perspective

An odd one out at Shot Espresso, Parsons Green

tubes playing with perspective Shot Espresso Parsons Green

The view from the ‘conservatory’ in Shot Espresso, Parsons Green

A couple of weeks ago we were wandering around the Parsons Green area in search of a coffee. Near the station, was a small shop front with a familiar name. Not quite a chain, but the logo of Shot Espresso is well known to me from its relatively new outlet in Victoria. It turns out that the Parsons Green branch is one of four outlets for Shot Espresso which started just around the corner in Fulham.

The staff were very friendly and took our order before we found seats at the back of the café. Although there was plenty of seating near the counter it was all taken, clearly this is a popular haunt on a Saturday afternoon. This did mean however that we found a cosy table in a small but very bright area, almost like a mini-conservatory. It seems we often have a long black and a soy hot chocolate and today was no exception. The hot chocolate was apparently perfectly well done my long black was fruity and drinkable, offering a perfect flavour backdrop against which to appreciate the area of the café.

Then a tricky decision. Ordinarily, I am not a fan of reviewing chains (though there is a question, does four branches equal a chain or not?). I’m a great fan of what an independent coffee shop can bring to an area, a place where the owners can be found behind the counter and you can really get to know a friendly space. However Shot Espresso is not that large a chain and the branch at Parsons Green had the feel of a local. The staff when we were there certainly took an interest in the running of the shop and, another factor in my decision to review, there were so many things to notice here.

infinity, shot espresso

Infinite tables? The logo on the table next to us at Shot Espresso Parsons Green.

I’ve already mentioned the light in the conservatory, there were also the light fittings in the main part of the bar. Wooden outlines of cubes around a light bulb that played with your image of perspective. On the tables next to us, the symbol of the manufacturers was similar to the symbol of infinity, why? But then, an oddity that prompted a mathematical curiosity. On each table was a miniature watering can holding sugar. It’s almost a game:

You have a mug of coffee, a cup of hot chocolate, a doughnut and this watering can on your table. Which is the odd one out and why?

If you answered the watering can, you would have been correct. Topologically the mug of coffee, cup of hot chocolate and the doughnut are the same whereas the watering can is quite different. What does that even mean? It means that in terms of shape, a doughnut can be morphed into a coffee mug which can clearly be morphed into a tea cup as they each have one hole through them. The watering can however has multiple holes, not just to hold it and to let the water out but also, in this ornament design, at the join of the body to the spout (look carefully). This means that there is no way that you can transform a watering can into a doughnut, they are different categories of shape.

table at Parsons Green Shot Espresso

A coffee cup and a miniature watering can. But which has more in common with a doughnut?

This field of mathematical study (which is known as topology) has, in recent years, taken on enormous significance to physics in terms of understanding some odd effects including the way that some materials conduct electricity (or not). Indeed, it has become so important that it was the subject of the 2016 Nobel Prize (you can read the citation here). And yet, even for someone who works in solid state physics and should have a mathematical background, trying to get my head around this subject is extremely difficult.

Which got me thinking about something similar. When teaching, it is sometimes apparent how much mathematics appears as if it is another language. And in parallel with language, it requires a fluency to appreciate its beauty. And further, even with a fluency, to appreciate some use of the language requires more than just fluency but immersion, a concentration, an attention to the words. Perhaps an analogy is needed. Although fluent in English, I do not usually immerse myself in reading it. Consequently, I find the poetry of John Betjeman amusing and ‘readable’, but the poetry of Gerard Manley Hopkins very difficult. With patience, and advice from others, occasionally I can gain a flash of insight into a poem of Hopkins and realise the brilliance of the language but more often I struggle. What I would never imagine doing is saying “I can’t read English, I was never good at it in school”.

And it is here that it seems to me the parallel with mathematics ends. For while we can have fun with algebra, understand some of the beauty in calculus and perhaps struggle with topology, we nonetheless seem happy in our society to say “I can’t do maths, I was useless at it in school”. We accept boasts about mathematical illiteracy when we would blush to say similar things about our native language (whether it is English or another language).

Why is that?

watering can, Shot Espresso, Parsons Green

A closer look at the watering can. The number of holes in the join to the spout would make this useless as a plant watering device.

