May 11 2009

The Awesome Power Of Zero

Brush and floss daily. Have fava beans and a nice Chianti with your liver. One plus one is two. The list goes on and on and we never question the contents. We should. I’ll begin the questioning process by asking is one and one always equal to two? In fact is one actually the same as two? What if I can demonstrate it? Ah, I see the scepticism written all over your face. Well, buckle up, my friend, and follow as I prove that one actually equals two.

(Please don’t run away if you are mathematically challenged or if the word ‘mathematics’ leaves you in a cold sweat. Just come along for the ride.)

Claim

1 = 2

Proof

Let a be any real number and let b refer to the same number so

a = b (equation 1)

Multiply both sides of equation 1 by a so that equation 1 becomes

a2 = ab (equation 2)

Subtract b2 from both sides of equation 2

a2 – b2 = ab – b2 (equation 3)

Recall from your school days that a2 – b2 = (a + b)(a – b) and ab – b2 = (a – b)b so equation 3 becomes

(a + b)(a – b) = b(a – b) (equation 4)

Divide both sides of equation 4 by a- b

a + b = b (equation 5)

We started this proof by letting a = b so equation 5 reduces to

b + b = b (equation 6)

Now b + b = 2b so equation 6 becomes

2b = b (equation 7)

Divide both sides of equation 7 by b and we are left with

2 = 1

QED

Uh! Oh! Is there something wrong with mathematics?

We use mathematics to engineer cars, bridges and planes among many other things. It all seems to work very well, thank you very much. Obviously the so called “proof” that I outlined above is flawed so, class, as an exercise figure out where the flaw is. I’ll provide the answer next week.

In the meantime take a good, hard look at the liver nestled among the fava beans.


EDITED: Don’t look at the comments until you figure out the answer. Or already know the answer. Or can’t be bothered working out the answer.

May 2 2009

I Hope the Water Forgets This

A cool glass of water sits before me looking very inviting. As I reach out for the glass I ponder (that’s right! not for me this regular thinking business; pondering is what I do.)

It is sometime in the late 18th century. In a room somewhere in Germany a man stands with a flask in his hand. He places an ingredient into the flask and fills the flask with water. He is trying to be precise: he wants the flask to contain one part ingredient to a hundred parts water. The man is Samuel Hahnemann. He has invented homeopathy. He has has just made a 1C homeopathic solution.

Samuel Hahnemann takes some of his 1C solution and dilutes it, again using one part solution to one hundred parts water. He now has a 2C solution. He repeats the process (3C) and again (4C) until he reaches his goal, a 15 C solution. He has now diluted his original ingredient 1030 times (for those that can’t remember mathematical notations, 1030 is a one followed by thirty zeroes.)

“Mr. Hahnemann?”

“Ah, Mr. Jones. You have a question?”

“Indeed, I do. Do you realize that you have, at best, only one or two molecules of your original ingredient in that flask? In fact, it most likely has no molecules of the ingredient?”

“Of course it has molecules.”

“Maybe one or two at best. Let’s take a closer look at your process. Suppose you were using 56 grams of iron as your ingredient. Those 56 grams contain 6.02×1023 (Avogadro’s number) molecules. After your 1C dilution you are left with about 1022 molecules. After 2C, 1020 molecules. After 10C you are left with 10,000 molecules. By the time you reach 12C you have, at best, one or two, but most likely no molecules left.”

“Hmmmm!”

It is sometime in the late 20th century. Homeopaths now recognize that very little, if any, of the original ingredient remains after several dilutions. The curative powers of nothing seem silly even to them so they have come up with a new mechanism for homeopathy. It isn’t necessary, they say, that any of the ingredient’s molecules remain at all. They have “discovered” that water has “memory” and remembers the ingredient.

“Mr. Homeopath?”

“Ah, Mr. Jones. You have a question?”

“This water memory, it seems to be extremely selective, doesn’t it?”

“How so?”

“It seems like water only remembers the ingredient that you, the homeopath, want it to remember and completely forgets about every other type of molecule it met in the past. It can’t recall the molecules of bottles, tanks, fish poop. Nothing but the ingredient.”

“Well, we do use the purest water.”

“One with no other molecules in it?”

“That’s right. No other… um…”

And so I finished pondering and drank my glass of water. The water came out of the faucet in the kitchen so it should have met many a molecule along its way. I wonder which one it remembered. Probably something arid because it cured me of thirst.


Dr. Stephen Barrett has an excellent review of homeopathy on Quackwatch. The Reader Responses are worth looking at.

