Myuncle

I am sure the OP doesn't doubt the existence of time as a human idea to keep track of movements in space, but that doesn't mean that time exists in reality. Many ideas exist only in our imagination and fantasy, but they don't exist in reality. Space, matter and movement, not only exist in our mind, but they exist in reality as well. The idea of two identical unities, doesn't exist in reality, but thanks to that we can have math, we can write 1=1, we can measure everything, and agree on these measurements, very useful indeed. The idea of a centaur, it does exist as an idea in our imagination, but not in reality, it can be a very useful idea for art purposes, but again it doesn't exist, just like Santa Claus. Heck, if I can understand that, I am sure everyone can understand it. That can be said for centaurs as well.

If matter could move in every direction without splitting, in theory things could happen at once, which is science fiction.

Any wave is made by atoms moving in only one direction.

Interesting question. The most obvious answer would be that matter, atoms, quarks, can move only in one direction. We can move, walk, run, only in one single direction, unless we split ourselves...

If division implies a subtraction for me it's fine, I would like to read it explicitly everywhere. On wikipedia or in the dictionaries, normally they never talk about any subtraction, they just say it's the inverse of multiplication, so in theory, yes, there is a shrinking involved, and I am just being anal about it...It's always good to see a consensus in definitions. Even multiplication it's nothing but a shortcut for addition. I can calculate 3x76556 with additions, but it would take me a year to write it down...So I suppose that, in the past, the origin of multiplication was the need to create a shortcut for long tedious additions, and the origin of division was to create a shortcut for long tedious subtractions.

What's your take on this? Does division imply any subtraction? Is a division the same thing as a fraction? Does the sign "÷" means exactly the same thing as "/"? I don't teach any children.

But the equations I wrote are 20÷4=5x4, and 20/4=5. Using "÷" only for division, and "/" only for fractions.

If you imply that you divide and discard the rest, you are absolutely right, but in fact, aren't we just being lazy in writing, and still confusing divisions with fractions? Let's say we have to apply divisions and fractions to geometry. Kids are introduced to a rectangle, they are given the measurement of the area and of one side (width or length), and they have to find out the other side, without knowing any formula, making a very useful effort in finding the formula by themselves, this would be very educational. So, the length of one side of the rectangle is 4, but 4 what? 4 mm? Not necessarily, they can be 4 squared biscuits. The given area of the rectangle is 20 squared biscuits. Now the kids will easily align 4 biscuits to make one side, and they are left to wonder what to do with the rest of the biscuits (20-4=16), they will make a useful effort to align the rest of the biscuits, they don't discard or ignore any of them, until they finished the rectangle, and they will notice that the other side of the rectangle has magically only 5 biscuits. So, some of them will realize that initially they are simply dividing 20 biscuits into 4 rows, then they will have to ignore 15 biscuits to find out the length of the other side, some of them won't realize it, but that's not a problem, at least they are making a healthy effort to find out the formula, which is, divide the area by a given side, (20÷4=5x4) and discard (or ignore) 15. So are we just dividing 20 biscuits by 4 to find the other side of the rectangle? No, there is a discarding process. So, without being lazy, the formula should be written not with a division, but with a fraction, 20/4=5, and again the verb fractioning shouldn't be confused with dividing.

Why are you so concerned about your point, have a look at this http://www.mathsisfun.com/decimal-fraction-percentage.html

You are right. Instead of "=", we could use the sign "≈" ? That's how I would have liked to be taught when I was a kid, even before algebra. That would make things easier maybe, if taught very early. They can. Show them 7 tennis balls, ask them to divide them by 3 in equal parts. They will tell you immediately that it's impossible. Now show them 7 biscuits, ask them to divide them by 3 in equal parts, they don't have any problem to tell you that you need to brake 1 biscuit in 3 equal parts. I would insist with biscuits in class, teaching that division is the art of separating things in equal parts, without discarding any. Once they learn that, they would learn fractions much better, later in life, a fraction is much more than a division, you are keeping a portion and discarding the rest, this portion is magic, it reveals a ratio, a proportion, a constant relation between two things.

