There is no infinity.

I was recently reading “Statistics for Dummies” by Deborah J. Rumsey (yeah, I know, but I'm on the road and grabbed something statistics related from the library I could read on my Kobo), and ran across this tidbit:

The probability that X is equal to any single value is 0 for any continuous random variable (like the normal). That’s because continuous random variables consider probability as being area under the curve, and there’s no area under a curve at one single point.

Her example of a continuous random variable is the length of fish caught in a fishing contest. Now I know I am just Joe Schmuck, with almost no knowledge of statistics, and even less credentials, but that statement, to be charitable, is just silly. I am sure if I were to challenge Dr Rumsey to a public debate on this, she would crucify me, as she would be well prepared with mathematical theorems backed by centuries of publications in peer reviewed journals, but that doesn't change the fact that she is now qualified to write speeches for George W.

Any half-wit, unencumbered by accepted truisms in statistics, can tell you that her statement is utter nonsense. This here fish I have on the end of my fishing line happens to be X cm long, but Dr Rumsey tells me there is a zero chance of that fish existing, so it can't exist, so that must be some very unusual crocodile wiggling on the end of my line. The other obviously troublesome problem with her statement is that it applies equally to any other length of fish you'd like to consider, so by definition there are no fish at all in that lake, or any other lake for that matter. And if there are no fish, then the population (or sample) size is zero, so there is no mean and no sigma, and Dr Rumsey doesn't have a probability distribution, and thus can't actually say anything about the probability of catching a fish of a certain length – her statement is internally inconsistent.

I've used the concept infinity in my previous life as a scientist. I always thought of an infinite value as something that was so big, that if it was any bigger it wouldn't make any difference. I get it – it can be useful. Integrating from -∞ to ∞ can make for some clean, pretty math. Modern physics relies heavily on mind-bending mathematics (the race is on to add more dimensions to M-theory), and so infinity can be a useful tool for modelling the real world.

Things start to go haywire when you begin to think of infinity, literally, as a real thing. Some physicists have suggested that the universe is infinite, and they're not invoking some trickery like warping space-time so that a traveller on a space ship would travel in a big circle around the universe and eventually arrive back where they started – they mean that the extent of the universe is truly without bound. I know that at very large and very small scales, human intuition GPF's, but “say what?” I have to ask. Infinite you say? I just can't buy that. A quantum fluctuation on steroids produced the Big Bang (which, interestingly, was silent) and somehow that produced an infinite amount of space and matter? No way.

Following this to its logical (illogical?) conclusion, leads to all sorts of problems. An infinite universe implies an infinite number of stars, an infinite number of planets earths, and an infinite number Barack Obamas. You see, if the astronomical bodies of the universe formed essentially at random (which all the evidence supports), and you have an infinite number of planets, that means an infinite number of them will be exactly like earth. No all of them mind you, but still an infinite number. Thinking about that idea alone is enough to make you bleed through your eyes – take the infinite number of planets and divide them by 26 wappagazillion, and you're left with ... an infinite number of planets. So even though planets exactly like earth are extremely rare, there are just as many earths as all the rest of the planets combined: infinitely many. I would have thought that simple observation was enough for some philosopher to disprove infinity once and for all [maybe one has – I didn't check – but this Schmuck's blog is about writing, not solving great mathematical problems]. But I'm getting side tracked yet again. So we've got an infinite number of planets exactly like earth, and on each one we've got life evolving randomly, and since we've got an infinite number of them ... well the result in a infinite number of earths with Barack Obama and Vlad Putin getting their knickers in a knot over a small, impoverished country in eastern Europe, and making life hell for millions (a small price to pay for their ego games, and darn if I can't stay on topic today). So, there are an infinite number of Joe Schmucks out there too. How can anyone really believe that?

The flaw in Dr Rumsey's statement is that she has fallen into the infinity trap. Her implicit assumption is that there are infinitely many possible fish lengths. If you accept this, then it follows that the width of the area under her probability curve for any given fish length is infinitely small (a pompous way of say zero), and so the “area under the curve” for a given fish length is zero, and so is the probability of me having a fish on the end of my line. It is all so sensible when you think about it like this, but it is also a pile of rubbish.

