mm-445 Subject: Re: Limit Superior and Limit Inferior picture of the idea of lim sup and lim inf. Miao >I am having trouble understanding the defintion of limit superior and limit >inferior. Can anyone tell me what the lim sup and lim inf mean without being >too technical with the math terms... > A sequence of real numbers doesn't have to converge, but if it's > bounded, it will have at least one convergent subsequence. (I'll > stick to the bounded case here.) Look at the limits of all of > its convergent subsequences; it turns out that these form a > bounded set of real numbers, and as such it has a supremum (least > upper bound. (Recall that every bounded set of real numbers has > a supremum.) This supremum is the lim sup of the original > sequence. What's more, it turns out that some subsequence of the > original sequence actually converges to this supremum. In other > words, the lim sup of the sequence is the largest real number to > which some subsequence converges. Similarly, the lim inf is the > smallest real number to which some subsequence converges. > Here's a more technical that might still be of some help; I've > included a few examples and a graphical way of thinking about the > lim sup of a sequence. > Suppose that you have a bounded sequence of real numbers x(n). > Look at a tail of the sequence, for instance, the one starting > with a(k): > a(k), a(k+1), a(k+2), ... . > The set of points > {a(k), a(k+1), a(k+2), ...} > is a bounded set of real numbers, so it has a supremum (least > upper bound); call this number u(k). Thus, u(0) is the supremum > of all of the terms of the sequence, u(1) is the supremum of all > except a(0), u(2) is the supremum of all except a(0) and a(1), > and so on. Notice that u(0) has to be at least as big as every > single a(n), while u(1) only has to be as big as a(1), a(2), > a(3), ...; this means that u(1) can't be any larger than u(0) and > might be smaller. In general we have > u(0) >= u(1) >= u(2) >= ... . > Since this is a monotone sequence, either it has a limit u, or it > decreases without bound (i.e., tends to -oo). This limit u is > the lim sup of the original sequence a(n). > A concrete example might help. Consider the following sequence: > 100, 100, 100, 100, 1/2, 2/3, 3/4, 4/5, ..., > where a(n) = (n-3)/(n-2) if n > 3 and x(n) = 100 otherwise. (I > start n at 0.) Here u(0) = u(1) = u(2) = u(3) = 100, but for > each k > 3 we have u(k) = 1, and therefore lim sup a(n) = 1. > Here's a less trivial example: a(n) = 1 + (-1/2)^n. Then a(0) = > 2, a(1) = 1/2, a(2) = 5/4, a(3) = 7/8, and so on. Clearly the > terms are alternately above and below 1, and you can check that > if n is even, u(n) = a(n) = 1 + (1/2)^n, while if n is odd, u(n) > = a(n+1) = 1 + (1/2)^(n+1). Thus, the sequence of u(n)'s is > 2, 5/4, 5/4, 17/16, 17/16, ...; > since this sequence converges down to 1, lim sup a(n) = 1. > One more: a(n) = 1/n if n is prime, and a(n) = -n otherwise. The > sequence starts out like this: > 0, -1, 1/2, 1/3, -4, 1/5, -6, 1/7, -8, -9, -10, 1/11, -12, ... > Clearly u(0) = u(1) = u(2) = 1/2, u(3) = 1/3, u(4) = u(5) = 1/5, > and so on. In general u(k) = 1/p, where p is the smallest prime > greater than or equal to k; since there are infinitely many > primes, such a p always exists. > Here's another way of thinking about it that may help. Suppose > here that u = lim sup a(n), with all of the notation as above. > Suppose that w is a real number with w > u. Recall that u is the > limit of the u(k)'s and that u(0) >= u(1) >= u(2) >= ... is a > non-increasing sequence. This means that from some point on all > of the u(k)'s will be less than w; say u(m) < w. But u(m) is the > supremum (least upper bound) of a(m), a(m+1), ..., so it's at > least as big as all of these terms: a(n) <= u(m) for all n >= m. > This implies that starting with a(m), every term of the original > sequence is less than w. If you were to graph the sequence, > plotting n on the x-axis and a(n) on the y-axis, the horizontal > line y = w would lie entirely above the graph of the sequence > from x = m onward. This happens for any w > u. > On the other hand, consider a w < u, and look at any u(k). We > already know that u(k) >= u, since the u(n)'s are a > non-increasing sequence converging to u, so u(k) > w. And u(k) > is the supremum of the set {a(k), a(k+1), a(k+2), ...}, so by the > definition of supremum there must be some m >= k such that > w < a(m) <= u(k). In geometric terms this means that now there > are infinitely many points of the graph of the sequence that lie > above the line y = w. > To sum up: Imagine graphing the sequence as described above, so > that the point corresponding to the term a(n) is (n, a(n)). Pick > any real number w and draw the line y = w. If w > lim sup a(n), > from some point on the line will lie entirely above the graph of > the sequence. If w < lim sup a(n), the line will lie below > infinitely many points on the graph of the sequence. And if w = > lim sup a(n), either of these things can happen, or neither. > Brian === Subject: Test (was Re: Calculus Question) Is there a calc question or not. If so please post under a new, appropriately labeled subject header. There are designated areas for tests, such as alt.test. RTFM. === Subject: Combinations, sets inside the median bell The probability median or FFG median plays a very important role in random events. (A digression: Everything is random, as I pointed out in various the Randomizing: An Art of Scientific osophy, Science of osophical Art, osophy of Artistic Science, Art of osophical Science, Science of Artistic osophy, osophy of Scientific Art page. Here, the term random refers to events of lower probabilities. In other words, events with higher degrees of randomness, such as gambling or lottery.) I have written several programs that generate random numbers or combinations inside the normal or Gauss curve: BellBet.EXE, BelLotto.EXE, and especially BellCurveGenerator.EXE. The latter had been the most comprehensive generating program; it was slow, however, when generating combinations aimed at the first prize. The combinations, or numbers, or sets were taken sequentially from the FFG median area. The method of designing the FFG median area was quite precise at that time. We constantly develop. I discovered a more precise method of establishing the FFG median bell or zone. The latest version of BellCurveGenerator.EXE is founded on the most precise formula of creating the FFG median area. The combinations are generated randomly, therefore more closely to the nature of the events. The user can select the amount of combinations, or numbers, or sets to generate. The software is far faster than any previous incarnation. Read all the info and then download the freeware BellCurveGenerator.EXE: Generate a wide variety of combinations inside the FFG median bell: pick lotteries, lotto, horse racing, roulette, sports betting, soccer pools 1x2. http://www.saliu.com/median_bell.html Our thoughts strayed constantly and without boundary The ringing of the Division Bell had begun. (Pink Floyd, High Hopes, the Division Bell album) Said Tabaki Paravicius, netizen extraordinaire: You ain't seen nothing quite like it, axiomatic bella donna! BellCurveGenerator has all the bells, and whistles, and curves of a celestial body. Ion Saliu The osophical Science of Winning http://www.saliu.com/winning.html === Subject: Re: Combinations, sets inside the median bell did you ever see that guy that tried to predict wrong lotto numbers to win? i havent heard from him lately, he is probably laying back in his jaccuzi drinking mai tais in hawaii any way, would this program do just that? >The probability median or FFG median plays a very important role in >random events. >(A digression: Everything is random, as I pointed out in various >the Randomizing: An Art of Scientific osophy, Science of >osophical Art, osophy of Artistic Science, Art of >osophical Science, Science of Artistic osophy, osophy of >Scientific Art page. Here, the term random refers to events of lower >probabilities. In other words, events with higher degrees of >randomness, such as gambling or lottery.) >I have written several programs that generate random numbers or >combinations inside the normal or Gauss curve: BellBet.EXE, >BelLotto.EXE, and especially BellCurveGenerator.EXE. The latter had >been the most comprehensive generating program; it was slow, however, >when generating combinations aimed at the first prize. The >combinations, or numbers, or sets were taken sequentially from the FFG >median area. The method of designing the FFG median area was quite >precise at that time. We constantly develop. I discovered a more >precise method of establishing the FFG median bell or zone. >The latest version of BellCurveGenerator.EXE is founded on the most >precise formula of creating the FFG median area. The combinations are >generated randomly, therefore more closely to the nature of the >events. The user can select the amount of combinations, or numbers, or >sets to generate. The software is far faster than any previous >incarnation. >Read all the info and then download the freeware >BellCurveGenerator.EXE: Generate a wide variety of combinations inside the FFG median bell: >pick lotteries, lotto, horse racing, roulette, sports betting, soccer >pools 1x2. >http://www.saliu.com/median_bell.html Our thoughts strayed constantly and without boundary >The ringing of the Division Bell had begun. >(Pink Floyd, High Hopes, the Division Bell album) >Said Tabaki Paravicius, netizen extraordinaire: You ain't seen nothing