Mathematician G. H. Hardy called proof by contradiction, or reductio ad absurdum, one of a mathematician’s finest weapons.
Without getting all technical, it’s the technique of assuming the opposite of what you’re attempting to prove and then using logical steps to show that assumption leads to an absurd conclusion.
The classic example of the technique is the proof that the square-root of 2 is irrational (that is, it cannot be exactly expressed as a fraction). The proof rests on a piece of maths that we all learned in primary school; simplifying fractions. If we have a fraction such as 4/8 we can see that both the numerator and the denominator (the fancy book-larnin’ words for the top and bottom of the fraction) can be divided by 2, to give us 2/4, we can then divide by 2 again, to get 1/2, and that is the fraction in its simplest form.
I won’t work through the proof that the square-root of 2 is irrational (there are many worked examples a Google away) but it starts by assuming that it can be written as a fraction, a/b. Then, through some sub-GCSE algebraic juggling, we can show that both a and b can be simplified, to give c/d. So far so good, but then we can run through the exact same process again, to give an even simpler representation of root 2, e/f. Then again, to give g/h, and so on, forever, never arriving at a simplest form.
A fraction that can be simplified forever is an absurdity, but every step in the logic is mathematically correct, so the only possible conclusion is that our initial premise was wrong, and that the square-root of 2 cannot be represented as a/b and is, therefore, irrational.
Pythagoras, legend has it, believed that every number could be represented by simple fraction, so when his student, Hippasus, proved that the square-root of 2 was irrational, Pythagoras ordered him drowned at sea.
I guess that’s a timely warning about what can happen if you completely wrap yourself up in an unfounded belief, and then find the absurdity at the end of it. Especially if it’s so absurd that comedians can get a laugh just by repeating it out loud.
I took my dog, Luna, to the pub the other day. A couple with a daughter, probably about 7, asked if they could say “Hello” to her, because they were thinking of getting a Malinois (a type of Belgian Shepherd), after seeing the film Dog. I did tell them that they’re a lot of work, that they’ll need to find a good dog trainer, and that, although they learn very quickly, they also learn bad habits very quickly. All the usual coded warnings. I guess this blog is what I’d have said if I had time to string together 1,000 words in my head.
A lot of the rehoming ads for Belgian Shepherds mention that they’re being rehomed because the family that bought them as puppies didn’t research the breed. I’m very pleased to say that I can’t be accused of that. No, indeed, I went and Googled ‘Belgian Shepherd’, and what I took away from that extensive research was, ‘Sort of a slightly smaller German Shepherd’.
This, it turns out, is a bit like describing a Scotch bonnet chilli as sort of a small version of a bell pepper – the description isn’t wrong, as far as it goes, but it omits a lot of information that you really should have before deciding to take a bite.
If you can’t be bothered to Google ‘Belgian Shepherd’ (perhaps because you aren’t considering buying one) then, briefly, they’re a herding dog (you probably didn’t need Google for that) which comes in 4 types – the long-haired Groenendael and Tervuren, the rough-coated Laekenois, and the short-haired Malinois (which is what Luna is, and which is generally regarded as the least suitable of the 4 for domestication). They’re all working dogs, which is to say that they have the energy and hardiness to spend all day, every day, on the side of whatever passes for a hill in Belgium, rounding up animals that don’t have the brains to neatly round up themselves.
The other thing you’ll see in the many, many rehoming posts for Malinois is that they’re looking for a home “with breed experience.” In case you’re not up on your dog-adoption lingo, this one means, “We’re looking for people who absolutely, definitely know what they’re letting themselves in for.”
We did not have breed experience.
Admittedly, Luna wasn’t our first dog, or even our first working dog, which might explain some of our reckless abandon. We went to get her during the pandemic (she wasn’t a pandemic pup, one of our dogs had just died). Restrictions meant that only two of us could go inside at a time. My wife & daughter went first and came out unsure, wondering if she was going to be too energetic for us. I went in and the damn dog got into my arms and went to sleep. This, it turns out, was a one-time-only offer.
Following on from that never-to-be-repeated doze, here’s what I’ve learned in the past 10 months:
They are a working dog, they need work. It doesn’t have to be rounding up sheep. To a dog, finding and retrieving a ball for you is no more or less work than gathering a flock of idiot bovines together, but if your Malinois doesn’t have a job then it will come to you to be given one, and if you don’t supply one it will go and find its own work to do… this may be expensive.
Dear god, you need to find a good trainer, who knows the breed. Mechelle of Curlabull training, who we use, has focussed almost exclusively on telling me what an idiot I am – from the very first session, where I laughed about puppy Luna lying down and not wanting to walk across the room… “You do NOT laugh at this breed!”, through to, “You cannot just say <weedy voice> ‘No’ to this dog! Armies use these dogs. You can literally shoot her and she will come back for more!” – and it’s been worth every single penny. You need to invest the time and effort in training, because…
Owning a dog that’s perceived as aggressive is a lot of worry. There is a heartbeat between the development stage where people you meet in public react, “Aw, the cute little puppy is running at me”, and them moving to, “Arg! This vicious attack dog is running at me! I am going to be mauled!”. I have apologised to a lot of strangers in the past 10 months.
