The following are just a few pointers relating to the hardness of materials.  Everyone learns a bit about hardness in science class -- diamonds are very hard, 10 on the scale -- but many people never fully integrate that knowledge into their everyday lives.

When you go to a fine steakhouse, they'll serve you a sizzling steak on a metal plate sitting on a wooden base.  It's so tender, it cuts like butter.  Actually, it might not really be all that tender; the secret to how nicely it cuts is that metal plate.  You see, the proprietors of that steakhouse know that you'll be a happier customer if the steak is easy to cut, which means they need to provide a sharp knife.  You can't keep a knife sharp, though, if you're using it on a porcelain dish!  Porcelain is harder than steel -- even the high-carbon steel that top-grade steak knives are made of.  Each time a customer scrapes the cutting edge of a steak knife against a porcelain dish, that knife gets a bit duller.  So the secret is:  Don't give the customer anything that he can use to dull that knife!  A plate made of relatively soft metal is ideal; it looks special, it's durable, it's heat-resistant -- you can heat it up with the steak in order to help keep the steak sizzling while it's being served -- but most importantly of all, the customer can hack little scratches into that plate all night without dulling the knife he's using.  And no, cutting the steak itself doesn't dull the knife; steel is harder than meat.

BTW, the wood base is just a convenient way to carry a hot metal plate and prevent it from burning the table.  Wood is a pretty good thermal insulator.

Steakhouses use other tricks.  At least one steakhouse chain has used a promotion in which you get a free knife with every steak.  That's right, you eat your steak and then take the knife home with you.  The next customer gets a new knife.  They roll the cost of the knife into the price of the steak dinner.  You think you're getting a nice prize -- and may come back a few times just to complete the set -- while they save the costs of washing and resharpening that knife.

Now think about how things work in your kitchen and dining room.  I'll bet you don't have any metal plates, do you?  If you're serving steak -- or chicken, or pork, or anything else that calls for the diner using a "steak knife" against your porcelain dishes -- you may have been wondering why those knives don't seem to cut as well as they did when they were new.  Now you know.  One solution -- presuming you're unwilling to go out and buy a set of metal plates -- is to cut everything into bite-size pieces in the kitchen so nobody at the table has any need for sharp knives.  Another solution would be paper or plastic plates.

In the kitchen you're likely to have an entire assortment of knives.  If you're not using a cutting board of some type, they're all dull.  That's what a cutting board is about:  It's a surface upon which you can cut things without dulling your knife.  Traditionally a cutting board is wood, but wood is a disaster from a sanitation standpoint; any nasty contamination in a piece of meat can find its way into the grain of the wood and fester there forever.  Trained chefs will only use a wooden cutting board before cooking meat, so any contaminants are killed by the cooking process.  All in all, a plastic or metal cutting surface probably makes more sense.

A relatively recent development is the ceramic knife.  At first they were stupid expensive and difficult to find, but now Walmart sells them.  The whole point of a ceramic knife is hardness; ceramic is harder than steel, so it holds an edge better.  Once you use a ceramic knife, you'll understand why this is a good thing.  They are sharp and they stay sharp.

You will notice, though, that while there are many types of ceramic kitchen knives available, you can't find a set of ceramic steak knives.  That's because ceramic steak knives would be a big mistake!  You know those porcelain dishes that have dulled all your old steel steak knives?  Well, when you cut a steak on a porcelain dish with a ceramic knife, the porcelain loses.  The ceramic knife is harder than the dish, so it cuts the dish.  You'll find a nice array of scratches all over your fine china.  There's no fix for that, you'll have to throw them away and get new dishes.

It's been known for centuries that ceramic is harder than steel and therefore ceramic knives should cut well.  The reason they haven't appeared until fairly recently was the difficulty in making them strong enough and durable enough that they wouldn't shatter as soon as you tried to cut something.  Fortunately, the technology for making strong ceramic knives is now a reality -- but you still don't want to be using one to pry open a can of paint.

When you need to sharpen a knife, you need to carefully rub it against something that's harder than the knife.  With a steel knife, that's pretty easy; almost any rock is harder than steel, and so is concrete and various other construction materials.  Perhaps the biggest challenge is finding a surface that is smooth enough to sharpen and hone without leaving the edge looking all ragged.  Traditionally the "Arkansas stone" has been valued for its fineness in this regard.

When you need to sharpen a ceramic knife, though -- which you might eventually need to do -- you'll need to be more careful about what you use to sharpen it.  Many sharpening stones will fail miserably because the ceramic is harder than the stone.  You can usually tell what's happening by checking the marks on the surfaces.  The ceramic knife is usually white, but if it develops dark areas while you're rubbing it against something, that means the item you're rubbing it against is getting worn away rather than the ceramic!  Try something else.

Another popular item for sharpening knives is -- a ceramic hone!  Again, ceramic is harder than steel, so it works great on steel knives, and it's even finer than an Arkansas stone so it leaves a nicely polished edge.  But it's not going to work well on a ceramic knife.

