25th Scavenger Hunt – 1/3

I’ve been participating for a few hunts to what has been known as Chrysta Rae’s Scavenger Hunt, as Google+ Scavenger Hunt, and which these days is the Photography Scavenger Hunt – and I may or may not be in the US right now for next week’s Scavenger meetup 😉

This was the 25th Hunt, and as a way to celebrate, we got a very large hunt: 26 words! They were the words of the first Hunt, to which I didn’t participate. And, as you’d expect from the number, there was one word per letter of the alphabet.

I did manage to submit a picture for each word – and I’m very proud of that – although the overall quality of the pictures is obviously very inconsistent 🙂 (I’m still VERY HAPPY with a significant amount of my shots, so there’s that 🙂 )

In this post and the following two, I’ll present what I submitted; I’ll present them in the same order as they were revealed in our community, because this way I don’t have to think as much 😉 And I’m adding a link to the community albums as well – these are definitely fun to browse!

Acorn

I thought I’d be stumped by Acorn until almost the last minute. And then I remembered that the Swiss card game Jass had an Acorn suite! So I went to my neighboring toy shop, bought a maxi set of Jass cards (which means I can now play Jass – I just need to learn how to play 😉 ) and, after a bit of tinkering, I arrived at the shot above. I’m not super happy with it because I think it’s quite boring, but I’m happy I found something to submit 🙂

Z

I recently started playing with lettering and brush pen calligraphy, so that made my submission for Z kind of obvious. The drill sheet comes from The Postman’s Knock, and the picture itself is pretty straightforward 🙂

Xylophone

I think my Xylophone entry is my favorite for this Hunt. SOME PEOPLE argue that a XYLOphone is necessarily wood – and they’re not wrong, BUT considering the Hunt album, it’s VERY CLEAR that Fisher Price has done A LOT for the popular image that comes to mind when saying “xylophone” 😉

So I made mine with glasses filled with water – something which, as far as I can tell, happens at roughly one wedding out of two at least 😉 – and I used food coloring to evoke said Fisher Price image. I then played with the angle of the light – the one I ended up shooting had the light pretty low, which allowed to get colored shadows, which I really, really liked, at the cost of fairly strong reflections, which I liked… less.

Post-processing was mostly color correction to get a better visual (especially on the red and the orange) – I’m almost tempted to correct it now since I’ve seen that I had forgotten to correct the little dots at the bottom of the glasses for consistency 🙂

And, for the record: this xylophone is _roughly_ in tune – I could play a few tunes on it without hurting my ears too much (I do not have a very good ear, though 😉 ).

Sponge

For my Sponge entry, I went on a day trip to Konstanz – which I documented already: Sea Life. I had gone there for the specific purpose of shooting a sponge picture, and I’m happy the trip worked out 🙂

Whistle

For Whistle, I knew I wasn’t going to be stuck, because I knew that, in the worst case, I’d setup and shoot Whistle Stop (the board game). But then I was actually too lazy to setup the game, so I fell back on this – which involved a significant amount of YouTube watching to be able to pull off a credible whistle gesture. And no, I still can’t whistle that way. I’m very disappointed.

Hamburger

My Hamburger submission was a cell phone picture snagged at Fork&Bottle during a dinner with friends. It was a “backup” shot that I ended up using almost as is.

Underwear

Underwear (careful, NSFW album) was the word I had estimated with the highest chance of stumping me when the list came out. That’s not the kind of theme I’m super comfortable with 😀 But in the end, I’m very happy with what I came up with. I was definitely going for a “Nike ad” kind of aesthetics, and I think I pulled it off. (Well, except for the Adidas bag below, I guess.) It was also an opportunity to experiment with real studio lights and reflectors than a colleague of mine had lent me (which allowed me to conclude that I really didn’t want the same softbox setup because it was a huge pain to assemble 😉 ).