To have an infinitely large number of fish lengths, the smallest possible difference in fish size must be infinitely small, but in real life that just isn't so. Fish are made of molecules – proteins and fats and those sorts of things – and molecules are made of atoms. Atoms are only so small – free quarks don't exist in nature, and that includes fish bodies. I am guessing that the smallest possible difference in the size of two fish can be no smaller than the size of an atom, and probably larger than that. So the smallest difference in fish lengths may be really, really small, but it isn't zero.

But remember, we are talking about the lengths of all fish caught in a fishing contest. The lengths of the fish need to be measured, and in practice, it's not possible to measure the length of a real fish to anything like atomic scales. Think about it, we need some repeatable process so we can reliably say what the length of a given fish is, and attempting to measure the length down to scales where Brownian motion and Heisenberg uncertainty are important just isn't going to generate reliable, repeatable results – not to mention a slimy, floppy (or flopping if it is freshly caught) fish just doesn't lend itself to atomic precision length measurements. Her probability distribution is a distribution of actual measurements, not hypothetical measurements, and we can't measure the length of something with infinite precision – this is not dependent on our technology, it just isn't physically possible. In practice, I think you'd be doing pretty well to manage +/- 0.1 mm, in which case the width of the area under the curve becomes small, but in some ways a long ways from zero.

Her statement is based on the assumption that the smallest difference in fish lengths is infinitely small and we can measurement with infinite accuracy – both those assumption are wrong because they rely on applying infinity to real life physical things. Her continuous random variable isn't really continuous, and neither is any other you care to dream up.

There is no infinity, and maybe that is a fish on the end of my line after all.

Life on the road

It is closing in on two years since we landed in Sydney, and thinking about the last two years gives rise to many questions. Which is harder to believe, that I've been resident of Australia for almost two years, or that I've been homeless for two years. Who do I despise more: Stephen Harper or Tony Abbott? How long until the Australian housing market implodes? How badly does Nobel Prize committee wish they could have Barack Obama's prize back?

We've been on the road for much of the past two years – initially with just a car and a tent, but for the last 16 months, with our vehicle towing a small caravan. “Back home” we were wont to go on road trips, typically of 4-6 weeks length, invariably to the southwest US states in Nelson's rainy seasons (spring and fall), and usually for rock climbing, but once for a ski traverse in the Sierras. When imagining our move to Oz, I drew upon those experiences, and had trouble picturing us travelling about living in a small caravan for more than 6 months, as 6 weeks usually seemed long enough, but here we are, almost two years in, and no end in sight. 

We have had a few months at the mother-in-law's in Sydney as we got our selves settled in the country, and five months house sitting in Cairns, which has really helped stave off the road weariness. But still, I'm surprised at our staying power.

The Podmobile

I think there are a fair number of reasons we're still going strong, but most importantly, our home on the road is certainly an upgrade – we have a much better setup in our “van” than we had with our Boler in Canada:

1. It is a bit bigger, and we each have our own bed (complete with reading lamp – “pods” we call them, hence the “Podmobile”), and the beds are permanently beds and don't have to be made up into the kitchen table every morning (like in the Boler). 
2. The Podmobile has a bigger and better fridge, that has a workable freezer even in the heat of Australian summer. 
3. Our new rig also has excellent 12V LED lighting (partially my work, partially the previous owner's), so the Podmobile is very well lit which is really important during the 12+ hour dark nights.
4. A huge plus are my off-the-grid mods to the van, which mean that so long as we have sun for the photovoltaics (which we almost always do) we generally have as much power as we need to run electronics like MP3 players, cameras, mobile phones, and computers. So long as we have a source of water and food, we can happily live off the grid indefinitely.

The Internet

Even for anti-social, cave-dwelling Luddites like ourselves, connecting to the outside world, at least sporadically, is really important. With a smart phone, a good data plan (half the cost or less compared to Canada), and an in-house tech-head, we are much more connected that we used to be when travelling in the States. Anti-technology extremists that we are, we didn't have a cell phone back then, which made planning trip logistics and communicating with loved ones a chore. Now, when we're in range of a cell tower (sometimes frequently, sometimes only every couple weeks even with my external antenna – it is a big, mostly empty country) a few magic finger swipes turn our mobile phone into a portable WiFi hotspot, and presto our laptops (one each) are connected to the Internet with minimal fuss in the comfort of our pods or sitting at the kitchen table that doubles as an office desk. Whether it is keeping in touch with family, spraying on Crackbook, checking out the weather forecast, downloading eBooks and podcasts, or getting e-brochures for the next national park ... it is now hard to imagine life without a portable Internet connection.

