Difference between revisions of "Universality"
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Universal, [[Universality]] or [[Universal properties]]/[[Universal Property]] are technical terms defined in [[Technical Term::Mathematical Logic]], however, as the word implies, its philosophical and operational implication reaches beyond the scope of mathematics, and logics. When used properly, universality can be a powerful tool to examine or categorize things/events that have generally applicable properties. It can have direct operational implication in designing data-intensive applications and engineering artifacts, particularly in the area of [[Internet of Things]] ([[IoT]]). | Universal, [[Universality]] or [[Universal properties]]/[[Universal Property]] are technical terms defined in [[Technical Term::Mathematical Logic]], however, as the word implies, its philosophical and operational implication reaches beyond the scope of mathematics, and logics. When used properly, universality can be a powerful tool to examine or categorize things/events that have generally applicable properties. It can have direct operational implication in designing data-intensive applications and engineering artifacts, particularly in the area of [[Internet of Things]] ([[IoT]]). | ||
=Universal Constructs= | =Universal Constructs= | ||
There is a data type called: [[Partially ordered set]], or [[POSet]], being considered as the universal data type for all representables. As a mathematically rigorous property that applies to all cases in a domain explicitly represented by a fixed, often finite set of symbols. A short statement about Universality can be found on page 131 of Davey and Priestly <ref> B. A. Davey, H. A. Priestley, Introduction to Lattices and Order, Second Edition, Cambridge University Press, May 6, 2002, P. 131</ref>. More over, [[Eugene Wigner]]'s talk on [[Paper/The Unreasonable Effectiveness of Mathematics in the Natural Sciences|The Unreasonable Effectiveness of Mathematics in the Natural Sciences]]<ref>{{:Paper/The Unreasonable Effectiveness of Mathematics in the Natural Sciences}}</ref>, is also a good place to get a sense of [[universality]]. | The notion of universality has been discussed under a few different names. For example, Leibniz calls it [[Monad]], which is a kind of universal construct that he claims to be the building block for anything, including material world, and non-material world, such as [[consciousness]]. The notion of [[Monad]] has since been extended by software engineers and mathematicians to model complex systems<ref>[[Don't fear the Monad]]</ref><ref>{{:Video/YOW! 2013 Philip Wadler - The First Monad Tutorial}}</ref>. There is a data type called: [[Partially ordered set]], or [[POSet]], being considered as the universal data type for all representables. As a mathematically rigorous property that applies to all cases in a domain explicitly represented by a fixed, often finite set of symbols. A short statement about Universality can be found on page 131 of Davey and Priestly <ref> B. A. Davey, H. A. Priestley, Introduction to Lattices and Order, Second Edition, Cambridge University Press, May 6, 2002, P. 131</ref>. More over, [[Eugene Wigner]]'s talk on [[Paper/The Unreasonable Effectiveness of Mathematics in the Natural Sciences|The Unreasonable Effectiveness of Mathematics in the Natural Sciences]]<ref>{{:Paper/The Unreasonable Effectiveness of Mathematics in the Natural Sciences}}</ref>, is also a good place to get a sense of [[universality]]. | ||
=Idealized Space= | =Idealized Space= | ||
Revision as of 17:05, 20 February 2022
| Universality | |
|---|---|
| Term | Universal |
| Knowledge Domain | Science, Mathematics, Mathematical Logic |
| Parent Domain | Cognitive Science |
Universal, Universality or Universal properties/Universal Property are technical terms defined in Mathematical Logic, however, as the word implies, its philosophical and operational implication reaches beyond the scope of mathematics, and logics. When used properly, universality can be a powerful tool to examine or categorize things/events that have generally applicable properties. It can have direct operational implication in designing data-intensive applications and engineering artifacts, particularly in the area of Internet of Things (IoT).
Universal Constructs
The notion of universality has been discussed under a few different names. For example, Leibniz calls it Monad, which is a kind of universal construct that he claims to be the building block for anything, including material world, and non-material world, such as consciousness. The notion of Monad has since been extended by software engineers and mathematicians to model complex systems[1][2]. There is a data type called: Partially ordered set, or POSet, being considered as the universal data type for all representables. As a mathematically rigorous property that applies to all cases in a domain explicitly represented by a fixed, often finite set of symbols. A short statement about Universality can be found on page 131 of Davey and Priestly [3]. More over, Eugene Wigner's talk on The Unreasonable Effectiveness of Mathematics in the Natural Sciences[4], is also a good place to get a sense of universality.
Idealized Space
Another way to talk about universaily, is to think of it as a way to express the most ideal situation for representing certain concepts[5]. There are also ways to operationalize the transformation of computable structure, such as work done by Michael Arbib[6].
Namespace Management as a way to represent Idea Space
For the purpose of representability, using concrete names to denote ideas is a necessary practice. However, the practical matter of managing namespaces at large can be challenging. Therefore, using a general-purpose namespace management tool, such as MediaWiki, can be a pragmatic solution. Clearly, Wiki is not just about its database, but also the integrative user experience that come with its browser-friendly nature, so that everyone can use this namespace management infrastructure anywhere. Henceforth, Wiki's namespace management can be thought of as a kind of universal data abstraction mechanism. The three aspects of namespace management can be stated as:
- Scalability: The sizes of application-specific namespaces can be scaled to requirements
- Highly Available: The functionality of namespace management is always available
- Security: Namespace data content can be protected in ways that will not be contaminated or destroyed.
References
- ↑ Don't fear the Monad
- ↑ Skills Matter, ed. (May 1, 2020). YOW! 2013 Philip Wadler - The First Monad Tutorial. local page: Skills Matter (formerly YOW! Conferences).
- ↑ B. A. Davey, H. A. Priestley, Introduction to Lattices and Order, Second Edition, Cambridge University Press, May 6, 2002, P. 131
- ↑ Wigner, E. P. (1960). "The unreasonable effectiveness of mathematics in the natural sciences. Richard Courant lecture in mathematical sciences delivered at New York University, May 11, 1959". Communications on Pure and Applied Mathematics. local page. 13: 1–14. Bibcode:1960CPAM...13....1W. doi:10.1002/cpa.3160130102. Archived from the original on 2020-02-12.
- ↑ Beskin, Daniel (Apr 19, 2020). Daniel Beskin- Category Theory as a Tool for Thought- λC 2019. local page: LambdaConf.
- ↑ Arbib, Michael; Manes, Ernest (1979). "Intertwined Recursion Tree Transformations and Linear Systems". Information and Control (No. 40, ed.). local page: Academic Press: 144-180.