The End of the World is Nigh.....

The Aztec calender stops in december 2012, so linear predictions that the end of the (digital) world is expected in the autumn of 2011 may be premature ;-)

What am I talking about? The IP4 address space (of 4*10⁹ IP addresses) is expected to run out late next year (around september 11th?) and the infrastructure folks worldwide are ill-prepared and only now gradually switching into panic mode :-(

Fifteen years ago IP6 (i.e version 6 of the protocoll supporting 340 sextillion IP V6 addresses) was defined, but seemingly no-one has picked up the ball and run with it. Thus panic mode.

Why panic mode?

Well, IP4 and IP6 are incompatible. Your home IP4 equipment won't work in an IP6 net; no eMails, no webservers. So converters are needed. But there is no international agreement on the conversion. Russia and China (and the DHS?) want to define theirs on a national basis, assigning lifetime address ranges to each user (to make them identifiable and trackable). Some commercial service-providers want to use a priority bit for which they could charge premium rates (greedy capitalism). The more democratic users (most of us) prefer the dual-stack approach without an (implicitly second class non-)priority bit. Until all this is settled politically, we are not going to have a fully functional IP V6 (and V4-converting) net, or V6 home kit. But time is running out :-(

Copyright ^© Stu Savory on March 27, 2010 permalink Comments Email

4, 15, 23, 24, 35, 42 :-)

Terry Pratchett is one of my favourite authors. In his Discworld^® series of stories, any event which has odds of a million to one against is bound to happen! Douglas Adams (Hitchhikers' Guide to the Galaxy) 5-part trilogy also features an infinite improbability drive. In both cases we smile indulgently at these quantum fantasies - suspending our disbelief, further to enjoy the far-fetched fiction.

Having enjoyed these books (and others of their ilk) we return to humdrum reality :-(

And then along came the Bulgarian state lottery. On september sixth 2009, live on television, the aforementioned numbers 4, 15, 23, 24, 35 and 42 popped out of the randomisation machine. That's an analog machine, whirling numbered table-tennis balls around and expelling them one at a time after remixing the remaining balls. It is NOT a digital pseudo-random number generator. Nobody won that week.

Eighteen people - sceptics of probablility theory who realised the machine has no memory and thus all configurations are theoretically equally likely - or maybe some were fans of Terry Pratchett and/or Douglas Adams - chose those same six numbers (4, 15, 23, 24, 35 and 42) for the following week's (september 10th) lottery.

And they came up again!!! 4, 15, 23, 24, 35 and (see HHGTTG) 42, albeit in a different sequence. The odds against that happening are about one in four million!

But because 18 people suspended their disbelief simultaneously, each will win only 10,164 leva (about £4,700). Marvin was right :-(

Needless to say, an official investigation is going on to see if there was any mafia-like manipulation. The lottery organisers described it as a freak coincidence and pointed out that the numbers were drawn in a different order. The lotto-responsible Bulgarian minister of sport Svilen Neykov said the commission established to investigate would provide answers towards the end of the week. I wonder if they also had read Pratchett and/or Adams? Or maybe they just like listening to Carl Orff's O Fortuna ;-)

Stu Savory on March 24, 2010 permalink Comments Email

I beg to differ!

T here is a commonly used expression "Dumb Yanks!" :-(

Why do we get this impression? Obviously, not all of them are stupid. Well, a large minority is, as evidenced by the Redneck and Teabagger contingent. But it would seem that their educational system is failing them, teaching them myths and misconceptions which are genuinely wrong. Seemingly, they have not been taught to question such myths and misconceptions either. I'll rephrase that : the version of "history" - even about their own nation - many Americans have, differs from what I was taught and now believe. Here are half a dozen examples of American myths :-