quite like it, axiomatic bella donna! >BellCurveGenerator has all the bells, and whistles, and curves of a >celestial body. >Ion Saliu The osophical Science of Winning >http://www.saliu.com/winning.html > === === Subject: Re: ti-86 - how to use <, >, etc in graph >anyone know where in the menu I can select those? (e.g. y = x < 2; y = x >(greater than or equal to) 2) I believe one of my students found them in a menu called TEST. I don't have a TI-86 myself so I can't check. You might find documentation at TI's Web site, http://education.ti.com -- Stan Brown, Oak Road Systems, Cortland County, New York, USA http://OakRoadSystems.com Address munging may or may not reduce the spam you get; it surely reduces the number of useful answers you get. http://www.cs.tut.fi/~jkorpela/usenet/laws.html === Subject: Re: ti-86 - how to use <, >, etc in graph >anyone know where in the menu I can select those? (e.g. y = x < 2; y = x >(greater than or equal to) 2) > I believe one of my students found them in a menu called TEST. I > don't have a TI-86 myself so I can't check. === Subject: Re: Span and intersection > Daniel, although the special figures did not come out properly on my > viewer either, I think the question was not about a sum but about an > intersection. That is: under what conditions is the span of the intersection of > two SETS of vectors the same as the intersection of the spans of the > two sets of vetors. > Example: if one set is {<1,0,0>,<0,1,0>} and the other set is > {<0,1,0>,<0,0,1>} then the span of the first is all vectors of the > form and the span of the second is vectors of the form > <0,c,d>. The intersection of those two spaces is the set of all > vectors of the form <0,b,0>. The intersection of the two sets is {<0,1,0>} and it's span is > <0,b,0> just as before. Is this always true? No, {<1,0,0>, <0,2,0>} and {<0,1,0>, <0,0,1>} is a counter example The intersection of the spans is the set of vectors of the form {<0,b,0>} The interestion is the empty set, so is the span of the intersection === Subject: Re: F:R->R^2 > Dear all, I know that there's a function f:[0,1]->[0,1]x[0,1] which is > continuous and surjective. But, how to construct such function f: R->R^2, which is also > continuous and surjective. > Try using arctans. g: x |--> arctan x is bijection from R to (-1,1), maybe it would help you (along with its inverse) === Subject: Computationl Geometry Problem Ladies and Gents, I have a problem which my undergrad maths is not sufficient to solve can anyone here help ? I have a collection of closed 2D 'shapes' defined by an ordered series of points. These shapes are not regular and are not guaranteed to be convex hulls - they may contain concavities. For example: [apologies for ascii art - a fixed font makes these more readable] +-----+ ! / + + ! ! + ! ! + ! ! +------+ and +---+ / + + ! / ! + ! ! +-----+ If necessary I can guarantee that the origin lies within this shape. I also have a curve defined by an ordered collection of 2D points which I know form part of one of the shapes in my collection but I don't know which one. Moreover, the curve formed by this set of points is not necessarily to the same scale as my shapes are, it may be enlarged. It may also be rotated. It will not be inverted in anyway. I do not know if the curve has been enlarged or rotated nor by how much. I need to determine which of the shapes my curve 'fits'. This is an easy task for humans but I have no idea where to even start doing it computationally. For example my curve may be: + / / + +----+ ! In this case, the curve I have is the right hand side of the second shape, enlarged by a scale factor of 2 and rotated anti-clockwise through 90 degrees. My first thought was to derive an equation for the shapes and then derive an equation for the curve and do some sort of comparison between these equations. The problem here is that the shapes are closed loops and therefore clearly not functions and polynomial fitting is about the limit of my ability. Also I'm not sure how I would go about accounting for the scale. Is there some scale free mechanism for defining the shape of a curve which can be used to compare them ? Is there some other 'partial congruency' test ? Is a holistic curve fitting approach the best way to go about it or would it be better to consider each shape and the curve as a series of line segments ? Confusedly Dave === Subject: Re: Computationl Geometry Problem > Ladies and Gents, I have a problem which my undergrad maths is not sufficient to solve can > anyone here help ? I have a collection of closed 2D 'shapes' defined by an ordered series of > points. These shapes are not regular and are not guaranteed to be convex > hulls - they may contain concavities. For example: [apologies for ascii art - a fixed font makes these more readable] > +-----+ > ! / > + + > ! ! > + ! > ! + > ! > ! > +------+ and +---+ > / > + + > ! / > ! + > ! ! > +-----+ > If necessary I can guarantee that the origin lies within this shape. I also have a curve defined by an ordered collection of 2D points which I > know form part of one of the shapes in my collection but I don't know which > one. Moreover, the curve formed by this set of points is not necessarily to the > same scale as my shapes are, it may be enlarged. It may also be rotated. It > will not be inverted in anyway. I do not know if the curve has been enlarged > or rotated nor by how much. > I need to determine which of the shapes my curve 'fits'. This is an easy > task for humans but I have no idea where to even start doing it > computationally. For example my curve may be: + > / > / > + +----+ > ! In this case, the curve I have is the right hand side of the second shape, > enlarged by a scale factor of 2 and rotated anti-clockwise through 90 > degrees. > My first thought was to derive an equation for the shapes and then derive an > equation for the curve and do some sort of comparison between these > equations. The problem here is that the shapes are closed loops and > therefore clearly not functions and polynomial fitting is about the limit of > my ability. Also I'm not sure how I would go about accounting for the scale. Is there some scale free mechanism for defining the shape of a curve which > can be used to compare them ? You could convert the point sequence representation of all these into a representation which for each edge the angle it makes with the previous edge and also the relative length of the edge to the length of the previous edge. Of course, for non-closed curves you will need to come up with an arbitrary value to denote that any relative length and angle is allowed. Then taking a curve and a closed polyline in this representation you pick a point wihtin the closed polyline, assign the relative length of the edge starting from that point to the undefined relative length of the first edge of the curve, do the same for angle and check to see whether the relative angles and lengths for all edges in the closed polyline match. If your figures are given as sequences of coordinates, you need to be careful with precision and other oddities as floating point calculations do not follow the rules of the algebra of real numbers. Perhaps simply allowing a small epsilon of mismatch in comparing the angles and relative lengths will do. -- Aatu Koskensilta (aatu.koskensilta@xortec.fi) Wovon man nicht sprechen kann, daruber muss man schweigen - Ludwig Wittgenstein, Tractatus Logico-osophicus === Subject: Re: Computationl Geometry Problem > Ladies and Gents, I have a problem which my undergrad maths is not sufficient to solve can > anyone here help ? I have a collection of closed 2D 'shapes' defined by an ordered series of > points. These shapes are not regular and are not guaranteed to be convex > hulls - they may contain concavities. For example: [apologies for ascii art - a fixed font makes these more readable] > +-----+ > ! / > + + > ! ! > + ! > ! + > ! > ! > +------+ and +---+ > / > + + > ! / > ! + > ! ! > +-----+ > If necessary I can guarantee that the origin lies within this shape. I also have a curve defined by an ordered collection of 2D points which I > know form part of one of the shapes in my collection but I don't know which > one. Moreover, the curve formed by this set of points is not necessarily to the > same scale as my shapes are, it may be enlarged. It may also be rotated. It > will not be inverted in anyway. I do not know if the curve has been enlarged > or rotated nor by how much. > I need to determine which of the shapes my curve 'fits'. This is an easy > task for humans but I have no idea where to even start doing it > computationally. For example my curve may be: + > / > / > + +----+ > ! In this case, the curve I have is the right hand side of the second shape, > enlarged by a scale factor of 2 and rotated anti-clockwise through 90 > degrees. > My first thought was to derive an equation for the shapes and then derive an > equation for the curve and do some sort of comparison between these > equations. The problem here is that the shapes are closed loops and > therefore clearly not functions and polynomial fitting is about the limit of > my ability. Also I'm not sure how I would go about accounting for the scale. Is there some scale free mechanism for defining the shape of a curve which > can be used to compare them ? > Is there some other 'partial congruency' test ? > Is a holistic curve fitting approach the best way to go about it or would it > be better to consider each shape and the curve as a series of line segments > ? Confusedly > Dave Here is something to think about that may point in the right direction. Angles. A rectangle is still a rectangle if rotated or magnified. What stays the same under these operations? The angles. I suggest something along the following lines: Your curve is an ordered set of points, correct? Let [p_1, p_2, p_3, ..., p_n] be your points. Then, find the angle between the segment (p_1, p_2) and the segment (p_2, p_3). You will need to find say the dot product, then worry about orientation, etc. Now, form an array of these angles. Compute this type of array for each of the shapes in the list. Then compare the sequence of angles in the curve with the sequence of angles in the shapes looking for a match. Now, since the curves are PART of the shape, you will need to slide the sequence of the curve. Here's what I mean: Say the curve is [24, 51, 172] and the shape it matches is [18, 50, 6, 24, 51, 172]. Compare the curve with the first 3 terms [18, 50, 6], then slide one term right to compare with [50, 6, 24]. Continue to the end. Don't forget to wrap-around in case your curve spans the beginning/terminal point of the shape. Clearly there are some fine points to worry about. 