No, really, you never fully relax on a walk. The best way I can describe it is that I have been a motorcyclist for more than 25 years now, but every time you get kitted-up to go out on the bike there’s always a little voice asking, “Will this be the time it goes disastrously wrong?” Well, it’s the same every time I take Luna for a walk. I know she’s not aggressive to people or other dogs. I know her recall is good. I know what distractions work well with her… but, still, there’s always the worry that she is an incredibly strong, and strong-willed, dog with a keenly honed ‘prey’ instinct and, to make matters worse, people or dogs who act afraid of her are the most likely to wind her up.
It’s not an accident that these dogs get used by police forces. The breed’s default excited behaviour is to ‘mouth’ – to gently clamp their jaws on your wrist, ankle or loose piece of clothing. It takes a lot to train this out of them, but once you’ve sat and watched them destroy a bone you’ll almost certainly want to make the effort. You’ll also want to think very, very carefully about whether your children will understand that it’s fine to run and play with the dog but they have to know when to stop.
Don’t get me wrong, if you put in the time then you end up with a wonderful dog, but if you want just a family pet, that’s going to lounge in front of the fire all day then you’re better off elsewhere. I’m glad we did it, and I’d have another Mali in a heartbeat, but would I feel brave enough to adopt one of the dozens and dozens that are 6-18 months old… no, I’ve got just the wrong amount of breed experience for that.
Oh, and don’t make your decision based on a Hollywood film and a chance encounter with a bloke in the pub. They are a serious dog and deserve a serious commitment and complete self-honesty about what you’re looking for in a pet, and what you’re willing to invest in them.
Here’s what the left-wing press don’t want you to know – last year slightly over 625,000 people arrived in Britain. Let me put that number in perspective for you, that’s more than the population of Bristol. Bristol is a nice place, but if it doubled in size in a single year then it would be a shit-hole. Do you want Bristol to become a shanty town? No, of course not. Even if you don’t actually visit there, it’s still nice to know it’s there, being all picturesque and what-not. Let’s save Bristol!
Those 625,000 new people invariably arrived not speaking a word of English, without a penny to their name, without a trade, without any paperwork. Even by rocking up here they’d already cost the UK tax-payer money, in some cases tens of thousands of pounds, and tied up valuable resources that were sorely needed by the people already living in this country. Let’s save money! Let’s save British lives!
We can be statistically sure that some of those 625,000 will become criminals, even murderers. Some will contribute nothing useful to British society. Mark my words, in a few years time plenty of those 625,000 will be acting like they’re somehow morally superior to those who were on these islands long before they arrived. And, yet, if even one of them dies trying to make Britain their home we will throw more money into working out how that happened and how it can be prevented from happening again. Let’s end this madness!
I hope that, by now, you’re fully on-board with the urgency with which we must stop babies being born in this country. A Bristolsworth of new babies, with their stupid chubby little faces, being born every year in this country is completely unsustainable, and I say that as a Christian.
This is why I’m proposing a plan to off-shore all new babies to Afghanistan. Afghanistan has proven itself far better than us at picking which are the toughest babies, with 10% not passing their first year. It has recently proved that it can cut education by 50%, and it has a notable human rights record. At this time, when other, short-sighted, governments are isolating Afghanistan, we have the opportunity to make a deal that will save the British public millions.
The babies that we off-shore there will also benefit, of course. Housing is cheaper, for a start, and, given the recent end to its lengthy period of unrest, Afghanistan is surely poised for an economic boom and the creation of thousands of new high-tech jobs.
Not only is this policy good for Britain, it will be popular with the voters as well. Not just with the childless, the elderly, and those with a pick & mix approach to Christianity. No, ask anybody who’s actually had to look after a baby for any length of time and they will happily send them halfway across the world, to be somebody else’s problem.
Babies to Afghanistan makes Britain better. It makes Britain sustainable. It is humanitarian. It is Christian. It is amazing that it isn’t already Conservative policy. For the good of us all we must send the babies to Afghanistan!
Over the weekend, in amongst the many tweets about J K Rowling, somebody posted a link to this blog, which examines whether the gender critical movement is being led by men.
While the blog is a lot of handwaving and ‘that isn’t the part I want to focus on’…
…it does also use survey data to ‘prove’ its central thesis, and that’s of interest to me. Hence me valiantly overcoming the crippling irony of a gender critical man arguing that men don’t run the gender critical movement to write this short piece.