1. Columbus discovered the USA - I beg to differ! I maintain that Columbus never even set foot in mainland America. The nearest he got was the Bahamas.
2. America became independent on July 4, 1776 - I beg to differ! Independence from England was not granted until September 3, 1783 because the war raged for 7 more years after the Declaration of Independence was unilaterally signed on or about July 4, 1776. Not until September 3, 1783 did Britain's King George III and US leaders sign the definitive Treaty of Peace.
3. America's first President was George Washington - I beg to differ! During the American Revolution, the Continental Congress (or the 'United States in Congress Assembled') chose Peyton Randolph as the first President. He was succeeded in 1781 by John Hancock, who presided over the independence from GB (see above). Only THEN did he become America's first popularly elected post-1783 President, actually he was number 15, a full 8 years after Randolph!
4. Walt Disney drew the Mickey Mouse cartoons - No, I think not. Disney's number one animator, Ub Iwerks did! Walt Disney merely did Mickey's voice in the first sound movies of him.
5. Witches were burned at stake in the Salem (Massachusetts) witch trials of 1692 - I beg to differ! 150 were arrested, 31 tried and 20 executed of whom only 14 were women. Most were hung, one was crushed under heavy stones, NONE were burned at the stake!
6. Edison invented the electric light first - I beg to differ! English scientist Sir Humphry Davy invented arc lighting using a carbon filament. Edison's assistants, after much experimentation, found the right filament that would let lamps burn for days on end instead of the carbon filament's 12 hours or so.

Comments (2) :
Pergelator (USA) reacted with his own version of my list, viz:- "You don't have to beg, we all know you are different. As for your myths, I happen to like most of them. Where did you get your versions? They are similar to what I have heard, but not quite right.

• Columbus discovered the USA. No, Columbus discovered America, as in the continents. There was no USA back then. Actually, I don't know if he ever landed on either North or South America, maybe he just disovered some islands in the Caribbean. And he wasn't the first, the Vikings were first, but they neglected to tell anyone. In any case Columbus found receptive ears for his story, which triggered an invasion, so to speak.
• America became independent on July 4, 1776. America declared their independence on July 4, 1776. It just took a while for the rest of the world to be persauded of that fact.
• America's first President was George Washington. The USA didn't really get organized until the constitution was written, and George was the first President of the new organization. All those guys who came before don't count.
• Walt Disney drew the Mickey Mouse cartoons. Walt Disney was the King of Disneyland. I never saw him draw anything.
• Witches were burned at stake in the Salem (Massachusetts) witch trials of 1692. No, burning at the stake was a peculiarly European tradition.
• Edison invented the electric light first. Edison invented the first practical electric light bulb. It may have been one of his minions who actually happened upon the particular material that made the bulb work, but in the grand tradition of simplified history, minions don't count.

Copyright ^© Stu Savory on March 22, 2010 permalink Comments Email

17β-hydroxyandrost-4-en-3-one double-win :-)

Back on March 12th I did a long article about Cancer. Blake asked if there was any correlation between testosterone (testosterone is the common name for the hormone with chemical structure 17β-hydroxyandrost-4-en-3-one) and prostate cancer? However it has taken me a week to find out.....

A US study sampling 2000 men has shown that young men who suffered hair loss by the age of 30 (=baldies) later have an up to 45% smaller chance of suffering from prostate cancer. So that's good news for us early baldies. Both phenomena are due to baldies having higher testosterone levels than non-baldies, (explanation: high testosterone levels make your hair fall out). You ladies knew about the higher testosterone levels intuitively already, whence your preference for us bald guys ;-)

Saturday Update : FWIW, today is the first day of spring ;-)

Copyright ^© Stu Savory on March 19, 2010 permalink Comments Email

BTW, Apple have delayed the release of the iPad until the beginning of April (All Fool's Day?) in the USA and the end of April (Walpurgisnacht?) here in Germany, I'm told.

