Pollen is not good for my brain, and there's been a lot of it for the past couple of weeks.
I'm waking up like someone has been spraying pollen into my bedroom all night.
Temperatures over 70F are too much.
It is a miracle that I even found the laptop to write this.
In the meantime, grab a cup of coffee and settle in to watch this...
Hither Green is directly south of Greenwich. The equivalent distance west is Putney. The route is direct and sensible until it gets to Clapham, and then... I won't spoil it.
What struck me was how many junctions and lines going everywhere there are in south London. Then you get to Clapham and you have four choices: main lines through Richmond (for Reading), Wimbledon (for Woking, Porstmouth and Weymouth), Croydon (for Gatwick and Brighton), and the Overground south and north. Those lines are incredibly simple: there aren't any junctions on the Reading line until Virginia Water and then there's only one more at Ascot. None of which stops this train taking the most complicated route to Woking.
Yes. I had nothing better to do. It was hot. I did scrub through the final section of the journey from Ascot.
Tuesday, 21 June 2022
Friday, 17 June 2022
Camera Maths, or Why The Crop Ratio Works
I still think there's something odd about APS-C cameras. 'Odd' means 'It doesn't quite do what my old full-frame film camera did with the same settings'.
Time for some maths.
We will work all these examples with a full-frame (35.8 x 23.8 mm) sensor with a 50 mm lens at f8, and an APS-C (23.6 mm x 15.6 mm) with a 35mm lens at f8. Shutter speed is on Auto.
Let's look at how much light is getting in.
The f-number is the ratio of focal length to diameter of the shutter pupil. So the diameter of the full-frame shutter pupil diameter is 50/8 = 6.25mm giving an area of 3.142*3.125^2 / 2 = 15.34 sq mm. Which is a proxy for how much light is getting in. The APS-C will have a shutter pupil diameter of 35/8 = 4.375 mm, giving an area of 3.142*(2.19)^2 / 2 = 7.53 sq mm. The APS-C has 7.53 sq mm of light falling on 365.8 sq mm of sensor, or 2.06%. For the full-frame, it's 15.34 / 853 = 1.8%.
Slightly more light per sq mm falls on the APS-C sensor. If we want the same, we will need 7.53*1.8/2.06 = 6.6's worth of light, which means a pupil radius of sqrt(6.6/3.142) = 1.45 mm, a diameter of 2.9 mm and an f-number of 35/2.9 = 12. Or I could increase the shutter speed by 14%. Shutter speeds don't do that. ISO's don't either.
Let's look at depth of focus.
According to Wikipedia, depth of focus is roughly
2u^2 Nc / f^2
for a given circle of confusion (c), focal length (f), f-number (N), and distance to subject (u). The circle of confusion is conventionally 0.05 mm. For the full-frame lens and a subject 5 metres away, the depth of field is 2*(5000)^2 * 8 * 0.05 / 50^2 = 8000 mm, which is from 4m in front of the subject to 4m behind them.
The only thing that changes in this calculation when we switch to the APS-C sensor is the focal length, from 50 to 35. It changes to 16.3 m (!), 8 metres in from to 8 metres behind. That's a whole lot of extra depth of focus.
Why does the APS-C have a shorter focal length and why that one? Everybody does this, but we should understand why.
The 35 mm sensor has an area of 35.8 * 23.8 = 852 sq mm. The Fuji APS-C has an area of 23.6 * 15.6 = 365.8 sq mm. So the APS-C sensor is 43% of the full-frame area. Or the 35 mm is 2.33 times larger than the APS-C.
The APS-C sensor is showing you a smaller part of the full-frame image for a given focal length. To get the same image with an APS-C lens, we have to have a shorter focal length (shorter focal length = wider and higher picture). How much shorter?
The answer involves some school geometry. (Graphics are not my strong point.)
The focal point of the lens is behind the sensor. (I know, I learned it at school, and I'm still nodding along. Optics is magic, not physics.) The distance behind the focal point and the sensor is the focal length. (Which has nothing to do with the length of the lens. It's the length of the path the light takes between the front lens and the sensor: lenses with huge focal lengths are obtained by using mirrors. Lots of mirrors.) But I digress.