1) Dot product, etc. (floating point arithmetic) introduces roundoff errors, so, you may want to allow a little slop when comparing for a match. Something like: if |curveangle_1 - shapeangle_1| < tolerance, then angles are the same, move to next pair of angles. 2) Orientation of the curve: [23, 5, 7, 9] vs. [9, 7, 5, 23]. That's the best I can think of off the top of my head. Hope this helps. Brett === Subject: Re: Computationl Geometry Problem [shapes and curve] Following Brett's idea to use angles, here is an example of what could be done (example written in mathematica): angle[{{x1_,y1_}, {x2_,y2_}, {x3_,y3_}}] := ArcSin[(-x2*y1 + x3*y1 + x1*y2 - x3*y2 - x1*y3 + x2*y3)/ Sqrt[((-x1+x2)^2 + (-y1+y2)^2)*((-x2+x3)^2+(-y2+y3)^2)]]; compare[shape_List, curve_List]:= Module[{curveLength, curveAngles, shapeAngles, angleDeviations, tolerance = 10.^-3}, curveLength = Length[curve]; curveAngles = angle /@ Partition[curve,3,1]; shapeAngles = angle /@ Partition[shape,3,1]; angleDeviations = (#-curveAngles& /@Partition[shapeAngles, curveLength-2,1])//Chop[#, tolerance]&; Count[angleDeviations,{0,0}] ]; Test : curve={{0.,0.},{2.,4.},{8.,0.},{10.,0.}}; shape1={{1.,1.},{2.,3.},{5.,1.},{6.,1.},{6.,0.},{1.,0.},{1.,1. }}; shape2={{0.,1.},{2.,3.},{4.,1.},{5.,1.},{5.,0.},{1.,0.},{0.,1. }}; compare[shape1,curve] 1 compare[shape2,curve] 0 Hoping this can help you --- jfa === Subject: Re: Computationl Geometry Problem 3QLpj-NoP*NzsIC,boYU]bQ]H'y<#4ga3$21: > Is there some scale free mechanism for defining the shape of a curve which > can be used to compare them ? You could use the sequence of pairs (angle, ratio of left and right edge lengths) at each vertex of the shape... -- David Eppstein http://www.ics.uci.edu/~eppstein/ Univ. of California, Irvine, School of Information & Computer Science === Subject: Planning to buy a calculus textbook! I'm a senior in high school, and I'm taking AP calculus. The book I'm using is by Larson, ISBN 0669327093, which is the 5th edition, and it sucks! I'm looking for a better book (to buy for my own) to use, which would clearly explains much wider types of problems. The one I'm using only shows about 3 examples; on the excercise, I have to sit there for hours trying to even begin understanding how they even got the answer (answer to odd questions on back). Usually the next day my teacher show us how that certain problem was done AFTER he assigns the homework. === Subject: Re: Planning to buy a calculus textbook! > I'm a senior in high school, and I'm taking AP calculus. The book I'm using > is by Larson, ISBN 0669327093, which is the 5th edition, and it sucks! I'm > looking for a better book (to buy for my own) to use, which would clearly > explains much wider types of problems. The one I'm using only shows about 3 > examples; on the excercise, I have to sit there for hours trying to even > begin understanding how they even got the answer (answer to odd questions on > back). Usually the next day my teacher show us how that certain problem was > done AFTER he assigns the homework. I enjoy the Edwards & Penny book. You should also be able to get a student solution manual for it that will have the answers worked out in detail. -- email: wtwentyman at copper dot net === Subject: Re: F:R ->R^2 continuous, surjective. > I know that we can construct a continuous surjective map > from f:[0,1]->[0,1]x[0,1]? But, how about f:R -> R^2 ? Take any continuous bijection g:R -> (0,1), and define h:(0,1)^2 -> R^2 as h(x,y) = (g^-1(x),g^-1(y)). Then f, g, g^-1, and h are all continuous and surjective, and therefore so is h.f.g; since h.f.g:R -> R^2, that's a function you are looking for. g(x) = cosh(x/2) is the first thing that comes to mind. meeroh -- If this message helped you, consider buying an item from my wish list: === Subject: tricky proof show that 2* |z+3i| = |z| <--> |z+4i| = 2 i interpret this as: show that 2* |z+3i| = |z| is equivlant to |z+4i| = 2 i simplified |z+4i| = 2 by setting z = x+yi and got x^2+(y+4)^2 = 2^2 which of course is the equation for a circle with radius 2. But i dont know how to proceed in from here === Subject: Re: tricky proof ok its NOT tricky. I solved it ;) Balcha Abanefso skrev i meddelandet > show that 2* |z+3i| = |z| <--> |z+4i| = 2 > i interpret this as: > show that 2* |z+3i| = |z| is equivlant to |z+4i| = 2 > i simplified |z+4i| = 2 by setting z = x+yi and got > x^2+(y+4)^2 = 2^2 which of course is the equation for a circle with radius > 2. But i dont know how to proceed in from here === Subject: Re: Mega Foundation, change in plans mea mega culpa! given tetrahedra whose edges are diagrammed into two (-handed) sets of three zig-zag-zogs, show a set of inequalities analgous to the trigonal ones (a + b >= c with the other two permutations). > Now I'll use other means to get things done. This experiment is over. --still not 3M-compliant? http://tarpley.net === Subject: Re: Mega Foundation, change in plans I find their public paper http://www.ultrahiq.org/Mega/WhyMega.htm to be an interesting commentary on what they can do for mathematics > publishing. Not quite sure if you're serious with that comment, but... One of the limits of people is TIME. I, myself, simply cannot possibly look at, read, listen to, think about every intelligent and worthwhile idea in the world. I'd love to, mind you, but I do have a job and that job is somewhat demanding of my time exactly because it is an academic job. I see the same limitation in other people around me. This means that I am thankful every time I can get someone intelligent to sit down and actually grant me the privilege of listening to my ideas, thinking about them, commenting on them, giving me constructive input. This is a privilege that I value highly. For someone to give serious consideration to my ideas and to spend actual time pointing out their weak spots and exposing their strengths is a privilege. A privilege that cannot be valued highly enough. Peer review is a privilege! One of the surest signs of a crackpot is their rejection of peer review. Their insistence that those who have thought about an issue before somehow are NOT qualified to comment on their work. The moment on intellectual commerce, they have made it clear that they do not wish to play within the only successful intellectual framework humans have ever created. For all human progress has always been scientific progress -- nothing else has changed in the last 10000 years. And the monopoly on intellectual commerce is not something that was ever granted any one person or institution (by whom??), it is something that the scientific method and the academic executive body around it *acquired*. Anybody is free to publish anything anywhere -- and in a hundred or two hundred years the mega society may be so lucky as to be another scientology or LDS or whatever church. Or, much more likely, they'll go the way of so many crackpots who thought they should throw the privilege of peer review back into the faces of those who were willing to elevate him into the circle of their peers. And by this intentional intellectual self-destruction the academic process is being selected as the stronger and better one again and again. Until it achieves a monopoly. For humanity to achieve anything, the achievement must be shared amongst humans. Humans must critique and help and correct and encourage and stop each other. Because there is nobody else anywhere who would do it FOR us. We can only listen to each other, and anybody who imagines that they should be listened TO but who isn't willing to listen to others himself; who wants to speak but rejects the repies out of hand is a selfish drain on the totality of human attention. === Subject: Re: Mega Foundation, change in plans >>I find their public paper >>http://www.ultrahiq.org/Mega/WhyMega.htm >>to be an interesting commentary on what they can do for mathematics >>publishing. > Not quite sure if you're serious with that comment, but... I'm serious that it's interesting. I think the author is misguided, however, and agree with your position below. In effect, I suspect they would be willing to publish almost anything, with little or no content at all. It's the perfect place to send the cranks so they can believe they've made an accomplishment, even though in fact they will have proven their status by submitting there. One of the limits of people is TIME. I, myself, simply cannot possibly > look at, read, listen to, think