Surely there are few who are genuinely mathematically illiterate, at least, not to the extent that it is ‘boasted’ about within society. Indeed, you find many who are happy to admit that they don’t “do” maths, actually just mean that they would prefer to use their phone to calculate something. Just as with a spoken language, the language of mathematics requires practise. For it is practise that allows us to appreciate the fun of mathematics just as it is practise that allows us to read poetry. Why do we deny ourselves the fun of a language because it is fashionable to admit illiteracy in it?

If you would like to push yourself with some mathematical poetry, you can read about topology, coffee and doughnuts here or in more detail here and more information on the 2016 Nobel Prize can be found here. In the meantime, if you see something mathematically beautiful in a café, please do share it, either here in the comments, on twitter or on Facebook.

Enjoy your coffee, tea or doughnuts.

Shot espresso can be found at 28 Parsons Green Lane, SW6 4HS

 

 

 

 

Some perspective at Over Under, Earls Court

Over Under Coffee Earls Court

Follow the arrow! Over Under Coffee in Earls Court.

Whenever I’m heading somewhere that I haven’t been to for a while, I check the London’s Best Coffee app to see if any new cafés have popped up in the area since my last visit. So when I was in Earls Court recently, I was very happy to be alerted to a new café on the map with a review by Beanthereat.

Over Under Coffee is at 181A Earls Court Road but is tucked around the corner from the main road and so thank goodness for the helpful arrow (and the map which told me I should be on top of it). Once found, we ordered coffee and banana bread and took a table to sit down. The friendly staff behind the counter were quite confident of the ingredients in the banana bread as it is made locally by a lady in Fulham (whose name I have sadly forgotten). The coffee and banana bread formed a great combination for a mid-morning snack. Coffee is roasted by Assembly roasters over in Brixton and came with lovely interference patterns in the bubbles on the surface together with dancing white mists, which never fail to fascinate me.

On the table next to ours was a small Kilner jar for sugar and two succulent plants. The Kilner reminded me of the use of air valves in coffee packaging (which are non-recyclable plastic) and the interesting experiment by Roasting House coffee roasters to investigate whether they are actually needed for freshly roasted coffee (which you can read about here). However it was a picture above the table that prompted the thought-train for today’s Daily Grind. A charcoal sketch, the picture featured a tree in the foreground with a fence behind it. From a very early age we are taught how to represent 3D objects on a 2D sheet of paper, the idea of perspective seems ingrained on our minds. But how intuitive is it really?

perspective in coffee

A picture at Over Under. Note the smaller reflections of the (more distant) light fittings.

Although the ancient Greek artists could convey an idea of depth in their art, the development of a mathematical understanding of perspective only came with Filippo Brunelleschi (1377-1446), although a written account of the mathematics of perspective did not arrive until Leon Battista Alberti (1404-1472). Alberti’s method for drawing in perspective used not just a vanishing point, but an additional diagonal vanishing point in order to construct a sense of depth and an accurate depiction of perspective (a description of Alberti’s method is here). The development of the understanding of perspective during the Renaissance meant that for some paintings, the ‘viewing depth’ can actually be calculated, while other artworks managed to create optical illusions whereby objects would jump out at the viewer as if they are in 3D. Works such as Andrea Pozzo’s ceiling in the chiesa di Sant’Ignazio in which a flat ceiling appears magnificently domed. Or, closer to home,  Samuel van Hoogstraten’s work in the National Gallery in London in which the viewer looks through a peep hole to see the interior of a house complete with a dog that appears to be sitting up inside the painting. Such paintings required a knowledge of the mathematical rules behind the depiction of perspective. Isn’t it surprising that the understanding of these rules is so recent?