The same survey also shows that men are less likely than women to support transgender people using the facilities of their chosen gender, or competing in sports against natal members of that gender. However, the golden rule of surveys is that you only get answers to the questions you’ve asked, and once you start making assumptions based on those answers you quickly get into the thicket of wild speculation, as our blogger does…
If I told you, correctly, that multiple surveys show that women are more likely than men to believe in god, and concluded therefore that most religions are run by women, then you’d clearly see the issue of assuming that the answer to one question is also the answer to another. Personally, I think that there’s some fascinating research to be done into why women are more likely than men to support trans rights – is it a socialisation thing, is it men patriarchally feeling they have to defend women, is it that men understand better what men are like – but it’s clearly a mistake to jump to the conclusion that because more men than women hold these views that it follows men are the driving forces behind then gender critical movement.
As it happens, the BBC survey into gender issues in Scotland, which came out 6 months after this blog was written, shows that men and women closely follow the debate in about equal numbers, suggesting at least that the difference in opinions isn’t down to how much attention they’re paying to the topic.
Our blogger, though, is very much off on one by this point.
She looks at data from a couple of other surveys, which also show that men are more likely to hold gender critical views – which is what you’d expect, if the results of the first survey were a real effect – and takes this as undeniable proof that men are leading the GC movement. How, then, to account for all of the women who are very vocal in the same movement? In one of the most genuinely remarkable paragraphs I have ever seen in a blog, that must also be the high-water mark of denying women agency, all these remarkable women are written off because they work with men!
Why, you may ask, are all of these shadow-lingering men running the gender critical movement. There is an answer, of course.
Leaving aside the level of projection, which is enough to display the widescreen version of Ben Hur on the moon, the only self-consistent interpretation of this argument is, The men who say transwomen are men are only saying that because they know transwomen are women and want to misogynistically bully them. It assumes it is literally impossible for any man to hold the honest, good faith view that not every man who says he’s a woman is one. This is your brain on gender ideology.
The corollary of that would then be that either women can believe that transwomen are men – which would mean that there was a genuine difference between the sexes – or that women are so in thrall to men that they can be persuaded by them to lie in fairly sizeable numbers. The author doesn’t make clear which option she favours.
What she does favour, apparently, is women coming together to fight male dominance, in a paragraph that reads like it’s talking about exactly the opposite movement to the one she’s rallying against.
And, just to add to that effect, she closes with a line which she probably thought was clever irony, but which only actually makes sense if you accept that women’s role is fighting against trans rights.
I’m hoping that someone is going to get in touch and tell me that the blogger is actually a gender critical satirist. If she is then I take my hat off to her, because the blog did make me laugh a lot. If, however, this was a serious piece then that’s not funny. Not funny at all.
This is Gender Critical Uber-commander Andrew R signing off.
[This blog contains significant spoilers for Terry Pratchett’s Monstrous Regiment novel]
Last year an argument erupted on Twitter – the home of the pointless argument – about what Terry Pratchett’s views on the trans debate would have been. The debate was settled, in as much as it can ever be, by his daughter saying that he would have supported trans rights. Of course, Sir Terry died in 2015, before the argument really kicked into its full insanity. If I’d died in 2015, and anybody had thought to ask my daughter, then she’d probably have said that I’d have been supportive of trans rights. Hell, there’s probably an alternate reality where J K Rowling died in 2015 and trans rights supporters are sharing quotes about Hermione and Fleur using polyjuice potion to turn into Harry as proof that JKR would have been fighting for trans rights.
Frankly, it all seems a little pointless. If a photo emerged of Pratchett with his beard dyed in the trans flag colours and wearing a Kill all TERFs t-shirt it wouldn’t alter that he wrote funny, engaging and endlessly quotable books. Either side trying to recruit the dead seems a little tasteless and a lot pointless. All I’m complaining about today is a claim I’ve seen a few times that his novel Monstrous Regiment is pro-trans, or contains trans characters or, indeed, is in any way about trans at all. And I’m annoyed because it takes a very specific reading of the novel to come to that conclusion. Specifically, it takes a reading that skips the final 50 pages.
The novel’s central character is Polly Perks, the daughter of an innkeeper in the warlike country of Borogravia, who disguises herself as a boy and takes the name Oliver in order to join the army to find her older brother, who also joined up and is now missing. The central joke of the novel is that all the recruits are in turn revealed to be women in disguise. The clue is in the book’s title, a reference to Scottish protestant John Knox’s book, The First Blast of the Trumpet Against the Monstruous Regiment of Women, a 16th century text which argued that rule by female monarchs was counter-biblical.
It probably shouldn’t be a surprise that a movement which has been quick to claim as trans historical figures who cross-dressed or obscured their sex for any reason has been just as quick to claim this book as their own. The problem with this reading is that none of the characters even briefly entertains the idea that they’re men. More importantly, the reasons they have for joining up are all rooted in patriarchy; one is looking for the father of her unborn child, so that she doesn’t end up at the Girl’s Working School, two others are running from mistreatment and, it’s hinted, sexual abuse at that very place, others are frustrated by the limits that society places on what women are allowed to do. Polly’s own, slightly shameful, reason for looking for her brother is that she needs him alive to inherit the inn when her father dies, as Borogravian law doesn’t allow women to inherit property. Even dressing in male clothes is an abomination in the eyes of their god, Nuggan.
