Wednesday, March 31, 2010
Destination Moon
Tuesday, March 30, 2010
Sean Carroll vs Sam Harris: BATTLE OF THE MILITANT ATHEISTS
by Steven Colyer, Author of The Origins of the Jews by a Non-Jew: Ur in Babylon; the Mitanni Kingdom of the Hittite Empire; and Khazaria
As an American born in 1956, I and my contemporaries grew up in the 1960's and 1970's on the comedy of the husband-wife team of Jerry Stiller and Anne Meara, a Jewish-American husband and Irish-Catholic-American wife, and they were delightful. They made us laugh, in a more genteel and bygone age when words like "fuck" and "shit" were not necessary to get the joke across.
More famous though was their son, Ben Stiller, whose last movie may have bombed, but we'll always have "There's Something About Mary" and "Meet the Parents." Gaylord Focker, indeed!
Anyone know what Ben Stiller looks like lately? Is this him?:
Well, no, that's not him. That's "New Atheist" Sam Harris of California, author of "The End of Faith" and "Letter to a Christian Nation".
If you don't know who he is, you should. Click here to read his Wikipedia entry. Ten bucks says he wrote it himself. Whatever, he's an interesting cat.
Here's another interesting cat, Temporal Physicist Sean Carroll of CalTech, another "New Atheist" and author of "From Eternity to Here: The Quest for the Ultimate Theory of Time", and the current front-runner in the ongoing "Who will Replace Carl Sagan as The New Great Popularizer of Science ?" contest:
Click here to read Sean's Wikipedia entry. Ten more bucks says he wrote that himself too.
I like both these guys, even though I disagree with them on many fundamental issues that they deem important, and which I've "been-there-done-that" with during the 22-yr-period when I too was an atheist (age 15-37). I also agree with each on certain issues.
So who are these guys, other than devout followers of the fastest growing religion in America and on the planet: Atheism?
Well for starters, each is a highly intelligent and knowledgeable man with a Dale Carnegie-esque, Cicero-esque ability to speak well in public. I would pay money to see them debate in person, right after I watch a live debate between Peter Woit and Lubos Motl on Superstrings theory.
More importantly, they are having an incredible debate with each other based on a short talk Sam gave at TED, which is included in Sean's dislike of that talk in a blog entry by Sean, here.
Sam was not amused by Sean's words, and responded with an ungentlemanly slur, the details of which, Sam's response, and Sean's response to Sam's response, can be seen here.
What are we fellow intellectuals to make of all this? Will this brouhaha ever end? Will we get around to real work someday, or is watching this much more fun and entertaining in an exciting way such as having a front row seat at Wimbledon at the net? And if so, will our necks hurt afterwords?
What I get is that just as in every last religion, its members don't always agree with each other. Shrug.
In any event, it's entertaining. Pass the popcorn, please, it looks like we're in for a hell of a ride.
It's great to be an American. :-)
As an American born in 1956, I and my contemporaries grew up in the 1960's and 1970's on the comedy of the husband-wife team of Jerry Stiller and Anne Meara, a Jewish-American husband and Irish-Catholic-American wife, and they were delightful. They made us laugh, in a more genteel and bygone age when words like "fuck" and "shit" were not necessary to get the joke across.
More famous though was their son, Ben Stiller, whose last movie may have bombed, but we'll always have "There's Something About Mary" and "Meet the Parents." Gaylord Focker, indeed!
Anyone know what Ben Stiller looks like lately? Is this him?:
Well, no, that's not him. That's "New Atheist" Sam Harris of California, author of "The End of Faith" and "Letter to a Christian Nation".
If you don't know who he is, you should. Click here to read his Wikipedia entry. Ten bucks says he wrote it himself. Whatever, he's an interesting cat.
Here's another interesting cat, Temporal Physicist Sean Carroll of CalTech, another "New Atheist" and author of "From Eternity to Here: The Quest for the Ultimate Theory of Time", and the current front-runner in the ongoing "Who will Replace Carl Sagan as The New Great Popularizer of Science ?" contest:
Click here to read Sean's Wikipedia entry. Ten more bucks says he wrote that himself too.
I like both these guys, even though I disagree with them on many fundamental issues that they deem important, and which I've "been-there-done-that" with during the 22-yr-period when I too was an atheist (age 15-37). I also agree with each on certain issues.
So who are these guys, other than devout followers of the fastest growing religion in America and on the planet: Atheism?
Well for starters, each is a highly intelligent and knowledgeable man with a Dale Carnegie-esque, Cicero-esque ability to speak well in public. I would pay money to see them debate in person, right after I watch a live debate between Peter Woit and Lubos Motl on Superstrings theory.
More importantly, they are having an incredible debate with each other based on a short talk Sam gave at TED, which is included in Sean's dislike of that talk in a blog entry by Sean, here.
Sam was not amused by Sean's words, and responded with an ungentlemanly slur, the details of which, Sam's response, and Sean's response to Sam's response, can be seen here.
What are we fellow intellectuals to make of all this? Will this brouhaha ever end? Will we get around to real work someday, or is watching this much more fun and entertaining in an exciting way such as having a front row seat at Wimbledon at the net? And if so, will our necks hurt afterwords?
What I get is that just as in every last religion, its members don't always agree with each other. Shrug.
In any event, it's entertaining. Pass the popcorn, please, it looks like we're in for a hell of a ride.
It's great to be an American. :-)
Thursday, March 25, 2010
PERELMAN - RUSSIAN to ENGLISH Google Translation - Wow
Grigori Perelman, the only Winner (so far) of the The Clay Institute's Millennium Prize, for proving Poincaré's Conjecture:
This is a bit messy, sorry, but it's so funny I had to put it up ASAP. By "funny" I mean how "Translate a page" by Google converts Russian to English. For an easier read click here
- Случай Перельмана - уникальный, - сказал Life News налоговый инспектор Межрайонной налоговой инспекции Санкт-Петербурга Владимир Соловьев. - The case of Perelman - unique - Life News said the tax inspector Interregional Tax Inspection of St. Petersburg Vladimir Solovyov. - Если он заберет причитающиеся ему деньги, сразу возникнет вопрос о налогах. - If he will take the money owed to him, just a question about taxes. Есть три варианта ставки с наград: 13 %, 35 % и вообще без налога, как, например, Нобелевская премия. There are three possible rates with the awards: 13%, 35% even without the tax, such as the Nobel Prize.
В практике российского законодательства этот случай уникален и ни в каких документах и законах не прописан. In practice, Russia's law, this case is unique, and in any documents and laws are not registered.
- Поэтому решать, каким налогом облагать Перельмана, будет министр финансов Алексей Кудрин или даже президент, - продолжает Соловьев. - Therefore, to decide which tax is levied Perelman, will be Finance Minister Alexei Kudrin, or even the president - continues Soloviev. - Если расценивать данную премию наравне с Нобелевской, то математик получит ровно миллион долларов. - If you viewed this on a par with the Nobel prize, the mathematician will receive exactly one million dollars. В случае если Минфин интерпретирует данную выплату как доход физического лица, то, соответственно, налог будет равняться 13 %. If the Treasury interprets this payment as income to the individual, then, accordingly, the tax will be equal to 13%. Также министр может приравнять премию к подарку, что по налоговому кодексу РФ облагается налогом в 35 %. Also, the Minister may equate to a bonus gift, that the Tax Code shall be taxed at 35%.
Сам гений до сих пор не принял точного решения насчет судьбы своего миллиона. Sam genius has not yet received the exact solution about the fate of his millions.
- Вновь повторю: я еще ничего не решил, - сказал по этому поводу сам Григорий Перельман. - I say again: I have not decided anything yet, - said on this occasion he Grigory Perelman. – Не знаю, заберу ли премию. - I do not know, I'll get a prize. И очень сомневаюсь, что все то, что вы мне рассказали о налогах, соответствует действительности. I very much doubt that everything that you told me about taxes, untrue.
43-летний математик, доказавший гипотезу Пуанкаре, в очередной раз всколыхнул мировую общественность, заявив, что размышляет над тем, взять ли присужденную ему Математическим институтом Клэя Премию тысячелетия размером в один миллион долларов. 43-year-old mathematician, proving the Poincaré conjecture, has once again stirred the world community, saying that is reflecting on whether to take the award to him Clay Mathematics Institute Millennium Prize size of one million dollars.
- Я еще не принял никакого решения, - сказал по телефону Перельман. - I have not yet taken any decision, - said by telephone Perelman. - Если что-то решу, первым об этом узнает институт Клэя, который и учредил премию. - If you decide something, first finds out Clay Institute, which established the prize. Но пока ничего не решено. But so far nothing has been decided.
