Yom Kippur is a day of atonement, fasting, and prayer. One enters the synagogue at 7 or 8 in the morning, and aside from a brief break before the afternoon service for around 2 hours (if you're lucky), you don't leave until nightfall.
Occasionally in the service there is some mental downtime, which is when I came up with this ...
Natural Number Spanning
Spanning with 1
The number 1 can be used to make any natural number (defined as excluding 0) though addition. N = 1 + 1 + 1 ... N times. Or simply N = 1*N.
So any set of two or more numbers (e.g. {n,m}) can be combined some number of times to make any natural number if one of the numbers is 1. You simply ignore all the other numbers in the set.
Spanning with 2
Let's say you don't have 1 in your set. The simplest set is {2,3}. Can this set S be used to make any natural number greater than 1? Yes.
Proof: The number 2 can be used to make any even number 2, 4, 6, ... And odd number can be created using 3 plus an even number.
Using a similar proof, it is possible to make any natural number of N or greater, if N is an odd number, either with a series of 2's or the number N plus a series of 2s.
The set {2, N} where N is an even number cannot be used to create any odd numbers.
Spanning with 3 and 4
What about the set {3,4}? The number 4 can be used to create every second even number. Furthermore, two 3's make 6; add 4's to this to get the remaining even numbers. Use 3 plus one of these numbers to get all odd numbers, except for the number 5.
Spanning with other sets
The question is: Given the set {m,n}: n > m. Is there a number P such that for all numbers P or greater you can combine multiples of m and n to create that number? How many numbers between n and P can't be so created?
I would be surprised if this wasn't already explored somewhere in mathematical theory. It's king of like using polyominoes to cover a plain or a chessboard.
A related mathematical subject is Bézout's identity for relative primes.
Yehuda
Saturday, September 22, 2007
Friday, September 21, 2007
Interesting Board Games on eBay
Following my last post on Amazon deals, I thought it might be interesting to take another look at what's cooking in one day on eBay.
I've done this type of post before, but honestly, there's just too much stuff to write about. I could devote an entire blog to nothing but interesting board and card games finds on eBay ... if I had nothing else to do.
Tantalizer board game
A dexterity game from the late 1960s where you have to perform all the actions by looking in a mirror.
Terminator 2 board game
Somehow, a board game is not the first thing I think of when this movie comes to mind.
Yotchie
Plays like Yahtzee. There's no information on Google about the game.
Peter Rabbit game
I love these beautiful games from the early 20th century.
The Illegal Game
People love commenting on politics and current events with a board game. Whether it's illegal immigration, drug scandals, or Britney Spears, there's always someone willing to put an event on a board game with the intent of mocking it.
The mocking is through contrasting whatever behavior is the subject of the game with wholesome behavior that is expected from a game for children. Also, the sarcasm of players striving to win a game by simulating actions that should never have been done in real life.
Stash
As an example, here's a Monopoly style game of trying to corner the drug market.
Lot of 10 games and 2 TV games
There's always the hope that a game lot will contain something interesting stuck in the middle of it, and therefore be kept away from bidders who only check the headlines.
And remember "TV games" with rifles? Just this week a parent's magazine was up in arms because of the new space-gun like controllers for the Wii.
Pilgrim
I've seen a lot of bad Christian themed games, but this looks like the worst ever.
Krull
As if the movie wasn't bad enough.
Great American Flag Game
Made in the 1940's. Might not mean much to you, but did you ever see the 48 star American flag?
Luckie Strike
Well, it's spelled "luckie", not "lucky", but that looks like a box of cigarettes to me.
Voodoo Skull
Uh huh.
Speaking of eBay auctions, I've never been able to figure out where to put this AuctionAds box. I don't have any room left on my sidebars. I'll see if it works here.
See you on the other side of Yom Kippur.
Yehuda
I've done this type of post before, but honestly, there's just too much stuff to write about. I could devote an entire blog to nothing but interesting board and card games finds on eBay ... if I had nothing else to do.
Tantalizer board game
A dexterity game from the late 1960s where you have to perform all the actions by looking in a mirror.
Terminator 2 board game
Somehow, a board game is not the first thing I think of when this movie comes to mind.
Yotchie
Plays like Yahtzee. There's no information on Google about the game.
Peter Rabbit game
I love these beautiful games from the early 20th century.
The Illegal Game
People love commenting on politics and current events with a board game. Whether it's illegal immigration, drug scandals, or Britney Spears, there's always someone willing to put an event on a board game with the intent of mocking it.
The mocking is through contrasting whatever behavior is the subject of the game with wholesome behavior that is expected from a game for children. Also, the sarcasm of players striving to win a game by simulating actions that should never have been done in real life.
Stash
As an example, here's a Monopoly style game of trying to corner the drug market.