The small unit do succeed in turning the tide of war in Borogravia’s favour, whereupon they are arrested and subjected to a tribunal in front of the military’s high command. Here the idea that any of the characters were trans starts to fall apart.
‘Firstly, may I offer on behalf of all of us, I think, our thanks for the incredible job you have done? A splendid effort. But, sadly, the world we live in has certain…rules, you understand? To be frank, the problem here is not that you are women. As such, that is. But you persist in maintaining that you are. You see? We can’t have that.’
Monstrous Regiment, p. 304
The tribunal initially offers to recognise that the women assisted the army and then return them to their homes, and offer which the majority of them decide to reject, despite warnings that it is the best offer they will get. They are saved by their aged, rotund, red-faced sergeant, Jack Jackrum, whose catchphrase is Upon my oath, I am not a violent / dishonest / swearing / gossiping man, but…, and who, over his decades in the army, has found that good many of the high command are also female, including the leader of the army, General Froc.
Backed into a corner, the high command offer that would be, effectively, the extension of trans rights to the soldiers.
Froc looked at her colleagues on either side. An unspoken question harvested unsaid answers.
‘Yes, well,’ she said. ‘All seems clear to us, in the light of new developments. When beardless lads dress up as gels, there’s no doubt that people will get confused. And that’s what we’ve got here, sergeant. Mere confusion. Mistaken identities. Much ado, in fact, about nothing. Clearly they are boys and may return home right now with an honourable discharge.’
Jackrum chuckled and stuck out a palm, flexing the fingers upwards like a man bargaining. Once again, there was the communion of spirits.
‘Very well. They can, if they wish, continue in the army,’ said Froc. ‘With discretion, of course.’
Monstrous Regiment, p. 314
The next word in the book is No, as Polly rejects this offer as well.
Polly plunged on. ‘Sir, a day or two ago I’d have rescued my brother and gone off home and and I’d have thought it a job well done. I just wanted to be safe. But now I see there’s no safety while there’s all this…stupidity. So I think I’ve got to stay and be a part of it. Er…try to make it less stupid, I mean. And I want to be me, not Oliver.’
Monstrous Regiment, p. 315
The general relents and agrees that the women can join the army, as women, providing they keep the secret of the women who went before them, but the important thing is that the central character of the novel explicitly rejects the offer of being seen by the army and the world as a man called Oliver. The importance of being yourself and knowing who you are is familiar territory for Pratchett readers, and what is clear here is that Polly is not a transman.
Polly’s later conversation with Sergeant Angua, also makes it clear that even if she had been, she’d still have been female.
‘You followed us,’ said Polly.
‘So you must have known we weren’t men.’
‘Oh, yes,’ said Angua, ‘My sense of smell is much better than my eyesight, and I’ve got sharp eyes. Humans are smelly creatures. For what it’s worth, though, I wouldn’t have told Mister Vimes if I hadn’t heard you, you don’t need to be a werewolf for that. Everyone’s got secrets they don’t want known. Werewolves are a bit like vampires in that way. We’re tolerated…if we’re careful.’
‘That I can understand,’ said Polly.
Monstrous Regiment, p. 330
Probably quite a few women involved in the gender critical debate, or on the edges of it, or very deliberately keeping quiet about it, are all too aware that women also are tolerated…if they’re careful.
I did see someone specifying that Monstrous Regiment contains a trans character. The most likely candidate is revealed near the end of the book, as Polly and Sergeant Jackrum have a private chat.
‘Upon your oath, you are not a dishonest man,’ said Polly. ‘Good one, sarge. You told people every day.’
Monstrous Regiment, p. 338
Jackrum, we learn, joined the army as a young woman, to be with her boyfriend, fought alongside him and saw him killed in action. She carried his child, who was then passed to her granny to raise, and continued on in the army, finding it easier than working on a pig farm with three lazy brothers. Jackrum no longer knows how old she is, or how long she’s been in the army – it’s suggested elsewhere in the book that it may have been 50 or 60 years – but now plans to retire and set up a high-class brothel, continuing to live as a man, and acting as the bouncer for her establishment.
Is Jackrum trans? Again, no surprise that she’s being claimed as such and there’s no arguing that she has spent the vast majority of her life living as a man, but there’s an interesting insight when Polly suggests an alternative retirement plan.
‘You don’t want to go back and see your grandchildren?’
‘Wouldn’t wish meself upon him, lad,’ said Jackrum firmly. ‘Wouldn’t dare. My boy’s a well-respected man in the town! What’ve I got to offer? He’ll not want some fat ol’ biddy banging on his back door and gobbing baccy juice all over the place and telling him she’s his mother!’
Polly looked at the fire for a moment, and felt the idea creep into her mind. ‘What about a distinguish sergeant major, shiny with braid, loaded with medals, arriving at the front door in a grand coach and telling him he’s his father?’ she said.
