{"id":69362,"date":"2023-08-15T00:06:37","date_gmt":"2023-08-15T04:06:37","guid":{"rendered":"https:\/\/world.edu\/?p=69362"},"modified":"2023-08-15T00:06:37","modified_gmt":"2023-08-15T04:06:37","slug":"arithmetic-has-a-biological-origin-its-an-expression-in-symbols-of-the-deep-structure-of-our-perception","status":"publish","type":"post","link":"https:\/\/world.edu\/arithmetic-has-a-biological-origin-its-an-expression-in-symbols-of-the-deep-structure-of-our-perception\/","title":{"rendered":"Arithmetic has a biological origin \u2013 it\u2019s an expression in symbols of the \u2018deep structure\u2019 of our perception"},"content":{"rendered":"

\"\"<\/p>\n

Everyone knows that arithmetic is true: 2 + 2 = 4.<\/p>\n

But surprisingly, we don\u2019t know\u00a0why<\/em>\u00a0it\u2019s true.<\/p>\n

By stepping outside the box of our usual way of thinking about numbers, my colleagues and I have recently shown that\u00a0arithmetic has biological roots<\/a>\u00a0and is a natural consequence of how perception of the world around us is organised.<\/p>\n

Our results explain why arithmetic is true and suggest that mathematics is a realisation in symbols of the fundamental nature and creativity of the mind.<\/p>\n

Thus, the miraculous correspondence between mathematics and physical reality that has been a source of wonder from the ancient Greeks to the present \u2014 as explored in astrophysicist Mario Livio\u2019s book\u00a0Is God a mathematician?<\/a>\u00a0\u2014 suggests the mind and world are part of a common unity.<\/p>\n

Why is arithmetic universally true?<\/strong><\/h4>\n

Humans have been making symbols for numbers for more than 5,500 years. More than 100 distinct notation systems are known to have been used by\u00a0different civilisations<\/a>, including Babylonian, Egyptian, Etruscan, Mayan and Khmer.<\/p>\n

\"\"

Different cultures have developed their own symbols for numbers, but they all use addition and multiplication. Wikimedia Commons, CC BY-SA<\/p><\/div>\n

The remarkable fact is that despite the great diversity of symbols and cultures, all are based on addition and multiplication. For example, in our familiar Hindu-Arabic numerals: 1,434 = (1 x 1000) + (4 x 100) + (3 x 10) + (4 x 1).<\/p>\n

Why have humans invented the same arithmetic, over and over again? Could arithmetic be a universal truth waiting to be discovered?<\/p>\n

To unravel the mystery, we need to ask why addition and multiplication are its fundamental operations. We recently\u00a0posed this question<\/a>\u00a0and found that no satisfactory answer \u2013 one that met standards of scientific rigour \u2013 was available from philosophy, mathematics or the cognitive sciences.<\/p>\n

The fact that we don\u2019t know why arithmetic is true is a critical gap in our knowledge. Arithmetic is the foundation for higher mathematics, which is indispensable for science.<\/p>\n

Consider a thought experiment. Physicists in the future have achieved the goal of a \u201ctheory of everything\u201d or \u201cGod equation<\/a>\u201d. Even if such a theory could correctly predict all physical phenomena in the universe, it would not be able to explain where arithmetic itself comes from or why it is universally true.<\/p>\n

Answering these questions is necessary for us to fully understand the role of mathematics in science.<\/p>\n

Bees provide a clue<\/strong><\/h4>\n

We proposed a new approach based on the assumption that arithmetic has a biological origin.<\/p>\n

Many non-human species, including insects, show an ability for spatial navigation which seems to require the\u00a0equivalent of algebraic computation<\/a>. For example, bees can take a meandering journey to find nectar but then return by the most direct route, as if they can\u00a0calculate the direction and distance home<\/a>.<\/p>\n

\"\"

Bees can integrate their zig-zag flight path to calculate the straightest route back to the hive. Nicola J. Morton, CC BY-SA<\/p><\/div>\n

How their miniature brain (about 960,000 neurons) achieves this is unknown. These calculations might be the non-symbolic precursors of addition and multiplication, honed by natural selection as the optimal solution for navigation.<\/p>\n

Arithmetic may be based on biology and special in some way because of evolution\u2019s fine-tuning.<\/p>\n

Stepping outside the box<\/strong><\/h4>\n

To probe more deeply into arithmetic, we need to go beyond our habitual, concrete understanding and think in more general and abstract terms. Arithmetic consists of a set of elements and operations that combine two elements to give another element.<\/p>\n

In the universe of possibilities, why are the elements represented as numbers and the operations as addition and multiplication? This is a meta-mathematical question \u2013 a question about mathematics itself that can be addressed using mathematical methods.<\/p>\n

In our\u00a0research<\/a>, we proved that four assumptions \u2013 monotonicity, convexity, continuity and isomorphism \u2013 were sufficient to uniquely identify arithmetic (addition and multiplication over the real numbers) from the universe of possibilities.<\/p>\n