## The Most Important Number in Photography: F-Stop Numbers

Photography measures the light used by either doubling it or halving it in a odd series of “f-stops”. How the numbers 1.4, 2, 2.8, 4, 5.6, 8, 11, 16 and 22 double or halve anything is what I’ll try to answer. If light were water then the aperture would be the diameter of pipe to let the water flow in onto the sensor. We cannot measure the light transmitting capacity absolutely by the diameter of the aperture since wider lenses gather up more light from a larger field of view than the narrow slice taken by telephoto lenses. The f-stop numbers refer to how wide the diameter is compared to the length of lens. A lens with a focal length of 50mm at f/2 has an aperture that is 25mm: its focal length, indicated by the letter “f”, divided by 2; or 50mm divided by 2; or 25mm. This is why the number seem backwards with small numbers indicating wider apertures and bigger number indicating narrower apertures.

You would think than an aperture of f/2 would let in twice the light of f/4, but really f/2 lets in four times of the light of f/4. One thirtieth of a second is obviously twice the exposure as on sixtieth of a second, but what f stop is twice f/4? The answer is f/2.8. “What is this weird number ’2.8′?”, you might ask. The answer is to be found with that number “1.4″.

“1.4″ is the rounding-up of the square root of 2 to one decimal point. We have seen the square root of 2 when looking at lens lengths. each multiplication of lens length by the square root of 2 gives us view that is half as wide in angle of view and dividing the length by the square root of 2 gives us a view that is twice as wide. Which is why wide angle lenses have shorter lengths than telephotos.

The origin of the square root of two can be explained by the simple slave Ion in the Socratic dialogue named after him by Plato. At first Ion makes the naive mistake of dividing the sides of a square in half in an effort to make a square that is half the area.

This is false way of cutting a square in half. Dividing the sides in half results in a square one quarter the size of the original.

Plato encourages him to try again and Ion eventually works out the solution. This is a visual interpretation of the solution.

By cutting a square from one corner to its opposite corner we get two right-angled triangles that are one half the area of the original square. Cut one triangle into four equal right-angled triangles: A. B. C. and D. Re-arrange these triangles to make one square. This resulting square is one half the area of the original square, just like the triangle in the first step.

While squares are not aperture, or should I say, few apertures are squares; all aperture shapes, be they pentagons or circles, follow the same rule. The square root of 2, or its approximation, 1.4, is the key. Dividing the aperture by 1.4 will halve the aperture and multiplying the diameter by 1.4 will double it.

The multiples of 1.4 are approximately: 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, and 22. That series is exactly what you see on an aperture ring. On a 50mm lens f/1.4 will give you an aperture of 35mm, f/2 is an aperture of 25mm, f/2.8 is 18mm and so on.

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## The Most Important Number in Photography: Lens Length

The square root of 2 is the most important number in photography. It’s an awkward number that seems to go on randomly into its lesser decimal points, but it describes something very simple, doubling and halving. Photography is calculated by halving and doubling. When used for the aperture, it the square root of 2 calculates for half the light or twice the light. When used for the lens length, it is half the field of view or twice the field of view. To make calculations simpler we round the square root of 2 to the first decimal point to get “1.4″.

When 1.4 is used as the factor in the length of a lens it roughly halves or doubles the angle of view of lenses. It is roughly because the image area for 135 “full frame” and APS-C cameras is a rather awkward rectangle of 3:2. It would make more sense to speak of the angle of view any lens provides. But we don’t. Divide a lens length by 1.4 and the angle of view is doubled; multiply the length by 1.4 and the angle of view is cut in half.

While cropping an image would do the same as narrowing the angle of view, there would be a loss in resolution corresponding to the image thrown away. Rather than lose all that potential detail in an image, it  is better to change the length of the lens. During a game it is impossible for the photographer to walk onto the field to take the photo, so they must use a telephoto lens. Correspondingly, it is impossible to photograph large objects in cramped conditions, like an architectural façade in a narrow street, without a wide angle lens.

But it is a common mistake by amateur photographers to zoom in and out just in order to crop the image when the real benefit of changing the length of the lens is changing the perspective. The perspective changes the emotion of the photo. Photographers learn that wide angles give drama and narrow angles are much cooler.

And before zoom lenses a photographer were force to use their feet to walk closer or back away to get things in frame. The other choice was to pick a convienent lens length for the job. The lenses had to be significantly different enough to justify changing lenses. If the issue can be solved with some moderate cropping or the photographer taking a few steps then another lens would be redundant. The resulting series of lens lengths is an odd set of numbers they are primarily determined by 1.4. These “prime” lenses with fixed focal lenses are still used today because they are cheaper, better quality and faster than any zoom lens.

