Eunoia

Saturday, January 31, 2009

SF : Through Alien Eyes...

R emember that in 2008 a lady ISS astronaut let go of her toolbag and it went sailing off into space? Well it will probably re-enter the atmosphere and burn up there. But let us suppose instead that it drifted off for ever into space and was found at a later time by a race of aliens cruising by who had had no contact with any humanoid race so far. They come from a system poor in metals, their's is a ceramic spaceship, all joints are sewn and/or glued.

What would they make of it? What can you deduce just by doing non-destructive testing? Well, you can deduce the size of human hands easily enough (assuming you know what a hand is ;-). How do you group things into sets together? Why are the things we call spanners (and the screwdriver) magnetised? What do the set {pliers, hammer, screwdriver, axe} have in common that they need(?) insulating handles? Is it coincidence or design that the ring spanner has the same internal(ring end) as external(open end) across-flats distance? Why is the screwdriver tip black? Why is the hammerhead waisted? Why does the double-open-ended spanner have different sizes? Why does only the English wrench have adjustable jaws? Why are the hammer and axe handles not made of metal? Why the open spanner heads offset? Why is the axe handle red? And most of all, why are they all made mostly of metals?

Assume for the moment that you are a tiny tentacled alien (no hands), or a dolphin even, but with a powerful brain. What could YOU deduce from this mixed bag of stuff? Apart from the obvious fact that they are well preserved artefacts of spacefarers? Answers please on a stamped, addressed xyfgwhl by Monday, alternatively by Email ;-)

Comments :
George, alias Decrepit Old Fool, wrote on March 23rd :-
"If the aliens built spaceships I'd have to assume they were able to manipulate objects. They'd also have advanced knowledge of chemistry and metallurgy assuming they came from a planet with metals. Which if they didn't, they'd figure out that we did. Of course the aliens wouldn't confine themselves to non-destructive testing, and they'd figure out the tools are a ridiculously tough chrome-vanadium steel alloy. That would suggest that they are designed for application of torque and force. Clearly the pliers are force-multipliers, and the wire-cutters concentrate that force along a thin line so they must be cutting implements. The compound leverage and locking feature of the Vise-grips is for additional force and for holding, which suggests that the creatures who built it have a limited number of articulated limbs. They'd be able to get some idea of the size of our hands by the dimensions of the tools and the travel of the pliers. They might think the screwdriver is a prying implement. Black tip is easy - the chrome plating might come off so the black phosphate tip is less vulnerable to corrosion. Which suggests it interfaces with something so maybe it has some function other than prying. The hammer claw a prying device. They'll be scratching their brain cases about the waisted hammer tip, though."

Brilliant! Well deduced, George. You did better than most of my students :-)


Friday, January 30, 2009

Lordy, Lordy :-(

M ilord, art thou corrupt? Or, at the very least, "ethically challenged"?

In the UK, Labour peers are prepared to accept fees (of up to £120,000 a year) to "amend" laws in the House of Lords on behalf of business clients, a Sunday Times sting investigation has found. Call them bribes? Naw! Lobbyists' fees!

Actually, I'm astounded that ANYBODY is surprised by this, after all it has been going on in the House of Lords for five hundred years or more! I recollect that as long ago as the late 16th century the scottish poet Alexander Montgomerie wrote bitterly :-

		My Lords, late lads, now leiders v our lauis,
		Except your gouns, some hes not worth a grote,
		Your colblak consciense all the country knawis;
		How can ye live, except ye sell yr vote?


Thirsty, January 29, 2009

Explain, McCain!

I'm sure that there is a perfectly reasonable and innocent explanation for this photo. Even without anyone having to call Bill Clinton as an expert witness ;-)

Well, I'm not sure that this close-up shot would count as a reasonable explanation ?


Wednesday, January 28, 2009

Getting too Highbrow(se) again?

Several of you - specifically Morag(Scotland), Gro(Norway), Thunderbutt(USA), FourDinners(England), Wally(Oz) and Ffiona(Eire) - have complained that my blog is getting too highbrow again, and want me to simplify it some more.
OK, OK, wilco. Indeed, checking the stats, I seem to have lost about 100 daily readers recently. FourDinners sums it up : "Bloody hell old bean. I have reached the conclusion reading your blog is inadvisable at 01:30 a.m. on a busy night shift. My brain hurts!!! ;-)". Ffiona says that the maths is (are?) too heavy, and sent me this link to Billy Connolly discussing algebra for non-mathematicians. Enjoy!

So I'll reduce the maths to thrice monthly, and make the blog more lowbrow, OK?

Thankfully, Joseph (USA) counteracts with this positive comment :-
"I don't think you're getting too highbrow, Stu. I enjoy the maths posts as they get me to thinking about a subject I usually ignore (the only maths I was ever good at in school was trigonometry, go figure)."

Before I stop doing maths (fat chance!), Jean-Luc (Belgium) wants to know "if the expansion of PI contains the digits 0123456789 in that order?" Well yes, isn't that obvious? But I can't tell you where exactly :-( Look, PI is irrational ( proof here) and so has infinitely many digits, distributed randomly. Thus ANY finite sequence of digits MUST occur somewhere in that infinite sequence. See my blog entry dated 19/3/2008 for examples with sequences of zeroes and/or nines as examples. QED!


Tuesday, January 27, 2009

Golomb rules!

There ain't no such thing as a mathematical dirty joke, it was asserted down at the pub's geeks' meet. So I rose (sic!) to the challenge and gave them one :-

"A mathematician is someone who pops a Viagra to improve the blood flow to his brain and who is disappointed when his problem then turns NP-hard ;-)"

Well, they laughed (being maths-minded geeks) and my joke was accepted as a (barely) adequate refutation. But then Heidi wanted to know what the NP in NP-hard means, preferably with an example understandable to a lay-woman (her own word ;-)

Well,P (polynomial) and NP (non-polynomial) are terms used when talking about computational complexity. There are (P) problems whose solution times grow as a simple polynomial of the number of cases to be considered. If you are looking for someone in an apartment block, you have to look in at most N apartments. If the apartment block were a cube of side S, you have to look in at most S3 apartments.

