Monday, March 30, 2009
The REAL Star TrekASA has recently launched a telescope - Kepler - specifically designed to look for Earth-like exoplanets orbiting other stars. Once found, the next obvious wish is to go there for a closer look, having already buggered our own planet. But how to get there? We have no Warp drive like Captain James T Kirk, Spock, Scotty et al, and so our only alternative would be a relativistic rocket - sez our friend Albert.
Such a colony ship would not be like the Enterprise, think more along the lines of Noah's Ark. The most comfortable continuous acceleration for Terran occupants would be one Gee, indistinguishable from Terran surface gravity, sez our friend Albert again.
Now c = 1 lightyear per year and g = 1.03 lightyear per year2, so plugging these numbers into Albert's special relativity equations tells us that it would take 3.6 subjective years to reach Alpha Centauri (4.3 lightyears away), assuming we turn the relativistic rocket around mid-journey, turning thrust into braking, to arrive slowly. However, to get to Vega (27 lightyears away) would only take 6.6 subjective years and the centre of our galaxy (30,000 lightyears away) would only take 20 subjective years. Indeed, our neighbouring Andromeda galaxy (2 million lightyears away) would only take 28 subjective years! So doing a Star Trek is all feasible within a human lifetime, thanks to tiiiime diiiilaaaation, sez our friend Albert. But calling home is a different question :-(
And then there's the question of fuelling this relativistic rocket with its continuous 1 g of thrust. The most efficient (100%) I can come up with is a Photon drive - specifically a Gamma Ray laser - powered by combining regular matter with anti-matter. The fuel tank would have to be non-material, so probably magnetic, so the antimatter would have to be kept in an ionised state all the way into the annihilation chamber. So for the trips mentioned above, I did the maths and calculated how much annihilation fuel would be needed :- A mere 38 kg to Alpha Centauri, 887kg to Vega, but nearly a million tons to the centre of our galaxy and a whopping 4.2 thousand million tons to fly to the Andromeda galaxy :-( . . . so for that we'd need an antiproton-scoop Ramship :-(
There are a couple of other minor(?) problems too. As you get up to c you head into increasingly energetic cosmic rays and other particles (interstellar hydrogen) . Even the cosmic background radiation is Doppler-shifted until hot enough to melt all known materials. And of course, as you blast off, you bathe Earth in the intense Gamma rays of your exhaust plume, not exactly a good idea for those left behind :-( Conversely, you would announce your impending arrival by a high intensity blast of Gamma radiation pointed straight at the target planet. This is not guaranteed to assure a friendly reception from any indigent advanced population; they might shoot back! :-(
Saturday, March 28, 2009
Remembering Adam Riese450 years ago today, Adam Ries died. We all remember him gratefully, here in Germany. He wrote 3 books about a simple method of doing arithmetic, in German. That way, the common people learned how to do arithmetic and could check the workings of merchants etc., thus avoiding being ripped off :-) Before this, the only texts were in Latin and even used Roman numerals. Ries used Arabic numerals throughout. His textbooks were the standard arithmetic textbooks for over 200 years in Europe. This picture is a scan of my facsimile copy, rare originals are WELL beyond my pocketbook ;-)
What was it like, doing addition in Roman numerals? First of all, you had to get rid of any subtractive prefixes, converting them into additive suffixes. Thus IXX (19) would have to be rewritten as XVIIII. Next you just concatenate the two Roman numbers. So 19 + 129 say, becomes XVIIII CXXVIIII. Thirdly you must sort the letters from large to small, getting CXXXVVIIIIIIII. Replace e.g. groups of 5 Is by a V, pairs of V by an X etc, getting CXXXXVIII. Finally, conversion back to the usual subtractive prefixes - if appropriate - gives us here IICL (=148 as we would expect).
Subtraction has its own algorithm, but is just as easy. Change any subtractive prefixes into additive suffixes, as above. Example XCCI-LXIX (191-69) becomes CLXXXXI - LXVIIII. Looptag : Eliminate any common symbols that appear in both of the numbers to be subtracted, that would be the L and an X and an I in this example, leaving CXXX - VIII. Consider the largest remaining symbol in the smaller number (here the V). Find the first symbol in the larger number which is bigger than it, and expand it. So in this example an X expands e.g. into VV and we have CXXVV - VIII. Loop back to the looptag, eliminating common symbols again (this gives us CXXIIIII - III in our example) as often as necessary until nothing is left to subtract. Convert back to subtractive prefixes if appropriate (here we had CXXII, which is 122, correct :-)
Multiplication can be done by the Russian peasants' method, using binary arithmetic. But doing division in Roman numerals boils down to repeated subtraction since they would have not known about the Newton-Raphson iteration. In practice, the Romans used a variation of the abacus, using small stones in little pits hand-scooped in the ground.
