Why is the product of two negative numbers positive?
Take -4 x -4 = 16 for example. Shouldn't it be -16?
Conjecture:
-4 x -4 = -16
Proof:
-4 x -4 = (-1 x 4) x (-1 x 4)
=-1 x (4 x 4) by distibutive law
=-1 x (16)
=-16
QED
What'sup?
Wednesday, February 27, 2008
Tuesday, February 26, 2008
Doomsday Vault
A vault has been built that is supposed to keep mankind going if a "doomsday" event occurs. http://en.wikipedia.org/wiki/Doomsday_vault
What would you put into the Doomsday Vault?
What would you put into the Doomsday Vault?
Saturday, February 23, 2008
More Math!!
In the puzzle opposite, place all the numbers 1 through 10 in the boxes so that each total shown across, down and diagonally is correct. The number 2 has been entered to help you get started.
Words 2
A 73459 1624 can result in 467 123759!
The letters of the two sets of words are the same but rearranged.
The letters of the two sets of words are the same but rearranged.
Words!!!
Here is a fun word puzzle:
At home teens sometimes live in these: 86324 3117 (two words)
When they go to college, teens live in these: 813762134
Same letters spell different words!
At home teens sometimes live in these: 86324 3117 (two words)
When they go to college, teens live in these: 813762134
Same letters spell different words!
Multiplication Puzzle
A B C D E
x 4
_______
E D C B A
(The number A B C D E times 4 equals E D C B A)
A, B, C, D and E are single digits 0-9
(I'll clean it up later)
x 4
_______
E D C B A
(The number A B C D E times 4 equals E D C B A)
A, B, C, D and E are single digits 0-9
(I'll clean it up later)
Friday, February 22, 2008
Hints and Solutions
By popular request, we are now providing both hints and solutions to the puzzles that we post. The link to the Hints blog is on the right of this blog. On the Hints blog, the link to the solutions post is listed. The Hints blog and the Solutions blog both have links back to the Family blog!!! Wow. Have fun.
Thursday, February 21, 2008
Fabulous Chemistry Videos
Following is a link to some absolutely fabulous chemistry videos. Often teachers are dry and pedantic. But Dr. Sadoway is amazing. Even if you only watch the videos and do no reading, these are worthwhile.
http://web.mit.edu/3.091/www/videos.htm
http://web.mit.edu/3.091/www/videos.htm
Variable Man
"Can any of us fix anything? No. None of us can do that. We're specialized. Each one of us has his own line, his own work. I understand my work, you understand yours. The tendency in evolution is toward greater and greater specialization. Man's society is an ecology that forces adaptation to it. Continued complexity makes it impossible for us to know anything outside our own personal field - I can't follow the work of the man sitting at the next desk over from me. Too much knowledge has piled up in each field. And there are too many fields."
From "The Variable Man" by Philip K Dick
From "The Variable Man" by Philip K Dick
Wednesday, February 20, 2008
Castro
As I was born in 1952 and Castro assumed power in Cuba in 1959, Castro has had control of Cuba for almost all of my life. How do you fell about Castro's resignation? What differences might the change make?
Feynman Math Puzzle
The following puzzle was sent from Richard Feynman (Nobel Prize 1965 in Physics") to his mother in a letter. The puzzle was for his father. The puzzle was not original with Feynman. He got it from an 1936 article in American Mathematical Monthly. "A" represents the same number where ever "A" appears. The dots can be any number but "A". All you need are basic math skills and understanding like addition, multiplication, long division, and subtraction. Who can get the answer first? Have fun!!
..............................................................................
Hints can be found at http://tomlinhoolyhints.blogspot.com/
Monday, February 18, 2008
Teen Email Exchange
R to I:
Dear I,
I just wanted to check in and find out how you're doing, I heard from H that you were in the hospital. I sincerely hope all is well. :)
Take care, R
I to H:
H,
I believe you can imagine the shock and surprised I felt when I received an email from R earlier today, in which she bid me to get better from my hospitalization, as she was informed by you. Not only did I believe that I was, in fact, quite ambulatory since you last saw me, but it seems that such a hospitalization would be quite inconvenient at this time. It was fairly distressing to be informed that I am bed-ridden at such short notice. However, I must thank you for allowing R to inform me of this situation, as it is quite concerning.