The key bit of camera geometry is the angle in red, called the field of vision. (Wrong notation in the picture.) School geometry says the it is the angle $\theta$ such that
The magic maths is this: for a given distance $D$ away, the width of the picture that the sensor will capture is $2 D \tan(\theta)$. This is why you move forwards to get nearby things you don't want in the frame, or backwards to include more of them.
Since we want the same field of vision with the APS-C as the full frame, the angle stays the same, and we can set
(Now you know why nobody explains why you use the crop ratio.)
So using the same f-stop and the industry-rule of thumb equivalent lens sizes, the APS-C gives us - for the same shutter speed - a slightly brighter, ever so slightly narrower picture with way more depth of focus, than a full-frame. The difference in brightness is not enough at sensible ISOs to affect the shutter speed, even if you have shutter speed or ISO on auto, so it will be slightly brighter.
The ISO / shutter speed is way too coarse to adjust for the small change in brightness. But that depth of field can be adjusted, by halving the f-stop you would use on a full-frame, and letting the camera make the shutter speed adjustment.
Time for some maths.
We will work all these examples with a full-frame (35.8 x 23.8 mm) sensor with a 50 mm lens at f8, and an APS-C (23.6 mm x 15.6 mm) with a 35mm lens at f8. Shutter speed is on Auto.
Let's look at how much light is getting in.
The f-number is the ratio of focal length to diameter of the shutter pupil. So the diameter of the full-frame shutter pupil diameter is 50/8 = 6.25mm giving an area of 3.142*3.125^2 / 2 = 15.34 sq mm. Which is a proxy for how much light is getting in. The APS-C will have a shutter pupil diameter of 35/8 = 4.375 mm, giving an area of 3.142*(2.19)^2 / 2 = 7.53 sq mm. The APS-C has 7.53 sq mm of light falling on 365.8 sq mm of sensor, or 2.06%. For the full-frame, it's 15.34 / 853 = 1.8%.
Slightly more light per sq mm falls on the APS-C sensor. If we want the same, we will need 7.53*1.8/2.06 = 6.6's worth of light, which means a pupil radius of sqrt(6.6/3.142) = 1.45 mm, a diameter of 2.9 mm and an f-number of 35/2.9 = 12. Or I could increase the shutter speed by 14%. Shutter speeds don't do that. ISO's don't either.
Let's look at depth of focus.
According to Wikipedia, depth of focus is roughly
2u^2 Nc / f^2
for a given circle of confusion (c), focal length (f), f-number (N), and distance to subject (u). The circle of confusion is conventionally 0.05 mm. For the full-frame lens and a subject 5 metres away, the depth of field is 2*(5000)^2 * 8 * 0.05 / 50^2 = 8000 mm, which is from 4m in front of the subject to 4m behind them.
The only thing that changes in this calculation when we switch to the APS-C sensor is the focal length, from 50 to 35. It changes to 16.3 m (!), 8 metres in from to 8 metres behind. That's a whole lot of extra depth of focus.
Why does the APS-C have a shorter focal length and why that one? Everybody does this, but we should understand why.
The 35 mm sensor has an area of 35.8 * 23.8 = 852 sq mm. The Fuji APS-C has an area of 23.6 * 15.6 = 365.8 sq mm. So the APS-C sensor is 43% of the full-frame area. Or the 35 mm is 2.33 times larger than the APS-C.
The APS-C sensor is showing you a smaller part of the full-frame image for a given focal length. To get the same image with an APS-C lens, we have to have a shorter focal length (shorter focal length = wider and higher picture). How much shorter?
The answer involves some school geometry. (Graphics are not my strong point.)
The focal point of the lens is behind the sensor. (I know, I learned it at school, and I'm still nodding along. Optics is magic, not physics.) The distance behind the focal point and the sensor is the focal length. (Which has nothing to do with the length of the lens. It's the length of the path the light takes between the front lens and the sensor: lenses with huge focal lengths are obtained by using mirrors. Lots of mirrors.) But I digress.
