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Thursday, August 16, 2012
Sunday, April 8, 2012
Greetings
nly = no link yet
Click here to email me
games
-- Spider Solitaire Winning Probabilities
-- nly - tournament draw sheets
health
-- nly - the most effective and cheapest atheletes' foot preventer
-- nly - using massagers
-- nly - exercise
mathematics
-- Elliptic Modular Function
-- knot
music
-- nly - How to learn music and keep it learned
-- nly - Chopin editions (usually Mukilli is best)
-- nly - Pieces I like to play
-- nly - Recordings I like the best
politics
-- nly - fiscal policies
-- The Freedom Constitution, Human Rights
-- nly - separation and divorce
science
-- Acceleration and Speed
-- Acceleration, Speed, and Distance in space travel.
-- electromagnetics - Biot-Savart
---- Jay's double integral cylindrical coordinates formulation
---- Biot-Savart stuff
-- nly - mathematics
-- nly - A Line Initiator surface
-- MathGraf - A Math/Graphics array processing and general
purpose interpreting computer language
nly = no link yet
Click here to email me
games
-- Spider Solitaire Winning Probabilities
-- nly - tournament draw sheets
health
-- nly - the most effective and cheapest atheletes' foot preventer
-- nly - using massagers
-- nly - exercise
mathematics
-- Elliptic Modular Function
-- knot
music
-- nly - How to learn music and keep it learned
-- nly - Chopin editions (usually Mukilli is best)
-- nly - Pieces I like to play
-- nly - Recordings I like the best
politics
-- nly - fiscal policies
-- The Freedom Constitution, Human Rights
-- nly - separation and divorce
science
-- Acceleration and Speed
-- Acceleration, Speed, and Distance in space travel.
-- electromagnetics - Biot-Savart
---- Jay's double integral cylindrical coordinates formulation
---- Biot-Savart stuff
-- nly - mathematics
-- nly - A Line Initiator surface
-- MathGraf - A Math/Graphics array processing and general
purpose interpreting computer language
Freedom Constitution
Click here to go to the top level page, where you can email me
In mathematics there are things called basis functions. A polynomial in x has powers of x as its basis functions. There follows some ideas on basis functions for a "Freedom Constitution".
Abortion rights:
-- A mother carrying a baby should have the right to abort. If others have devised a relatively comfortable way of aborting which will not kill the baby, and commit to caring for the baby; then they may take the baby.
Equality rights:
-- Governments may not treat
---- single people any differently than people in non-single relationships.
---- a parent any differently than a non-parent.
---- people differently because of their race, relationships with others, or sex.
-- The above implies:
---- Governments must treat people in same sex relationships the same as other relationships.
Kidnapping:
-- Definition: Restricting a person's ability to go where they want.
-- This should not be allowed, unless the person is a danger to society.
-- Anyone kidnapping should be removed from society.
-- Governments that kidnap (prevent people from leaving their country) should be removed from society. Examples: recent Lybian government & the present Syrian government
In mathematics there are things called basis functions. A polynomial in x has powers of x as its basis functions. There follows some ideas on basis functions for a "Freedom Constitution".
Abortion rights:
-- A mother carrying a baby should have the right to abort. If others have devised a relatively comfortable way of aborting which will not kill the baby, and commit to caring for the baby; then they may take the baby.
Equality rights:
-- Governments may not treat
---- single people any differently than people in non-single relationships.
---- a parent any differently than a non-parent.
---- people differently because of their race, relationships with others, or sex.
-- The above implies:
---- Governments must treat people in same sex relationships the same as other relationships.
Kidnapping:
-- Definition: Restricting a person's ability to go where they want.
-- This should not be allowed, unless the person is a danger to society.
-- Anyone kidnapping should be removed from society.
-- Governments that kidnap (prevent people from leaving their country) should be removed from society. Examples: recent Lybian government & the present Syrian government
Spider Solitaire winning probabilities
Click here to go to the top level page, where you can email me
I think that what makes Spider Solitaire so intriguing to some of us is that it seems to have an unlimited number of configurations. Thus, it challenges us & there is no boredom. There are 8 decks of 13 cards. This means there are 104 (8 x 13) cards. If there was an 8 suit game, the # of possibilities is 104 x 103 x 102 x ... x 1 (104 factorial = 104! = a huge #). In the 4 suit game there are 2 of each card in each suit. In the 2 suit game there are 4 of each card in each suit. In the 1 suit game there are 8 of each card in the suit. As the duplication increases, the odds of winning increase.
Following the rules I've chosen, I've had a win rate of about 88% of the 1 suit games, 56% of the 2 suit games, & 16% of the 4 suit games for quite a long time now.