Copyright ^© Stu Savory on March 15, 2010 permalink Comments Email

A regular blogreader, who wishes to remain anonymous, has recently been diagnosed with late (stage four) cervical cancer :-( She has asked me to tell you her tale and implore you to go for your annual checkups regularly. She is being very strong about it. There is nothing I could say which would express my deep sadness for her. No words. So the least I can do is post her words for you and add a few of my own. I have several friends with the big C, so I'll mention their cases and my own experiences with the prevention clinic visits. But I'll have to do some grim statistics too, to get the message across :-(

Her tale : I just think it's important that people make the effort to go and get regular check-ups. Men too, for prostate cancer (that's sort of your equivalent, isn't it?) It's uncomfortable and embarrassing, but it doesn't take long and I can pretty much guarantee it's better than the alternative.

After I was diagnosed they told me that because of the way the tumour was growing, they couldn't operate and would have to give me chemo- and radiotherapy. The radio meant going in five days a week for a session and the chemo meant going in once a week for a session. Both are painless (apart from when they put the catheter in your hand for the drip. And at this point, can I just say -- without meaning to be sexist -- if you ever need anything to be done that involves needles, get a woman to do it. For some reason men are just bloody useless with these things. I have no idea why), but it also meant several biopsies (painful) and uncountable probes (I went to a teaching hospital, so I got an audience, too). I've had every single orifice in my body invaded. Every single one (eight for a woman: count them). In case you're wondering, the ears were because some chemo drugs can make you deaf if you have an ear infection in the first place, so they had to rule that out. I can tell you now I have no ear infection, and I'm not deaf. The nostrils were for oxygen for when I was having problems breathing due to anaemia brought on by loss of blood because of the tumour; the urethra was due to bladder complications, because of the tumour. I now have a hole in my bladder -- because of the tumour -- and was advised to have an operation which would reroute a bunch of stuff and leave me with a bag hanging out of my side. They kindly said they would try to save my bowel -- if they couldn't it would mean two bags. Oh joy. The arse probes were obviously to see if my bowel was ruptured (it is, due to the cancer). Who would have thought it could get so complicated? Just as an aside, when I told my friend this he mentioned that he used to play rugby with a guy who had a colostomy bag -- and no one ever tackled him... Every cloud..

I said radiation isn't painful, but towards the end I had to have brachytherapy which meant going under general anaesthetic four times and each time they would insert some weird stuff into my vagina and when I woke up it would be bloody painful, and would be reduced to begging for drugs (morphine and ketamine seems to do the trick. I pointed out to the doctor that he could get a fair amount of money from that out on the street and he gave me a withering look that said: "And you really think you're the first wag to come up with that one...") Then they scurry out of the room and blast you with radiation for 15 minutes.

I've had countless blood transfusions which isn't painful but is very boring. And why is it that I always, but always, end up in the bed next to the mental woman? There's always one no matter which ward you go into and she's always in the bed next to me. I told the doctor once that I was discharging myself and wasn't going to stay the night (they wanted me in for observation for one of my numerous ailments due to the cancer) and he wouldn't let me go. But I pointed to the woman in the next bed who was making such a racket moaning and wailing and talking in tongues and asked, "Does she sleep?" he said, "I don't know; I only work the day shift.." And I quite categorically said, "I'm outta here." He thought about it and said, "You've got a point. I'll put you in a different ward." Which he did. And I ended up next to another nutter. This one was about 4,000 years old and didn't wail (good), she muttered. Constantly. (Bad.) During the night she kept up this tantra and kept throwing all her clothes off and furiously masturbating. This, you can imagine, deprived me of sleep. When I got out of bed to go to the loo, all I could think of was "don't look.. don't look.... don't look", so of course I involuntarily looked just at that one moment, the very only moment that she had a moment of sanity and we made eye contact and she gave me a look as if I was the Devil's own spawn for being such a pervert and watching her in such a state. What can you do?