Newspaper

Another uninspired shot for Newspaper 😉 I almost snagged a picture from someone reading a newspaper on the train, but I didn’t manage to actually gather the courage to do that. So instead, I setup my tripod and my camera timer to take pictures every few seconds while I prepared newspaper for recycling (in Switzerland we have to bind paper together to recycle it) – so at least I learnt how to program my camera timer for that sort of sequence 🙂

Tire

I don’t exactly remember when I got the idea of “ooooh I need LEGO” for the Tire theme, but it was early enough that I had made a few attempts at setting things up with my regular collection of toys and concluded that I needed a figure at another scale than what I had. That made it quite obvious that I needed a LEGO Technic figurine – so I hit Bricklink, ordered a couple, and they arrived a few days later (so I’m now the owner of a couple of LEGO Technic guys.)

I honestly wish I had taken the time to re-shoot this one – at least to get a black road instead of my white-ish balcony. (I tried to edit it in post-processing and failed miserably 😉 ). Part of my issue there was that I couldn’t think of a place where I could find believable black terrain and not feel super self-conscious with my setup So to me, this one falls into the category of “I liked my idea, I’m really not convinced about my implementation”.

That’s it for this first reveal post – more to come!

52Frames, weeks 17, 18 and 19

I haven’t posted my 52Frames pictures in the past three weeks over here, so let’s fix that!

Week 17 – Upside Down

Fine, this one I had already posted when I talked about the Zürich Botanical Garden. Reflections were explicitly on topic for the “Upside Down” theme, and I accidentally found that one, so there it is. I’m a bit disappointed that I didn’t get a cleaner reflection – but it’s pretty hard to find a ripple-free moment at a time where there’s a lot of visitors, including some who throw stones in the pond 🙂

Week 18 – The Dark Side

I’ll admit a lack of time, inspiration and motivation for The Dark Side theme – especially since I hurt myself that week! (I sprained my ankle, I’m fine, but it’s still SUPER annoying.) So I snapped that one and called it “The Dark Side of Holidays” 😉 With a bonus dark chocolate line-up 😛

Week 19 – Textures

I was actually looking forward to the Texture theme, because I was envisioning a “hunt for textures” photo-walk, which, considering the picture of Week 18… kind of did not happen. Thankfully, SOMEONE has been baking and working on their buttercream piping skills, so I got a yummy texture picture for their efforts 😉

Zürich Botanical Garden

Last week-end, the weather was quite nice, and I wanted to go for a walk – so we ended up in the Zürich botanical garden. I had been a couple of times, but in particular I don’t think I had ever entered the large greenhouses – despite their pretty characteristic look.

The main issue with greenhouses is that their climate is, by design, not very compatible with, well, me – I still had a very good time taking pictures of the different specimens there.

The words: “OH THOSE ARE SO CUTE” have been uttered:

as well as “THESE CACTI ARE SO FLUFFY!”

The outside of the garden was also very nice – the frogs were very noisy (probably to compensate for the fact that they were not very visible) and I found some weird stuff too.

The full gallery is available on SmugMug and on Google Photos.

Sea Life in Konstanz

Last week, I went on the other side of the German border to go visit the Sea Life aquarium in Konstanz to take pictures. Here my favorites – and the full album is available on Google Photos or on Smugmug.

I enjoyed my visit – the aquariums are well presented, there’s a lot of information, and it seems very kid-friendly (which made MY life slightly more complicated because there was so many things at a lower level 😉 ). I think I may have missed some stuff – because it seems weird that an aquarium would not have any jellyfish (so I probably missed the jellyfish 😦 ).

On the photography side, I went with my K-1 fitted with my trusty 24-70/2.8 (I cannot BELIEVE I actually hesitated buying that glass. It’s wonderful.) I’m quite happy that it’s definitely possible to push the ISO to 6400 in low-light and to still get reasonable results – the noise is visible, but not too problematic. Autofocus was however sometimes pretty/very hard to get. I still need to study how to handle noise properly in Darktable, because right now I’m blindly applying a preset that I got… somewhere, and that does the job well enough, but I think there’s room for improvement there.

52Frames – Week 16 – Nature

Last week’s theme for 52Frames was “Nature” – I’ll admit that, to me, this is an example of a theme that doesn’t necessarily makes me want to go much out of my comfort zone and/or try to do something original. That, or my creative streak is currently busy with the Scavenger Hunt 😉

In any case: here are some flowers!

