Drinking alcohol is usually under 40% ABV (spirits) and a lot lower for wines (11-13%ish) or beers (3-6%ish).

That leaves a lot of space for other things and flavours - and much like cheap "orange flavour drink" doesn't compare with freshly squeezed orange juice, the mixers will have a huge affect on flavour, the good stuff is more expensive.

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.

Great explanation, thanks!

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Sure, in the same way that, when you don't know about fractions, you can say 3 divided by 2 isn't possible, because there's no integer that, when multiplied by 2, gives you 3.

But you don't do that, because inventing the idea of a number 3/2 is pretty useful, and lets you do many calculations that you couldn't do without it. In particular, you get ideas like "3/2 is the same kind of no-solution-is-possible as 6/4 is".

Imaginary numbers are the same kind of thing. They aren't "impossible", and "imaginary" is just a name (you could call them the "Bob numbers" if you wanted to). They are a perfectly well-defined algebraic object. They're only imaginary in the sense that they don't fit onto the number line, and human intuition about numbers tends to come from ideas like length that happen to be real-valued.

But in practice, imaginary numbers show up all the time in descriptions of the world around us. In particular, they're critically important in quantum mechanics, where the fact that the states of particles aren't real-valued is essential to the theory (many quantum-mechanical phenomena actively require this). They also turn out to produce very compact representations of things like periodic behavior, as with a spring or a pendulum. And relativity tells us that the relationship between space and time is the same kind of thing as the relationship between the number "3" and the number "3i".

You could do all of this with objects that are just pairs of real numbers (a,b), defined in such a way that (a,b) "times" (c,d) = (ad + bc, ac - bd) and (a,b) "plus" (c,d) = (a + c, b + d). But the object you've invented has exactly the same properties as imaginary numbers do, so why add the extra complexity?

Well, "taste" is a very subjective criteria, to start with. But, in the case of Vodka and Gin, two spirits which you can bottle as fast as you can make it (no aging requirements), what affects the quality of the spirit are the ingredients used to create it.

Specifically, what grain are you using when you distill it into alcohol, or what botanicals you use to infuse a flavour in creating your Gin. Both of these things can and will, impact the "taste".

In the case of whisky, there are aging requirements in most jurisdictions. Most of these also involve specifying the type of container used to age the spirit (wood). Aging in a wooden barrel allows for the lignen within the wood to be broken down by the volatility of the alcohol. In turn, the wood absorbs some of the harsher characteristics of that spirit, mellowing the taste. The longer the aging (to a degree) the more this impacts taste. Further, if you are aging the spirit in a barrel previously used for something else (like say wine), that too, will have an effect on taste.

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That's awesome!

I think your premise is wrong, but that could just be a language problem on my part. As to your actual question. When something has no solution 'no solution' is the solution. Try to devide any number by zero. The calculator will no just make up a number. When you do it manually the solution looks something like this: L={}

Just not that war. The one that actually happened in the real world. That’s the moral of the story.

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Missing the point. Some may have prepped for a war they wanted, but no one wanted the war we actually got. The lesson of WWI was forgotten in only 20 years; don’t take anything for granted.

In light Of all this discussion, there's a great video about the J58, and how it operates in various speed modes.

https://m.youtube.com/watch?v=F3ao5SCedIk

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Rainbows happen when light from the sun behind you hits water droplets in front of you, and gets bent back towards you. The places where the light of each wavelength gets bent by the right amount to reach your eyes are in a circle around the line from the sun through your head. So what you see is however much of a circle as the landscape around you allows - usually about half a circle. And different colours get bent by different lines amounts, so the colours get smeared out into circles of different widths.

It's possible to see a full circular rainbow under the right conditions (say, from a plane or high-enough ground); there are photos out there. Google it.

I saw full rainbow circles while flying a little Cessna around 5000’ above the ground. It was a memorable experience.

Like boiling the water?

Sure we can!

They are actually circular.

The thing is they appear as a circle with the center being in the exact opposite side of your head from where the sun is.

If you look at a rainbow the sun is behind you and the center of the rainbow is exactly on the opposite side of where you head is.

There is a line from the sun, though your skull to the apparent center of the rainbow.

Obviously since the sun tends to be in the sky, the center of the rainbow tends to be below the horizon.