And don't get me going on the pervy radiation guy who used to stare transfixed at my vajayjay while I was trying to get my knickers back on after each session. I thought I might be being paranoid, so I put him to the test and came in one day wearing a tiny red thong (I have quite a nice bottom) to see if there was any difference in his "staring". Well, naturally, it turned out to be his day off, so the two slightly bemused female nurses got a rare treat instead.

In nearly all cases, from what I've heard, cervical cancer is caused by the HPV virus. But in my case, I don't have that, so the doctors presume it's from years of smoking (how exactly they think I've been smoking my cigarettes, I don't know. Call me Monika Lewinsky?) But joking aside, there is supposed to be a connection, so, Ladies, that's another thing to take on board.

Being sick is also very expensive -- loss of earnings, hospital bills etc.

Now, last time I went to the doctor, the MRI results said that the cancer was back. The radio and chemo worked first time round, but left me feeling very sick and also sterile. This is ok because I've never wanted children, but it could be a dreadful blow to most women. This time it appears the cancer is back at Stage 4 which is as bad as it can get. The doctor just said, "Have you looked into palliative care?" He said an operation was out of the question, my body can't handle any more radiation and that the only thing he could think of was a different type of chemo which would probably make me very sick and had a less than 5% chance of working. Now, the first time I had chemo they took me off it early because it was "doing me more harm than good" and over the past year or two I know from experience that "a less than 5% chance" is doctor speak for "clutching at straws". I mentioned this to said doctor and he nodded his head slowly and said, "Yes, but that's all I can offer you." I took a moment to absorb this and said, "Hey! If I'm really on the way out, does that mean I can drink and smoke as much as I want and not feel guilty?" And he said, "Knock yerself out."

Stu, I don't know if you want to use any of this information, but as we all know, a lot of cancers are treatable if they're just caught in time. It would be great if you could somehow help people to think about their health and prevent or cure this dirty little disease. I'm only 39 and could kick myself for not just going for regular check ups!

Stu says : The important thing is getting diagnosed at an early stage! An erstwhile young acquaintance who lives nearby has breast cancer and I don't think she is going to make it :-( Just because you are young doesn't make you immune to the big C. Another young (24) friend in Berlin has leukemia, but it was caught early and he's been through chemo and radio and things are looking up for him :-) Another -older- Berlin friend is due to start treatment this month. An erstwhile acquaintance and another close friend - both my age - have had to have prostate OPs. After the subsequent rehab and anti-incontinence training they are now leading normal lives again.

Two of the more common screening tests for prostate cancer here in Germany are the DRE and PSA tests. DRE stands for digital rectal examination wherein the doctor shoves his gloved, lubricated finger up your backside, feeling for the shape, size and hardness of the adjacent prostate gland, maybe even 'milking' it. Ouch! Unpleasant, but not really painful. Some guys gays even like it ;-)

The PSA test measures the blood level of prostate-specific antigen, an enzyme produced by the prostate (The risk of prostate cancer increases with increasing PSA levels). So you merely have to give a blood sample. Although a low PSA test is good at excluding cancer, the PSA test does register a lot of false (high) positives. PSA levels can change for many reasons other than cancer. Two common causes of high PSA levels are enlargement of the prostate (benign prostatic hypertrophy (BPH)) and infection in the prostate (prostatitis). It can also be raised for 24 hours after normal ejaculation, which for younger men may mean almost continuously ;-) The excess false positives imply that, even with a high PSA result, you still have only about a 10% chance of having a malignent cancer :-) Unfortunately, it needs a painful biopsy the confirm or deny the PSA result :-(

So you go to an ambulatory clinic and drop your pants, whereupon they leave you standing around in a draught for an hour ;-) Then you have to lie sideways on a couch while a pretty nurse squeezes ice-cold lubricant up your backside and across your pubic bones before going off for her tea-break or whatever. Then along comes the doc - accompanied by a number of nurses (maybe some hobby-proctologists and the caretaker too), all of whom will watch from short range while the doc shoves a cold steel probe up your rectum, while quoting a theme line from 'Dads Army' - "They don't like it up 'em you know!" . So I farted loudly, making them back off a yard or three ;-)