Monstrous Regiment, p. 342
In other words, Jackrum’s life has been guided not by being trans, but by the limitations of a patriarchal society. She joined the army as a man because she couldn’t join as a woman. She continued in the army because men demanded less work from other men than they did from women. She decides to end her days as a man because, although she’d have fought the same battles and won the same medals, an old man can be a hero, whereas an old woman can only be a ‘biddy’.
And she told people, every day, that she wasn’t a man.
At its very soul, Monstrous Regiment is a book about feminism and it takes a spectacular misreading of it to see it as anything other. But as trans rights activists want to claim feminism as belonging only to them perhaps that’s really why they’ve been so quick to claim this book as theirs.
It’s been a busy old week for trans politics in Scotland. The Court of Session ruled against the challenge to the official guidance given for the sex question on the national census, If you are transgender the answer you give can be different from what is on your birth certificate, in part it seems by interpreting the word can as meaning only that it is physically possible to do so.
Meanwhile, the court of appeal ruled that the Scottish government had exceeded its powers in single-handedly redefining sex, for the purposes of its gender representation act, which said that the boards of public bodies had to be at least 50% women or men in skirts, which seems meaningless, given that it’s Scotland we’re talking about.
The results were also published of a major study, undertaken by Savanta: ComRes on behalf of the BBC, into attitudes towards aspects of the trans debate in Scotland.
This was a sizeable study, with 2,038 online responses gathered. These were random respondents, from Savanta’s panel, and not a self-selecting sample, so we should expect them to be reasonably representative.
As required by British Polling Council rules, the full set of data tables have been published and can be downloaded here
It’s routine for published tables to exclude the initial questions, which determine basic demographics, which means that the first nugget of information has to be wheedled out indirectly. Because the 2nd question is only asked to ‘cisgender respondents’ we know that 7 of the people who took part identified as being trans. If you don’t have your calculator handy, that means that from a reasonably robust sample of the population, 0.34% of respondents were trans.
If you’re interested, 2 of the 7 were aged 16-24, a further 2 aged 25-34, and 1 each in the 35-44 and 45-54 brackets and 1 aged 65 or over, 6 of the 7 were white, 3 were from white-collar households and 4 from either unskilled or economically inactive households, and none of them voted Lib Dem in the 2021 Holyrood election. Make of that what you will.
Here’s where it would have been interesting to know about those demographic questions, because throughout the data tables the male and female breakdowns add up to 2,031. This either means that respondents were asked separately if they were trans or not and those who answered ‘Yes’ weren’t counted as either male or female, or, more likely, a standard market research gender question was asked, with the usual options of male, female, non-binary/other, and only those who selected the 3rd option were counted as trans.
This isn’t a huge error but it’s annoying that more care wasn’t taken. I imagine any trans respondents were annoyed to be asked the 2nd question, from which only non-binary (not cis) people were excluded, asking them if they knew any trans people.
On the plus side, the first published question tackles one of the main issues any survey on this topic faces, and asks the respondent what they think transgender means. The options range from self-identification, They express their gender differently to the sex they were registered as at birth, through to the more old-school meaning of transsexual, They have had gender reassignment surgery to permanently transition from their sex registered at birth. There are two intermediate options; they’ve had a medical diagnosis of gender dysphoria or they’ve obtained a gender recognition certificate, which unsurprisingly proved popular with no-one. There were also options to say you didn’t know (11% of respondents) or you’d prefer not to say (just 27 people were too bashful to answer).
I think the two sides of the gender debate largely agree that you are trans if you say you are (while, of course, violently disagreeing about what that means), so it’s fair to say that the self-identification answer is the correct one, and was the one chosen by 51% of respondents.
This means that if you read any survey about this issue that doesn’t define terms then half of the respondents won’t correctly understand the questions. That’s important.
This survey does, at the start of the next question, clarify that transgender is ‘a general term for people whose gender identity is different from the sex registered at birth‘, so we at least know for future questions that respondents were steered along the right path. This, however, makes it annoying that those of us reading the data are denied some important information before a key question, question 4, which determines the level of support for making the process of obtaining a gender recognition certificate easier.
Fifty-seven percent of respondents support making the process easier, with just 20% opposing such a move (18% have no opinion and 5% don’t know), but the question opens with ‘Given this[sic] information on the previous pages’…without telling us what the information on the previous pages was. This is, in my opinion, a more serious oversight than the mix-up with the gender question. BPC rules demand that questions are asked in a neutral fashion and must be published in full, but we are here effectively being denied the context of the question.
The reason this is interesting is that the follow-up questions ask about specific reforms of the process. A plurality of respondents (44% vs 37%) oppose cutting the time applicants must prove they have lived in their acquired gender from 2 years to 6 months, removing the requirement for a medical diagnoses enjoys only marginal support (40% vs 38%), and reducing the legal minimum age for application from 18 to 16 is opposed by the majority of respondents (53% vs 31%). The only place where support is overwhelming is in favour of making it a criminal offence to make a false declaration when applying for a gender recognition certificate (60% support, 16% oppose). While this new criminal offence is the key, indeed the only, safeguard for the Scottish government’s planned reform of the GRC process, it’s hardly the gender critical position to oppose this.