The Climate

The weather here is much more comfortable to be camped out in a small RV than shoulder seasons in the US. The fact that Australia has climatic zones from temperate to tropical, and we move around with the seasons, means we don't wait out rain very often (4 months since the last rain), are generally warm enough to be comfortable, and only rarely have been too hot. Most of the time there is a water source nearby that doesn't freeze over each night, so if shower facilities are lacking we can usually go for a swim and thus it is rare for us to go to bed feeling dirty.

The Lessons Learned

We have also learned a few lessons, things that we need to do, to avoid the dreaded “road weary” burnout:

1. Don't drive too far each day. Hard core travellers will think we're wastes of skin, but if we can limit our daily time in the vehicle to 4 hours or less (we loathe driving), we are oh so much happier. This sometimes means we take quite a while to travel some not very interesting sections, but for us, it is a very favourable tradeoff indeed, and cuts down on the marriage councillor costs.
2. Don't try to pack too much into each day. We have a habit of being too literal with the carpé dium thing, and attempt to jam pack each and every day, with not a wasted moment. We used to underestimate how long it takes in an unfamiliar town to get groceries, petrol, and information about our upcoming adventures. We now try to schedule conservatively to avoid the headless chicken dance, and budget in some rest days (something that does not come easily to Wife).
3. Recognize the early signs of travel burnout, and find some quiet, out of the way spot, to just hang out for a week – something that in the past would have horrified us. Now, mind you, the ideal chill-out spot, needs to have activities, but they needn't be amazing, and they need to be accessible without the use of the vehicle – leaving the vehicle parked is a key part of chill-out week.

The Housing Market

The fact that we don't own a house, and have no idea where in Australia we would like to settle, means that any incipient ideas about ending the road trip and settling down wither on the vine, so to speak. And with housing prices in Oz in a horrific bubble, the house accountant thinks it is a good thing we're not wanting to settle down yet. When we moved here, the $AUD was worth $CDN1.2 and housing prices were in the stratosphere; I said that when the Aussie buck dropped to 80¢ Canadian and housing prices fell 30%, we'd buy a house. The dollar is half way there, but housing is still hanging in. I figger that China will blow up within a few years and Australia's mineral export economy will get monkey-hammered and we'll get our buying opportunity.

We won't want to live this way forever, but all in all, we are just way more comfortable on the road here, and without a home to go back to (or look after), we seem to be happy to just keep on exploring the island. Keep on keeping on ...

The 10 Year Itch

In the fall of 2011, Wife and I decided it would be a good idea to move to Australia. Well, truthfully, she finally caved after a decade of me pleading, but I digress. A year later, I had been granted permanent Australian residence, we'd sold our lovely home and acreage near Nelson, had disposed of most of our worldly possessions, and up-and-moved down under.

Here is something I'll tell you for free: moving countries is a major hassle. I way underestimated what was involved. The 90 page residency application was only the beginning. There was also the need to acquire drivers licenses, health care insurance, an automobile, etc. Everything is just different enough to be really confusing – two years on and I still haven't really figured out the Australian health care system.

On the Nadgee Howe

And then there is banking and investing. Oh my, what fun it was dealing with those. In Australia, your credit worthiness is based on your income, not your assets. If, like me, you've just arrived in country (and thus have no Australian income history), you could literally be Bill Gates (literally!), and you could not, for love nor money, get a credit card. No chance. Nada. Without a credit card or a credit rating, just try getting a mobile phone. Good luck to you – you'll need it. And despite their promises to the contrary, once I left Canada, TD Canada/TD Waterhouse has made my life a living hell – OK, maybe I am prone to a bit of exaggeration, but calling my experience a huge (and expensive) pain in the arse would understate the fun. And don't get me started on dealing with Revenue Canada.

