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[math-fun] SQRT occurring in inventory management optimization ?
by Henry Baker 06 Mar '18

06 Mar '18

I seem to recall a classical inventory management problem whose optimum solution involves a sqrt function. Since I never took a Operations Research course, I think that this problem showed up in a calculus class & used Lagrange multipliers. But after Googling a while, I couldn't find it. Anyone here recall a similar problem?

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Re: [math-fun] SQRT occurring in inventory management optimization ?
by Dan Asimov 05 Mar '18

05 Mar '18

I don't know that one, but I once had a pure math problem that used a square root, too. Does anyone know which one I'm thinking of? —Dan ----- I seem to recall a classical inventory management problem whose optimum solution involves a sqrt function. Since I never took a Operations Research course, I think that this problem showed up in a calculus class & used Lagrange multipliers. But after Googling a while, I couldn't find it. Anyone here recall a similar problem? -----

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[math-fun] everywhere
by françois mendzina essomba2 05 Mar '18

05 Mar '18

Hello... %e^z=(sqrt(1+z^2/n^2)+z/n)^n; sin(z)=(1/(2*%i))*((sqrt(1-z^2/n^2)+%i*z/n)^n-(sqrt(1-z^2/n^2)-%i*z/n)^n); cos(z)=(1/(2))*((sqrt(1-z^2/n^2)+%i*z/n)^n+(sqrt(1-z^2/n^2)-%i*z/n)^n); n-----infinity FME...

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[math-fun] Averaging functions on trees
by Dan Asimov 04 Mar '18

04 Mar '18

Let G be an infinite connected graph G = (V, E) where V is a countably infinite set and E is a subset of V x V - diagonal, satisfying 1) and 2): ----- 1) Every edge e in E has 2 endpoints, and any 2 vertices v,w in V bound at most one edge. 2) If for any v in V, deg(v) denotes the number of edges v belongs to, then for all v we have 2 <= deg(v) < oo. ----- Let C denote all functions V(G) —> reals: C = {f : V(G) —> R} For any v in V let the star star(v) of v be the set of vertices w at the other end of all edges vx containing v: star(v) = {x in V | vx is in E} Define A : C —> C by letting A(f) at a vertex v be the average of f(x) on the star of v: A(f)(v) = (Sum_{x in star(v)} f(x)) / |star(v)|. Question: Which f in C approach a limit under iteration of A: lim A^n(f) = f^ n—>oo for some f^ in C ??? —Dan

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Re: [math-fun] Infinite games
by Dan Asimov 03 Mar '18

03 Mar '18

Here's another (potentially) infinite game: Starting from zero, players write down successive ordinals in turn. The loser is the first person whose turn is illegible. —Dan >From: "Adam P. Goucher" <apgoucher(a)gmx.com> ----- Here's a fun game which works with any finite number k of players: Players take turns* to name positive integers that haven't already been named. When you name an integer, you subsequently 'own' it. Play continues (possibly beyond time omega) until every integer is owned. Clearly, it must stop before time omega_1. * For a positive integer n, Turn(n) is the sum (reduced modulo k) of the base-k digits of n. For an ordinal alpha, Turn(alpha) is the sum (again reduced modulo k) of the Turns of the coefficients of alpha in Cantor normal form. This is really fair. An integer n is described as 'dominated' by a player if there exists an infinite set S containing n such that all finite sums of elements from S are owned by that player. The winner is the person who dominates the smallest integer. (A winner exists by Hindman's theorem, and is unique by the fact that you can only dominate an integer you own.) > From: "Dan Asimov" <dasimov(a)earthlink.net> > One kind of infinite game discussed by logicians is determined by the choice of a > subset X of the half-open unit interval [0, 1). > > Then each player in turn selects a bit from {0,1}, and if the countable bitstring > thus created lies in X then the first player (W) wins; if not, the second player (B) wins. > > The Axiom of Determinacy states that every such game has a strategy for one player > or the other. Meanwhile, the Axiom of Choice can be used to show there exists a > subset X of [0,1) whose corresponding game has no strategy for either player. > > I'm hoping for a totally explicit game perhaps played by placing counters on > unoccupied cells of a board, as in Hex (or Conway's Angels & Devils game). > ----- > On Saturday, March 3, 2018, 4:36:13 AM PST, Fred Lunnon <fred.lunnon(a)gmail.com> wrote: > If your game has length \omega , how do you know who wins? WFL > On 3/3/18, Dan Asimov <dasimov(a)earthlink.net> wrote: > > I am curious: Do people know of interesting infinite two-player games, > > preferably without chance playing a role? > > > > I'm mainly interested in discrete 2-player games with one player going > > first and with play alternating thereafter. Such that in some sense, > > except for that first player / second player thing, the challenge > > facing each player is as symmetrical as possible. > > > > Though I will not rule out continuous games. -----

