alan2here

can I edit my post on page 2 please?

How does the inefficient one work? Can you apply it to the code examples I gave? Here is a simpler example in 1 dimension. " n = -[b]detail[/b] result = {} while (n < ([b]detail[/b] * 2)) { n++ result.∪=(n) } " = " result = modulo([b]target[/b], 1) "

I don't think you can beet [math]101_{2}[/math] = [math]5_{10}[/math] for storing integers in binary from a space saving point of view.

Say one has a procedure that describes the placement of objects in some number of dimensions, such as pixels on a grid in a raster image, or nodes in a vector image. Lets say that for example the procedure describes the drawing of a filled in a circle, in the raster example for a larger circle completion takes longer as more pixels need to be set as inside and in the vector version a smoother circle takes longer as more edge nodes are required. In all cases for a generic "any algorithm of this type" the image may need to be rendered entirely before it's possible to know what any one part of the image looks like. This sort of procedure is sometimes refered to as generating data and then "push"ing it onto an image. Given the details of this procedure such as it's computer code, equation etc..., but no additional knowledge of the problem such as how a circle is supposed to work, can the representation of the problem (code\equation) be reworked algorithmically (not requiring a person) into a form where a "pull" request can be made, by this I mean a request on a location of the image for the state of that location, such as weather it is inside or outside the shape that doesn't require the computing of the entire image. A less trivial example could be one of the many different ways of drawing the Sierpinski triangle known as the chaos game into a form where a position could be queried for it's distance from the nearest part of the shape. The chaos game involves repeating an action N number of times where the larger N is the greater accuracy the shape is, in order to convert this algorithm N may have to be made infinite, the same would apply to the circle example. Below are two equivalent functions. At the end of both functions "result" is taken as the result, in the first case "detail" represents the level of detail and a set of coordinates are returned, in the 2nd case the detail is infinite and only one point can be queried at a time, this point is "target_x" and "target_y". " ang = 0 [b]result[/b] = {} while (ang < 10) { ang += [b]detail[/b] x = sin(ang) y = cos(ang) [b]result[/b].∪=({x, y}) // add the set {x, y} to the end of the set } " = " [b]result[/b] = sqrt([b]target_x[/b] ^ 2 + [b]target_y[/b] ^ 2) " lets now suppose that we had a problem we didn't know in such detail but we have the "push" form of the problem. In this case it is the chaos game. " p = {0, 0} // the point that moves around corners = {{0, 0}, {0, 1}, {1, 0}} // the three corners of the triangle, sorry it's not equilateral [b]result[/b] = {} n = 0 while (n < [b]detail[/b]) { n += 1 p = half_way_between(p, corners.at(random_integer_0_1_or_2()) result.∪=(p) // add p to the end of the set } " = " ? " I'm not as intrested in a solution to this one problem as a generic solution.

I still don't quite get why turning numbers into a fractal is useful. Why not use binary representation to define numbers formally? A variation of this almost seems useful in certain OO programming context where 3 = {{}{}{}} would probably have benefit in terms if abstraction, but would be very inefficient. A fraction, or a floating point like implementation seems like a good way of representing a real number.

An article I read in focus magazine stated that numbers could be represented only using sets as proposed by Von Neumann. The concept as stated by the article is that "The number 1 is defined simply as the set containing just one thing: the Empty set. The next number, 2, is then the set containing 2 things: the Empty set, plus the set representing the number 1 - and so on, each successive number being built out of the previous set, plus the empty set." Therefore 1 = {} 2 = {{}, {}} 3 = {{}, {{}, {}}} and so where [math]s_{n}[/math] is the set that represents the number n and n > 0 [math]s_{n}[/math] = {{}, [math]s_{n-1}[/math]} Is this correct and how is this abstraction helpful compared with for example? 3 = {{}, {}, {}} or 3 = {1, 1, 1} or 3 = 3

If SIN is not a function what is it, an algorithm? If I were coding it from scratch I would use a function, in a programming languege, which is really an algorythm. In this sence sum, product and factorial are not functions either. How about to the power of?

Thanks for taking an interest. Can you post a diagram? I found your long paragraph hard to follow. My idea does not take into account the time it takes for a magnet to sence the effect of another as it is insignificant at thease speeds.

