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One of the initiatives to provide a new international standard for the kilogram is the International Avogadro Project. Essentially this involves producing extremely perfect spheres of silicon atoms. There are currently two of these, perfected by a master lens-maker called Achim Leistner. The Wikipedia article references his ability to feel imperfections at an atomic scale, and I have seen the same claim made in a documentary on the subject.

Is it actually possible for humans to feel bumps or imperfections that might only be a few atoms 'high'?

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    Actually the feeling of touch itself is an illusion!-futurism.com/why-you-can-never-actually-touch-anything – pericles316 Feb 29 '16 at 10:28
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    I don't see any claim that he can feel individual atoms, or any details about how precise his touch is. Sorry to burst the bubble. – D J Sims Feb 29 '16 at 10:47
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    @Mustang "The research team has called his extraordinary sense of touch "atomic feeling"" en.wikipedia.org/wiki/Achim_Leistner – DavePhD Feb 29 '16 at 12:27
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    "Leistner describes his job as “massaging atoms.” He works by hand because he believes — and the most advanced computer imaging has confirmed — that no machine can match his touch. Taking a 1.01-kilogram silicon ball crudely cut on a 3-D lathe to within 10 micrometers of sphericity, Leistner spends several months polishing ...until he can feel the molecular structure of the cubic silicon crystal itself with his fingertips, 12 edges and eight corners barely protruding from the rounded surface." wired.com/2011/09/ff_kilogram – DavePhD Feb 29 '16 at 12:43
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    It's all anecdotal, but when I worked with AFMETCAL in Heath, OH, they had humans polishing the gage blocks under heavy-duty microscopes to get them so perfectly smooth that they had to be slid apart due to lack of air between the surfaces, and they'd weld together overnight from particles jumping back and forth. However, that was not a sense of touch thing, just very deft touch with extremely fine tools guided by microscope views. – Sean Duggan Feb 29 '16 at 13:21
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According to Feeling Small: Exploring the Tactile Perception Limits, studying randomly selected people with no previous experience:

the lowest amplitude of the wrinkles so distinguished was approximately 10 nm, demonstrating that human tactile discrimination extends to the nanoscale.

Leister stated in the interview Making the world's perfect Kilo :

this can only be done by hand because you actually have to feel what is happening. When you’re taking off a nanometre or 5 nanometres, or 10 nanometres or 20 nanometres, some of the errors we’re trying to correct are in the vicinity of only a few nanometres.

So human touch can work down to the 10 nanometer scale with no specific training, and Leister isn't really claiming to be much better than that.

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