The key bit of camera geometry is the angle in red, called the field of vision. (Wrong notation in the picture.) School geometry says the it is the angle $\theta$ such that
$\tan(\theta) = \frac{\text{sensor width}}{2* \text{focal length}}$
The magic maths is this: for a given distance $D$ away, the width of the picture that the sensor will capture is $2 D \tan(\theta)$. This is why you move forwards to get nearby things you don't want in the frame, or backwards to include more of them.
Since we want the same field of vision with the APS-C as the full frame, the angle stays the same, and we can set
$\frac{\text{sensor width}}{2*\text{focal length}}$ (full-frame) = $\frac{\text{sensor width}}{2*\text{focal length}}$ (APS-C)
or 35.3/100 = 23.6/2*(APS-C focal length),
giving APS-C length = (23.6*100)/(2*35.3) = 33 mm.
Which is 2mm shorter than the industry-standard equivalent of 35mm.
(Now you know why nobody explains why you use the crop ratio.)
So using the same f-stop and the industry-rule of thumb equivalent lens sizes, the APS-C gives us - for the same shutter speed - a slightly brighter, ever so slightly narrower picture with way more depth of focus, than a full-frame. The difference in brightness is not enough at sensible ISOs to affect the shutter speed, even if you have shutter speed or ISO on auto, so it will be slightly brighter.
The ISO / shutter speed is way too coarse to adjust for the small change in brightness. But that depth of field can be adjusted, by halving the f-stop you would use on a full-frame, and letting the camera make the shutter speed adjustment.
Labels:
Maths,
photographs
Tuesday, 14 June 2022
Taking Pictures With the X-E4: Some Default Settings and Habits
(I had a series of posts about how I took a bunch of under-exposed pictures. Re-reading them recently, every one was close to gibberish. I've done the right thing, and removed all but the last two. The one about crop ratios and camera maths stays, as does this one about my default settings, which has been edited to make sense.)
Nobody writes detailed instruction manuals anymore. I used to like those. Now one has to experiment. Which is easy to do on a technology one already knows, but learning a new technology by experiment is very messy.
So the result of learning what I could about digital camera technology as implemented in the X-E4 is this:
My default settings are 0 for the exposure compensation; f4 for the aperture; A = aperture priority for shutter speed, and an ISO bracket between 160 and 800. There's a post that explains the f4 setting choice.
I assigned the Quick Menu to the Q button, and reduced the number of options to eight. One is always the Custom settings. The others are: ISO, Film Simulation, sensor format, Clarity, Grain Effect, Colour Chrome and screen brightness.
I created two custom settings: one for colour film (Provia) and the other for black-and-white (Acron). I turned the Autosave Custom Settings to OFF, so I could see that I had to Save the changes. When you save a Custom Setting, all the other settings are saved with it as well as the ones you consciously changed. Aspect ratio, file size, sharpness, the works. This is actually a Good Thing, because there are many other things you may want to tweak along with the film type.
I bought a BlackRapid RS-4 Camera Sling. This wonderful gadget lets you slide the camera along the strap up to your face. Ordinary straps make you move the strap. Watch a YT video about the BlackRapid.
I am also bedding-in two habits: checking the dial settings before I take the first shot, in case anything got jogged; and looking at the first shot I take to make sure it is in the mode I want. So the photos I took on the next river ride were a lot better than the horrible ones I took going down to Barking.
Also, here's a video. It's not great, and the wind noise is terrible, but it's one of the first videos I shot with this camera.
Nobody writes detailed instruction manuals anymore. I used to like those. Now one has to experiment. Which is easy to do on a technology one already knows, but learning a new technology by experiment is very messy.
So the result of learning what I could about digital camera technology as implemented in the X-E4 is this:
My default settings are 0 for the exposure compensation; f4 for the aperture; A = aperture priority for shutter speed, and an ISO bracket between 160 and 800. There's a post that explains the f4 setting choice.