And then there are the much harder NP problems, whose solution times grow exponentially with the number of cases to be considered (T=k*eN). The traditional example given is the one of calculating the minimal length route for a travelling salesman. But another one is a good exercise to give to schoolchidren, finding the marks on Golomb rulers. Golomb rulers just have marks at whole numbers, there being no subdivision into fractional intervals (half-inch, eigth-inch, tenth-of-a-centimeter etc). The problem I give the schoolchildren is to find the minimal set of marks for a ruler of a given size. This is an NP (exponential) problem.

Consider a ruler to measure up to 3. It will have a 3 marks at 0,1 and 3. You can measure 2 units between the 1 and 3 marks. Consider a ruler to measure up to 6. It will have 4 marks at 0,1,4 and 6. You can measure 2 units between the 4 and 6 marks. You can measure 3 units between the 1 and 4 marks. You can measure 5 units between the 1 and 6 marks. Question for the kids : a Golomb ruler with 5 marks can measure up to 11 units long. Where are the marks? There are two different answers.

Solution times grow exponentially. You might be able to calculate the shortest Golomb rulers with 5,6 or 7 marks as G(5)=11 units long, G(6)=17 and G(7)=25 using pencil and paper only. But G(8)=34, G(9)=44, G(10)=55 and G(11)=72 were only solved by using a computer (in 1972). Continuing up the scale (sic!), it took several months for 12 networked computers in 1995 to find that the shortest Golomb rule with 19 marks is G(19)=246. G(24)=425 took 42,000 networked PCs four years!

The calculation of G(25)=480 took 125,000 PCs 8 years. We are now working on ruler G(26) ; wonder how many computers that will need and how long that will take?

Sizing optimal Golomb rules is NP-hard.


Monday, January 26, 2009

A pronounced difference ;-)

When you ask an American for one word with which they associate their politicians these days, it is "Obama!".
Ask the same of Germans about their politicians and they will say "Erbarme!"


Sunday, January 25, 2009

Scunnered :-(

A ´hm fair scunnered wi' maisel' :-(

It's Burns Nicht the noo - a braw bricht minlicht nicht - and I'm not partying :-(

Fowks whit spak thae Scots leid around the world will be celebrating our national poet Robbie Burns tonight at myriad parties, with steaming Haggis being piped ceremoniously into the dining room, jigs and reels being danced and much uisghe being reverently consumed. It's the 250th anniversary of Burn's birth.

And I'm stuck at home with lumbago (back pain), unable to jig or reel, just hobble :-(

Also, I'm suffering a severe attack of homesickness as a result of this. At least I can revel in the memories of the motorcycle trip I took through Scotland last summer :-

And so the wife (SWMBO) and I will enjoy re-reading the blogged reports of that pleasant trip and consume not a few tumblers of auld whisky by ourselves. Cheers :-)

Poor devil! see him owre his trash,
As feckless as a wither'd rash,
His spindle shank a guid whip-lash,
His nieve a nit:
Thro bloody flood or field to dash,
O how unfit!


Friday, January 23, 2009

Complex Primes Anecdote :-)

The blogosphere is a wonderful place! It brings together people who would not otherwise normally talk to each other ;-) Just this month, I got an eMail from Wendy Laubach, a Houston (Texas) lawyer and Republican contributor, so to say "Out of the Red" ;-) She had a maths question and anecdote about the complex primes, and here is the gist of our conversation, with my explanatory notes added.

I already blogged about me re- discovering the complex primes, back in december of 2006. Follow that link if you want to refresh your memories / look at a sketch of them.

Anway, enough intro, here are Wendy's anecdotes in her first mail :-

I'm trying to remember a story my father once told me about a table of the complex primes. Something about a Dutch mathematician who was forced to work for the Nazis in occupied Holland. Supposedly he had been laboring to create a huge table of the complex primes of the sort pictured on your website. He snookered the Nazis into believing it was an important research project that would further the war effort in some incomprehensible way, and convinced them to allocate a lot of manpower to him for the purpose of expanding the pattern. They worked on it happily for years.

After the war, the Dutch mathematician sold the pattern to a fabric manufacturer, which made tablecloths or some such thing. My father (John Kilpatrick) said that a colleague of his at Rice University in Houston, Texas, used the pattern for the black and white tiles in his kitchen and great room. He experienced tremendous difficulty in impressing on the workmen that the pattern had to be followed exactly. He made them tear up and replace errors every morning. The same guy was supposed to have had a proof of the 4-color theorem built into the dividing lines of his screen door.

To which I replied :-

"The Dutch POW may have known that the complex primes (Gaussian integers) are computationally hard to find, being combinatorally explosive, and so might be useful for a cryptographic system (=codes/codebreaking), which is why he could interest the Abwehr in them. The 'pattern' is irregular, if there were a pattern, we would be able to predict whether a number is prime. As it is, we have to try all the divisions. That is why modern cryptography uses the factorisation of very large numbers made by multiplying two huge primes. The multiplication is easy to do, but the factorisation is hard, so this is a one-way function (like a trapdoor). BTW, the proof of the 4-colour theorem (4 on a plane, it's 7 on a donut) is very long, and would not have fitted onto a screen door even in a 6 point typeface. So that one is certainly just an urban legend :-("

Upon retrospection, that is an anacronism, public key cryptography using the factorisation of very large numbers was not invented until the early seventies. The first (secret) invention of asymmetric key algorithms was by James H. Ellis, Clifford Cocks, and Malcolm Williamson at GCHQ in the UK in the early 1970s, preceding Diffie-Hellman who rediscovered it in 1976 and went public with it :-(

Regarding the Complex primes graphic, Wendy responded :-

"I think what my father said was that the complex prime graph was random-looking within each quadrant, but each quadrant was repeated, which caused the whole graph to look somewhat radially symmetric. Symmetric probably isn't the right word, but the pattern had a clear center, spreading out evenly from dense at the center to thin at the margins. The origin of the pattern was a post that marked the corner of the kitchen, which took up one quarter of the roughly square open-plan living area. But yes, the exact placement of each little black square was unpredictable to the eye and had to be figured out by painstaking attention to the chart. So you can imagine the consternation of the workers, who felt that a black square moved a little to the left or right could hardly matter to anyone -- then their crazy client would show up and proofread and insist that this black tile had to go HERE, not THERE."

