### Pocket Mathematics

, 1995

"... Mathematics is in a dramatic and massive process of changing, mainly due to the advent of computers and computer science. Our aim is to present a pocket image of this phenomenon; a "case study" will give us the opportunity to describe some of these new ideas, problems, and techniques. Part ..."

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Mathematics is in a dramatic and massive process of changing, mainly due to the advent of computers and computer science. Our aim is to present a pocket image of this phenomenon; a "case study" will give us the opportunity to describe some of these new ideas, problems, and techniques. Particularly, we will be concerned with foreseeable mutations in the interaction between deductive and experimental trends.

### HOW TO RUN ALGORITHMIC INFORMATION THEORY

, 1995

"... Hi everybody! It’s a great pleasure for me to be back here at the new, improved Santa Fe Institute in this spectacular location. I guess this is my fourth visit and it’s always very stimulating, so I’m always very happy to visit you guys. I’d like to tell you what I’ve been up to lately. First of al ..."

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Hi everybody! It’s a great pleasure for me to be back here at the new, improved Santa Fe Institute in this spectacular location. I guess this is my fourth visit and it’s always very stimulating, so I’m always very happy to visit you guys. I’d like to tell you what I’ve been up to lately. First of all, let me say what algorithmic information theory is good for, before telling you about the new version of it I’ve got. 1

### A NEW VERSION OF ALGORITHMIC

, 1995

"... Algorithmic information theory may be viewed as the result of adding the idea of program-size complexity to recursive function theory. The main application of algorithmic information theory is its informationtheoretic incompleteness theorems. This theory is concerned with the ..."

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Algorithmic information theory may be viewed as the result of adding the idea of program-size complexity to recursive function theory. The main application of algorithmic information theory is its informationtheoretic incompleteness theorems. This theory is concerned with the

### THE BERRY PARADOX

, 1994

"... videotaped; this is an edited transcript. It also incorporates remarks made at the Limits to Scientific Knowledge meeting held at the Santa ..."

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videotaped; this is an edited transcript. It also incorporates remarks made at the Limits to Scientific Knowledge meeting held at the Santa

### PANU RAATIKAINEN ALGORITHMIC INFORMATION THEORY AND UNDECIDABILITY

"... Algorithmic information theory, or the theory of Kolmogorov complexity, has become an extraordinarily popular theory, and this is no doubt due, in some part, to the fame of Chaitin’s incompleteness results arising from this field. Actually, there are two rather different results by Chaitin: the ..."

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Algorithmic information theory, or the theory of Kolmogorov complexity, has become an extraordinarily popular theory, and this is no doubt due, in some part, to the fame of Chaitin’s incompleteness results arising from this field. Actually, there are two rather different results by Chaitin: the

### Exploratory experimentation in experimental mathematics: A glimpse at the PSLQ algorithm

"... From a philosophical viewpoint, mathematics has traditionally been dis-tinguished from the natural sciences by its formal nature and emphasis on deductive reasoning. Experiments—one of the corner stones of most modern natural science—have had no role to play in mathematics. However, in the ..."

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From a philosophical viewpoint, mathematics has traditionally been dis-tinguished from the natural sciences by its formal nature and emphasis on deductive reasoning. Experiments—one of the corner stones of most modern natural science—have had no role to play in mathematics. However, in the

### The Discrete Charm of Second-Order Simulacra

, 2008

"... Abstract. We examine a case in which non-computable behavior in a model is revealed by computer simulation. This is possible due to differing notions of computability for sets in a continuous space. The argument originally given for the validity of the simulation involves a simpler simulation of the ..."

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Abstract. We examine a case in which non-computable behavior in a model is revealed by computer simulation. This is possible due to differing notions of computability for sets in a continuous space. The argument originally given for the validity of the simulation involves a simpler simulation of the simulation, still further simulations thereof, and a universality conjecture. There are difficulties with that argument, but there are other, heuristic arguments supporting the qualitative results. It is urged, using this example, that absolute validation, while highly desirable, is overvalued. Simulations also provide valuable insights that we cannot yet (if ever) prove. If we could take as the finest allegory of simulation the Borges tale where the cartographers of the Empire draw up a map so detailed that it ends up exactly covering the territory…, this fable would then have come full circle for us, and now has nothing but the discrete charm of second-order

### C/C++ Implementation of Functions of the Class LT 0.

"... This report describes an on-going implementation, in C/C++, of the functions and schemes of the formal system LT0, presented in the paper Caporaso, Pani and Covino [1]. The final aim is to be able to effectively construct a "small manageable " Exponential Diophantine Equation which ..."

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This report describes an on-going implementation, in C/C++, of the functions and schemes of the formal system LT0, presented in the paper Caporaso, Pani and Covino [1]. The final aim is to be able to effectively construct a &quot;small manageable &quot; Exponential Diophantine Equation which represents (in the sense of Chaitin [2]) an algorithmical random binary sequence.