So Adam Riese's method, pushing coins along & between lines and recording results in Arabic numerals was a great improvement and was very popular until the 18th century.
Friday, March 27, 2009
How many guns are enough?ecently there has been a school-shooting in Germany, killing 16 people, mostly teenage schoolgirls :-( The killer - a former pupil at the school - ran amok with his father's Beretta P92 9mm pistol, which had been left lying around in the parent's bedroom. The teenage boy had a record of being psychologically disturbed (depression), having been in treatment just last year, the national press reported.
Needless to say, this has caused much heartsearching discussion in the national media, in particular about which steps could be taken to prevent a repetition.
Firstly, German law requires that ALL firearms be kept in a locked steel cabinet and the munition be stored elsewhere. It would seem that the killer's father (the owner of the guns) had broken the law here. Then it turns out that the father - a registered member of the local shooting club - had 18 (eighteen!) guns (all registered, the press reports). I ask you, who NEEDS 18 guns?
I would guess that 80% or more of people here own NO guns. Our hunting cabinet contains just three, (a shotgun, a hunting rifle and a pistol). Who needs more?
The boy had been training with air-guns since he was 11, it is reported. Firearm training is only allowed to those over 14, afaik. The 17 year old lad was also an avid user of Counterstrike, an ego-shooter program in his PC (I deliberately avoid the use of the word 'game'). He also played Gotcha, which I understand is shooting at people, albeit with a low-energy softair rifle. How much do these hobbies desensitize you? Enough so that he shot his soft-air gun at other children not even playing the 'game', nor wearing any protective equipment, witnesses reported in the national press :-(
What is my shooting experience (pistols), you may ask?
My favourite was a
TOZ 35 small bore (.22") free pistol.
The Free Pistol target is 50 meters away & has a 10 ring of 5cm diameter, each ring increases by 5 cm.
Just for macabre comparison purposes, someone poking up his head just enough to see over a wall 50 meters away
(½ head = 13cms exposed) is the size of the 8-ring, not to hard for a
In practice though, a pistol is almost a point-blank weapon. This killer fired 112 shots killing 16 people, ALL with head shots at point-blank range. He missed all of the shots beyond 10/15 yards. For macabre comparison purposes, rapid fire pistol competitions are held at 25 meters with human chest-size targets.
As far as rifles are concerned, the longest sniping hit ever was at 1½ miles. The Bisley (UK) big-bore ranges are at 1000 yards and 300 yards. But if you look at the usual (deer)-hunting distance, it's probably 100-200 yards, even with telescopic sights. But these numbers here are irrelevant because amok-killers always go for the short distances typical of ego-shooter (e.g. Counterstrike) scenarios :-(
So what could done as prevention measures? Well, I understand that the UK has banned handguns competely. Ego-shooter programs could be banned for minors ( under 18), although I doubt that would stop kids getting a copy. Similarly, the minimum ages for 'Gotcha' and firearm practice could be raised (e.g. to 18). Keep classroom doors locked as default rather than just in known emergencies. Spot checks on gun-owners to verify their weapons were stored properly. Target-shooting clubs could be restricted to small-bore and/or single-shot weapons. No weapons in the household if anyone there has a known mental problem / criminal record. All these approaches are under discussion, we shall see what the politicians implement.
Of course society trains people to kill : soldiers, secret-service agents, martial-arts practitioners, not all of whom are even-tempered. You can't untrain them either, nor in the case of the martial arts freaks even disarm them. A dangerous latent skill set :-(
In Switzerland, soldiers got to take their assault rifles home. I assume that's still the case, it certainly was when I lived there. The rules differ in different countries. So I would appreciate comments from other gun-owners (e.g. Kees Kennis in South Africa) about the situation in their countries. What do your politicians/police do to prevent gun/knife crime? And how effective are these measures? Are they any use at all?
She who will not be named (Belgium) wrote (in my translation) : "Afaik, amok-killers are going for police-assisted suicide! Here (Belgium) - as in Holland - we do not forbid euthanasia/assisted suicide as you do in Germany, although it is forbidden (theoretically) for juveniles. In a recent survey here, 90% of hospital staff were pro-euthanasia." Any mistakes in this translation are mine (Stu). I'm not sure how that answers the question; I think he wanted revenge on the girls who spurned him. Surely the point is to make illegal access to weapons more difficult, not to make suicide easy?
Joseph A Nagy Jr (USA) wrote : "Take a look at crime statistics here in the U.S. New Hampshire has the most lax gun laws in the nation. Rate of crime (gun related or otherwise)? Lowest in the nation. Washington, D.C. has the strictest gun laws in the nation (not so strict since a recent supreme court ruling, but not statistically significant, yet). Rate of crime (gun related or otherwise)? Highest in the nation. Both numbers are per milli.