Blarg, I
I to R;
Thanks R. However, it seems that I might need another week for the presentation. [Due to UVA mid-terms]
I
--------------------
Ahhh. Teens.
Dear I,
I just wanted to check in and find out how you're doing, I heard from H that you were in the hospital. I sincerely hope all is well. :)
Take care, R
I to H:
H,
I believe you can imagine the shock and surprised I felt when I received an email from R earlier today, in which she bid me to get better from my hospitalization, as she was informed by you. Not only did I believe that I was, in fact, quite ambulatory since you last saw me, but it seems that such a hospitalization would be quite inconvenient at this time. It was fairly distressing to be informed that I am bed-ridden at such short notice. However, I must thank you for allowing R to inform me of this situation, as it is quite concerning.
Blarg, I
I to R;
Thanks R. However, it seems that I might need another week for the presentation. [Due to UVA mid-terms]
I
--------------------
Ahhh. Teens.
Switching Parties
Yesterday was my "catch up on WSJ" day. In one article that discussed how close Obama and Clinton are, they assumed that Obama would get it but said that if he does he probably could not get the White House over McCain. One reason is that he is so far left. The author said that political analysts are thinking that many Democrates will vote for McCain and that it could end up being a landslide win for McCain. Interesting.
Sunday, February 17, 2008
Scrabbles with Scrabble
Assumming the word Scrabble was the first word used in a game of Scrabble, how many other Scrabbles could be built? Parameters are of course the rules and number of occurrences of the letters.
Okay. You can't actally start with Scrabble but somone might put down crab, then next person s and ble. So taking that kind of approach. How many words "scrabble" could be created.
By the way, they called it scrabble on purpose and not scabble so you could not start with the word scrabble directly (8 letters).
Okay. You can't actally start with Scrabble but somone might put down crab, then next person s and ble. So taking that kind of approach. How many words "scrabble" could be created.
By the way, they called it scrabble on purpose and not scabble so you could not start with the word scrabble directly (8 letters).
Brain Waves from Eureka
The following was from the Eureka link under mathematics:
"The same rules of physics that govern molecules as they condense from gas to liquid, or freeze from liquid to solid, also apply to the activity patterns of neurons in the human brain. University of Chicago mathematician Jack Cowan will offer this and related insights...
“Structures built from a very large number of units can exhibit sharp transitions from one state to another state, which physicists call phase transitions,” said Cowan, a Professor in Mathematics and Neurology at Chicago. “Strange and interesting things happen in the neighborhood of a phase transition.”
When liquids undergo phase transitions, they evaporate into gas or freeze into ice. When the brain undergoes a phase transition, it moves from random to patterned activity. “The brain at rest produces random activity,” Cowan said, or what physicists call “Brownian motion.”...
These include the delta waves generated during sleep, the alpha waves of the visual brain, and the gamma waves, discovered during the last decade, which seem related to information processing. “The resting state of brain activity seems to have a statistical structure that’s characteristic of a certain kind of phase transition,” Cowan said. “The brain likes to sit there because that’s the place where information processing is optimized.”"
Isn't math great?
"The same rules of physics that govern molecules as they condense from gas to liquid, or freeze from liquid to solid, also apply to the activity patterns of neurons in the human brain. University of Chicago mathematician Jack Cowan will offer this and related insights...
“Structures built from a very large number of units can exhibit sharp transitions from one state to another state, which physicists call phase transitions,” said Cowan, a Professor in Mathematics and Neurology at Chicago. “Strange and interesting things happen in the neighborhood of a phase transition.”
