Sometimes, Our Brains Think Infinity Is Smaller Than Real Numbers. What The Heck?

Back in elementary school , infinity made sense . It was the number you used to win arguments : “ no , you nurse worse , timesinfinity ! ”

Now that we ’re old , though , we ’d go for to have a more nuanced and technical range of the construct . alas , a late work has bump that most of us … likely do n’t .

“ Traditional cognitive skill has focused on phenomena found in sensorial experience , but eternity is solely unlike , ” Michal Pinhas , principal investigator of the Quantitative Thinking and Cognition Lab at Ariel University and source of the field of study , toldPsyPost .

“ Understanding eternity requires nonfigurative intellection that endure beyond concrete representations and workaday experience , which I receive both puzzling and challenging , ” the research worker said .

So , first things first : whatisinfinity ? For mathematician and philosophers , it’smore of a conceptthan a bit : “ In a strict but non - numerical sense that think over its etymological account , ‘ unnumberable ’ mean ‘ having no limit or ending ’ , ‘ boundless ’ , ‘ unlimited ’ , ‘ interminable ’ , ‘ boundlessly great in extent ( or duration , or some other respect ) ’ , ” notes theStanford Encyclopedia of Philosophy . “ This rigorous , non - numerical sense is often applied to God and divine dimension , and to space , prison term and the macrocosm . ”

But “ there is also a strict , mathematical sense , ” it continues , “ according to which ‘ unnumerable ’ quantities or magnitudes are those that are mensurable but that have no finite bill ; and ‘ innumerable ’ lines or surface or volumes are mensurable lines or surfaces or volumes that have no finite measure . ”

Of naturally , writing all that every time you have a total to work out would get ho-hum reasonably quickly , and so mathematicians came up with a handy shorthand : the symbol ∞.

There ’s just one problem with that , though : on the face of it , it make people intend of it as a issue like any other . In a series of four experiment , participant were necessitate to judge which of two flesh was larger – sometimes it was a pair of telephone number , like 5 , or 44 , but sometimes the infinity symbol was included .

In that last typesetter’s case , the chore should have been simplest of all – after all , nothing beats eternity . But in fact , the experimentation revealed a more complex picture of how we comprehend turn and figures , with even visual pool cue such as the size of the font play into how we comprehend a note value .

“ I was surprised , ” Pinhas told PsyPost . “ In certain condition , people work on the eternity symbol as smaller than multidigit numbers . ”

More generally , people seemed to perceive the infinity symbol as “ representing a concrete bit , rather than an abstract construct distinct from numbers , ” said Pinhas – just another point on the number blood , in other word , albeit one very far off to the rightfulness .

This was plain from their response meter in the chore , Pinhas explained . See , generally , mass take a routine longer to figure out which number is turgid when the two are close in value , and are quicker when they ’re further aside . you’re able to try it yourself – the difference between , say , 5 and 67,321 probably hits you immediately , while sorting 13.102 and 13.201 might make your brain intermission for a second .

But this effect also seems to have pasture up in the experiments : when asked what was bigger between the infinity symbolic representation and a small number , participants were faster to oppose than when a enceinte number was exhibit – as if they perceived a number like 999 as being “ closer to infinity ” than one like 5 .

The truth , of course , is that neither is close , because infinity is n’t a fixed tip – both numbers are “ infinity away ” from infinity , if you wish . But “ while we often think of eternity as ‘ the largest ’ or ‘ something beyond all numbers , ’ our minds do n’t always process it that way , ” Pinhas told PsyPost .

Now , it ’s important to observe that the study only present a limited motion-picture show . Most of the participants were psychological science or engineering undergrads , which is hardly generalizable to most the great unwashed , and only the lemniscate – that ’s the technical name for the sideways - eight symbolisation we use to denote infinity – was used . “ It ’s possible that other symbolic representation of eternity might be processed differently , ” Pinhas said , and “ in fact , fresh inquiry in my lab indicate this may indeed be the case . ”

Still , it ’s an intriguing penetration into the ways our brains grapple with construct that defy hunch . After all , we ’re basically a group of anthropoid with dream – we were never mean to be dealing with abstract construct , so it ’s an interesting interrogation as to how we deal ( or , patently , mismanage ) to do so .

“ The goal is to gain abstruse perceptivity into how the human idea handles concept that lack lineal , concrete connections to everyday experience , and how this influences reason and determination - making , ” Pinhas explicate .

“ This research highlights how deeply our understanding of numerical concepts is rout in forcible experience , ” the researcher concluded . “ It also raises broader questions about how our mind comprehend abstract concepts in world-wide . ”

The subject is publish in theJournal of Experimental Psychology : Learning , Memory , and Cognition .