Hence we find ourselves in the strange position where vastly more people support making the GRC process easier than oppose doing so, but nobody is actually strongly in favour of any of the particular methods of making it easier that have been proposed. This is generally the point where those of us who work with survey data all the time go for a smoke break and shake our fists at the sky, yelling, “What do you mean, you bastards???”
With my word-count in mind, this is a decent length questionnaire and, so far, we’ve made it to question 5, so I’m not going to go through step-by-step, but I did want to touch on a final issue. It’s long been the assertion of the trans-rights side of the argument that the majority of women support them, and looking down the Male/Female column throughout these data tables you’ll consistently see more women than men supporting the trans-rights side of the argument.
However, this is a reasonably well put-together survey, asking reasonable questions, and allows us to dig a little deeper. Question 7a, for example, asks whether the respondent agrees that it’s important for legislation to continue to provide for single-sex spaces, such as hospital wards or changing rooms. Here 64% of women agree, compared to only 59% of men. Disagreement is just 8% amongst women. Unfortunately, we can’t break this down further by both gender and age, but we can see that even in the youngest age group (16-24) agreement still wins hands down (47% vs 15%)
The follow-up question, on whether transwomen should be able to use women’s toilets seems to contradict this, with the plurality of women (45%) saying that they should be able to, compared to only 20% who say they should not.
The issue with this question is that it offers only 4 options. Either transwomen are allowed to use female toilets, they are not, you have no opinion, or you don’t know. There is no nuance and once you, not unreasonably, remove the no opinions and the don’t knows you have a super-majority of women (70%) in favour of TW being allowed to use female toilets. Expect to see that number a lot in future arguments.
How fortunate, then, that at question 12, a little more detail is obtained. Question 12 asks when transwomen should be able to use single sex spaces, such as toilets and changing rooms. Here the options are either by simply identifying as a woman, by going through a process to legally change their sex, by legally changing their sex and having sex-change surgery, not at all, or don’t know.
Here the numbers are much more finely balanced. Both overall and looking at female respondents only, a minority (28% and 36%, respectively) say that transwomen who have not surgically changed sex should be allowed to enter female spaces. Excluding the don’t knows splits female respondents almost evenly, with 43% saying that uncut transwomen should be allowed in and another 43% saying only after surgery, and 14% saying, no, not at all.
I suspect we’re going to see very carefully selected portions of this poll shared by both sides for quite some time to come, and it is fascinating. It would be great to see an anonymised data set released, to allow some proper drilling down into the data, but I hope at least it shows others polling in the same field that there’s better ways than asking pointless questions, like “Do you agree that transwomen are women?”
Just annoying that a poll that got so much right when asking about gender managed to mess up the question on gender. Let’s hope others do better.
WARNING: This blog contains racist language and Wordle strategies that are of no use to any living person.
It started with a Twitter discussion about the best starting word for Wordle, of course.
It was Twitter, so everybody had strong opinions on the subject, of course.
And, of course, of course, of course, I did something in Excel.
I didn’t mean to. We were talking about the best opening words, so I innocently downloaded a list of 5-letter words and pasted it into an Excel column, then wrote a formula to work out, for each letter of the alphabet, what fraction of words it appears in. Once you have that it’s easy to assign each word a score, by adding up the frequency of all its letters (excluding duplicates).
My argument was that the best starting word was the one that scored the highest (i.e. it contained the most frequently used letters). Despite this logic being based on actual, literal, numbers it was not universally accepted.
The thread provided seven loose strategies for the starting word:
Start with AROSE, my highest scoring word.
Actually, you should ignore the letters in AROSE, because you can easily fill them in afterwards, actually.
Rise to the challenge with YEAST, the word I typically use (or rather used) as my starting one
Take into account that S is the most common starting letter for words – STARE was the highest scoring word I had starting with S
Put the S at the end, where it belongs. TEARS (unsurprisingly) scores the same as STARE and was the highest scoring word ending in S in my list
Just start with the first word that comes into your head
Make guesses that you know are wrong, to get extra letters.
I discounted strategy 7 straight away, because you could also get extra letters by guessing answers that might be right. That is one of many things I regret from my youth, 4 days ago.
Anyway, I quickly spotted that with my word scoring list I could add a mask for letters I knew were in the right place. If, for example, you know that the R in AROSE is in the correct place then the mask ?R??? will filter out all of the words that don’t have R as their second letter. Similarly, if you know that the A and the O are incorrect then you can remove all the words containing either of those letters, and if the S and the E are correct, but in the wrong place then you can remove both the words that don’t have either of those letters and the ones which fit the masks ???S? and ????E.