about every intelligent and worthwhile > idea in the world. I'd love to, mind you, but I do have a job and that > job is somewhat demanding of my time exactly because it is an academic > job. I see the same limitation in other people around me. This means that I am thankful every time I can get someone intelligent > to sit down and actually grant me the privilege of listening to my > ideas, thinking about them, commenting on them, giving me constructive > input. This is a privilege that I value highly. For someone to give > serious consideration to my ideas and to spend actual time pointing > out their weak spots and exposing their strengths is a privilege. A > privilege that cannot be valued highly enough. Peer review is a privilege! One of the surest signs of a crackpot is their rejection of peer > review. Their insistence that those who have thought about an issue > before somehow are NOT qualified to comment on their work. The moment > on intellectual commerce, they have made it clear that they do not > wish to play within the only successful intellectual framework humans > have ever created. For all human progress has always been scientific progress -- nothing > else has changed in the last 10000 years. And the monopoly on intellectual commerce is not something that was > ever granted any one person or institution (by whom??), it is > something that the scientific method and the academic executive body > around it *acquired*. Anybody is free to publish anything anywhere -- and in a hundred or > two hundred years the mega society may be so lucky as to be another > scientology or LDS or whatever church. Or, much more likely, they'll > go the way of so many crackpots who thought they should throw the > privilege of peer review back into the faces of those who were willing > to elevate him into the circle of their peers. And by this intentional intellectual self-destruction the academic > process is being selected as the stronger and better one again and > again. Until it achieves a monopoly. For humanity to achieve anything, the achievement must be shared > amongst humans. Humans must critique and help and correct and > encourage and stop each other. Because there is nobody else anywhere > who would do it FOR us. We can only listen to each other, and anybody who imagines that they > should be listened TO but who isn't willing to listen to others > himself; who wants to speak but rejects the repies out of hand is a > selfish drain on the totality of human attention. -- email: wtwentyman at copper dot net === Subject: Re: Mega Foundation, change in plans > One of the surest signs of a crackpot is their rejection of peer > review. As an illustration of how badly JSH needs peer review, try searching Google for the combination: Author: James Harris, Text: Oops I got over 80 hits! -- There are two things you must never attempt to prove: the unprovable -- and the obvious. -- Democracy: The triumph of popularity over principle. -- http://www.crbond.com === Subject: Re: Mega Foundation, change in plans >>My paper Advanced Polynomial Factorization is being published by the >>Mega Foundation, a society of the highest I.Q.'s in the country. Mega Foundation (correct me if I am wrong) was started by Chris Langan. To read some of his stuff go to crank.net: >http://www.crank.net/proof.html >and follow the Cognitive-Theoretic Model of the Universe link. >>I'd like to take some credit here. I asked James more than four years ago >>to contact Chris Langan. See 1063143790.v3.net >>It's interesting that two so-called cranks seem to be able to understand >>one another: Chris finding James's paper worthy of publication, and James >>finding Chris's forum worthy of his material. Typically if you try to put >>two cranks together, each will insist that he not be lumped in with such a >>nut. >>Maybe it takes the Smartest Man in America (as Esquire magazine anointed >>Chris) to understand James's work. Maybe James has found parallels to his >>own work in Chris's Theoretic Model. I anticipate a fruitful, fascinating >>collaboration. While stumbling around the Mega site I managed to log on to something that > let me read the conferences. So far, only James has contributed to the > Object mathematics thread. Looking back through previous Math threads we > find that one Russel Rierson is a frequent contributor. Here is one of his > contributions: === ================================= > Topic: 0 = infinity = 1 (1 of 5), Read 60 times > Conf: Math If new types of mathematical notation are discovered, then trying to grapple > with the equation of 1 = 0 = infinity will become more managable and > plausable. T@[F@(DX)] = @F[@T(DX)] The operation_F(DX-->0) = operation_T(DX-->infinity) = operation_@(DX-->1) A circle is a closed loop whereby we always return TO the starting point and > we have zero displacement. One trip around the loop and we have unity = 1. > An infinite number of trips still = zero displacement. So with the correct mathematical compositions ... 0 = infinity = 1. Russ > === ================================= So yes. Fruitful, fascinating and, erm, plausable. > After stumbling around their site that has no obvious search > capabilities, I find it amazing that anyone would pay them 25 cents to > be involved, much less the $25 they're asking. Aparently you have to > pay if you want to have a chance to see that there is no content. I > don't think I've ever seen a site that relies so heavily on the ego of > readers to get someone in. Bizarre. Any sci.math readers who want to read, or post to, the Mega Foundation Math Conference may proceed as follows: Go to: http://www.megasociety.net/MegaBoard/ Click on Theory of Everything. This takes you to http://megafoundation.net/~ctmu/login Click on new user. This takes you to http://megafoundation.net/~ctmu/new Create a new user profile for yourself. Click Create. This takes you to http://megafoundation.net/newuser and you should see a list of conferences down the left hand side. No payment is required. -- Clive Tooth http://www.clivetooth.dk === Subject: Re: Mega Foundation, change in plans > Any sci.math readers who want to read, or post to, the Mega Foundation Math > Conference may proceed as follows: > Go to: > http://www.megasociety.net/MegaBoard/ > Click on Theory of Everything. This takes you to > http://megafoundation.net/~ctmu/login > Click on new user. This takes you to > http://megafoundation.net/~ctmu/new > Create a new user profile for yourself. Click Create. This takes you to > http://megafoundation.net/newuser > and you should see a list of conferences down the left hand side. > No payment is required. Note that a poster can subsequently edit any post that they have posted. So it may be best to quote in full anything that you are replying to. -- Clive Tooth http://www.clivetooth.dk === Subject: Re: Mega Foundation, change in plans Any sci.math readers who want to read, or post to, the Mega Foundation > Math > Conference may proceed as follows: Go to: > http://www.megasociety.net/MegaBoard/ > Click on Theory of Everything. This takes you to > http://megafoundation.net/~ctmu/login > Click on new user. This takes you to > http://megafoundation.net/~ctmu/new > Create a new user profile for yourself. Click Create. This takes you to > http://megafoundation.net/newuser > and you should see a list of conferences down the left hand side. No payment is required. > Note that a poster can subsequently edit any post that they have posted. So > it may be best to quote in full anything that you are replying to. OK, I put on some rubber gloves and created a profile. It looks like Mr. Harris has wasted little time insulting professional mathematicians and whose who slavishly follow them. It will be interesting to see what he responds to questions about his proofs. === Subject: Re: Mega Foundation, change in plans Any sci.math readers who want to read, or post to, the Mega Foundation >>Math >Conference may proceed as follows: >Go to: >http://www.megasociety.net/MegaBoard/ >Click on Theory of Everything. This takes you to >http://megafoundation.net/~ctmu/login >Click on new user. This takes you to >http://megafoundation.net/~ctmu/new >Create a new user profile for yourself. Click Create. This takes you to http://megafoundation.net/newuser >and you should see a list of conferences down the left hand side. >No payment is required. >>Note that a poster can subsequently edit any post that they have posted. So >it may be best to quote in full anything that you are replying to. > OK, I put on some rubber gloves and created a profile. It looks like Mr. Harris has wasted little time insulting professional > mathematicians and whose who slavishly follow them. It will be interesting to see what he responds to questions about his > proofs. My only observations are: 1) there seems to be very low activity in the math discussions. 