Related papers: Isaac Newton as a Probabilist
In 1963 Edward Lorenz revealed deterministic predictability to be an illusion and gave birth to a field that still thrives. This Feature Article discusses Lorenz's discovery and developments that followed from it.
We study how the paradigm of Newton's science, based on the organization of scientific knowledge as a series of mathematical laws, was definitively accepted in science courses - in the last decades of the XVIII century, in England as well…
Times magazine selected Albert Einstein, the German born Jewish Scientist as the person of the 20th century. Undoubtedly, 20th century was the age of science and Einstein's contributions in unraveling mysteries of nature was unparalleled.…
Charles L. Dodgson, also known as Lewis Carroll, in his book "Pillow problems" from 1893 asked for the likelihood of a random triangle to be obtuse. Clearly, the answer to Dodgson's question depends strongly on the assumed random…
In a letter to Born, Einstein wrote: "Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the old one. I, at…
An extended analysis is given of the program, originally suggested by Deutsch, of solving the probability problem in the Everett interpretation by means of decision theory. Deutsch's own proof is discussed, and alternatives are presented…
This study examines the potential of using math-themed postage stamps in mathematics lessons as a tool to engage students and integrate the subject with history, art, and culture. Since the first mathematical stamps appeared in the early…
The problem of induction has persisted since Hume exposed the logical gap between repeated observation and universal inference. Traditional attempts to resolve it have oscillated between two extremes: the probabilistic optimism of Laplace…
Transcript of G.J. Chaitin's 2 March 2000 Carnegie Mellon University School of Computer Science Distinguished Lecture. The notion of randomness is taken from physics and applied to pure mathematics in order to shed light on the…
By using ideas on complexity and randomness originally suggested by the mathematician-philosopher Gottfried Leibniz in 1686, the modern theory of algorithmic information is able to show that there can never be a "theory of everything" for…
We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One…
Newton, in notes that he would rather not have seen published, described a process for solving simultaneous equations that later authors applied specifically to linear equations. This method that Euler did not recommend, that Legendre…
The beautiful theory of statistical gambling, started by Dubins and Savage (for subfair games) and continued by Kelly and Breiman (for superfair games) has mostly been studied under the unrealistic assumption that we live in a continuous…
Although the differential calculus was invented by Newton, Kepler established his famous laws 70 years earlier by using the same idea, namely to find a path in a nonuniform field of force by small steps. It is generally not known that…
In Book 1, Proposition 7, Problem 2 of his 1687 Philosophiae Naturalis Principia Mathematica, Isaac Newton poses and answers the following question: Let the orbit of a particle moving in a central force field be an off-center circle. How…
In 1837, the first computer program in history was sketched by the renowned mathematician and inventor Charles Babbage. It was a program for the Analytical Engine. The program consists of a sequence of arithmetical operations and the…
Suppose you look at today's stock prices and bet on the value of the first digit. One could guess that a fair bet should correspond to the frequency of $1/9 = 11.11%$ for each digit from 1 to 9. This is by no means the case, and one can…
We consider the following one-player game called Dundee. We are given a deck consisting of s_i cards of Value i, where i=1,...,v, and an integer m\le s_1+...+s_v. There are m rounds. In each round, the player names a number between 1 and v…
Since the mathematicians of ancient Greece until Fermat, since Gauss until today; the way how the primes along the numerical straight line are distributed has become perhaps the most difficult math problem; many people believe that their…
(l) I have enough evidence to render the sentence S probable. (la) So, relative to what I know, it is rational of me to believe S. (2) Now that I have more evidence, S may no longer be probable. (2a) So now, relative to what I know, it is…