If you read my blog regularly, chances are you write software and therefore can't, because your tools don't exist in the visual world. They're just magic strings of minuscule magnets on a rapidly spinning chunk of plastic…
I took my chef's knife to the sharpener a few days ago. Cost a whopping $4 to have him put a wicked edge on it, and I watched it happen. I saw him carefully run the blade along a belt sander (for lack of a better term) a few times to give it the rough shape, then he used a bench grinder to finish the edge, a steel to hone it, and finally a jeweler's wheel to polish it. Not five minutes elapsed before he handed it back to me, wrapped in butcher's paper for the journey home.
If he let me loose in his shop, there's no way I could have achieved the same result. But given ten knives, I bet I could get a pretty good edge on the last few (after undoubtedly destroying the first couple). Nothing like his result, to be sure, but significantly sharper than the initial state.
Sharpening a knife is a pretty simple task, because a knife is an inherently simple item, but it's just one example. Consider a master furniture maker. He can take the same wood you and I buy at Home Depot or Lowe's and with his tools and expertise turn it into a beautiful bureau or armiore. Turn me loose in his shop and I'd probably be able to make a functional dresser in twice the time it'd take him to make an exquisite one. With some more experience, both using the tools and in furniture construction overall, I've no doubt I could make something I'd be proud to have in my home. It wouldn't be the same quality as something the master craftsman created, no question, but better than the prefab stuff you might otherwise buy.
So what's special about these tasks? Nothing, really. Most things are of a similar nature: cooking, playing music, grooming dogs, surfing, etc. Attaining mastery of a given profession requires certain in-born characteristics, but attaining laudable proficiency is pretty much available to anyone willing to put in the time (barring physical disabilities and such).
Every chest of drawers provides a way to organize and store clothes. People spend a lot of money on well made dressers that are made of pretty woods, appeal to their personal tastes (mission, contemporary, etc.), or are simply of a higher quality of manufacture. None of which has the least to do with holding clothes. Every dresser I've ever seen holds clothes with about equal proficiency, but even though the drawers are a bit sticky, I still use the one I had as a child.
Now consider software development. The tools are invisible. The process is invisible. The result is intangible. As far as a profession for a craftsman goes, programmers are fucked. Sure, we get paid because people are willing to pay for the benefits of our software, but it's 100% functional. No one buys software because it's well made or "pretty". They might pick between two vendors because one is less error-prone, but that's still functional.
Every database application provides a way to organize and store data. No one spends extra money on a database system because it was made with snazzy buttons, appeals to their sense of style, or was produced by a higher quality process. Every database system I've used is inconvenient in one way or another (no OFFSET, no CTEs, etc.), and every one is built using some completely opaque process by unknown automatons in some office building somewhere.
It has occurred to me that the reason for this could simply be that programming is so damned hard it can't be automated. As a result, there's no way to produce the gradations of craftsmanship that you see in dressers (from the mass-produced pressboard affairs to the hand-crafted hardwood masterpieces). With software all you get are the hand-crafted versions. Sure, some of them are simply horrible, but they're all hand-crafted.
Which brings me back to the point: programming is opaque for everyone that isn't also a programmer. There's absolutely no way you can take your average Joe, sit him next to you while you write something, and then give him your workstation and have him do the same. Unlike the furniture maker where a simple demo is enough to get the gist of what is happening, with software it's all abstract and divorced from anything tangible. My mom (who is fairly technically adept) doesn't have any idea what the hell Subversion is, and even if I sufficiently explained it, there's no way she would understand how massively beneficial vendor branches are. Heck, a lot of programmers don't understand vendor branches. And yet a one-year old can run her fingers over a piece of wood and tell you if you need to keep sanding (if not run it through the planer again).
Further, there's absolutely no way Joe (or my mom) can look at two pieces of software and compare their "quality" on any meaningful level. He can make distinctions like "this one crashes more", or "that one has confusing icons", but that's it.  Even a competent programmer looking at a piece of software has the internals almost completely hidden from them. Very careful observation can provide certain clues (the query optimizer must be making decision X based on inputs A, B and C), but by and large, everything is opaque. Again, contrast this with a fine bureau where you can see the carefully planed wood, the perfectly matched dovetail joints on the drawers, and the complete lack of any visible fasteners.
I certainly consider myself a craftsman. I hope to justify calling myself a master someday, but today is not that day. And yet every evening, as I'm walking out the front door to head home, I think to myself at how completely impossible my work is to appreciate. My kids ask what I did today, and I have no meaningful answer to give. The best I can do is "fixed some bugs", or "had an architecture meeting". I can't explain to my non-programmer friends what I do, or why it has such appeal. I live a dual life: a "normal" one and a programmer one. They are as compatible as fire and ice. I greatly enjoy the praise and criticism I receive from my peers regarding stuff I share, especially when it helps make others' lives easier, but I'd trade it all to bring something home from work one day, show it to Lindsay and Emery, and have them say "Wow, Daddy, that's amazing."