2) no one observed on the to Is this difficult questions that training in math will make the answers more obvious to someone with lower intelligence than to someone with higher intelligence and limited training in math. 3) JSH is talking *about* his proof without providing it. He did, however, post the code to his prime counting function and his definition of the Object Ring. Do you think it will upset him that he's being followed? -- email: wtwentyman at copper dot net === Subject: Re: Mega Foundation, change in plans Do you think it will upset him that > he's being followed? Why then did he tell where he was going? === Subject: Re: Mega Foundation, change in plans Do you think it will upset him that >he's being followed? > Why then did he tell where he was going? > I think he was trying to show off that he has finally gotten published. He hasn't realized yet that while he *is* technically published, it's in a journal that means nothing. -- email: wtwentyman at copper dot net === Subject: Re: Mega Foundation, change in plans > My only observations are: > 1) there seems to be very low activity in the math discussions. > 2) no one observed on the to Is this difficult questions that training > in math will make the answers more obvious to someone with lower > intelligence than to someone with higher intelligence and limited > training in math. > 3) JSH is talking *about* his proof without providing it. He did, > however, post the code to his prime counting function and his > definition of the Object Ring. Do you think it will upset him that > he's being followed? I hope not. -- Clive Tooth http://www.clivetooth.dk === Subject: Re: Mega Foundation, change in plans >>My only observations are: >>1) there seems to be very low activity in the math discussions. >>2) no one observed on the to Is this difficult questions that training >>in math will make the answers more obvious to someone with lower >>intelligence than to someone with higher intelligence and limited >>training in math. >>3) JSH is talking *about* his proof without providing it. He did, >>however, post the code to his prime counting function and his >>definition of the Object Ring. Do you think it will upset him that >>he's being followed? > I hope not. > trusting that when I found that great math, someone in the world >> would recognize it. >> That faith in the broad populace was mislaid, and in fact, mostly I >> got insults, and lies. >> My paper Advanced Polynomial Factorization is being published by >> the >> Mega Foundation, a society of the highest I.Q.'s in the country. Are you going to be nice enough to tell us *where* in that mess you > plan > to post your work or are you gone forever? I'm interested in > following your adventures. >> See the Table of Contents in the URL mentioned in William Rex >> Marshall's post earlier in this thread. If you really want to read James' work I think you would need to pay >> $25 and subscribe. I can't imagine that many people on sci.math will >> do that. I find their public paper http://www.ultrahiq.org/Mega/WhyMega.htm to be an interesting commentary on what they can do for mathematics > publishing. It's also interesting that looking at the site in Mozilla > apparently doesn't work as they intended, considering the line I see > about a redirect when not logged in. Nice HTML header too: Society, a high-IQ group > open to anyone scoring at the 1/1,000,000 level, approximately IQ 170 or > higher. Ultranet, Ubiquity, > Chris Langan, Gina LoSasso, Bob Seitz, severely-gifted, severely gifted, > extremely-gifted, > extremely gifted, Telenet, Telemach Network for Gifted Youth, Triple Nine, > Gifted, highly gifted, profoundly gifted, superior intelligence, > intellect, intellectual, cognitive ability, clever, brain, HiQ, > quick, brilliant, brilliance, brainpower, think, thinking, thought, brainy, > whiz kid, HIQ, Will Hunting, Einstein, prodigy, > american mensa, intertel, ispe, prometheus society, Top One Percent Society, > Triple Nine Society, TNS, Vidya, 999, 99.9, high IQ, High-IQ, Hi-Q, High-IQ > society, ultra-smart, super-smart, precocious, Four Sigma, 4 sigma, genius, > One-in-a-Thousand Society, mega society, Thinkfast, Mega, Prometheus, > Mega Test, Titan Test, LAIT, SAT, GRE, Stanford-Binet, Cattell, CTMM > Ron Hoeflin, Paul Cooijmans, Darryl Miyaguchi, > Gift of Fire, Noesis, Telicom top one percent = one in a thousand ? Maybe they should add bag of hammers to their keywords. === Subject: Re: Mega Foundation, change in plans mensanator@aol.com (mensanator) pushed briefly to the front of the ^ > Ultranet, Ubiquity, ^ > Chris Langan, Gina LoSasso, Bob Seitz, severely-gifted, severely gifted, ^ > extremely-gifted, ^ > extremely gifted, Telenet, Telemach Network for Gifted Youth, Triple Nine, ^ > Gifted, highly gifted, profoundly gifted, superior intelligence, ^ > intellect, intellectual, cognitive ability, clever, brain, HiQ, ^ > quick, brilliant, brilliance, brainpower, think, thinking, thought, brainy, ^ > whiz kid, HIQ, Will Hunting, Einstein, prodigy, ^ > american mensa, intertel, ispe, prometheus society, Top One Percent Society, ^ > Triple Nine Society, TNS, Vidya, 999, 99.9, high IQ, High-IQ, Hi-Q, High-IQ ^ > society, ultra-smart, super-smart, precocious, Four Sigma, 4 sigma, genius, ^ > One-in-a-Thousand Society, mega society, Thinkfast, Mega, Prometheus, ^ > Mega Test, Titan Test, LAIT, SAT, GRE, Stanford-Binet, Cattell, CTMM ^ > Ron Hoeflin, Paul Cooijmans, Darryl Miyaguchi, ^ > Gift of Fire, Noesis, Telicom ^ > ^ > top one percent = one in a thousand ? ^ Maybe they should add bag of hammers to their keywords. Hehe. I can see how hammer would be insufficiently exclusive, but unfortunately bag of hammers makes me think of bag of spanners, as in face like a .... Was this the comic effect you were after? Perhaps fistful of hammers would be better, bringing to mind the $$$s that JSH has always felt should be rightfully his. Anyway, IIRC JSH wields a Hammer, not just any old hammer. Andy -- sparge at globalnet point co point uk Give me a nice smooth, peaty island malt any day. Tomorrow would do nicely. Bob Goddard, uk.rec.sheddizen === Subject: Re: Mega Foundation, change in plans > mensanator@aol.com (mensanator) pushed briefly to the front of the > ^ > ^ > Ultranet, Ubiquity, > ^ > Chris Langan, Gina LoSasso, Bob Seitz, severely-gifted, severely gifted, > ^ > extremely-gifted, > ^ > extremely gifted, Telenet, Telemach Network for Gifted Youth, Triple Nine, > ^ > Gifted, highly gifted, profoundly gifted, superior intelligence, > ^ > intellect, intellectual, cognitive ability, clever, brain, HiQ, > ^ > quick, brilliant, brilliance, brainpower, think, thinking, thought, brainy, > ^ > whiz kid, HIQ, Will Hunting, Einstein, prodigy, > ^ > american mensa, intertel, ispe, prometheus society, Top One Percent Society, > ^ > Triple Nine Society, TNS, Vidya, 999, 99.9, high IQ, High-IQ, Hi-Q, High-IQ > ^ > society, ultra-smart, super-smart, precocious, Four Sigma, 4 sigma, genius, > ^ > One-in-a-Thousand Society, mega society, Thinkfast, Mega, Prometheus, > ^ > Mega Test, Titan Test, LAIT, SAT, GRE, Stanford-Binet, Cattell, CTMM > ^ > Ron Hoeflin, Paul Cooijmans, Darryl Miyaguchi, > ^ > Gift of Fire, Noesis, Telicom > ^ ^ > top one percent = one in a thousand ? ^ Maybe they should add bag of hammers to their keywords. Hehe. I can see how hammer would be insufficiently exclusive, but > unfortunately bag of hammers makes me think of bag of spanners, as > in face like a .... Was this the comic effect you were after? It's a quote from Mystery Science Theater 3000 that goes dumb as a bag of hammers > Perhaps fistful of hammers would be better, bringing to mind the > $$$s that JSH has always felt should be rightfully his. Anyway, IIRC JSH wields a Hammer, not just any old hammer. Andy === Subject: Re: Mega Foundation, change in plans >mensanator@aol.com (mensanator) pushed briefly to the front of the ^ > ^ > Ultranet, Ubiquity, >^ > Chris Langan, Gina LoSasso, Bob Seitz, severely-gifted, severely gifted, >^ > extremely-gifted, >^ > extremely gifted, Telenet, Telemach Network for Gifted Youth, Triple Nine, >^ > Gifted, highly gifted, profoundly gifted, superior intelligence, >^ > intellect, intellectual, cognitive ability, clever, brain, HiQ, >^ > quick, brilliant, brilliance, brainpower, think, thinking, thought, brainy, >^ > whiz kid, HIQ, Will Hunting, Einstein, prodigy, >^ > american mensa, intertel, ispe, prometheus society, Top One Percent Society, >^ > Triple Nine Society, TNS, Vidya, 999, 99.9, high IQ, High-IQ, Hi-Q, High-IQ >^ > society, ultra-smart, super-smart, precocious, Four Sigma, 4 sigma, genius, >^ > One-in-a-Thousand Society, mega society, Thinkfast, Mega, Prometheus, >^ > Mega Test, Titan Test, LAIT, SAT, GRE, Stanford-Binet, Cattell, CTMM >^ > Ron Hoeflin, Paul Cooijmans, Darryl Miyaguchi, >^ > Gift of Fire, Noesis, Telicom >^ ^ > top one percent = one in a thousand ? >^ Maybe they should add bag of hammers to their keywords. >Hehe. I can see how hammer would be insufficiently exclusive, but >unfortunately bag of hammers makes me think of bag of spanners, as >in face like a .... Was this the comic effect you were after? >Perhaps fistful of hammers would be better, bringing to mind the >$$$s that JSH has always felt should be rightfully his. >Anyway, IIRC JSH wields a Hammer, not just any old hammer. Very curious. There are plenty of people around here who spend a lot of time making fun of JSH. And there are various people who often state that such behavior is inappropriate, or various other uncomplimentary adjectives. You're the only person I recall who enjoys doing both. >Andy === Subject: Re: Mega Foundation, change in plans >mensanator@aol.com (mensanator) pushed briefly to the front of the >^ > ^ > Ultranet, Ubiquity, >^ > Chris Langan, Gina LoSasso, Bob Seitz, severely-gifted, severely gifted, >^ > extremely-gifted, >^ > extremely gifted, Telenet, Telemach Network for Gifted Youth, Triple Nine, >^ > Gifted, highly gifted, profoundly gifted, superior intelligence, >^ > intellect, intellectual, cognitive ability, clever, brain, HiQ, >^ > quick, brilliant, brilliance, brainpower, think, thinking, thought, brainy, >^ > whiz kid, HIQ, Will Hunting, Einstein, prodigy, >^ > american mensa, intertel, ispe, prometheus