Digital computers use numbers based on flawed representations of real numbers, which may lead to inaccuracies when simulating the motion of molecules, weather systems and fluids, find scientists.

The study, published today in Advanced Theory and Simulations, shows that digital computers cannot reliably reproduce the behaviour of ‘chaotic systems’ which are widespread. This fundamental limitation could have implications for high performance computation (HPC) and for applications of machine learning to HPC.

Professor Peter Coveney, Director of the UCL Centre for Computational Science and study co-author, said: “Our work shows that the behaviour of the chaotic dynamical systems is richer than any digital computer can capture. Chaos is more commonplace than many people may realise and even for very simple chaotic systems, numbers used by digital computers can lead to errors that are not obvious but can have a big impact. Ultimately, computers can’t simulate everything.”

The team investigated the impact of using floating-point arithmetic — a method standardised by the IEEE and used since the 1950s to approximate real numbers on digital computers.

Digital computers use only rational numbers, ones that can be expressed as fractions. Moreover the denominator of these fractions must be a power of two, such as 2, 4, 8, 16, etc. There are infinitely more real numbers that cannot be expressed this way. (https://www.sciencedaily.com/releases/2019/09/190923213314.htm)

An irrational universe.

Full of irrational people.

Trying to analyze it rationally.

Under the illusion that number we have invented can draw a sketch of the cosmos. And yet, nothing we have invented is anywhere to be seen but on a piece of paper. Can you limit the birth of a star on a piece of paper? Can you contain the death of the universe on an equation?

We believe we can.

And sadly, we do.

And at the moment we do, the universe indeed dies…

And a small voice will whisper in our ear…

Congratulations. You have now understood it all.

How irrationally rational everything is!

And inside the darkest night you will dance.

Laughter.

And for a brief moment the forest will look at you.

Crying.

And for a brief moment the forest will see nothing…

But an empty broken CD. Full of data. Full of life…