When liquids undergo phase transitions, they evaporate into gas or freeze into ice. When the brain undergoes a phase transition, it moves from random to patterned activity. “The brain at rest produces random activity,” Cowan said, or what physicists call “Brownian motion.”...
These include the delta waves generated during sleep, the alpha waves of the visual brain, and the gamma waves, discovered during the last decade, which seem related to information processing. “The resting state of brain activity seems to have a statistical structure that’s characteristic of a certain kind of phase transition,” Cowan said. “The brain likes to sit there because that’s the place where information processing is optimized.”"
Isn't math great?
Thursday, February 14, 2008
LOST
I was lost when I first watched LOST but this season I am really lost with LOST. In fact, I think I lost ground with LOST. And with each episode I get more and more lost. I keep hoping I will find a plot and some understanding but those are geting more and more lost too. I think I will finally lose LOST!
Feynman
As Esh and I drive to UVA we have been listening to tapes. We finished the audio tapes of the new Einstein book and it was great. We are now going through tapes that cover Feynman's letters to various people at different stages of his life. Here are some of his words:
On the contrary, it's because someone knows something about it that we can't talk about physics. It's the things that nobody knows about that we can discuss. We can talk about the weather; we can talk about social problems; we can talk about psychology; we can talk about international finance... so it's the subject that nobody knows anything about that we can all talk about!
All mass is interaction.
It doesn't seem to me that this fantastically marvelous universe, this tremendous range of time and space and different kinds of animals, and all the different planets, and all these atoms with all their motions, and so on, all this complicated thing can merely be a stage so that God can watch human beings struggle for good and evil — which is the view that religion has. The stage is too big for the drama.
To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.
On the contrary, it's because someone knows something about it that we can't talk about physics. It's the things that nobody knows about that we can discuss. We can talk about the weather; we can talk about social problems; we can talk about psychology; we can talk about international finance... so it's the subject that nobody knows anything about that we can all talk about!
All mass is interaction.
It doesn't seem to me that this fantastically marvelous universe, this tremendous range of time and space and different kinds of animals, and all the different planets, and all these atoms with all their motions, and so on, all this complicated thing can merely be a stage so that God can watch human beings struggle for good and evil — which is the view that religion has. The stage is too big for the drama.
To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.
Vagina Monologues
"The Vagina Monologues" is a play about women, their bodies, their rights as humans.
http://en.wikipedia.org/wiki/The_Vagina_Monologues
With the atrocities against women occurring worldwide, it is time that this violence and constant denegration stopped. Our bodies are our bodies; our minds are our minds. We should never be slaves to anyone. We should not have to ask permission to do anything as we are as much adults as men. We are as important as men and absolutley nothing short of that. We have the right to be challenged and to challenge others. Women taking charge of their lives will make families better, nations better, the world better.
http://en.wikipedia.org/wiki/The_Vagina_Monologues
With the atrocities against women occurring worldwide, it is time that this violence and constant denegration stopped. Our bodies are our bodies; our minds are our minds. We should never be slaves to anyone. We should not have to ask permission to do anything as we are as much adults as men. We are as important as men and absolutley nothing short of that. We have the right to be challenged and to challenge others. Women taking charge of their lives will make families better, nations better, the world better.
Wednesday, February 13, 2008
What Will You Do?
What will you do with your tax rebate?
Couples get $1200 plus $300 per child, and the checks will be mailed in May.
Couples get $1200 plus $300 per child, and the checks will be mailed in May.
So why is Huckabee...
...still running? He has practically NO chance of getting the nomination!
Who will be Obama's and McCain's running mates?
Who will be Obama's and McCain's running mates?
Wilbur
Wilbur is our family's youngest. Our vet found him and his brother on the doorstep of his office some years ago.
We think Wilbur is autistic as he shows hightened senses. He spends most of everyday under a comforter, only to come out at night for kisses and hugs. He is affectionate, polite, and has the innocence of a child and is completely domesticated. When he found himself outside one time, he was totally shocked, bolted inside and hid for 36 hours.