It is the experience of many gun owners that living in a state where the gun laws are so lax, or at least have reasonable concealed carry laws, that the rate of crime drops due to the criminals fear of being shot (according to a survey done of criminals from areas with such lax gun laws). The unstable and criminal element will always find a way to try and bring death and destruction to others. A gun is just a tool as much as a knife or any other weapon is. Should the unstable have guns or weapons of any kind? No, I don't think so. But the genie is out of the bottle. You cannot put it back in again."
Gwyneth (Wales) took the official line :
"Peidiwch a dibynnu ar eraill. Os ydych chi'n amau rhywbeth, rhowch ybod i ini." Shades of 1984, lass,
do we really need a nation of denunciants? Look at the old DDR Stasi for a bad example worth not repeating :-(
Drinking Sapphire Wine (writing from Australia) commented : " I'm an odd case for Australia - definitely not a typical example if that's what you're interested in. I have never fired a gun/rifle. We had an air rifle at my house when I was a kid that had a childproof lock on it that my father lost the key to about a week after getting the rifle. He was advised to have it as we lived on a farm and there'd been a problem with feral dogs. We also had a lot of restricted drugs on premises as he had a home emergency GP clinic for when farmers had medium level injuries in our area. The rifle was around for a year or two (unusable and I don't even think we had ammunition for it. Then we sold it off and put security screen on instead and built an enclosure so our dogs had a protected area in case feral dogs managed to leap the fence. I don't like guns. Won't have one in my house. In my experience though they can have a real purpose, they usually end up in the hands of drunk farmers arguing over a boundary line or a teenager suffering an acute bout of depression.
After the mass murder in Port Arthur some pretty strong gun laws were introduced in Australia along with a buy back scheme. Hand in your guns (legally procured or otherwise) and get some money. It then became harder to get permits and there were all sorts of limitations imposed.
A large number of people living in rural areas have rifles to shoot wild pigs, feral cats and other pests but also to cull the kangaroo populations. Though it has a purpose, it is also a widely engaged in sport (by creepy violent rednecks IMHO) and is often rather more brutal than is publicised. Dogs are often used in conjunction with rifles. The most common result of these events from what I can gather is people shooting their dogs or people accidentally shooting each other while their dogs get torn to shreds by wild pigs. Occasionally people get attacked by their own dogs or the pigs which gives me a warm glow.
Gun violence in Australia isn't terribly bad - but whether that bears any relationship to the laws, I have no idea. We lose far more people to car accidents annually than we do to gun related violence.
Computer game violence as a contributor? Well I am undecided. From a very early age I watched the Conan the Barbarian film obsessively but I am yet to pick up a sword and decapitate anyone. I do think parents need to be far more responsible for the media (TV, film, games, internet) their children are exposed to. Many advertisements and primarily the news these days, are not something I would want a small child seeing though and it's harder to restrict. I know more and more people who are restricting media in their house due to their children (as in the TV cord is removed not just unplugged when the parents aren't watching with them) but there is only so much parents can do as well.
I am a believer that pistols shouldn't be available to the public - I would like it if the police didn't have them also because no one is immune to human error. There have been numerous cases in Australia of police shooting someone suffering a mental illness (but was harmless) because they are trained to go for their gun and were nervous. I agree with the UK law in that respect.
A girl my age shot herself in the face at 20-something years of age with her parent's shotgun. Not something anyone could anticipate but of course a gun furore amounted as a result along with calls to ban various bands that she listened to. She suffered from depression and on a downward swing a shotgun was available and she acted stupidly. A friend's son did similarly but in that case hung himself. No one banned rope. I think both incidents are equally horrible and the primary thing to address there is depression not the mode of death.
*shrugs* It's not an easy thing for me to have an opinion on. There are always people who will do extreme things due to their mental or emotional health. I think strict gun/rifle laws are necessary to limit the number of incidents. I don't think it will solve societies problems but I think it could help.
I thoroughly agree that society trains people to kill, when their time is served are soldiers/police properly re-trained/de-briefed before re-entering society? I don't think they properly are over here. In a town I lived in, there have been numerous cases of army guys torturing animals - they get desensitised and "amped up" from training but then are expected to play nice and behave like normal members of society. So they go out and torture animals or get into huge brawls or, in one horror of a case, throw Molotov cocktails at homeless people - a similar problem is had here with football players. These incidents seldom involve guns.