The first lens for the 135 “full frame” format, a Leica, were designated 5 cm. I suspect this rather round number was due to Germany’s drive for standardization in industrial production. 5cm or 50mm is called a normal lens, even if it a a bit narrow in angle of view to be identical to the angle-of-view found with the human eye. 43mm would be closer to the mark for a truly neutral lens.

The first wider angle of view lens was 35mm, which is 50mm divided by 1.4. I suspect the use of the square root of 2 is related invention of German industrial standardization you might know; the standardization of paper sheet sizes for printing. The standard A5 sheet of paper common to offices in Europe has the interesting property that folded in half the resulting rectangle has exactly the same ratio of sides, the square root of 2. While the sensitive area of the 135 format is 3:2 (36mm x 24mm), using 1.4 to generate a series of lens lengths does allows the photographer to switch lenses rather than have more than half the resolution from the film or sensor cropped away when trying to frame the image.

In practice certain lengths have been adjusted according to their most common use. 70mm is slightly too severe in its perspective. The slightly longer length of 80mm or 85mm is more flattening and flattering. 85mm is also closer to twice the 43mm of a truly neutral angle of view. I assume other length are a matter of better differentiating them from their neighbours or simply a compromise due to optical design limits.

Defining lenses by their focal length in millimetres is odd enough, but the numbers seem random. But if we start with 50mm as the standard and then divide or multiply that number by the square root of 2 then we get a theoretical series that is quite close to what we see on the market today. Every length fits a certain use and gives a distinct feeling to the photograph.

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## OpenStreetMap GPS Traces Lacking for Toronto

One can clearly make out the Gardiner Expressway along the bottom and Bloor-Danforth along the top. The Lakeshore Line of the GO Train is also clearly visible.

427 & 401 interchange is familiar to anyone driving out to Pearson Airport. The complex lane changes needed to successfully navigate one of the world’s most heavily used interchanges are rendered as a graceful sweep of curves.

OpenStreetMap now has GPS traces so you can see the cumulative passage of vehicles with GPS transponders: buses, trains, taxis, trucks, ferries, and even airplanes. While Eric Fischer sees this as an opportunity to fix mismapped roads, the traces in Toronto seem too few and many are corrupted. The TTC makes the traces on all its vehicles public, but are noticeably absent here. No sign of the 504 King car and no 6 Bay Street bus. Parts of the city seem to have very sketchy data; there are only fragments around Regent Park and Moss Park. The tall buildings in places like Financial District seem to play havoc with the data turning the regimented grid of Toronto into random squiggles. There are some unexpected things like the GO trains coming in to and going out of Union Station and the Toronto Island Ferries embarking and disembarking from  Jack Layton Terminal. In a way the squiggles and gaps express the chaotic nature of traffic in downtown Toronto. Other parts of the city like the dry-mounth and white knuckle interchange of the 427 and 401 become graceful swoops.

## Sibling Fight for Toronto Centre

The byelection in Toronto Centre has been the most heated election I have voted in. We’ve had people posting flyers, calling on the phone, and knocking on our door to talk every day. I thought it would be a sleepy election since the candidates McQuaig and Freeland are almost identical, but, I just got a robo call from a what was identified as a political interest group on election day, something just not done here in Canada. I’m skeptical enough to think that this may not be what is seems. Last night I had to deal with a party volunteer who had been roughed-up. Thuggery in elections makes my heart sink and I hope the parties can agree to clean up their acts.

I should be used to dirty politics; I’m from British Columbia where the Social Credit Party were called fascists and the NDP were called communists. It wasn’t an election until arson was involved in an attack. But I wasn’t of voting age back then as I am now. Worst of all, this is the Liberals versus the NDP, two parties made up of family, friends, and people I admire.

There is some history as to why this election should be so heated. The riding has been a Liberal stronghold for decades and is often the seat of the party leader. This has served the constituents well enough as the Liberals have formed many governments and the Conservatives have never shown the least bit of interest in the issues of concern for voters in Toronto anyways. But it was always a Hobson’s choice for voters. It was a choice between something or nothing. Now that the NDP is the official opposition the seat is in play.

Mulcair may be a difficult person to love, but he’s done more to hold the Conservatives’ feet to the fire since the the days of Jean Chretien. The Liberals on the other hand have been pulling their punches. The Liberals are not committing themselves as they wait to see what the defining issue will be in the next federal election. In a Westminster system of government, debating prowess still counts. So Mulcair holds the attention of the chattering class.