We think Wilbur is autistic as he shows hightened senses. He spends most of everyday under a comforter, only to come out at night for kisses and hugs. He is affectionate, polite, and has the innocence of a child and is completely domesticated. When he found himself outside one time, he was totally shocked, bolted inside and hid for 36 hours.
Tuesday, February 12, 2008
Cocoa
Once consumed by the Aztecs in the form of a drink called Nahuatl, chocolate is purchased and consumed in copious amounts this time of the year. What is your favorite type: white , milk or dark?
Joke
As a child, my father, who commuted on the New Haven RR every day, told me the following joke:
A passenger who commuted every day on the train noticed that toward the end of the trip each day another passenger would go to the end of the train and shred his newspaper. He would then throw the newspaper strips off of the train onto the tracks.
Finally the first passenger asked the other why he shredded his newspaper and threw it on the tracks every day.
"It is to keep the elephants away."
"There aren't any elephants around here."
"See...it is working!"
A passenger who commuted every day on the train noticed that toward the end of the trip each day another passenger would go to the end of the train and shred his newspaper. He would then throw the newspaper strips off of the train onto the tracks.
Finally the first passenger asked the other why he shredded his newspaper and threw it on the tracks every day.
"It is to keep the elephants away."
"There aren't any elephants around here."
"See...it is working!"
Holy Smoke
At 3:00 AM this morning I woke up with a start! I could smell a strong odor of smoke! We let the dogs out and looked around outside. It ends up that it is fom the Dinwiddie brush fires! What an awful smell.
Sunday, February 10, 2008
Thumbs Up
When you place your hands together with interlaced fingers, which thumb is on top? I read somewhere (not sure if it is accurate or not) that it supposed to show brain dominance.
Saturday, February 9, 2008
Tax Rebate
What is everyone planning to do with their tax rebate? We will probably put it into savings; but we might buy a new washer and dryer.
BTW for all of the anti-Bush people out there, please forward your refund check to us! We can put it to good use!
BTW for all of the anti-Bush people out there, please forward your refund check to us! We can put it to good use!
Clowns
How do all of you feel about clowns? I am not afraid of them but I don't like them. They seem fake and mean to me.
Friday, February 8, 2008
Physics Building Poster
On my way out of UVA's physics building after having used their women's facility, I noticed a poster on the bulletin board for a symposium somewhere. Although I know chaos is a mathemtical field and it can be involved in particle physics experiments, and non-linear methods is a type of math technique, the title on the poster struck me. It was titled "Reduce Your Chaos Through Non-linear Methods." So what would this mean to a non-physics person?
* TO A MOTHER OF EIGHT: Use lots of duct tape configured in mobius strips.
* TO A MAILMAN: Don't bother sorting the mail and drive any route you want!
* A PATIENT ON HOUSE: Have Lupus and don't allow them to do a lumbar puncture.
* TO A MOTHER OF EIGHT: Use lots of duct tape configured in mobius strips.
* TO A MAILMAN: Don't bother sorting the mail and drive any route you want!
* A PATIENT ON HOUSE: Have Lupus and don't allow them to do a lumbar puncture.
Dear Mr. Ware
Dear Mr. Ware,
As you are my state government representative, I felt the need to let you know about a situation that is happening on Interstate 64 between Richmond and Charlottesville. Apparently someone has deicded to improve the rest areas along this route. Port-O-Potties have been established outside of, and in addition to, the normal restrooms (if you can call them that). As I have traveled over the years between various east coast states, I noticed that Virginia's rest areas have much to be desired. I am not sure this new addition will help. Although they have a very refreshing bright green color giving them a cheery appearance, outside toilets just do have the same alure that inside ones do, no matter how bad (and they are sometimes vey bad) they are. As it appears these are going to remain in place for some time, please at least place "No Smoking" signs on the doors of the outside individual stalls.