Perhaps gun restriction is the first step but investigation into violence in society is a very long walk. Over here there is the usual touting of violent games and marijuana ("the gateway drug" according to the Howard government) as true evils causing violence. Most of the pot-heads I know sit down and play games for 6 hours straight and eat themselves obese while listening to 'Moby'. Violence is the last thing on their mind - Chinese takeout is usually the primary though. Alcohol is a massive part of "Aussie culture" and every domestic dispute I have witnessed, every major brawl ending in accident or injury has occurred in conjunction with excess alcohol consumption (often also involving disputes relating to their romantic involvments - we could ban relationships "Brave New World" style?).
Gamers don't tend to drink hugely - ruins their high score. ;P
Oh and on a last note, there are gun collectors just as there are stamp collectors. My uncle is one and he was intelligent enough to have the firing pins removed along with a few other things so they were merely a collection. He got broken into and some of them were stolen from their locked display case. I have no doubt that firing pins etc were replaced and repaired and they went into circulation. Gun collections shouldn't have to be outlawed but it is terribly easy for them to be turned into working guns. "
Brian (UK) asks what I have against
Gudrun (Switzerland) points us to a very relevant Eddie Izzard excerpt :-)
Decrepit Old Fool (USA) comments : "I grew up in a house that was full of guns; my dad collected & restored antique guns and clocks. It was a matter of pride for him that they were all in working order, even the flintlocks and Civil War guns. We were allowed to own guns at a young age with rigorous safety training. The result is that I could no more point a gun at a person than I could hold my breath for an hour. I don't own any guns today, and my "home defense weapon" is an old golf club. Too many people play shooter games to make a case that such diversions result in violence; something else must be going on. In all the cases I've read about, it comes down to alienation, to bullying, to cruelty. We can try to ban guns but I have no idea how to ban those other things. The most we can do is to raise our children to stand up against them and be kind to the less popular. That, and training for teachers and school administrators. My nightmare is if a truly alienated person with a modest knowledge of chemistry were to decide some mayhem. We would be wishing for the days when they only used handguns."
Wednesday, March 25, 2009
Geocaching 104 :-)
Surprise! There is an overlap between two of my hobbies. For decades, the wife and I have always kept English Bulldogs. The current (mother & son) pair are shown in the sidebar. This year I have taken up Geocaching as a hobby, to motivate me to get more outdoor exercise. I've blogged about it here and here and here. Recently I sent a DIY trackable Geocoin on its way, said GeoCoin has its own blog, tracking its travels from Geocache to Geocache. Just recently I was surfing for a more professional trackable GeoCoin and found the one shown on the right, marketed by a firm in England.
Must get a couple of these GPS-carrying-bulldog coins for my bulldogging friends :-)
In the meantime, here's a
fascinating geocache for my Scottish readers. Old Edinburgh!
Monday, March 23, 2009
The first 200 miles...y new plaything has arrived! A Triumph Street Triple, as mentioned to you back on February 13th. It has 675 cc three cylinder engine, producing 98 hp (reduced from 106 hp to halve the price of the insurance :-)
This is one OK machine, and the 3 little cylinders are surprisingly torquey. I even managed to get the number plate I asked for, OK! Obviously I'm still running it in, so I haven't banked it over all the way down to the edge yet, still ˜6mm rubber to go ;-)
It weighs 100 kg less than my big long-distance tourer (an FJR 1300) which I still have. This makes it much more agile, with very light handling and superb brakes. So in the curvy canyons, winding woods, and heady hills I should be able to leave the big bikes standing, once I've run the bike in properly (just another 800 miles) ;-)
The cockpit has an analog revcounter with gear-change LEDs on the right. The speedo (below the rev-counter) is LCD digital, which is new for me; I would have preferred it to be analog. There is a multi-function LCD display to the left of the rev-counter. Lots of stuff I don't need like a lap-timer, maximum and average speed (71 kph so far) recorded, avg. fuel consumption (6 l/100km so far). There is NOT a countdown fuel-gauge, just a lamp when you are on reserve(50 km). The fueltank is small, refuelling when the reserve lamp came on was after a mere 240km (150 miles), I'm used to over 400km on the FJR, so I'll have to keep an eye on that. The LCDs (including the tacho) are all but illegible in bright sunlight, so I've learned that 2500 rpm in 4th trickles me through villages at 30mph, and 6000 rpm in 6th gives me ˜70 mph for the country roads. Calculated max is 216 kph (˜135mph?), calculated because I'm still running it in.
What needs changing? The mirrors give me an excellent view of my own elbows, so I'll be adding after-market extenders to the mirror arms. And because I'm used to the fully-faired FJR, I'm finding the naked bike breezily cold (OK, OK, it was only 4°C on thursday and friday); so I'll add a little windscreen. Otherwise, I'm happy with it :-)
Sunday, March 22, 2009
Baaaaa-d Baaaa-Studs Rule, OK!
