Posts tagged thought

Notation as a Tool of Thought

notation, programming, maths, mathematics, thought, thinking, Language

Mathematical notation provides perhaps the best-known and best-developed example of language used consciously as a tool of thought. Recognition of the important role of notation in mathematics is clear from the quotations from mathematicians given in Cajori’s A History of Mathematical Notations [2, pp.332,331]. Nevertheless, mathematical notation has serious deficiencies. In particular, it lacks universality, and must be interpreted differently according to the topic, according to the author, and even according to the immediate context. Programming languages, because they were designed for the purpose of directing computers, offer important advantages as tools of thought. Not only are they universal (general-purpose), but they are also executable and unambiguous. Executability makes it possible to use computers to perform extensive experiments on ideas expressed in a programming language, and the lack of ambiguity makes possible precise thought experiments. In other respects, however, most programming languages are decidedly inferior to mathematical notation and are little used as tools of thought in ways that would be considered significant by, say, an applied mathematician.

via http://www.jsoftware.com/papers/tot.htm

The Root of Thought: What Do Glial Cells Do?

neuroscience, neurology, consciousness, creativity, thought, glia, astrocytes

LEHRER: You suggest that glia and their calcium waves might play a role in creativity. Could you explain? KOOB: This idea stems from dreams, sensory deprivation and day dreaming. Without input from our senses through neurons, how is it that we have such vivid thoughts? How is it that when we are deep in thought we seemingly shut off everything in the environment around us? In this theory, neurons are tied to our muscular action and external senses. We know astrocytes monitor neurons for this information. Similarly, they can induce neurons to fire. Therefore, astrocytes modulate neuron behavior. This could mean that calcium waves in astrocytes are our thinking mind. Neuronal activity without astrocyte processing is a simple reflex; anything more complicated might require astrocyte processing. The fact that humans have the most abundant and largest astrocytes of any animal and we are capable of creativity and imagination also lends credence to this speculation. Calcium is also released randomly and without stimulation from astrocytes’ internal stores in small bursts called ‘puffs.’ These random puffs can lead to waves. It is possible that the seemingly random thoughts during dreams and sensory deprivation experience could be calcium puffs becoming waves in our astrocytes. Basically, it is obvious that astrocytes are involved in brain processing in the cortex, but the main questions are, do our thoughts and imagination stem from astrocytes working together with neurons, or are our thoughts and imagination solely the domain of astrocytes? Maybe the role of neurons is to support astrocytes.

via http://www.scientificamerican.com/article/the-root-of-thought-what/

Does Language Influence Culture?

Language, culture, thought, time, causality, WSJ

Pormpuraawans, we found, arranged time from east to west. That is, seated facing south, time went left to right. When facing north, right to left. When facing east, toward the body, and so on. Of course, we never told any of our participants which direction they faced. The Pormpuraawans not only knew that already, but they also spontaneously used this spatial orientation to construct their representations of time. And many other ways to organize time exist in the world’s languages. In Mandarin, the future can be below and the past above. In Aymara, spoken in South America, the future is behind and the past in front. In addition to space and time, languages also shape how we understand causality.

via http://www.wsj.com/articles/SB10001424052748703467304575383131592767868