Гипотезу Пуанкаре целый век не мог доказать ни один ученый. Poincare conjecture for a century could not prove any one scientist. А в 2002 году Перельман выложил в Интернет свое доказательство этой задачи. And in 2002, Perelman put it to the Internet their proof of this problem. Несколько лет математики с мировым именем проверяли верность решения и пришли к выводу, что оно правильное. Several years of mathematics with a worldwide reputation verified loyalty solutions and concluded that it is correct. Именно за это американский математический институт Клэя и решил присудить петербуржцу миллионную Премию тысячелетия. It is for this American Clay Mathematics Institute and decided to award the prize Petersburgians millionth millennium.
Ученый-затворник практически не выходит из своей трехкомнатной квартиры в Купчино, где живет вместе с 81-летней мамой Любовью Лейбовной. Scientific reclusive almost never out of his three-room apartment in Kupchino, where he lives together with the 81-year-old mother love Leybovnoy.
Жилище Перельманов совсем не похоже на хоромы миллионеров: все комнаты завалены книгами, бумагами и многочисленными рукописями Григория Яковлевича. Residence Perelman is quite unlike the mansions of millionaires: all the rooms are piled high with books, papers, and numerous manuscripts Gregory. В одной из небольших комнат в углу стоит старинное запыленное пианино, в зале - маленькая скрипка и контрабас. In one small room in the corner stands an old dusty piano in the hall - a small violin and double bass.
Соседи изредка сталкиваются с гениальным математиком. Neighbors occasionally faced with a brilliant mathematician. Только тогда, когда он выбирается в ближайший магазин за молоком и хлебом. Only when it is selected in the nearest store to buy milk and bread. Быстрой походкой, проверяя на ходу почтовый ящик в подъезде, Григорий спешит в супермаркет, закупается и также скоро идет обратно, словно боится потерять драгоценные минуты, необходимые для решения новых "задач тысячелетия". Quick step, checking on the move a mailbox in the hallway, Gregory rushes to the supermarket, bought and soon also goes back, as though afraid of losing precious minutes needed to meet the new "millennium problems".
- Он постоянно думает о чем-то своем, - говорит соседка Перельманов. - He is always thinking about something else - a neighbor said Perelman. - Видно, что нипочем ему слава и почести разные. - It is evident that transcend his glory and honor different. Удивительный человек! Amazing man!
This is a bit messy, sorry, but it's so funny I had to put it up ASAP. By "funny" I mean how "Translate a page" by Google converts Russian to English. For an easier read click here
At $ 1 million Perelman claims MOF
14:13, Moscow, Thursday, March 25, 2010
Fate award for the opening of Russia's brilliant mathematician from St. Petersburg was in the hands of Finance Minister KudrinМинистр финансов Алексей Кудрин лично назначит налоговую ставку, если гениальный ученый Григорий Перельман все-таки решит забрать присужденную ему Премию тысячелетия в миллион долларов. Finance Minister Alexei Kudrin personally appoint the tax rate, if a brilliant scientist Grigory Perelman nevertheless decides to take the Millennium Prize awarded to him a million dollars.
- Случай Перельмана - уникальный, - сказал Life News налоговый инспектор Межрайонной налоговой инспекции Санкт-Петербурга Владимир Соловьев. - The case of Perelman - unique - Life News said the tax inspector Interregional Tax Inspection of St. Petersburg Vladimir Solovyov. - Если он заберет причитающиеся ему деньги, сразу возникнет вопрос о налогах. - If he will take the money owed to him, just a question about taxes. Есть три варианта ставки с наград: 13 %, 35 % и вообще без налога, как, например, Нобелевская премия. There are three possible rates with the awards: 13%, 35% even without the tax, such as the Nobel Prize.
В практике российского законодательства этот случай уникален и ни в каких документах и законах не прописан. In practice, Russia's law, this case is unique, and in any documents and laws are not registered.
- Поэтому решать, каким налогом облагать Перельмана, будет министр финансов Алексей Кудрин или даже президент, - продолжает Соловьев. - Therefore, to decide which tax is levied Perelman, will be Finance Minister Alexei Kudrin, or even the president - continues Soloviev. - Если расценивать данную премию наравне с Нобелевской, то математик получит ровно миллион долларов. - If you viewed this on a par with the Nobel prize, the mathematician will receive exactly one million dollars. В случае если Минфин интерпретирует данную выплату как доход физического лица, то, соответственно, налог будет равняться 13 %. If the Treasury interprets this payment as income to the individual, then, accordingly, the tax will be equal to 13%. Также министр может приравнять премию к подарку, что по налоговому кодексу РФ облагается налогом в 35 %. Also, the Minister may equate to a bonus gift, that the Tax Code shall be taxed at 35%.
Сам гений до сих пор не принял точного решения насчет судьбы своего миллиона. Sam genius has not yet received the exact solution about the fate of his millions.
- Вновь повторю: я еще ничего не решил, - сказал по этому поводу сам Григорий Перельман. - I say again: I have not decided anything yet, - said on this occasion he Grigory Perelman. – Не знаю, заберу ли премию. - I do not know, I'll get a prize. И очень сомневаюсь, что все то, что вы мне рассказали о налогах, соответствует действительности. I very much doubt that everything that you told me about taxes, untrue.
43-летний математик, доказавший гипотезу Пуанкаре, в очередной раз всколыхнул мировую общественность, заявив, что размышляет над тем, взять ли присужденную ему Математическим институтом Клэя Премию тысячелетия размером в один миллион долларов. 43-year-old mathematician, proving the Poincaré conjecture, has once again stirred the world community, saying that is reflecting on whether to take the award to him Clay Mathematics Institute Millennium Prize size of one million dollars.
Четыре года назад Перельман уже потряс мир отказом от медали Филдса и не приехал в Испанию в день вручения, объяснив это тем, что главная награда для него - правильное доказательство теоремы. Four years ago, Perelman had already shocked the world rejection of the Fields Medal and has not arrived in Spain on the day of delivery, explaining that the main reward for him - the correct proof of the theorem. Но сейчас математический гений колеблется. But now, mathematical genius range.
- Я еще не принял никакого решения, - сказал по телефону Перельман. - I have not yet taken any decision, - said by telephone Perelman. - Если что-то решу, первым об этом узнает институт Клэя, который и учредил премию. - If you decide something, first finds out Clay Institute, which established the prize. Но пока ничего не решено. But so far nothing has been decided.
Гипотезу Пуанкаре целый век не мог доказать ни один ученый. Poincare conjecture for a century could not prove any one scientist. А в 2002 году Перельман выложил в Интернет свое доказательство этой задачи. And in 2002, Perelman put it to the Internet their proof of this problem. Несколько лет математики с мировым именем проверяли верность решения и пришли к выводу, что оно правильное. Several years of mathematics with a worldwide reputation verified loyalty solutions and concluded that it is correct. Именно за это американский математический институт Клэя и решил присудить петербуржцу миллионную Премию тысячелетия. It is for this American Clay Mathematics Institute and decided to award the prize Petersburgians millionth millennium.
Ученый-затворник практически не выходит из своей трехкомнатной квартиры в Купчино, где живет вместе с 81-летней мамой Любовью Лейбовной. Scientific reclusive almost never out of his three-room apartment in Kupchino, where he lives together with the 81-year-old mother love Leybovnoy.
Жилище Перельманов совсем не похоже на хоромы миллионеров: все комнаты завалены книгами, бумагами и многочисленными рукописями Григория Яковлевича. Residence Perelman is quite unlike the mansions of millionaires: all the rooms are piled high with books, papers, and numerous manuscripts Gregory. В одной из небольших комнат в углу стоит старинное запыленное пианино, в зале - маленькая скрипка и контрабас. In one small room in the corner stands an old dusty piano in the hall - a small violin and double bass.
Соседи изредка сталкиваются с гениальным математиком. Neighbors occasionally faced with a brilliant mathematician. Только тогда, когда он выбирается в ближайший магазин за молоком и хлебом. Only when it is selected in the nearest store to buy milk and bread. Быстрой походкой, проверяя на ходу почтовый ящик в подъезде, Григорий спешит в супермаркет, закупается и также скоро идет обратно, словно боится потерять драгоценные минуты, необходимые для решения новых "задач тысячелетия". Quick step, checking on the move a mailbox in the hallway, Gregory rushes to the supermarket, bought and soon also goes back, as though afraid of losing precious minutes needed to meet the new "millennium problems".
- Он постоянно думает о чем-то своем, - говорит соседка Перельманов. - He is always thinking about something else - a neighbor said Perelman. - Видно, что нипочем ему слава и почести разные. - It is evident that transcend his glory and honor different. Удивительный человек! Amazing man!
Wednesday, March 24, 2010
Obama Taps 2001 NPP Carl Weiman to Key White House Position
Click here for the details from the Vancouver Sun regarding 2001 Nobel Laureate Carl Weiman's appointment by President Obama to a key science advisory position, but before you do I would like to point out a quote from that article to which I can definitely relate:
"Scientific measurement is something that scientists naturally embrace, and yet it's surprising that we haven't applied that to the teaching side of the house as we have on the research side of the house," he said. "Where we have measured what students are learning, the results are often surprising and, to be blunt, disappointing."