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Re: [math-fun] Infinite games
by Dan Asimov 03 Mar '18

03 Mar '18

One kind of infinite game discussed by logicians is determined by the choice of a subset X of the half-open unit interval [0, 1). Then each player in turn selects a bit from {0,1}, and if the countable bitstring thus created lies in X then the first player (W) wins; if not, the second player (B) wins. The Axiom of Determinacy states that every such game has a strategy for one player or the other. Meanwhile, the Axiom of Choice can be used to show there exists a subset X of [0,1) whose corresponding game has no strategy for either player. I'm hoping for a totally explicit game perhaps played by placing counters on unoccupied cells of a board, as in Hex (or Conway's Angels & Devils game). —Dan ----- On Saturday, March 3, 2018, 4:36:13 AM PST, Fred Lunnon <fred.lunnon(a)gmail.com> wrote: If your game has length \omega , how do you know who wins? WFL On 3/3/18, Dan Asimov <dasimov(a)earthlink.net> wrote: > I am curious: Do people know of interesting infinite two-player games, > preferably without chance playing a role? > > I'm mainly interested in discrete 2-player games with one player going > first and with play alternating thereafter. Such that in some sense, > except for that first player / second player thing, the challenge > facing each player is as symmetrical as possible. > > Though I will not rule out continuous games. -----

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[math-fun] Infinite games
by Dan Asimov 03 Mar '18

03 Mar '18

I am curious: Do people know of interesting infinite two-player games, preferably without chance playing a role? I'm mainly interested in discrete 2-player games with one player going first and with play alternating thereafter. Such that in some sense, except for that first player / second player thing, the challenge facing each player is as symmetrical as possible. Though I will not rule out continuous games. —Dan

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[math-fun] Cuba audio: ultrasonic+ultrasonic=audible
by Henry Baker 02 Mar '18

02 Mar '18

It's possible that multiple *different* ultrasonic spying devices may have interfered with one another in the recent Cuba incident! (Spy v Spy)*nonlinear => Intermodulation Distortion + Oops! This obviously violated the spooks' Hypocritic Oath: First, Do No Harmonics! https://spqr.eecs.umich.edu/papers/YanFuXu-Cuba-CSE-TR-001-18.pdf On Cuba, Diplomats, Ultrasound, and Intermodulation Distortion University of Michigan Tech Report CSE-TR-001-18 Chen Yan 1 , Kevin Fu 2 , and Wenyuan Xu 1 1 Department of Systems Science and Engineering, Zhejiang University 2 Computer Science & Engineering, University of Michigan March 1, 2018 Abstract This technical report analyzes how ultrasound could have led to the AP news recordings of metallic sounds reportedly heard by diplomats in Cuba. Beginning with screen shots of the acoustic spectral plots from the AP news, we reverse engineered ultrasonic signals that could lead to those outcomes as a result of intermodulation distortion and non-linearities of the acoustic transmission medium. We created a proof of concept eavesdropping device to exfiltrate information by AM modulation over an inaudible ultrasonic carrier. When a second inaudible ultrasonic source interfered with the primary inaudible ultrasonic source, intermodu- lation distortion created audible byproducts that share spectral characteristics with audio from the AP news. Our conclusion is that if ultrasound played a role in harming diplomats in Cuba, then a plausible cause is intermodulation distortion between ultrasonic signals that unintention- ally synthesize audible tones. In other words, acoustic interference without malicious intent to cause harm could have led to the audible sensations in Cuba.