What an awesome lot of effort & enthusiastic planning went into this choreography :-)
Ewe-Tube from the hills of Wales! Creative shepherding rules!! Go, sheepdogs, go! :-)
Saturday, March 21, 2009
Killer Condoms :-(nce again, Benny 16, Pope of The One True Church™ , whose whole religion is based on a Miss-conception, has put his red Gucci-shoed foot in it! After his PR disaster reinstating that holocaust-denying anti-semitic Pious bishop, he is now proclaiming that 'condoms make the AIDS situation in Africa worse' or words to that effect.
Giving him the Benny-fit(sic!) of the doubt, he's merely saying 'Go forth and multiply'. But even that is wrong in this overcrowded world. Stupid eunuch!
But maybe he'd just been reading the article I've reproduced on the left, which is living(?) proof that condoms can kill ;-) Perhaps this is the only method of wearing a condom approved by The One True Church™ ? Your inchage may vary ;-)
Friday, March 20, 2009
Early Japanese Classics restored, on show recently.
Paul Gockel's Honda CB500 Four, beautifully restored.
Michael Gockel with his father's Honda CB750 on the left,
The Kawasaki 3 cylinder 2-stroke H1, spindly framed inspirer of terror (in the rider!).
My very own 1970 Honda CB750 in its 2008 Cafe´ Racer guise,
Wednesday, March 18, 2009
Homework, 1953 :-)ust found an old exercise book in an old case in the attic, containing my 1953(?) primary school maths homework; something mother had kept. The writing is all but illegible now, so here's a transcript and a contrast-improved scan of the sketches I made. Quite insightful for a 9 year-old little lad, even if I say so myself :-)
To Do : Get area of a circle.
Figures drawn :
6 Steps taken to get answer :
See fig. 1) Area of a rectangle is height H times width W (by definition).
See fig. 2) Area of a parallelogram is width times height too. But the height is the dotted line. The two triangular bits at the ends add up to a rectangle, so I can use the whole width W times dotted height H.
See fig. 3) The two triangular bits at the ends in Fig 2 added up to a rectangle. So the area of this triangle is H times W times ½ twice (left and right halves).
See fig. 4) This is a hexagon made from 6 equilateral triangles. So the area of the hexagon is 6 times ½W times H. Now 6 times W is the perimeter length. So the area of the hexagon is ½H times perimeter length. If we split each triangle down the middle on the dotted line, the area would still be ½H times perimeter length.
See fig. 5) This is a circle of radius R (= H so far). If we split into lots of thin triangles, ever so thin, the area would still be ½H (=R) times perimeter length. So very many very thin triangles make it look like a circle [Remark 2009 : hey, looka dat! Intuitive grasp of integral calculus at age nine already!]
Step 6) But perimeter length = Pi times 2 times R (by definition).
Remark 2009 : I see I got an A+ for method, but a C for neatness. Story of my life:(
Tuesday, March 17, 2009
St. Patrick's DayAn Irishman, one Paddy O'Murphy, proposed to his girl on St. Patrick's Day.
He gave her a ring with a synthetic diamond. The excited young lass showed
it to her father, a jeweller. He took one look at it and saw it wasn't real.
The young lass on learning it wasn't real returned to her future husband, and protested vehemently about his cheapness.
'In honour of St. Patrick's Day, ' he smiled 'I gave you a sham rock.' ;-)
So there there were these gays from America touring Ireland and looking for a little bit of action in the night life. But in Cork they couldn't even find a single gay bar. So they asked a barman and were told "Sure and there's none in Cork, but you could try Dublin". So they drove north and tried there. Again no luck, and in Dublin they were told "Sure and there's none in Dublin, but you could try Belfast". So they drove north and tried there. Again no luck, and in Belfast they were told "Sure and there's not a gay in Belfast, but you could try the top northwest corner of Northern Ireland, in the little town of Derry". And Begorrah, all the gays of Ireland were gathered there, breathing heavily, because they were enamoured of the Derry air ;-)
It was St. Patrick's day again but Murphy didn't want the green coloured beer again. The previous night, a barman had mixed Creme de Menthe into his Guinness to turn it green. Murphy's toenails grew so suddenly, curling down, that they had tipped him over backwards, which would explain his headache the following morning.
So he decided to go for a Paddy Cure ;-)
Once there, he had to wait his turn, so he sampled from the jar of green-coloured peanuts on the counter. When his turn came, he remarked about their peculiar taste and asked how they'd managed to dye the peanuts green. "Sure and you shouldn't have eaten those. Dey'se not peanuts, Dey'se leper corns!" :-(
Monday, March 16, 2009
Unfortunate Given names ;-). . . what WERE their parents thinking?