... Simon Peacock, Dean of Science, UBC
Here's hoping Dr. Weiman can change that.
Tuesday, March 23, 2010
Is Double-Special Relativity in Play ?
Click here for a FQXi overview article on the subject, and the man himself, with much less Maths.
Monday, March 22, 2010
Astronaut Buzz Aldrin To Debut on "Dancing With the Stars" Tonight
He's eighty years old, and he's still got it. From the second man on the moon on the first manned trip to its surface, to being 80 and doing anything he wants. Good for you Buzz.
Buzz is a strong advocate of better Math and Science Education in American schools, and is doing this to draw attention to his cause, and ours.
Tonight, Buzz will perform the cha-cha.
It sounds so weird to say that. :-)
Here's the man:
UPDATE (3/23): Space.com has a nice recap of Buzz and the show last night: here.
Remember, my fellow Americans and Earthians, and be proud ... July , 1969 ...
"That's one small step for a man, one giant leap for Mankind."
Damned straight.
UPDATE: You knew it was too good to last. Fourty years later, Buzz is once again the second man out.
Buzz is a strong advocate of better Math and Science Education in American schools, and is doing this to draw attention to his cause, and ours.
Tonight, Buzz will perform the cha-cha.
It sounds so weird to say that. :-)
Here's the man:
UPDATE (3/23): Space.com has a nice recap of Buzz and the show last night: here.
Remember, my fellow Americans and Earthians, and be proud ... July , 1969 ...
"That's one small step for a man, one giant leap for Mankind."
Damned straight.
UPDATE: You knew it was too good to last. Fourty years later, Buzz is once again the second man out.
Saturday, March 20, 2010
FROM OVER THERE TO OVER HERE: The Quest for the Ultimate Theory of Movement as Emergent
by Steven Colyer
(Author of FROM OVER THERE TO STILL OVER THERE: The Quest for the Ultimate Theory of Position, or Why Mona Lisa Never Stops Smiling)
As a fellow happily-married man, I dedicate this book to this guy and his wife . . .
. . . in the hope that they understand that satire is the sincerest form of flattery, as well as for Sean's wonderful book From Eternity to Here: The Quest for the Ultimate Theory of Time and the nice blog he started to explain it, where the errors are noted by the readers.
PROLOGUE
I don't believe in Prologues. Screw them. Epilogues are cool though, I'll write one when I finish.
INTRODUCTION
There are three things about Movement, three questions, which we take for granted. Unfortunately we only know the answer to the first two:
1) WHAT is Movement? Answer: Self-evident.
2) HOW does Movement work? Answer: Statics, Kinematics and Dynamics
3) WHY does Movement exist? Answer: We don't know. (The attitude of the general public being: "It exists because it exists, who cares except you? Stop asking such deep friggin questions and do something constructive with your time like helping me move this pile of wood.")
?
Time! Movement!
We don't know why movement exists, but many fine minds are tackling the issue. In this book you will meet these fine minds and in the blog to follow after the book, you may ask them further questions.
Movement, defined, is a object moving from one place to another. Mathematically, L sub-2 minis L sub-1, or in vector notation (for those willing to dip their toes in the mathematical pool ... come on in the water's warm), B - A. It is quite the phenomenon, is it not?
But enough of the Introduction crap. I don't like Introductions either, unless they're short like this one. So, one last paragraph.
Prepare yourself for an epic journey. You are about to go places and learn things you never knew existed. You will meet men like Clausius, Carnot, and Boltzmann. You will learn that Statistical Mechanics aren't boring. You will question that everything you thought you knew about reality, may be wrong.
PART 1 - THE BORING STUFF WE ALREADY KNOW
Chapter 1 - The Ancient Greeks
(later)
Chapter 2 - When Men Wore Long Powdered Wigs
(later)
Chapter 3: The 1800's - Humanity Starts To Kick Ass
If you ever wish to win an intellectual debate with an atheist, or least shut him up for a minute from going on and on about Dawkins, try stumping him with this question:
"OK, bright boy. If God doesn't exist then please explain how movement emerged from that crazy 'Quantum Fluctuations' insanity you keep spouting about and worship."
That should change the direction of conversation. Away from Dawkins, particularity. And what's bad about that?
In truth we do not know how Movement, that is to say Dynamics to give it its proper name, emerges. God or no God, that which we take most for granted turns out to be the spookiest thing of all. Scares the crap out of me, let me tell you. So much so, I decided to write a book about it.
Our journey begins in the 1800's, in France and Germany, and from Scotland to the Mississippi River and a boy named Huckleberry ....
Section 3.1 End of the Dark Night: Movement Begins (Watt and Twain)
In Chapter 2 we explored the importance of France's Rene Descartes, his Cartesian Coordinates and views on Statics, Germany's Gottfried Leibniz and his views on Dynamics (as well as pre-saging both Relativity and Quantum Mechanics), and England's Isaac Newton's contrarian views on both, not surprising since Newton had a knack for knowing which side of the bread was buttered, and was a master debater therefore.
We saw that Leibniz was right where Newton was wrong, and that at least mathematically, Leibniz' and Descartes' views were complementary rather than adversarial.
In this section we will introduce where and when these origins were put into practice to the degree of obviousness a child can recognize, particularly with Scotland's James Watt, who perfected the steam engine for fun and profit of the capitalists of his day, and a child from Hannibal, Missouri by the name of Sam Clemens, later: Mark Twain, who would write with great astonishment of that most mobile of steam engine applications of his day: the Mississippi River steam-powered riverboat.
And so, if you'll pardon the pun, the Industrial Age gathers steam.
To be continued ...
PART II - THE BORING BUT IMPORTANT STUFF ABOUT THE PHILOSOPHY OF MOVEMENT
Chapter 4: WHAT Movement Is and Isn't.
We will not concern ourselves with the HOW? and WHY? of Movement for the time being. Oh, we'll get there. For now we concern ourselves with the self-evident WHAT?, in which we wish to explore that it is not quite as self-evident as our Tom Sawyer-esque woodpile-mover friend would have us believe.
At first we take it for granted that without Time, there is no Movement. We can and we do. But should we?
The thing that made me question this were two seemingly unrelated concepts, those being electric charge and entropy.
For although we can talk of position (previously covered) as being time-static (hence the entire field of Statics), what we must also recognize is that at a particular moment in time, each system has a particular fixed electric charge, even if zero, and a particular fixed degree of randomness (entropy).
Although electric charge can change, it often doesn't. An electron will always be -1 e, and a positron and a proton +1 e. Entropy, on the other hand, is extremely time dependent, like velocity and acceleration. So they seem quite different.
But are they?
Here, let's use "examples" as a teaching tool, one of my faves.
To be continued ...
(Author of FROM OVER THERE TO STILL OVER THERE: The Quest for the Ultimate Theory of Position, or Why Mona Lisa Never Stops Smiling)
As a fellow happily-married man, I dedicate this book to this guy and his wife . . .
PROLOGUE
I don't believe in Prologues. Screw them. Epilogues are cool though, I'll write one when I finish.
INTRODUCTION
There are three things about Movement, three questions, which we take for granted. Unfortunately we only know the answer to the first two:
1) WHAT is Movement? Answer: Self-evident.
2) HOW does Movement work? Answer: Statics, Kinematics and Dynamics
3) WHY does Movement exist? Answer: We don't know. (The attitude of the general public being: "It exists because it exists, who cares except you? Stop asking such deep friggin questions and do something constructive with your time like helping me move this pile of wood.")
?
Time! Movement!
We don't know why movement exists, but many fine minds are tackling the issue. In this book you will meet these fine minds and in the blog to follow after the book, you may ask them further questions.
Movement, defined, is a object moving from one place to another. Mathematically, L sub-2 minis L sub-1, or in vector notation (for those willing to dip their toes in the mathematical pool ... come on in the water's warm), B - A. It is quite the phenomenon, is it not?
But enough of the Introduction crap. I don't like Introductions either, unless they're short like this one. So, one last paragraph.
Prepare yourself for an epic journey. You are about to go places and learn things you never knew existed. You will meet men like Clausius, Carnot, and Boltzmann. You will learn that Statistical Mechanics aren't boring. You will question that everything you thought you knew about reality, may be wrong.
PART 1 - THE BORING STUFF WE ALREADY KNOW
Chapter 1 - The Ancient Greeks
(later)
Chapter 2 - When Men Wore Long Powdered Wigs
(later)
Chapter 3: The 1800's - Humanity Starts To Kick Ass
If you ever wish to win an intellectual debate with an atheist, or least shut him up for a minute from going on and on about Dawkins, try stumping him with this question:
"OK, bright boy. If God doesn't exist then please explain how movement emerged from that crazy 'Quantum Fluctuations' insanity you keep spouting about and worship."
