It helps to think of the sign as a direction. Above zero/below zero, credit/debit, above sea level/below sea level, etc. When the sign changes, you change direction.

So, +1 is "take a step," and -1 is "turn around and take a step" which means you move backwards one step.

With --1, you're essentially saying "turn around, then turn around, then take a step," which results in you just spinning about and moving forward just like with +1.

The rotation can sometimes be surprisingly chaotic, though. Saturn's moon Hyperion wobbles so wildly that it was impossible to plan for a probe flyby to cover unexplored areas.

Ne.

The reason you're asking is also a part of why they've started calling it Low Energy Nuclear Reactions. Firstly, because "cold" in the stellar sense is a lot more hot than in the human sense, and secondly because "cold fusion" does not have a good track record for predicting anything which gives it a bad rep.

If you put 10 coins into your bank account and the balance ends up being +3 coins, how much balance did you have to start with?

Technically speaking, yes, you can say that "no solution is possible" since there is no such thing as an anti-coin (or even "half a coin," depending on how you define it) but life becomes immensely easier if you accept the concept of "negative coins" to represent debt. That way you can easily have a balance of -7 on your account and offset that by just adding money to the account.

A similar thing happens with imaginary numbers. Instead of representing things which flip between two states (positive and negative) they rotate between four states, and like negative numbers, that enables a lot of extremely important math.

Mostly just because they make a mess out of the flow of the program. Modern languages have tools you can use to perform complex logic with a syntax that doesn't seemingly arbitrarily hop all over the code to get things done.

GOTOs were useful in the early neolithic era when Grog first invented COBOL and the concept of a "loop" was novel, but nowadays there are better options. If you find yourself in need of using one, chances are that whatever structure you have in mind can be represented in a way which doesn't need a GOTO.

There is no real reason. Base 10 as the default system probably comes from counting with fingers, but there's no reason we couldn't do math in base-12 if we counted with joints instead.

Ancient Babylonians counted with base-60. We still measure time in increments of 12 and 60 because of that, but also because both 12 and 60 are convenient bases to work with since they're easily divisible by 2, 3, 4 and 6.