QuoteIt is mathematical, but a practical maths not often taught in schools, etc. For instance, if I pile one pile of dirt on top of another pile of dirt I end up with one pile of dirt. That is practical. And it shows:
Originally posted by: ricarleite
Yes, but it's not mathematically accurate.
1 pile of dirt + 1 pile of dirt = 1 pile of dirt.
You would not believe how many people will say "but mathematically there's twice as much dirt"! They're not even close to the practicality. A pile of dirt is an arbitrary mass. No one said the two piles of dirt were of equal volume in the first place; and either way when they are combined they form one pile of dirt, not two. You cannot add two piles of dirt together and end up with twp piles of dirt, because it is in adding them together that they form one, by the very definition of the question. The dots question are the same.
If you ask someone to put pen to paper and draw no more than 4 straight connected lines that connect all the dots together; you are specifying a practical question, for which there is a practical answer - not a purely mathematical one. You can't show they're wrong mathematically if they provide my solution, if you say "You need FOUR lines" they can just draw a 4th line that goes back to another dot. Then their solution would be 4 lines, but with an unnecessary line.
If you ever saw a product which contains more than 100% in total of the ingredients, would you think there was an error involved? Let me share this with you. If you mix 500ml of vodka with 500ml of water, you do not get 1kg of liquid. It's actually less than 950ml of fluid. What are you going to do about that? Complain that it's not mathematical? That there was 500ml of water, and 500ml of vodka and just because you've changed their location their weight should not have changed? Ask where the other 50ml went to?
If I packaged a product that was made of equal portions of vodka and water, and listed my ingredients with percentages, then on the packaging it would read: Contains: 53% vodka and 53% water. Again this is practical, it may not be mathematical but it is practical, accurate and demonstrable under real world conditions. It would, in fact, be illegal for me to write 50% for each of vodka and water. Percentages must be accurate, if in 1kg of my product there is 530ml of water, then my product (according to its weight) contains 53% water, I cannot write 50%, because it does not contain 500ml of water to the kg, it contains 530ml of water to the kg. The same goes for the vodka.
Now I could intend instead to trick the consumer by writing only one percentage, thus: Contains: 53% vodka and water. People would then assume that it is 47% water. But it's not. It is however 53% vodka - or 530ml, which is what my claim is.