And finally the riding is due to be split because of recent surge in population. It’s hard to believe that there is any room to spare in Canada’s most densely populated electoral district, yet it continues to grow and will keep growing as every empty lot is turned into a condo tower. The poll by poll results may define which party the new riding will belong to for decades to come.

## Why Would Rob Ford Do That?

When people ask “why would he do that?”, it always a compound question that is only partly a real question. Mostly it is just a plea to agree with them in moral outrage. The real question of “why would Rob Ford demand that the police release the video that he said did not exist?” has its answer in Rob Ford’s peculiar genius. Our mayors behaviour can be interpreted by speculating on his psychology, but this is just so much scuttle butt and only gets us so far. The better approach is to assume there is reason to his strange demand. And I believe it is, as he asserts, to defend himself. It is not a defence against the shame of appearing to have smoked crack. Rob Ford has a bigger problem.

We can start with what we are legally allowed to say. The trial of Alexander Lisi seems to be about his illegal activities in an effort to suppress “the video” of our mayor doing something that looks bad. There is no evidence to charge our mayor as part of a criminal conspiracy and, unless Lisi accuses the mayor, he will never be charged. We may not be able to believe our mayor could be ignorant of Lisi’s activities and we may believe it was our Mayor who gave the orders and is ultimately responsible; but, unless there is a conviction, Rob Ford is free to continue being our mayor, and we are legally obligated to never speak our minds.

But, given a certain hypothesis, then his demand for the police to let us see the video shows us a sharp tactical mind that hides behind the harmless appearance of Rob Ford. The Ford brothers’ greatest strength is the elite’s persistent self-satisfied underestimation of them.

Ford has already publicly announce the he does not “throw friends under the bus” in regards to Alexander Lisi. It would be natural to assume Lisi would feel obligated to return the loyalty. Lisi is likely to assert that his activities were done on his own initiative and without the influence of either of the Ford brothers.

A demand to see the video is truly brilliant. For starters, the video is not Chief Blair’s to give. The video is in the custody of the crown and it is likely a key piece of evidence for the prosecution of Alexander Lisi or, at least, a public viewing would be considered prejudicial to Lisi’s defence. To release the video would be to throw the case against Lisi. Without the case against Lisi, no one else can be prosecuted for the crimes committed. If there are others involved, then sabotaging the case against Lisi is in their interest. With Lisi out of jeopardy, he is unlikely to roll on any co-conspirators.

The other point that cannot be repeated enough is that smoking crack is not a crime. A video of the Rob Ford smoking crack is not a video of a crime being committed. To make a case for possession, the prosecution cannot go forward without the drugs as material evidence. Whatever was in the pipe is gone. All we have is an image. The image looks bad, but it is only an image.  Any competent defence lawyer would quickly sow doubt and uncertainty about what actually happened in front of the camera. Maybe not enough to persuade most people, but enough to discourage a prosecutor or to keep Ford Nation true to their faith in Rob Ford.

Even if Rob feels the need to admit to have smoked crack in the past, he has never denied it; he has only said that he does not smoke crack and is not an addict. He can always use this to put his enemies on their back foot by shaming them for attacking him on something they would be inclined to forgive in others. Nevermind his own history of vindictiveness towards drug users. It would be a small price for him to pay considering the potential for much worse.

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## Vicky Pollard, Mayor of Toronto

Rob Ford reminds me of Matt Lucas’ comic character of Vicky Pollard. She seems lacking, but she turns her inability to stay on topic into a weapon to disarm anyone who would make her accountable for her bad behaviour. Ford and Vicky both freely use fraudulent outrage to change the subject. In a way, we take delight in Vicky’s ability to confound authority figures while doing whatever she likes. In a way, I admire Ford for being able to tap into the resentment of the suburbs to beat everyone, including his supposed friends, into submission. It has a certain brutal efficiency. Too bad that he seems unable to make any substantial contribution to the city. We’ll be spending decades sorting out what he actually accomplished from his BS. That Matt Lucas is overweight and his character is lower class does not diminish the power of Vicky Pollard because we love to hate such people. Both Vicky and Rob Ford exploit our prejudices to the hilt, by goading us and then shaming us. Or attempting to shame us even when we refuse to be goaded. As we know, bullies like Vicky inevitably end up alone, starved of the lackeys that give her power. Similarly, people like Giorgio Mammoliti are just figuring out that Ford is not their friend and they need to walk away. Don’t expect Ford to stop trying to blag us all even after being caught dead to rights; Vicky Pollard never does.