Several other sceptical blogs deal with homeopathy. JREF is a good place to start while Thinking Is Real has a nice post on homeopathy and the “swine” flu.

EDITED: changed from hydrogen molecules to iron since water molecules have a couple of hydrogen atoms happily bonding with an oxygen atom.

April 25 2009

Babushka Dreams

The faint light in the bathroom woke me. The Librarian was still asleep by my side so who was in the bathroom?The woman stepped out, her naked body silhouetted against the light. She was extremely tall and voluptuous. Her red eyes glowed and she growled hungrily. A wave of fear engulfed me but I remained calm. I knew that I was still asleep.

I forced myself awake.

There was a faint light in the bathroom. The Librarian was still asleep by my side. Was there someone in the bathroom? The woman stepped out, her naked body silhouetted against the light. She was a little taller than me and curvy. Her red eyes glowed with annoyance and she hissed hungrily. A wave of fear engulfed me but I remained calm. I knew that I was still asleep.

I forced myself awake.

It was dark in the bathroom. The Librarian was still asleep by my side. But something was wrong. There was someone else in the room. The woman was standing by the bed, leaning over me. She was small and lithe. Her red eyes glowed angrily and she snarled hungrily.  A wave of fear engulfed me but I remained calm. I knew that I was still asleep.

I forced myself awake.

It was dark in the room. The Librarian was still asleep by my side. The clock’s red LEDs glowed 5:00AM. She was small and furry and her claws were digging into my chest. Bloody cat was hungry.

(Yes, I know the nested dolls are called Matryoshka dolls but most people know them as Babushka dolls.)

April 19 2009

I Don’t Like Cricket. I Love It.

In a couple of months the new look Aussies will land on English soil to defend an urn full of ashes. I can’t say I’m full of optimism for our chances but I’m looking forward to a great series. In anticipation of the event and in an attempt to fire a few salvos in the battle for the Ashes – and because I have run into a rather large block that strike fear into writers of all persuasions — I present to you some cricket related humour including some that are firmly at the expense of the English cricket team (sorry Sy and others, including relatives – I can still stay with you when I visit, right?)

Let’s begin with an explanation of the laws of cricket for those of you who aren’t clear about the game:

 

There are two sides, one out in the field and one in. Each player that’s in the side that’s in goes out, and when he’s out he comes in and the next player goes in until he’s out. When they are all out the side that’s out comes in and the side that was in goes out and tries to get those that are now in, out. Sometimes there are players who are still in and not out.

There are two men called umpires who stay out all the time and they decide when the men who are in are out. When both sides have been in and out twice, including the not outs, that’s the end of the game.

 

Got that? Good. Now we can go on to some jokes I found floating around the Web.

 

Q: What is the height of optimism?

A: An English batsman putting on sunscreen.

Q: What’s the English version of a hat trick?

A: Three runs in three balls.

Q: What do you call an Englishman with 100 runs against his name?

A: A bowler.

 

Sometimes the best humour comes from the commentary box. Here are some examples:

 

Richie Benaud: He’s usually a good puller but he couldn’t get it up that time.

Richie Benaud (referring to a streaker): A slight interruption there for athletics.

Brian Johnston: Ray Illingworth has just relieved himself at the pavilion end.

Brian Johnston: The bowler’s Holding, the batsman’s Willey.

Trevor Bailey: On the first day, Logie decided to chance his arm and it came off.

Steve Waugh (in response to “what’s your favourite animal”): Merv Hughes

Jim Maxwell: The sight of Bright holds no fright for Wright (to which someone riposted “that’s right”)

Tony Greig: Marshall’s bowling with his head.

 

And finally a definition courtesy of the Cricket Jokes site.

 

COMMENTATOR

He’s venerable.His eyesight is not as good as it was in 1938 but it’s remarkable how he can still pick an inswinger or an outswinger from 200 metres. What’s going on in the centre can be a wretched inconvenience when he’s just recalling that marvellous incident on the fourth day of the Fifth Test in 1948. He is superb at describing seagulls and most graceful at 5pm when he refers to the long shadows moving across the ground.At 6pm during the summing up he can usually cause a shock by actually referring to the days play.

April 9 2009

The City of Cranes

The cranes are everywhere. Not the spindly, leggy kind. Not the “wax on, wax off, no can defend” kind. No, these cranes are the “lift very heavy loads from here and move them over there” kind. No matter which direction you face your view encompass a crane or two. The city has become one large construction site. Someone in some government department obviously decided that the best thing for Perth is to knock it down and rebuild it. Bonus points will be awarded if they can do it while making things more difficult for pedestrians..