The doc then waggles the probe around gayly (sic!) whilst positioning the gun via an ultrasound pic from the sensor he scans across your pubic bone. Then BANG, the probe shoots a spring loaded needle, subjectively about the size of a rhinocerous's horn, through the wall of your rectum and into the prostate gland, capturing a sampleof the flesh therein. This biopsy is repeated five more times (thankyou Samuel Colt!) leaving you a whimpering heap. No anaesthetics, did I mention that?

You are then given a towel and a crap-nappy for the next six hours and told to sod (sic!) off home to wait for the results which take a couple of days to arrive. What they don't tell you is how difficult it is to drive home without actually sitting on the driver seat ;-) Next and subsequent occasion, I took a toroidal 'piles' cushion with me ;-)

Histological examination of the six biopsy flesh samples will indicate whether you have cancer or 'just' benign prostatic hypertrophy (BPH). If the former, they will whip out the whole prostate on short notice, leaving you with some urinary incontinence which required thee weeks retraining (learn how to piss again) for each of my friends. In the case of BPH, I repeat the painful and messy biopsy every 6 months just to be sure the high PSA is not indicating a malicious cancer. TEST EARLY AND OFTEN!

Why do she and I both emphasize early diagnosis? This table gives the grim answer. Column one shows the stage as diagnosed, column two the percentage of patients surviving after 5 years. Grim prospects indeed!

As you see, you need to catch the cancer as early as possible. And keep a stiff upper lip, rather after the manner of W.E.Henley's 1865 poem "Invictus (unconquered)"

Out of the night that covers me,
Black as the pit from pole to pole,
I thank whatever gods may be
For my unconquerable soul.

In the fell clutch of circumstance
I have not winced nor cried aloud.
Under the bludgeonings of chance
My head is bloody, but unbowed.

Beyond this place of wrath and tears
Looms but the Horror of the shade,
And yet the menace of the years
Finds and shall find me unafraid.

It matters not how strait the gate,
How charged with punishments the scroll,
I am the master of my fate:
I am the captain of my soul.

A couple of useful links :-

• Cancer guide overview
• How Is Cervical Cancer Staged?
• prostate cancer
• Breast cancer checkup movie

Again, get your cancer checks done annually, readers, even if inconvenient!
As my lady co-author points out :
"I had absolutely no idea there was anything wrong until it was too late :-("

So, fellow bloggers, please link to the permalink provided below to help spread this message. Nonbloggers should mail the permalink to friends, asking them to read this.