Fortunately, a diamond grit hone is a fairly commonplace item these days, and diamond is harder than ceramic.  When you use a diamond hone to sharpen a ceramic knife, you'll notice white deposits on the surface of the hone.  That's the indication that the hone is successfully removing particles of the ceramic, meaning you are making progress.

Everyone with a pair of prescription glasses is concerned about what they use to clean them.  Prescription lenses are expensive, you need to use them every day, and you hope they'll last at least a coupla years before they get all scratched up and need replacing.  And lenses are plastic nowadays which isn't nearly as hard as glass, so they scratch easier.  So, use only lens cloths or lens tissues, right?  Well, surprisingly enough, the primary idea behind lens cloths and lens tissues is to be lint-free; you don't want little fibers all over your lenses right after you get though wiping them clean.  But as far as avoiding scratches is concerned, you can use pretty much any tissue or paper towel that's handy.  Plastic lenses are harder than cellulose fibers.

What you don't want to use is any cloth that's been through the laundry!  True enough, plastic lenses are harder than cotton, but tap water usually contains some level of minerals such as calcium or iron.  When this water is allowed to air dry on a glass, it leaves water marks -- little mineral deposits.  It leaves those same deposits on cloth, you just can't see them -- but those mineral deposits are hard and will scratch hell out of your prescription glasses!  So avoid wiping your lenses with anything that's ever been wet.

Camera lenses are a different issue.  They may be glass or plastic, but the really high-dollar ones have optical coatings on the lenses.  Only clean them according to the directions that came with the camera.  And, of course, keep a lens cap on them when not in use to minimize the amount of cleaning they'll need.

When doing the household chores, often a cleaning job depends on using a scrubbing medium that is softer than the item being cleaned (so it won't scratch it) but harder than the dirt!  This can get very challenging when the dirt is pretty hard, such as mineral deposits from water drying on surfaces.  The surface itself being relatively soft, such as a fiberglass shower stall or a resin countertop, doesn't help.  Scouring cleansers such as Comet and Bon Ami try to provide an abrasive component that won't scratch most common kitchen and bathroom surfaces -- they can be used freely on porcelain, glass and chrome -- but it still might be a mistake to use them on countertops or plastic microwave oven doors.  If there's any doubt, always test an area that doesn't show before scrubbing the entire surface.

So, you've got a glass coffee pot that's hopelessly stained?  I suggest steel wool.  That's right, glass is harder than steel, so steel wool won't scratch glass.  If you don't believe me, try it on some cheap glass you don't care about first.  Of course, those water spots are hard, too, so whether or not the steel wool will actually take them off is another question.  It might take some work.  If the glass has paint or other markings on it, obviously there's a risk that the steel wool will take them off -- but it hasn't taken the markings off my coffee pot yet.  I dunno what they use to make those markings, but it's pretty tough.

If your kitchen sink is stainless steel you can skip this paragraph.  However, if you have a porcelain sink -- which is actually made of cast iron with a porcelain coating -- you've probably noticed that that sink can get really dirty and ugly after a while and you have to give it a good scrubbing with a scouring cleanser to get it looking bright and clean again.  Here's the problem:  That porcelain coating is harder than the metal pots, pans, and flatware you've been piling in it!  Any metal item that rubs against the surface of that porcelain is going to leave a mark.  A stainless steel butter knife that only touches it lightly will only leave a barely-noticeable mark, but an aluminum pot -- or a stainless steel frying pan with aluminum cladding on the bottom -- will leave a big ugly black streak wherever it rubs against the surface of that sink.  That mark is actually microscopic particles of metal that have been rubbed off of your pot and embedded in the surface of the porcelain -- which means you're not doing your pots any favors, either.

Recommendations?  Well, my primary recommendation would be to get a stainless steel sink!  But I couldn't even talk my own wife into that, she insisted upon a porcelain sink, so we've gotta deal with it.  Obviously, the first priority is to try to keep those pots and pans off the sink.  Laying a wash cloth in the bottom of the sink before setting the pots and pans in there will do wonders toward keeping that sink looking nice.  You barely have to worry about the flatware as long as you don't forceably rub them against the sink.  You'll still have to scour the sink every now and then, but now that you know what's causing the marks it'll probably be a lot less often.

The mineral deposits left by tap water have been mentioned several times in the above paragraphs.  These deposits are very difficult to remove from glasses and other surfaces -- including your car, if you wash your car with that water and let it air dry.  There is an excellent way to minimize that problem, though, and that is to rinse the tap water off before it dries using purified water that doesn't have any minerals in it.  You can get purified water for about 30 cents per gallon from a machine in a grocery store if you bring your own container -- so save up some milk jugs.  Rinsing an entire car after washing it can take three or four gallons, but you'll be happy with the results.  Or you can take it to the car wash; any professional car wash facility includes its own water purification system for exactly this reason.  Likewise, rinsing your glasses and other dishes with purified water may seem like a bit much, but you may find the results most gratifying.