Lot of 10 games and 2 TV games
There's always the hope that a game lot will contain something interesting stuck in the middle of it, and therefore be kept away from bidders who only check the headlines.
And remember "TV games" with rifles? Just this week a parent's magazine was up in arms because of the new space-gun like controllers for the Wii.
Pilgrim
I've seen a lot of bad Christian themed games, but this looks like the worst ever.
Krull
As if the movie wasn't bad enough.
Great American Flag Game
Made in the 1940's. Might not mean much to you, but did you ever see the 48 star American flag?
Luckie Strike
Well, it's spelled "luckie", not "lucky", but that looks like a box of cigarettes to me.
Voodoo Skull
Uh huh.
Speaking of eBay auctions, I've never been able to figure out where to put this AuctionAds box. I don't have any room left on my sidebars. I'll see if it works here.
See you on the other side of Yom Kippur.
Yehuda
Thursday, September 20, 2007
50% Off Board Games at Amazon
Every once in a while I'll throw these out for you, since I'm so nice. These are all good games, at least 50% off.
That's Lord of the Rings: the Duel.
Yehuda
That's Lord of the Rings: the Duel.
Yehuda
Session Report, in which I don't win Cosmic Encounter
The latest Jerusalem Strategy Gaming Club session report is up. Games played: Bridge, Leonardo Da Vinci, Cosmic Encounter.
I lose due to some bad luck and troublesome opponents.
Omniana
Omniana is a strange new fantasy "game" where players get a handful of cards to battle each other with. The cards provide only descriptions of your strange characters; no numbers, dice or statistics.
Your job is to describe why you should win the battle, given your character, the situation, and any advantages you have. Non combatants decide for each battle who the victor is.
Sounds like an amazing mix of roleplaying, card game, and imagination exercise.
Game News
Novometro joins a gaming club and plays Carcassonne.
New Scientist lists science board games.
Terry humorously notes the communist precursors to popular capitalist board games.
An article from Bahrain talking about the resurgence of board games comes close to talking about Euro-games. It mentions all the usual good points, and briefly mentions Essen and the German game of the year.
The Pittsburgh Tribune covers Arkham Horror and other games played by the Gaming Association of Southwestern Pennsylvania (GASP).
The Baltimore Sun covers a school doing things right by having the kids learn through play.
Yehuda
I lose due to some bad luck and troublesome opponents.
OmnianaOmniana is a strange new fantasy "game" where players get a handful of cards to battle each other with. The cards provide only descriptions of your strange characters; no numbers, dice or statistics.
Your job is to describe why you should win the battle, given your character, the situation, and any advantages you have. Non combatants decide for each battle who the victor is.
Sounds like an amazing mix of roleplaying, card game, and imagination exercise.
Game News
Novometro joins a gaming club and plays Carcassonne.
New Scientist lists science board games.
Terry humorously notes the communist precursors to popular capitalist board games.
An article from Bahrain talking about the resurgence of board games comes close to talking about Euro-games. It mentions all the usual good points, and briefly mentions Essen and the German game of the year.
The Pittsburgh Tribune covers Arkham Horror and other games played by the Gaming Association of Southwestern Pennsylvania (GASP).
The Baltimore Sun covers a school doing things right by having the kids learn through play.
Yehuda
Wednesday, September 19, 2007
The Disconnect Between Casual Game Sites and the Women Who Play at Them
Surveys that I've seen indicate that the majority of casual online game players are women. This article citing the Casual Games Association claims that women are an astonishing 74 percent of online casual game buyers.
Apparently, this fact hasn't yet reached the brains of those responsible for online gaming sites.
There are two serious and depressing realties about online gaming as it relates to women:
"Games for girls"
There's nothing inherently wrong with any type of game, whether it's combative, world-building, roleplaying, or makeup. But there's something seriously wrong with casual gaming sites - whose majority of players are women - if the builders think that "games for girls" means the following:
onlygirlsgames.com
games2girls.com
gogirlsonly.com
girlgames5.com
hotgamesforgirls.com
Among this fluff I found a few rays of hope:
girlgamezone.com notes that girls play more than makeup and dress up games, and even complains about the stereotyping. But most of the links are still to these sorts of games.
damegames.com and womengamers.com actually overcome the stereotypes and offer a complete assortment of games.
By the way, the only site labeled "games for boys" had a football game. And I think the label was an accident.
Game sites associated with porn
There are several strata of online gaming sites, each of which encompasses around a third of the sites:
As a result, the vast majority of all game sites lead to adult entertainment sites and either have, or directly link to, flashing pictures of cartoon breast closeups.
As a result, the online game industry is in close league with the online porn industry. I'm sure there are women interested in what the online porn industry has to offer, but I suspect that it is far less than the number interested in the online game industry.
Either the people who build the game portals are unaware of this. Or so much money is made from the links to the animated porn games that they can afford to lose nearly half of their potential audience.