That should change the direction of conversation. Away from Dawkins, particularity. And what's bad about that?
In truth we do not know how Movement, that is to say Dynamics to give it its proper name, emerges. God or no God, that which we take most for granted turns out to be the spookiest thing of all. Scares the crap out of me, let me tell you. So much so, I decided to write a book about it.
Our journey begins in the 1800's, in France and Germany, and from Scotland to the Mississippi River and a boy named Huckleberry ....
Section 3.1 End of the Dark Night: Movement Begins (Watt and Twain)
In Chapter 2 we explored the importance of France's Rene Descartes, his Cartesian Coordinates and views on Statics, Germany's Gottfried Leibniz and his views on Dynamics (as well as pre-saging both Relativity and Quantum Mechanics), and England's Isaac Newton's contrarian views on both, not surprising since Newton had a knack for knowing which side of the bread was buttered, and was a master debater therefore.
We saw that Leibniz was right where Newton was wrong, and that at least mathematically, Leibniz' and Descartes' views were complementary rather than adversarial.
In this section we will introduce where and when these origins were put into practice to the degree of obviousness a child can recognize, particularly with Scotland's James Watt, who perfected the steam engine for fun and profit of the capitalists of his day, and a child from Hannibal, Missouri by the name of Sam Clemens, later: Mark Twain, who would write with great astonishment of that most mobile of steam engine applications of his day: the Mississippi River steam-powered riverboat.
And so, if you'll pardon the pun, the Industrial Age gathers steam.
To be continued ...
PART II - THE BORING BUT IMPORTANT STUFF ABOUT THE PHILOSOPHY OF MOVEMENT
Chapter 4: WHAT Movement Is and Isn't.
We will not concern ourselves with the HOW? and WHY? of Movement for the time being. Oh, we'll get there. For now we concern ourselves with the self-evident WHAT?, in which we wish to explore that it is not quite as self-evident as our Tom Sawyer-esque woodpile-mover friend would have us believe.
At first we take it for granted that without Time, there is no Movement. We can and we do. But should we?
The thing that made me question this were two seemingly unrelated concepts, those being electric charge and entropy.
For although we can talk of position (previously covered) as being time-static (hence the entire field of Statics), what we must also recognize is that at a particular moment in time, each system has a particular fixed electric charge, even if zero, and a particular fixed degree of randomness (entropy).
Although electric charge can change, it often doesn't. An electron will always be -1 e, and a positron and a proton +1 e. Entropy, on the other hand, is extremely time dependent, like velocity and acceleration. So they seem quite different.
But are they?
Here, let's use "examples" as a teaching tool, one of my faves.
To be continued ...
Friday, March 19, 2010
GOTTFRIED LEIBNIZ (1646-1716)
From Wiki's entry on Leibniz:
Leibniz contributed a fair amount to the statics and dynamics emerging about him, often disagreeing with Descartes and Newton. He devised a new theory of motion (dynamics) based on kinetic energy and potential energy, which posited space as relative, whereas Newton felt strongly space was absolute. An important example of Leibniz's mature physical thinking is his Specimen Dynamicum of 1695.[30]
Until the discovery of subatomic particles and the quantum mechanics governing them, many of Leibniz's speculative ideas about aspects of nature not reducible to statics and dynamics made little sense. For instance, he anticipated Albert Einstein by arguing, against Newton, that space, time and motion are relative, not absolute. Leibniz's rule is an important, if often overlooked, step in many proofs in diverse fields of physics. The principle of sufficient reason has been invoked in recent cosmology, and his identity of indiscernibles in quantum mechanics, a field some even credit him with having anticipated in some sense. Those who advocate digital philosophy, a recent direction in cosmology, claim Leibniz as a precursor.
From the Encyclopedia Britannica:
Contrary to Descartes, Leibniz held that it would not be contradictory to posit that this world is a well-related dream. If visible movement depends on the imaginary element found in the concept of extension, it can no longer be defined by simple local movement; it must be the result of a force. In criticizing the Cartesian formulation of the laws of motion, known as mechanics, Leibniz became, in 1676, the founder of a new formulation, known as dynamics, which substituted kinetic energy for the conservation of movement.
Wednesday, March 17, 2010
Blooming - A Problem with Ray Guns
"Ray guns are in our future, and always will be."
... Skeptical retired U.S. Air Force General, since proven wrong.
Yes, Ray Guns exist. They're being used now to give headaches to suspicious characters approaching checkpoints - sort of a low level "stunner" of sci-fi fame. They're low power infrared lasers with wide dispersion, yes, but they're a start. We're quite a ways from Star Wars type blasters, but we've started down the road.
The dispersion thing is a real drawback, but Science marches on, and these are engineering problems for the present and immediate future and long-term. It's only a matter of time.
Still ...
From the Wikipedia article, "Directed-Energy Weapon":
Blooming
Laser beams begin to cause plasma breakdown in the air at energy densities of around a megajoule per cubic centimeter. This effect, called "blooming," causes the laser to defocus and disperse energy into the atmosphere. It can be more severe if there is fog, smoke, or dust in the air.
There are several ways to stop or reduce blooming:
- The beam can be distributed over a large mirror that focuses the power on the target, to keep energy density in the air too low for blooming to happen. This requires a large, very precise, fragile mirror, mounted somewhat like a searchlight, requiring bulky machinery to slew the mirror to aim the laser.
- A phased array. For the usual laser wavelengths this method would need billions of micrometre-size antennae, and no way to make these is known. Phased arrays could theoretically also perform phase-conjugate amplification (see below). Another advantage is that phased arrays do not require mirrors or lenses, can be made flat and thus do not require a turret-like system (as in the first approach) to be aimed, though range will suffer at extreme angles (that is, the angle the beam forms to the surface of the phased array).[1]
- A phase-conjugate laser system. Here, a "finder" or "guide" laser illuminates the target. Any mirror-like ("specular") points on the target reflect light that is sensed by the weapon's primary amplifier. The weapon-power amplifier then amplifies inverted waves in a positive feedback loop, destroying the target with shockwaves as the specular regions evaporate. This avoids the blooming problem because the waves from the target passed through the blooming, and therefore show the most conductive optical path; this automatically corrects for the distortions caused by blooming. Experimental systems using this method usually use special chemicals to form a "phase conjugate mirror." In most systems, the mirror overheats dramatically at weaponized power levels.
- A very short pulse that finishes before blooming interferes.
Monday, March 15, 2010
ABOUT ME
Mr. Inquisitive, pretending he's Sherlock Holmes:
I have changed the "About Me" section in the right-hand column. Please read and give feedback as to whether or not I have bitten off more than I can chew.
I still have much to learn about Fusion but it has always endlessly fascinated me. This may or may not lead to future employment at the PPPL = Princeton Plasma Physics Laboratory in Plainsboro, NJ, or somewhere similar.
I have always loved Plasma, the 4th state of matter, as well.
Hopefully the "About Me" will change yearly as my knowledge and interests progress.
Time will tell, as it always does.
Future interests include but are not limited to: Quantum Chromodynamics, Quantum Hall effect and other types of Bose Condensate physics, Nonlinear Feedback Automatic Control Systems and Analysis, and Phenomenological Quantum Gravity beginning with Loop Quantum Gravity, Causal Dynamical Triangulations, and MOG (unless MOG is falsified in which case not-MOG).
I have changed the "About Me" section in the right-hand column. Please read and give feedback as to whether or not I have bitten off more than I can chew.
I still have much to learn about Fusion but it has always endlessly fascinated me. This may or may not lead to future employment at the PPPL = Princeton Plasma Physics Laboratory in Plainsboro, NJ, or somewhere similar.
I have always loved Plasma, the 4th state of matter, as well.
Hopefully the "About Me" will change yearly as my knowledge and interests progress.
Time will tell, as it always does.
Future interests include but are not limited to: Quantum Chromodynamics, Quantum Hall effect and other types of Bose Condensate physics, Nonlinear Feedback Automatic Control Systems and Analysis, and Phenomenological Quantum Gravity beginning with Loop Quantum Gravity, Causal Dynamical Triangulations, and MOG (unless MOG is falsified in which case not-MOG).
Fusion: Spherical Tokamak
National Spherical Torus Experiment
From Wikipedia, the free encyclopedia
| Type | Spherical tokamak |
|---|---|
| Operation date | 1999– |
| Major radius | 0.85 m |
| Minor Radius | 0.68 m |
| Magnetic field | 0.3 T |
| Heating | 11 MW |
| Plasma current | 1.4 MA |
The National Spherical Torus Experiment (NSTX) is an innovative magnetic fusion device based on the spherical tokamak concept that was constructed by the Princeton Plasma Physics Laboratory (PPPL) in collaboration with the Oak Ridge National Laboratory, Columbia University, and the University of Washington at Seattle.