Wendy's dad's colleague's floor tile pattern would have looked like this when done :-

Let me also point you to a graphic of the complex primes at Wolfram's MathWorld.

As regards the map-colouring door anecdote, I replied to Wendy thus :-

"4-colour map ? : there is a map on a torus of just 7 countries but which needs all 7 colours. Maybe that was on his door? See http://enderton.org/eric/torus/torus2.html ".

The fundamental group of a torus is Abelian, so you could unwrap it onto a door.

Wendy responded "The torus map requiring 7 colors must be what was on the screen door. It's consistent with what I remember of the story, and it would make a reasonable pattern..... Wouldn't it be fun if some blogreader recognized the Dutchman's Complex Primes story and knew more particulars?"

Although Wendy and I may never agree on politics, we do share a common interest in things mathematical. And the blogosphere brought us together, which is what makes it such a wonderful place, a global village indeed, everyone adjacent :-)

Also, Google tells me that Wendy does have some surprisingly liberal views on foreclosuring HOAs(sic!), worth reading for any US homeowners reading this blog. So there are indeed some political issues where we get pretty close to one another :-)


Wednesday, January 21, 2009

Geocaching 101

My wife has a poor sense of direction, and so wanted a hiker's GPS for Xmas. That way (sic!), when she goes out with the dogs on her own (when I'm away) for a walk in the woods, it won't be left up to the dogs to find where she parked the car ;-) That's her motivation she said, (that, and finding shops again ;)

So I bought her a Garmin eTrex H (see the photos below), for under €80 at Amazon. The package also contained a leaflet on Geocaching, a GPS-exploiting treasure hunt.

You consult one of the Geocaching websites and choose a cache you want to seek. The site gives the latitude and longitude of the cache. You set these coordinates into the GPS (see photo, left) and - following a compass-display (see centre photo) which points to the cache - you drive/hike to it. Accuracy of the GPS is within about 10 meters, so you need to use your eyeballs at the end. Tip : approaching the cache from two different directions (90° apart) will give you an intercept within a foot or two, making the eyeballing task much easier. For control-freaks, the GPS collects odometer stats too (photo right), if you need to know your speeds, mileages, exercise times etc.

The cache will usually be a waterproof plastic box containing a logbook and pen so that you can log your visit. There may also be a small toy etc. as a 'treasure'. If you take this, you are morally obliged to replace it by one of your own. Replace the cache exactly where you found it for the next Geocacher. When next online, go back to the same website and log your visit. This is politeness to let the cache-owner know of the activities at, and the condition of, his/her cache. Simple? Yes. But we'll do it for the (dogs'/our) exercise. But some of the caches can be hard to reach, I'm told. Imagine hiking all the way up a ravine only to find you are on the wrong side of the river :-(

But to quote the German poet Goethe (1749-1842) "All theory, dear friend, is grey..." (Faust, part 1). And so we had to try out this new-found toy. I asked the GPS for the coordinates of our house and then consulted Geocaching.com for the nearest simple cache, which turned out to be less than a mile away. Waypoint programmed, excited dogs leashed, off we hiked. It being early january at the time, it was around twenty below (Celsius) and in three feet of snow, hardly ideal hiking conditions :-(

Arriving within the proximity zone of the cache, which turned out to be about +/- 6 meters, the likely hides were a) in a niche in an old stone wall, b) under a bush and c) in a (hollow?) tree. The search was made more difficult by the 3 feet of snow and the -20°C temperature, nor did the dogs know what they were supposed to be sniffing. Third try lucky: under the snow, the roots of the tree turned out to be hollow and there was the cache, a waterproof blue plastic box with loglist and a Donald Duck toy.

Was it exciting? No! Well, for the dogs, yes, and maybe for a juvenile. But not really a hobby for me. But maybe this one was too easy, or the inclement weather was putting me off. So I decided to talk to experienced Geocachers. The aforementioned website gave the coordinates of a pub for their monthly meet, and so I decided to gatecrash it.

Luckily, the website had named the pub too, because the coordinates turned out to be 150 yards off (not a good advert for the hobby, I thought). There were some 25 people there, I sat at a table of eight. All very friendly, patient and helpful with my newbie questions, like "What makes this hobby fun? Why do you do it?"

As I suspected, the traditional cache find type (as I had done) was too simple for many and so they make it more difficult for themselves. One example : multiple caches. The website takes you to the first of several. This cache contains the coordinates of the next one and so on. Or it contains a puzzle/quiz/code which you have to solve in order to get the coordinates of the next cache. Iterate as desired for more difficulty. An example I was given had cache 1 being in the skull of a dead feral pig in the woods, cache 2 was a tiny piece of paper hidden in a discarded snail-shell stuck up a tree-trunk etc; all deviously inventive hiding places :-)

Geocachers do it for the scenery and for the 'excitement' of the search, I was told.

Then there are "Travel Bugs" (numbered dog-tags) in some caches. You take these with you, look up their number online to find their purpose/destination and deposit them in some other cache 'nearer' to that destination. Example: "I want to go to Manchester (UK) and then return to Detmold (Germany)". The website DB says it has been enroute for months, but still hasn't left our state (NRW) :-(

There may also be a beautiful "coin" (self-medallion) which you can report having seen. The owner gathers satisfaction from these reports, I was told ;-) ??? Several were circulated in the pub. And of course you can organise "Flash Mobs" as events too :-)

And so, part of the enjoyment is to have hidden your own cache(s), tracking the discoveries thereof via its database entry on the website, I was told. Similarly for your own "Travel Bugs" and "Coins". WTF? I guess I'll have to try this before I pronounce judgement though; maybe surrogate travel is enjoyable? Certainly cheaper!

