SketchTurner

What sort of speeds could you get out of a computer that somehow used 4D calculations as a sort of "thinking space" to become more efficient?

Exactly. It incudes the water so the water has an effect on it. It's simple physics

Ok what I believe is happening is the water acts upon the boat which pulls the anchor. The anchor pulls the Earth. Now due to the huge difference in mass noone would notice the effect of the Earth being pulled but effectively the kinetic energy lost by the water would be gained by the Earth

Hmm boiling sulphuric acid. I remember a day back at college when I decided to leave a beaker of sulphuric acid over a bunsen. Ended in the floor being evacuated for half an hour while the fumes cleared...

Here's a table attatched. It shows part of a bigger table showing the properties of shapes in other dimensions ezspreds1.doc

Cheers that helped a bunch and now I know that what I was doing was actually relevant to something. After a bit of searching I did find the 4-simplex referred to as a "Pentachoron" but I wasn't sure if it was just made up for that one example. For now I'm using a simple logical way of naming them relating to the number of points and their maximum dimension. The names I used of the "Simplexes" for each dimension are as follows: Pentatetron - 5 Points, 4 Dimensions Hexapentons - 6 Points, 5 Dimensions Heptahexons - 7 Points, 6 Dimensions Octoheptons - 8 Points, 7 Dimensions Nonoctons - 9 Points, 8 Dimensions Decanonons - 10 Points, 9 Dimensions I also came across the Schläfli method of numbering shapes like this. The sequence starting with a triangle would be: {3}{3,3}{3,3,3}{3,3,3,3}{3,3,3,3,3}{3,3,3,3,3,3}{3,3,3,3,3,3,3} and so on.

I'm doing a little project at the moment to do with how triangles relate to tetrahedrons and I have some interesting results which have allowed me to calculate what the 4D version would look like. I Made a simple model to test and it worked out right. The only problem now is that none of the shapes I've found have names as far as I know. Is there a name for a 4D shape made from 5 tetrahedrons? It also has 10 faces and 10 edges if that helps. Theres a 5D shape too consisting of 15 tetrahedrons (or 6 of the 4D shapes). Thanks if anyone knows.

Thought I'd add that looking at a 4D shape in 3D is like trying to see a picture of a 3D shape drawn on a piece of paper. Obviously it isn't 3D but you can make the picture 'pop out' of the page with your mind. To understand 4D you have to view the 3D representation from all sides and then 'pop it out' in your mind. Hard to explain really but after looking at the model I found it quite easy.

Ok forget the title for now obviously it's leading people away from what I actually did. I was just saying that it's easier to investigate triangles and tetrahedrons than squares and cubes. About the 4D shape, I made it, looked at it and with a little thinking it's not too hard to comprehend how it would work

