According to Wikipedia...
1) The oldest known mathematical object is the Lebombo bone, discovered in the Lebombo mountains of Swaziland and dated to approximately 35,000 BC.[10] It consists of 29 distinct notches deliberately cut into a baboon's fibula.[11] There is evidence that women used counting to keep track of their menstrual cycles; 28 to 30 scratches on bone or stone, followed by a distinctive marker.[12]
2) The majority of recovered clay tablets date from 1800 to 1600 BC, and cover topics which include fractions, algebra, quadratic and cubic equations, and the calculation of regular reciprocal pairs (see Plimpton 322).[20] The tablets also include multiplication tables and methods for solving linear and quadratic equations. The Babylonian tablet YBC 7289 gives an approximation to √2 accurate to five decimal places.
3) The Babylonians had a true place-value system, where digits written in the left column represented larger values, much as in the decimal system. They lacked, however, an equivalent of the decimal point, and so the place value of a symbol often had to be inferred from the context.
4) The oldest mathematical text discovered so far is the Moscow papyrus, which is an Egyptian Middle Kingdom papyrus dated c. 2000–1800 BC.[citation needed] Like many ancient mathematical texts, it consists of what are today called word problems or story problems, which were apparently intended as entertainment.
5) In China, the Emperor Qin Shi Huang (Shi Huang-ti) commanded in 212 BC that all books in Qin Empire other than officially sanctioned ones should be burned. This decree was not universally obeyed, but as a consequence of this order little is known about ancient Chinese mathematics. From the Western Zhou Dynasty (from 1046 BC), the oldest mathematical work to survive the book burning is the I Ching, which uses the 8 binary 3-tuples (trigrams) and 64 binary 6-tuples (hexagrams) for philosophical, mathematical, and mystical purposes. The binary tuples are composed of broken and solid lines, called yin (female) and yang (male), respectively (see King Wen sequence).
6) The earliest civilization on the Indian subcontinent is the Indus Valley Civilization that flourished between 2600 and 1900 BC in the Indus river basin. Their cities were laid out with geometric regularity, but no known mathematical documents survive from this civilization.[27]
7) The Surya Siddhanta (c. 400) introduced the trigonometric functions of sine, cosine, and inverse sine, and laid down rules to determine the true motions of the luminaries, which conforms to their actual positions in the sky. The cosmological time cycles explained in the text, which was copied from an earlier work, correspond to an average sidereal year of 365.2563627 days, which is only 1.4 seconds longer than the modern value of 365.25636305 days. This work was translated into to Arabic and Latin during the Middle Ages.
8) In the 12th century, Bhaskara first conceived differential calculus, along with the concepts of the derivative, differential coefficient, and differentiation. He also stated Rolle's theorem (a special case of the mean value theorem), studied Pell's equation, and investigated the derivative of the sine function. From the 14th century, Madhava and other Kerala School mathematicians further developed his ideas. They developed the concepts of mathematical analysis and floating point numbers, and concepts fundamental to the overall development of calculus, including the mean value theorem, term by term integration, the relationship of an area under a curve and its antiderivative or integral, the integral test for convergence, iterative methods for solutions to non-linear equations, and a number of infinite series, power series, Taylor series, and trigonometric series. In the 16th century, Jyeshtadeva consolidated many of the Kerala School's developments and theorems in the Yuktibhasa, the world's first differential calculus text, which also introduced concepts of integral calculus.
Showing posts with label trivia. Show all posts
Showing posts with label trivia. Show all posts
Thursday, December 24, 2009
Friday, October 16, 2009
Hidden worlds
The underwater "flying turkey" creeps me out, but the squids and octopi are way cool. I especially like how male squids will split their coloring to show a potential mate his "softer" side, while still showing aggression towards potential rivals.
I never realized that the canopy of the redwood forest was once considered a "desert", devoid of other life. This video corrects that belief in spades. And I never knew that redwoods can grow back into themselves.
Wednesday, September 23, 2009
How the Internet Works
How the Internet Works
Actually, I've been wanting to write commentaries on my favorite talks at TED.com and I've finally decided to just jump into it. I'll probably be doing these in spurts.
The talks I am focusing on in this post deal with how the Internet works from a very social standpoint. This first one explains many geeks views on resource sharing:
(If the video doesn't work, go to http://www.youtube.com/watch?v=P65XdTlk4vA )
When I first watched it, I giggled a lot because it reminded me of the days when I visited local computer boards (BBSes) and conversed with people through WWIVNet. Back in 1992, it took a few days to get packets from Florida to Texas, because you had to rely on certain BBS sysops to make long distance calls (at their own expense), once or twice a day, to send and receive the packets. When I watched the video a second time, with my daughter, I realized that there are many people today, who don't understand the underlying mindset of those who were/are part of the creation and maintenance of the Internet. So I ask you to watch this video and share it, so that more people understand why computer geeks give such bemused looks when people talk about controlling internet access.