I have put many of my thoughts about OS design into this document. I appoligise in advance as some of the document contains OO programing jargon. Feedback is welcome. http://with-logic.co.uk/docs/TheOSProblem.docx

A lookup post could help maybe not this one but a lot of thease sorts of things. I'm thinking aloud here. ([math]\neq[/math] 0)/0 = infinite = inf (>0)/0 = inf positively large (<0)/0 = inf negitively large 0/0 = undefined inf (- or /) inf = undefined inf positively large (+ or *) inf positively large = inf positively large inf negitively large - inf negitively large = inf negitively large inf (+ or -) finite = inf undefined (operator or function) anything generally = undefined undefined * 0 = 0 undefined ^ 1 = 1 or -1 anything \ self = 1 Maybe this table is going to get too big. inf = undefined in a way. It's either a range or a set of two ranges. sorry, got a bit off topic.

http://img693.imageshack.us/img693/3950/calcw.png http://rapidshare.com/files/325308950/operators.xlsx.html http://www.filehosting.org/file/details/91934/operators.xlsx Above is an image of a spreadsheet and two link to the spreadsheet itself. My thoughts are based on the way that multiply can even if not the most efficient way of performing the calculation can be thought of as repeated add, and power repeated multiplication. Although there are differences beyond that and other calculations just as simple and multiply that don't have names. Columns C and D of the spreadsheet show the descriptions of increment and decrement. Thease add and subtract 1. I don't show how thease occur as they are in my model the simplest components. In a way everything in the spreadsheet is describes as being some form of repeated increment and decrement. Columns E and F show add and subtract. They take the inputs f and s meaning first and second. f operator s = 6 2*3 = 6 The calculation for both starts at f and is incremented or decremented s times. Unless what it means it is already evedent to you ignore the result row for now. The next operation is multiply. This time we start at 0 not f and (add f) s times. The next is devide. I should have put "untill >" in B7. This is a sort of bailout. You finish the calculation if this occurs. r means the result of the calculation and t means the number of times it occured before it was stoped. This is shown in column A. Iv'e also filled in power but then got stuck on the next two. I'm also not sure if log takes f and s as parameters where f is the number and s is the base or if it is better to think of it as taking two parameters of equal importance as a function to take the averege of three numbers might. In this case it's inputs should perhaps be. s1 and s2 where 1 and 2 are subscript. Can mod and log be neetly modeled in this way? K2 as f, s or s1, s2? What would go in L1? Is there ever a time where both times and untill are populated? Should I use differnt terminoligy anywere in my description?

It's hard enough in 2D. Also, nobody has produced an answer yet.

In the game it can only be 1D or 2D due the difficulty of drawing symbols or placing counters in an environment of 3 or greater dimentions. For the sake of this challenge and Hash theory then yes, it is multidimensional. Suprisingly there are non trivial 1D games. As already stated, yes. A winning condition for a certain player may involve unspecified space, his own and other players symbols. When specifying the winning conditions empty space is generally used for unspecified except sometimes where it is unclear where a central character dot is used. Obviously each winning condition involves an infinite amount of unspecified space. Yes, of course. It's a lovely game in part because of this flexabilty, you can have a long game or a short game. A game that tends towards draws or not. A game where each player must spend several minutes thinking about their move or one where movies are spotted quickly. I may tackle this at some point. It's not that hard for players or a program to generate rules that generally work quite well, but you can never be sure that a rule will behave as you expect. In the game itself a 90 degree rotational symmetry symbol and a horizontal or vertical reflection symbol may be used by the winning conditions to show that other versions are allowed. This is usefull for players but as stated already just complicates things for us as it's just a way of drawing lots of conditions in such a way as not to appear complicated. Also in the game the "* wins =" is drawn as a large verstion of the symbol being defined above and to the left of the winning condition definitions.

