlled by any group. It is the latter notion which allowed for the shift to price behavior as the core actor of abstract market models. The effort to transform investment knowledge into a science is crowned by the formulation of basic views of the random walk hypothesis. The first mathematical formulation of the random walk hypothesis plays a decisive role in the development of mathematical finance (more specifically, of the options pricing theory). The main tenet of the random walk hypothesis is that securities prices move independently of each other, and that future movements do not depend on past movements. One of the most important implications of this hypothesis is that in the long run, the market cannot be controlled by any group or person.Less

This chapter examines the emergence and consequences of a vernacular “science of financial investments.” While many eighteenth-century writers saw financial knowledge as devilish and destructive (centered upon the bodily and verbal skills required by street transactions), these new authors set out to build a science of investments grounded in observation and calculation. Among the main outcomes of this process are the rationalization of investor behavior and the representation of financial markets as supra-individual, quasi-natural entities, which cannot be controlled by any group. It is the latter notion which allowed for the shift to price behavior as the core actor of abstract market models. The effort to transform investment knowledge into a science is crowned by the formulation of basic views of the random walk hypothesis. The first mathematical formulation of the random walk hypothesis plays a decisive role in the development of mathematical finance (more specifically, of the options pricing theory). The main tenet of the random walk hypothesis is that securities prices move independently of each other, and that future movements do not depend on past movements. One of the most important implications of this hypothesis is that in the long run, the market cannot be controlled by any group or person.

*Hanoch Gutfreund and Jürgen Renn*

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691174631
- eISBN:
- 9781400888689
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691174631.003.0016
- Subject:
- Physics, History of Physics

This chapter shows how Einstein has developed and described the mathematical apparatus that is necessary to formulate the physical contents of the general theory of gravity. It first discusses the ...
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This chapter shows how Einstein has developed and described the mathematical apparatus that is necessary to formulate the physical contents of the general theory of gravity. It first discusses the transition from the special to the general relativity principle. According to Einstein's understanding of such a general relativity principle, physical laws are independent of the state of motion of the reference space in which they are described. The chapter argues that such a generalization of the relativity principle to include accelerated reference frames is possible because all inertial effects caused by acceleration can be alternatively attributed to the presence of a gravitational field. The model of a rotating disk is then used to show that general relativity implies non-Euclidean geometry and that the gravitational field is represented by curved spacetime. After the introduction of these basic concepts and principles, the chapter presents the mathematical formulation of the theory.Less

This chapter shows how Einstein has developed and described the mathematical apparatus that is necessary to formulate the physical contents of the general theory of gravity. It first discusses the transition from the special to the general relativity principle. According to Einstein's understanding of such a general relativity principle, physical laws are independent of the state of motion of the reference space in which they are described. The chapter argues that such a generalization of the relativity principle to include accelerated reference frames is possible because all inertial effects caused by acceleration can be alternatively attributed to the presence of a gravitational field. The model of a rotating disk is then used to show that general relativity implies non-Euclidean geometry and that the gravitational field is represented by curved spacetime. After the introduction of these basic concepts and principles, the chapter presents the mathematical formulation of the theory.

*Thomas P. Trappenberg*

- Published in print:
- 2019
- Published Online:
- January 2020
- ISBN:
- 9780198828044
- eISBN:
- 9780191883873
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198828044.003.0001
- Subject:
- Neuroscience, Behavioral Neuroscience

This chapter provides a high-level overview of machine learning, in particular how it is related to building models from data. It starts with placing the basic concept in its historical context and ...
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This chapter provides a high-level overview of machine learning, in particular how it is related to building models from data. It starts with placing the basic concept in its historical context and phrases the learning problem in a simple mathematical term as function approximation as well as in a probabilistic context. In contrast to more traditional models, machine learning can be characterized as non-linear regression in high-dimensional spaces. This chapter points out how diverse subareas such as deep learning and Bayesian networks fit into the scheme of things and motivates further study with some examples of recent progress.Less

This chapter provides a high-level overview of machine learning, in particular how it is related to building models from data. It starts with placing the basic concept in its historical context and phrases the learning problem in a simple mathematical term as function approximation as well as in a probabilistic context. In contrast to more traditional models, machine learning can be characterized as non-linear regression in high-dimensional spaces. This chapter points out how diverse subareas such as deep learning and Bayesian networks fit into the scheme of things and motivates further study with some examples of recent progress.