I assigned the Quick Menu to the Q button, and reduced the number of options to eight. One is always the Custom settings. The others are: ISO, Film Simulation, sensor format, Clarity, Grain Effect, Colour Chrome and screen brightness.
I created two custom settings: one for colour film (Provia) and the other for black-and-white (Acron). I turned the Autosave Custom Settings to OFF, so I could see that I had to Save the changes. When you save a Custom Setting, all the other settings are saved with it as well as the ones you consciously changed. Aspect ratio, file size, sharpness, the works. This is actually a Good Thing, because there are many other things you may want to tweak along with the film type.
I bought a BlackRapid RS-4 Camera Sling. This wonderful gadget lets you slide the camera along the strap up to your face. Ordinary straps make you move the strap. Watch a YT video about the BlackRapid.
I am also bedding-in two habits: checking the dial settings before I take the first shot, in case anything got jogged; and looking at the first shot I take to make sure it is in the mode I want. So the photos I took on the next river ride were a lot better than the horrible ones I took going down to Barking.
Also, here's a video. It's not great, and the wind noise is terrible, but it's one of the first videos I shot with this camera.
Labels:
Fuji X-E4,
London,
photographs
Friday, 10 June 2022
Tuesday, 24 May 2022
Why Some People Still Won't Go Back To The Office (for Janet Daly)
The Upper Classes asked one of their personal secretaries, Janet Daly, to write an article making the Lower Orders look unreasonable and ungrateful for not wanting to return to their offices, or indeed, work in the jobs that, in 2019, the Lower Orders had been so grateful to their Lords and Masters for providing. These, with my comments, are some of her comments.
notoriously awful extremely good.
When you can't get a CEO for £4.5m a year, it's because you aren't prepared to pay the market price. When you can't get a Project Manager for £45,000 a year, it's because people have unrealistic expectations. When you can't get an office cleaner for minimum wage, it's because people don't want to work.
There are plenty of adults who want full-time employment. Just not at the chiselling low rates and poor conditions the employers had pushed them down to in 2019.
Something like 800,000 economic migrants to the UK went back home in spring / summer 2020. The Dutch are likely in a similar position. Add in a number of older people who retired or quit looking in 2020, and now can collect their State Pension, plus part-time workers who decided that, after all, the benefits of working were getting over-rated, and this is a long way to explaining shortages.
And "financial independence". That's a target that moves further and further away every decade.
But I digress. Let's get back to those "spontaneous, live connections, which you cannot control or anticipate, with people you do not necessarily know or understand".
My memory of daily work was seeing the same people, whom I knew and understood as well as I needed to for my daily purposes, at the same time every day, and having the same connections with them every day. We had face-to-face contact, but I think I would characterise it as stylised rather than "spontaneous (and) live".
In Spring 2020, about half the working population were still leaving the house five days a week to go to work. And still are now. A lot of the younger laptop-jobbers rushed back into the office in Autumn 2020 and stayed there through 2021 because a) they were going bonkers working from home, b) they had some kind of reasonable workplace life, c) the workplaces were reasonable spaces.
Sometimes the cause is standing really still and keeping really quiet so you don't notice it.
The big organisations spent two decades squeezing more people into less space, and providing fewer chairs per person every time a department moved from one floor to another. Most large organisations do not have the office space for all the staff who have an address there, and the organisation has no intention of renting any more.
By 2019, work in large organisations had become miserable. Start with the 1.6 people / desk ratios of the open-plan office, move on to the cursory toilet-cleaning, the queues for the lift to get food for lunch, the ineffective air-conditioning that could not shift the smell of food from 11:30 to 14:30, the DIE training, the cramped offices, the packed trains and tubes, the lack of contact with one's manager from one end of the week to the next, the people around you forever on conference calls, the noise, and the noise-cancelling headphones needed to deal with it, and the endless bureaucratic nonsense from IT, HR and everyone else who never produced anything. Work conversations were held over e-mails, and office chatter went over IM. Nobody actually talked. Not even about work. And in a call centre, you are not supposed to be talking to your co-workers, you're supposed to be answering calls. In a processing office, such as issuing new passports or driving licenses, you're supposed to be processing, not talking. Places like that employ specially-picked supervisors who get blood from a stone by crushing it. Nobody in their right mind wants to go back to a 2019-style call-centre or a processing office. In a large organisation, people come a distant fourth after property, cleaning and personal computing equipment costs.
