Archive for the ‘love and logic classes’ Category
Love & Logic class starting Jan 6th, in Parker Colorado see my website for details
i've always loved logic puzzles, and i just finished a class in linear algebra. unfortunately, this question didn't enter my mind until about a week after the class was over.
anyway, what i'm wondering is, is there a way to solve logic puzzles (i'm talking about the kind with a few grids, and you have a few facts, and you need to figure out who did what when, or some variation on that) using linear algebra? i would imagine that that's how computers would solve them. but i'm wondering if all the matrices are related, and if i could, i don't know, take a transpose of one matrix, or find an inverse and use that? i tried to do a little research on my own, but there are way too many results for me to go through. thanks!
It seems unlikely that linear algebra will help very much, because the properties of grids arising in logic puzzles are difficult to capture using linear algebra alone. (Many statements you might want to make about a grid arising in a logic puzzle— e.g. that it have at most one nonzero entry in every row and in every column, or that it have fewer than a specified given number of nonzero entries in a particular set of rows or columns— are simply more easily expressed in terms of logical conditions (not in terms of matrix and vector arithmetic). In this sense, the extra structure these grids have is not very 'linear algebraic' in nature; to describe it using linear algebra would be confusing rather than enlightening.
One distinguishing feature of logic puzzles is that the entries of the grids often come, not from an infinite set of 'scalars' that can be added and multiplied, but from a finite set (often just 'empty' or 'x') which might or might not have its own arithmetic.
There are things called "finite fields" over which one can do most of linear algebra. If you take your scalars to be only 0 and 1, with arithmetic modulo 2, much of what you learned in linear algebra goes through for this field, and the arithmetic in this field very much mimics logical operations (with 0 as 'false' and '1' as 'true', say, addition modulo 2 corresponds to the logical 'xor', and multiplication modulo 2 is logical 'and'). But even then, there are a lot of things you want to do with logical operations— not just 'xor' and 'and', but 'or' and 'not'— which is not quite in the realm of linear algebra, for the reason that the some of these operations are _not_ linear maps. You may find web searches on Boolean algebra useful, though; computers are great with it, and from a programming point of view it is often more fundamental than the basic operations of linear algebra (most computers, even those that are decades old, have the ability to do Boolean calculations _in hardware_; the same cannot be said of matrix multiplication).
I am reminded of another puzzle type that is somewhat related to linear algebra: Sudoku puzzles. They contain grids of numbers, and could conceivably be dealt with using linear algebra, but the restrictions that give Sudoku games their unique flavor are not easily dealt with in 'matrix arithmetic' form. If you wanted to program a computer to solve Sudokus in a 'logical' fashion, you would be better off working just at the level of logical operations. (The technique of "backtracking" is probably the simplest way to get a computer to solve these and other puzzles. See the link below.)
Another puzzle type that comes to mind is one where an empty square grid is given, along with the sums of the entries in each row and column (and sometimes diagonal), and the goal is to fill in the blanks with numbers (understood to be positive integers, often in some fixed range, and often, with no number used more than once) so that the totals come out right. This is a problem that _can_ almost be solved in terms of linear algebra (since such an empty grid is equivalent to a system of linear equations in a certain number of unknowns), but the conditions that make the solution unique (having integer entries; having positive entries; using no integer more than once) are not easily expressed in terms of linear algebra. Ditto the problem of finding "Latin squares" of various orders: the conditions required to make a Latin square a Latin square are more easily expressed without the language of linear algebra.
I have included some links that will hopefully be of some use in your study.
***EDIT****
That humming in the background is my fan XD
Hahaha I LOVE Lion’s logic in this video.
“Then use a ONE handed sword.”
“YOU, I just said.” oh man, he’s amazing… *hugs Lion*
Anyways, an amusing little scene with Stahn and Lion from ToW: Radiant Mythology again
Duration : 0:0:57
So my 9 year old stays home alone 30 minutes everyday while I transition to home. I wrote a note stating this " DO NOT TOUCH TV until you have cleaned Living rm 1 & 2 areas" Love mom. I taped it to the TV, and this is what happened.
So I get home and theres a note taped to the outside of the door. Hmmm jeesh i hope i'm not getting a notice or something….Read it and this is what it states..
" Dear mom, Thanks but no thanks" Love ———— (my daughters name inserted here).
The living rooms did not get cleaned, and she's watching tv when I walk through the door. I walk over to tv and shut it off. She says hey I was watching that. i say oh, really? Well i'm really tired, and now I have 2 living rooms to clean by my self. She then says that she needs a ride to dance class. I say oh, really? Thats a shame because I won't have energy to take you after cleaning this mess. She storms to her room, and thats the end
So I ask you love and logic experts, what would you have done
*applauds mum*
well done!
i like your style
i too have a 9yo and at that age they are old enough to start taking some responsibility for tasks around the home and that is to be part of family life where we all help each other.
