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For the source, see this article in the Smithsonian.

A material based on a technique, called kirigami (a relative of the folding technique, origami) of cutting a flexible three dimensional pattern into a surface has demonstrated increased friction between a slippery surface, such as, but not necessarily confined to, ice, and the sole of a shoe. In the case of the shoe-sole, the pattern is cut into a thin sheet of steel. The increase in friction is estimated as 20% to 35%, at the current state of development. The information I have seen concentrates on reducing falls among the elderly, and says nothing about its potential use in sports, such as climbing.

Assuming a comfortable, light weight, and durable climbing shoe can be made with a kirigami sole, is this innovation (not yet on the market) substantial enough to be likely to change climbing grades and/or the rules for climbing competition? Please base your answers on the results of other effective innovations in sports gear on the rules and practices of the sports to which they are applicable.

The flexible kirigami sole mimics the motion of a snake's skin as she slithers, or the action of a cheetah's semi-retractable claws in a high speed chase.

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Probably yes and no. A high friction sole may be very useful on slabs (and in modern bouldering competitions even overhangs are made slabby by adding an outrageous amount of big volumes) but they are pretty much useless in steep terrain with small edges as footholds. So the effect is very different depending on the terrain. Competitions surely would be affected by this as the goal of competition route setting is to create problems that are on the limit of "state of the art" climbing. However, competition climbing is changing styles all the time. Just look at pictures or videos of a competition 10 or 15 years ago when bouldering was basically just very small holds connected by static moves.

The other thing is grading. Difficulty grading itself should not be subject to equipment. This means that innovations in protection (cams, bolts), climbing shoes, chalk or the widespread availability of training facilities (climbing gyms) should not change the rating. To my knowledge, all these innovations have made climbing safer and the higher grades more accessible. There was a time when UIAA 6 was considered the very limit as it was a closed scale. Nowadays most people will soon climb UIAA 7 after they started and progression into UIAA 8 (french 7a) or higher is probably possible for almost everyone willing to dedicate enough time and effort.

So all in all, a high friction shoe might make some friction based climbs more accessible to everybody but it won't be a help for many climbs of today with "proper footholds", especially in lower and medium grades

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