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Ok what about the inverse square law, that’s a really good one. explains why you get less spray paint per unit area if you move the can away from a surface. it can be seen as a cone with a point source at the nozzle. I'm sure the inverse square law is really radial. but under the constraint of the circular hole in the nozzle it becomes directional. a cone. so the formula for a cone should be related to the inverse square law if you catch my meaning. so the cone and the inverse square law are cousins if you catch my drift. These are the sorts of Math-o-rama pictures and real world understandings of abstract formulae that I wonder if some people see.

That is unfair. On the up side, at least you get the benefit of their expertise in your environment. Makes you lift your game. (there needs to be an emoticon for determination).

That was a total fluke. I didn’t realise there was a similar thread in the relativity section until later. I was trying to find out what gifted mathematicians saw to keep them continuously interested in a subject some consider too abstract.

If you look at all this from a practical point of view, it makes much more sense. A balanced mind and body are the ideal outcome. Many scientific discoveries have been artistic in inspiration. Most early scientists were well rounded in their education. The complexity in specific fields means that specialisation is almost a necessity. What you are seeing is an attempt at a practical approach to a real life needs. (I must have endured endless lectures on topics that I thought would never be of any practical use. I was mistaken.) As far as the system being to blame for bright kids not being recognised and treated accordingly,…well, what is a system other than a group of people. More specifically - your teachers.

"In 1901, Ludwig Schlafli showed that there are only six regular polychora1, or polytopes in hyperspace. One may believe with more dimensions, there are more regular polytopes. However, the fourth dimension is as complex as it gets. This is because each dimension's increasing "freedom" nullifies its complexity. In fact, all higher dimensions each only have three regular polytopes." so, thinking dimensionally then, a triangle is rather special. and in reality it is also special. The laws of our real universe wont allow it to distort by racking over . (A square and other shapes can.) now if this whole game is about the relationships between the three dimensions of Length Area and Volume, then by understanding the above quote, the law of A squared plus B squared equals C squared becomes interesting. It’s an extrusion of a triangles “area”, into the last real dimension (we are calling it “Volume”). Now the same law that constrains a triangle in reality also constrains it in mathematics. It’s interesting that the parabola Y = X squared, is a one dimensional representation of that two dimensional relationship. It’s like a stick man you draw on paper getting up and walking off your page and saying "hey draw a picture of me now". Ps, I’m not so sure that a parabola is a justifiable representation of Y = X^2. I can now see the excitement and temptation preoccupying the early mystic Greek mathematicians and even modern physicists. It’s like having a tool to look out the window at God.

Personality comes in to it quite a lot. I gave a couple of really good high color books to a set of twins this week. The girl is enjoying the pictures and puzzles, the boy is not interested in the slightest, he’s out in the yard hunting worms. We like to think that he is studying for his career as a unemployed labourer.

agree.

I’m starting to visualise it, with the realisation that a sphere can not really be drawn on paper- without the use of shading - to trick the mind to flip into three dimensional mode. So I’m thinking of the original use for math as to keep track of sheep, get in tax... and later to get buildings straight. At what point did it spin off into imaginary dimensions, and is that really a thing you can do rationally?

I’m having trouble visualising it. I thought Hyperspace was a thing invented to allow Han Solo’s space ship to escape the Death star. This is what I have dug up so far. Around 200 B.C., Euclid's extraordinaire proved that there are only five regular polyhedra, polytopes in three spatial dimensions: the tetrahedron, cube, octahedron, icosahedron, and the dodecahedron. In 1901, Ludwig Schlafli showed that there are only six regular polychora1, or polytopes in hyperspace. One may believe with more dimensions, there are more regular polytopes. However, the fourth dimension is as complex as it gets. This is because each dimension's increasing "freedom" nullifies its complexity. In fact, all higher dimensions each only have three regular polytopes. A Geometric Approach Differentiating between figures in the first few dimensions can be quite a task. One of the simplest ways to view higher dimensions is by slicing. A simple three-dimensional figure, a cube, can be sliced parallel to its sides to give a square, a two-dimensional figure. A hypercube, the cubic equivalent in four dimensions, therefore can be sliced to give cubes. When you take a sheet of paper and look at it from the top, you see a rectangle. If you turn in on its side, you see a line. Between the rectangle and line, you see rhombuses, parallelograms, and other quadrilaterals. When you try to draw a cube, notice what shapes are used to create it. If you drew a cube from a corner view, you would need parallelograms and other quadrilaterals. From that view, you won't see any squares, although squares are what make up a cube. This strange phenomenon occurs anytime a polytope is rotated. So when you look at a hypercube rotating, don't expect to see just perfect cubes, rather look for distorted ones. It’s from here. http://temporal_science.tripod.com/introduction/special1.htm

If, X is a line. X squared is an area. X cubed is a volume. What do you suppose X to the power of four is?

