Drugs, Flowers, Multiplication

1. Drugs

One thing I hadn't realised until today is that I had no idea how people smoke something like crystal meth because to me smoking means setting something on fire and inhaling the burning fumes. I hadn't considered that something where the substance is heated (as opposed to burnt) to turn it into a gas could be considered as smoking.

2. Skeleton Flower

There's a plant called the skeleton flower (Diphylleia grayi) which turns transparent on contact with water.

3. Multiplying Numbers up to 10

Today I learnt a method of multiplication found in sixteenth century texts. To multiply two numbers, 8 and 7, in the example, subtract each from 10. Multiply the results of these subtractions to get 6, which is the units value. Subtract one of the original numbers by the result of subtracting the other number from ten, so in this case 8-3 (or 7-2) to get 5. Put these answers together to get 56. See table below.

Number	Number subtracted from 10
8	10-8=2
7	10-7=3
8-3=5	2x3=6

I don't know how they would handle numbers such as 7x6 where the product of the result of the subtractions is two digits, in this case, 3x4=12 although it would be simple enough to carry the one.

Number	Number subtracted from 10
7	10-7=3
6	10-6=4
7-4=3	3x4=12

In this case the 1 from 12 should be added to the 3 but whether this is how people in the sixteenth century handled it is a mystery to me.

Why does it work?

Suppose the first number is x and the second y.

Number	Number subtracted from 10
x	10-x
y	10-y
x-(10-y)	(10-x)(10-y)

Since the result in the first column represents a digit in the tens column, we multiply it by 10 before adding it to the result in the second column, to get the result below.

10(x-(10-y)) + (10-x)(10-y) = (10x-100+10y) + (100-10x-10y+xy)
                            = xy

This proves that this method does indeed produce the product xy of x and y.