Month: September 2022

TRANSITION. “We suggest that the brain before verbal language was merely a percept processor and that afterwards it was able to conceptualize, i.e. operate with concepts. Each concept linked all the percepts associated with that concept.” https://link.springer.com/chapter/10.1007/978-3-030-59177-9_13 View in LinkedIn

DEEP MATHS. “We conclude that the human mind naturally makes associations, creates categories or sets and hence has the natural mathematical structure of set theory.” https://link.springer.com/chapter/10.1007/978-3-030-59177-9_13 View in LinkedIn

SETS AS A PRECONDITION. “We further suggest that verbal language emerged as a primitive form of set theory in that a set of percepts that are associated with each other or are similar are linked together with a word acting as a concept that unites all the members of that set. In a certain sense the primitive form of set theory we just described seems to be a pre-condition for the emergence of verbal language.” https://link.springer.com/chapter/10.1007/978-3-030-59177-9_13 View in LinkedIn

EMERGENT SYSTEMS. “It is not possible to determine the causal linkage between the primitive form of set theory and verbal language. It is not that set theory caused verbal language to emerge or that language allowed set theory to emerge. Rather we would claim, invoking complexity theory and emergent dynamics, that mathematical set theory and verbal language self-organized into an emergent supervenient system.” https://link.springer.com/chapter/10.1007/978-3-030-59177-9_13 View in LinkedIn

ROOTS IN NUMBERS. “Not only did mathematical thinking lead to verbal language but it also gave rise to written language through the development of mathematical notation. The very first notation for recording quantities were tally sticks. The tally stick, however, gave no indication of what was being tallied but they were the first forms of notated concrete numbers.” https://link.springer.com/chapter/10.1007/978-3-030-59177-9_13 View in LinkedIn

NUMBER EVOLUTION. “The next step in the evolution of numerical notation were three-dimensional clay accounting tokens that archeologist Denise Schmandt-Besserat discovered in the Fertile Crescent of Mesopotamia between the Tigris and Euphrates rivers that were used from 8000 BCE to about 3000 BCE.” https://link.springer.com/chapter/10.1007/978-3-030-59177-9_13 View in LinkedIn

CLAY TABLET WRITING. “The impressed token shape signs for the large and small measure of wheat came to represent the numerals 10 and 1 respectively. The second class of signs, etched signs representing the commodities and hence represented words. The Sumerians quickly realized that they could represent spoken words other than agricultural commodities with etched signs and so writing emerged to represent spoken language and also abstract numbers.” https://link.springer.com/chapter/10.1007/978-3-030-59177-9_13 View in LinkedIn

BOOKKEEPING ORIGINS. “Writing was invented by accountants and not by writers, but writers harnessed the accountant’s idea of creating written symbols for spoken words. And mathematicians harnessed the accountant’s idea of notating abstract numbers to develop a notation for mathematics that led to more sophisticated mathematical thinking.” https://link.springer.com/chapter/10.1007/978-3-030-59177-9_13 View in LinkedIn

THE EVOLUTIONARY CHAIN. “Having demonstrated how speech, writing and mathematics are interlinked we now turn to show how they are actually part of a larger evolutionary chain of interlinked languages composed of speech, writing, mathematics, science, computing and the Internet.” https://link.springer.com/chapter/10.1007/978-3-030-59177-9_13 View in LinkedIn