Hazh is a game I invented for which I have yet to document the rules. It is based on a number of players taking it in turns cyclically to draw symbols onto a grid of a given size, each grid square can hold only one symbol. When one of a set of given spatial pattern of symbols appears anywhere on the grid a player wins. Thease winning conditions are agreed on before the game starts by drawing them symbolically beside the grid. The notation used is designed to group the conditions such that they are perceptually easy to understand, not to be mathamatically easy to describe, it is also irrelevant to creating a generic solution to this problem therefore I will use a more generic but somewhat similar notation in my examples. For example a game of Hazh could be played to mimic noughts and crosses. In this game the grid would be of the size 3x3, two players would be playing, one using a 'O' symbol and the other an 'X'. The winning conditions would be. O wins = OOO , O O O , O O O , O O O X wins = XXX , X X X , X X X , X X X The grid could be larger, this would automatically allow players to match there shape anywhere on the board. One player could have differnt shapes required to win than another or there could be a combination one player needs that involves another players symbols etc... For additional challenge the board is allowed to be set to wrap as if toroidally. ........................................ The question I am asking given this scenario is. How trival will a given game will be? This could be answered in part only, for example. How many moves will be taken before a player wins? It will probably be an approximation, should presume all players play well and be answered given less calculation than is required by simulation. Usefull values for answering this question could be, for example. board area. lowest number of symbols in winning conditions. etc... For example (* = all players) * wins = ** , * * Would allow any player to win by getting two of his symbol in a left\right or up\down line. This game is trival, when played on a 1x1, 2x1 or 1x2 non wrapping grid as no player can win (I also consider games that end in only a few moves or strongly favour the order of players to be trivial), any other combination results in the player who goes first winning. A simpler verstion of this statement would be. Any game where any player has a win condition involving three or less pieces will result in a trival game. I am aware that playing well is subjective and that the challenge is difuclt or immposible but hopefully intresting.

Can you add data from other sources to cleverbot? For example you could presume each post is a question to the post after it and the answer to the one before in a conversation back and forth between two people on Twitter for example? I presume it takes the most common answer the question? Is there some randomness, so if one answer is verry common and another is almost as common then the almost as common one will be given sometimes just much less often? Cleverbot: If you were an animal, what animal would you be? Me: human Cleverbot: Ew haha. Me: what about you? Cleverbot: Oh just chiiling my love. You could get around this problem, the bot could look back if there is enough information. 1. User: what about you? Lots of potential answers, therefore. 2. Cleverbot: Ew haha. User: what about you? Only a few potential answers, so most likely show the most popular one etc...

The rep-rap does appear to have a lot of metal components that could be plastic although if it can't produce any metal then it can't produce circuitry as well as the matinance issues that I was not aware of. I think it was steel powder one machine used to create metal parts, is this likely to be a good way forward? I think things like woods metal are too expensive. A possibility is mechanical or another means of computation, another is using a semi-conductor that is more easely maneged instead of metal.

You answer as if my question refereed to a trivial, unimportant detail. This is the difference between a really useful 3D printer that one could own as a non engineer and a mediocre one that you may see in a factory.

Could rep-rap print the ball bearing system all in one go?

If it is possible to do this As intecatly as this http://www.youtube.com/watch?v=t2sCCN3tpp0 There are even multiple open source designs for such machines. And we can use metal powder as well as plastic powder and filler powder (which we can). Then what is the problem with giving such a machine it's own design and letting it make a copy of itself? It might need a folding part or to be built in two parts as to obay the laws of size. Such a machine is reliant on energy but should be able to make it's own supply structure. The only things it would need from outside would be plastic, filler and metal powder and an electricity supply or materals to harvest power such as magnets.

What makes you think that it would be tied to speed?

When I first discovered relativity I found it perplexing. Information travels at the speed of light but matter never gets that fast. Yet 3 bodies could be in a line moving forward. One is stationary as far as it can tell although really there is nothing definative to compare it with. The second is moving past the first at close to the speed of light with the third moving close to the speed of light past the second. They all get to being in line from having a staggered start and take a photo continuing at there relative speeds, the light from the flash reaches the finish line of this race at the same time with each body staying in the center of his bubble of light but keeping the same speeds as they had before. Two apparent contradictions, the third body being more than the speed of light faster than the first and the problems caused by the light, thease speeds and distances respectively don't make sence. They can however all be explained by space and time destorting, in short the answer to a relativerty question in the form of "these things can't both be true" is "length contraction and time dilation make it work". I was wondering if similarly possibility distorts (and here I am not the first to consider possibility as a sort of dimention) relative to each observer in cases involving quntum mechanics, strings or cats in boxes that seem equally perplexing?

