February 2024
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2 Reads
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February 2024
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2 Reads
February 2024
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17 Reads
The 2022 Prizes from the International Mathematical Union featured two focusing on mathematical physics: a Fields Medal to Hugo Duminil-Copin, and the Carl Friedrich Gauss Prize for Applications of Mathematics to Elliott H. Lieb. Duminil-Copin (and his teacher, Stanislav Smirnov, 2010 Fields Medal) developed rigorous ways of thinking of a lattice at its critical local connection probability that leads to a path through the lattice (Fig. 2.1). They employed a discrete complex analysis. Then, they develop ingenious ways of describing that lattice at the critical point, ways amenable to rigorous mathematical proof. In a lifetime of work, Lieb has employed mathematics as the usual physicists’ starting point to reveal the physics. For example, Lieb and collaborators (1964) showed how that Ising lattice might be thought of as a quantum field theory (with annihilation and creation operators). Themes are: Technique is physical. Rigor is revealing. Tricks are physical. And, mathematical physics often leads to deep mathematics.
February 2024
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3 Reads
The practice of mathematics applied to physics, more particularly mathematical physics, leads to demands for explicitness and rigor. The features of this practice are in effect unavoidable—although derivations of the same fact may go by different routes. Rigor matters substantively.
February 2024
Much as The Creation happens in the Hebrew Bible: There is Nothing, what we call a vacuum. And then there is Something: orderliness, when there was symmetry; particular particles when there was none of that sort before.
February 2024
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1 Read
Many mathematical or physical paper would seem to magically go from one line to the next, the reader unable to figure out the logic of the transition. Such legerdemain, whether it be magical or in doing physics, is no less impressive if you know how it is done, for you yourself would have to train extensively to actually perform these sleights of hand. What you might have ignored turns out to have needed informed careful attention. Yet, to be struck by legerdemain you must have actually read the paper, so that the device or method would stop you cold. Where did that come from? How do you get from line A to line A + 1? (I should note that much of the discussion below will benefit from having those papers in front of you.)
February 2024
Kinship and Particles; Primes and Particles; Effective Field Theory; Packaging Functions Connecting Spectra to Symmetries; Multiples Ways of Computing Partition Functions; Algebraic, Arithmetic, Analytic; The Right Particles or Parts.
February 2024
Packaging spectra leads to insight about structure. And various modes of packaging, leading to the same packaging function, reveal surprising features of the packaged system.
February 2024
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7 Reads
Mathematics and physics have been borrowing notions from each other for a very long time. Some mathematical object or construction provides a superb model of the physical world. Some physical account instantiates a more general mathematical object or construction, avant la lettre, that mathematical notion only then discovered. Abstract mathematical constructions are found to be useful by physicists, sometimes decades after the mathematicians have lost interest in them. Physical theories develop as they will, while across town, there is mathematics that will enlighten the physicist—but by chance such enlightenment may take place, if it does, decades later than would be ideal.
November 2022
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16 Reads
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1 Citation
Optical Engineering
September 2020
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2 Reads
The two-dimensional Ising model of a ferromagnet allows for many ways of computing its partition function and other properties. Each way reveals surprising features of what we might call Ising Matter. Moreover, the various ways would appear to analogize with the mathematical threefold analogy of analysis, algebra, and arithmetic, due to R. Dedekind and H. Weber, 1882, and more recently described by A. Weil.
... For an insurance company, the insurance clerk not only needs to master the coverage and amount of each type of insurance but also requires the insurance clerk to master each customer's purchase of insurance. rough these professional knowledge and situations, insurance salesmen need to do their best to sell insurance [5][6][7]. It can be seen from the above description that the data of insurance business is numerous, multisource, and complex, which is a difficult task for insurance business, that consumes a lot of human and material resources [8]. ...
April 2018
Journal of Planning Education and Research
... Trahan's attitude is close to the way that mathematicians treat long proofs. By the 1980s, according to Krieger (2004), a variety of rigorous proofs were provided of various fundamental facts about our world, many of them lengthy and complex and involving much calculation (Krieger, 2004): ...