In the UK, the BBC has recently reported about a parenting website which has collected some of the worst given name - surname combinations. Just how (very?) embarrassing to their bearers are these :-
Anna Sasin, Barb Dwyer, Barry Cade, Carrie Oakey, Daisy Picking, Doug Hole, Hazel Nutt, Ivy Plant, Jenny Taylor, Jim Hall, Jo King (sic!), Justin Case, Mary Christmas, Olivier Moron, Paige Turner, Pearl Button, Rob Mee, Sidney Harbour-Bridge, Simon Swindells, Sue Mee, Stan Still, Terry Bull, and (forestry worker?) Tim Burr.
The original BBC report is to be found here.
And of course in MY school, the register was sorted by surname, and the names read out surname first, then given name. So I know how the folks mentioned above feel ;-)
PI-day, March 14, 2009
PI Day Mnemonicsoday is PI-day, the way Americans write dates (3.14). And so at precisely 33½ seconds to two (1:59:26.5) the electronic clock will show 3.14159265, whereupon we will celebrate PI-day by reciting the following mnemonics, wherein you merely need to count the number of letters in each word in order to get PI :-)
Then there is the traditional competition, reciting the first 100 digits of PI error-free. To do this I have a whole mnemonic poem, it starts like this ...
Sir, I bear a rhyme excelling
However, in the 32nd decimal place we come across the first zero; I use a special mnemonic exception to get around this problem, saying "Oh!" :-)
Interestingly, in 1995, David Bailey, Peter Borwein, and Simon Plouffe came up with an efficient way to calculate the N-th digit of PI (albeit to base 16) without having to calculate all of the previous digits! By 'efficient' I mean that it is linear in time and only logarithmic in its space requirements :-)
PI = SUMk=0 to infinity 16-k [ 4/(8k+1) - 2/(8k+4) - 1/(8k+5) - 1/(8k+6) ].
Friday, March 13, 2009
The Devil's Staircaseiding my trusty steed through the Harz mountains last summer, I saw a hiker's signpost "Teufelstreppe" (Devil's Staircase) whereupon my mathematical mind thought 'this I HAVE to hike', so I parked the bike and went for a walk. Indeed this hike is mostly horizontal, but the vertical bits are really steep. It is a natural staircase, alternating vertical risers and horizontal flats (well, nearly) and the devilish thing about it is that the risers and flats are all different sizes, so you can't take a rhythmic run up or down them ; rather like the staircases in Scottish castles. The narrow spiral staircases in Scottish castles also have stairs of different sizes so an attacker can't run up them. They also ascend clockwise so that a right-handed attacker is carrying his sword on the tight inside of the spiral and thus has rather limited manoeverability. The top step is usually very high, emerging through a low door, so any attacker emerges with his head down, making it easier to cut off ;-)
But anyway, where was I? Why did the Devil's Staircase trigger my mathematical mind?
There is a mathematical function known as The Devil's Staircase, see sketch on the left. Express any number 0 < X <1 in base 3. Truncate the base 3 expansion after the first 1 digit. Rewrite all 2 digits as 1, so there are only zeroes and ones in the number, so we can interpret it as a base 2 number, calling it Y. Plot Y against X to get the irregularly stepped function shown in my sketch.
Remember that I told you about Cantor Dust points on 28th December? Remove the middle third of a line recursively and the points left behind are the Cantor Points? Our function Y is not differentiable at the Cantor set points (where the 'risers' are vertical), but has derivative zero (=horizontal flats) everywhere else (= practically everywhere) because Y "rises" at the Cantor points whose total length is zero. Devilish indeed ;-)
Of course it would be the crowning pun if the Harz Mountains park rangers would allow this magic square to be inscribed on the rock at the top of the Devil's Staircase :-
What's devilish about that? All the numbers in the square are prime, no repeats, and the rows and columns and diagonals all sum to 666, the number of the beast ;-)
A worthy magic square for a Friday the 13th, don't you think?
Thursday, March 12, 2009
Suum cuique :-("Suum cuique" translates literally from the Latin into English as "To each his own," but idiomatically means "To each what he deserves". And of such stuff is political correctness, and/or hypocritical newspaper reporting made. Plato used this phrase ("to ta auton prattein kai me polypragmonein dikaiosyne"), as did Cicero (106BC - 43BC ): "Justitia suum cuique distribuit". Prussia's King Frederick the Great used it as his motto, and it is still used by the German military police (the Feldjäger). The Nazis used it as propaganda tho', wrought in iron on the gate of Buchenwald concentration camp.
And so, when a schoolchildren's arm of a Christian political party innocently used it to plead for keeping the 3-tier secondary school system, their seniors fell upon them, stopping the action and the national council of Jews got their knickers in a twist :-(
In parallel, the Vatican is worried about such thorny problems as : When Jesus was resurrected (to perfection), was his foreskin (previously chopped off by a Mohel) resurrected with him? And pleading birth control and abortion should be illegal.