Nobody seemed to have any paranoic or privacy concerns about their travel patterns being tracked by the black-helicopter brigade, although in the US the FBI has exploded some caches on the basis they might be something terrorist (typical US paranoia?). Just as well the Geocacher didn't get shot on sight, the Yanks would do that! In fact, I bet their Department of Homeland Security already has a classified category ready for this kind of suspicious people (i.e : the Cachers Under National Terrorism Suspicion) ;-)


Tuesday, January 20, 2009

Jimi's Inauguration Day Tune :-)


Monday, January 19, 2009

End of the Bush Era tomorrow :-)

And so this is my last chance to quote this excellent Thanksgiving cartoon for you ;-)


Saturday, January 17, 2009

Ditching...

... is the word used to describe having to put a landplane down in the water. Today I want to give you a sketch of the quick decision processes of the pilot who had to ditch his Airbus in the Hudson River (rare open space in NY) earlier this week.

I am one of those pilots who has seaplane and floatplane ratings, and thus have had some experience of 'landing' on water (see photo, left). My good friend Klaus, a real-estate agent in Alaska who flies his clients out to remote lakes, has of course many more hours in his floatplane than I do and MUCH more water experience. Every little helps.

According to press reports, the pilot took a birdstrike shortly after take-off. The (heavy?) bird went through one of his two jet engines, destroying it. Jet engines are built to survive a 3 pound bird, but a heavier one (goose etc) will take the engine out. First, you put the nose down to maintain flying speed. Then you identify the dead engine (instruments, or the 'dead foot=dead engine' rudder reaction rule). On a prop-twin you then feather this engine. With a single engine plane as shown in my photo, you do not have a choice you are going down! With a twin-engine plane, you can fly it on a single engine; this is practiced A LOT, and you have to demonstrate it successfully on your multi-engine rating check-flight every six months.

However, it is reported that this Airbus hit a flock of birds which took out BOTH engines, leaving the Airbus as a glider! Only if you are high enough and have enough speed already, do you have the option of turning back to the airport. It's not just a 180° turn, it's shaped more like a question mark to get you back onto the same runway. Even in a single like the Cessna shown above, you will need at least 6 or 700 feet altitude. An airbus needs quite a bit more. That turn can kill you if too tight.

In a steep (=tight) turn at low speed the inside wing will be flying slower than the outside wing. Thus, if too slow, the inside wing will stall, losing all lift, and the plane will flip on its back and spin in. This is not regarded as a good thing (!), so try to land as straight ahead as possible. In a densely built-up area like New York, there is (almost) nowhere to go without hitting skyscrapers. So the pilot made IMHO the correct decision, turned a mere 120° and ditched it in the Hudson river, which is straight.

Ditching means slowing the plane as much as possible until just above minimum-sink-rate, thus reducing the energy of the plane, keep the wheels up if possible (which would otherwise catch the water and tip the plane over forwards, breaking it), then stall it onto the water (nose up) tail first so that the tail takes the brunt of the strike.

The pilot seems to have done this well too, indeed there were NO casualties we were told. Well done, Chesley Sullenberger, rather you than me! Give the man a medal !!

Addendum : Your Questions Answered

I do not have a type-rating for the A320 Airbus, so please send your A320-specific questions to blogging airline pilot Dave, who does. That said, here are the questions I could answer : Speed? An A320 Airbus can fly pretty slowly, about 200 km/h. AFAIK, he splashed down at about 270 km/h (176 mph). Flaps? For the slowest possible touchdown, max flaps and leading edge slats would need to be extended. I don't know if the A320 uses hydraulics to do that, but losing both engines would lose hydraulic pressure, I guess. But on the post-crash photos, flaps are down and L/E slats are out. Could he have made it to another airport? IMHO, no. Kennedy was behind him, further than La Guardia (where he took off). Newark was too far away on the other side of Jersey City. Teterboro was borderline reachable(?), but is a small general aviation airfield with short (for an Airbus) runways, in a built-up area. I know, I've flow in and out of there at night under VFR. He was way above Maximum Landing Weight too! Approach? Speed like I said, exactly level so that a wingtip doesn't touch first, spinning the plane. Then lift the nose more to decrease rate of descent, and slow the plane as much as possible, without letting it stall in even from 20 only feet. Ideally, stall it on splashdown. What happened to the engines then? Nacelles probably tore off when they hit the water; they'll be on the river bed, somewhere downstream. In the water? Afaik, there is no requirement that landplane aircrew can swim. Survival time depends on water temperature, I don't know how cold it was. "With the air and water temperatures at the time of the incident, people could remain in the water only two to three minutes before the onset of hypothermia, said John Peruggia, chief of emergency medical services for FDNY."

Klaus's Komment : Alaskan Bush-Pilot, Real-Estate Agent, & good friend explains :-

You mentioned in your blog about the "famous Hudson river landing" floatplanes & seaplanes, I'm sure not all of your blog readers (especially the non-pilot ones) know the difference... To begin with, most land plane pilots incorrectly refer to all planes as "float planes" or "seaplanes" which are not technically correct terms and causes serious seaplane aficionados to cringe. It is an esoteric point, but a float plane is a land plane that has been fitted with floats, and a seaplane is a plane that is designed with a watertight hull for water operations. As Cessna 185 on floats is a "float plane" and a Grumman Goose is a "sea plane". The definitions are further complicated by the FAA license being one for a "sea plane" regardless of the type used to obtain license.

I started my seaplane rating in 1991 in a Cessna 172, after 10 hrs. we switched to my own Cessna 185 & after 10 more hours I did get my SES (single engine sea rating) private, a more experienced pilot doesn't need 20 hrs for a seaplane rating but at that time I had just 52 hrs total flying time under my belt in a Cessna 150, after I got my instrument rating in 1993 I added on my commercial SES & SEL & MEL also in 1993 ( all this did happen in May 1993 in N-Carolina, ("first in flight") in July 1993 I was also checked out in the DeHavilland Beaver (type rating, flying for hire) to fly our lodge guests around, in 1997 I was checked out in the DeHavilland Turbo-Beaver, with a Pratt & Whitney PT6A-28, 650 hp at sea level, flew that for 225 hrs until we sold it in 1999, my total float time is around 3,000 hrs., 2,500 hrs. of those in Piston-Beavers the rest in Cessna 172, Cessna 185, Cessna 206 & Taylorcraft, I have only 965 hrs on wheels ( Beaver & Cessna 185, Cessna 172), so this year I will break through the 4,000 hr. mark ( other than 35 hrs. in N-Carolina, all flown in Alaska) in my N 8134G, Beaver on amphibious floats, after all this told I have never flown a "seaplane", the ones I really like are too expansive ( Grumman Goose & Mallard with Turbo), but I love the Beaver very much & that is also not a "cheap airplane" :-(

Wow, Klaus has more time on floats than on wheels! I have just over 30 hours on floats, 16 in a real seaplane (a Lake Amphibian) and a mere 9 on skis (glacier landings!), the rest being on wheels, from a 20-ton twin down to my trusty 4000+ hr PA28.