Then, by having my letters table only count the letters in words that hadn’t been excluded, I could generate new scores for each letter, and then new scores for all the non-excluded words and Excel would be offering me my next guess. I’d accidentally made an Excel sheet that could play Wordle!
Having such a sheet it would be criminal not to use it to prove my AROSE hypothesis, by having it pick answers at random and play Wordle against itself.
It should be said, straight away, that it’s not quick. After every guess it has to evaluate the formula alongside each of my list of 5,756 words and, for example, the one to work out whether each word is a valid guess or not looks like this:
This means that the macro I wrote, to make and evaluate guesses and play game after game, has to slow itself down, so that Excel’s formula recalculation can keep up. Even so, it’s much faster than a human player and can play 1,000 games in about an hour…and 1,000 games seemed like a sensible number to generate some statistics.
The first try was with AROSE as the starting point and, an hour later, it returned a win rate of 91%, losing only 90 games in the 1,000 it ran. Of the 910 games it did win, it did so in an average of 4.16 guesses. Both of these results seemed pretty good to me, and my gut feeling was it was better than human player could do.
The next 1,000 games used my starting word, YEAST, and the results were promising. The win rate was slightly lower, at 90.4%, and the average number of guesses was slightly higher, 4.2.
My work was done. AROSE was the best starting word, YEAST was good, but not quite as good, and my little Excel sheet was playing Wordle perfectly.
Really, just as a formality, I ran it against some of the other strategies.
TEARS returned a win rate of 92.9%, the highest yet, and the lowest average number of tries, just 4.06.
This wasn’t too much of an upset. Although 92.9% is undoubtedly higher than my golden boy, AROSE, it’s not significantly so, statistically speaking. In other words, the chance was greater than 5% that the difference between the two win rates was down to random chance, rather than representing a genuine performance difference. TEARS had got lucky.
STARE, however, proved harder to explain. It produced a win rate of 95.4%, which is significantly better than AROSE. My WORLD was crumbling.
Strategy 2 – avoid the common letters – brought it tumbling down. Completely off the top of my head I picked CAMPS as a word that mixed common letters with mid-tier ones, and it produced a score of 95.4%!
If a word that I’d picked at random could do so well then what was the next test, starting with a random word, going to do?
My theory was that picking at random would be a terrible strategy. No-one would, for example, pick LOLLY as a starting word, but my random selector could. Stupid random selector. There was not, therefore, unrestrained joy when the random words strategy returned a win-rate of 92.4%.
Again, this wasn’t statistically significantly higher than the word I’d been asserting, 24 hours earlier, was unbeatable, but it was annoying that all these insignificant differences were insignificantly higher.
In a fit of pique, I selected the lowest scoring word, GYPPY, as a starting point.
Here, at last, finally I found a word that performed worse than AROSE. Yes, indeed, out of its 1,000 games it got 3 fewer right than AROSE had. Three! FUCKING THREE!!!
If you’ve been keeping count you’ll know that, by now, I’ve played 7,000 games, which means that there’s about a 70% chance that one of the games would have guessed the answer first try. Well, it did, and it was fucking GYPPY.
GYPPY can fuck right off!
[Apologies, by the way, for using that word. I didn’t vet the list of words, which wouldn’t have helped anyway, because I didn’t know what it meant, and it was selected for use by an algorithm. I’ll not mention it again]
Those first 7 games also gave me a list of “hard” words –387 answers that one or more of the runs had failed on. Just for comparison I tried all the start words I’d used so far against that list of words.
AROSE, you will not by now be surprised to hear, stunk; solving just 32.6% of them. Even YEAST did better, with 35.9%. Both were well behind TEARS’ 42.1%, STARE and starting with a random word both managed to crack 48.1% of them, and CAMPS got 60.7%!
Why was CAMPS so good? In an effort to explain I picked the exact mid-point of the league table of words, PEAKY, and tried that. In results that are blindingly obvious in hindsight, it scored almost exactly the same as starting with a random word.
More than ten thousand games of Wordle had so far taught me:
My “best possible” starting word was worse than pretty much everything else I’d tried
CAMPS was a supernaturally good starting word, but I had no idea why
Ergo, I had no idea what a good strategy was any more
A wise friend suggested I should move to a two-word strategy. The one she uses starts with ATONE and then, unless she gets 2 green letters or 3 yellows (or, presumably, a green and 2 yellows) she moves on to SHIRK.
This was the discounted strategy 7, selecting a word that you know is wrong, to get more letters (which Wordle doesn’t allow, if you play in hard mode, but nobody does, so screw that).
The wise friend also mentioned she was thinking of moving to using STONE then HAIRY and I, being in the slow-learners class at school, suggested that DOLES and TRAIN would be better, because they use all 10 of the most common letters in 5-letter words.
Just for completeness I paired up the unbeatable CAMPS with another mid-tier word that I’d pulled out of my arse, DOUGH (the word, not the arse), and ran that as well.