Meanwhile Bristol Palin and her boyfriend (temporary Fiance´until the US election blew over) have split up, leaving granny Sarah to look after the bastard. If they'd been Democrats, they would at least have had the birth-control and/or abortion options (not sure about that though, guess I'll have to ask John Edwards ;-)
Meanwhile, Roman Catholic and Orthodox Jewish officials in New York are mounting an intense lobbying effort to block a bill before the State Legislature that would temporarily lift the statute of limitations for lawsuits alleging the sexual abuse of children. Well, I'll be buggered, how surprising that lobbying effort is!
While all this was going on, we have a
Hell, I'm glad I'm an Atheist. Suum cuique!
Wednesday, March 11, 2009
High-Security keyboard ;-)
Ancient keys, some of which are fakes (for decoration only) as you can surely deduce because the keyhole end has a hole in it. Keys property of my artistic friend Claudia.
Now here's a mind-blower for you :- We live in a world of 3 spatial dimensions; these keys are in principle 2-dimensional and are rotated in the 3rd dimension to perform their intended function. Now the $64,000 question for my geeky blogreaders is :- "What would keys (and locks) look like in a world of 2 spatial dimensions?"
My reply to "Is it even possible to live in only two dimensions?".
Our digestive tract in 2D would either have to be shaped
interlockingly like a jigsaw-puzzle piece or it would divide us into two halves so that we fell apart ;-)
Or it would be a blind alley(mentation) and we would have to crap by regurgitation :-( Sick transit, Gloria ;-)
Now think about housing. All accomodation would have to be subsurface lest any high building stop people walking about. Therefore the entrances would be flaps in the ceiling, horizontal when closed so that others could walk over them and opened by lifting up/dropping down. NOW you can maybe think about locking them....
Writing from Switzerland, Genevieve quotes Don Marquis, a
US humorist, thus :-
Monday, March 9, 2009
Bank Angles :-)Chance blogreader Ines from Spain had been googling for any news or blog articles about street fighting on Friday 13th as a result of the economic downturn, she tells me. One of the assemblies of search words she used was "Friday 13th street fighting banks economist stock market profligate spending". As chance would have it, Google failed her, returning my blog as the most relevant site ;-)
She then got distracted and read my article, which mentioned my new motorcycle in spe. Off topic, she tells me she has never ridden a motorbike and asks "How far can you lean them over before the wheels slide out from under you sideways?"
Well it depends on your ability (and fear), the grip of the tyres and the road surface. I probably bank it over about 5° on ice, 35° in the rain and about 45° in the dry on grippy tarmac. The tyres I use would allow 53°, so I like to keep 5°-8° in reserve.
The photo on the left, taken by the rear-pointing camera on Alex's Fireblade, shows your truly in the foreground. Alex's bank angle can be judged by the apparent slope of the grass verge. As you can see, I'm banked over slightly more than Alex, else the bike would appear vertical. But there is plenty of space under my inside boot and I'm not even hanging off the saddle. The photo on the right shows blogreader Doctor C42 on his Triumph, who is also using a conservative angle of bank. The sketch in the centre shows about what is maximally feasible on a public road, some 50° off vertical.
Now a racing motorcycle uses 'slick' (=treadless) tyres with very soft rubber (which only lasts about 120kms!) and race-track surfaces are very grippy, so the racers can lean over another 10° or so. They also 'hang off' the inside so as to keep the bike more upright for better ground clearance. Left is Carl Fogarty, right is Valentino Rossi.
Subjectively, Ines, it looks like this to the rider - taken with a forward-looking video camera - the stills show Braddan Bridge (left) and Quarter Bridge (right), both on the TT circuit of the Isle of Man, which is a public road merely closed for the races.
As you see in the racers' photos above, those guys feel for the road with their knees to check their bank angles, which is why they have those hard slider pads on the knees of their leathers. Personally, I'm more old school/conservative; I feel for the road with the edge of my boot (gets ground down every season, needing a cobbler visit :-)
Saturday, March 7, 2009
Data Presentation 101 ;-)
Homework assignment :
Friday, March 6, 2009
To tow, or not to tow ;-)This YouTube Video is for those of you who have ever had your car towed ...
Wednesday, March 4, 2009
School Science : a cheap DIY spectroscope :-)s many of my regular blogreaders will know, I sometimes get invited into (secondary) schools to give the kids a motivational and interesting lesson. I've blogged about teaching kids codebreaking ( here, and here) and teaching two different unusual ways of multiplying ( here and here). But now it's a Physics lesson. We built a DIY spectroscope to demonstrate quantum theory to 11 and 12 year-olds.
First we took an empty cereal-box (family size, cornflakes as it happened) as shown in this cross-section sketch. Then we cut a slit across the narrow side (on the right here), about four to six inches down from the top.
