The Bladder Monster

As I mentioned last week, I’ve been ill. For those who wanted the grisly details, well: here you go.

Warning: this blog post contains frank subjective descriptions of the symptoms of slightly-icky medical conditions including photographs. It’s probably safe for all audiences, but you might not want to be drinking anything while you read it.

The trouble began, I suppose, about a month and a half ago, when a contracted what seemed to be a minor urinary tract infection. If you’re a woman then, statistically-speaking, I probably don’t need to tell you what that is, but for the benefit of the men: it’s what happens when bacteria (or, sometimes, a fungus or virus) infects the renal system: the kidneys, bladder, ureters, and especially the urethra. It’s not pleasant: it gives you the feeling of needing to pee the whole time, makes it harder to pee, and – when you do – it feels a little bit like you’re piss is made of lava.

Microscope view of infected urine.
This urine contains white blood cells (the big circles) and bacteria (the tiny ‘wormlike’ things). Healthy urine contains little to none of these. Anybody else feel like they’re playing Spore?

Despite it not being common for men (more on that later), I’ve had mild UTIs on a couple of occasions in my life, and I’d always found that ensuring that I got plenty of water and a full RDA of vitamin C was more than enough to make it clear up all by itself within a couple of days. So that’s what I started doing. But then things took a turn for the worse: I started getting a stabbing pain in my left kidney. Recognising this as being pyelonephritis, I went to the doctor who prescribed me a course of the antibiotic ciprofloxacin. Within a couple of days I was feeling right as rain (of course I continued to finish the course of drugs, although I was interested to see that that advice is starting to become controversial).

Dan and Annabel have a picnic in the park.
Happy, healthy, and out for a picnic.

Naturally I was a little disappointed when, the week before last, I started getting UTI-like pain again, followed very swiftly this time by pain in my bladder that constantly felt a little like I was recovering from being punched. Back to the doctor I went, where (after the usual tests to work out what the most-likely best-antibiotic to use was) I was prescribed a course of nitrofurantoin. I’d never had this particular drug before, and it wasn’t initially clear which of the escalating ill-effects I was experiencing were symptoms of the infection and which were side-effects of the medication: it started with joint pain, then nausea, then diarrhoea, then a full-on fever. It was at the point that I was fully-clothed in bed, running a temperature and soaked in sweat but still feeling cold and shivering that Ruth called 111, who told her to take me to A&E.

(Which, like her care for me in general, she did fabulously well, except for a little bit where she sort-of ran me over in the car park of the hospital: thankfully some friendly paramedics were standing around and were able to drag me into the building. Anyway, I don’t have much memory of that bit and I certainly don’t have any amusing photos, so I’ll skip over it.)

Dan, shortly before inpatient admission but already recovering from the worst parts of his hospital visit, last week.
Feverish to the point of delirium, I don’t have much recollection of the first few hours(?) in the hospital. But I was alert enough to request that a photo was taken for the inevitable blog post. Ruth, however, insisted upon waiting until I apparently looked a lot less like I was about to die: so here it is!

A few tests later, the medical staff seemed confident that what I was experiencing was not an allergic reaction to the antibiotic (however, I see that they still made a note of it as a risk on my notes!) but was a progression of the infection, which seemed to have crossed over from the tissues of my renal system and into my bloodstream and was now generally causing havoc by attacking the rest of my body. They hooked me up to a drip of an intravenous antibiotic and kept me stocked with painkillers, then sent me up to the urology ward and set me up with a “bed” (urology mostly deals with outpatients, and so my ‘bed’ was actually a trolley, but they wanted to keep me close to the urologists in case of any complications).

The view from my hospital ward window: Oxford city is visible in the distance.
It was only the following morning, with the delirium passed, that I realised that I was on the sixth floor. Looking out of my window, I could just make out the spires of the Bodleian Library in the distance, so I dropped my coworkers an email to apologise for not being on my way there.

A consultant switched me to a week’s course of yet-another different antibiotic – co-amoxiclav – and recommended keeping me in for another night. Now, I think that co-amoxiclav is a really interesting drug, so I’m going to be a bit of a nerd and tell you about that for a bit (I promise we’ll get back to my health in a moment: if you don’t want the science bit, just scroll past the diagrams to the next photo).