Proof by induction and proof by contradiction

This is the translation of an older post in French: Raisonnement par récurrence et raisonnement par l’absurde.

Let’s have a pretty short post so that I can refer to it later – I have another monster-post in the works, and I realized I needed the following elements to make it work, so here’s another post! I’m going to talk about two fundamental tools in the “proof toolbox”: the proof by induction and the proof by contradiction. These are tools that are explained in high school (well, they were in my French high school 20+ years ago 😉 ), and that you’ll see everywhere all the time, so let’s explain how it works.

Proof by induction

The idea of the induction proof is dominoes. Not the ones with the dots on them, the ones that you topple. You know that if you topple a domino, it falls. And if a domino falls, the next one falls as well. And you topple the first domino. Hence, all the dominoes fall.

Proofs by induction work in the same way. Suppose you have a property that depends on an natural number (positive integer), and you want to prove that it’s true for any natural number. First, you show that it’s true for a small natural number, say 0, 1 or 2 (sometimes the property doesn’t make much sense for 0 or 1). Then, you show that, if it’s true for a natural number $k$, it’s also true for $k+1$. So you have the “start” of the dominoes, the toppling (“it’s true for 0”), and the “chain” of dominoes (“if it’s true for $k$, it’s true for $k+1$“). If these two conditions are true, all the dominoes fall (“the property is true for all natural numbers greater than 0”).

Now this is where I’m a bit annoyed, because I have a an example that works, but the induction proof kind of sucks compared to another, which is much prettier. So I’m going to show both 😉

Suppose that I want to prove that the sum of all integers from 1 to $n$ (that is to say, $1 + 2 + 3 + 4 + ... + (n-2) + (n-1) + n$) equals $\displaystyle \frac{n(n+1)}{2}$. I start with $n=1$: $\displaystyle \frac{1(1+1)}{2} = \frac 2 2 = 1$, so the base case is true.

Now, I suppose that it’s true for an arbitrary natural number $k$ that the sum of the integers from 1 to $k$ is equal to $\displaystyle \frac{k(k+1)}{2}$, and I compute the sum of integers from 1 to $k+1$: $1 + 2 + 3 + ... + (k-1) + k + (k+1)$. This is equal to the sum of the integers from 1 to $k$, plus $k+1$. By induction hypothesis, this is equal to $\displaystyle \frac{k(k+1)}{2} + k+1 = \frac{k^2 + k + 2k + 2}{2} = \frac{k^2 + 3k + 2}{2}$. For my proof to work out, I want the sum of integers from 1 to $k+1$ to be equal to $\displaystyle \frac{(k+1)(k+2)}{2}$. And it so happens that $(k+1)(k+2)$ is precisely equal to $k^2 + 3k + 2$.

So I have my base case, my induction step, and I proved exactly what I wanted to prove.

Now for the alternative, prettier proof. You consider a table with two lines and $n$ columns:

1  2   3   4  ... n-2 n-1 nn n-1 n-2 n-3      3   2  1

and you compute the sum of all the numbers in the table. You can add up, for each column, both lines. Every column sums to $n+1$: it’s the case for the first column, and at each step, you remove 1 from the first line, and you add 1 to the second line, so the sum stays the same (there’s actually a “hidden” induction proof in there!) There are $n$ columns, so if I add all these results, it sums to $n(n+1)$. But if I group the sum in a different way, the first line is equal to the sum of integers from 1 to $n$, the second line as well… so $n(n+1)$ is two times the sum of the integers from 1 to $n$, which concludes the proof.

Proofs by contradiction are sometimes dangerous, because they’re often misused or overused. I know some mathematicians who argue that a proof by contradiction is not very elegant, and that when one arises, it’s usually worth it to make the extra effort to try to turn it around in a non-contradiction proof. I still like the reasoning behind it, and it sometimes makes life much easier.

We want to prove that a proposition A is true. To prove A by contradiction, you make the hypothesis that A is false, you unroll a series of consequences that would be implied by the fact that A is false, and you arrive at something that you know is impossible. And if the fact that A is false implies an impossibility, it means that A is true, otherwise the universe collapses and it’s messy.