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## Eastern Gardiner: What Can We Do?

The Gardiner East Public Forum summarizes our options clearly as maintain, improve, replace, or remove. It is tempting to dive into the details of each design proposal and make a cost-benefit analysis, but that is not how we do things in Toronto. The harsh reality is that it is all about perceptions and how it will be spun to appeal to voters. Reasons are just  ammunition.

Our motive for finally taking on the eastern section of the Gardiner is that it may soon collapse. Since this is the immediate issue, the option to maintain the current structure would be the easy political solution. But this solution only appears to be the cheapest option as it does not unlock the potential of the land around the expressway.

When the Gardiner was built, there was nothing but industrial land around it. Industry is leaving and the land around expressway now has the potential to fulfill other needs that would easily fit into our current plans to develop Toronto’s waterfront. Such development would bring needed revenue for the city through new the tax payers that would move in. This tried and true method of increasing revenues for the city only works if the land is made attractive enough. How much is enough is up for debate. This would not be a plan of “build it and they will come” because Torontonians are already moving into the surrounding area to be closer to where they work. This would not just be good economics, but it would also make our city a better place to live.

Any plan to improve the eastern section of the Gardiner is likely to satisfy no one, but it would at least seem like prudence. Such as plan has all the costs of refurbishing the expressway to its original condition plus additional costs to make the land around it more attractive to investment. But these improvements can be directly connected to clearly defined issues. Need green space: build a park. Find the underpasses to be dark and intimidating: put in some lights. I don’t think this will be decided on the cold costs of the construction compared to the benefit the city will derive from it. Politically the price tag of any option will be less of a deterrent than an appearance of luxury. Torontonians will not spend money on showy public works; if it looks indiscreet then it would immediately become of focus of resentment for everyone not living downtown. Improving the existing structure would succeed because we might accept it as a story of mending old clothes over buying a new sexy dress.

Or we could go out and buy a sexy new dress. Starting fresh has the promise of solving several issues in one grand sweep. All the replacement plans include building new public transit. While we need it, Torontonians are so divided that the majority would block any transit development to be built downtown. The Downtown Relief Line might as well be named the Elitists’ Private Railway. I am attracted by designs that involve replacing the eastern Gardiner as these designs would be a satisfying single cut to a Gordian Knot. But such big plans can create new problems if we are not careful. Unfortunately, public opinion is pretty much the antithesis of careful considered thought. In more prosperous times the mood might be an enthusiastic “yes”. But in these timid times a mere insinuation can turn public opinion into a blunt “no”. There are plenty of politicians who would want to look like they are busily going about the people’s business by provoking a “no”. How much such a plan costs is not as important as it being too flashy and it triggering some fear in the voters.

If, God forbid, any section of the Gardiner collapses before work begins then the remainder of the expressway will be demolished to appease the voters. Buildings and structures that commit the crime of failing are swiftly put to death in almost all cases. Private car owners would demand something similar to the expressway they know and then and only then would a plan to replace the Gardiner have a chance. But such a disaster could also have a diametrically different outcome: nothing.

These days city council couldn’t organize a piss-up in a brewery. Opportunities to deal with manifest issues come and go while we debate phantom issues and score empty political points. It is possible city hall would be unable to organize a replacement structure and we might learn to live without the Gardiner. No eastern Gardiner Expressway is the essence of the remove option. This has happened to other cities, and it is not so bad. Although I can see the traffic stopped on the Gardiner at rush hour, it is not as important to our needs as its bulk might suggest. Once gone, we might not feel the need to replace it. Removing the expressway is an impossible task politically, but events may be allowed to take the initiative.

## Economic Terms That Confuse Politics

Trying to discuss politics often gets mired to common confusion over the most basic concepts. Bad politicians benefit from this confusion and it is up to citizens to call them out when they cross the lines between intelligent debate and willfully bending the truth to their own selfish ends. I won’t even get into the hyperbole of “Communist” and “Fascist” that has rendered any discussion of political theory into meaningless barking. Let us just look at simple day-to-day economics. This formerly neutral territory is quickly becoming politicized, with ideologues gleefully swapping similar, but different words to avoid discussing uncomfortable truths about our world.