society, Top One Percent Society, >^ > Triple Nine Society, TNS, Vidya, 999, 99.9, high IQ, High-IQ, Hi-Q, High-IQ >^ > society, ultra-smart, super-smart, precocious, Four Sigma, 4 sigma, genius, >^ > One-in-a-Thousand Society, mega society, Thinkfast, Mega, Prometheus, >^ > Mega Test, Titan Test, LAIT, SAT, GRE, Stanford-Binet, Cattell, CTMM >^ > Ron Hoeflin, Paul Cooijmans, Darryl Miyaguchi, >^ > Gift of Fire, Noesis, Telicom >^ ^ > top one percent = one in a thousand ? ^ Maybe they should add bag of hammers to their keywords. Hehe. I can see how hammer would be insufficiently exclusive, but >unfortunately bag of hammers makes me think of bag of spanners, as >in face like a .... Was this the comic effect you were after? >Perhaps fistful of hammers would be better, bringing to mind the >$$$s that JSH has always felt should be rightfully his. Anyway, IIRC JSH wields a Hammer, not just any old hammer. > Very curious. There are plenty of people around here who spend > a lot of time making fun of JSH. And there are various people > who often state that such behavior is inappropriate, or various > other uncomplimentary adjectives. You're the only person I > recall who enjoys doing both. >Andy > A boy's gota have a hobby...... > === Subject: Re: Smallest number without a name > (Apropos of a lesson in which I teach students how to read numbers and the > paradox of the lowest number without any special properties.) > Going with the convention that a thousand million is a ion and a > thousand ion is a trillion, what comes after a trillion? Is there an > official line on this? > What is 999 999 999 999 999 + 1? > If it's a quadrillion (and that's a poor name) then what comes after that? > What is the lowest number without a name? For a Bonus Point this must be > different in different languages. Any information on that? > cheers > dd Hi dd, First, let's discuss only positive numbers, least things get out of hand. If a number is the lowest number without a name it has a name; namely, without a name!! --- And this is true in all languages. Best wishes, Jim === Subject: Re: Smallest number without a name > First, let's discuss only positive numbers, least things get out of > hand. Maybe we should stick to positive integers. Every positive real has uncountably many positive reals that don't have names less than it. > If a number is the lowest number without a name it has a name; namely, > without a name!! --- And this is true in all languages. Similarly, there is no lowest number whose shortest name contains fewer than a hundred letters. And yet there are only a finite number of names that contain fewer than a hundred letters... -- Evan Kirshenbaum +------------------------------------ HP Laboratories |Any programming problem can be 1501 Page Mill Road, 1U, MS 1141 |solved by adding another layer of Palo Alto, CA 94304 |indirection. Any performance |problem can be solved by removing kirshenbaum@hpl.hp.com |one. (650)857-7572 http://www.kirshenbaum.net/ === Subject: Re: Smallest number without a name > If a number is the lowest number without a name it has a name; namely, >> without a name!! --- And this is true in all languages. Similarly, there is no lowest number whose shortest name contains > fewer than a hundred letters. Well, there's one. > And yet there are only a finite number of names that contain fewer than > a hundred letters... I don't quite see the paradox you're trying to get at. Suppose you have identified the lowest number whose shortest name contains fewer than a hundred letters... then what? If you substitute more for fewer, you might have something. -Aaron J. Dinkin Dr. Whom === Subject: Re: Smallest number without a name >> If a number is the lowest number without a name it has a name; namely, >> without a name!! --- And this is true in all languages. Similarly, there is no lowest number whose shortest name contains > fewer than a hundred letters. Well, there's one. And yet there are only a finite number of names that contain fewer than > a hundred letters... I don't quite see the paradox you're trying to get at. Suppose you have > identified the lowest number whose shortest name contains fewer than a > hundred letters... then what? If you substitute more for fewer, you might have something. Yeah, I might, mightn't I. Sigh. -- Evan Kirshenbaum +------------------------------------ HP Laboratories |To find the end of Middle English, 1501 Page Mill Road, 1U, MS 1141 |you discover the exact date and Palo Alto, CA 94304 |time the Great Vowel Shift took |place (the morning of May 5, 1450, kirshenbaum@hpl.hp.com |at some time between neenuh fiftehn (650)857-7572 |and nahyn twenty-fahyv). | Kevin Wald http://www.kirshenbaum.net/ === Subject: Re: Smallest number without a name > What is 999 999 999 999 999 + 1? > If it's a quadrillion (and that's a poor name) then what comes after that? > Why do you consider quadrillion to be a poor name? I would think > that a poor name would be one that *didn't* follow a recognizable > pattern... An aesthetic judgment really, it just sounds clumsy to me. (Similarly I think the sign for infinity is a poor one). Of course it fits the pattern just fine. cheers dd === Subject: Re: Smallest number without a name While it was 9/9/03 10:14 pm throughout the UK, Robert Low sprinkled little black dots on a white screen, and they fell thus: thousand, two hundred and five, ... etc. If you're looking for the first one whose name is a composite of > others in English, that's either thirteen or twenty-one, depending > on how fussy you feel like being. Actually eleven and twelve are as composite as thirteen et al. ATMS they come from OHG einlif and zwelif. Or depending on which source you believe, from OE endleofan one over and twelf two left. Stewart. -- My e-mail is valid but not my primary mailbox. Please keep replies on on the 'group where everyone may benefit. === Subject: Re: Smallest number without a name Originator: mtx014@linux.services.coventry.ac.uk (Robert Low) >While it was 9/9/03 10:14 pm throughout the UK, Robert Low sprinkled >> If you're looking for the first one whose name is a composite of >> others in English, that's either thirteen or twenty-one, depending >> on how fussy you feel like being. >Actually eleven and twelve are as composite as thirteen et al. >ATMS they come from OHG einlif and zwelif. Cool; it's possible to be fussier than me. (I was only considering numbers whose English names were composites of English names. And I didn't know the etymology of eleven and twelve, which might have contributed :-)) -- Rob. http://www.mis.coventry.ac.uk/~mtx014/ === Subject: Re: Smallest number without a name > http://www.unc.edu/~rowlett/units/large.html http://www.catb.org/~esr/jargon/html/Q/quantifiers.html (Be sure to read all of the entry, the best part is at the end) http://www.catb.org/~esr/jargon/html/A/attoparsec.html http://www.catb.org/~esr/jargon/html/M/microfortnight.html -- Gary G. Taylor * Rialto, CA gary at cdfound dot org / http:// geetee dot cdfound dot org The two most abundant things in the universe are hydrogen and stupidity. --Harlan Ellison === Subject: Re: Smallest number without a name rec.puzzles, uk.education.maths === Subject: Re: Smallest number without a name >What is the lowest number without a name? > All integers have names. If you say so, however over 99.99% of those names have never been or ever will be used and over 99% of those names are so long that nobody can ever speak or write them, not even a computer with mega gigs and stacks of CD's. Let n be the lowest number without a name. So n is named 'the lowest number without a name'. But now it's not the lowest number without a name. Thus you see, there's no lowest number without a name. that all numbers have names. Riddle of the day: what's the largest number that can be written? === Subject: Re: Smallest number without a name Originator: mtx014@linux.services.coventry.ac.uk (Robert Low) >>What is the lowest number without a name? >> All integers have names. >If you say so, however over 99.99% of those names have never been or ever >will be used and over 99% of those names are so long that nobody can >ever speak or write them, not even a computer with mega gigs and stacks of >CD's. Since only finitely many names will ever be used, and there are infinitely many integers, it's rather more than 99% that will ever be spoken or written. If you want to use percentages, 0% of all integers will ever be named explicitly. (But using percentages is a dodgy proposition, since there's no uniform measure on the whole set of integers.) -- Rob. http://www.mis.coventry.ac.uk/~mtx014/ === Subject: Re: Smallest number without a name While it was 10/9/03 10:28 am throughout the UK, Robert Low sprinkled little black dots on a white screen, and they fell thus: there are infinitely many integers, it's rather > more than 99% that will ever be spoken or written. We could give each of our infinite monkeys a number, and get them to name each number. Then the name of every integer will've been used. Stewart. -- My e-mail is valid but not my primary mailbox. Please keep replies on on the 'group where everyone may benefit. === Subject: Re: Smallest number without a name > We could give each of our infinite monkeys a number, and get them to > name each number. Then the name of every integer will've been used. Get back to us when you've finished giving each of them a number. -- Evan Kirshenbaum +------------------------------------ HP Laboratories |Sometimes I think the surest sign 1501 Page Mill Road, 1U, MS 1141 |that