Amoxicillin, with lactam ring highlighted.
This is amoxicillin. I’ve highlighted in blue the lactam ring, which is the important bit.

Co-amoxiclav is a mixture of two drugs. The first is the antibiotic amoxicillin. Amoxicillin belongs to a class of antibiotics (which includes penicillin) called β-lactams, which is the most-commonly used family of antibiotics. These antibiotics contain a four-point lactam ‘ring’ (highlighted in blue above), and the way that they work is that this part of the molecule bonds with a particular protein common to all gram-positive bacteria. Normally this protein is responsible for producing peptidoglycan, which is an essential ingredient in the cell walls of these kinds of bacteria, but when it gets locked to a β-lactam ring it stops working. As a result, when the bacterium reproduces the new child doesn’t have a proper cell wall, and can’t survive long in even the least-hostile environments.

Of course, we’re in a medical arms race right now because some of the bacteria which we’re targetting with antibiotics are becoming resistant. And here’s one what that they’re doing so: some of these bacteria have evolved to produce beta-lactamase, also bonds with beta-lactam rings, adding an OH to them and making them useless. Bummer, eh?

Clavulanic acid, with beta-lactam ring highlighted in blue.
And this is clavulanic acid. Recognise that shape on the left-hand side of the molecule (highlighted in blue)? Yup: it’s another lactam ring.

The second drug in co-amoxiclav, then, is clavulanic acid, which was discovered in the 1970s and started being added to drugs in the 1980s. Despite having a β-lactam ring (as you’ll see in blue above), clavulanic acid by itself it isn’t an effective antibiotic (for reasons I can’t quite get my head around – anyone want to help me?). But what it’s great at is bonding that lactam ring to beta-lactamase, thereby deactivating the bacterial counter-offensive and allowing the amoxicillin to carry on working, combating resistance.

So what you’ve got in co-amoxiclav is a an antibiotic and a chemical that counteracts the effects of a chemical that deactivates that antibiotic. Wow! It’s things like this that really make me wish I had a brain for biology!

A cannula in the back of Dan's hand.
These things aren’t terribly comfortable when you’re trying to sleep.

I was eventually discharged from hospital and released to go home for lots of bed rest and water, along with a further week’s course of co-amoxiclav. Unfortunately it turns out that I’m one of the unlucky folks for whom amoxicillin makes me dizzy, so I spent most of that week lying down in-between wobbly vertigo-filled trips to and from the bathroom. But it worked! Within a few days I was feeling much better and by the end of last week I was able to work from home (and actually feel like I was useful again!).

Free of symptoms and off the drugs, I returned to work properly on Monday morning and everything seemed fine. Until, late in the morning, I went to the bathroom and started pissing blood.

A kitten lying on its side.
I took a picture, but it’s too grim even for this blog post. Here, have a kitten instead. Do an image search for ‘gross haematuria’ if you want a clue: the kitten will still be waiting here when you need it.

Now apparently blood in your urine, while horrifying when it happens to you unexpectedly, isn’t actually a sign of a medical emergency. I was starting to get bladder pain again, quite intensely, so I excused myself from work and called the urology ward, who decided that I wasn’t in bad enough a condition to go and see them but sent me straight to my GP, who gave me another fortnight’s worth of co-amoxiclav. They’re monitoring my progress with urine and blood samples and if by Friday it’s not having an impact, they’re going to want to send me back to hospital (hopefully only as an outpatient) and pump me full of the intravenous stuff again. So… fingers crossed for a good result out of these drugs.

Co-amoxiclav tablet in packaging.
My co-amoxiclav tablets each come individually wrapped in a nitrogen-filled foil bag. I’ve no idea what it is that they’re concerned that they’ll react with, but I’m eating three of them a day anyway.

I was hoping that by this point I’d be writing this blog post and telling you all about how I’d fought the bladder monster and won. But it looks like I won’t be able to claim that victory for another week or two, yet. All I know is that I searched for “bladder monster” and found this. Yeah: that feels about right.

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Dan Q posted a note for GC4H3P7 Alleyways of Oxford – Brasenose Lane

This checkin to GC4H3P7 Alleyways of Oxford - Brasenose Lane reflects a geocaching.com log entry. See more of Dan's cache logs.

Spotted another ‘cacher today. Hunting for geocachers is turning out to be almost as much fun as hunting for geocaches! Photo attached (photo is in GZ, so there might be minor spoilers depending on whether you think the photographed ‘cacher is looking in the right place, or not!)