First plasma was obtained on NSTX on Friday, February 12, 1999 at 6:06 p.m. NSTX is being used to study the physics principles of spherically shaped plasmas—hot ionized gases in which nuclear fusion will occur under the appropriate conditions of temperature, density, and confinement in a magnetic field. Fusion is the energy source of the Sun and all the stars. Scientists believe it can provide an inexhaustible, safe, and environmentally attractive source of energy on earth.
Magnetic fusion experiments use plasmas composed of one or more of the isotopes of hydrogen. For example, in 1994, PPPL's Tokamak Fusion Test Reactor (TFTR) produced a world-record 10.7 megawatts of fusion power from a plasma composed of equal parts of deuterium and tritium, the fuel mix likely to be used in commercial fusion power reactors. NSTX is a "proof of principle" experiment and therefore employs deuterium plasmas only. If successful it will be followed by similar devices, eventually including a demonstration power reactor, burning deuterium-tritium fuel.
NSTX produces a plasma that is shaped like a sphere with a hole through its center (a "cored apple" profile, see Mega Ampere Spherical Tokamak), different from the "donut" (toroidal) shaped plasmas of conventional tokamaks. This innovative plasma configuration may have several advantages, a major one being the ability to confine a higher plasma pressure for a given magnetic field strength. Since the amount of fusion power produced is proportional to the square of the plasma pressure, the use of spherically shaped plasmas could allow the development of smaller, more economical fusion reactors. NSTX's attractiveness may be further enhanced by its ability to produce a high "bootstrap" electric current. This self-driven internal plasma current would significantly reduce the power requirements of externally driven plasma currents required to heat and confine the plasma.
Sunday, March 14, 2010
DARK FLOW
Perhaps the strangest of astronomical concepts is "dark flow", that the entire observable universe seems to be being drawn to a point outside the observable universe of 13.7 Bly radius. Click here for a recent Discover blog article on the subject.
That's FAST !
beep, beep!
An attosecond is 10-18, a billionth of a billionth, of a second. An attosecond is to a second as a second is to the age of the universe. In three attoseconds, a beam of light traveling 300,000 kilometers per second can get only from one side of a water molecule to the other. And the electron of a hydrogen atom, dissolved in a hazy cloud of quantum mechanics probability, sloshes from one side of the atom to the other every 24 attoseconds — a fundamental oscillation dubbed the atomic unit of time.
Click here for more on our technological limits, timewise.
An attosecond is 10-18, a billionth of a billionth, of a second. An attosecond is to a second as a second is to the age of the universe. In three attoseconds, a beam of light traveling 300,000 kilometers per second can get only from one side of a water molecule to the other. And the electron of a hydrogen atom, dissolved in a hazy cloud of quantum mechanics probability, sloshes from one side of the atom to the other every 24 attoseconds — a fundamental oscillation dubbed the atomic unit of time.
Click here for more on our technological limits, timewise.
Saturday, March 13, 2010
Phenomenological Quantum Gravity
From a talk by Sabine Hossenfelder at Loops '07. Click here for a synopsis of her talk.
Off-topic: For fun, click here for Monty Python's ode to our insignificance from "The Meaning of Life". lol
Yes, it's "The Galaxy Song", starring Eric Idle! From this blog article I just saw at Discover blogs re "Dark Flow".
Off-topic: For fun, click here for Monty Python's ode to our insignificance from "The Meaning of Life". lol
Yes, it's "The Galaxy Song", starring Eric Idle! From this blog article I just saw at Discover blogs re "Dark Flow".
Wednesday, March 10, 2010
A Galaxy Blows Up - maybe Larry Niven is right
Click here for the sordid details on this recent astronomical observation.
Sell your General Products stock, today, heh.
Astronomers Falsify MOND
Pretty, but false:
MOND, a competing theory of gravity, has been falsified by a large and long study by astronomers. Also known as TeVeS for Tensor-Vector-Scalar gravity theory, it proposed an alternative explanation to gravity in which dark energy and dark matter needn't exist.
Oh well, we'll toss that one on the LeSage gravity pile of nice ideas but back to the drawing board.
Space.com breaks the bad news ==> here.
MOND, a competing theory of gravity, has been falsified by a large and long study by astronomers. Also known as TeVeS for Tensor-Vector-Scalar gravity theory, it proposed an alternative explanation to gravity in which dark energy and dark matter needn't exist.
Oh well, we'll toss that one on the LeSage gravity pile of nice ideas but back to the drawing board.
Space.com breaks the bad news ==> here.
Tuesday, March 9, 2010
Lubos didn't accept this post ... and then he did ... and then after my response he didn't accept me counter-response ... typical
I start this page as a dump for failed attempts to communicate to Lubos' posters. He doesn't give them the full story.
For example, on this page the following post by me was deemed unworthy. I mean, c'mon, it's not that bad is it?
I wrote:
Lubos, there is an obvious interest in financing a book by you on String Theory. I would certainly buy that book. However, wouldn't such a book be outdated at the end of this year when the LHC starts spitting out new things? Not to worry, it takes about 2 years to write a book. If you haven't started, now might be a good time. The sooner you start the sooner you finish, yes?
I like Robert of Ottowa's request for diagrams and Maths and 2nd the notion. I would write the prose version first, for intelligent laymen who are more laymen than knowledgeable about Math, on the right pages. On the left pages, I would, in say blue-box fashion, put in the Maths and figures for those of us who have taken Calculus. I find too many Science books feel the reader would be scared away with too many Mathematics, but reading around I see many of us are starved for more (outside of textbooks).
Also, besides Robert of Ottowa, I hear there's a Mike of Toronto who has/is financing many things in Quantum Gravity ... :-)
UPDATE: Since I wrote the above, Lubos actually did let my comment go through. Then poster Shawn Halayka responded:
... all wrapped up in a format that focuses on the use of Mathematica.
P.S. Steven, you are joking about this Mike person, right? Smile
To which I responded:
Am I kidding about Mike Lazaridis of Canada, founder of Research in Motion (Blackberry) and chief benefactor of Perimeter Institute, who along with Richard Branson of the UK is one of the few rich guys in the world that doesn't suck? Well yes, yes I am kidding, obviously! Didn't ye note the smiley after me comment, laddie? Obviously, given how Lubos goes after Lee Smolin of Perimeter, Lazaridis is one person Lubos can avoid asking for financing. Shrug.
For Lubos: Have you ever reviewed "String Theory for Dummies" by Andrew Zimmerman Jones? Neither you nor Woit have commented on that from what I've seen. Is it the title? That's an American "joke" that doesn't translate well across our borders. We're so specialized here as Lubos will tell you that we all admit being "dummies" on most topics.
In any event "String Theory f.D." seems quite pro-Strings, so I'm surprised the yin and the yang of Strings haven't commented. Everyone's got too much to read these days, I guess.
Also to Lubos, I ran across the following webpage by Robert Tucci, Ph.D. Physics, that mentions you, titled
Why String Theorists Should Switch Fields to Quantum Computing
It's meant to be comical, I hope.UPDATE: I also submitted the following to Woit/Columbia U's blog "Not Even Wrong" under "Short Items." It probably won't go through because of the word: "entertainment", but I chose to be honest:
Thank you very, very much Peter for that very funny Why String Theorists Should Switch Fields to Quantum Computing.
I laughed so hard reading it, it reminded me of the first time I read John Baez' "The Crackpot Index." A very pleasant memory.
I especially liked the reply "no PW and LM?" as though a great entertainment would be lost to us. May that never be so. Relax, it won't.
Monday, March 8, 2010
Alice in Algebraland: An Imaginary Tale, Continuously Transforming
From this article by Melanie Bayley of U. Oxford.
Complex numbers, for example, consist of two terms - a real component and an "imaginary" component formed of some multiple of the square root of -1, now represented by the symbol i. They are written in the form a + bi.
The Victorian mathematician William Rowan Hamilton took this one step further, adding two more terms to make quaternions, which take the form a + bi + cj + dk and have their own strange rules of arithmetic.
finit
From this article by Melanie Bayley of U. Oxford
What would Lewis Carroll's Alice's Adventures in Wonderland be without the Cheshire Cat, the trial, the Duchess's baby or the Mad Hatter's tea party? Look at the original story that the author told Alice Liddell and her two sisters one day during a boat trip near Oxford, though, and you'll find that these famous characters and scenes are missing from the text.
As I embarked on my DPhil investigating Victorian literature, I wanted to know what inspired these later additions. The critical literature focused mainly on Freudian interpretations of the book as a wild descent into the dark world of the subconscious. There was no detailed analysis of the added scenes, but from the mass of literary papers, one stood out: in 1984 Helena Pycior of the University of Wisconsin-Milwaukee had linked the trial of the Knave of Hearts with a Victorian book on algebra. Given the author's day job, it was somewhat surprising to find few other reviews of his work from a mathematical perspective. Carroll was a pseudonym: his real name was Charles Dodgson, and he was a mathematician at Christ Church College, Oxford.