Over Under Earls Court

Coffee with bubbles showing interference patterns at Over Under Coffee

Another art work with an interesting use of perspective that will bring us, in some way, back to Over Under Coffee is Raphael’s fresco “School of Athens“. The two figures of Plato and Aristotle stand at the centre of a diverse group of philosophers including Socrates, Zoroaster, Euclid, Diogenes the Cynic and, possibly, an image of Hypatia of Alexandria. Although the use of perspective for the architecture draws your eye towards the centre of the picture, two spheres (held by Zoroaster and Ptolemy) on the right hand side of the picture are drawn as circles rather than ellipses. Spheres viewed from an angle should be represented as ellipses if drawn correctly according to the rules of perspective. Did Raphael make an error in perspective (that may work better for our eyes?) or is the degree to which these two spheres are distorted within the limits of the fresco brush and so not visible in the picture? An episode of Radio 4’s In Our Time discusses this picture at length including a deep conversation about the significance of Plato pointing upwards towards the heavens and Aristotle indicating towards the Earth. Plato’s wisdom and Aristotle’s knowledge, above and below, much like the weave logo that brings us back to Over Under Coffee.

Over Under Coffee can be found at 181A Earls Court Road, SW5 9RB.

 

 

Getting some perspective at Skylark, Wandsworth

Skylark Wandsworth

A sunny day at the Skylark on Wandsworth Common

It is late spring in the northern hemisphere and when the weather is fine, what better way to spend it than with a coffee in the middle of Wandsworth Common at the Skylark Cafe? With a number of tables outside and, if the weather turns bad, several more tables inside, Skylark is a lovely place to spend some time while wandering in West London. On the day that we were there, Skylark was frequented by a large number of families however, it was a Saturday afternoon and so it is quite possible that on a week-day it will be a bit quieter. The coffee is roasted by Caravan and they have an interesting array of cakes inside, but it was the plants on the tables outside that caught my attention. Each table had a pot of thyme on it, but the thyme smelled of lemon. Perhaps it was lemon thyme, but something that looks like one thing and smells of another is a nice introduction to this week’s Daily Grind which is all about appearances, reality and perspective.

The thyme was growing in a metal flower pot which reflected the wooden table top. From the photo (below, left), it is clear that the pot is cylindrical but if we stop and think about it, how do we actually know that? The image is two dimensional, no third dimension is possible through a computer screen. What clues in the picture tell you that the pot is cylindrical? The bending of the lines of the table top? This is a pattern that we have learned, we have found from experience that something that is circular will bend straight lines in this way.

perspective, flower pot

What shape is the flower pot?

How we see things and what we think we are seeing was a subject that bothered George Berkeley (1685-1753). How can you know that anything external to yourself is real? Everything you touch, everything you see, hear, taste or smell is, ultimately, a response in your brain to a stimulus. It is not easy to prove that anything ‘outside oneself’ really exists. Indeed, Berkeley argued for the theory that what was ‘real’ was only the sensations in your mind. The theory was famously challenged by Dr Samuel Johnson (1709-1784) who used to drink coffee at the Turks Head in Gerrard St. in what is now Chinatown. Johnson hurt himself by kicking a stone, while saying of Berkeley’s theory: “I refute it thus“. Does Johnson’s sore foot really refute the theory though? How can we avoid Berkeley and find our world again?

Writing about science at the turn of the twentieth century, Pierre Duhem (1861-1916) argued that “All the time we view scientific theory as an attempt at an explanation, we will be limited in what we consider an acceptable explanation by our metaphysical beliefs. Only by accepting that theory is in fact a description, a cataloguing, do we free ourselves from all but the primary metaphysical belief that the world exists“. In other words, in order to ‘do’ science we have to rely on (at least) two beliefs a) that the world outside exists, b) it is consistent, that is, governed by laws that are knowable. Neither of these premises can be ‘scientifically’ proven, instead they lie at the base of our belief system, even if we do tend to take them for granted. It is far easier after all to live in the world, if we assume that it exists.

Americano, Caravan coffee, Skylark, Wandsworth

Coffee at the Skylark

None of this should stop us doing science. Whatever we are investigating with our experimental (or theoretical) tools it is beautiful and the more that we understand the mathematics that describe the world, the more beautiful the world outside becomes. I cannot prove, scientifically, that the world outside exists, I could possibly argue that it does based on philosophical ideas but I will never be able to prove it. I understand that the pot on the table at Skylark is a three dimensional cylinder because of the way that the light is  bent on reflection and from my, admittedly intuitive, understanding of perspective. Perhaps we also need some perspective in appreciating what we can, and cannot, prove with science.

 

Skylark Cafe is on Wandsworth Common.

Quote taken from “The Aim and Structure of Physical Theory”, Pierre Duhem, 1910.