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French mathematician Blaise Pascal (1623-1662) did not see the need for negative numbers. Augustus de Morgan (1806-1871), an English mathematician, thought numbers less than zero were unimaginable. see: http://www.und.edu/instruct/lgeller/negnum.html

look at the words for ages. see if you really know what each word means..... usually if you really understand the words you already have the answer. then think if you have ever seen any similar type of question or words. compare those to your presesnt question. if you come up empty ..research the words using google. good luck.

so... that's what algebra was designed to do. still a cruel thing to put school children through.

Wouldn’t the mass of the earth be different if it was hollow? and doesn’t the mass of a planet influence it's orbit and the orbit of other bodies? ssooo...are Kepler’s equations correct. or are they all off the mark, because they used a solid earth as a starting point. it's all very info-tiaining... "Kepler seems to have married his first wife, Barbara, for love (though the marriage was arranged through a broker). The second marriage, in 1613, was a matter of practical necessity" see here... http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Kepler.html

And…I find myself at Princeton. who else can I trust, in this sea of superstition? http://www.princeton.edu/~pear/

yes. Don't worry. I'm putting this down to chance. tell you something funny. replaying my thought processes in slow motion around the said "dead dog" incident.... First I looked into the dog (Labrador) face... and then had the thought: "something is wrong with that dog, bet it will be dead soon" So I looked across the dogs pelt condition and thought it looked good . So then looked at the way the animal was moving and thought it also looked good. So then I thought to myself: "why did you just have that stupid thought. it makes no sense". Then the poor critter stopped, dropped and was no more. Strange huh. Now, let me at Sheldrake. (this all sounds very interesting).

Gee thanks. I feel so much better now. ...but....before you all hire me out as “pet assassin” … While researching “how Elephants know it’s time to head off to the Elephant graveyard”….I found this semi scientific possibility. http://en.wikipedia.org/wiki/Rupert_Sheldrake

Possibly...it's a bit tatty looking now...is it on one of the corners directly beneath the radial hub point of the glass roof?

And in winter...the plant refuses to maintain the leaf structures as they are of reduced benefit...so it ejects them. some plants are just leafs. one plant is a really really massive leaf the Ravenala from Madagascar. And if you look at this plant long enough...you will see the answer to many other plant structure questions.

I watched a man walk his dog yesterday. For some reason as it passed something made me think that the dog would soon die. The dog stopped in it’s tracks and simply died. This is the second time this has happened to me. The last time it was a cat. Ever heard anything like this before?

You came ...you saw...you played Nintendo?? Nullo metro compositum est! Do you know how long it's going to take me to fish through that sea of words to find the core concepts. You sure can make pretty good complex sentences though. Please can we have it in smaller chunks....I fear that too much of a good thing becomes a bad thing.

lol. what can I make with it? why is a social issue in a physics topic. was the tone of that first post a bit sulky? Actually I really enjoyed it. I have never seen language that I could call truly " Baroque "...until now. Very nice.

You must have picked a funny speed to try it. The ball wants to keep going at the same speed as the car...so say...50 mph forward. But the particles of air slow the ball down..... as the ball will try to push them out of the way to get through, they will not want to move aside. So if you were going at the right speed and the ball was a particular size...yes ..it could have almost no movement in the direction of the car. Well that’s how I figure it anway.

check out this... it should give you the idea on why the simple stuff works. http://everyschool.org/u/logan/culturalmath/pythag.htm

Thanks for the pointers. Nice to have a expert point of view. It's going to take me a long time to think this through.

yes. thats why I use the pulled muscle analogy. it's preventable it's repairable, and its inevitable in certain situations.

it's ok. I have seen it several times. Thanks, hope you get good help in learning to detect and manage it. so with the caught between a rock and a hard place situation....I mean what’s the point going beyond your present mental strength level? You will only pull a brain muscle and be out of the game for ages... how is that going to help you? It's not like you can beat it, you have no choice but to ease up on the pressure until you get mentally stronger. I see what you mean…. but can you see my point about the futility of trying to fight it by increasing the effort. it's like one of those finger pop toys.

I’m trying to get some sort of intuitive grasp if imaginary numbers.. Does anyone have any inkling whatsoever as what they might be like or any analogy that might give me some point to start from. Or do we just send off our equations into the unknown and be happy when they return still making sense in the real world?

Can you give an example? I'm not sure what you mean by that choice between paying the rent and reducing pressure.

how were you going to start? (I'm well rusty on this stuff). Why do you suppose the first thing asked is to show how three equations all come to equal "0". does that sound like anything you have heard before?

I see that thought come up more and more these days. I'm not sure what to make of it. perhaps it is the zeitgeist.

when your eyes read the question and you came to the word "rose" what did you think? I thought...”what the are they talking about...I see no roses”...just what looks like that side of a dice. what do they mean by "rose"? so I never even started solving the mathematical sequence until all the words made sense to me.