Friday, January 16, 2009

Truth Maintenance & Belief Revision...

... are techniques used in AI (artificial intelligence) to ensure consistency of the AI system's knowledge base. Today I'll give you an easy introduction to how they work.
Oh what a tangled web we weave
When first we practice to deceive.  (Robbie Burns)

If a system contains a contradiction, you can prove ANYTHING in such a system.
This is generally 'not a good thing', as eny fule noes (thankyou, Nigel Molesworth ;-)

Should an assumption prove to be wrong, we need to disregard some deductions made from it. I'll explain in a minute why only 'some' and not 'all'; bear with me.

For this example, I restrict myself to 1st order predicate logic (in particular to Horn Clauses). This will keep the TMS explanation easier (he said, hopefully ;-).

Look at the sketch shown above. If assumption A collapses, then its immediate conclusions ( if A then B1, B2) B1 and B2 become invalid and need to be undone; whereupon their immediate conclusions (C1, C2,C3,C4,C5) become invalid too and also need to be undone. An avalanche (domino effect) may result, invalidating many of the deductions made so far. This showed a simplified forward-chaining system. But things are a little more complicated than that. Please now look at the sketch shown below.

This is a backward-chaining system. We read it bottom-up, not top-down as we did for the previous (forward chaining) example. There is a rule at the bottom which reads IF (B1 and B2) or (B3 and B4) then C. There are four rules deducing B1,B2,B3 and B4 above that which read :-
1) IF (A1 and A2) or A3 THEN B1
2) IF A2 and A3 then B2
3) IF A3 and A4 then B3
4) IF A4 or A5 then B4.

Now let us assume that A3 is an assumption which turns out not to be true.

Then (by rules 2 and 3) B2 and B3 are no longer deducable and thus must be undone. And (rule 1 says) B1 may or may not be deducable depending in whether (A1 and A2) was true. This explains why I used 'some' and not 'all' a couple of paragraphs above.

And so, what a Truth Maintenance or a Belief Revision system does is to roll back all the conclusions which may no longer be drawn, substitute in the new value for A3 which replaces the old one (perhaps timestamping that for accountability/ logging reasons), and then roll forward any chained deductions to be made from the new A3.

Please appreciate that any real AI system may have hundreds or thousands (even tens of thousands) of rules and so there may be a problem doing all of this in real time. This is especially true when there are sensor inputs (many A3s) changing frequently. Also remember that any of the terms (like A3) may also be dynamic rules themselves!

Now why would we build such a thing? To check design documents for consistency. I refer you to wednesday's Brainless Builders pictures for counter-examples ;-) If we encode architects' drawings into the AI system's formalism we could have avoided these expensive mistakes. Similarly (and easier to do), encoding contracts in such an AI system enables us to check them for consistency* (finding the loopholes is another, more difficult, task ;-). The same applies to parliament's new law proposals etc. etc.

Now I haven't gone into issues of global consistency versus having several sub-domains which merely maintain local consistency. This is a blog not a textbook :-)

*"The purpose of artificial intelligence is to fight natural stupidity!" S.Savory, 1983.


Wednesday, January 14, 2009

Brainless builders & asinine architects ;-)

Thanks are due to Thomas B. for the heads-up on these. Mouseover for commentary.


Tuesday, January 13, 2009

Israeli Gaza plan revealed :-(

OMG, the Abrahamistic religions are all basically violent. This time it's the Jews, but the other two are just as bad. If you really need a religion, at least choose a pacifist one!


Monday, January 12, 2009

Spoiling Heidi's Maths Joke ;-)

H eidi, she of the 600cc Honda, came into the Biker's Cafe´waving a piece of computer printout and saying "Hi, Stu, you're a Maths geek, I found this neat little Maths joke on the Internet for you, what do you say to that?".

So, while they were all chortling at the cartoon, I took a quick peek at it and quickly decided to tease Heidi and so said "Nothing!" ;-)

"You've got nothing to say?"

"No. There's just nothing I don't understand about it, lass" I teased her. "The top line is Newton's differential equation for gravitational attraction, using polar coordinates. So we're talking about celestial orbital mechanics. That page is just a derivation of Kepler's laws of orbital motion, showing that the planets orbit in ellipses. surely there's nothing NOT to understand about it!" I teased her, keeping a straight face. "It's all pretty straightforward differential calculus there :-)"

Unfortunately, an amused twinkle in my eye gave the game away, and they realised I was pulling their collective legs. So I broke into my usual rant that almost everyone seems to reject even simple Maths these days, I think because it is taught badly. And that is the wryly sad point behind this very joke, namely that most people will turn off their brains at the sight of even one equation, let alone a derivation like this one :-(

So what can we do to make Joe Public - or his schoolchildren - more numerate? Currently they balk at simple algebra let alone straightforward calculus such as that shown in the joke above. Geometry is forgotten after leaving school, and a majority can't even do enough arithmetic without using a calculator to appreciate THIS joke :-

2 + 2 = 3.9 recurring

which is perfectly true, but annoys most people nevertheless ;-) YMMV.


Saturday, January 10, 2009

Where was I ?

Practice your grasp of spherical geometry and tell me where this picture was taken?

Charles Pergiel came up with the first correct answer, I quote :-

Helgoland!
I made up a spreadsheet with all the data from the picture. 
I used a tape measure and a globe to try and figure out 
where the picture was taken, but all the data seemed contradictory.
Then I realized that the distance to Dune was in meters, not miles! 
And presto chango, we have the result.
I thought about trying to figure out the spherical trig, 
but from my work with the tape measure, 
the data on the sign do not seem very accurate.