Suspected 'cacher on Brasenose Lane

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How can I make the most of my 3/4 monitor set-up?

This self-post was originally posted to /r/KerbalSpaceProgram. See more things from Dan's Reddit account.

I can span KSP across them, but that doesn’t really help me as much as I’d like. What’d be really useful would be the ability to show the orbital view on one monitor and the staging view on another. Is there any way to achieve such a thing?

Normally when I’m faced with a problem I just add more boosters/struts, but that doesn’t seem to be helping this time.

Calculating Pi (when you’re ill)

So, I’ve not been well lately. And because a few days lying on my back with insufficient mental stimulation is a quick route to insanity for me, I’ve been trying to spend my most-conscious moment doing things that keep my brain ticking over. And that’s how I ended up calculating pi.

Dan, shortly before inpatient admission but already recovering from the worst parts of his hospital visit, last week.
When I say I’ve been unwell, that might be an understatement. But we’ll get to that another time.

Pi (or π) is, of course, the ratio of the circumference of a circle to its diameter, for every circle. You’ll probably have learned it in school as 3.14, 3.142, or 3.14159, unless you were one of those creepy kids who tried to memorise a lot more digits. Over the years, we’ve been able to calculate it to increasing precision, and although there’s no practical or theoretical reason that we need to know it beyond the 32 digits worked out by Ludolph van Ceulen in the 16th Century, it’s still a fascinating topic that attracts research and debate.

Graph illustrating the calculation of digits of pi over the millenia. Note the logarithmic scale on the left and the staggered scale on the bottom axis.
Our calculation of pi has rocketed since the development of the digital computer.

Most of the computer-based systems we use today are hard to explain, but there’s a really fun computer-based experimental method that can be used to estimate the value of pi that I’m going to share with you. As I’ve been stuck in bed (and often asleep) for the last few days, I’ve not been able to do much productive work, but I have found myself able to implement an example of how to calculate pi. Recovery like a nerd, am I right?

A "pi pie", from a Pi Day celebration.
Pi goes on forever. Pie, sadly, comes to an end.

Remember in school, when you’ll have learned that the formula to describe a circle (of radius 1) on a cartesian coordinate system is x2 + y2 = 1? Well you can work this backwards, too: if you have a point on a grid, (x,y), then you can tell whether it’s inside or outside that circle. If x2 + y2 < 1, it’s inside, and if x2 + y2 > 1, it’s outside. Meanwhile, the difference between the area of a circle and the area of a square that exactly contains it is π/4.

A circle of radius 1 at the intersection of the axes of a cartesian coordinate system.
Think back to your school days. Ever draw a circle like this? Do the words “Cartesian coordinates” ring any bells?

Take those two facts together and you can develop an experimental way to determine pi, called a Monte Carlo method. Take a circle of radius 1 inside a square that exactly contains it. Then randomly choose points within the square. Statistically speaking, these random points have a π/4 chance of occurring within the circle (rather than outside it). So if we take the number of points that lie within the circle, divide that by the total number of points, and then multiply by 4, we should get something that approaches the value of pi. You could even do it by hand!

Output of Dan's demonstration of the Monte Carlo method as used to approximate the value of pi.
I wrote some software to do exactly that. Here’s what it looks like – the red points are inside the circle, and the black points are outside.

The software illustration I’ve written is raw JavaScript, HTML, and SVG, and should work in any modern web browser (though it can get a little slow once it’s drawn a few thousand points!). Give it a go, here! When you go to that page, your browser will start drawing dots at random points, colouring them red if the sum of the squares of their coordinates is less than 1, which is the radius of the circle (and the width of the square that encompasses it). As it goes along, it uses the formula I described above to approximate the value of pi. You’ll probably get as far as 3.14 before you get bored, but there’s no reason that this method couldn’t be used to go as far as you like: it’s not the best tool for the job, but it’s super-easy to understand and explain.

Oh, and it’s all completely open-source, so you’re welcome to take it and do with it what you wish. Turn off the graphical output to make it run faster, and see if you can get an accurate approximation to 5 digits of pi! Or slow it down so you can see how the appearance of each and every point affects the calculation. Or adapt it into a teaching tool and show your maths students one way that pi can be derived experimentally. It’s all yours: have fun.