You see, Janet, the Upper Class do understand why some of their workers are not coming back.
What management gets is what it really wanted.
Management don't want the workers back in. They might have to spend money on buildings.
(Yep, I know. Right after I post something about keeping the nonsense out of my head, I do this. But it was such an egregious article.)
The minicab firm on which I have relied for years – one of the largest in north London – is now unable to provide me with rides home from evening events. Because I know them well, I asked them frankly what the problem was. The controller explained that they now had only four or five drivers who were prepared to work after 5.30pm, and even those, he said, were “very picky” about the jobs they would take.Never attribute to sweeping social trends what can be explained by local economics. My guess is that there just isn't the demand later in the evenings that there used to be, and a chunk of that is passengers (drunks) nobody wants. It's not the driver's attitude, it's the lack of business after 5:30 in the evening. Her cab company won't say that, because they have already adjusted to the lower levels (than 2019) of demand.
This is not, I gather, an unusual problem and the scarcity is not confined to drivers. A good many shops and hospitality venues are now desperately seeking staff. Teenage school pupils have never found it so easy to get weekend work in places that would once have hired adults full-time. But there are apparently fewer and fewer adults who want full-time employment.It's not just the eateries of north London. The Dutch are having the same problem. In what industries? "Most vacancies are in... retail, business services and healthcare" reports Dutchnews.nl. Strange, because the salaries and working conditions in those sectors are
When you can't get a CEO for £4.5m a year, it's because you aren't prepared to pay the market price. When you can't get a Project Manager for £45,000 a year, it's because people have unrealistic expectations. When you can't get an office cleaner for minimum wage, it's because people don't want to work.
There are plenty of adults who want full-time employment. Just not at the chiselling low rates and poor conditions the employers had pushed them down to in 2019.
Something like 800,000 economic migrants to the UK went back home in spring / summer 2020. The Dutch are likely in a similar position. Add in a number of older people who retired or quit looking in 2020, and now can collect their State Pension, plus part-time workers who decided that, after all, the benefits of working were getting over-rated, and this is a long way to explaining shortages.
There is something very big at stake here. It is to do with the role that work plays in individual lives and in the wider society. There was a time when what you did for a living was about something more than simply the money you earned. It was one of the things that gave a sense of personal identity, purpose and context to your life. Children were asked what they “wanted to be” when they grew up because that was thought to be one of the key sources of a sense of self.We'll grant the non-sequiter. A sense of self from a job comes from the skills and knowledge it requires and the community, if any, in which the job is worked. When employers do not train their staff, there is no sense of self to be had from the job. Nobody gets a sense of self from a zero-hours job. They get a sense of being exploited, or being a mug. Nobody gets a sense of self from being told there are no desks for them, will they please go home. Nobody gets a sense of self from being over-worked and under-paid. Nobody gets a sense of self from doing a job they could lose next week. Nobody gets a sense of self working for a supervisor who is a bully or a can't be trusted. Nobody gets a sense of self from being told how to think about other people. Nobody gets a sense of self from having to fake smiles and double-plus goodthink eight hours a day. That covers almost everyone with a job, except Daily Telegraph columnists.
“Going out to work” isn’t just an entry into grown-up responsibility and financial independence: it is the normal way for all those self-contained households to encounter one another in real face-to-face contact. Working from home is an attenuated version of this: a way of avoiding spontaneous, live connections, which you cannot control or anticipate, with people you do not necessarily know or understand.Ah yes, "grown-up responsibility". A term that changes in meaning with every generation.
And "financial independence". That's a target that moves further and further away every decade.
But I digress. Let's get back to those "spontaneous, live connections, which you cannot control or anticipate, with people you do not necessarily know or understand".
