Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

Beauty is truth in mathematical intuition

20.11.2008
First empirical evidence for the use of beauty as truth in mathematical intuition reported.

Rolf Reber, together with mathematician Morten Brun and psychologist Karoline Mitterndorfer, all from the University of Bergen, Norway, have reported first empirical evidence for the use of beauty as truth and provided an explanation for this phenomenon, based on the processing fluency theory of beauty (see below). The study has been published in the December 2008 issue of Psychonomic Bulletin & Review.

Mathematicians and scientists reportedly used beauty as a cue for truth in mathematical judgment. French mathematician Jacques Hadamard, for example, wrote in 1954 in his famous book “The psychology of invention in the mathematical” field that a sense of beauty seems to be almost the only useful “drive” for discovery in mathematics. However, evidence has been anecdotal, and the nature of the beauty-truth relationship remained a mystery.

In 2004, Rolf Reber (University of Bergen), Norbert Schwarz (University of Michigan), and Piotr Winkielman (University of California at San Diego) suggested – based on evidence they reviewed – that the common experience underlying both perceived beauty and judged truth is processing fluency, which is the experienced ease with which mental content is processed. Indeed, stimuli processed with greater ease elicit more positive affect and statements that participants can read more easily are more likely to be judged as being true. Researchers invoked processing fluency to help explain a wide range of phenomena, including variations in stock prices, brand preferences, or the lack of reception of mathematical theories that are difficult to understand.

Applied to mathematical reasoning, processing fluency, stemming either from familiarity with problems or from attributes of a task, is predicted to increase intuitively judged truth. As a first step towards testing this assumption, the authors of the study demonstrated in two experiments that symmetry, a feature known to facilitate mental processing and to underlie perceived beauty, is used as heuristic cue to correctness in arithmetic problems.

The researchers constructed additions, consisting of dots. For example, 12 dots plus 21 dots equaled 33 dots. Half of the additions were correct; the others were wrong, such as 12 dots plus 21 dots equaled 27 dots. Half of the additions had symmetric dot patterns (symmetric additions), the other half asymmetric patterns (asymmetric additions). These additions were presented briefly, e.g., in one experiment 1800 milliseconds, and student participants without training in mathematics had to decide immediately after the addition disappeared whether it was correct or incorrect. Participants were more likely to judge symmetric additions than asymmetric additions to be correct. As this was also the case when additions in fact were incorrect, the finding cannot be explained by the fact that symmetric additions were easier to count or to estimate: In this case, symmetric additions that were incorrect would have been less likely to be judged correct. The results clearly show that participants used symmetry as an indication to correctness, or beauty as truth.

The authors have shown that people who do not have enough time to analyze the problem use heuristic cues in order to assess the correctness of a proposed solution. This simple setup serves as a model for the more complicated situation where a mathematician has discovered a plausible solution to a problem and now wants a quick assessment of whether this solution “feels” right. These findings suggest a solution to the mystery why beauty serves as a cue for truth in the context of mathematical discovery.

Contact: rolf.reber@psysp.uib.no

Margareth Barndon | alfa
Further information:
http://pbr.psychonomic-journals.org/content/15/6/1174.abstract
http://www.uib.no

More articles from Life Sciences:

nachricht Symbiotic bacteria: from hitchhiker to beetle bodyguard
28.04.2017 | Johannes Gutenberg-Universität Mainz

nachricht Nose2Brain – Better Therapy for Multiple Sclerosis
28.04.2017 | Fraunhofer-Institut für Grenzflächen- und Bioverfahrenstechnik IGB

All articles from Life Sciences >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: Making lightweight construction suitable for series production

More and more automobile companies are focusing on body parts made of carbon fiber reinforced plastics (CFRP). However, manufacturing and repair costs must be further reduced in order to make CFRP more economical in use. Together with the Volkswagen AG and five other partners in the project HolQueSt 3D, the Laser Zentrum Hannover e.V. (LZH) has developed laser processes for the automatic trimming, drilling and repair of three-dimensional components.

Automated manufacturing processes are the basis for ultimately establishing the series production of CFRP components. In the project HolQueSt 3D, the LZH has...

Im Focus: Wonder material? Novel nanotube structure strengthens thin films for flexible electronics

Reflecting the structure of composites found in nature and the ancient world, researchers at the University of Illinois at Urbana-Champaign have synthesized thin carbon nanotube (CNT) textiles that exhibit both high electrical conductivity and a level of toughness that is about fifty times higher than copper films, currently used in electronics.

"The structural robustness of thin metal films has significant importance for the reliable operation of smart skin and flexible electronics including...

Im Focus: Deep inside Galaxy M87

The nearby, giant radio galaxy M87 hosts a supermassive black hole (BH) and is well-known for its bright jet dominating the spectrum over ten orders of magnitude in frequency. Due to its proximity, jet prominence, and the large black hole mass, M87 is the best laboratory for investigating the formation, acceleration, and collimation of relativistic jets. A research team led by Silke Britzen from the Max Planck Institute for Radio Astronomy in Bonn, Germany, has found strong indication for turbulent processes connecting the accretion disk and the jet of that galaxy providing insights into the longstanding problem of the origin of astrophysical jets.

Supermassive black holes form some of the most enigmatic phenomena in astrophysics. Their enormous energy output is supposed to be generated by the...

Im Focus: A Quantum Low Pass for Photons

Physicists in Garching observe novel quantum effect that limits the number of emitted photons.

The probability to find a certain number of photons inside a laser pulse usually corresponds to a classical distribution of independent events, the so-called...

Im Focus: Microprocessors based on a layer of just three atoms

Microprocessors based on atomically thin materials hold the promise of the evolution of traditional processors as well as new applications in the field of flexible electronics. Now, a TU Wien research team led by Thomas Müller has made a breakthrough in this field as part of an ongoing research project.

Two-dimensional materials, or 2D materials for short, are extremely versatile, although – or often more precisely because – they are made up of just one or a...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

Fighting drug resistant tuberculosis – InfectoGnostics meets MYCO-NET² partners in Peru

28.04.2017 | Event News

Expert meeting “Health Business Connect” will connect international medical technology companies

20.04.2017 | Event News

Wenn der Computer das Gehirn austrickst

18.04.2017 | Event News

 
Latest News

Wireless power can drive tiny electronic devices in the GI tract

28.04.2017 | Medical Engineering

Ice cave in Transylvania yields window into region's past

28.04.2017 | Earth Sciences

Nose2Brain – Better Therapy for Multiple Sclerosis

28.04.2017 | Life Sciences

VideoLinks
B2B-VideoLinks
More VideoLinks >>>