Logical-Mathematical Intelligence
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Warm up Exercise : Wason Selection Task

You are in possesion of a card set. On one side there is a shape, a circle or a triangle. On the other side there is a colour, blue or yellow. There is one rule: If there is a circle on one side of a card, then the other side is blue. You have four cards placed on a surface next to each other, one depicting a circle, one a triangle, one is blue and one is yellow.Which card or cards do you need to turn around in order to confirm the abovementioned rule?

Defining criteria

What is logic and what is mathematics?

The Merriam-Webster Dictionary defines logic as follows: a science that deals with the principles and criteria of inference and demonstration: the science of the formal principles of reasoning

mathematics is the science of abstract structures and patterns, constructed out of different statements, which need to be proven true

Identifiable set of operations & Symbol system

object -> actions -> statements -> relationships

Henri Poincaré distinguished between the memory for steps in a chain of reasoning and the appreciation of the links between propositions. The later was regarded as the more important ability for a mathematician.

There are symbol systems for encoding actions performed upon objects and symbol systems for relations between objects.

1 + 1 = 2 | 2 - 1 = 1 | 2 x 2 = 4 | 4/2 = 2

Prodigies

Extraordinary Individuals are Individuals with...

... remarkable counting abilities, such as Shakuntala Devi: she was able to multiply two 13 digit numbers in 28 seconds in 1980

... intuitive understanding, such as Srinivasa Ramanujan: he wrote down nearly 3.900 new results (theorems, identities and equations)

... insight into abstract structures, such as Alexander Grothendiek: he worked on a rebuilding of algebraic geometry

Developmental trajectory

Developmental trajectory

Psychometry

Brain / Experimental psychology / Psychometry

Evolutionary plausibility

Evolutionary plausibility

The Origins of Mathematics

Agricultural Societies

Ancient Egypt

Mesopotamia/Babylon

Ancient China

Ancient India

First sign of mathematics-Nile Bank

calendar

religion: Nile river god Hapi

measuring device

landmeasure

measure unit

legth and area calculation

decimal system

binary counting system

fractions

Eye of Horus: geometric theory

accurate value of pi

Pyramid - the golden ratio, right angle

Power of proof: Acient Greece

Pythagoras

right-angled triangles

the harmonic serie

Euclid

300BC "The Elements": axioms

Archimede

Śūnyatā: Indian

the decimal place-value system

0 and infinity

pi

Brahmagupta

negative numbers

unknowns in equations

trigonometry

Al-Khwarizmi

algebra

Urban, industrial & digital societies

Urban, industrial, digital societies

Relations to other Intelligences

bodily-kinesthetic:::linguistic:::visual-spatial:::personal intelligences:::musical

Bodily-kinesthetic intelligences

bodily-kinesthetic

Visual-spatial intelligences

visual-spatial

Personal intelligences

personal intelligences

Musical intelligences

Logial-mathematical thinking and music?

Pythagoras Musica Universalis

Rhythms and intuitive counting

Musical notation and polyphony

12-Tone music and Arnold Schönberg

Stochastic music and Iannis Xenakis

Algorithms and generative music

Linguistic intelligences

Logial-mathematical thinking and language??

Crosslink between phonology, music and mathematical description

Semantics and symbol manipulation

logics and reasoning

Mediator of mathematics

Vectorization of language

Human & Machine

Vectorization, stochastic and noise

IQ test

Turing test

Q+ model?

Non-computational problems

Outset exercise