After all being his mum i do the majority of the cooking, cleaning and laundry which HE benefits from so i don't feel bad about asking that he does a few simple tasks in return that are well within his capabilities. I find that although i do need to remind him to do them , he accepts that and does what he is asked without grumbling because he does make the connection between getting what he wants and mummy getting what she asks for in return.
Which is why i totally approve of what you are doing too
if you don't get what you ask for then she doesn't get what she wants either as a direct result - don't weaken mum and she will get the message loud and clear
plus it will benefit her far more later on in life too
congrats!
more brilliance from del!
No video
This track was created with damon albarn who is part of the gorillaz. It was made before the gorillaz were formed and can be seen as the gorillaz first unofficial track as it was made by the same people
Lyrics:
Yeah, that’s the funky funky , ay bust it, yo, yo
Deltron tremendous force to end your courssssse
Every whim is enforced
I send men with torches to raid your fortress
And in the process radiate your optics
Subconsciously haunt emcees
Super human technician atomic inner dimension
Too mental with intuition
Typographical aptitude let my lasers clap at you
Mapped the route, psychologically crappin out, what youlaughing bout?
Imitations getting penetrated in free simulations
In my emcee training class remain in mass
Never get liquidated convert energy
Into matter instantly, with a pen and pad
Calculate the Sino graph, heat the center of gravity
Abolish apathy graphically packing 380’s
With body heat sensitive bullets you need safety
Fest on your face and neck
Mental armory levitate legs for my monarchy
No malarkey my flows embarking
Zionically sparking brain cells til they’re sparkling
(chorus) x2
No one knows the time passing by.
I remake my universe every time I use a verse
To fulfill my destiny, emcees rest in peace
Side barriers provide care within
From impurities every word sees your attention like thirddegree
I subjugate you other fake performers while the bass of yourface
No sense you be in attempt fleeting
Emcees siphon my likeness
Biting my insides like five enchiladas
This plain of existence is amazingly different
From my orbital oratory always going for the glory
You pop wide open from my slice slogans
I stay in effect with alien tech
Make you wanna say he’s the best
With synchronization with commendation its armor plated hard to fake it
Never carbonated, scar your matrix
Virtually uncertainty, murk your mediocre sheets and sofa
With my style of energy, del embling
A realm where anything, is possible
NASA scientists can’t define this
Mechanical mind set diamond alignment
(chorus)
Mathematical astro grapple a flow, pterodactyl
Very factual crash course, last resort,Âcast me off
At last we warp to my own world, my own neurological cubbyhole
Open the airshaft I’ll be there fast!
With spare raps to tear back their mass
Deltron experimental critical literal
Professor test the pitiful
Micronautalyst interchangeable
All of this gamma grammar far from bema
Got mind control bandannasÂ
To control your clan with scanners
Brand the planet like a band of bandits
Who man the cannons and guns with random
Sub atomic, love of logic, bug with phonics
Tub of chronic low in bridle with controlling ciphers
Unraveling rhyme, in traveling time
Alien life form mail in a pipe bomb
Deltoid life long I write songs
Monarch absolute, serve a glass of proof
When I vanish leave my spirit in a planet
On top of the surface my words and wit emerging
(chorus)
Duration : 0:4:59
I'm stuck on this question from my logic class. It's asking me to translate "a man loves a woman" into symbolic logic where I have to use L (x,y).
Can someone please help?
It depends on what kind of symbolic logic and notation you've bought into. Say you have M = {x:x is a man}, W = {y:y is a woman}. I would imagine that you're saying L(x,y) is order significant so it means the set of (x,y) such that x loves y (L(x,y) = {(x,y):x is in M, y is in W, and x loves y}). "Is in" could be the epsilon symbol. Now you need existential quantifiers for x,y. Usually the backwards E is used. I'll call it bE. So bE x in M and bE y in W such that L(x,y). "in" could be the epsilon symbol and such that could be the backward epsilon symbol.
M = {x:x is a man}
W = {y:y is a woman}
L(x,y) = {(x,y):x is in M, y is in W, and x loves y}
bE x in M and bE y in W such that L(x,y)
Recently Kim’s been obsessing over museums, her new “hobby.” Here she reads from her latest report, “The Creation of Value: meditations on the logic of museums and other coercive institutions.” Mildly unpleasant Dead Pinky Story also included (free poster available for download at www.PinkyShow.org).
Duration : 0:7:32
Love and Logic in the large ponies at Capital Challenge 2008—CLASS WINNER! score of 89!
Duration : 0:1:7
EARLY CHILDHOOD PARENTING MADE FUN!
Learn how to have responsible, respectful kids who are fun to be around! This 5-week class will cover the Love and Logic basics as designed by the Love and Logic Institute, Inc. This class is suitable to parents of children birth to six years-old.
SUNDAYS, 11:11 A.M. -12:40 P.M.
at Eastside Foursquare Church (www.eastsidechurch.org)
MARCH 1 through APRIL 5 IN ROOM 105
COST IS $35 for workbook and handouts
Duration : 0:0:49