intelligent life exists Palo Alto, CA 94304 |elsewhere in the universe is that |none of it has tried to contact us. kirshenbaum@hpl.hp.com | Calvin (650)857-7572 http://www.kirshenbaum.net/ === Subject: Re: Smallest number without a name >>We could give each of our infinite monkeys a number, and get them to >>name each number. Then the name of every integer will've been used. >Get back to us when you've finished giving each of them a number. > Okay, I'm back. You take a minute to give the first one a number. Then half a minute to give the second a number, then a quarter of a minute for the third, an eighth for the fourth, etc. You're done in two minutes. Jon Miller === Subject: Re: Smallest number without a name We could give each of our infinite monkeys a number, and get them >>to name each number. Then the name of every integer will've been >>used. Get back to us when you've finished giving each of them a number. Okay, I'm back. You take a minute to give the first one a number. Then half a > minute to give the second a number, then a quarter of a minute for > the third, an eighth for the fourth, etc. You're done in two > minutes. Ah, I hadn't realized that you were capable of unbounded speed, handing out ever-longer names in ever-shorter amounts of time. That does make it easier. -- Evan Kirshenbaum +------------------------------------ HP Laboratories |Other computer companies have spent 1501 Page Mill Road, 1U, MS 1141 |15 years working on fault-tolerant Palo Alto, CA 94304 |computers. Microsoft has spent |its time more fruitfully, working kirshenbaum@hpl.hp.com |on fault-tolerant *users*. (650)857-7572 http://www.kirshenbaum.net/ === Subject: Re: Smallest number without a name >>We could give each of our infinite monkeys a number, and get them >>to name each number. Then the name of every integer will've been >>used. >Get back to us when you've finished giving each of them a number. >Okay, I'm back. >>You take a minute to give the first one a number. Then half a >>minute to give the second a number, then a quarter of a minute for >>the third, an eighth for the fourth, etc. You're done in two >>minutes. >Ah, I hadn't realized that you were capable of unbounded speed, >handing out ever-longer names in ever-shorter amounts of time. That >does make it easier. > I don't even have to do that. I just have the monkeys do the work themselves. If it takes one monkey a minute to hand out a number, then it takes two monkeys a half a minute to together hand out the next number, and four monkeys a quarter minute to together hand out the next number, etc. Each monkey works with the same finite speed. Jon Miller === Subject: Re: Smallest number without a name > Ah, I hadn't realized that you were capable of unbounded speed, >handing out ever-longer names in ever-shorter amounts of time. That >does make it easier. > I don't even have to do that. I just have the monkeys do the work > themselves. If it takes one monkey a minute to hand out a number, then > it takes two monkeys a half a minute to together hand out the next > number, and four monkeys a quarter minute to together hand out the next > number, etc. Each monkey works with the same finite speed. This won't work. After one minute, you have one monkey who gives a number to the second monkey, but after the 1.5 minute, the two monkeys can only give a number to _one_ more monkey, so after 1.5 minutes, you have three monkeys who can give numbers out. It takes 0.3333 = 1/3 of a minute for the three monkeys to give a number to the fourth, it takes 1/4 of a minute to give a number to the fifth, etc. The total time is thus 1 + 1/2 + 1/3 + ..., which diverges. Of course, after the 1.5 minute mark, you could have the two monkeys giving numbers to two more monkeys in 0.25 minutes, and then the four giving numbers to four more in 0.125 minutes, but then you have unbounded speed again. Besides, how easy it is to get monkeys to co-operate? (Hey, it's hard to get _humans_ to co-operate.) -- Christopher Heckman === Subject: Re: Smallest number without a name Ah, I hadn't realized that you were capable of unbounded speed, >handing out ever-longer names in ever-shorter amounts of time. That >does make it easier. >>I don't even have to do that. I just have the monkeys do the work >>themselves. If it takes one monkey a minute to hand out a number, then >>it takes two monkeys a half a minute to together hand out the next >>number, and four monkeys a quarter minute to together hand out the next >>number, etc. Each monkey works with the same finite speed. >This won't work. After one minute, you have one monkey who gives a number >to the second monkey, but after the 1.5 minute, the two monkeys can only >give a number to _one_ more monkey, so after 1.5 minutes, you have three >monkeys who can give numbers out. Why can only numbered monkeys hand out numbers? > It takes 0.3333 = 1/3 of a minute for the three monkeys to give a number to the fourth, it takes 1/4 of a minute to give a number to the fifth, etc. The total time is thus 1 + 1/2 + 1/3 + ..., which diverges. >Of course, after the 1.5 minute mark, you could have the two monkeys giving >numbers to two more monkeys in 0.25 minutes, and then the four giving numbers >to four more in 0.125 minutes, but then you have unbounded speed again. >Besides, how easy it is to get monkeys to co-operate? (Hey, it's hard to >get _humans_ to co-operate.) > It seems to me that if I can assume infinitely many monkeys, then I can also assume infinite cooperation between the monkeys. And infinite divisibility of tasks as well. Parkinson's Law doesn't apply, because it's empirical. Jon Miller === Subject: Re: Smallest number without a name Ah, I hadn't realized that you were capable of unbounded speed, >handing out ever-longer names in ever-shorter amounts of time. That >does make it easier. I don't even have to do that. I just have the monkeys do the work > themselves. If it takes one monkey a minute to hand out a number, > then it takes two monkeys a half a minute to together hand out the > next number, and four monkeys a quarter minute to together hand out > the next number, etc. Each monkey works with the same finite speed. Okay, let's push on this. Four monkeys have handed out the number to the next monkey, presumably each handing out a quarter of the number, and the next monkey assembles it so that he can say it (we'll ignore the amount of time it will take to say it for the moment). They presumably also hand out their quarters to the eight monkeys that are going to hand out the next number, and these monkeys both compute the next number and figure out how to partition it among the eight of them in a constant amount of time? I'm not buying it yet. It seems that you're going to (occasionally) have to do an unbounded amount of work to calculate the next number, as each monkey jostles his neighbor and says add one. If this communication takes a finite amount of time, you'll never finish. -- Evan Kirshenbaum +------------------------------------ HP Laboratories |Sometimes I think the surest sign 1501 Page Mill Road, 1U, MS 1141 |that intelligent life exists Palo Alto, CA 94304 |elsewhere in the universe is that |none of it has tried to contact us. kirshenbaum@hpl.hp.com | Calvin (650)857-7572 http://www.kirshenbaum.net/ === Subject: Re: Smallest number without a name > I don't even have to do that. I just have the monkeys do the work > themselves. If it takes one monkey a minute to hand out a number, > then it takes two monkeys a half a minute to together hand out the > next number, and four monkeys a quarter minute to together hand out > the next number, etc. Each monkey works with the same finite speed. > Okay, let's push on this. Four monkeys have handed out the number to > the next monkey, presumably each handing out a quarter of the number, > and the next monkey assembles it so that he can say it (we'll ignore > the amount of time it will take to say it for the moment). They > presumably also hand out their quarters to the eight monkeys that are > going to hand out the next number, and these monkeys both compute the > next number and figure out how to partition it among the eight of them > in a constant amount of time? I'm not buying it yet. It seems that > you're going to (occasionally) have to do an unbounded amount of work > to calculate the next number, as each monkey jostles his neighbor and > says add one. If this communication takes a finite amount of time, > you'll never finish. Wrong series! It's not 1 + 1/2 + 1/4 + 1/8 + 1/16 +... , it's 1 + 1/2 + 1/3 + 1/4 + 1/5 + .... At each stage, only ONE monkey gets a number. Sums to infinity, ogres are like onions, end of story, bye bye, see you later. -- Geoff === Subject: Re: Smallest number without a name in a constant amount of time? I'm not buying it yet. It seems > that you're going to (occasionally) have to do an unbounded amount > of work to calculate the next number, as each monkey jostles his > neighbor and says add one. If this communication takes a finite > amount of time, you'll never finish. > Wrong series! It's not 1 + 1/2 + 1/4 + 1/8 + 1/16 +... , it's > 1 + 1/2 + 1/3 + 1/4 + 1/5 + .... You do realize that doesn't converge, right? > At each stage, only ONE monkey gets a number. Huh? He said > I don't even have to do that. I just have the monkeys do the work > themselves. If it takes one monkey a minute to hand out a number, > then it takes two monkeys a half a minute to together hand out the > next number, and four monkeys a quarter minute to together hand out > the next number, etc. Each monkey works with