Sorry, I was not at all clear. Your room neighbors only one maintenance passage and it is behind the smart wall. The carpet tab is very thin at the bottom and the roll is either below and behind the smart wall or further back as not to get in the way of other things. For the sofa tab with the front missing I meant by the front the side facing the room when the tab is open, the tab is on the end of the wall so that you don't get a sofa in the middle of the room. There are little ledges that drop down around it to give the impression that there is a slightly raised laminate floored part of the room as the carpet tab prevents the sofa tab ending right at the bottom. The cupboard like tabs can go anywhere. You probably want the sliding one that is the desk to go in one end as well to be against a wall and it has an unfolding leg, maybe the TV should just go into a cupboard tab as most modern TV's are quite light and it preserves space on the smart wall. There is also the utility (shared appliances) and the toilet room ones but they should fit with just a little step for the carpet. Layout would have to be carefully considered for everything to fit. Is this what you meant?

Only one wall has components behind it (at least components that apply to your room). I shouldn't think especially thick. A large OLED light panel could be provided optionally with a window facade also available to clip on. Alternivivly (or also) light could be channeled using mirrors or/and using light tubes to areas not adjacent to the edge of the building. One of the tabs would probbably need to contain the end of the directed light. Ventilation could be managed in a similar way. Sorry. I meant "comfortable". I wish I could correct that on my original post. Not a problem, when you bath there will be nothing in the room except things you have out at the moment being only things you might want to bath with (small shelf containing soap, duck, possibly ledge to sit on) and the edges are waterproof, all the electric things including wall sockets are in tabs and currently behind the smart wall.

The slum idea causes me to me cringe. This should start as being even better than owning a conventional house with all that redudent space, super econemy verstions could come later. It's only going to work well with lots together in a large building. I can't imagine them working well stand alone so gas, electric etc... would be easy enough, it does however add another service which is all the things the service passage is responsible for. There are hygene advanteges as well as disadvanteges. The toilet could easely be segmented by being in a large enough tab (lets call them tabs for lack of a better word) to go inside while on it. There are also automatic cleaning possiblites, the whole room for example could be disinfected automatically for example while you were out as could shared appliances between requests.

Tiny houses are nothing new, in Japan they are big (no pun intended) but are often quite unpleasent. Other verstions of the idea such as caravans totally fail. I have what is probbably a new idea. Imagine a single room, the room has waterproof possible pool like walls and floor, nice for an odd shaped swimming pool but no use for a house. Across the bottom of one wall is something that looks like nothing but upon eximation opens into a slot with the edge of a carpet inside, pull at the carpet and it unrolls covering the floor clipping in neer the floor at the other side. You chose the color and style of this carpet on purchising the space and can for a fee have it changed at any time. Above the carpet slot on this same wall there are other slots which look untill opened like blank pieces of wall, pushing at them opens them up revealing variously sized draws, one has no front side and ends neer the floor at the back of the room, it contains a sofa, one contains a set of taps, several resemble large cupboards and a coupple surfaces one containing a TV. You sit with the sofa, carpet and TV surface extended, anyone who entered this room would presume you had a verry minimal existance probbably not knowning that there was loads of stuff hidden in the other side of the room. They may wonder why you have a small step in your house with a raised laminately floored part apparently just for your sofa. Afterwards you close the sofa and TV surface draws and open a large cuboard like draw pulling out some other things which you arrange in the room, you then open another containing a nice wooden table with an antique look, it's big and looks heavy and works much like the sofa draw. Friends arrive and you have dinner, you could have cooked with the option of owning your own oven or sharing one with the rest of the row which is automatically cleaned between uses but on this occurence you ordered a pizza to be delivered, your guests are initially baffled by the imposiblty of how you got so many large items into your small house though a small door and wonder where the other rooms are in your house as this room seems verry much set up as a dining area not a multipurpose area for living in but it all seems homely enough. Afterwards you put everything away back into the wall including the carpet you pull out the taps and run a bath filling the room one quarter full with water. Getting things delivered and changed would be easy via mantinance passeges behind the smart wall and moving house would be much simpler. The whole thing would be cheep as it takes up verry little space and as comthatable as you like. You could even rent more space possibly including large spaces that you might use for a sports court for just one week.