Comments (13) :
Ina (D) wrote "I posted what you have written on your blog today on my facebook profile... it really is a wake up call :-( Thanks for sharing this though. "
Chip has provided a link. Thanks, Chip (=Sterling).
Four Dinners wrote a longer mail, from which I have excerpted "Cancer. At 39??? Oh hell. I'm so so sorry. I've never asked for a check as I've had 'tummy trouble' for several years ..... it wasn't cancer as, after 5 years I reckoned I'd be dead. Many of the on going examinations took in things like the prostate. They couldn't get a camera down my throat though - quick gag reflex. Eventually they gave up as I threatened to punch someone and gave me a general (anaesthetic) On waking up my throat felt fine. "All ok Doc?" He turned around and I'd given him a black eye. I had no idea!!!! Love and hugs to the young lady. How can you show such spirit and humour ? ..... Extraordinarily brave! You take care old bean" Stu replies : prostate check with a camera down your throat? Just how far do they push that thing in? Still, probably tastes better than doing it the other way around ;-)
Anke (D) wrote in German, so I excerpt and translate : " I read this yesterday . . . the lady is to be admired, . . . I wish her all the best! "
Jenny (Ibiza) asks "Best wishes for your co-blogger! If they punch through your rectum into the prostate, isn't there a chance of an infection? And do you get shit in your ejaculate?" Rather intimate questions, lass! :-( ... But in the name of science.... You get a strong preventative antibiotic starting 3 days before the biopsy and lasting a week. The ejaculate is bloody for a few days, so it is best to empty it manually(!), avoiding blowjobs for a week, if that's what you REALLY wanted to know ;-)
Keith (NZ) felt sick "I'd rather have not have known all that!" Be that as it may, Keith, don't let it put you off going to your GP (=Doc) for a DRE and PSA checkup!
Rachel (Israel) commented: "Oh how sad! I wish her a successful treatment. I've booked a wipe(?) for next week because of her story; please tell her that !" OK, Good!
Joseph A Nagy Jr (USA) tells us his cancer survival story : "Thanks to Sterling (=Chip), I saw your post on cancer and I must say, I commend you (and the bravery of your female friend for sharing so much of her story) for making this post. As you may (or may not) know, I am a cancer survivor. Stage II synovial sarcoma of the left elbow (it's the same cancer that Robert Urich had near his groin which eventually killed him), though I'm not sure if it was IIA or IIB, probably B as they were very worried about its size and the fact that it was still growing with intensive radiation therapy. I was diagnosed 5 January 1995, before my 17th birthday (19th of May). You are right in saying it can strike you at any age. When I was staying at the Ronald McDonald House (a place where parents and pediatric patients can stay while receiving care) I was a personal witness to just how young some of the patients were (it broke my heart to see 6+ year old's bald from chemo, and it still makes me cry to think that some of them didn't make it (one in particular had leukemia, a particularly virulent cancer that has taken someone I cared deeply about while she was still a teen (we were in the same grade))). I can proudly say that I've been in remission ever since at least September of 1995 (and probably since before then, seeing as how they told my parents I had received too many rounds of chemo)."
Marie (F) said "Thankyou both for writing so humourously about a sad and difficult subject; that way we could actually stand to read it all the way through. Well done!"
Liz (Wales) [no, not that Liz Wales ;-)] wrote : "Since Husband had cancer nearly 20 years ago he's been much more willing to go and check things out with the doctor, and to pay attention to his health. Cancer focuses the mind like that."
Barbara O'Brien (USA) who blogs progressively at The Maha Blog and sometimes at Crooks and Liars (she tells me) read this article and wanted to do a guest post and for me to link to a commercial site of hers. However, I turned her down as this is not a 'health'-centered blog, nor do I link to commercial sites. Nevertheless, if you are interested in her progressive agenda or in health issues, I can recommend the links given above. Nice to see an alpha-blogger reading here sometimes, I'm sure it'll help get my co-blogger's message across :-)
Blake (Canada) asked "..... if there is any correlation between testosterone and prostate cancer? " Have to research that for you Blake; stand by, I'll get back to you.
Don (USA) tells us about a US VA scandal :- Nuclear Commission fines VA over 97 from 116 BOTCHED prostate cancer radiation therapies :-(

Copyright ^© Stu Savory on March 12, 2010 permalink Comments Email

Valleys of Neptune

Comments (3) :
Wendy (Oz) tells me that Led Zeppelin have a song called Boogie with Stu and goes on to say "I don't know what kind of music you like, Stu, but apparently Robert Plant gets annoyed when people say that Led Zeppelin is Heavy Metal. It's not; it's mostly folk music. Having said that, this one's not very folky, but it made me think of you (and I like the mandolin)." I range as widely as Rammstein and Zakk Wylde and Janis :-)
Four Dinners : "I will certainly have a listen to this! Hendrix was 'before his time' and died before his time came!"
Rick (SF, USA) quips : "Aren't you glad this album went one planet further out? ;-)"

Copyright ^© Stu Savory on March 11, 2010 permalink Comments Email

Magic 1089 :-)