Ok, this might take a couple of replies for me to put this in a way people can understand but here's a first shot at it. Last night I was about to go to sleep when I had a strange thought - Why do people view the universe as three perpendicular vectors (up/down, left/right, back/forth). Also similarly the 2D universe would be viewed and measured according to a square grid. But why cubes and squares? Sure they seem an obvious way to look at things with the nice right angles but when trying to link the 2D to the 3D it makes things a lot more complex. For example: Take a square. Simple 2D object, four corners, four edges, one face and of course being 2D it’s completely flat. However because there are four corners it is possible to distort the shape three dimensionally making it no longer a 2D object. (If you don’t know what I mean just take a square of card, hole 3 corners flat to a table and pull the other up. It folds an you now have two triangles) So my idea was that the square was not an easy shape to use as a basis for investigating patterns in different dimensions. A much better shape is the triangle. It’s the simplest possible 2D shape therefore making it the easiest to compare across dimensions. I’ll explain – The triangle is the simplest 2D shape just as a pyramid is the simplest 3D shape. They both have the least possible number of corners and edges for their dimension. So what about the first dimension? Well the equivalent would be a single line with two points and a connecting line. This may seem the simplest possible conceivable as it is one line however to investigate number patterns I had to use two lower dimensions – 0D (a single point with no dimensions infinitely small) and “No D” where there is nothing. Right here’s the explanation: I will use the term “points” to describe endpoints of a line or corners of a shape. I will use the term “lines” to describe the lines between two points or the edges of a shape. I will use the term “faces” to describe areas enclosed by three lines (triangles). I will use the term “volumes” to describe 3 dimensional objects (in this case all will be tetrahedrons which I’ll call pyramids because it’s easy to type). “4ths and 5ths” will be the fourth and fifth dimensional equivalents. To keep with the rules of the lines, triangles and pyramids, the 4D and 5D shapes must be the simplest possible in their dimension and every point must connect to every other point in the shape. Starting with “No D” there are no points therefore no lines, faces and so on. In 0D there is 1 point but no lines, faces etc. In 1D there are 2 points and 1 connecting line but no faces or volumes In 2D there are 3 points, 3 lines and one face but no volumes In 3D there are 4 points, 6 lines, 4 faces and 1 volume Here’s where the patterns come in. It’s also where it’s a lot easier to explain with a model but I’ll try. My theory was that according to a pattern emerging a 4D shape would have to be made of 5 points, 10 lines, 10 faces and 5 volumes. I simply too a bunch of toothpicks and some plasticine and made a model of a pyramid. To make the 3D model of the 4D shape I added another ‘point’ in the centre and connected it to all the other points in the pyramid. The result was a shape consisting of 5 points, 10 lines, 10 faces and 5 volumes (if you make the model you can count 4 pyramids using the central point and 1 using only the outer points. Ok, time for a spreadsheet. First I drew a rough table and worked out the rules. Simple to figure and obvious now I think about it but the number of points from 0D onwards are triangular numbers. The number of lines (starting at 1D) goes up in pyramid numbers. I simply took the relationship between integers, triangle numbers and pyramid numbers and extended it with a simple equation. I've included the table and a small example of it with the equation showing so you can play around with it. That’s about where it ends, it’s only been a few hours since I thought of it so you can’t expect much. I wouldn’t be surprised if somebody had thought of this before but I thought I’d share it anyway. I’ll answer anything you don’t understand about this (except for why I was thinking about triangles in bed). okspreds.doc

I'm not saying we're going to try to destroy the planet, just that if it came down to it we wouldn't go without a fight

Ha I could do that with just a box of matches - no need for gene modification

So in a sense you'd have to have genetically modified 'little green men'. Hmm sounds familiar. Well they'd be slow due to the lack of energy (notice how plants don't actually do much?) but if they were little (maximise 'surface area:volume' ratio) and green (to photosynthesise) then you could have men. Well men with tough skin who moved very little and didn't think much.

I figure if the human population does go extinct then so will nearly everything else. At the moment we can 'care' for the environment but if it got to the point where it was either save a species from extinction and die ourselves or shoot it and eat it then i think most people would value their own life over the suvival of an entire species. The same with trees. If you were next to the last forest on earth and it was freezing cold but you knew you could start a fire with the wood from the forest then you would go cut down the tree if it was your only source ofheat. Look on this as a generalisation of all the worlds resources and all the population stood around using the resources. Noone is going to kill themselves just so there will be 1/7m more fuel, food and water for the rest of the planet. This self serving mentality which is deeply present in (nearly) all humans by their very nature would lead to a devestating destruction of life before the last human died. We would use all possible knowledge and resource to keep ourselves going until there was nothing left to use. The only life left would be that which was inacessable to us (in the deep ocean or in sealed caves).

I know it would be extremely difficult in practice if not impossible but could an animal (in theory) be modified to breathe fire as an attack or defence? If the animal could be modified to produce a flammable organic liquid in a gland in its mouth and have an 'ignition spark' (generated in a similar way to how the electric eel makes electricity) at the opening of its mouth, then could it not create an aerosol of fuel and ignite it when provoked?