Speaking about controlling the Internet, leads us to this next video:
(If the video doesn't work, go to http://www.youtube.com/watch?v=-hFk6FDrZBc )
When I first saw the title "How the Internet strengthens dictatorships", I was more than a bit sceptical of its content. After watching it, I realized that Evgeny Morozov formalized something that I had always realized was going on--not only on the Internet, but in mass media and with many institutions. I just had never truly connected it all. I appreciate this video, because knowing about how things are spun is the best way not to get sucked into it. But at the same time, you have to realize how very, very prevalent it is and don't get too down on yourself if you occasionally get caught up in a spin cycle. If there is one thing I've learned in life, it's that insisting you can't be fooled is practically a guarantee that you will be. Better to accept the possibility and cope with it.
Actually, I've been wanting to write commentaries on my favorite talks at TED.com and I've finally decided to just jump into it. I'll probably be doing these in spurts.
The talks I am focusing on in this post deal with how the Internet works from a very social standpoint. This first one explains many geeks views on resource sharing:
(If the video doesn't work, go to http://www.youtube.com/watch?v=P65XdTlk4vA )
When I first watched it, I giggled a lot because it reminded me of the days when I visited local computer boards (BBSes) and conversed with people through WWIVNet. Back in 1992, it took a few days to get packets from Florida to Texas, because you had to rely on certain BBS sysops to make long distance calls (at their own expense), once or twice a day, to send and receive the packets. When I watched the video a second time, with my daughter, I realized that there are many people today, who don't understand the underlying mindset of those who were/are part of the creation and maintenance of the Internet. So I ask you to watch this video and share it, so that more people understand why computer geeks give such bemused looks when people talk about controlling internet access.
Speaking about controlling the Internet, leads us to this next video:
(If the video doesn't work, go to http://www.youtube.com/watch?v=-hFk6FDrZBc )
When I first saw the title "How the Internet strengthens dictatorships", I was more than a bit sceptical of its content. After watching it, I realized that Evgeny Morozov formalized something that I had always realized was going on--not only on the Internet, but in mass media and with many institutions. I just had never truly connected it all. I appreciate this video, because knowing about how things are spun is the best way not to get sucked into it. But at the same time, you have to realize how very, very prevalent it is and don't get too down on yourself if you occasionally get caught up in a spin cycle. If there is one thing I've learned in life, it's that insisting you can't be fooled is practically a guarantee that you will be. Better to accept the possibility and cope with it.
Monday, June 26, 2006
The World eBook Fair
http://www.worldebookfair.com/
The World eBook Fair welcomes you to absolutely free access to a variety of eBook unparalleled by any other source. 1/3 million eBooks await you, all free of charge for the month from July 4 - August 4, 2006, and then 1/2 million eBooks in 2007, 3/4 million in 2008, and ONE million in 2009.
The World eBook Fair welcomes you to absolutely free access to a variety of eBook unparalleled by any other source. 1/3 million eBooks await you, all free of charge for the month from July 4 - August 4, 2006, and then 1/2 million eBooks in 2007, 3/4 million in 2008, and ONE million in 2009.
Sunday, September 11, 2005
A constitutional republic
I was sent an article from a major publication recently and it occurred to me for the umpteen hundredth time that most people slept through their US Government classes.
If you check out the US entry in the CIA World Factbook, you will see that we are listed as a Constitution-based federal republic; strong democratic tradition.
Now, when this country was first created, it had thirteen former colonies that had very different cultures and ideals. None of these newly declared states wanted to totally give up their rights of self-government to a central government. They wanted to be able to decide certain things themselves. If those people on the other side of the state line wanted something different - more power to them.
But there were worries that a strong federal government might override the states' sovereignty by using the excuse of an emergency to come in and take control. And actually, JFK sort of did this in 1963 against Gov. George Wallace, ordering the governor's own National Guard to turn against him and forcibly integrate the University of Alabama. Of course that was to uphold a federal mandate. In the case of looters, who are breaking no evident federal law, the Posse Comitatus Act of 1878 explicitly forbids using the military (unless a governor uses her National Guard under "state status") in a domestic police function.
What this means is that according to the law, the STATES are given the chance to solve the problem themselves FIRST. The federal government is not allowed to step in without the governor's permission. After all, the governor is supposed to have a better idea of what the citizens of his state are in need of than the feds in Washington D.C. Only when the state government cannot handle a crisis that the feds have the right to step in. Theorhetically, a president could get impeached for infringing on a state's sovereignty - that would indeed be seen as a move towards dictatorship.
