The way a Galileo thermometer works is, you've got a column of transparent liquid of known density. Suspended in the liquid are a bunch of rigid spheres or whatever, each of which has a different density and a different color. You can gain information about the temperature of the liquid (and thus, to a close-ish approximation, its environment) by observing which spheres are floating and which spheres have sunk. This is obviously not cutting-edge technology. In fact at this point I believe it is pretty much a novelty item. But! It seems to me that if you have a fluid with a known temperature, but an unknown/changing density, the same principle could be used to monitor the density (aka "specific gravity"). Is anyone aware of this being done? My thought is that you would sanitize several spheres of known density (similar to the spheres from a Galileo thermometer) and add them to the fermenter along with the wort. They would all float at first, but as each one dropped you would know that a particular SG threshold had been crossed. Of course the precision would be pretty crude, but it might be helpful for figuring out when, say, ~75% of fermentation had been completed or whatever. I can think of a few objections. First, you might not be able to detect the spheres visually (for instance, if you are brewing in an opaque fermenter, or if you are brewing a dark beer). Second, yeast and other crud (or even CO2 bubbles) could stick to the spheres, changing their buoyancy and corrupting the measurement. Third, if you can see into your beer, you could just stick a sanitized hydrometer in there for the duration of the fermentation. Fourth, it would be pretty important to measure the fermentation temperature accurately. But I can still imagine it being feasible. Maybe you could have a button that you push that causes the spheres to flash LEDs a few times (each in a different color), allowing you to locate them even if the beer is murky. Maybe they could be detected remotely, by radio signal or something. (I don't know.) I'm just throwing it out there!
I have one of those thermometers with the small colored globes, so I know what you are describing. I don't know of any usage of this type of gizmo in the brewing process, although the logic seems like it certainly could work. But the practicality may not be present to make it a feasible device for a major reason that you suggested. You mentioned several ways that the visibility of the globes would be a detriment to being able to use this method, and I'll and one more way - krausen bubbles. You wouldn't be able to see which globes are still floating once krausen forms. So, to me there are just too many strikes against using these things to make them practical.
Temperature is not that important to density over the range of most fermentations. Most homebrew hydrometers are calibrated for 60F or 68F. Assuming 60, lager fermentation at 50F reading 1.050 would be 1.049 if raised 10 degrees. An ale fermentation at 70F reading 1.050 would be 1.051 at 60F. Furthermore, knowing that gravity has stabilized is arguably more important than knowing it precisely. For the most part, I just pitch yeast and forget about it and check in on it several days later; gravity doesn't inform my actions, per se. One place where gravity might inform your actions is if you were adding nutrients throughout the fermentation or wanted to stabilize your brew chemical before it reached terminal gravity. Both of these are more of a wine/mead thing than a beer thing. The beer procedures I can think of where know gravity could be helpful include raising temps for diacetyl rests or otherwise trying to drive the fermentation. The other place I could see wanting to know gravity is in experiments where you are trying to interpret what the yeast are doing. You mentioned some higher tech approaches at the end of your post. You might already be familiar with the beer bug?
But you really cannot do this and have to work out the same every time. I try to explain this to wine/mead/cider makers that one year it may be perfect and after that you can never hit it right again. Stopping an active fermentation is not an easy feat.
Noted. Just repeating my understanding that some people try to use the gravity info to guide this action; never tried it myself. I prefer to let the yeast run the show.
These are used to check the density of auto coolant. Very crude but it gets the job done and that is enough. I like your total homebrewer hack approach. This is the stuff that put us on the map. Even the word Homebrewed has come to mean "extraordinary fix with ordinary equipment". Soda kegs for beer. Half barrels for kettles. Crack open an old hot water heater to get the propane flame assembly and so on. So kudos for that. But using a hydrometer is really easy. These floating balls would eliminate the need to grab a sample but that's not really an obstacle imo. And hydrometers are not really that temperature sensitive. Cheers.
I like the idea but as others have stated, feel it would be tough to monitor the spheres in the beer. I feel it would be better to have a sight glass built into the side of a the fermentation vessel and have a built in hydrometer there. That being said, I envision this like old weight scales situations where you plop one in beer you are about to buy and it sinks and you curse out the barkeep on selling watered down beer.