The 19th century was a turbulent time for mathematics, with many new and controversial concepts, like imaginary numbers, becoming widely accepted in the mathematical community. Putting Alice's Adventures in Wonderland in this context, it becomes clear that Dodgson, a stubbornly conservative mathematician, used some of the missing scenes to satirise these radical new ideas.
Even Dodgson's keenest admirers would admit he was a cautious mathematician who produced little original work. He was, however, a conscientious tutor, and, above everything, he valued the ancient Greek textbook Euclid's Elements as the epitome of mathematical thinking. Broadly speaking, it covered the geometry of circles, quadrilaterals, parallel lines and some basic trigonometry. But what's really striking about Elements is its rigorous reasoning: it starts with a few incontrovertible truths, or axioms, and builds up complex arguments through simple, logical steps. Each proposition is stated, proved and finally signed off with QED.
For centuries, this approach had been seen as the pinnacle of mathematical and logical reasoning. Yet to Dodgson's dismay, contemporary mathematicians weren't always as rigorous as Euclid. He dismissed their writing as "semi-colloquial" and even "semi-logical". Worse still for Dodgson, this new mathematics departed from the physical reality that had grounded Euclid's works.
By now, scholars had started routinely using seemingly nonsensical concepts such as imaginary numbers - the square root of a negative number - which don't represent physical quantities in the same way that whole numbers or fractions do. No Victorian embraced these new concepts wholeheartedly, and all struggled to find a philosophical framework that would accommodate them. But they gave mathematicians a freedom to explore new ideas, and some were prepared to go along with these strange concepts as long as they were manipulated using a consistent framework of operations. To Dodgson, though, the new mathematics was absurd, and while he accepted it might be interesting to an advanced mathematician, he believed it would be impossible to teach to an undergraduate.
Outgunned in the specialist press, Dodgson took his mathematics to his fiction. Using a technique familiar from Euclid's proofs, reductio ad absurdum, he picked apart the "semi-logic" of the new abstract mathematics, mocking its weakness by taking these premises to their logical conclusions, with mad results. The outcome is Alice's Adventures in Wonderland.
Algebra and hookahs <=== where John Ellis met the penguin
Take the chapter "Advice from a caterpillar", for example. By this point, Alice has fallen down a rabbit hole and eaten a cake that has shrunk her to a height of just 3 inches. Enter the Caterpillar, smoking a hookah pipe, who shows Alice a mushroom that can restore her to her proper size. The snag, of course, is that one side of the mushroom stretches her neck, while another shrinks her torso. She must eat exactly the right balance to regain her proper size and proportions.
While some have argued that this scene, with its hookah and "magic mushroom", is about drugs, I believe it's actually about what Dodgson saw as the absurdity of symbolic algebra, which severed the link between algebra, arithmetic and his beloved geometry. Whereas the book's later chapters contain more specific mathematical analogies, this scene is subtle and playful, setting the tone for the madness that will follow.
The first clue may be in the pipe itself: the word "hookah" is, after all, of Arabic origin, like "algebra", and it is perhaps striking that Augustus De Morgan, the first British mathematician to lay out a consistent set of rules for symbolic algebra, uses the original Arabic translation in Trigonometry and Double Algebra, which was published in 1849. He calls it "al jebr e al mokabala" or "restoration and reduction" - which almost exactly describes Alice's experience. Restoration was what brought Alice to the mushroom: she was looking for something to eat or drink to "grow to my right size again", and reduction was what actually happened when she ate some: she shrank so rapidly that her chin hit her foot.
De Morgan's work explained the departure from universal arithmetic - where algebraic symbols stand for specific numbers rooted in a physical quantity - to that of symbolic algebra, where any "absurd" operations involving negative and impossible solutions are allowed, provided they follow an internal logic. Symbolic algebra is essentially what we use today as a finely honed language for communicating the relations between mathematical objects, but Victorians viewed algebra very differently. Even the early attempts at symbolic algebra retained an indirect relation to physical quantities.
De Morgan wanted to lose even this loose association with measurement, and proposed instead that symbolic algebra should be considered as a system of grammar. "Reduce" algebra from a universal arithmetic to a series of logical but purely symbolic operations, he said, and you will eventually be able to "restore" a more profound meaning to the system - though at this point he was unable to say exactly how.
When Alice loses her temper
The madness of Wonderland, I believe, reflects Dodgson's views on the dangers of this new symbolic algebra. Alice has moved from a rational world to a land where even numbers behave erratically. In the hallway, she tried to remember her multiplication tables, but they had slipped out of the base-10 number system we are used to. In the caterpillar scene, Dodgson's qualms are reflected in the way Alice's height fluctuates between 9 feet and 3 inches. Alice, bound by conventional arithmetic where a quantity such as size should be constant, finds this troubling: "Being so many different sizes in a day is very confusing," she complains. "It isn't," replies the Caterpillar, who lives in this absurd world.
Wonderland's madness reflects Carroll's views on the dangers of the new symbolic algebra
The Caterpillar's warning, at the end of this scene, is perhaps one of the most telling clues to Dodgson's conservative mathematics. "Keep your temper," he announces. Alice presumes he's telling her not to get angry, but although he has been abrupt he has not been particularly irritable at this point, so it's a somewhat puzzling thing to announce. To intellectuals at the time, though, the word "temper" also retained its original sense of "the proportion in which qualities are mingled", a meaning that lives on today in phrases such as "justice tempered with mercy". So the Caterpillar could well be telling Alice to keep her body in proportion - no matter what her size.
This may again reflect Dodgson's love of Euclidean geometry, where absolute magnitude doesn't matter: what's important is the ratio of one length to another when considering the properties of a triangle, for example. To survive in Wonderland, Alice must act like a Euclidean geometer, keeping her ratios constant, even if her size changes.
Of course, she doesn't. She swallows a piece of mushroom and her neck grows like a serpent with predictably chaotic results - until she balances her shape with a piece from the other side of the mushroom. It's an important precursor to the next chapter, "Pig and pepper", where Dodgson parodies another type of geometry.
By this point, Alice has returned to her proper size and shape, but she shrinks herself down to enter a small house. There she finds the Duchess in her kitchen nursing her baby, while her Cook adds too much pepper to the soup, making everyone sneeze except the Cheshire Cat. But when the Duchess gives the baby to Alice, it somehow turns into a pig.
The target of this scene is projective geometry, which examines the properties of figures that stay the same even when the figure is projected onto another surface - imagine shining an image onto a moving screen and then tilting the screen through different angles to give a family of shapes. The field involved various notions that Dodgson would have found ridiculous, not least of which is the "principle of continuity".
Jean-Victor Poncelet, the French mathematician who set out the principle, describes it as follows: "Let a figure be conceived to undergo a certain continuous variation, and let some general property concerning it be granted as true, so long as the variation is confined within certain limits; then the same property will belong to all the successive states of the figure."
The case of two intersecting circles is perhaps the simplest example to consider. Solve their equations, and you will find that they intersect at two distinct points. According to the principle of continuity, any continuous transformation to these circles - moving their centres away from one another, for example - will preserve the basic property that they intersect at two points. It's just that when their centres are far enough apart the solution will involve an imaginary number that can't be understood physically (see diagram) .
Of course, when Poncelet talks of "figures", he means geometric figures, but Dodgson playfully subjects Poncelet's "semi-colloquial" argument to strict logical analysis and takes it to its most extreme conclusion. What works for a triangle should also work for a baby; if not, something is wrong with the principle, QED. So Dodgson turns a baby into a pig through the principle of continuity. Importantly, the baby retains most of its original features, as any object going through a continuous transformation must. His limbs are still held out like a starfish, and he has a queer shape, turned-up nose and small eyes. Alice only realises he has changed when his sneezes turn to grunts.
The baby's discomfort with the whole process, and the Duchess's unconcealed violence, signpost Dodgson's virulent mistrust of "modern" projective geometry. Everyone in the pig and pepper scene is bad at doing their job. The Duchess is a bad aristocrat and an appallingly bad mother; the Cook is a bad cook who lets the kitchen fill with smoke, over-seasons the soup and eventually throws out her fire irons, pots and plates.
Alice, angry now at the strange turn of events, leaves the Duchess's house and wanders into the Mad Hatter's tea party, which explores the work of the Irish mathematician William Rowan Hamilton. Hamilton died in 1865, just after Alice was published, but by this time his discovery of quaternions in 1843 was being hailed as an important milestone in abstract algebra, since they allowed rotations to be calculated algebraically.
Just as complex numbers work with two terms, quaternions belong to a number system based on four terms (see "Imaginary mathematics"). Hamilton spent years working with three terms - one for each dimension of space - but could only make them rotate in a plane. When he added the fourth, he got the three-dimensional rotation he was looking for, but he had trouble conceptualising what this extra term meant. Like most Victorians, he assumed this term had to mean something, so in the preface to his Lectures on Quaternions of 1853 he added a footnote: "It seemed (and still seems) to me natural to connect this extra-spatial unit with the conception of time."
