August 31, 2006
No Victoria Cross
It turns out that Victoria Cross medals can sell for over $120,000, and Joshua hasn't bought one, after all. But we did take some photos of the Dead Man's Penny (medal + documents) that he bought at auction.
August 30, 2006
In the trenches
1) I've been reading books about World War I (again), this time this one and this one, both loaned to me by Joshua. Tomorrow I return them and he's going to show me the WWI medals he's been buying online at auction. With any luck, I'll go away with a photo of myself wearing the Victoria Cross. I'm also desirous of visiting WWI battlefields, although it's hard for me to picture dragging Gloria and the kids there. I need to find some kind of technology conference in Verdun or Ypres.
2) Succeed in excavating my office to desktop surfaces, paying bills and once again identifying the key clutter issueI have too many books.
3) Have got the first draft The Phi-Values of Various Games done, in its entirety, all 78 pages of it (and it's going to get longer) but can't make further progress (or at least, have convinced myself that I can't make meaningful further progress) until Aaron comes back from Burning Man. Greg and others are at Burning Man, too. Maybe I'll go sometimeha! I dont think so. The problem with Burning Man is the same problem with Nebraska and with the novels of Willa Catherthey are too sandy. I'm not fooled when they call it a playa, instead. I'm going to be happier when I'm out of the mode of writing up math papers and can return to trying to solve math problems, instead. It's much more interesting and although I usually have little tangible to show after a day of working on math problems, it's more gratifying somehow. Just a little adventure, like a trip to a Jelly Bean factory, or an exploration of a castle. That's how I think of it. No one writes papers about trips to Jelly bean factories or castles, right? You just go, and have fun. Going to the Halifax Games at DAL meeting only reaffirmed this desire to actually do math, and not talk about it, or write about it. Yet if I indulge this desire to work on the math instead of writing about it, I will condemn Phi Values to be late. So, nomust keep writing/editing. Am I burning out?
August 29, 2006
Mental images summoned as I attempt my IT band stretching exercises
1) Flimsy screen door and granite boulder, immovably positioned behind the bottom of the door. Rock allows the door to be pushed open only 2 inches. Exercise: "Pushing the top of the door only to its full range of motion, hold for 30 seconds. Repeat." Will door snap off hinges? Probably.
2) Ancient elastic bands under high tension surround a box full of undetonated and highly unstable explosives. Exercise: "Extend band twelve inches from box. Reach full range of motion and hold for 30 seconds. KISS YOUR A** GOODBYE."
3) Corpse with developing rigor mortis on putrefying pillow. Exercise: "Grasping leg of corpse firmly with one one hand, bend it backward behind you. Make sure you keep squeezing the pillow between your legs and hold for thirty seconds." No, thank you.
Laptop on deathbed
Better than a disk crash, I guess. Anyway, time to get a new laptop.
August 28, 2006
Michiko Kakutani buries bloggers and Franzen in mass grave
Not really about bloggers, but still:
While some readers will want to give Mr. Franzen points for being so revealing about himself, there is something oddly preening about his self-inventory of sins, as though he actually reveled in being so disagreeable. And while it doubtless takes a degree of self-absorption for anyone to write a memoir [readblog], in the case of this book the author's self-involvement not only makes for an incredibly annoying portrait, but also funnels the narrative into a dismayingly narrow channel.
Shostakovich Prelude and Fugue in G minor 
August 26, 2006
Tasso street partyLenny Susskind and frog cookie
Working out the misere transition algebra T(*2) with Meghan Allen and Angela Siegel
Working out the misere transition algebra T(*2) with Meghan Allen and Angela Siegel
Originally uploaded by thane.
Some books I bought at Erin & Chris's garage sale for $1
1) The Making of the President, 1960 [ Theodore H White. Always wanted to read it. Or so I thought. At least this is my big chance. ]
2) Justine [ Lawrence Durrell the first of the "Alexandria Quartet." Like the names of various flowers, French cities, and events of the 14th century, this book has flitted in and out of my attention, always whispering "Ahbut you should know more." Also, there was the little matter of the Sigmund Freud quotation on the frontispiece: "I am accustoming myself to the idea of regarding every sexual act as a process in which four persons are involved. We shall have a lot to discuss about that." Clearly it wouldn't do to leave this book unpurchased? ]
3) State of the Nation, John dos Passos.