If you are high up in an airplane or similar you may be able to see the full circular rainbow if the sun is low enough.

The sun shines at the water droplets in the air and due to the way light going from air to water and back works part of it ends up back where it came from. Sort of like a mirror.

So if you just had a single color of light shining at water droplet in the air from behind you, you would see a single thin ring of that color.

Since different wavelengths of light get thrown back at slightly different angles you don't see just one white ring but a spectrum of visible light drawn out across the rainbow

It works light a prism splitting up light into a rainbow of colors when the light goes from air to glass and back to air and the surfaces where the glass to air interface are, are at an angle.

The raindrops are made of water not glass and they are spherical not prism shaped, but it is the same general principle.

The spherical shape also means that the light acts the same way in any direction all raindrops that are at a certain angle from the line from the sun through you will send the light back at you.

That angle is about 42°.

There are additional fainter rainbows at different angles that you don't really see easily with your eyes, but that can appear on photographs.

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Bigger objects bend space more.

Place a marble on the trampoline. When you stand on the trampoline, you the marble will roll towards you. The heavier you are, the faster the marble will roll towards you.

The more you can stretch the trampoline, the more you affect other objects on it.

Get too heavy, and you’ll poke through, like a black hole.

They aren't. They're circles (or they would be, if rain were falling throughout your field of view).

A rainbow appears in a circle of a particular size (the size has to do with the refractive index of water, so it's the same for all rainbows) centered around a point opposite the Sun in the sky (the "antisolar point"). But since the Sun has to be up for a rainbow to appear, the antisolar point is necessarily below the horizon, so less than half the rainbow is visible if you're on a flat surface.

If you're in a position where there can be rain "below" the horizon in your sky (as if, for example, you're in a plane or on top of a high mountain), you can sometimes see the full circle of the rainbow. But most people live on approximately flat surfaces or at the bottom of valleys, not near the tops of steep hills, and it's hard to get the geometry right to have the Sun above you and the rain below, so rainbows are normally just small portions of a circle.

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In all three of these types of jet engines, air from the front enters, is compressed, and is mixed with fuel. Then the fuel is burned and the resulting hot gas leaves out the back of the engine. Because the fuel heats up the air, it's hotter when it leaves than when it enters, so you get more energy from letting it expand than you spent on compressing it.

In a turbojet, a fan at the front pulls in and compresses the air, and an inverted fan called a turbine captures some energy from the departing air to keep the fan spinning. In a ramjet or scramjet, the engine draws in air by flying forward into it ("ramming" into the air), and compresses the air by having internal geometry that air has to increase in pressure to pass by.

The difference between a ramjet and a scramjet is that in a ramjet, the compressing geometry slows the compressed air to below the speed of sound before the added fuel starts burning, whereas in a scramjet the combustion happens in air that's moving faster than sound. "Scramjet" is short for "supersonic combustion ramjet."

Fluids (liquids and gases) form layers based on their density, which we find by dividing their mass (how much stuff there is and how heavy it is) by their volume (how much space they take up).

Gases (and indeed most substances) expand as they get hotter; the amount of stuff, and therefore mass, stays the same but the volume increases - therefore the density falls.

Hotter air is thus less dense than colder air and so it rises, causing the colder, more dense air to fall.

As you get higher in the atmosphere, there's more space to occupy (think concentric circles; they get bigger and bigger as the radius increases). With more space to occupy, again the density is going to decrease as the gases spread out. This also causes them to cool down (Boyle's Law, Charles' Law and the ideal gas law are a bit beyond a 5 year old though).

Also most of the sun's energy that comes to earth hits the surface (gas molecules are TINY so most of the sun's rays will miss them and some of the ones that do hit them bounce off) so the surface warms up far more than the atmosphere does. The surface then loses heat to the atmosphere. Since this heat starts at ground level, the air closest to the ground has more chance to absorb it and therefore the air closer to the ground will be hotter than air higher up.

The surface beneath our feet usually has fairly high resistance. So voltage fades away quickly, electricity doesn't travel too far. If there's a live wire in the earth underground that's broken, a front hoof and a back hoof can be at very different voltages, so the power travels through the horse in preference to the earth. This is not a good thing.