And I’ll update you on my health at some other point.

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One of my favourite hosting companies is recruiting using anonymous online interviews, in an effort to combat industry sexism

This link was originally posted to /r/girlsgonewired. See more things from Dan's Reddit account.

The original link was: https://blog.bytemark.co.uk/2015/05/20/bytemark-is-hiring-by-anonymous-interview

So, in May 2015, we made the huge decision to start an anonymous recruitment process. The biggest change compared to tradition recuiting is this – your first two interviews are truly anonymous. We conduct them over instant messaging and run our skills tests remotely too.

You won’t even have to give your real name or a CV in the initial stages. We don’t know anything about you that you don’t choose to present in the interview.

That makes us work hard for explicit goals. We want to know about your:

Most valuable skills
Ability to learn
Ability to work effectively in a team

We make decisions based on those factors. Avoiding the “X factor” of cultural fit, which we’ve seen as an excuse for all kinds of implicit and explicit bias across industries.

We also want to be respectful of your time, your enthusiasm and your interests – we’ll test not just what you know but what you can learn. Our focus is on letting you put your abilities to the fore, without fear that you’ll be judged on irrelevant things. We define the job, we define the skills, and we want to test those without bias.

Our culture comes from you, the best person for the job at the end of the process. Of course we still need to meet you, we want to meet you. But we will start our interviews on the solid foundation of anonymity. Only at the final stages will you be asked to come in for a face-to-face interview.

Is it possible to ‘blow’ a whistle or other wind/brass instrument underwater? How?

This self-post was originally posted to /r/askscience. See more things from Dan's Reddit account.

Wind and brass instruments (which I’ve just learned are collectively ‘aerophones’) work because since characteristic of their shape causes the air that is pushed or drawn through them to vibrate at particular frequencies. They work in air whether you’re down a mine or at the top of a mountain, so there’s clearly some tolerance to pressure variation. I presume, therefore, that you could play them using other gases too (e.g. by connecting a whistle to a pump in a nitrogen atmosphere, for example), albeit presumably with a change in pitch (we have whistles driven by an air/steam mixture on steam locomotives, for example).

But I wonder: can such an instrument be used with other fluids? How about a liquid, like water? Can I pump water through an underwater whistle in order to make a whistle-like noise? What are the physical constraints on doing so (e.g do I need a higher pressure difference in water)?

If it’s not possible, why not? What could be done, hypothetically, to construct an aerophone-style (“hydrophone”?) instrument that would work underwater?

tl;dr: Could I pump water through an underwater whistle to ‘blow’ it? If not, how can I ‘fix’ that?

Guess where I woke up this morning, MegaMasons?

This link was originally posted to /r/MegaMasonsLounge. See more things from Dan's Reddit account.

The original link was: http://i.imgur.com/vUxVG6Z.jpg

Dan in hospital

So yeah: that’s not entirely pleasant. A couple of days ago I was diagnosed with what was supposed to be a minor bladder infection and given antibiotics. Then yesterday I became feverish and collapsed. And now I’m in hospital.

But on the upside, they’ve spent all night pumping me full of some kind of intravaenous antibiotic that must be made from like unicorn spunk and leprechaun tears or something because it’s frankly magical: feeling so much better today than yesterday.

Just wanted to say hi. Hi, all!

[x-post /r/MegaMegaMegaLounge] [Graph] Tracking ‘engagement’ across the MegaLounges. Why are some Megas more-active than others? (interpretation in comments)

This link was originally posted to /r/MegaMegaMonitor. See more things from Dan's Reddit account.

The original link was: https://i.imgur.com/3aXKsxq.png

Engagement level by MegaLounge

In /u/10_9_‘s recent thread about gilding trends, /u/razerxs made an interesting observation: that the huge ‘drop offs’ in membership of MegaLounges after /r/MegaMegaMegaLounge does not correlate with their expectations, based upon the level of activity in /r/MegaLoungeV. /u/razerxs

observed that e.g. /r/MegaLoungeV is a highly-active sub, which isn’t necessarily what you’d expect if the activity level was based entirely upon the number of people permitted to have access.

I started wondering if there might be a better predictor of engagement levels. I experimented by looking at the ratio of how many people ‘subscribe’ to each MegaLounge to how many people are permitted into there. This isn’t a perfect measure of engagement, of course, but my thinking was that of the people who are invited into a MegaLounge, only some of those will add it to their front page… but that those who add it to their front page are more-likely to actively participate.

