The foundations of mathematics and physics no longer start with fundamental entities and their pr... more The foundations of mathematics and physics no longer start with fundamental entities and their properties like spatial extension, points, lines or the billiard ball like particles of Newtonian physics. Mathematics has abolished these from its foundations in set theory by making all assumptions explicit and structural. Particle physics has become completely mathematical, connecting to physical reality only through experimental technique. Applying the principles guiding the foundations of mathematics and physics to philosophical analysis underscores that only conscious experience has an intrinsic nature. This leads to a version of realistic monism in which the essence and totality of the existence of physical structure is immediate experience in some form. Identifying physical structure with conscious experience allows the application of mathematics to the evolution of consciousness. Some of the implications from Gödel's Incompleteness Theorem are connected to creativity and ethics.
As the Platonic philosophy of mathematics is increasingly being questioned, computer technology i... more As the Platonic philosophy of mathematics is increasingly being questioned, computer technology is able to approach Platonic perfection in limited domains. This paper argues for a mathematical philosophy that is both objective and creative. It is objective in that it limits the domain of mathematics to questions that are logically determined by a recursively enumerable sequence of events. This includes the arithmetical and hyperarithmetical hierarchies but excludes questions like the Continuum Hypothesis. This philosophy is creative in recognizing that Gödel's Incompleteness Theorem implies one can only fully explore this mathematics by considering an ever increasing number of incompatible possibilities without deciding which is correct. This is how biological evolution created the mathematically capable human mind.
As computer CPUs get faster, primary memories tend to be organized in parallel banks. The fastest... more As computer CPUs get faster, primary memories tend to be organized in parallel banks. The fastest machines now being developed can fetch of the order of 100 words in parallel. Unless memory and compiler designers are careful, serious memory conflicts and resulting performance degradation may result. Some of the important questions of design and use of such memories are discussed.
Abstract TRANQUIL is the algorithmic language which will be used to write programs for ILLIAC IV,... more Abstract TRANQUIL is the algorithmic language which will be used to write programs for ILLIAC IV, a parallel computer which has been described by Barnes et al. ILLIAC IV is designed to be an array of 256 coupled processing elements (PE's) arranged in four ...
As the Platonic philosophy of mathematics is increasingly being questioned, computer technology i... more As the Platonic philosophy of mathematics is increasingly being questioned, computer technology is able to approach Platonic perfection in limited domains. This paper argues for a mathematical philosophy that is both objective and creative. It is objective in that it limits the domain of mathematics to questions that are logically determined by a recursively enumerable sequence of events. This includes the arithmetical and hyperarithmetical hierarchies but excludes questions like the Continuum Hypothesis. This philosophy is creative in recognizing that Gödel's Incompleteness Theorem implies one can only fully explore this mathematics by considering an ever increasing number of incompatible possibilities without deciding which is correct. This is how biological evolution created the mathematically capable human mind.
The foundations of mathematics and physics no longer start with fundamental entities and their pr... more The foundations of mathematics and physics no longer start with fundamental entities and their properties like spatial extension, points, lines or the billiard ball like particles of Newtonian physics. Mathematics has abolished these from its foundations in set theory by making all assumptions explicit and structural. Particle physics has become completely mathematical, connecting to physical reality only through experimental technique. Applying the principles guiding the foundations of mathematics and physics to philosophical analysis underscores that only conscious experience has an intrinsic nature. This leads to a version of realistic monism in which the essence and totality of the existence of physical structure is immediate experience in some form. Identifying physical structure with conscious experience allows the application of mathematics to the evolution of consciousness. Some of the implications from Gödel's Incompleteness Theorem are connected to creativity and ethics.
As the Platonic philosophy of mathematics is increasingly being questioned, computer technology i... more As the Platonic philosophy of mathematics is increasingly being questioned, computer technology is able to approach Platonic perfection in limited domains. This paper argues for a mathematical philosophy that is both objective and creative. It is objective in that it limits the domain of mathematics to questions that are logically determined by a recursively enumerable sequence of events. This includes the arithmetical and hyperarithmetical hierarchies but excludes questions like the Continuum Hypothesis. This philosophy is creative in recognizing that Gödel's Incompleteness Theorem implies one can only fully explore this mathematics by considering an ever increasing number of incompatible possibilities without deciding which is correct. This is how biological evolution created the mathematically capable human mind.
As computer CPUs get faster, primary memories tend to be organized in parallel banks. The fastest... more As computer CPUs get faster, primary memories tend to be organized in parallel banks. The fastest machines now being developed can fetch of the order of 100 words in parallel. Unless memory and compiler designers are careful, serious memory conflicts and resulting performance degradation may result. Some of the important questions of design and use of such memories are discussed.
Abstract TRANQUIL is the algorithmic language which will be used to write programs for ILLIAC IV,... more Abstract TRANQUIL is the algorithmic language which will be used to write programs for ILLIAC IV, a parallel computer which has been described by Barnes et al. ILLIAC IV is designed to be an array of 256 coupled processing elements (PE's) arranged in four ...
As the Platonic philosophy of mathematics is increasingly being questioned, computer technology i... more As the Platonic philosophy of mathematics is increasingly being questioned, computer technology is able to approach Platonic perfection in limited domains. This paper argues for a mathematical philosophy that is both objective and creative. It is objective in that it limits the domain of mathematics to questions that are logically determined by a recursively enumerable sequence of events. This includes the arithmetical and hyperarithmetical hierarchies but excludes questions like the Continuum Hypothesis. This philosophy is creative in recognizing that Gödel's Incompleteness Theorem implies one can only fully explore this mathematics by considering an ever increasing number of incompatible possibilities without deciding which is correct. This is how biological evolution created the mathematically capable human mind.
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