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Sorry, those weren't even english sentences, let alone economics. They were just disconnected phrases. No, there is no necessary connection between the size of a trade deficit and the value of the currency. The long run value of the currency is set by the money supply, which is not determined by the trade deficit. The trade deficit tracks a capital inflow and a savings shortfall, that more capital is invested here than is saved by domestic residents (whether they are citizens or not).

But you did not address my question about gains from trade. I ask, because it seems there is a common loose confusion on the subject, that the trade deficit tracks some net "score" of whether we are making money in foreign trade or losing money in foreign trade.

It simply doesn't. The trade deficit has nothing to do with whether we make money by trade of lose money by trade.

In fact, we make money by trade. When a given trader doesn't, he stops what he is doing because he has no reason to throw his money away. Nobody ever enters a trade saying "gee, here is a swell way to give away $500 billion for nothing". The myth apparently stems from one entry accounting or a fixation on the money side of any trade.

When you go to a GM dealer and drive away an SUV, you don't think you lost money on the deal because he has the cash from your auto loan and all you have is an automobile. If the automobile was a good buy for you, a transaction you entered voluntarily and happily, you are happy about it precisely because the SUV is worth more to you than the money in the auto loan.

The gains from trade mean, the fact that the money is worth more to the dealer and the SUV less, and the SUV more to you and the money less. That's why you are both happier with the corresponding item in the other guy's hand. The car dealer isn't sitting there thinking, "gosh darn it, that customer just stole one of my SUVs! Sure, he paid for it. But now he has that SUV and I don't! I've lost a whole car!"

Gains from trade exist whether money changes hands net, or not. If you did the GM dealer's showroom as a contracter, and he paid you $20K, and you bought an SUV from him and paid him $20K, there are still gains from trade - twice. Because the showroom is worth more to him than its labor cost to you. And the SUV is worth more to you than its (equal) money cost. Those two differences are the gains from the trades. If the showroom cost $25K, the dealer paid you $5K and an SUV. But was still happy about it or he wouldn't have bought it from you. That he has a $5K "deficit" with you is not something he bothers his head about.

So, again, why does this work for ordinary domestic trade, but not international - in your opinion?