This is not a calculus question, but rather a question about calculus. I was watching some very bright kids the other day really enjoying calculus. I have to admit playing with symbols and numbers is not my favourite pastime. When you look at a calculus equation what do you see? Do you see a series of approximations of the real world. Like when I see the sentance “the cat played with the ball ”, I see a picture of a cat playing with a ball. I do not see the letters or the words. I was wondering ,when you read a calculus equation do you picture, spheres being intersected by planes? or lines folding out to become planes and then extruding to become blocks? Or is it more like solving a crossword puzzle using learned methods?

I can see your mind is set. Don’t inject it or it will cause heart failure. Your kidneys are going to regulate the amount your body gets no matter how much you oversupply it. You can buy straight pills of the stuff. Have you thought about looking at improving the way the house is built rather than simply giving the builders more bricks.

Don’t poison yourself bud. next you will be eating paperclips because you are low on iron. The body requires these things in a particular form. Can you not find normal food with high levels of the required material. Apricots, raisins. Your kidneys will regulate the excess quantities. Better still, can you put the raisins and apricots into a blender then fill your paint ball pellets up with the juice. Then you can just lick yourself each time you get shot.

This is reminding me of the ancient sailors setting out over the Pacific ocean. Quite Sure that they were heading for the edge of the world. They saw that the Earth was flat, their eyes told them that, but can you imagine their surprise when they got to the edge of the world and it was the beginning again. How would they understand (from what they knew) that sitting at home in their kitchen, they were already standing on the edge of the world - and the real exit door was straight up.

best ask the people at the lifters club in the link. looks like they use a PC monitor as an easy place to get that sort of voltage. Please remeber that electricity can kill you.

It seemed like a paradox to me as well. I was wondering what the calculus would make of it.

If a body moves from A to B then before it reaches B it passes through the mid-point, say B1 of AB. Now to move to B1 it must first reach the mid-point B2 of AB1 . Continue this argument to see that A must move through an infinite number of distances and so cannot move. Zeno of Elea 450 BC ?

Thanks, one more to add to the collection. Just found out that the observer had a report that said, after following up the success of applicants screened with these tests, the results showed that you would have just as much success by reading their tea leaves ps. tried to answer some of those Enneagram type tests in different ways. sure enough you can make them give exactly the personality type you want - by getting into a particular mindset before you start. I even got one to come out almost dead flat across all traits,(that taxed the old memory a bit).

why are we talking about bees now? The sinusoidal path of the wing is not the thing . it's how Air at the scale of an airplane behaves as we expect , but when you get a small thing like a bee , the air seems to act counter intuitively. because at that threshold the air starts to look like soup. the size of the air molecules relative to the bee is now a factor. Albert was getting at a certain point. anyone know what point he was alluding to.

The reason I'm so interested in this, is that I saw a really strange variation on this theme working in front of me many years ago. It was a massive contraption, far greater in size than the small models shown on the pictures. I was asked to keep the exact details to myself. What I don't get is what the patent application is going on about re anti-grav. What do you think the patent paper is saying about the underlying principle? I mean, we know how roughly how the air is being shifted, but what did the author think was happening?

I suspected that the air was being shifted by high voltage. any more details of what’s happening around the lead edge.

So has anyone seen any really interesting methods of categorizing personality? This is what I have so far….. The most simple one is the front line police one … Good guys and bad guys. There is a US high school one from films… the geeks, the stoners ..etc etc. There are the ancient ones Colic and Phlegmatic … There are the Occult ones, Leo, Virgo, Scorpio… There are the Multiphasic ones …Extrovert, Introvert… Have you come across any others ?

How to cancel out earth gravity. This looks like it can work, if not for the reasons stated. Second opinions required. Ps. I have seen some private experiments on variations on this theme. http://www.rexresearch.com/gravitor/gravitor.htm some demos. http://jnaudin.free.fr/html/liftbldr.htm

Thank you. The best of luck.