This part of the reason I get so disgusted with the ignorant people make comments about any president having dictator-like powers. The state governors have powers that keeps this from happening. But if we keep insisting that the federal government fix everything immediately, then we weaken that check and balance. Of course, there is something in place when the governor does screw up and the president should step in then, but we shouldn't be so surprised when they don't step in immediately. Presidents who have done so in the past always get flack for doing it, no matter what their political party.
I'm not saying that everything worked like it should recently. In fact, I think there were major screw-ups on all levels and Brown deserved to be removed. I just don't want us to forget why we let the states ask for help from the feds, instead of the feds just moving in like an overbearing parent and making everything right. It's not supposed to be a parent/child relationship between the federal government and the state governments. They are supposed to be more of less equals. If you are a competant adult, you don't want someone else barging in when you have a problem unless it's an emergency you can't handle. That's true for the states too.
If you check out the US entry in the CIA World Factbook, you will see that we are listed as a Constitution-based federal republic; strong democratic tradition.
Federal republic - a state in which the powers of the central government are restricted and in which the component parts (states, colonies, or provinces) retain a degree of self-government; ultimate sovereign power rests with the voters who chose their governmental representatives.
Now, when this country was first created, it had thirteen former colonies that had very different cultures and ideals. None of these newly declared states wanted to totally give up their rights of self-government to a central government. They wanted to be able to decide certain things themselves. If those people on the other side of the state line wanted something different - more power to them.
But there were worries that a strong federal government might override the states' sovereignty by using the excuse of an emergency to come in and take control. And actually, JFK sort of did this in 1963 against Gov. George Wallace, ordering the governor's own National Guard to turn against him and forcibly integrate the University of Alabama. Of course that was to uphold a federal mandate. In the case of looters, who are breaking no evident federal law, the Posse Comitatus Act of 1878 explicitly forbids using the military (unless a governor uses her National Guard under "state status") in a domestic police function.
What this means is that according to the law, the STATES are given the chance to solve the problem themselves FIRST. The federal government is not allowed to step in without the governor's permission. After all, the governor is supposed to have a better idea of what the citizens of his state are in need of than the feds in Washington D.C. Only when the state government cannot handle a crisis that the feds have the right to step in. Theorhetically, a president could get impeached for infringing on a state's sovereignty - that would indeed be seen as a move towards dictatorship.
This part of the reason I get so disgusted with the ignorant people make comments about any president having dictator-like powers. The state governors have powers that keeps this from happening. But if we keep insisting that the federal government fix everything immediately, then we weaken that check and balance. Of course, there is something in place when the governor does screw up and the president should step in then, but we shouldn't be so surprised when they don't step in immediately. Presidents who have done so in the past always get flack for doing it, no matter what their political party.
I'm not saying that everything worked like it should recently. In fact, I think there were major screw-ups on all levels and Brown deserved to be removed. I just don't want us to forget why we let the states ask for help from the feds, instead of the feds just moving in like an overbearing parent and making everything right. It's not supposed to be a parent/child relationship between the federal government and the state governments. They are supposed to be more of less equals. If you are a competant adult, you don't want someone else barging in when you have a problem unless it's an emergency you can't handle. That's true for the states too.
Saturday, June 25, 2005
MIT Blog Survey
How some of the data looks so far:
Gender
Male - 6216
Female - 8513
Year Born
Chart is hard to read, but I'm on the older tail - about 1.5 or 2 standard deviations away from the mean, I would guess.
Year Started Blogging
Most people started their blogs in 2003. I actually had an online journal in 1998.
Top 3 Reasons for Blog
1) To journal life - 10153
2) Keep in touch - 9515
3) Editorials - 7344
% of buddy list is family
>10% - 7771
10% - 1414
20% - 724
30% - 334
And I can't read the other numbers...
Tuesday, March 15, 2005
Now, I feel old...
While talking to someone, I realized that people younger than me, (which would be MOST of the people who read this site) probably don't have a clue what some of the things I talk about are. For a time reference, I learned to program in 1976 - the same year the home version of PONG became popular. (Sears got the marketing rights the year before.) Before then, it was an arcade game, like pinball, which was created in 1972. I was eight years old in '72 and didn't go to bars and pool halls. So as far as I was concerned, Pong didn't exist until Sears started doing ads for it. By that time, I was playing the text version of Star Trek and had already solved most of the Collosal Cave with my mom and sister. Watching two lines and a ball move wasn't that exciting to me.
Anyway, to help some of you all out, I found some links:
Good computer history site with pictures and a glossary of old terms. But not extensive enough in my opinion.