4) MRS. BJORKEN'S DIARY OF 1974 RUSSIAN VISIT, just next to In Memoriam: Joan G Bjorken, (1936-1983), and I thought, "ah, samizdat!" documents, or at least self-published. I've now worked out that she was the wife of James D. Bjorken, a physicist and senior administrator at FermiLab, now possibly still affiliated with the Stanford physics department.
In reading through these interesting pamphlets, I learned that Joan Bjorken established the Infant Care Center at Fermilab [Introduction of the "In Memoriam" pamphlet, by Leon Lederman].
With this fantastic photo of her talking to kids, presumably at Fermilab:
The things you find at a Palo Alto garage sale!
August 25, 2006
Peggy's Cove, Nova Scotiaplenty of people wandering around, but for a moment they were all hidden behind the lighthouse, and I took this photo.
"If there is a doctor on this flight, would you please identify yourself?"
I took this photo just after we landed in San Francisco and pulled up at the gate (from Toronto, as scheduled). You can just about see the doctor's white hair and the EMT guy standing behind him in the center of the photo. You can't see the patient, even if you enlarge the photo. He's sitting down. After I took the photo, the patient got up and walked off the plane, seemingly without any problem.
After today's MRI and a meeting with a sports medicine guy at the Palo Alto Medical Foundation, I've got a diagnosis for my pesky left knee problems Iliotibial Band Syndrome.
"There's no need for surgeryyou need to stretch and strengthen your left leg. I'd give you a PT referral, but it all comes down to the stretching."
I'd gotten this probable diagnosis already from Christine (Gloria's personal trainer), 10 months ago.
She knew what she was talking about (even as she marvelled at my inflexibility).
"The MRI scans do not lie," summarized the Sports medicine guy.
August 23, 2006
JP about to enter the mysterious 2 and 1/2th floor of the Dalhousie math department
August 22, 2006
August 19, 2006
Page served to me at YouTube
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500 Internal Server Error
Sorry, something went wrong.
A team of highly trained monkeys has been dispatched to deal with this situation. In any case, please report this incident to customer service.
Also, please include the following information in your error report:
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[ I think there are some growing pains at YouTube nowadays ]
Water loving animals
Someone should let that dog go outside!
August 18, 2006
Seems like I should type it in, even though it's impossibly boring [such concerns haven't stopped me in the pastwhy now? ]
I stubbed my right pinky finger at morning basketball, but only have myself to blame. It was an easy pass to me and I was lazy in catching it.
The photo doesn't do justice to the color; it's ugly. Maybe it's broken?
We visited Cole's soon-to-be middle school today and I was reminded of another playtime mishap. It happened when I was in middle school (of course, it was called "Junior High" back then). Some girls were playing a game where they took one of their saddle shoes almost off their foot, leaving toes still in the shoe. They were having a contest to see who could kick off their shoe the hardest at a wall, about 20 feet away. I could hear the loud whack as each black and white and shoe slammed into the wall. The wall had a ledge, and I climbed up on top of it. I surprised them by jumping to the ground between the high velocity saddleshoes and the wall. I took Mary Luth's right saddleshoe directly in the left eye, which survived despite this Darwinian pressure in favor of its extinction.
in the Guardian
For example, it was very difficult for an Me-109 to shoot down a Stringbag. The trick was to wait for the enemy to come almost within range, then cut right back on speed, and make the steepest possible turn at 60 knots. This was a "sixpence inside a half-crown" and the fighter could not bring its guns to bear.
[ From an obituary of Lord Kilbracken. I've got to figure out how to get myself a cool title like that"Lord Kilbracken." Nice. I like these Guardian "Old Boy" obituaries, with their inevitable introductions describing youthful indiscretions"Born in Belgravia, he had just finished with Eton, and was ready for Oxford, when he chose to enlist. School life had not been uneventful; he had been Eton's unofficial bookmaker (with a daily turnover of £30) and was almost expelled when discovered..."and then later, more sober accomplishments. The best obituaries are always Churchillian. Joshua said is it's possible to buy certain similar-sounding titles, maybe he said "Lord of the Manor" is one of that type? He did say that the droit du seigneur no longer applies. I must enquire. ]
August 16, 2006
Looks like Bruce has a new 3D photo rig?