So then why the heck did we do it? My favourite flippant answer is “because I couldn't bear living under Stephen Harper's rule.” I wish I had that sort of conviction to my political opinions, but sadly I don't, and if I did, I suppose I would have stayed in the Frozen North to fight the good fight for the end of his tyrannical rule, rather than gone paddling on the Great Barrier Reef. But my hedonistic nature aside, things haven't worked out so well in that regard anyway, as Harper's evil brother, Tony Abbott, was recently elected as Australian PM. Abbott, the ALP, and their neo-con agenda is just so deja vu all over again, that I sometimes feel like I'm stuck in a bad dream. Canada was too stupid to learn from the mistakes of the Americans, so I don't know why I imagined the Aussie's would be any different.

Burrawarra Point, NSW

The truth is, I seem to be a sort of 10-year guy. As Sandy is Australian by birth, most folk are surprised to learn that I was the one who was agitating to move to the Antipodes, but it is true. After ten years of living in the same place and doing basically the same stuff, I am bored and want something different. Something to stir things up a bit, and get me out of my comfort zone. We'd been in Nelson for going on 11 years ...

OK, so I wanted a change, but why Oz? Why not Saskatchewan? Or the Maritimes? I have lived my whole life, up until 2012, in Canada, and since my mid-20s have been fanatical about mountaineering, rock climbing, and backcountry ski touring. This basically means I have been freezing cold most of my adult life, and the rest of the time I was only moderately cold, wet, and miserable. As they say, in Canada there are 10 months of winter and then 2 months of crappy skiing. To me, Australia seemed like a fairy tale land: the sun always shines, the air is always warm, the beaches are amazing, and the landscapes are stunning (mostly true, not as true as I thought, true, true). Not that Canada is such a bad place – it isn't, it is a wonderful place, and there are many things I love about the place. But Oz just seemed so different (and comfortable) as an outdoor playground – different forests, different (and whacky!) creatures, and different outdoor sports to learn (I'm talking sea kayaking and surfing and the like, not footie and cricket, which the Aussie's are mad about). What's not to like?

That bloody itch!

We've been in Australia for going on two years now, and it has pretty much been one long, grand adventure. The climate really is a dream compared to Canada. It makes camping and travelling – which we've been doing pretty much continuously – so much more pleasant. The beaches ... I don't think I'll ever get tired of the beaches ... walking barefoot on an endless perfect sand beach with the surf rolling in: magical. The warm water, salt and fresh, is lovely – we swam more times in our first month in Oz than 20 years in Canada. And the place is stuffed with truly wonderful places to discover. I find it amazing to think we've driven from the Snowy Mountains to the tropics without leaving the country. I'm old now, so was ready to let mountaineering go as an activity, but sea kayaking Australia's beautiful coastlines is a perfect replacement.

In some ways Australia has been very much like I had imagined, and other ways it has been very different, but overall, I am loving the place.

Hinchinbrook

And the ten year thing? I highly recommend it – life is too short to get stuck in a rut, and getting stuck is so easy.

A Year Down Under

[A re-post from last year.]

Lake Nuga Nuga

It's been over a year since Sandy and I moved down to Oz, and what a year it has been.

Huntsman spider

It is easy to think of Australia as a big flat, hot, dry place. But really it is a place of incredible beauty, amazing diversity, and at times, shockingly wild weather. Stunning beaches of the coastal plain are backed by the escarpment of the Great Dividing Range; high tablelands are laced with rainforests, gorges, and slot canyons; the temperate lands of Victoria and Tasmania are bracketed by the wet tropics of the “Top End”.

Garie Beach, NSW

For a Canadian, everything is new, different, and exciting – I feel like a kid in a toy store wondering what weird and whacky landscape or creature we'll encounter next. Ferns become trees; the conifer is replaced by the iconic eucalypt and the towering fig; the call of the raven becomes the screeching, laughing, and ringing of a 24-hour avian cacophony; the grizzly becomes the croc and the tiger shark; the glacier-clad mountain becomes the waterfall in a deep canyon, the endless sandy surf beach, and the deserted tropical island.

Goanna

In the past year, I have photographed more sunsets and gone swimming more times than in my previous 50 years combined – Australia really is a country that needs to be lived outdoors.

Blue gum

Kanangra

Lake Nuga Nuga

North Queensland coast

Hinchinbrook