Helgoland is correct! Well done, Charles, you are the first with the correct answer. BTW, the Brits and Germany swapped Helgoland for Zanzibar, pre WW1, otherwise that famously overpopulated novel might have been called "Stand on Helgoland" ;-)


Friday, January 9, 2009

My woolly hat :-)

You don't just "buy" these little woolly hats, you have to earn them!

You earn them by doing a volunteer stint as a marshal at the Tourist Trophy and/or Manx Grand Prix motorcycle races on that Mecca for true bikers, the Isle of Man. The races are held over closed public roads - true road-racing - and one lap is 37 miles long. For this reason they need a large number of volunteers for crowd safety, race-track safety, first-aid etc etc. These volunteers are the roadside marshals, with all the privileges and duties of a warranted police officer during road-closure for that fortnight.

The photo shows the marshal group at Hilberry during the 2002 MGP. The young lady in the yellow jacket is a local WPC (policewoman), there because the Governor was visiting that day. Off duty, she rides a mean green 600cc Ninja; given her local knowledge she's just as fast through the corners as I am on a bike twice the size ;-)

No, outside built-up areas, there are NO speed limits on the island, it's the open road! The current lap record is at over 120 mph, over public roads, with tight uphill corners like Gooseneck, hairpin bends (at Ramsey and Governor's Bridge), snaking S-curves across tram-lines (at the Bungalow), and even hump-backed bridges (Ballaugh Bridge).

So , being a marshal means turning out for duty before 5.a.m. because the practice sessions need rider- and track-safety too, but it also means getting to jump the queues in the bakery when picking up the packed lunch you ordered. You also get to see the racing unobstructed, because you are standing on the side of the track :-)

As you can guess, I'm mighty proud of my little woollen hat, pleasurably earned :-)


Thursday, January 8, 2009

The Googling :-)

Heads Up !

Found a neat little set of five videos on YouTube, entitled The Googling.
There are 5 short (under 4 minute) episodes, all paranoically funny and SFW :-)


Wednesday, January 7, 2009

Arachnophilia :-)

I spyed 'er on the web somewhere ;-) I hope she's going after my flies ;-)


Tuesday, January 6, 2009

Back out, shovelling snow :-(

Nineteen below zero last night and another six inches of snow. And since the law requires us to clear the sidewalk after 7 a.m., I've been outside shovelling snow. Deep, heavy snow. Took me 20 minutes to shovel it all off the sidewalk into the gutter, so that the neighbourhood children could walk to school without falling over outside my property (liability issue - due care and diligence - really). Barely had I finished, when the council's red snowplow came down our road (a rare event!) and shoved it all back onto my clear sidewalk :-( Buggerem! Why couldn't they have come by at 6 a.m. as they usually do? So I had to do it all over again. And now as a result I have lower back pain again :-(

What a two dimensional word 'back' is in English. Get 'back in' to form, 'back out' of an agreement, 'back up' your files and 'back down' from a confrontation. But AFAIK, there is no 'back left' or 'back right'. Why not, I wonder ? Well, sailors have backboard* (=port =left) of course, but a 'back right'? Nothing I've ever heard being said. YMMV.


Monday, January 5, 2009

A bit on the side

H aving had a discussion in Chip's comments about the Pros and Cons of full-content RSS feeds, I noticed that all of the RSS-feeds I see all dropped the bloggers' sidebars. Now sidebars are a useful resource collection provided thoughtfully by most blog authors, so today I'll talk about Sidebar Design - meaning what I put in it, where and why - with counterexamples from other people's blogs.

Sidebars contain mostly link lists. The links used most frequently by your blogreaders should be at the top (and thus immediately visible [without scrolling] as the page is rendered). Less frequently used resources can be further down the sidebar. Rarely used links can be omitted as irrelevant. Your site's statistics package should be able to sort the resources by frequency of use. Occasional photos lighten linklist monotony :-)

My happenstance blogreaders arrive - via a search engine - directly into an archive file. And so to enable them to get to the current blog entry quickly the topmost link in the sidebar takes them there. Otherwise it would be difficult for them to get current.

The next issue is that of communicating with the author. If you have a (restricted) comments policy, state it, and show blogreaders how to comment/ register if needed. Your Email address should be immediately visible. I choose to display it as a GIF picture so that spam-bots can not read it, thus saving myself a lot of spam-mail :-)

Next up is a link to a photo gallery. Not many people use that link, so I'll be taking it down soon. Next comes the Impressum, which is required by our German law here. The Maths Trivia link is not generic, but very popular according to my site statistics, which is why I provide the resource there. Readers are also interested in other readers, so the recent readership link [a generic feature again] goes to a map of the most recent 100 readers' locations. It used to go to a list of their URLs, but spambots and scrapers misused that list, so I replaced it by an anonymised map.

A popular feature is the ability to Search this Site. The sitemap, on the other hand, was hardly used and so I dropped it. At a reader's request, the next link goes to Technorati's (superficial) listing of who recently linked here. Next up is the XML for those wishing to access the blog via an RSS feed. My feed just gives headlines, informing you when a new blog posting appears, not full content (pace Chip). Finally, by reader request, there is a link to my YouTube videos. Note that this block of links is always visible when the page first appears, even on a small 800*600 screen. Note also that this block is sorted alphabetically, to make things easier to find than by usage.