Where geometry allowed the exploration of space, Hamilton believed, algebra allowed the investigation of "pure time", a rather esoteric concept he had derived from Immanuel Kant that was meant to be a kind of Platonic ideal of time, distinct from the real time we humans experience. Other mathematicians were polite but cautious about this notion, believing pure time was a step too far.
The parallels between Hamilton's maths and the Hatter's tea party - or perhaps it should read "t-party" - are uncanny. Alice is now at a table with three strange characters: the Hatter, the March Hare and the Dormouse. The character Time, who has fallen out with the Hatter, is absent, and out of pique he won't let the Hatter move the clocks past six.
Reading this scene with Hamilton's maths in mind, the members of the Hatter's tea party represent three terms of a quaternion, in which the all-important fourth term, time, is missing. Without Time, we are told, the characters are stuck at the tea table, constantly moving round to find clean cups and saucers.
Their movement around the table is reminiscent of Hamilton's early attempts to calculate motion, which was limited to rotatations in a plane before he added time to the mix. Even when Alice joins the party, she can't stop the Hatter, the Hare and the Dormouse shuffling round the table, because she's not an extra-spatial unit like Time.
The Hatter's nonsensical riddle in this scene - "Why is a raven like a writing desk?" - may more specifically target the theory of pure time. In the realm of pure time, Hamilton claimed, cause and effect are no longer linked, and the madness of the Hatter's unanswerable question may reflect this.
Alice's ensuing attempt to solve the riddle pokes fun at another aspect of quaternions: their multiplication is non-commutative, meaning that x × y is not the same as y × x. Alice's answers are equally non-commutative. When the Hare tells her to "say what she means", she replies that she does, "at least I mean what I say - that's the same thing". "Not the same thing a bit!" says the Hatter. "Why, you might just as well say that 'I see what I eat' is the same thing as 'I eat what I see'!"
It's an idea that must have grated on a conservative mathematician like Dodgson, since non-commutative algebras contradicted the basic laws of arithmetic and opened up a strange new world of mathematics, even more abstract than that of the symbolic algebraists.
When the scene ends, the Hatter and the Hare are trying to put the Dormouse into the teapot. This could be their route to freedom. If they could only lose him, they could exist independently, as a complex number with two terms. Still mad, according to Dodgson, but free from an endless rotation around the table.
And there Dodgson's satire of his contemporary mathematicians seems to end. What, then, would remain of Alice's Adventures in Wonderland without these analogies? Nothing but Dodgson's original nursery tale, Alice's Adventures Under Ground, charming but short on characteristic nonsense. Dodgson was most witty when he was poking fun at something, and only then when the subject matter got him truly riled. He wrote two uproariously funny pamphlets, fashioned in the style of mathematical proofs, which ridiculed changes at the University of Oxford. In comparison, other stories he wrote besides the Alice books were dull and moralistic.
I would venture that without Dodgson's fierce satire aimed at his colleagues, Alice's Adventures in Wonderland would never have become famous, and Lewis Carroll would not be remembered as the unrivalled master of nonsense fiction.
Imaginary mathematics
The real numbers, which include fractions and irrational numbers like π that can nevertheless be represented as a point on a number line, are only one of many number systems.Complex numbers, for example, consist of two terms - a real component and an "imaginary" component formed of some multiple of the square root of -1, now represented by the symbol i. They are written in the form a + bi.
The Victorian mathematician William Rowan Hamilton took this one step further, adding two more terms to make quaternions, which take the form a + bi + cj + dk and have their own strange rules of arithmetic.
finit
Sunday, March 7, 2010
Gunnar Källén (1926-1968)
From Wiki:
Gunnar Källén, born February 13, 1926 in Kristianstad, Sweden and died October 13, 1968 in Hannover, Germany in a plane accident. Källén was a leading Swedish theoretical physicist and a professor at Lund University until his death at the age of 42.
Källén earned his doctorate at Lund in 1950 and worked between 1952 and 1958 at CERN's theoretical division, which then became the Niels Bohr Institute in Copenhagen. He also worked at Nordita 1957-1958 and then began a professorship at Lund University.
Källén's research focused on quantum field theory and elementary particle physics. His developments included the so-called Källén-Lehmann representation of correlation functions in quantum field theory, and he made contributions to quantum electrodynamics, especially in renormalizing. He also worked with the axiomatic formulation of quantum field theory, which led to contributions to the theory of functions of several complex variables. He collaborated on the Pauli-Källén equation.
Källén worked for several years at the Bohr Institute. Källén was flying his own plane from CERN in Geneva in a plane accident in 1968. His two passengers, one of them his wife, survived the crash.
Click here and read the replies as to why this man's work is important.
Gunnar Källén, born February 13, 1926 in Kristianstad, Sweden and died October 13, 1968 in Hannover, Germany in a plane accident. Källén was a leading Swedish theoretical physicist and a professor at Lund University until his death at the age of 42.
Källén earned his doctorate at Lund in 1950 and worked between 1952 and 1958 at CERN's theoretical division, which then became the Niels Bohr Institute in Copenhagen. He also worked at Nordita 1957-1958 and then began a professorship at Lund University.
Källén's research focused on quantum field theory and elementary particle physics. His developments included the so-called Källén-Lehmann representation of correlation functions in quantum field theory, and he made contributions to quantum electrodynamics, especially in renormalizing. He also worked with the axiomatic formulation of quantum field theory, which led to contributions to the theory of functions of several complex variables. He collaborated on the Pauli-Källén equation.
Källén worked for several years at the Bohr Institute. Källén was flying his own plane from CERN in Geneva in a plane accident in 1968. His two passengers, one of them his wife, survived the crash.
Click here and read the replies as to why this man's work is important.
l-r: Vernon Hughes, Gunnar Källén
Saturday, March 6, 2010
PHONONIC GRAVITY (Thermodynamic Verlindic Phonons in Quantum Einstein Gravity)
"Gravitons do not exist when gravity is emergent. Gravitons are like phonons. In fact, to make that analogy clear consider two pistons that close of a gas container at opposite ends. Not that the force on the pistons due to the pressure is also an example of an entropic force. We keep the pistons in place by an external force. When we gradually move one of the pistons inwards by increasing the force, the pressure will become larger. Therefore the other piston will also experience a larger force. We can also do this in an abrupt way. We then cause a sound wave to go from one piston to the other. The quantization of this sound wave leads to phonons. We know that phonons are quite useful concepts, which even themselves are often used to understand other emergent phenomena.
"Similarly, gravitons can be useful, and in that sense exist as effective "quasi" particles. But they do not exist as fundamental particles."
... Erik Verlinde, Jan 15,2010
One of the more interesting aspects about former string theorist* Erik Verlinde's latest work is his contention that the "graviton" should not be treated as a "particle", as it is in String Theory, but rather as a "phonon", as in acoustics. The reader can read all about phonons here at Wikipedia. I wish to call attention to the last section of that entry, which is this:
The thermodynamic properties of a solid are directly related to its phonon structure. The entire set of all possible phonons that are described by the above phonon dispersion relations combine in what is known as the phonon density of states which determines the heat capacity of a crystal.
At absolute zero temperature, a crystal lattice lies in its ground state, and contains no phonons. A lattice at a non-zero temperature has an energy that is not constant, but fluctuates randomly about some mean value. These energy fluctuations are caused by random lattice vibrations, which can be viewed as a gas of phonons.[notes 1] Because these phonons are generated by the temperature of the lattice, they are sometimes referred to as thermal phonons.
Unlike the atoms which make up an ordinary gas, thermal phonons can be created and destroyed by random energy fluctuations. In the language of statistical mechanics this means that the chemical potential for adding a phonon is zero. This behavior is an extension of the harmonic potential, mentioned earlier, into the anharmonic regime. The behavior of thermal phonons is similar to the photon gas produced by an electromagnetic cavity, wherein photons may be emitted or absorbed by the cavity walls. This similarity is not coincidental, for it turns out that the electromagnetic field behaves like a set of harmonic oscillators; see Black-body radiation. Both gases obey the Bose-Einstein statistics: in thermal equilibrium and within the harmonic regime, the probability of finding phonons (or photons) in a given state with a given angular frequency is:
is the frequency of the phonons (or photons) in the state, 
is Boltzmann's constant, and 
is the temperature.
Steve here. Regarding the above, why is that important? I feel it's important because phonons require a large number of "particles" (wave crests?) in order to exist. A single particle does not a phonon make. Neither does a single particle have Entropy, nor Temperature. These are all collective things, requiring many particles to have meaning. In regards to how many are required is where I feel future work will focus. On a recent trip to Bell Labs Pure Physics Research Division** in Murray Hill, NJ, 2009 Nobel Prize in Physics co-winner and former Bell Labs Scientist George E. Smith was shown certain state-of-the art experiments going on using the Quantum Hall effect that may at some future time be helpful in this regard. More information will be made available in the future regarding this particular avenue following publication.