Case in point: there used to be a covered, pedestrian overpass that spanned Wellington Street. Commuters could make their way from the Wellington Street Bus Station into the City with ease and comfort. This was a boon when it was raining. Actually it was also a boon when the Summer sun was trying to strip the skin off your bones. The overpass was such a convenience that it had to go, of course. It was torn down so commuters now have to cross a large expanse of open space and wrestle with traffic. Someone collected a truckload of bonus points for that decision.

“Excuse me, but that overpass you tore down; was it in danger of collapsing?”

“No, sir! It was very well built, sir. It would have stayed up another hundred years.” The civil servant was as proud as punch. “Another thousand years.”

“So why did you pull it down?”

“It was old, sir!” The civil servant was shocked to his very core.

And that’s the crux of the matter. It seems like a lot of the work is simply carried out because someone wants to replace a slightly weathered building with a shiny new one. The cynic in me can’t help but think that this flurry of activity is designed to deflect our attention from the lack of progress in, say, putting more beds in hospitals and providing the requisite staff to look after their occupants. People won’t see the miasma at street level when their eyes are turned towards the sky.

I hope that I’m wrong. I hope that there will be a shiny, new City once the cranes leave. Until then we have to put up with the ugliness of a construction site that is the City of cranes.

April 1 2009

Everything You Added Was Wrong

For thousands of years we have tacitly assumed that 1 + 4 = 5. This is a false assumption says April Schlemiel, head of the Department of Mathematics at Caper University, California. Professor Schlemiel argues that numbers obey laws that are actually quite different to what we have always used. She likens these laws to the Laws of Relativity.

“Relativity turned Physics on its head,” she said, “by showing that space and time are intricately linked with the matter it contains; the matter in the Universe curves space-time which in turn influences the motion of matter. In a similar way numbers and the operations on numbers are intricately linked; addition, for example, curves the number continuum while numbers influence the operation itself. In other words 1 + 4 is not exactly 5.”

In a paper presented at the International Mathematical Symposium, Professor Schlemiel offered proof for her revolutionary theorem, The Relativity of Numbers. It was the mathematical equivalent of a blockbuster movie. While a few present adopted a “wait and see” stance, April Schlemiel won the support and acclaim of the world’s best mathematical minds.

“It makes sense if you think about it,” says Unas Quatro, Professor of Advanced Mathematics at Lackey University, London. “Throughout history we’ve seen mathematics used to elaborate the theories of physics which in turn creates new mathematics to deal with the new ideas. I won’t be surprised if we soon see a quantum theory of numbers as well.”

So what does this mean for the rest of us average citizens? Not to worry, says Professor Schlemiel.

“Relativity applies at speeds approaching the speed of light. In the same way the Relativity of Numbers is only significant in the large number domain under complex operations. We can go on adding 1 to 4 and continue using 5 as the answer because it is 5 to all intensive purposes.”

After a slight pause she grinned slyly and added that perhaps we should worry after all since the national debt is rapidly approaching the relativistic domain.

March 27 2009

Only Cricket Fogies Will Understand

It happened last year during one of those spring cleaning marathons that plague a man now and again. In the process of moving years of accumulated junk from one corner to another, I found it. Buried beneath a plastic Christmas tree, numerous toys and boxes full of assorted knick knacks was my old cricket bag. Moments later I was on the phone organizing a a session at the local cricket nets. A few moments after that I was racing off to the nearest sporting goods store to replace the items in my kit bag which now resembled the swamp thing – there was enough mould in that bag to guarantee the world wouldn’t run out of penicillin for several years.

So we met at the nets and, as a former opening batsmen, I had the honour of batting first. Waves of nostalgia swept over me as I padded up, strode to the crease and took guard. The bowler, much younger than most of us old timers, raced in and unleashed a thunderbolt. It was full and just inside off stump so I moved onto the front foot and played a majestic off drive.

Then I straightened up, threw the ball back to the bowler and put the middle stump back into the ground.

I obviously wasn’t the batsmen I used to be twenty five years ago.

I had to ease myself back into form. The rest of my batting stint was a master class in the defensive shot. The backward defensive shot, to be precise, because somewhere in the intervening twenty five years the cricket ball had morphed into a deadly weapon. Going forward really wasn’t an option and yet, by the end of my batting stint I felt I could outperform Geoffrey Boycott and Bill Lawry and Chris Tavare. (I think I just went too far. It takes a very special talent to out block Tavare.)

So much for my attempt to rekindle my batting prowess. Surely things would be better with the ball. I picked one out of the motley collection and paced my run-up – sixteen steps. Just like twenty five years ago. Contrary to popular opinion, I am not a complete fool so I knew I should warm up a little. With that in mind I merely jogged the sixteen steps and delivered my first ball. It sailed back over my head.