To kids I would teach directly 7÷3=2.3333333333333333333333333333333+2.3333333333333333333333333333333+2.3333333333333333333333333333333 or simply 7÷3=2.3333333333333333333333333333333×3

Yes, all I would like, is to help kids (and myself...) to understand better. Kids can be our best teachers simply because they have no prejudices, and their questions can seriously make you feel uncomfortable. Does the definition of division implies equal parts and subtraction? I don't know, it would be useful to clarify this . Math is all based on the concept that a unity is identical to another unity, 1=1, that's all theory, but in practice it might not even exist, since an orange is not exactly identical to an other orange, an atom might not be exactly identical to an other atom, a quark might not be identical to a quark, etc. So 1=1? Only in theory, only in our fantasy and imagination, but not in reality. If we use math, it means that, anyway we all agree that in theory a unity is identical to another unity, that's a very useful agreement between humans, very convenient, that allows us to agree on measurements and quantities.

Why do we teach our kids that 6 ÷ 3 = 2? If I divide 6 oranges in 3, what I get is not 2 oranges, but 2+2+2, without subtracting 4 oranges. So why don't we teach 6 ÷ 3 = 2+2+2, 1÷2 = 0.5+0.5, etc etc? If I say "I would like a quarter of this cake", then I am not dividing, but I am dividing and subtracting, I am doing a fraction, 1/4. Don't you think divisions shouldn't be confused with fractions?

Why not building solar chimneys on top of a magma chamber of an active volcano (shutting the chimney from the base during the eruptions of course...)?

And also no fresh water is needed, they could use salty water in the South Pole

It's always an option, but is it worth it now? Tropical deforestation is responsible for approximately 20% of world greenhouse gas emissions, 35% of harvested trees are used for paper manufacture. Can't we give up all the paper at all? Or a few nostalgic will complain about e-books and how good were the "old days" when they could read a book in real paper?

Yes, it's important what you say, the weather it's already screwd up, we have to do something, doing nothing it's not an option anymore. Since we can't nuke a hurricane with an atom bomb I was thinking about kilometres of sheet suspended in the air by lots of drones.

The drones together transport a huge sheet of plastic or plywood in the middle of the hurricane, is it possible?

No, I had to read textbooks in secondary school, now for me reading it's just a hobby. If we know the elements of orange juice, why the natural and the artificial juices taste so different?

Why mystical nonsense? I am here to learn, you can teach whatever you want without patronizing. Don't you have any doubts at all? What if all the unknown elements disappear during the combustion process?

How do they isolate them, and is there enough proof to suggest that these are the only elements found in DNA? DNA was isolated by Miescher in 1869, he discovered a microscopic substance in the pus of discarded surgical bandages, that doesn't mean that DNA didn't exist before 1869. Thanks, but don't rush me.

But if in the DNA there are a lot of new unknown elements, how can you disprove it? how can you isolate them?

Both things they have in common the fact that they exist and they are in front of us, and I was thinking that when a living organism turn into elements when it dies that doesn't mean that a living organism is a compound of those elements, therefore I suppose there are an infinite number of elements and we don't even know their existence....(just saying)

Since we can turn any living creature into elements (Hydrogen, oxygen, carbon, etc), but we can't turn carbon, oxygen and hydrogen into a living organism (without the help of another living organism), do you think the periodic table is useful?

In the next 10 or 20 years we will choose how to look like, thanks to new genetic treatments, stem cells. Also nano bots inside your body will modify bones, cartilage, and every single cell, we will choose how to look like. This can be very useful in the future. For example if humans want to colonize a planet much bigger than the Earth, only short and small people can adapt to this new planet, so we will need to quickly change our body. Or if we will colonize a very small planet or the Moon, only tall people will adapt to this lack of gravity, and so on...There is no limit of what we can do with the new technologies coming up in the next decades.