Next comes the statistic collector, displaying total visitors so far (bragging?). The little pix-from-the-web button is just a space-filler, for amusement only ;-) This is followed by a photo of the author, so you can see who is blogging fer ya. Anonymous bloggers will prefer to use an avatar here. To personalise my blog, I moved the personal information forward into the sidebar. Others may prefer just to have an "About" link to a separate "Profile" page, depending on the particular blogging tool that they use. By reader request, there is now finally a link to a panoramic photo of where I live :-)

Then comes the blogroll, kept short to the ones I read regularly, sorted alphabetically so that readers can find entries easily, but split into two groups (daily reads and the ones I read at least once a week). The icon that follows defines the target audience as 'Reading Level = Undergrad', I try to write for bright 15-year-olds, but keep drifting UP (I'm opposed to the usual modern dumbing-down, I don't even want dumb readers!). Most blogs don't even define their target audience, so how can they write for it? :-(

The next segment gives the headlines of my recent writings, linking to each one. This list used to be a year long, but was shortened by reader request to two months. The purpose is to let rare visitors get an overview of stuff missed since their previous visit. The headlines provide better orientation than the archives which are merely linked by date, one month at a time. This 2-D list is rarely used by readers, but is there for the sake of completeness. The next segment is the mission statement (most blogs don't even have one); it tells the readers what to expect AND it helps keep me focussed ;-)

Finally, there is a list of group-blogs to which I contribute (=stuff too trashy for this blog), the link disclaimers in English and in German (required by law here), a humourous content disclaimer which is a CYA, and for the people who come for the (ir)regular book tips, a link to Amazon.

Did I miss anything important to you? If so, please mail me.

What is NOT in my sidebar ?
No advertising! I do not wish to insult my blogreaders' intelligence! Nor do I see the need to help Google make even more money ;-) And I don't need peanuts from them!
No blog-awards! Mutual self-congratulation circles are SO smug, it's quite appalling!
No list of recent visitors! I respect your privacy (I just do a world map, see above).
No list of sound bites There are better sources than my eclectic tastes ;-)

Finally, people ask "Why is the sidebar on the right?" Because some search engines only examine the first 512 bytes of your HTML, I wanted them to see the latest blog content which thus needed to be in the left column due to the way the HTML is written. Plus, the latest blog content comes first and thus displays faster since the code for the sidebar comes afterwards and can be slow. Who cares if the sidebar is slow to appear?


Saturday, January 3, 2009

Financial ripoff schemes - old and new

The biggest financial ripoff scheme last year - bailouts aside - was a Ponzi scheme done (by his own confession) by Bernhard Madoff. Madoff is a Jewish banker in New York, so I had thought there would be the usual antisemitic outcry about Jews. This has either been played down by the media or it has been replaced by a quiet Schadenfreude satisfaction when it was seen that Madoff's customers had often been rich Jews themselves. Anti-semitism has been going on since the middle ages - even Shakespeare had his Shylock. Due to the New Testament episode where Jesus cast the money-lenders out of the temple, Christians were not allowed to lend money (or rather, take interest for doing so) during the middle ages. And so that task was left to the Jews who were despised for it. Hence Shylock and anti-semitism.

But that's not my subject today; instead I want to outline some early financial ripoff schemes. Ponzi was an Italian immigrant to the US who ran a pyramid investment scheme in 1920. That is, he promised a high return on investment, and 'achieved' this for early investors by diverting monies from later investors to the earlier ones (and no small amount to himself). This works as long as people keep joining the sheme, but collapses as soon as the new inflow stops or slows down. Entering a known Ponzi scheme can even be rational, in the economic sense, even at the last round of the scheme if a government will likely bail out those participating in the Ponzi scheme. Let's see what happens to Madoff's securities swindle?

Historically, one of the best known early pump-and-dump schemes (combined with insider trading) was the UK's South Sea Bubble (1711-1720). To cut a long story short, the officers of the company sold shares at inflated prices, spreading unfounded rumours about fantastic wealth to be achieved (insider dealing) and selling their shares after inflating their value (Pump and dump). They were later suitably punished by parliament as far as I remember my schoolboy economics lessons. A similar scheme was being run in France at the time by Scots gambler John Law.

The South Sea Bubble* inspired many other proposals. People asked Parliament's (or the King's, I'm not sure) permission to found share-companies for a number of ridiculous activities (parliament later made all these companies retroactively illegal).

  • A share company for trading in hair.I'm quoting these applications directly !
  • A share company for a wheel of perpetual motion, capital one million (in 1720!).
  • A share company for extracting silver from lead, i.e transmutation.
  • A share company for the transmutation of quicksilver (which is liquid mercury) into a malleable fine metal.
  • A share company for the making of hot air (for drying malt). At least that was an honest prospect description, beaten only by my favourite, I quote :-
  • A share company for carrying on an undertaking of great advantage; but nobody to know what it is [sic!]. The guy took £2000 before skipping the country ;-)

The contemporary English writer Daniel Defoe (1661-1731) , he who wrote Robinson Crusoe, wrote this poem about such bubble companies at the time :-

Some in clandestine companies combine;
Erect new stocks to trade beyond the line;
With air and empty names beguile the town,
And raise new credits first, then cry 'em down;
Divide the empty nothing into shares,
And set the crowd together by the ears.
Another contemporary UK poet Alexander Pope (1688-1744) penned these lines :-
At length corruption, like a general flood
Did deluge all; and avarice creeping on
Spread, like a low-born mist, and hid the sun,
Statesmen and patriots plied alike the stocks,
Peeress and butler shared alike the box;
And judges jobbed, and bishops bit the town,
And mighty dukes packed cards for half-a-crown:
Britain was sunk in lucres sordid charms.
So there's nothing new under the sun, Horatio! Neither the subprime problem nor the bailouts. As beautifully related by John Bird and John Fortune in this YouTube video ;-)


Friday, January 2, 2009

Looking back : My 7th year blogging now!

For my faithful followers ;-)

Wow! How time has flown! I've been blogging now for six whole years already!

That's about 1300 blog posts (that's a guess, I haven't counted them), albeit of very varying quality ;-) Over 1½ million visitors, with over 2½ million page views. Currently averaging about 1200-1500 visitors daily, depending on which weekday it is. Thanks!!!

For no reason in particular, this blog has run under a variety of blog names, viz:-

  • Notta Blog (January - June 2003)
  • Stu Savory's Blog (July 2003 - December 2007)
  • Yclept 'Ole Phat Stu' (January - October 2008)
  • Eunoia (November 2008 - present)
But the blog's mission statement has stayed more or less the same :-

Mission statement Version 2 : "This blog shall dispense easy snippets of simple but rare educational information in an entertaining manner, and bash (political) incompetence too. Occasional pix of trip reports are also OK."