Next we cut a peephole - about one inch square - in the top of the box; this will be our viewport for looking at the spectra we make.
Thirdly we cut a slit at 45° through the box in its left side. The slit is about 1/10 of an inch wide. Then we took a discarded CD (one of those old AOL giveaways) and - wearing safety glasses - snapped it in half across the edge of a desk. We put the CD into the 45° slit and held it in place with some black duct tape (to keep any stray light out).
Hey presto, our DIY spectroscope was finished, total cost under 1 Euro !
First off, we pointed it out the window to see the spectrum of sunlight. Ignoring for a moment the narrow dark lines of absorption spectra (not readily visible in such a simple spectroscope as this), we could thus show that the thermal emission spectrum is continuous, red-orange-yellow-green-blue-indigo-violet, the ROYGBIV mnemonic.
Then we looked at the spectra of three different lamps I had borrowed, left to right here, they are an Argon lamp, a Neon lamp and a Mercury lamp. Each has its own set of spectral lines, I explained why later (see the section on Bohr's atoms below).
Finally we looked at one of these new-fangled flourescent lamps designed to replace the simple lightbulb, which also appear to give white light like a regular bulb does.
Next up, of course, was to explain WHY we see separate lines in these spectra.
I outlined Nils Bohr's model of the atom as a central nucleus with the electrons flying around in certain fixed shells (ALL explanations are 'lies-to-children', just in varying degrees of sophistication). When electrons fall back from a higher shell into a lower one, they emit a quantum of light (=the squiggly lines in my sketch). Because the shells have certain fixed levels, the quanta have specific wavelengths. These are the different colours we see here. Each element has its own characteristic spectrum of colours, some with few lines (like Mercury or Sodium) and others with lots of lines (like the Neon spectrum , above), i.e. you can identify stuff from its spectrum.
"But how does our DIY spectroscope work? There isn't a prism in it!" one bright child asked. Well that's because the CD is made up of a lot of parallel (if curved) lines and so acts like a diffraction grating. But then the end-of-class bell rang, so I had to leave them to look up 'diffraction grating' in Wikipedia for their homework.
I was subsequently told that over half the class had made their own DIY spectroscopes at home, so the lesson must have gone down well. Budding physicists, all of them :-)
Why don't you try this too, at home? Science is FUN!
Monday, March 2, 2009
Geocaching 103 : Your own cacheeocaching is a modern treasure hunt hobby using a handheld GPS receiver to find hidden caches. I gave you an introduction in Geocaching 101, and covered the internet based tracking system in Geocaching 102. Reread for background.
Today I want to tell you about making your own cache. This example is my second cache, the first was merely a plastic 35mm film can with a logroll; very boring. This second cache was designed to be more attractive. Of course it had the obligatory log book and pencil, but let me tell you about the rest of the contents I put in it :-)
I chose a Tupperware box big enough for a 3½ inch floppy - transparent so that anyone suspicious of it could check the contents without opening it (these are terrorist times ;-) - and labelled it as an official geocache, asking any random finder (known to insiders as Muggles ;-) to please leave it where they found it. See photo left. Inside I put half a dozen sundry initial swap-items - discussed below - see photo right. Geocachers who want to take any of these items have to swap-in an item of their own.
Contents, left to right. Gutschein fuer FTF is a freebie ticket for the FTF (First to Find). I put one of these in all my caches,
it entitles the FTF to a free coffee at my place, whose coordinates are encoded on the card.
That way I hope to benefit from talking to experienced enthusiastic hobbyists.
Coordinates encoded to discourage Muggles ;-)
All printed items are laminated to make them waterproof, lest the Tupperware box leaks.
Continuing in the photo on the right : a shooting medal from Milano (Italy) as hint to a further hobby, a box of matches from a hotel in Scandanavia I can recommend (swiped on one of my bike trips) , a paper clip and a pencil sharpener to go. Total value < 10 €.
Finally, for many Geocachers the most interesting content, a trackable 'Geocoin'. See photo left. Actually this is an old shooting medal of mine, the 1971 international Lake Constance pistol competition. Instead of using a professional tracking service, this item is trackable in a DIY way. The instructions are printed on the back (and waterproofed). They say the medal wants to go home, but can only move south. Any finder takes the GeoCoin and puts in any other cache south of this one, mailing me where he/she found it. Sometime it should reach the town hall in the town of Konstanz on the Swiss border :-) Progress from cache to cache is (to be) tracked on the website stated.
I placed this cache nearby, quite a nice view, to encourage the people who prefer quick 'drive in' caches. For any Geocachers reading this who want to see what happens to the cache , it will be called MMIX-B at www.geocaching.com :-)
Five visitors on the very first day, all wanting to be FTF :-)
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