Think of any three digit number with the digits in decreasing order (e.g. 952). Reverse it (e.g. 259) and subtract this from the original (952-259=693). Reverse this and add it to the intermediate result. The answer will always be 1089 (e.g. 693+396) ! Useful trick to know to win a pint in the pub. Don't do it too often though ;-)

U.S Freshmen / UK schoolkids can run through the algebra to prove this result :-)

Copyright ^© Stu Savory on March 10, 2010 permalink Comments Email

Birthdays today :-(

• Yuri Gagarin, cosmonaut, would have been 76.
• Bobby Fischer, chess champion, would have been 67.
• Mickey Spillane, author of detective novels, would have been 92.
• Barbie Dolls, introduced 51 years ago today by Mattel and still going

Only the good die young . . .

Copyright ^© Stu Savory on March 9, 2010 permalink Comments Email

Packing Pyramids

J ust last week Alicia asked about optimal packing densities for polyhedra; this is a partial answer, just covering tetrahedra, the only current research I'm following.

Turns out that there is quite a race going on to prove lower bounds for the optimal packing density of tetrahedrons! Back in 1972 Ulam conjectured that ALL convex bodies can be packed denser than the spheres I talked about last week. So where do we stand today?

Aristotle claimed the answer was 100% (like for cubes), and because he was Aristotle, everyone just believed him for 1800 years. Not until the 15th century did anyone (Regiomontanus) actually try! In 1904 Hilbert (he of the famous '23 problems' list) asked about the crystalline (regular) pattern densities. Minkowski set the lower bound at 9/38 (~23.7%) in the same year. Quite a while later, in 1961, Grömer upped it to 18/49 and Hoylman proved this to be the maximum for crystalline pattern densities in the same year. But what about irregular patterns, can they be denser?

Yes! Conway and Torquato found a pattern in 2006 with a density of 71.66%, still below Ulam's conjecture. In 2007 Chaikin, Wang and Jaoshvili went to the toy store, bought a bunch of tetrahedral game dice, and shook them up in a big box getting a density of 75% +/- 3%, thus confirming Ulam's conjecture for tetrahedra :-)

Elizabeth Chen (2008) found a packing with 77.86% density. Almost immediately Torquato and Jiao pushed it up to 78.2%, followed by Haji-Akbari with 78.37%. Then Haji-Akbari achieved 78.58%, overtaken by Torquato and Jiao with 82.23%. Xmas 2009 and Kallus, Elser and Gravel reached 100/117 = 85.47% only to be passed again a few days later by Torquato and Jiao with 85.551%. Now Elizabeth Chen has jumped back in with 85.635%. The race continues, it's by no means over yet!

Me? I haven't found a packing over 80% yet, I'm dragging my heels :-( Go, Chen, go!!

Copyright ^© Stu Savory on March 8, 2010 permalink Comments Email

Attended the 5th PB/DT GeoCaching Event on tuesday and and grabbed^* (inter alia) this GeoCoin, a fine example of pride in the British Empire. I'm sure 4D will like it too :-) The Coin is owned by Hitch2162, an ex-pat who now lives in Austria. So my lad, from one ex-pat to another, here is the map of your GeoCoin's 35-hop travels so far :-)

GeoCoins travel the world as owner's surrogates from cache to cache, hitching hops from other members of the worldwide geocaching community. I have put it in GC24E52, my new mystery cache in D-33181 Fürstenberg, for the FTF^** to grab :-)

Comments (1) :
Hitch2162 (A) wrote : "Hello Eunoia ! Thanks for the link , nice to see you were interested in my Geo Coin ! Best regards from the hills of Styria !"

^* Actually, I was too fast, BakedBeans hadn't even logged it in at the event :-( I always deposit GeoCoins in advance in the event's log & had assumed everybody else does that too (because it saves mix-ups like this). Luckily the pre-event and post-event hops are pretty much in a straight line, so the GeoCoin mileage will not be effected :-) My bad though for not reading that BakedBean had not pre-logged the Coin into the event :-(

^**Kleiner Dino (aged 8). It was also his 50th Cache. Congratulations!