He took these photos there.
August 15, 2006
The Literary Engine 
The first Professor I saw was in a very large Room, with forty Pupils about him. After Salutation, observing me to look earnestly upon a Frame, which took up the greatest part of both the Length and Breadth of the Room, he said perhaps I might wonder to see him employed in a Project for improving speculative Knowledge by practical and mechanical Operations. But the World would soon be sensible of its Usefulness, and he flattered himself that a more noble exalted Thought never sprung in any other Man's Head. Every one knew how laborious the usual Method is of attaining to Arts and Sciences; whereas by his Contrivance, the most ignorant Person at a reasonable Charge, and with a little bodily Labour, may write Books in Philosophy, Poetry, Politicks, Law, Mathematicks and Theology, without the least Assistance from Genius or Study. He then led me to the Frame, about the Sides whereof all his Pupils stood in Ranks. It was twenty Foot Square, placed in the middle of the Room. The Superficies was composed of several bits of Wood, about the bigness of a Dye, but some larger than others. They were all linked together by slender Wires. These bits of Wood were covered on every Square with Paper pasted on them, and on these Papers were written all the Words of their Language, in their several Moods, Tenses, and Declensions, but without any Order. The Professor then desired me to observe, for he was going to set his Engine at Work. The Pupils at his Command took each of them hold of an Iron Handle, whereof there were fourty fixed round the Edges of the Frame, and giving them a sudden turn, the whole Disposition of the Words was entirely changed. He then commanded six and thirty of the Lads to read the several Lines softly as they appeared upon the Frame; and where they found three or four Words together that might make part of a Sentence, they dictated to the four remaining Boys who were Scribes. This Work was repeated three or four Times, and at every turn the Engine was so contrived that the Words shifted into new Places, as the Square bits of Wood moved upside down.
Plate V: The Literary Engine
Six Hours a-day the young Students were employed in this Labour, and the Professor shewed me several Volumes in large Folio already collected, of broken Sentences, which he intended to piece together, and out of those rich Materials to give the World a compleat Body of all Arts and Sciences; which however might be still improved, and much expedited, if the Publick would raise a Fund for making and employing five hundred such Frames in Lagado, and oblige the Managers to contribute in common their several Collections.
He assured me, that this Invention had employed all his Thoughts from his Youth, that he had emptyed the whole Vocabulary into his Frame, and made the strictest Computation of the general Proportion there is in Books between the Numbers of Particles, Nouns, and Verbs, and other Parts of Speech.
I made my humblest Acknowledgments to this illustrious Person for his great Communicativeness, and promised if ever I had the good Fortune to return to my Native Country, that I would do him Justice, as the sole Inventer of this wonderful Machine; the Form and Contrivance of which I desired Leave to delineate upon Paper, as in the Figure here annexed. I told him, although it were the Custom of our Learned in Europe to steal Inventions from each other, who had thereby at least this Advantage, that it became a Controversy which was the right Owner, yet I would take such Caution, that he should have the Honour entire without a Rival.
We next went to the School of Languages, where three Professors sate in Consultation upon improving that of their own country.
The first Project was to shorten Discourse by cutting Polysyllables into one, and leaving out Verbs and Participles, because in reality all things imaginable are but Nouns.
The other, was a Scheme for entirely abolishing all Words whatsoever; and this was urged as a great Advantage in Point of Health as well as Brevity. For it is plain, that every Word we speak is in some Degree a Diminution of our Lungs by Corrosion, and consequently contributes to the shortning of our Lives. An Expedient was therefore offered, that since Words are only Names for Things, it would be more convenient for all Men to carry about them, such Things as were necessary to express the particular Business they are to discourse on. And this Invention would certainly have taken Place, to the great Ease as well as Health of the Subject, if the Women in conjunction with the Vulgar and Illiterate had not threatned to raise a Rebellion, unless they might be allowed the Liberty to speak with their Tongues, after the manner of their Ancestors; such constant irreconcilable Enemies to Science are the common People. However, many of the most Learned and Wise adhere to the New Scheme of expressing themselves by Things, which hath only this Inconvenience attending it, that if a Man's Business be very great, and of various kinds, he must be obliged in Proportion to carry a greater bundle of Things upon his Back, unless he can afford one or two strong Servants to attend him. I have often beheld two of those Sages almost sinking under the Weight of their Packs, like Pedlars among us; who, when they met in the Streets, would lay down their Loads, open their Sacks, and hold Conversation for an Hour together; then put up their Implements, help each other to resume their Burthens, and take their Leave.