The graph shows three things. From the left axis, the blue and red lines show the number of people who are allowed into each MegaLounge and the number of people who are subscribed to each MegaLounge. As you might expect, there’s a gap between the two and the gap narrows in higher lounges, where there are fewer people.

But what I was interested in is whether and where this gap changes proportionally: is the “subscription rate” among eligible people higher in particular lounges, and can this been seen as a predictor of activity levels and engagement rates in each lounge? That’s what the green bars show (against the right-hand axis: note that it doesn’t start at zero). In general, across the MegaLounges up to and including /r/MegaLoungeSol, there does seem to be a slight upward trend: i.e. the higher a lounge you’re in, the more-likely that eligible people are to add that lounge to their front page. Beyond /r/MegaLoungeSol the bars jump around all over the place, probably because of the small number of people ‘up there’, and I suggest that we ignore them: accuracy of this as a predictor would be expected to be better where there were more subscribers: say, up to about /r/MegaLoungeDiamond.

What this would predict would be a “lull” at /r/MegaLoungeVIII. I don’t know if that’s your experience or not. And, interestingly, the ‘subscription ratio’ at /r/MegaLoungeV and /r/MegaLoungeX are also unusually low, bucking the overall trend. What does this mean? I don’t know. But if /r/MegaLoungeV really is to be considered one of the more “active” MegaLounges, then I think that we can safely say that my hypothesis – that we might be able to predict activity hotspots by looking at the subscription rate – is not backed up by the data.

Still: interesting stuff.

Supermarket “price match” deals are marketing genius

It’s been almost five years since Sainsbury’s supermarkets pioneered the “brand match” idea, which rivals Tesco and Asda later adopted into their own schemes, and I maintain that it’s one of the cleverest pieces of marketing that I’ve ever seen. In case you’ve not come across it before, the principle is this: if your shopping would have been cheaper at one of their major competitors, these supermarkets will give you a voucher for the difference right there at the checkout. Properly advertised (e.g. not in ways that get banned for being misleading), these schemes are an incredibly-compelling tool: no consumer should say no to getting the best possible prices without having to shop around, right?

A Sainsbury's Brand Match voucher worth 62p.
This voucher implies that I’d have saved 62p by shopping elsewhere. But that’s not the whole story.

But it’s nowhere near as simple as that. For a start, the terms and conditions (Asda, Sainsbury’s, Tesco) put significant limitations on how the schemes work. You need to buy at least a certain number of items (8 at Asda, 10 at the other two). Those items must be directly-comparable to competitors’ items: which basically means that only branded products count, but even among them, the competitor must stock the exact same size or else it doesn’t count, even if it would have been cheaper to buy two half-sized products there. There are upper limits to the value of the vouchers (usually £10) and the number that you can use per transaction or per month. “Buy X get Y free” offers are excluded. And there’s a huge list of not-compared products which may include batteries, toys, DVDs, some alcoholic drinks, cosmetics, homeware, flowers, baby formula, light bulbs, books, and anything (even non-medicines) from the pharmacy aisle.

Tesco Price Promise voucher worth 11p off my next shop.
A whole 11p off my next shop? That’s absolutely worth me carrying this piece of paper around in my wallet and trying not to lose it for a week.

But even if it only applies to some of your shopping – the stuff that’s easy to directly compare – it’s still a good deal, right? You’re getting money back towards what you would have saved if you’d have gone up the road? Not necessarily. Let us assume that on average the prices of these three supermarket giants are pretty much the same. Individual products might each be a little more expensive here and a little cheaper there, but if you buy a large enough trolley-load you’re not going to notice the difference. Following me so far? What does this mean for the voucher: it means that it no longer remotely represents what you would have saved if you’d actually been “shopping around”. Let’s take a concrete example:

Photo courtesy Johnathan Harford, used under a Creative Commons license.
A typical basket at any one of these supermarkets will, on average, come to about the same price… even if individual items vary wildly.