I've started writing a computer program to play using those rules. When I've finished & it's played many games, I'll publish the results.
If you already have a program & it wins at least close to the above #s, I would appreciate knowing about it.
I think that what makes Spider Solitaire so intriguing to some of us is that it seems to have an unlimited number of configurations. Thus, it challenges us & there is no boredom. There are 8 decks of 13 cards. This means there are 104 (8 x 13) cards. If there was an 8 suit game, the # of possibilities is 104 x 103 x 102 x ... x 1 (104 factorial = 104! = a huge #). In the 4 suit game there are 2 of each card in each suit. In the 2 suit game there are 4 of each card in each suit. In the 1 suit game there are 8 of each card in the suit. As the duplication increases, the odds of winning increase.
Following the rules I've chosen, I've had a win rate of about 88% of the 1 suit games, 56% of the 2 suit games, & 16% of the 4 suit games for quite a long time now.
I've started writing a computer program to play using those rules. When I've finished & it's played many games, I'll publish the results.
If you already have a program & it wins at least close to the above #s, I would appreciate knowing about it.
Elliptic Modular Function
I became interested in the elliptic modular function after seeing a beautiful poster made by Stephen Wolfram's Mathematica.
Acceleration & Speed
Click here to go to the top level page, where you can email me
Suppose we could fly in a plane or could teleport as fast as we wanted. How long would it take us to get anyplace on Earth using a constant acceleration & what would our maximum speed be?
Since it is about 24,000 miles around the Earth, the farthest point away is about 12,000 miles. No matter how far we want to go, we would need to accelerate for the first half of the time, then decelerate for the last half of the time to be able to stop at our destination. So to get 12,000 miles we would have to accelerate for 6,000 miles, then decelerate for the next 6,000 miles. Note that if we wanted to feel like we are always accelerating, we would face forward for the first half & then face backward the last half.
If we accelerate at 2.5 Gs for 15 minutes, how fast will we be going?
One G is about 32.2 ( actually 32.17404856...) feet/second, so 2.5 Gs is about 96.6 feet/second. The graph indicates that we will be going about 822 miles/minute. If we multiply by 60, we get over 49,000 miles/hour. Note that if we kept that maximum speed, we'd go around the Earth more than twice/hour.
When (NOT if) we develop teleportation abilities or a plane or other device that will take us that fast, there are two problems we should address. One is to make sure we don't hit some other plane or teleporting person. The other is the sonic boom. Sonic booms occur when we go thru the air at more than the speed of sound, which is 768 miles/hour at 68 degrees F in dry air. If we can teleport ourselves, then we probably could teleport air so that we make a tunnel of no air. Note that if we just move air out of the way near us, the movement of the air still creates a sonic boom. The simplest solution would be to make a tube of no air from start to destination. We could gently move the air out of the way in a second, travel thru it in 30 minutes, then gently let the air back into the tube. A slightly more complicated method would be to make several tubes one after another as we needed them, but still opening & closing them gently. Perhaps we would need an air traffic computer controller to prevent collisions.
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Suppose we could fly in a plane or could teleport as fast as we wanted. How long would it take us to get anyplace on Earth using a constant acceleration & what would our maximum speed be?
Since it is about 24,000 miles around the Earth, the farthest point away is about 12,000 miles. No matter how far we want to go, we would need to accelerate for the first half of the time, then decelerate for the last half of the time to be able to stop at our destination. So to get 12,000 miles we would have to accelerate for 6,000 miles, then decelerate for the next 6,000 miles. Note that if we wanted to feel like we are always accelerating, we would face forward for the first half & then face backward the last half.
From what I can gather on the Internet it seems that 4 Gs is significantly uncomfortable. When we fly on a commercial aircraft, there is a little less than 2 Gs on takeoff. From the picture we can see that we can go 6,000 miles in slightly less than 15 minutes at 2.5 Gs.
If we accelerate at 2.5 Gs for 15 minutes, how fast will we be going?
When (NOT if) we develop teleportation abilities or a plane or other device that will take us that fast, there are two problems we should address. One is to make sure we don't hit some other plane or teleporting person. The other is the sonic boom. Sonic booms occur when we go thru the air at more than the speed of sound, which is 768 miles/hour at 68 degrees F in dry air. If we can teleport ourselves, then we probably could teleport air so that we make a tunnel of no air. Note that if we just move air out of the way near us, the movement of the air still creates a sonic boom. The simplest solution would be to make a tube of no air from start to destination. We could gently move the air out of the way in a second, travel thru it in 30 minutes, then gently let the air back into the tube. A slightly more complicated method would be to make several tubes one after another as we needed them, but still opening & closing them gently. Perhaps we would need an air traffic computer controller to prevent collisions.
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