My memory of daily work was seeing the same people, whom I knew and understood as well as I needed to for my daily purposes, at the same time every day, and having the same connections with them every day. We had face-to-face contact, but I think I would characterise it as stylised rather than "spontaneous (and) live".
For the life of me, I cannot see this attitude – which lays such stress on “wellbeing” – as healthy and liberating. It looks to me more like a fearful retreat from the great world of possibilities that lie beyond your own door: a world full of challenging unknowns and fresh perspectives, which might shake the comfortable assumptions that you can maintain so easily at home.Working days for many people are a figure-eight, orbiting around the office for eight hours during the day, the bed for eight hours during the night, with a couple of hours between the two. Work is the same every day: it's designed like that. If there are "challenging unknowns" at work, someone did their job wrong. As for "fresh perspectives", these have to be sold to senior management or are useless. Anyone who works in a large company knows this. There are no possibilities on the 18:20 from Waterloo to Reading, and if you're not one of the first through the carriage doors, there are no seats either. There are no possibilities on the shopping run to Sainsburys, or in the hour in the gym. Everyone has their time allocated, and somewhere else to go already afterwards. There are no possibilities on a Friday night in Shoreditch either: just ask all the twenty-something men and women who arrived on their own, and went home on their own.
In Spring 2020, about half the working population were still leaving the house five days a week to go to work. And still are now. A lot of the younger laptop-jobbers rushed back into the office in Autumn 2020 and stayed there through 2021 because a) they were going bonkers working from home, b) they had some kind of reasonable workplace life, c) the workplaces were reasonable spaces.
Sometimes the cause is standing really still and keeping really quiet so you don't notice it.
The big organisations spent two decades squeezing more people into less space, and providing fewer chairs per person every time a department moved from one floor to another. Most large organisations do not have the office space for all the staff who have an address there, and the organisation has no intention of renting any more.
By 2019, work in large organisations had become miserable. Start with the 1.6 people / desk ratios of the open-plan office, move on to the cursory toilet-cleaning, the queues for the lift to get food for lunch, the ineffective air-conditioning that could not shift the smell of food from 11:30 to 14:30, the DIE training, the cramped offices, the packed trains and tubes, the lack of contact with one's manager from one end of the week to the next, the people around you forever on conference calls, the noise, and the noise-cancelling headphones needed to deal with it, and the endless bureaucratic nonsense from IT, HR and everyone else who never produced anything. Work conversations were held over e-mails, and office chatter went over IM. Nobody actually talked. Not even about work. And in a call centre, you are not supposed to be talking to your co-workers, you're supposed to be answering calls. In a processing office, such as issuing new passports or driving licenses, you're supposed to be processing, not talking. Places like that employ specially-picked supervisors who get blood from a stone by crushing it. Nobody in their right mind wants to go back to a 2019-style call-centre or a processing office. In a large organisation, people come a distant fourth after property, cleaning and personal computing equipment costs.
You see, Janet, the Upper Class do understand why some of their workers are not coming back.
What management gets is what it really wanted.
Management don't want the workers back in. They might have to spend money on buildings.
(Yep, I know. Right after I post something about keeping the nonsense out of my head, I do this. But it was such an egregious article.)
Friday, 20 May 2022
Alice, Bob and Charlie Math Problem
I ran across this on YT the other day.
It takes Alice and Bob 2 hours to do a task; Alice and Charlie 3 hours; and Bob and Charlie 4 hours. How long will it take for all three of them to do it?
It happens to tie in with something else I'm working on, so...
Almost everyone who didn't behave like a good pupil gave Alice and Bob the job. That way you pay four hours labour, but with three people, one of whom is all but useless by inspection, you're going to pay more than five and less than six hours. Or, Charlie would just get in the way and slow Alice and Bob down, which is pretty standard experience for anyone who has worked in teams.
To give the good pupil answer, you have to make a number of assumptions: a) you are not concerned with cost; b) three people can work together without getting in each other's way; c) the work rate of each person is not affected by a third person on the team. Since we are given no costs, we have to assume a). b) and c) have to be stated in the question, but are not.
