Calculus Of Ideas, A Quotes

“In a different direction, the necessity to model the analysis of noisy incomplete sensory data not by logic but by Bayesian inference first came to the forefront in the robotics community with their use of Kalman filters.”
― Ulf Grenander, Calculus Of Ideas, A: A Mathematical Study Of Human Thought

“Hence, the energy for independent thoughts is additive except for a term log[B(n1,n2)], the log of a binomial coefficient. Since binomial coefficients are always bigger than (or equal to) one, it follows that energy is super-additive. Combining thoughts demand more and more mental power as the sizes increase: the MIND is limited in the complexity of thoughts.”
― Ulf Grenander, Calculus Of Ideas, A: A Mathematical Study Of Human Thought

“Hence, the energy for independent thoughts is additive except for a term log[B(n1,n2)], the log of a binomial coefficient. Since binomial coefficients are always bigger than (or equal to) one, it follows that energy is super-additive. Combining thoughts demand more and more mental power as the sizes increase:”
― Ulf Grenander, Calculus Of Ideas, A: A Mathematical Study Of Human Thought

“In passing we mention Joseph Weizenbaum’s celebrated program ELIZA that mimics conversation between a patient and an analyst. It attracted a lot of attention, even a belief in the psychotherapist it simulates, to the extent that its inventor came to be surprised and even embarrassed by the misguided enthusiasm that the ELIZA program generated. The code supporting the program is simple, but the behavior is, at first, quite impressive. What we are after, however, is a code that rests on a pattern theoretic analysis of the human mind specifying the details of mental processes, and such codes will have to be complex. As we shall see it will take some complex software to achieve our goal, even roughly. To facilitate programming we shall write in MATLAB although this will result in slow execution. In a later stage we may compile the code into C++ or into executables, but at the moment we are not concerned with computational speed.”
― Ulf Grenander, Calculus Of Ideas, A: A Mathematical Study Of Human Thought

“In passing we mention Joseph Weizenbaum’s celebrated program ELIZA that mimics conversation between a patient and an analyst. It attracted a lot of attention, even a belief in the psychotherapist it simulates, to the extent that its inventor came to be surprised and even embarrassed by the misguided enthusiasm that the ELIZA program generated. The code supporting the program is simple, but the behavior is, at first, quite impressive. What we are after, however, is a code that rests on a pattern theoretic analysis of the human mind specifying the details of mental processes, and such codes will have to be complex. As we shall see it will take some complex software to achieve our goal, even roughly. To facilitate programming we shall write in MATLAB although this will result in slow execution. In a later stage we may compile the code into C++ or into executables, but at the moment”
― Ulf Grenander, Calculus Of Ideas, A: A Mathematical Study Of Human Thought

“goal is to build a model of the mind in pattern theoretic terms: Starting from simple, atomic, mental entities (the generators of pattern theory) we shall combine them into regular structures, thoughts, (configurations) later on to be controlled by probabilistic rules of connections.”
― Ulf Grenander, Calculus Of Ideas, A: A Mathematical Study Of Human Thought

“may exist mathematical laws of thought in principle derivable from physic/chemistry. Such laws would have to be probabilistic.”
― Ulf Grenander, Calculus Of Ideas, A: A Mathematical Study Of Human Thought

“We do not want to be seen as machines. Hence we tend to reject statements like the one by Karl Vogt, a 19th century German philosopher, who stated that “the brain produces thoughts as the liver produces bile, or the kidneys produce urine”.”
― Ulf Grenander, Calculus Of Ideas, A: A Mathematical Study Of Human Thought

“We shall venture into even more speculative reflections on possible neural structures that would be consistent with our calculus.”
― Ulf Grenander, Calculus Of Ideas, A: A Mathematical Study Of Human Thought

“the physical substrate for thinking, the neural system, but the very fact that it has the form of a network implies that thought also has graph structure. This in turn suggests that language and its grammars, evolved later, also should be expressed in terms of graphs.”
― Ulf Grenander, Calculus Of Ideas, A: A Mathematical Study Of Human Thought

“the physical substrate for thinking, the neural system, but the very fact that it has the form of a network implies that thought also has graph structure. This in turn suggests that language and its grammars,”
― Ulf Grenander, Calculus Of Ideas, A: A Mathematical Study Of Human Thought

“In the natural sciences we understand a phenomenon when we have reduced it one level into concepts that seem more elementary. For example, from the high level of continuum mechanics we descend one level to atomistic structures, from atomism one level down to electrons, protons, then to the quark level? We shall reduce mind activities to elementary ideas and mental operations on them. Connecting the ideas according to certain rules we will be led to an algebraic structure, one for each cultural sphere. Within such a sphere individuals are characterized by the usage they make of the mental concepts as expressed by a probability measure resulting in a calculus of ideas.”
― Ulf Grenander, Calculus Of Ideas, A: A Mathematical Study Of Human Thought

“On the one hand, a central part of this theory is the introduction of probability measures which describe what associations and deductions we are likely to make.”
― Ulf Grenander, Calculus Of Ideas, A: A Mathematical Study Of Human Thought

“Immanuel Kant: “Human reason is by nature architectonic”
― Ulf Grenander, Calculus Of Ideas, A: A Mathematical Study Of Human Thought