Are you also aware of the new outside hand washing stands? These consist of four soap dispensers, four pedal opearated (I am not sure how these would work for handicapped individuals) spigots that recycle the water between customers. Is this sanitary? Aren't there health laws governing these things?
Anyway, please check this sistuation out and make sure that this is the best thing for Virginia. I am not sure this new "enhancement" carries quite the same effect as the the rest areas in NC with their gorgeous lnadscaping, air conditioning, huge number of stalls in each ladies room with automatic flush toilets and motion sensor sinks.
Thank you very much.
Sincerely,
October Blogger
As you are my state government representative, I felt the need to let you know about a situation that is happening on Interstate 64 between Richmond and Charlottesville. Apparently someone has deicded to improve the rest areas along this route. Port-O-Potties have been established outside of, and in addition to, the normal restrooms (if you can call them that). As I have traveled over the years between various east coast states, I noticed that Virginia's rest areas have much to be desired. I am not sure this new addition will help. Although they have a very refreshing bright green color giving them a cheery appearance, outside toilets just do have the same alure that inside ones do, no matter how bad (and they are sometimes vey bad) they are. As it appears these are going to remain in place for some time, please at least place "No Smoking" signs on the doors of the outside individual stalls.
Are you also aware of the new outside hand washing stands? These consist of four soap dispensers, four pedal opearated (I am not sure how these would work for handicapped individuals) spigots that recycle the water between customers. Is this sanitary? Aren't there health laws governing these things?
Anyway, please check this sistuation out and make sure that this is the best thing for Virginia. I am not sure this new "enhancement" carries quite the same effect as the the rest areas in NC with their gorgeous lnadscaping, air conditioning, huge number of stalls in each ladies room with automatic flush toilets and motion sensor sinks.
Thank you very much.
Sincerely,
October Blogger
Going Green-An Obvious Truth
Well finally the Wall Street Journal, CNN and others are giving the public the real truth. Which to me has been obvious.
CNN stated this morning that Ethanol (from corn) might be more damaging than Gasoline. In part because the corn harvesters use so much gas to harvest the corn and other reasons.
Wall Street Journal finally let people know about the Mercury vapor in those stupid "Green" light bulbs. You have to dispose of them in a special way. Mercury is VERY poisonous.
Thinking of other things. Think of electric cars. Where do people think electricity comes from? The majority is from Coal. Well that is a non renewable resource and pumps lots of crap into the atmosphere. If from Nuclear, we have nuclear waste as well as the all the energy (driven by gasoline) to dig the holes to put the waste in and trucks to drive it there. Hydroelectric is decent but certainly limited.
And I just love the Go Green concerts where thousands of people drive and fly, sucking down gas, and use tons of electricity to power their lights, guitar amplifiers, etc. What is Green about that?
CNN stated this morning that Ethanol (from corn) might be more damaging than Gasoline. In part because the corn harvesters use so much gas to harvest the corn and other reasons.
Wall Street Journal finally let people know about the Mercury vapor in those stupid "Green" light bulbs. You have to dispose of them in a special way. Mercury is VERY poisonous.
Thinking of other things. Think of electric cars. Where do people think electricity comes from? The majority is from Coal. Well that is a non renewable resource and pumps lots of crap into the atmosphere. If from Nuclear, we have nuclear waste as well as the all the energy (driven by gasoline) to dig the holes to put the waste in and trucks to drive it there. Hydroelectric is decent but certainly limited.
And I just love the Go Green concerts where thousands of people drive and fly, sucking down gas, and use tons of electricity to power their lights, guitar amplifiers, etc. What is Green about that?
Thursday, February 7, 2008
Running Mates
At this point, it is difficult to estimate who will be the Democratic candidate but I think it will be Clinton. It looks like McCain will be the Republican candidate. Who do you think they will choose as running mates for the VP position?
I think McCain will choose Guiliani. I think Guiliani will allow him to get backing from Democrates in NY and CA which he will need to win.