I've always felt these questions are either a) posed by people who would not pass Logic 101, and/or b) are designed to see if you can make the "right" assumptions, in order to c) exclude awkward logical / lawyer-brained people who won't work well the Normies.
If you are going to use the good pupil assumptions, the correct reasoning starts by noticing that if you're going to "solve" for A, B, C, then those have to be the workrate (per hour) in order for the arithmetical operations to be meaningful.
Thus we get 1. a+b = ½ job / hr
It takes Alice and Bob 2 hours to do a task; Alice and Charlie 3 hours; and Bob and Charlie 4 hours. How long will it take for all three of them to do it?
It happens to tie in with something else I'm working on, so...
Almost everyone who didn't behave like a good pupil gave Alice and Bob the job. That way you pay four hours labour, but with three people, one of whom is all but useless by inspection, you're going to pay more than five and less than six hours. Or, Charlie would just get in the way and slow Alice and Bob down, which is pretty standard experience for anyone who has worked in teams.
To give the good pupil answer, you have to make a number of assumptions: a) you are not concerned with cost; b) three people can work together without getting in each other's way; c) the work rate of each person is not affected by a third person on the team. Since we are given no costs, we have to assume a). b) and c) have to be stated in the question, but are not.
I've always felt these questions are either a) posed by people who would not pass Logic 101, and/or b) are designed to see if you can make the "right" assumptions, in order to c) exclude awkward logical / lawyer-brained people who won't work well the Normies.
If you are going to use the good pupil assumptions, the correct reasoning starts by noticing that if you're going to "solve" for A, B, C, then those have to be the workrate (per hour) in order for the arithmetical operations to be meaningful.
Thus we get 1. a+b = ½ job / hr
2. a+c = ⅓ job /hr
3. b+c = ¼ job /hr
From which we get
4. b-c = 1/6 (eq 1- eq2)
From which we get
4. b-c = 1/6 (eq 1- eq2)
5. b = 5/24 (eq 3+eq 4, divided by 2)
6. c = 1/24 (substitute 5 in eq 2)
7. a = 7/24 (substitute 6 in eq 1)
so a+b+c = 13/24 (workrate / hr) time = 24/13 = 1.85 hrs.
Adding Charlie saves 9 mins, and costs a whole extra man-hour.
The math is fine, given the assumptions. it's the assumptions that are wonky.
If you have experience of the world.
If you're a high-school math problem-setter, you don't. So you make wonky assumptions.
so a+b+c = 13/24 (workrate / hr) time = 24/13 = 1.85 hrs.
Adding Charlie saves 9 mins, and costs a whole extra man-hour.
The math is fine, given the assumptions. it's the assumptions that are wonky.
If you have experience of the world.
If you're a high-school math problem-setter, you don't. So you make wonky assumptions.
Friday, 13 May 2022
Commenting on Current Affairs Means Letting Madness Take Up Space In Your Head
I've been finding it increasingly difficult to work up any enthusiasm for the foolishness of the world. You don't need me to tell you that the Ukraine War is awful, that Woke is a blight on the land, that the economy is a mess, and that anyone under forty has to be treated with kid gloves (vegan fake kid gloves, of course) lest they "call you out" for wrongthink.
The problem with commenting, especially political and economic commentary, is that you're always living someone else's life.
You expend a lot of thought and concentration on describing, interpreting and drawing the possible consequences of what other people are doing.
You're letting other people's madness take up space in your head.
I'm pretty darn sure I don't want that anymore. I hardly noticed when I had a day job, because day jobs are all about dealing with other people's madness, so it was more of the same.
I notice the madness of the things I comment on now I don't have a day job.
I think I want out.
The problem with commenting, especially political and economic commentary, is that you're always living someone else's life.
You expend a lot of thought and concentration on describing, interpreting and drawing the possible consequences of what other people are doing.
You're letting other people's madness take up space in your head.
I'm pretty darn sure I don't want that anymore. I hardly noticed when I had a day job, because day jobs are all about dealing with other people's madness, so it was more of the same.
I notice the madness of the things I comment on now I don't have a day job.
I think I want out.
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