Comparison to board games
A long time ago, board games had the same sexist divisions. There were once games What Shall I Be? for Girls and What Shall I Be? for Boys.
The cover of the game Battleship once pictured a father playing with his son while the wife and daughter cleaned up in the kitchen.
Those days are pretty much gone in board games. It's rather strange that this sexist division now exists in computer games.
Yehuda
Apparently, this fact hasn't yet reached the brains of those responsible for online gaming sites.
There are two serious and depressing realties about online gaming as it relates to women:
"Games for girls"
There's nothing inherently wrong with any type of game, whether it's combative, world-building, roleplaying, or makeup. But there's something seriously wrong with casual gaming sites - whose majority of players are women - if the builders think that "games for girls" means the following:
onlygirlsgames.com
games2girls.com
gogirlsonly.com
girlgames5.com
hotgamesforgirls.com
Among this fluff I found a few rays of hope:
girlgamezone.com notes that girls play more than makeup and dress up games, and even complains about the stereotyping. But most of the links are still to these sorts of games.
damegames.com and womengamers.com actually overcome the stereotypes and offer a complete assortment of games.
By the way, the only site labeled "games for boys" had a football game. And I think the label was an accident.
Game sites associated with porn
There are several strata of online gaming sites, each of which encompasses around a third of the sites:
- Strata one are the major and popular game sites with full communities, as well as publisher and distributor specific sites. These sites treat their visitors with respect.
- Strata two are the endless online game portals which exist only to bring in Google Ad revenue. Most of these are not offensive, although some link to the strata three sites.
- Strata three are the same as strata two, but for some reason a lot more skanky. These sites have flashing animated banners and boxes of barely dresses overdeveloped women. Clicking them leads to adult style animated game sites. Some of these sites also have banner ads for straight out adult entertainment.
As a result, the vast majority of all game sites lead to adult entertainment sites and either have, or directly link to, flashing pictures of cartoon breast closeups.
As a result, the online game industry is in close league with the online porn industry. I'm sure there are women interested in what the online porn industry has to offer, but I suspect that it is far less than the number interested in the online game industry.
Either the people who build the game portals are unaware of this. Or so much money is made from the links to the animated porn games that they can afford to lose nearly half of their potential audience.
Comparison to board games
A long time ago, board games had the same sexist divisions. There were once games What Shall I Be? for Girls and What Shall I Be? for Boys.
The cover of the game Battleship once pictured a father playing with his son while the wife and daughter cleaned up in the kitchen.
Those days are pretty much gone in board games. It's rather strange that this sexist division now exists in computer games.
Yehuda
The History of It's Alive!
A fascinating read from Jackson Pope of Reiver Games about how he took my game submission and eventually produced It's Alive! Go read it!
The Journal Gazette manages to get everything right about board games, and everything wrong about which ones.
Don't try to import Yogi playing cards into the U.A.E., as these are being confiscated for presenting images contrary to Islamic teaching. What the heck are Yogi playing cards?
And another killing over a card game, this time because the game group started playing before the guy arrived.
Yehuda
The Journal Gazette manages to get everything right about board games, and everything wrong about which ones.
Don't try to import Yogi playing cards into the U.A.E., as these are being confiscated for presenting images contrary to Islamic teaching. What the heck are Yogi playing cards?
And another killing over a card game, this time because the game group started playing before the guy arrived.
Yehuda
Tuesday, September 18, 2007
Star Wars: Revelations
Star Wars: Revelations
It seems I'm slow on the uptake for this one. This came out two years ago.
This is a short fan film (40 minutes) based on the Star Wars universe that fits between episodes 3 and 4. Like I felt when watching the Ryan vs Dorkman shorts, I'm astounded at the content creation capability that lies in the hands of amateurs. All that seems to be required is some technological talent, a lot of good will, some fanaticism, and modest funding. Who needs studios, anyway?
As for the film itself, the acting wasn't particularly good (of course, neither was the acting in SW III). I blame the actors in this case, more than the director; I think he got the best out of them that he could. And the lighting was pretty bad, at least on my screen.
Otherwise, it was enjoyable, well written and directed, nicely produced, and well effected.
Yehuda
It seems I'm slow on the uptake for this one. This came out two years ago.
This is a short fan film (40 minutes) based on the Star Wars universe that fits between episodes 3 and 4. Like I felt when watching the Ryan vs Dorkman shorts, I'm astounded at the content creation capability that lies in the hands of amateurs. All that seems to be required is some technological talent, a lot of good will, some fanaticism, and modest funding. Who needs studios, anyway?
As for the film itself, the acting wasn't particularly good (of course, neither was the acting in SW III). I blame the actors in this case, more than the director; I think he got the best out of them that he could. And the lighting was pretty bad, at least on my screen.
Otherwise, it was enjoyable, well written and directed, nicely produced, and well effected.
Yehuda
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