Young whippersnapper was pretty handy with the bat.

“Good…shot,” I said just a little out of breath. It was a sixteen step jog, after all.

I ran in for my next ball and bowled just that little bit faster. It sailed back over my head just that little bit higher.

“Very (gasp) good (pant, wheeze) shot (pant, pant).”

The young whippersnapper was starting to grate on my nerves. Flying Saucer Jones used to be a pretty handy bowler in the glory days. It was time to show him. I walked back to the top of my mark and summoned up all the energy I could muster. I raced in, eyes firmly on the whippersnapper’s feet. The ball was fast and furious. It swung in late and his stumps ricocheted off the back of the nets. The ball had torn through his defences.

Their were tears in my eyes. I had torn something in my bowling arm.

I obviously wasn’t the bowler I used to be twenty five years ago.

That was a year ago. In a couple of weeks we will do it again. I will dust off my cricket gear, check it for penicillin and head off to the nets.

Even if I’m not the cricketer I used to be twenty five years ago.

March 26 2009

On the (Perth) Buses

A bus trip in Perth was a relatively pleasant experience. So much so in fact that I used to catch up on reading during the commute to and from work. Granted, a lot of the buses were long past their purring stage but none had reached the wheezy, backfiring phase of their lives either and they were reasonably comfortable. Numerous seats meant that even in a packed bus the number of seated people outnumbered the unfortunate few who boarded late. Furthermore the buses had windows that actually opened and closed which ensured warmth in winter and reasonably cool conditions in summer.

On many occasions a bus trip came with a free entertainment package: a young lad engaged in an escalating argument with his invisible friend; a gentleman furiously castigating the contents of his key ring; a mute young man blatantly attempting to peek up every skirt in his vicinity. All of this and the ride and you would still have change from two dollars.

Perth’s public transport system was working reasonably well. So, of course, the management at the department of transport decided that it was time for a change The result is the following list of changes for our comfort and convenience:

1. The old buses allowed passengers to open its windows; this was a terrible oversight. Why, the blighters could poke various parts of themselves through the opening or launch various items at other vehicles. Can’t have that, of course. Litigation, you know. The new buses have large, permanently shut windows that let in a lot of light. And the summer heat. A lot of heat. A sauna emulating, energy sapping, oven full of heat.

2. The old buses had a ventilation system that relied on breezes blowing through its interior. The new buses have climate control. At the touch of a button on the driver’s control panel, cool air flows through the bus’ vents and caresses the passengers. Except it doesn’t work. Either that or the average driver is a devotee of the Marquis de Sade. Or likes the smell of sweat.

3. Did I mention the heat?

4. The old buses had unattractive interiors with unimaginative, regimented rows of seats. No style at all. The new buses are full of style. True, some rows remain but several seats now face each other across the aisle. The layout means there are far fewer seats so a packed bus sees more people standing than sitting. To be fair I must say that the front of the bus is friendly to people in wheelchairs and that friendliness also allows for a ramp that extends onto the footpath as needed.

5. I did mention the heat, didn’t I?

6. The in-bus entertainment is no more. They have been replaced by loud musical interludes courtesy of mobile phones and MP3 players. The mobile phones allow for a constant barrage of soap operas which other passengers can’t turn off or down: Ginny broke up with her boyfriend because he was sleeping with Trish; Bob knew he had a really great time last night because he couldn’t remember it; Betty is a hag. I have never liked soap operas and I like the mobile phone equivalent even less.

7. Are you sure I mentioned the heat?

A bus trip in Perth is a relatively hellish experience. There’s a lot of heat.

March 22 2009

What Year Is It Again? Which Country?

If people equate freedom of speech with watching child pornography, then the Rudd Labor Government is going to disagree.

Senator Stephen Conroy, the Minister for Broadband, Communications and the Digital Economy, 2007

 

Since when is arguing for freedom of speech automatically equivalent to support for child pornography? “Won’t you think of the children” arguments have a long history.

 

The state must declare the child to be the most precious treasure of the people. As long as the government is perceived as working for the benefit of the children, the people will happily endure almost any curtailment of liberty and almost any deprivation.

Adolf Hitler, Fuhrer, Mein Kampf, 1943

 

Just saying.