Teletypes similar to what my dad's first homemade computer had before he was able to snag a broken monitor and repair it. The ASR33 was the model I think we had.
Punch cards. Only when we got them, they already had holes punched in them. We used them for all sorts of crafts. At one time, people made Christmas wreaths with them.
The write-protect ring I talk about, you can find on this page. Do a CNTL-F and type in "tape". A short scroll down will show you a magnetic tape reel and the plastic ring I'm talking about.
I wanted to find a picture of the oscilloscope my dad had when I was little, but that would have taken me forever. Instead, here's a page about what an oscilloscope is.
History of the Apple II computer and Apple II text files.
If there is anything else I've mentioned that you don't get, leave a comment and I'll try to help.
Anyway, to help some of you all out, I found some links:
Good computer history site with pictures and a glossary of old terms. But not extensive enough in my opinion.
Teletypes similar to what my dad's first homemade computer had before he was able to snag a broken monitor and repair it. The ASR33 was the model I think we had.
Punch cards. Only when we got them, they already had holes punched in them. We used them for all sorts of crafts. At one time, people made Christmas wreaths with them.
The write-protect ring I talk about, you can find on this page. Do a CNTL-F and type in "tape". A short scroll down will show you a magnetic tape reel and the plastic ring I'm talking about.
I wanted to find a picture of the oscilloscope my dad had when I was little, but that would have taken me forever. Instead, here's a page about what an oscilloscope is.
History of the Apple II computer and Apple II text files.
If there is anything else I've mentioned that you don't get, leave a comment and I'll try to help.
Tuesday, November 30, 2004
Anagram fun
From http://www.wordsmith.org/anagram/
CORNICE MISS
ROM IS SCENIC
I'M CIRCE'S SON
CIRCE SIMONS
NO MISS CIRCE
CIRCE IN MOSS
I'M SIR SCONCE
SOCCER MINIS
COMIC RINSES
COMIC RESINS
COMIC SIRENS
COSMIC RESIN
COSMIC RINSE
COMICS RISEN
CONIC MISERS
ICE SCORNS MI
SEISMIC CORN
I CROSS MINCE
SERMONIC CSI
CRIME SCIONS
CRIMES COINS
I SCORN MESIC
I'M NICE CROSS
CRONIES MISC
COSINE SCRIM
SINCE MICROS
CRISES NOMIC
ICES CRIMSON
ICES MICRONS
I'M ONCE CRISS
MISC INC EROS
CORNICE MISS
ROM IS SCENIC
I'M CIRCE'S SON
CIRCE SIMONS
NO MISS CIRCE
CIRCE IN MOSS
I'M SIR SCONCE
SOCCER MINIS
COMIC RINSES
COMIC RESINS
COMIC SIRENS
COSMIC RESIN
COSMIC RINSE
COMICS RISEN
CONIC MISERS
ICE SCORNS MI
SEISMIC CORN
I CROSS MINCE
SERMONIC CSI
CRIME SCIONS
CRIMES COINS
I SCORN MESIC
I'M NICE CROSS
CRONIES MISC
COSINE SCRIM
SINCE MICROS
CRISES NOMIC
ICES CRIMSON
ICES MICRONS
I'M ONCE CRISS
MISC INC EROS
Saturday, November 27, 2004
way too funny
At this moment, my son wishes his mom didn't have as much chemistry
knowledge as she does. His grandparents took him to a new heath food
place and he got a Neopet(tm) branded treat called Tigerfruit
Crystals. While he was busy enjoying it, he read the ingrediants to
me, "Freeze-dried grape juice concentrate, maltodextrin, silicon
dioxide (prevents caking)."
"Silicon dioxide?" I said. "That's sand. But if it's ground small
enough, I suppose it wouldn't cause any harm and it would prevent
caking."
My son looked at me in disbelief. "Are you sure that's sand?"
I checked Google and sure enough, Mom's memory is correct on this.
Silicon dioxide is the most common form of sand. My son is now a bit
put off on the treat, but my daughter isn't phased by eating sand at
all.
knowledge as she does. His grandparents took him to a new heath food
place and he got a Neopet(tm) branded treat called Tigerfruit
Crystals. While he was busy enjoying it, he read the ingrediants to
me, "Freeze-dried grape juice concentrate, maltodextrin, silicon
dioxide (prevents caking)."
"Silicon dioxide?" I said. "That's sand. But if it's ground small
enough, I suppose it wouldn't cause any harm and it would prevent
caking."
My son looked at me in disbelief. "Are you sure that's sand?"
I checked Google and sure enough, Mom's memory is correct on this.
Silicon dioxide is the most common form of sand. My son is now a bit
put off on the treat, but my daughter isn't phased by eating sand at
all.
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