But for short Conversations a Man may carry Implements in his Pockets and under his Arms, enough to supply him, and in his House he cannot be at a loss: Therefore the Room where Company meet who practise this Art, is full of all Things ready at Hand, requisite to furnish Matter for this kind of artificial Converse.
Another great Advantage proposed by this Invention, was that it would serve as a Universal Language to be understood in all civilized Nations, whose Goods and Utensils are generally of the same kind, or nearly resembling, so that their Uses might easily be comprehended. And thus Embassadors would be qualified to treat with foreign Princes or Ministers of State to whose Tongues they were utter Strangers.
I was at the Mathematical School, where the Master taught his Pupils after a Method scarce imaginable to us in Europe. The Proposition and Demonstration were fairly written on a thin Wafer, with ink composed of a Cephalick Tincture. This the Student was to swallow upon a fasting Stomach, and for three Days following eat nothing but Bread and Water. As the Wafer digested, the Tincture mounted to his Brain, bearing the Proposition along with it. But the Success hath not hitherto been answerable, partly by some Error in the Quantum or Composition, and partly by the Perverseness of Lads, to whom this Bolus is so nauseous, that they generally steal aside, and discharge it upwards before it can operate, neither have they been yet persuaded to use so long an Abstinence as the Prescription required.
* * *
From Gulliver's Travels, PART III: A VOYAGE TO LAPUTA, BALNIBARBI, LUGGNAGG, GLUBBDUBDRIB AND JAPAN
Life of crime dept
1) Opening up the September Harper's magazine I found this on pg 6
SUBSCRIBER ALERT: Dear Harper's Magazine Readers, It has come to our attention that several of our subscribers have received renewal notifications from an independent magazine clearinghouse doing business under the names Magazine Billing Services, Publishers Processing Services Inc., and American Consumer Publish Assoc. These companies have not been authorized to sell subscriptions on behalf of Harper's Magazine...
OofI knew had just sent in some kind of renewal a couple of weeks ago. But I called the magazine and they had received it. I've got a grudging admiration for this scam, though, since I get this kind of notice all of the time and pay the bill without really thinking whether the soliciting agency is legitimate. I subscribe to quite a few magazines but do keep track of when their renewal dates occur. If I've fallen for it, it's probably a New Yorker subscription solicitation, not a Harper's one, that victimized me. I stopped getting the magazine and had to callthey said they hadn't received the renewal. But I'm certain I sent it in.
2) Later, a call from a robot. It informed me that my credit card number had been "stolen" and that it would be 5 to 6 days before I got a new one. I managed to interrupt the robot and get connected to a person. "Some kind of Internet break-in," was all the person would say. I wanted to know which merchant. "The investigation is continuing." It's inconvenient because I have lots of automatic charges on that card. Since the calling robot and customer service person both knew the issuing bank and branding on the card I don't think the robot call was a scam, and in any case they didn't ask for the number, and they knew the most recent charge on the card.
I need to resurrect dormant credit cards for my trip to Canada coming up next week.
Pennies for your thoughts
Joshua lent me the excellent Unknown Soldiers: The story of the missing of the first world war, by Neil Hanson, increasing my holdings of his books loaned, perhaps never to be returned. He also confessed to purchasing a Dead Man's penny at auction on a UK web site, for 16 pounds.
I was reminded that I had recently bought some somewhat rare US pennies for Cole in order to complete his collection of 20th century pennies. The rarest ones, each with about 2.5 million minted, were in the 1920s and 1930s (I've forgotten which years, exactly). In any case, I paid about $12.50 for each penny from the rare years. Comparing that to the roughly 900,000 GB dead in WWI, the numbers gibe, Dead Man Penny vs US Pennythe Dead Man's Penny is dearer.
Added later: From the deep archives: German WWI grave design competition
August 14, 2006
dramatic playground footage
This video of Cole on the monkey bars is almost six years old, but it's as thrilling now as it was when first filmed.
With a special cameo by Owen, working his way up the curving ladder.
August 12, 2006
Another look at the magic dragon
It's a little too dark in the video, but I got closer to it.
