Recent comments in /f/explainlikeimfive

BowzersMom t1_j6cjski wrote

That’s not true. Dehydration means you are taking in less water than you are losing to the point that your body isn’t working well. The first signs of mild dehydration include thirst, but also headaches, muscle cramps, dark urine, cool dry skin.

If you are just thirsty, you should drink some water. But just being a little thirsty doesn’t mean you are in danger of anything.

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Regulai t1_j6civzx wrote

So a lot of the time with math names like "imaginary" just leads to confusion. In general these are numbers we can use in math to calculate things, but that you cannot physically hold in your hand.

Forget imaginary and just think of negative. You cannot hold in your hands "negative 5 apples". You can however represent it with a note and poof you now have credit and debt, all because you are considering a number that cannot physically exist (negative of something). Imaginary numbers are just another leap in this sense going even deeper into math.

The point ultimately is that they let you calculate things that might otherwise be impossible to calculate by filling in gaps.

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lunatickoala t1_j6civq4 wrote

It's interesting how "useful day to day" can change so much in context. Logarithms are the basis for how slide rules work so in the time before personal computers when logarithms were more useful then than today.

And while most people don't actively use logarithms in their day to day life, they are incredibly important because human perception is generally logarithmic, not linear. The decibel scale is logarithmic because of this. There's even some evidence to suggest that logarithmic thinking might even be more natural. https://news.mit.edu/2012/thinking-logarithmically-1005

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lunatickoala t1_j6chnor wrote

Imaginary number is a bad name for them... and intentionally so. It was meant to be derogatory. Mathematics has a history of people not liking new developments because people think of math as a very logical and objective thing and those developments can fly in the face of what they believe.

There's an apocryphal story that someone in the Cult of Pythagoras proved that the square root of two is irrational and they were so outraged by the idea that a number could be irrational that they took him to sea in a boat and returned without him. They believed that all numbers could be expressed as a ratio of two integers and an irrational number by definition is one that can't be expressed as a ratio.

The Ancient Greeks also didn't believe in the idea of zero or negative numbers and both were very controversial in the Western world for many centuries afterwards. In math today, the standard form for polynomials to put all the coefficients on one side and set it to zero because it's really useful. For example, Ax^2 + Bx + C = 0 for the quadratic polynomial where B and C are allowed to be zero and A/B/C are all allowed to be negative. But up until I think the 1500s, Western mathematicians didn't have a standard form but a family of forms specifically to avoid zeroes and negative numbers. Ax^2 + Bx = C, Ax^2 = Bx + C, Ax^2 = C, Ax^2 = Bx, etc.

Imaginary numbers first saw real use in the cubic equation because the people who found it realized that in some cases it involved taking the square root of a negative number, which people believed to be nonsensical. However, the cubic equation worked because the imaginary numbers cancelled each other out. Thus, they were called imaginary because people didn't think they were "real" and were only a mathematical trick that happened to work out and not something that's meaningful.

To get a feel for what it was probably like when irrational numbers, zero, negative numbers, and imaginary numbers were first introduced, look at the comments whenever 1+2+3+4+5+6+... = -1/12 comes up.

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NameUnavail t1_j6cggpi wrote

>Note that the watt is a standard unit of power in the SI system. However we still use things like horsepower (1 HP = 746 W) and BTU/hr as non-SI unit measures of power. One used even today for engine power output and the other for cooling and/or heating

The US just has a furious hatred for standardisation, don't they ?

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JalarianDeAndre t1_j6cg4wc wrote

Imaginary numbers are 2D numbers.

To give a brief example, you could point to a map and say walk 5 meters east, and 5 meters south. This would also mean 5 -5i on a Cartesian graph. Also this is used in wave calculations as waves can be denoted as vectors and plotted on a graph.

The term imaginary is stupid. They should be called lateral or perpendicular numbers

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