My first trip when at liberty from daily surveillance as a slave will be to the milkmaids. Or cows generally.
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Sandwich maker.
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Arabic numerals and the concept of zero. All your maths are belong to me!
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You rely on the refrigerants expansion to dissipate heat away from the interior of the fridge.
https://www.google.co.uk/url?sa=t&source=web&rct=j&url=https://www.saylor.org/site/wp-content/uploads/2013/08/BolesLectureNotesThermodynamicsChapter10.pdf&ved=0ahUKEwjrj7SPj7DUAhUCrRQKHTRoAl4QFggpMAI&usg=AFQjCNExmr9qbpbmqHkVcneybicrNOGh8Q&sig2=4n37EYCP_rFqFXSuHL3PNQ
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Figure if you can force iron bar through a small hole you can extrude wire. Cover that in wax wrap it round another bar you can make a solinoid. Use that to make relays. Then try and build a full adder out of the relays.
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To answer your question seriously (if simplistically) it comes down to the relationship between volume, pressure, and temperature. With gases, as volume decreases, pressure increases, and as volume increases, pressure decreases. As pressure increases, temperature increases, and as pressure decreases, temperature decreases. So if you have a coil with gas being pumped through it, one part being low volume (high pressure) and another part being high volume (low pressure) there will be heat generated in the low volume section and heat removed (coolness generated) at the high volume side, in equal measures. Stick the low volume section on the outside of a box, and the high volume section on the inside of a box, and you have a fridge. At least thatâs what I remember from my science classes.
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There are lots of inventions simpler than a fridge, but itâs not so easy to separate them from the world they appeared in. I understand how a bicycle works, but doubt I could make one worthwhile on ancient streets. Maybe the simplest invention people missed is the fore-aft sail, but there are probably reasons it wouldnât actually be so good on ancient ships, and if nothing else they can already go against the wind by rowing. Plentiful slave labor ruins most advancement.
For staying alive, hopefully I can capitalize on the fact that I can write Roman letters and find work (more likely ownership 
) as a scribe. Then with luck, after learning enough language, I would eventually have a chance to write up at least a few more abstract ideas from our time. I know enough to give algebra a head start and make a case for a more Newtonian physics, save some astronomers some trouble down the road.
Biology is harder but amid the tree of life stuff there are some really important ideas. Contrary to the shirt, antibiotics arenât a simple case of blue molds being healthy, but you could at least suggest the key concepts of germs and contagion. And in the end, I would want to at least argue that women and slaves arenât actually inferior save in education; though seeing how well those ideas took in America, Iâm sure it would only be for the sake of saying I tried.
Alternately, make sandwiches. It worked for Arthur Dent, so who knows, itâs worth a shot.
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I think the big trick would be staying alive long enough to accomplish anything at all. But, assuming Iâm not dead or chained up somewhere awaiting execution as a witch, I could probably make the most difference in food safety and preservation.
The stuff needed for canning might not be available, but there are plenty of ways of excluding air using fat or wax. Getting folks to wash their hands would probably be pretty huge, too. Maybe I should actually make some soap for practice, just in case I am transported back to 1AD.
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A world where seven years of Latin in school finally pay off!
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Youâve received plenty of technical answers so far, so Iâll just add a (very impractical) demonstration of the principles that uses rubber bands for coolingâŚ
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Little know fact Davinci was actually a time traveler. His famous sketches were actually him trying to figure out how modern things worked that he had always taken for granted in his time.
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Gunpowder will always make you money.
Other good parlour tricks would be pin hole camera and the compass.
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You might have trouble finding film, but a camera obscura is eminently do-able.
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I think Iâd show people how to manufacture goods on a factory line.
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Also thinking I could create a Turing Machine and speed up computer systems development, and then Iâd use my computer to invent a time travel forward machine so I could rescue Alan Turing send him forward to someplace and time nice and gay friendly and keep him safe and sound and being the amazing person he was.
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I have died of dysentery⌠oh wait wrong game.
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Itâs an excellent point. The counter-point is that a lot of the inventions of the Middle Ages were really re-inventions, and discoveries re-discoveries, of things which science/natural philosophy was on the verge of making commonplace knowledge right before the collapse of the Roman Empire. Things like heliocentricity. They did already know a lot about how to use gears and water power. Something like a jacquard loom would have impressed them without freaking them out. Anything that took two or more things they already knew about and put them together into one new thing.
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âHow do I make a refrigerator?â
âHow do I make an electric motor?â
âHow do I make a steam engine, exactly?â
Those are all hard.
Yeah, but how would you convince them about the germ thâ
OMG telescopes and microscopes would be EASY 
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