Mauna Loa vs Mauna Kea
Mauna Loa may be Earth's largest volcano, but nearby Mauna Kea is taller (13796 ft vs 13677 ft) and has the cool telescopes.
Mauna Loa last erupted in 1984. I guess Kilauea (which is erupting now, and has been, more or less, for the last ten years, at least, I think), isn't counted as part of Mauna Loa?
Nature magazine (25 May 2006) says that Mauna Loa isn't dead, just sleeping, and that "its 1877 underwater eruption, which made the waters of a nearby bay boil, was much larger than was thought [...] contradicting the theory that this volcano is dying."
I still like Mauna Kea the best, even though I started gasping from the thin air up there.
In a classic experiment by Vilem Laufberger in Germany, hormone injections persuaded an axolotl to grow into a fully adult salamander of a species that no one had ever seen. More famously in the English-speaking world, Julian Huxley later repeated the experiment, not knowing it had already been done. In the evolution of axolotl, the adult stage had been chopped off the end of the life cycle. Under the influence of experimentally injected hormone, the axolotl finally grew up, and an adult salamander was recreated, persumably never before seen.
Richard Dawkins, The Ancestor's Tale, p98
axolotl huxley [google search]
[ binary arts / gathering for gardner ]
August 11, 2006
August 10, 2006
Found in the home office stacks
Five minutes ago I opened my copy of NJAS's and FJ MacWilliams's 1977 book The Theory of Error Correcting Codes to read what it had to say about Golay codes. It had been sitting undisturbed in my home office for, oh, I don't know, maybe 12 years. Probably longer.
Maybe twenty years.
Out dropped a printout of email from Don Knuth, dated 17 May 1987 that I had thought I had lost forever. Here's the story behind it.
About 20 years ago, I was about to be kicked out of the Stanford Computer Science department's PhD program for failing to pass the comprehensive exams. There were six parts to the exam. You had to pass all of them to pass the exam. I'd failed three times already, failing the "Systems" part each time. If I failed the exam again, they would kick me out of the program.
It was suggested that I meet with Don Knuth to discuss the situation. I had never met him before.
I went into his office and he told me a story about hating astronomy as an undergraduate. He failed his first astronomy exam. So he decided he would be the best astronomy student that there ever was. He forced himself to learn stupid things that he detested.
He became the world's greatest astronomy student. He passed all his Astronomy examinations after that, with the highest grades. Despite that, he never had an interest in the subject again (I doubted that, even then).
That was it. The meeting was over. I left his office. I considered the meeting to have been a big failure, although it was interesting to meet Knuth. I took the exam maybe one month later.
I passed the exam miraculously and then got this email from Knuth (click it to read it)
Added later: It's scary to think where I might have ended up had I not passed this exam. The way technology and computer science have gone, I'd probably be sitting in some lonely office, typing obscure blog entries for a vanishingly small readershipoh, uh, wait...
August 09, 2006
Here's an increasingly popular way to deliver messages to our house:
1) Put communication in a plastic bag.
2) Add a couple of rocks.
3) Throw the ensemble into our front yard as you drive by.
Added later: So far, this Google search on "rockbag marketing" returns zero results. Yet that's got to be the best name for it, right?
August 08, 2006
I received galley copies of the Gathering for Gardner (G4G7) Exchange Book today from Tom Rodgers.
It's got to be at least 700 pages of the coolest stuff on magic, puzzles, recreational math, and games. People really outdid themselves on their contributions. At the beginning of the book, there was exactly what I'd hope to find, somewhere, in itScott Kim's renderings of many of the participants' names as ambigrams.
I'm still amazed at how easily he dispatched my name
From the introduction by Jeremiah Farrell:
Are you a completist? Or perhaps you prefer to be a preservationist. If a completist you will cut, bend, fold, and generally mutilate these exchanges from the Seventh Gathering for Gardner by trying to solve every last puzzle or problem contained therein. Completists preserve nothing.
On the other hand complete, pristine sets from earlier Gatherings have become very, very collectible and apparently very expensive. I have heard that one copy of the spiral bound first exchange was sold recently for several thousand dollars. It was assembled by Scott Kim on January 16, 1993 with help from Tom Rodgers and Dana Richards. I don't know the details of the sale.[...]