March 21 2009

They Don’t Want Me Looking At Great Tits

I went looking for tits and boobies on the Internet today. No, not those tits and boobies – I was actually looking for the Greater Tit and the Booby Bird. “Why?” I hear you asking (unless, of course, you are a bird watcher). I’m glad you asked. It was prompted by the Australian Labor Party and their efforts to protect the children by telling me what I can and cannot look at in the privacy of my own home. To this end they eventually want all ISPs in Australia to implement the Labor Party’s Great Internet Filter.

As with most attempts at censorship the filter was supposed to target sites depicting children engaged in acts that are the purview of adults (forgive the obtuse wording – no sense in having my blog show up on a search for questionable sites). I’m sure that the majority of us are appalled by the existence of such material and wouldn’t oppose the eradication of sites catering to said material. Unfortunately, filtering the sites won’t make them go away. Such material is illegal everywhere in the world which means that one would be a moron of the highest magnitude to create a public web presence advertising these illegal activities. Surely those involved in such criminal pursuits would have their own networks, both electronic and physical, and these networks will continue in spite of the filters.

“We’ll protect the children” became “we’ll protect everyone” as the Internet Filter broadened its scope. There are now two lists. According to Stephen Conroy, the Communications Minister and architect of the filter, there is a level one, or “child safe”, list and a level two, or “unwanted content”, list. The nasty material – including the aforementioned illegal content as well as material depicting people and other animals knowing each other in a biblical sense, etc — will be on the level one list list while legal “art lover’s” material will be on the level two list. Conroy says that regular perverts like me can call our ISPs and tell them we want to opt out of the level two list.

So far this seems to be reasonable. We don’t want the universally reviled content and we can choose to view legal content that other people may not want. But what happens when the illegal sites change their URLs? What about new illegal sites that are bound to pop up in the future? The filter lists require constant updating. We all know that the government isn’t going to absorb the cost; neither are the ISPs. That leaves you and me, buddy. My already expensive internet bill is only going to dig deeper into my wallet. There are people in the ISP industry who claim that we will experience a drastic slow down in Internet access due to the filters. If this is true then not only will I pay more for my Internet access but I will receive a lot less for the privilege and I will receive it very slowly.

The above issues, large as they are, cannot compare to the biggest issue of all. Who decides what ends up on the absolute list? Both lists are, obviously, secret so we have no way of knowing what they contain. The Australian Communications and Media Authority (ACMA), are in essence the watchmen of the lists so it is apt to apply the maxim “who watches the watchmen?” The Christian party, Family First, suggests that online gambling and hardcore pornography should be on the level one list. The latter in particular means that I can indulge in sexual activity but I cannot look at anything depicting the same thing on the Internet. In fact I can watch other people making the sign of the double backed beast or buy books and movies explicitly depicting the same (provided the movies come from Darwin or Canberra) but I cannot look at it on the Internet.

Even more serious than the curtailing of my “art” appreciation, however, is the possibility that other topics can suddenly become lumped with the nastier items. Family First Senator Steve Fielding doesn’t like evolution or atheists or agnostics? Let’s add them to the level one list. Buddhists? Muslims? Pagans who dance naked under the full moon? On the level one list, they go. The government needs Fielding’s vote in other areas (such as the alcopops bill) so they are going to make concessions to his filtering requirements. (Interestingly Fielding decided to vote against the alcopops bill thus showing us that he obviously likes a tipple but hates “art”.)

A recently leaked copy of the level one list highlights the danger of the unwatched watchmen. The list contains the nasty items, as expected, but also contains several legitimate items such as the URLs of a dental surgery and a betting site. I wouldn’t normally give a second thought to publishing the link to a dentist’s web site. The problem is that ACMA can fine me 11,000AUD per day for publishing a link to any site on their lists.

“That will be $11,000 dollars.” says the ACMA representative giving me a look of disgust.

“What for?”

“You linked to this site and it is a forbidden site.”

“I didn’t know it was forbidden. It’s the site of a really good dentist. Why can’t I link to the site?”

“Because it is forbidden.”

“But I didn’t know that. How am I supposed to know that?”

“It is on the list.”

“I don’t have the list. Let me have a look.”

“You cannot! It is a secret list.”

“But then how do I know what sites I can’t visit.”

“They are on the list.”

“But I don’t have the list!!!”

“Only we have the list. It is secret.”

So that’s why I went looking for tits and boobies. Because I can, right now. If the filters become law I might have to call my ISP to tell them that I want to look at a Great Tit (which may well cause them to titter or ask me if I was referring to that boob, Conroy or Fielding, the great tit). This country I have loved so much may well become as draconian as China and it’s ilk. And that is a depressing, frightening thought. All of us, including lovers of ornithology, could be in for a rude shock.

And heaven help the feline fanciers if they went looking for pictures of pussies.