I think McCain will choose Guiliani. I think Guiliani will allow him to get backing from Democrates in NY and CA which he will need to win.
Wednesday, February 6, 2008
Driving Mimics Life
Last night as Esh was driving us to B&N, I started to think about what Ian was gaining from learning how to drive. As my thinking reviewed everything, I started to realize that learning to drive is only partially about the actual learning to drive. It is more importantly about gaining independence, doing rapid problem solving, realizing you can control your own car but not others (like realizing you can control your self but not other people). You learn respect for rules. To drive successfully you must believe in yourself. Learning to drive is really about learning how to "drive" your own life. It is important to growing up and accepting responsibility for self. I wonder if that is why women are discourged from driving in many contries; so they will remain dependent and immature. Sad. Hooray for independence!
Sunday, February 3, 2008
Brain Cloud
The flu has created a brain cloud inside my cranium. All I can do is blog and Sudoku and watch Monk. No math, no reading Artemis Fowl, and when I read the Macroeconomics book it reads as "markets blah blah blah free trade blah blah blah blah blah consumers.." What if the cloud begins to rain? Oh, I can't think of that one...brain cloud.
Pillsbury
Lately, we have been discovering the culinary bliss found in the blue Pillsbury round packages. This AM we had cinnamon twists......yum. What can I saw about their crescent rolls but scrumptuous. And the biscuits....oh....flaky goodness that makes it okay to play with your food by peeling each layer apart! We will all soon look like the Pillsury Dough Boy.
Saturday, February 2, 2008
A day in the life of teenagers
Esh's academic team came in a wonderful third in districts today. That was really good against hard schools. Unfortunately they needed to come in first or second to go on in the state. They had a really
good time and used fake names like Shrodinger, Nietzshe, Archimedes, Heisenburg, Copernicus.
They same group of four (plus a couple of others) are now playing D&D very loudly and
having a great time traversing dungeons, casting spells, raising the dead, fighting monsters, healing
and gathering treasure. In a minute, they will be eating pizza bread.
So from 8:30 AM until 2:30 PM they bent their brains and had fun competing. Then from 3:30 PM until
8:30 PM they will role play and be their "other person".
What a healthy way to be in your teen years.
good time and used fake names like Shrodinger, Nietzshe, Archimedes, Heisenburg, Copernicus.
They same group of four (plus a couple of others) are now playing D&D very loudly and
having a great time traversing dungeons, casting spells, raising the dead, fighting monsters, healing
and gathering treasure. In a minute, they will be eating pizza bread.
So from 8:30 AM until 2:30 PM they bent their brains and had fun competing. Then from 3:30 PM until
8:30 PM they will role play and be their "other person".
What a healthy way to be in your teen years.
Okay...so exactly...
- when will we win the lottery?
- how long will this flu that Gravity and I have last?
- when will Esh find out about college?
- who will be running for president?
- when will the land in Charlottesville sell?
- what scholarships will Esh get?
- when will the writer's strike end?
- when will we get snow?
- ..................
Books
Books smell good. Books are fun. Books feel good in your hands...the weight of knowledge. Old and new, they have added so much to humanity. No wonder the printing press was deemed the greatest contributioon to humanity of the past millenium.
At the Library
by Nikki Grimes
I flip the pages of a book and slip inside,
Where crystal seas await and pirates hide.
I find a paradise where birds can talk,
Where children fly and trees prefer to walk.
Sometimes I end up on a city street.
I recognize the brownskin girl I meet.
She's skinny, but she’s strong, and brave, and wise.
I smile because I see me in her eyes.
At the Library
by Nikki Grimes
I flip the pages of a book and slip inside,
Where crystal seas await and pirates hide.
I find a paradise where birds can talk,
Where children fly and trees prefer to walk.
Sometimes I end up on a city street.
I recognize the brownskin girl I meet.
She's skinny, but she’s strong, and brave, and wise.
I smile because I see me in her eyes.
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