A new way to support 3D-printed structures as they are being made is helping to create delicate biological structures and eventually organs.
Full story: <newscientist.com/article/dn28252-gel-scaffold-paves-way-for-3d-printing-of-biological-organs>
Author: Edward Nelson
Abstract: The aim of this work is to show that contemporary mathematics, including Peano arithmetic, is inconsistent, to construct firm foundations for mathematics, and to begin building on these foundations.
Comments:With an Introduction by Sarah Jones Nelson and an Afterword by Sam Buss and Terence Tao. 53 pages
I view the objects of pure mathematics (as long as they are not intended physical objects or processes ) as physical phenomena which occur in human brains. Of course I do not attribute to them any descriptive role, and they do not represent anything independent of humanity. On the other hand the laws of physics and the structure of human bains (and computers) are such that pure mathematics is not arbitray and it is more reproducible than most other thoughts or constructions. In fact it crystalizes in our brains (whn these are exposed to the appropriate sensory inputs) into very precise forms described by classical set theory.
Hence, however I do not believe in the existence of any Platonic reality. I reject formalism, i.e., the view that mathematics is an arbitrary game of symbols. I believe that mathematics is an exploration of such theories which natural intelligence (natural logic) can create, and they happen to be far from arbitrary.
But we will propose that there are some non-computable [hyper-computable?] reals with a direct physical significance.
Pure Mathematics and Physical Reality (Continuity and Computability)
The Meaning of Pure Mathematics
Journal of Philosophical Logic
Vol. 18, No. 3 (Aug., 1989), pp. 315-320
Published by: Springer
Stable URL: http://www.jstor.org/stable/30227216
Locally Finite Theories
The Journal of Symbolic Logic
Vol. 51, No. 1 (Mar., 1986), pp. 59-62
Published by: Association for Symbolic Logic
Stable URL: http://www.jstor.org/stable/2273942
- Brown UniversityPh.D. Applied Mathematics (1979), Sc.M. (1976), Sc.B. (1975)
- Cloudversed ResearchPublisher, 2011 - present
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