We examined the lint with a scanning electron microscope, which magnified it about 927 times by shooting electrons at it and noting how they bounced back. If we'd had a regular old optical microscope, we might have been able to reach this same level of magnification, though we'd be approaching the upper limits of that technology.
Electron microscopes can detect details hundreds of times smaller than optical scopes because electrons travel in more or less straight paths while visible light undulates in waves. The downside is that electrons can't see in color and can't travel much beneath the surface of things, no matter how transparent or translucent that surface might be.
All in all, however, if lint is what you're wanting to look at, then a scanning electron microscope might be just the tool for the job.
With its help, we calculated the width of this strand of whatever it is at about 20 microns–about one fiftieth of a millimeter. The hairs on our heads are usually more like 50 microns in diameter, so this probably isn't that.
This strand of whatever it is has obviously been through the wringer, even though our current washing machine doesn't have a wringer. The strand has been stressed, and were it not for a couple of microns of badly fraying inner strength at its core, it would have snapped completely.
Which does lead to speculation that what we're looking at here is My Last Nerve. . . .
But there are some other possibilities. Such as dog hair: dog hairs average about 25 microns in diameter, more or less in the same ballpark as this strand. Dog hairs often show a scaly pattern on their outer cuticles that looks kinda like the faint pattern we can sorta make out on what's left of the outer surface of this thing. And of course, finding a dog hair in the lint trap at our house, or pretty much anywhere else in our house, isn't completely freakish.
But really: could a dog hair get this mangled and shredded just from normal laundry processes? We want to beg off from a definitive answer; although we've worn many different hats over the years, we have never, ever presented ourselves as expert in the forensic analysis of dog hairs.
We've not yet, however, run out of options. Couldn't this thing be a fabric fiber from some item of clothing?
That electron microscope sure did come in handy.