Copyright ^© Stu Savory on March 5, 2010 permalink Comments Email

Filling boxes with balls : proof too hard to verify :-(

The question is simple "What is the densest packing of spheres in a cubical box?"

The answer is not so easy. There are just three crystalline (=periodic) packings for identical spheres: cubic lattice, face-centered cubic lattice, and hexagonal lattice. In 1611 Kepler (the same guy who came up with the discovery that the planets travel in elliptical orbits) showed that in a cubic lattice the spheres occupy PI/3*root(2) =~ 74.048% of a large box. He conjectured that this would be the maximal packing density. Not until 1831 was Gauss able to prove this for lattices. But what about non-periodic packaging? Can that get any denser? Can you (dis-)prove it?

So we did an experiment at a local primary school. We borrowed a large box from the caretaker and hundreds of table-tennis balls from a local club. Putting the balls in the box (and shaking it to let gravity pack them as densely as it could) repeatedly gave results just below Kepler's maximal packing density. The finite box size was the limitation, but at least the primary school kids had fun :-)

In 1958 Rogers showed the upper limit to be 77.963557%. Not until 1986 did Lindsey lower this upper bound to 77.844% followed 2 years later by Muder with 77.836%. Hayes proved Kepler's conjecture (upper bound = PI/3*root(2) even for non-periodic packaging) in 1998. But I have a problem with this. Hayes' proof is over 250 pages long and makes extensive use of computer calculations which need 3GB of storage space. Who could verify the proof? It would take over 20 man-years of effort!

The result? We believe Kepler's conjecture but can't verify Hales' proof thereof :-(

Comments (5) :
Alicia (A) asks "Obviously cubes can reach 100%, but what about filling a box with the other polyhedra of which the sphere is a limiting case?" Needs a separate post.
Pergelator has a couple of questions : "What are the relative dimensions of the spheres and the box? Are the boxes dimensions an even multiple of the spheres dimensions? Are there other arrangements of spheres besides the densist ones that would work better for odd sized boxes? And what, if anything, does this have to do with the way the big 3 automakers used to compute the volume of the trunks of their cars, which was to fill them with golf balls and then count the golf balls? Let's go bowling now, everybody's learning how..." Box is waaaay larger (~∞) than the balls to minimise the fractal problem. The latter is why automakers need to define the size of the measuring instrument (golf balls) used for measuring irregular volumes. Actually, I just looked at this as I'm trying to catch up in the tetrahedral packing race which has erupted over the last few months. I'll tell you more about that monday next week, OK? Personally, I think they use golfballs so that automakers top management can then buy the new golfballs as 'used' dirt cheap. Corruption is not limited to Greece ;-)
Jenny (Ibiza) asks "What's the fractal problem?" Need a separate post for that too.
Ed (USA) complains "Hey man, back off! Keep the Math simple for us eejits!" Wilco:-)
Four Dinners : "Balls and boxes. I have no idea why I like this as I have no idea....if you see what I mean..;-)"

Copyright ^© Stu Savory on March 3, 2010 permalink Comments Email

FlashFiction Competition ;-)

FlashFiction Competition being organised by Dan O'Shea
Under a thousand words each story. 
Church-based locations, but
King James version not compulsory.

Yankees being blasphemous
Online and  selling their stories
Under value,  'cos all are amusing.

Good writing, neat tales, including one from Four Dinners.
Obligatory reading I'd say, if you're looking for eternal
Damnation.

FWIW, this is agnostic acrostical ;-)

Comments (2) :
Alun (UK) laughs "Had to look up 'acrostical', but that's neat. Well writ, ya twit :-)"
Anna Pashen (Oz) found something even more painful ;-)

Copyright ^© Stu Savory on March 1, 2010 permalink Comments Email