Why are phonons important in the quantum realm of the very small? I feel they're important because of the notorious weakness of gravity at that scale. If as Verlinde speculates the phononic effect goes away with few particles, and if gravity is ruled by such effects, then the weakness of gravity is explained.
Next up we ask the question: Is there a current theory, in General Relativity-based Quantum Gravity, that might explain and explore the possibility that gravity "drops away" in the realm of the small. As it turns out there is such a theory, based on an idea by Steven Weinberg in the 1970's, and developed by Martin Reuter, a physicist at the University of Mainz in Germany. New Scientist magazine has a nice synopsis of the field, Quantum Einstein Gravity, from this article, the relevant bit repeated here:
* - worked in string theory.... Who hasn't?
** - Bell Labs Pure Physics Research Division - Yes, it still exists.
George E. Smith accepts the 2009 Nobel Prize in Physics
"Similarly, gravitons can be useful, and in that sense exist as effective "quasi" particles. But they do not exist as fundamental particles."
... Erik Verlinde, Jan 15,2010
One of the more interesting aspects about former string theorist* Erik Verlinde's latest work is his contention that the "graviton" should not be treated as a "particle", as it is in String Theory, but rather as a "phonon", as in acoustics. The reader can read all about phonons here at Wikipedia. I wish to call attention to the last section of that entry, which is this:
Thermodynamics
The thermodynamic properties of a solid are directly related to its phonon structure. The entire set of all possible phonons that are described by the above phonon dispersion relations combine in what is known as the phonon density of states which determines the heat capacity of a crystal.
At absolute zero temperature, a crystal lattice lies in its ground state, and contains no phonons. A lattice at a non-zero temperature has an energy that is not constant, but fluctuates randomly about some mean value. These energy fluctuations are caused by random lattice vibrations, which can be viewed as a gas of phonons.[notes 1] Because these phonons are generated by the temperature of the lattice, they are sometimes referred to as thermal phonons.
Unlike the atoms which make up an ordinary gas, thermal phonons can be created and destroyed by random energy fluctuations. In the language of statistical mechanics this means that the chemical potential for adding a phonon is zero. This behavior is an extension of the harmonic potential, mentioned earlier, into the anharmonic regime. The behavior of thermal phonons is similar to the photon gas produced by an electromagnetic cavity, wherein photons may be emitted or absorbed by the cavity walls. This similarity is not coincidental, for it turns out that the electromagnetic field behaves like a set of harmonic oscillators; see Black-body radiation. Both gases obey the Bose-Einstein statistics: in thermal equilibrium and within the harmonic regime, the probability of finding phonons (or photons) in a given state with a given angular frequency is:
is the frequency of the phonons (or photons) in the state, is Boltzmann's constant, and is the temperature.Steve here. Regarding the above, why is that important? I feel it's important because phonons require a large number of "particles" (wave crests?) in order to exist. A single particle does not a phonon make. Neither does a single particle have Entropy, nor Temperature. These are all collective things, requiring many particles to have meaning. In regards to how many are required is where I feel future work will focus. On a recent trip to Bell Labs Pure Physics Research Division** in Murray Hill, NJ, 2009 Nobel Prize in Physics co-winner and former Bell Labs Scientist George E. Smith was shown certain state-of-the art experiments going on using the Quantum Hall effect that may at some future time be helpful in this regard. More information will be made available in the future regarding this particular avenue following publication.
Why are phonons important in the quantum realm of the very small? I feel they're important because of the notorious weakness of gravity at that scale. If as Verlinde speculates the phononic effect goes away with few particles, and if gravity is ruled by such effects, then the weakness of gravity is explained.
Next up we ask the question: Is there a current theory, in General Relativity-based Quantum Gravity, that might explain and explore the possibility that gravity "drops away" in the realm of the small. As it turns out there is such a theory, based on an idea by Steven Weinberg in the 1970's, and developed by Martin Reuter, a physicist at the University of Mainz in Germany. New Scientist magazine has a nice synopsis of the field, Quantum Einstein Gravity, from this article, the relevant bit repeated here:
Martin Reuter, a physicist at the University of Mainz in Germany, has other ideas. He has been developing a different theory he calls "quantum Einstein gravity", which begins where the earliest approaches to quantum gravity left off.
After physicists successfully merged the classical theory of electromagnetism with quantum theory to create quantum electrodynamics in the 1940s, and later extended their methods to work with the strong and weak nuclear forces, they had hoped that they could likewise "quantise" gravity. The idea failed miserably, because of the way gravity behaves at small scales. As you zoom in on smaller distances, the strength of gravity increases, but gravity also acts on itself, creating a feedback loop that sends the gravitational force skyrocketing. Eventually the ability of general relativity to describe the fabric of the universe breaks down.
So most physicists went off in other directions, mainly towards string theory. Reuter, however, feels they were too quick to abandon the methods that had worked when applied to every other force in nature. He had been thinking about an idea proposed by physicist Steven Weinberg in the 1970s: that at extremely small scales, there might be a "fixed point" at which the strength of gravity no longer increases, no matter how much you zoom in. There is reason to think this might work. Quantum chromodynamics, the theory of how the strong nuclear force acts on quarks and gluons, says that the strong force decreases at smaller scales until it reaches a fixed point, where it goes to zero. If a similar point exists for gravity, it would mean that physics would be able to describe gravity down to the quantum realm.
When Weinberg proposed the idea, physicists didn't have the mathematical tools to calculate this fixed point in the four-dimensional space-time of general relativity. Then in the late 1990s Reuter developed such a method. His calculations were approximate, but they suggested that a fixed point for gravity might indeed lurk in the equations. "Personally, I am completely convinced that it exists," he says.
Intriguingly, in quantum Einstein gravity, space-time at the smallest scales is fractal and the number of dimensions shrinks from the familiar four to two. This is reminiscent of CDT, which leads some to wonder if they are two descriptions of the same theory. "Ultimately the two approaches could turn out to be equivalent," Reuter says.
Hello, Steve here again. My only contribution was to unite Verlinde's idea of gravitons as phonons with Weinberg/Reuter's view of Gravity falling off at small distances. I think this may be significant. I was never comfortable with the idea of a "graviton" as a "particle." I do believe Albert Einstein explained Gravity as geometrical consequence of reality in 1915. String Theorists promote "gravitons" since among the many Rube Goldberg bits their theory depends on, one bit is that a spin-2 massless particle "falls out" of their equations. Presto change-o and abracadabra, that MUST be a graviton, so they say. Yeah well, maybe, but maybe not too. I consider it a weak argument of opinion stated as fact, which is bad science.
Verlinde's recent Gravity as an Entropic Force has gotten considerable attention, both Pro and Con. If t'Hooft likes it, that's good enough for me, up to a point. Much more interesting is the criticism against it. At Sabine Hossenfelder's fair and balanced take on the subject, here, you can see how my thought process on this developed.
Perhaps most key in getting my brain to tie all this together was Dr. Andrew Thomas' take on the whole "Verlinde" situation as being not only a refreshing new way to look at an old problem (quite correct), but the "obviousness" of Entropy, a subject few Physicists have concerned themselves with since their younger undergraduate days, but a subject near and dear (and bread and butter) to Engineers such as Dr. Thomas (Ph.D., EE, Edinburgh) and myself.
Verlinde has been trivialized to some extent in the community for using "high-school physics." Not true. Third-year Undergraduate Thermodynamics II Mechanical Engineering Physics, is more like it.
One needn't get all tied up in Strings to make sense of the world. It may be explained in simpler terms than those who work at the cutting edge of Mathematics would prefer, but if so, then so be it.
When all else fails, ask an Engineer.
Ciao.
Steven Colyer
Pi Tau Sigma, BSME
Pi Tau Sigma, BSME
NJ
Well, that's it for today. I have to get myself into NYC to one of its wonderful art museums today with my 2 daughters for a required college art project for my oldest. It's always nice to get out with the girls and visit Manhattan, except that it will cost an obscene amount of money (as NYC always does) that I do not have (Hello, Loan Department!) and I'd rather be here exploring this new and exciting subject in more detail, but you can't have everything. Eh, the mental break will probably do me good. March 6, 2010.
Well, that's it for today. I have to get myself into NYC to one of its wonderful art museums today with my 2 daughters for a required college art project for my oldest. It's always nice to get out with the girls and visit Manhattan, except that it will cost an obscene amount of money (as NYC always does) that I do not have (Hello, Loan Department!) and I'd rather be here exploring this new and exciting subject in more detail, but you can't have everything. Eh, the mental break will probably do me good. March 6, 2010.
* - worked in string theory.... Who hasn't?
** - Bell Labs Pure Physics Research Division - Yes, it still exists.
George E. Smith accepts the 2009 Nobel Prize in Physics