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[math-fun] Math-Fun topics
by rcs＠xmission.com 02 Mar '18

02 Mar '18

We've had some new folks join us recently, who might be unaware of some of my arbitrary rules. The topics of politics and global warming are banned. Rich

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Re: [math-fun] next breakthrough?
by Henry Baker 02 Mar '18

02 Mar '18

I should have just gone ahead and indicated why undecidability scales. Basically, a TM with a given amount of time can *diagonalize* over all TM's who use a bit less time. "Diagonalize" means emulate and then disagree with. Similarly, a TM with a given amount of space can *diagonalize* over all TM's who use a bit less space. "A bit less" is a pretty small delta, because TM emulation can be done with only a small slowdown in time and a very small increase in space. With modern so-called "virtual machines" (VM's) and "containers", most web servers run as VM's on larger hardware. Indeed, "containers" are coming to web browsers, and there are some operating systems that are Russian dolls of VM's. At 10:01 PM 3/1/2018, Henry Baker wrote: >True, but TM complexity scales extremely rapidly with time and/or space (amount of tape), so even "approximations" to large amounts of time and space would require googols of universes to compute. > >So undecidability is pretty smooth/continuous in those dimensions. > >This complexity scaling is far above and beyond the P=NP issue, which gets you only one exponential -- at most. > >100GBytes of RAM on big server machines is quite common. That's quite enough "tape"/"space" for serious exponential stacking. > >At 06:10 PM 3/1/2018, Mike Speciner wrote: >>We don't build Turing machines. We build finite state machines, admittedly with very large numbers of states. So, technically, although not practically, undecidability doesn't apply. >> >>--ms >> >>On 01-Mar-18 20:17, Henry Baker wrote: >>>By "consequential", I think that you may mean "consequential" to >>>a large fraction of the population -- e.g., electrical engineers >>>and physicists are required to work with complex numbers. >>>Consequential enough to include in high school curricula. >>> >>>I'm still waiting for undecidable/non-Turing-computable to make >>>its way into the bulk of society; a lot of the incredibly stupid >>>comments by politicians might be avoided if they had had any >>>education in the *limits* of logical systems and mathematics. >>> >>>For example, no amount of "nerding harder" will enable computer >>>scientists to design a computer such that an arbitrary input >>>won't cause the computer do something "bad". >>> >>>It took physicists many centuries to convince a large fraction >>>of the population about the impossibility of perpetual motion >>>machines, so perhaps we may be facing the same thing here. >>> >>>Curiously, we have *more* trust in undecidability than we >>>have in the impossibility of perpetual motion, because the >>>"laws" of physics are still empirical facts, which might be >>>destroyed with the very next experiment, while undecidability >>>is a function of logic itself, and requires no reference to >>>the "real world". >>> >>>Regarding breakthroughs that are not yet known even to the >>>best of mathematicians, I would say that things related to >>>P=NP and cryptography are pretty high on the list. For example, >>>we are close to trusting cryptography hash functions with all >>>the money in the world (literally!), yet we have no *proof* >>>that these functions are hard to invert or hard to find >>>collisions for. With this much crypto currency in circulation, >>>there's obviously no need for a "Millennium Prize", since a >>>constructive counter-example would produce the richest person >>>in the world! >>> >>>With the recent advances in AI, we might also ponder the "end >>>of mathematics", but not for the usually suggested reason. AI >>>could end mathematics -- not by doing mathematics better, but >>>by doing enough other things better that no one needs mathematicians >>>anymore. This is where we seem to be headed with chess and Go; >>>once machines are so much better, everyone loses interest in the >>>games so no one plays anymore. >>> >>>At 03:47 PM 3/1/2018, Bernie Cosell wrote: >>>>i know this is vague, but my wife was reading about the history of >>>>i and wondered what the next great fundamental conceptual breakthrough >>>>might be. it took something like 1500 years for complex numbers to >>>>get understood and now they're used everywhere. it's now been >>>>about 250 years and she was wondering what might be the next >>>>breakthrough be that could be as consequential as complex numbers are.

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