Suppose that this is my somewhat-eccentric shopping list (I wanted to select a variety of comparable branded products), and I’m considering shopping at either Sainsbury’s or Tesco:

  • Mozzarella
  • Fish fingers
  • Clover spread
  • Whole milk
  • Crunch corner yoghurts
  • Fromage frais
  • Cadbury Mini Rolls
  • Frozen chips
  • Frozen petit pois
  • Goodfella’s deep pan pizza
  • Dough balls
  • Chocolate-dipped flapjacks
  • Dry white wine
  • Bagels
  • Multigrain wraps
  • Red Bull multipack
  • Angel Slices
  • Cheerios
  • Windolene
  • Cornettos

Not too unreasonable, right? I’ve made a spreadsheet showing my working, where you’ll see today’s prices for each of these items (along with the actual brands and package sizes I’ve selected), if you’d like to check my maths, because here comes the clever bit.

Sainsbury's Basics range baked beans and coleslaw
These products don’t count as comparable. And personally, I’m not sure that “basics”-range coleslaw is likely to even count as ‘food’.

Based on my calculation, taking my imaginary shopping list to Sainsbury’s will ultimately cost me £52.85. Taking it to Tesco will cost me £54.13. Pretty close, right, and I’m not likely to care about the difference because Tesco would give me a £1.28 voucher off my next shop which makes up for the difference (note that Sainsbury’s wouldn’t reciprocate in kind if it were the other way around, after a policy change they made late last year). But that’s not actually a true representation of the value of ‘shopping around’. As my spreadsheet shows, if I were to buy each item on my list at the supermarket that was cheapest, it’d only cost me a total of £43.75: that’s a saving of £9.10 (or about 17% off my entire shop) compared to the cheapest of these supermarkets. These schemes don’t give you a real “best of all worlds”. Instead, they give you, at most, a “best of all worlds, assuming that you’re still going to be lazy enough to only shop in one place”.

Ruth and JTA shopping in advance of Murder At The Magic College.
When you’re buying this much shopping, you’re unlikely to want to go to two different supermarkets to do it, however much money it might save you.

If you’re particularly devious of mind, you can exploit this. For example, suppose I went to Tesco but when I reached the checkout I split my shopping into two transactions. The first transaction contains the frozen goods, milk, wine, dough balls, flapjacks, and mini rolls. This comes out at £33.73, which is £10.38 more than Sainsbury’s would charge me for the same goods. Tesco therefore gives me a £10 voucher, which I immediately use on the second batch of shopping: the one which contains goods that are cheaper than their Sainsbury’s equivalents. The total price of my shopping: £44.13 – only 38p more than if I’d gone to both supermarkets and bought only the best-value goods from each (the 38p discrepancy comes from the fact that Tesco won’t ever give you a voucher worth more than £10, no matter how much you’re losing out).

Photo by 'alisdair' on Flickr. Used under a Creative Commons license.
“I’d like to run these through as two transactions, please.”

It’s not even that hard to do. Obviously, somebody’s probably written an app for it, but even if you’re just doing it by guesswork you can get a better result than just piling all of your shopping onto the conveyor belt together. Simply put the things which seem like a good deal (all of the discounted products, plus anything that feels like it’s good value) at one end of your trolley, and unload those things last. Making sure that you’ve got at least ten items on the conveyor, ‘split’ your shopping somewhere towards the beginning of these items. Then take any voucher you get from your first load, and apply it to the second.

It’s pretty easy, so long as you don’t mind looking like a bit of a tool at the checkout.

A Sainsbury's Brand Match voucher advising that my shopping was 1p cheaper than the competition. In total. Photo with thanks to Brett Jordan, used under a Creative Commons license.
Well that makes it all worthwhile then, doesn’t it?

But to most people, most of the time, this is nothing more than a strong and compelling piece of marketing. Either you get reminded that you allegedly “saved money”, on a piece of paper that probably goes into your wallet and helps to combat buyer’s remorse, or else we get told that we paid a particular amount more than we needed to, and are offered the difference back so long as we return to the same store within the next fortnight. Either way, the supermarket wins your loyalty, which – for a couple of pence on each transaction (assuming that the customer doesn’t lose the voucher or otherwise fail to get an opportunity to use it) – is a miniscule price to pay.

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Welcome to the planets, new astronauts!

This self-post was originally posted to /r/MegaLoungeNeptune. See more things from Dan's Reddit account.

I just wanted to give a wave to our three new astronauts, freshly arrived here in the planets just over the course of this last week. They are:

Happy space exploration!