1) Debt versus Deficit
In a world where most people are supposed to manage their household finances this should be well understood. Deficits may be a sign of living beyond your means, but debt is just how capitalism works. Everyone from the person who gets a car loan to the Corporation who launches a new product breaths the oxygen of credit and therefore debt. It is just a mechanism to raise capital in a timely manner so you can continue earning money. The car gets you to work and the new product keeps you competitive. Deficits are not always a sign that you are spending too much. Ambitious people go get a raise and corporations increase income. Companies sometimes lose money, but Companies that continually lower costs can get caught in a race to the bottom where they are left with a worthless product that no one wants to buy. Similarly, societies that don’t tax or provide services are left with territories that are ungovernable and where no one in their right mind would want to live. Taxes are just the cost of civilization.

2) Income versus Wealth
This is really the inverse of deficit versus debt, but has become more more important with the impoverishment of a large portion of what we used to call the first world. We felt ourselves to be invincible when so many of us become the first generation to own a home or get an education. A good income allowed most of us to gather together sufficient wealth to make us real participants in our economy and our society. Now this way of doing things is no longer fashionable. Our society seems to be regressing to merely existing for the benefit of a lucky few. What really steams me is that pundits continually use income interchangeably with wealth. The two are related; without income you cannot become wealthy (unless you inherited it), but wealth is the part you get to keep. The popular thing to say today is that if you are not wealthy you should stop spending. Difficulty with that is spending is often the means to more income and reduced spending among the majority is the definition of recession. Without a car, most people can’t go to work and not buying cars puts those who make them out of work.

3) Average versus Middle
This is the most insidious swapping of terms. Smart people who know better continually flim flam the public with this one. In statistics, these two numbers are often very close in what is known as normal distribution, but not everything follows normal distribution. Crowing about average wages is taking pride in a meaningless number. Personal wealth and income has never followed normal distribution: it has always followed the power law. Economist Vilfredo Pareto noticed back in 1906 that 80% of the land in Italy was owned by 20% of the population. The Pareto Principle has remained true and is becoming more extreme in our time. The power law always amazes undergraduate students as it runs counter to common sense.

Take note that the dishonest politicians takes advantage of our misguided common sense. Anyone who appeals to common sense is like a man making his way to the store exit with a bulging overcoat; only an idiot would not stop and search them for stolen goods.

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## Should I Write This Book?

Had a dream last night that Lisa gave me a book I really wanted as a gift. It was one of those cheap academic paperbacks you find being sold along the Seine in Paris. Maybe forty-eight pages with a cover of grey-blue card. It was a post-modern philosophical treatise on bodily fluids in art called “Snot”.

## Hidden Geography of Saint Lawrence

The Philpotts map was made just after the War of 1812. The city of York mapped then can still be seen in Toronto today.

The map made by Lieutenant Philpotts in 1818 shows several geographical details of old Toronto that have long disappeared but determine the shape of the city we see today.

Toronto’s street design is firstly determined by the same military need that had Lieutenant Philpotts creating the 1818 map. Toronto’s reason for being where it is was to make transportation and communication of British North America less vulnerable to attack by the USA. The Niagara River and the Detroit River could be closed by the US forts on both rivers and would quickly strangle the small British colony. Yonge Street bypassed both these choke points by linking Lake Ontario with Georgian Bay.  The Toronto Islands, a spit back then, made for a sheltered port and a natural terminus for Yonge Street. The town itself was built on the military grid that characterizes the entire road network of Ontario.

But the grid of Toronto streets is not uniform. There are bends, diagonals and slightly skewed diversions in the city. This 1818 map gives us clues as to why we have these deviations from what is otherwise a regular street pattern.

The most obvious influence is the old shoreline of Lake Ontario that neatly matches present-day Front Street. This also explains its paradoxical name when the lake shore is now over half a kilometer away.

There are also creeks and ravines that have been covered over and filled-in over the last two centuries. The most influential of these in Saint Lawrence is Taddle Creek, the same creek that ran through what is now the Saint George Campus of the University of Toronto. The diagonal on Richmond Street is an adjustment to the grid that follows the top of its ravine. The diagonal on King Street that causes it to eventually merge with Queen Street is the effect of a bridge that used to be near Parliament Street. The off-kilter direction of Sherbourne and Britain Street is due to another bridge over the same lost creek. The smaller bend at the end of the Esplanade and Distillery Lane follow the details of the shore around the lagoon that is now a playing field.

There are evenings when the air is still that I can smell stagnant water while walking on Berkley and I have always suspected there was a covered creek nearby. Certainly when walking through where this creek used to be one can still see the rise and fall of land that defined its course. Next time you walk through the city you might be able to see the traces of the natural landscape that used to exist.

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