My favorite example is to prove that $\sqrt 2$ is irrational, that is to say that you can’t write it as $\displaystyle \frac p q$ where $p$ and $q$ are integers.

I need a tiny preliminary lemma: I’m claiming that if an integer $n$ is even, then its square $n^2$ is even, and that if $n^2$ is even, then $n$ is even. If $n$ is even, I can write $n = 2k$ (with $k$ integer). Then $n^2 = 4k^2 = 2 \times 2k^2$, so $n^2$ is even. If $n$ is odd, I can write $n = 2k+1$, so $n^2 = 4k^2 + 2k + 1 = 2(2k^2 + k) + 1$, so $n^2$ is odd. So, if $n^2$ is even, then it can’t be that $n$ would be odd (because otherwise $n^2$ would be odd as well), so $n$ is even.

Now back to the irrationality of $\sqrt{2}$. We make the hypothesis that we can write $\displaystyle \sqrt 2 = \frac p q$. We can also make the assumption that the fraction is irreducible, because if it’s not, you can reduce it so that it is, so let’s assume that it’s the one we took from the beginning. (Note: a fraction $\displaystyle \frac p q$ is irreducible if there is no integer $k \geq 2$ such that $p$ and $q$ are both divisible by $k$. If $k$ exists, we divide $p$ and $q$ by $k$, and we get the fraction $\displaystyle \frac{p/k}{q/k}$).

So: I can write that $\sqrt 2 \times q = p$. If I square this equality, I get $2q^2 = p^2$. Since $q$ is an integer, $q^2$ is an integer, so $p^2$ is an even number (because it’s equal to twice an integer). But then, if $p^2$ is even, then $p$ is even as well, according to my preliminary lemma. So I can write $p = 2k$ and consequently $p^2 = 4k^2$. But then, since $2q^2 = p^2 = 4k^2$, I can also write $q^2 = 2k^2$, so $q^2$ is even, so $q$ is even as well. But that’s not possible: $\displaystyle \frac p q$ is irreducible, so $p$ and $q$ cannot be both even! So something is wrong in my reasoning, and the only thing that can be wrong is my initial hypothesis, that is $\sqrt{2}$ is rational. Hence, $\sqrt{2}$ is irrational. Cute, isn’t it?

Peter Bence in Zürich / Theater 11

On Tuesday, we went to the Zürich concert of Peter Bence. Peter Bence is a Hungarian pianist who gained his fame with piano covers/arrangements – I particularly like his Don’t Stop Me Now and his Bad. Generally speaking, the guy is impressive. He also happens to have held the record of the fastest piano hitting (with 765 hits in a minute 🙂 )

So when a friend mentioned to me that he was coming to Switzerland, I hesitated a bit, and finally went “why not” and bought a couple of tickets for the Zürich show. And I didn’t regret it 🙂

We got treated with two hours of a great show – an alternance of known covers, original pieces, and Bence discussing what he was doing and joking around with the audience. I’ve had a few favorite pieces during the evening: the John Williams medley, the Don’t Stop Me Now (with a bit of Bohemian Rhapsody) and the original piece he called Fibonacci. I was, however, not super convinced by his Somebody to Love – I assume it’s musically good, but to me it felt “messy” and didn’t trigger the “right” emotional response for me, I think.

On the “non-strictly-musical” part of the show, the audience was also asked to contribute during another original piece to clap our hands after a given musical phrase – that was fun, and everybody played the game… even when it came back a bit later. The “lighting” part of the show was also very impressive and working very well.

Theater 11 is not a very large venue (but I think I’ve only been to Hallenstadion in Zürich so far, which is… essentially 10 times larger), which I liked, because even when booking late (and with a low number of places left), we still had pretty good seats. However, there was some issues with the sound system (apparently worse from Bence’s perspective than from ours). I was kind of disturbed at the beginning by a low… hum, I guess, in the speakers – whether it disappeared or I got used to it quickly, I can’t say 🙂

Generally speaking, it was a very, very enjoyable experience, the show was great, and I’m really looking forward to Peter Bence’s album. And to re-listen to what’s on YouTube in the meantime 😉 And if you have the opportunity to see the show: it’s worth it!