the same finite speed. Okay. One monkey hands out a number. So two monkeys have numbers. Then two monkeys together hand out the next number. Now three monkeys have numbers. Then four monkeys hand out the next number. Where did that fourth monkey come from? I presumed that he was using 2^n scratch monkeys at each in his computation, which is okay, as the number needed is equal to the cardinality of the set of finite subsets of the natural numbers, which is itself countable, so they're available in the original set. But I'm pretty sure (see earlier argument) that the work needed to compute the next index is worst case linear in the number of scratch monkeys (or at least in the ordinal of the number handed out if you use some sort of tree structure), which means that the scheme won't work. -- Evan Kirshenbaum +------------------------------------ HP Laboratories |The Elizabethans had so many words 1501 Page Mill Road, 1U, MS 1141 |for the female genitals that it is Palo Alto, CA 94304 |quite hard to speak a sentence of |modern English without inadvertently kirshenbaum@hpl.hp.com |mentioning at least three of them. (650)857-7572 | Terry Pratchett http://www.kirshenbaum.net/ === Subject: Re: Smallest number without a name I don't know its proper name, but I call it Freddie. === Subject: Re: Smallest number without a name >What is the lowest number without a name? Horse. -- Peter Moylan Peter.Moylan@newcastle.edu.au http://eepjm.newcastle.edu.au (OS/2 and eCS information and software) === Subject: Re: Smallest number without a name >>What is the lowest number without a name? >Horse. > That's lower than pig? Jon Miller === Subject: Re: Smallest number without a name > What is the lowest number without a name? >> Horse. > That's lower than pig? It's hard to ride through the desert on a pig. === Subject: Re: Smallest number without a name >>What is the lowest number without a name? >Horse. >That's lower than pig? >It's hard to ride through the desert on a pig. > I've been through the desert on a pig with no name. Jon Miller === Subject: Re: Smallest number without a name jon.and.mary.miller@comcast.net spake thus: > >>What is the lowest number without a name? >Horse. >That's lower than pig? >It's hard to ride through the desert on a pig. I've been through the desert on a pig with no name. I've been through the dessert on a pig with no blanket. -- David I say what it occurs to me to say. === == The address is valid today, but I change it periodically. === Subject: Re: Smallest number without a name >> What is the lowest number without a name? > Horse. >> That's lower than pig? >It's hard to ride through the desert on a pig. Take away the pig's name and it's easier. -- Charles Riggs Email address: chriggs|at|eircom|dot|com === Subject: Re: Smallest number without a name > What is the lowest number without a name? >> Horse. > That's lower than pig? >>It's hard to ride through the desert on a pig. >Take away the pig's name and it's easier. As Tootsie recently reminded us, the naming of a pig depends on the intended ultimate fate of that pig. It is acceptable to ride through the desert on a pig with a name, provided that you don't plan to eat the pig at the end of the trip. It is never acceptable to eat a pig who already has a name. That's Kermit's excuse, and he's sticking to it. -- Peter Moylan Peter.Moylan@newcastle.edu.au http://eepjm.newcastle.edu.au (OS/2 and eCS information and software) === Subject: Re: Smallest number without a name > It is never acceptable to eat a pig who already has a name. That's > Kermit's excuse, and he's sticking to it. Oh Mona, Mona So much o' you to love A little bit too much o' you to take care of Somehow I'm not too convinced that Miss Piggy would let Kermit go down on her even if he wanted to. I think she sublimates her sexual impulses into food. === Subject: Re: Smallest number without a name >What is the lowest number without a name? >Horse. > That's lower than pig? > Jon Miller Lower would be a cow - pigs are oinkers === Subject: Re: Smallest number without a name (Peter Moylan) said: >What is the lowest number without a name? > Horse. If you say so. === Subject: Re: Smallest number without a name Yes, that's what he means. Note that not all Reals have names ... >What is the lowest number without a name? All integers have names. > ? > Do you mean by this that, eg, 'googolplex-1' is the name of the number > defined by googolplex-1 if not what do you mean? === Subject: Re: Smallest number without a name > What is 999 999 999 999 999 + 1? >> If it's a quadrillion (and that's a poor name) then what comes after that? Why do you consider quadrillion to be a poor name? I would think >that a poor name would be one that *didn't* follow a recognizable >pattern... Jeff Why should 10^15 have anything to do with four? > Though I accept that 10^9 has little to do with two. Names are ordinals, numbers are cardinals. Just as first, second, third, fourth corresponds to 0, 1, 2, 3 so million, ion, trillion, quadrillion correspond to 10^6 * 10^(3n) for n = 0, 1, 2, 3. === === === Subject: Re: Brian Eugene Stephen Sholter ? May 13th 1959 > ... but Shawn knows that > your penis is closer to your anus than to God... Then go yourself! === Subject: Re: calculus prequisities... I forgot to reply with the answer, but my teacher didn't convert it to decimal, he kept it rational, but the same process applies === Subject: Re: calculus prequisities... You may find this interesting...especially for other references in the future. http://mathworld.wolfram.com/Circle.html -- Dana = = = = = = = = = = = = = = = = = > what I tried (and hope its what the teacher's looking for): > original problem: x^2 + y^2 - (127/7)x - (15/14)y + (211/14) = 0 > So i complete the square... > x^2 + y^2 - (127/7)x - (15/14)y = (211/14) > (x^2 - 127x/7 + (blank))^2 + (y^2 - 15y/14 + (blank))^2 = 211/14 > + (blank) + (blank) > (x^2 - 127x/7 + 82.3)^2 + (y^2 - 15y/14 + .27)^2 = 211/14 + 82.3 > + .27 > *half of (-127x/7), then squared; same with -15/14 > (x - 9.07)^2 + (y - .5357)^2 = 97.6414 > *(x-h)^2 + (y-k)^2 = r^2 > so... > (x - 9.07) + (y - .5357) = 9.881 > so in conclusion, its x = 9.07, y = .53, and r = 9.881 > Can anyone confirm this? again, I hope its what the teacher's looking for. > And I have the drawing of the circle on a x,y graph also. === Subject: Re: calculus prequisities... It's been awhile for me doing circles, but this looks familiar. Here's what Mathematica gives... Here are your terms... a = 1; c = 1; d = -127/7; e = -15/14; f = 211/14; x value (-d/2)*a 9.071428571428571 y value (-e/2)*a 0.5357142857142857 Radius Sqrt[(d^2 + e^2)/(4*a^2) - f/a] 8.216226478805243 HTH if it is correct. -- Dana Using Windows XP & Office XP = = = = = = = = = = = = = = = = = > You may find this interesting...especially for other references in the > future. > http://mathworld.wolfram.com/Circle.html > -- > Dana > = = = = = = = = = = = = = = = = = message > what I tried (and hope its what the teacher's looking for): original problem: x^2 + y^2 - (127/7)x - (15/14)y + (211/14) = 0 So i complete the square... x^2 + y^2 - (127/7)x - (15/14)y = (211/14) (x^2 - 127x/7 + (blank))^2 + (y^2 - 15y/14 + (blank))^2 = > 211/14 > + (blank) + (blank) (x^2 - 127x/7 + 82.3)^2 + (y^2 - 15y/14 + .27)^2 = 211/14 + > 82.3 > + .27 > *half of (-127x/7), then squared; same with -15/14 (x - 9.07)^2 + (y - .5357)^2 = 97.6414 > *(x-h)^2 + (y-k)^2 = r^2 > so... (x - 9.07) + (y - .5357) = 9.881 so in conclusion, its x = 9.07, y = .53, and r = 9.881 Can anyone confirm this? again, I hope its what the teacher's looking for. And I have the drawing of the circle on a x,y graph also. > === === Subject: Re: Michael Senkiw - January 22nd 1979 [a load of absolute tripe] Is this a web-bot gone wild, a net.kook, or what? -- Hello. My name is Darth Vader. I am your Father. Prepare to die. === Subject: problem on constructing an interesting function A few months ago someone set me an interesting problem; Does there exist a function f: [0,1] -> R, such that for every sub-interval of [0,1] and every y in R, there exists an x such that f(x)=y. (for instance there must be a number within 0.2 and 0.2001 such that f(x)=60+pi). If so, construct one. I didnt give it much thought until a few nights ago. The solution seemed quite wacky to me. Can you give your opinions or solutions? === Subject: Re: stupid question > This will probably be easy for most of you, but I can't figure out the > steps for this problem or others like it: Find the point on the y-axis that is equidistant from (2,3) and > (-3,7). Daniel Google does not show ant answer to this one, so I might as well ... 1) pick some point P on the y axis. You know its coordinates are ( 0, y) with some still undetermined y because it is on the y axis. We're looking for this particular y. 2) You can now write down the distance of this point P from the first of your given points. This will have the y in it. Call it d1 if you want. [hint: It is probably easier to write down the *square* of the distance.] 3) You can also compute d2^2, the square of the distance between P and your second point. 4) The distances are positive definite, i.e. if they're equal, then the square of the distances is also equal. 5) This means you can equate the expressions obtained in (2) and (3). 6) This yields a single equation with a single unknown (y) in it. solve for that unknown. 7) This may look like a second order equation so it may seem that there are two solutions. However the y^2 term ought to cancel. -- q@p morse: --.- @ .--. .-.-.- --.. .- .--. - --- .-.-.- -.-. --- --