However, a readership survey taken in 2008 may lead to some slight changes. Positive feedback on Maths, Atheism, Crypto, Motorcycling and Sarcasm. Less US political rants (should be easy when Bush is gone?), but others want more! New subject requests include SF (science fiction) and aviation. The blog's level should not be too highbrow. So what do you think of this for a new mission statement? Feedback requested.

Mission statement Version 3 : "This blog shall dispense snippets of educational information in an entertaining manner, bash (political and religious) incompetence humorously , and cover hobbies like motorcycling, aviation, and occasional bits of SF."

Come to think of it, this is the only blog I've seen so far which actually has a mission statement ! It tells the reader what he/she can expect, and it keeps me focussed ;-)
Arianne Huffington regularly proclaims "only blog what you are passionate about" ;
I would add "and only blog stuff that you actually know something about" ;-)

Let me know what you think; a current Email address is :-)

A request that I reinstate commenting and one that I put full content into the RSS feed came under reappraisal, but I think I prefer to leave these things as they are.

BTW, here's what the blogstats show as your collective choices for Best of 2008 :-)


Thursday, January 1, 2009

TANSTAAFL

Except that there is :-)

And here is my TANSTAAFL anecdote : Many years back, I had a Vietnamese student called Than in my AI R&D lab. So when he finished his thesis he gave a goodbye breakfast. Now our German word for table - in the sense of 'groaning board' is 'Tafel', so needless to say, he headlined his 'thankyou-feast' invitation Than's Tafel :-)

Time for New Year resolutions again. I resolved once again!!! to try to lose weight ;-) And no more bubblegum in aerobics class! What New Year resolutions did YOU make?


--> Most recent Blog
Comments Policy


Impressum
Maths trivia
Recent readership
Search this site
Who links here?
RSS feed for Stu Savory's Blog RSS Feed
YouTube Videos
Eunoia, who is a grumpy, overeducated, facetious, multilingual ex-pat Scot, blatently opinionated, old (1944-vintage), amateur cryptologist, computer consultant, atheist, flying instructor, bulldog-lover, Beetle-driver, textbook-writer, long-distance biker, blogger and webmaster living in the foothills south of the northern German plains. Not too shy to reveal his true name or even whereabouts, he blogs his opinions, and humour and rants irregularly. Stubbornly he clings to his beliefs, e.g. that he's not really evil, or even anti-american, in spite of Dubya's efforts to convince him that he should be. Oh, and he also has a neat English Bulldog bitch 'Frieda'.

And her big son 'Kosmo', born April 2nd, 2007. The other 5 pups have found nice homes too, all gone.


Daily Blogreads
Bulldog Blog
Chip's Quips
Doug Alder
Finding life hard?
Kay's Thinking Cap

Weekly Blogreads
American Airspace
Balloon Juice
Barack Obama !
Cosmic Variance
Decrepit Old Fool
Easy Bake Coven
Flight Level 390
Frank Paynter
Frederik Pohl !
FreeMania
Greavsie
Groundhog Day
HaggisChorizo
Hakmao
Imagine (Kenju)
Indexed
Inspector Gadget
John Baker's Blog
Jonny B's secret diary
Kees Kennis
Making Light
Manic Street Preacher
Mike Golby
Musings (Kay)
Noded (JR)
One Good Move
Pharyngula
Rainy day thoughts
Sick Days
Stupid Evil Bastard
Texas Trifles
The Poor Mouth
The Magistrate's Blog
Too many tribbles
Xtreme English
Yellowdog Grannie

Who can read this?

Recent Writings
SF : Through Alien Eyes
Lordy, Lordy :-(
Explain, McCain!
Too Highbrow(se) again?
Golomb rules
A pronounced difference
Scunnered :-(
Complex Primes Tale
Geocaching 101
Jimi's Inauguration Tune
End of the Bush Era
Ditching...
Truth maintenance
Brainless builders ;-)
Israeli Gaza plan :-(
Heidi's Maths Joke
Where was I ?
My woolly hat
The Googling ;-)
Arachnophilia :-)
Back out :-(
A bit on the side
Financial ripoff schemes
Six years of blogging :-)
TANSTAAFL
Garden Photos 2008
Wait a second!
Winter Sun spectrum
Snowflakes
Feurio :-(
Finding Family
Fireworks on the 4th July
X-Plane @ iPhone
The Dragonfly of Chaos
Heartfelt awards ;-)
Xmas present tips ;-)
Xmas prezzy for W ;-)
Winter crop
Charlotte's Laptop :)
Shawn's Xmas letter
I have Piles ...
When O'bama commands
I Mecca bad pun
PISA reflections
Tora Tora Tora Redux
Atheism Primer ;-)
Out of print
Teutolab fun maths :-)
Pareidolia again :-(
NorVin

Archive 2008:
Jan Feb Mar Apr
May Jun Jul Aug
Sep Oct Nov Dec
*Best of 2008*

Archive 2007:
Jan Feb Mar Apr
May Jun Jul Aug
Sep Oct Nov Dec
*Best of 2007*

Archive 2006:
Jan Feb Mar Apr
May Jun Jul Aug
Sep Oct Nov Dec
*Best of 2006*

Archive 2005:
Jan Feb Mar Apr
May Jun Jul Aug
Sep Oct Nov Dec
*Best of 2005*

Archive 2004:
Jan Feb Mar Apr
May Jun Jul Aug
Sep Oct Nov Dec
*Best of 2004*

*Best of 2003*


Mission statement

Blogs I co-author


Link Disclaimer
ENGLISH : I am not responsible for the contents or form of any external page to which this website links. I specifically do not adopt their content, nor do I make it mine.
DEUTSCH : Für alle Seiten, die auf diese Website verlinkt sind, möchte ich betonen, daß ich keinerlei Einfluß auf deren Gestaltung und Inhalte habe. Deshalb distanziere ich mich ausdrücklich von allen Inhalten aller gelinkten Seiten und mache mich ihre Inhalt nicht zu eigen.

Content Disclaimer
This blog is not (even politically) correct. It consists of 72% satire & sarcasm, 31% scientific reporting, and at least 4% arithmetical errors ;-) Thus everything blogged here should be taken with a pinch or 3 of NaCl.


amazon.de



Index/Home Impressum Sitemap Search site/www