Shortly after G4G7 Karen and I decided to visit Mr Gardner in Norman, OK. We found him in good health and, although he rarely travels, very active. He has just completed a new book on wordplay and has sent it to a publisher. A long review of E. Brian Davies' Science in the Looking Glass: What do Scientists Really Know? occurred in the AMS Notices (Vol 52, No. 11) [another link to an article by Davies in the same issue].Also the MAA has contracted with Cambridge University Press to reissue all the columns of "Mathematical Games" in hardbound editions at the rate of two per year. "These will be reset so I am able to update all of them," Gardner excitedly exclaimed. He was working on the updates when we visited.
Feared aerial visitor alights on Tasso St
The worst omen is when the guy arrives and starts climbing the pole in our driveway, as he is here.
* * *OLD STORY* * *
ANIL: Check it out! There's an owl on that roof over there!
CHINESE ROOMMATE: What?
ANIL: An owl, on that roof, right there!
CHINESE ROOMMATE: [ moaning sound ] Ohvery bad luck! Just answer this, have you ever seen an owl land on our roof? Is it possible that it has landed on our roof?
ANIL: Uh, sure, I suppose it's possible.
CHINESE ROOMMATE: OOOO!
Cockburn in Counterpunch
Beyond raising money swiftly handed over to the gratified veterans of the election industry, both MoveOn and Daily Kos have had zero political effect, except as a demobilizing force. The effect on writers is horrifying. Talented people feel they have [to] produce 400 words of commentary every day, and you can see the lethal consequences on their minds and style, both of which rapidly turn to slush. They glance at the New York Times and rush to their laptops to rewrite what they just read. Hawsers to reality soon fray, and they float off, drifting zeppelins of inanity.
* * *
drifting zeppelins of inanity [google search]
August 07, 2006
From the Seattle Times, inside an article titled "Microsoft presentation goes from bad to worse":
Those digits should be familiar to Microsoft historians. The Intel 8080 was the chip inside the Altair 8800, the PC introduced in 1975. The Altair BASIC programming language, built by Bill Gates and Paul Allen, is the product on which Microsoft was founded, and 8080 is honored in Microsoft's main corporate number: 425-882-8080.
More from that article:
* * *
In a roomful of analysts and reporters, Boettcher tried to write a letter to his mother on Vista, using only his voice. The result was one of the worst Microsoft product demonstrations in recent memory.
Boettcher began by saying, "Dear Mom," but Vista couldn't understand. Repeated attempts to correct it failed. Eventually, the letter to Mom went like this: "Dear Aunt, let's set so double the killer delete select all."
Another number in the news, this time in the financial pages.
Who's the wiseacre in the Redmond CFO office?
Mathematical headline of the day
August 06, 2006
bobby fischer / etruscan sculpture
August 05, 2006
Misere Nim in Last Year At Marienbad
Crossword puzzle resolution
The missing letter is supposed to be a "G".
That makes "SUSSING" going down, for the clue "Figuring (out)."
added later Hjem explains:
For the across answer, TIGERSEYE, clued as "Quartz variety."
But my real problemI misspelled ADNAUSEAM. Google has more pages with the -UM spelling, but that doesn't make it right, hmmm...
The clue for 36 down is "How about it?" (with the quotation marks in the clue). I was satisfied with WHATSUP, but it was supposed to be WHATSAY.
Through the miracle of YouTube technology...
...you can watch me whine about today's (Friday) NYTimes crossword:
August 03, 2006
In 1906, Danish classics professor John Heiberg discovered the lost manuscript and identified the underlying text as unknown writings by Archimedes. Heiberg photographed many of the pages that showed the faint Archimedes text, but missed some important passages and was unable to photograph the parts of the pages beneath the palimpsest bindings. The parchment then fell into the hands of a private collector in France, who altered and damaged parts of the palimpsest. Lost again, it resurfaced at Christie's auction house in 1998 and was purchased by an anonymous donor for $2 million. Since then, the Archimedes Palimpsest has been in the care of The Walters Art Museum in Baltimore, Maryland, where they're conserving, imaging, and deciphering it.
The Archimedes Palimpsest contains seven of the Greek mathematician's treatises. Most importantly, it is the only surviving copy of On Floating Bodies in the original Greek, and the unique source for the Method of Mechanical Theorems and Stomachion.