November 2004
Notices of the American Mathematical Society
... The proposed CAS theory has provided new ideas for people to recognize, control, and manage complex systems, and is widely used in economic systems, ecosystems, and social systems (Auyang, 1999a(Auyang, , 1999bGuo, 2017;Krieger, 2001). The study of complexity is also valued by Chinese scholars, whose research on the science of complexity mainly covers the three aspects of methodology, mathematical theory, and application, and involves many subjects including geography, economics, biology, physics, management and philosophy (Comfort, 1999;Song, 2005). ...
March 2001
Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern Physics
... Representations are human inventions/constructs that stand in for the phenomena (Morgan and Morrison, 1999;Giere, 2005;Frigg and Hartmann, 2006;Windschitl et al., 2008;Schwarz et al., 2009). In physics, common types of representations include graphs, vector diagrams, equations, simulations, words, and pictures (Krieger, 1987). From the MI perspective, this means that instruction should focus on helping students to identify, use, and interpret representational tools that are useful in describing physical systems. ...
November 1987
American Journal of Physics
... Buck-Morss argues that the sensorium can be understood as a "form of cognition, achieved through taste, touch, hearing, seeing, smell-the whole corporeal sensorium" (Buck-Morss, 1992, p. 6). The idea of the urban sensorium, therefore, is fairly straightforward and is drawn from an understanding of developing a sense of the city through the five senses: sight, sound, smell, taste and touch (Krieger & Holman, 2007). Here, we restrict ourselves to an understanding of primarily the corporeality of the sensorium as a pedagogic mode rather than the more often associated category of the aesthetic. ...
December 2007
Journal of Planning Education and Research
... This optimistic tone about the use of photography is echoed by others in planning, geography and sociology. Martin Krieger (2004) states that planners, in particular, are in a strong position to document cities through photography. He encourages systematic photography of particular places or phenomena that then could become the basis of archives upon which future students and scholars can draw. ...
December 2004
Journal of Planning Education and Research
... Whereas the complexity of coordination in spatial planning increased with the centralization of the state and later its democratization (involving more actors), the history of spatial design is also tied to state development, but more indirectly, through the increase of patronage. Complex cities produced rich citizens and proud city governments that could engage in private and public works that were the product of a design philosophy, with the sum of city space given higher consideration than the separate parts (Braunfels, 1990;Rios, 2008;Krieger, 2000;Mumford, 1961). ...
March 2000
Journal of Planning Education and Research
... One of the major implications of this analysis is that literary fiction and narratology, and more generally public humanities, should enter the toolbox of urban planners on a permanent basis, and possibly also become part of their educational curricula (Dakin 1993;Krieger 1995). We see this perspective as particularly promising if properly framed within the emerging paradigm of the Narrative Policy Framework (Jones 2018), that systematizes the role of narrative in the policy process in cognitive, pragmatic and strategic terms. ...
April 1995
Journal of Planning Education and Research
... Our research also complements papers that have used online user-generated content to extract time-series data about consumer behavior ( [16]), health ( [17]; [18]), or finance ( [19]), or to obtain cross-sectional socioeconomic data ( [20]). A growing literature in urban tomography ( [21]) is demonstrating that adding geographical identification to such methods can improve research and practice in urban planning, urban sciences, environmental science or psychology, and architecture. For example, [22] shows the conditions under which user-generated opinions can be deemed reliable for planning decisions. ...
August 2010
Journal of Urban Technology
... Abdelzaher et al. [1] conclude the primary participatory sensing applications deeply. A number of early participatory sensing prototype systems have been built such as BikeNet [2], SoundSense [3], CenceMe [4,5], MetroSense [6], Bubble-Sensing [7], Urban Tomography [8,9], CarTel [10], Darwin [11], and Microblog [12] at the same time. These participatory sensing prototype systems lay the foundation of human sensing. ...
September 2009
Journal of Planning Education and Research