We developed fuzz testing, the sending of unstructured random input to an application program. With a few simple tools, we tested more than 80 command line utility programs on six versions of UNIX. As a result of this testing, we were able to crash a surprising (to us) number of programs: 25-33%. These crashes were typically caused by the use of risky programming practices that are well known to experienced programmers and the software engineering community.
And: Fuzzing Tools
click here for the whole cartoon
August 02, 2006
Euler on divergent series summation
One of the things that mathematicians do occasionally is put down the old guys, even people like Euler, for stupid reasons. Varadarajan's bookwhich doesn't do this at allgave me some ammunition I'd been curious to have myself concerning the viewpoint of 18th century mathematicians on divergent series.
Here's a question: what is the sum of the infinite series
It's customary for 20th (and 21st) century people to say "Tsktskfirst you have to tell me what the sum means, then I'll (try to) tell you what it is". It's customary to say that the old guys like the Bernoullis and Euler "lacked rigor" because they took these questions at face value, and tried to find their natural meaning.
Here's a fascinating extract from a 1760 paper by Euler, reproduced in Varadarajan's book:
Notable enough, however, are the controversies over the series 1-1+1-1 ... whose sum was given by Leibniz as 1/2, although others disagree. No one has yet assigned another value to that sum, and so the controversy turns on the question whether the series of this type have a certain sum. Understanding of this question is to be sought in the word "sum"; this idea, if thus conceivednamely the sum of a series said to be that quantity to which it is brought closer as more terms of the series are takenhas relevance only for convergent series, and we should in general give up this idea of sum for divergent series. Wherefore, those who thus define a sum cannot be blamed if they claim they are unable to assign a sum to a series. On the other hand, as series in analysis arise from the expansion of fractions or irrational quantities or even transcendentals, it will in turn be permissible in calculation to substitute in place of such a series that quantity out of which it is produced...
OKso this isn't a statement of the Tauberian results, but still, it reads like Euler has his heart in exactly the right place. How could it be otherwise? Varadarajan earlier points out this quotation from G. H. Hardy (a 20th century mathematician who was an expert on divergent series, among other things...)
It does not occur to a modern mathematician that a collection of mathematical symbols should have a 'meaning' until one has been assigned by definition. It was not a triviality even to the greatest mathematicians of the 18th century. They had not the habit of definition: it was not natural to them to say 'by X we mean Y' .... It is broadly true to say that mathematicians before Cauchy asked not 'How shall we define 1-1+1-1+1- ...' but 'What is 1-1+1-1+...?'
Varadarajan comments on Hardy (pg 128):
In many ways the great exception to this was Euler. He took divergent series seriously, used them to obtain beautiful results, and had definite views aobut what is meant by the sum of a divergent series and how they should be used...
A scientist weighs in on Intelligent Design
So, then, gravity may put the planets into motion, but without the divine power it could never put them into such a circulating motion as they have about the sun; and therefore, for this as well as other reasons, I am compelled to ascribe the frame of this system to an intelligent Agent.
Sir, I am your most humble servant,
Trinity College, Jan 17, 1692/93
[From the "Letter for Mr. Bentley, at the Palace of Worchester," in Newton's Philosophy of Nature: Selections from his writings, Hafner Library Classics, 1953 ]
August 01, 2006
Your new house is almost ready
This impressive steel house frame appeared a few blocks from our house.
House not done yet:
Added later: More photos I took in Aug 2003 when this house's steel framing was going up.
More from the Cockburn essay
"Crackpot realism" was the concept defined by the great Texan sociologist, C. Wright Mills in 1958, when he published The Causes of World War Three, also the year that Dwight Eisenhower sent the Marines into Lebanon to bolster local US factotum, Lebanese President Camille Chamoun.
"In crackpot realism," Mills wrote, " a high-flying moral rhetoric is joined with an opportunist crawling among a great scatter of unfocused fears and demands. .. The expectation of war solves many problems of the crackpot realists; ... instead of the unknown fear, the anxiety without end, some men of the higher circles prefer the simplification of known catastrophe....They know of no solutions to the paradoxes of the Middle East and Europe, the Far East and Africa except the landing of Marines. ... they prefer the bright, clear problems of war-as they used to be. For they still believe that 'winning' means something, although they never tell us what..."
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