The STONE/HAIRY combo managed to equal CAMPS’ 95.4% record, and with a slightly lower average number of guesses (4.06 vs 4.12). ATONE/SHIRK managed a practically-the-same result of 95.2%, CAMPS/DOUGH was nearly a whole percentage point worse than CAMPS by itself and, of course, my DOLES/TRAIN was bottom of the pack, with only 93.2% of games won.
I now, finally, realised the problem was the BEARS-trap, which is this; if you get to a point where you know the word is in the form ?EARS then there are a bunch of letters that could go first, B, D, F, G, etc. My algorithm was very good at getting to that point but would then go through the possible answers alphabetically. This was not a winning strategy, but no worse than simply guessing a first letter.
What was needed was to eliminate as many letters as possible before you get to your final guess, so that if you arrive there knowing the word looks like ?EARS then you’ve as few remaining answers as possible to test.
This will never be perfect, not least of all because you can’t eliminate 26 letters in 5 x 5-letter guesses but also because SEARS and REARS are also valid answers, so even if you had eliminated every other letter, it would still be a 50/50 chance.
My first line of attack was to extend the two-word strategy to a four-word strategy, QUICK/BROWN/FATLY/HEMP, with those being the first 4 guesses unless all the letters were discovered earlier.
Here, at last, I managed to topple the unexpected CAMPS from its top spot, with a win rate of 97.4%, higher at a p <0.01 rate of significance, i.e. there’s less than a 1% chance that the difference in scores was just luck. The trade off for this was the average number of guesses taken to win leaping up to 5.16.
At this point I did quite a lot of experimenting with a way to make the 4-word strategy more dynamic. My initial impulse was to value wrong guesses near the start of the game and then home in on an answer in the final couple of guesses.
Of course, if you find yourself in the BEARS-trap after guess 4 then what you need for guess 5 is a word that tests as many of the remaining possibilities as it can. Your 5th guess shouldn’t be anything like ?EARS, it should be testing possible first letters.
I realised that ‘possible’ was the key word in that sentence. At the start of the game you can guess words that will give you extra letters, willy-nilly, but as the answer takes shape you need to restrict yourself to words that will give you additional letters that could possibly be in the answer. If you have ?EARS then there’s no point guessing QUICK, even if you haven’t yet checked any of those 5 letters, because none of them can be right.
I adapted my formula, which were now also counting how many untried letters were in each word, to only count untried letters that appeared in words that fitted into possible answers and tested this solution with both AROSE and CAMPS as the starting word.
I’ve still no idea why CAMPS is so much better. Maybe it’s not the best starting word, but as it would take 240 days of continuous playing to try all the start words, I’m not about to check the lot.
Just for completeness I also ran AROSE and CAMPS against my list of ‘hard’ words. AROSE won in 86.3% of those games, CAMPS in 93.3%
Now, after more than 20,000 games of Wordle, I’m confident that I have a system that (a) works as near as dammit all the time and (b) is absolutely no use to anybody not using a computer to play for them, unless they can mentally tally up valid, untried letters and words containing them.
Oh, yes, and I was dead wrong about everything I said in that Twitter thread. Further tests are necessary to determine if this is generally true of all Twitter threads I post in.
This blog continues on from the events detailed in my previous blog, where a scammer applied for a loan in my wife’s name and then tried to convince her to “repay” the loan from her bank account to one of their choosing.
Their scheme was foiled before it ever really took off, as my wife happened to spot the money, £4,500, in her account before the scammers ever got in contact with her, so by the time they emailed and called she’d already spoken to the loan company’s fraud team.
Their fraud team were very helpful (although completely puzzled as to the point of a scam that involved getting money paid into an account the scammer had no access to). They gave her a fraud reference number, told her to cancel the direct debit that had been set up to repay the loan, said that they would add her to the Cifas voluntary registration scheme (which requires enhanced proof of ID for any credit applications), and that they would contact her bank directly, to reverse the transfer. This all happened on August 11th, and we expected it to be the last we’d hear about it. She’d dodged the scam and done everything right to sort it out. It was all over.
In fact, it was the last we heard of it until October 12th, when a letter dropped on our mat, telling my wife that she was in arrears on her loan payments, with an outstanding balance of £7,490.88 (£4,500+interest). This seemed a little unfair, on the grounds that (a) it was the loan company’s own finance team who had said to cancel the direct debit, (b) the money transfer had been reversed, and (c) she’d never taken out a loan in the first place.
The thing was, we realised, that we had no proof of our conversation with the fraud team, no proof that they’d accepted it was fraud, and no proof that they’d advised my wife to cancel the direct debit. If they were going to get heavy, with thing like arrears notices then that raised the possibility that this would end up in court, with us trying to get her to repay money that she’d never asked for and which had already been taken back. Hilarious as that court case would be, it would still be nice to be able to prove our side of the story. For this reason we decided that everything from here on in was going to written.
We emailed the loan company’s customer services team, explaining the whole situation again, and asking three key questions:
Would they please confirm that my wife didn’t owe them any money and stop sending her arrears notices
Would they also confirm that they had add my wife to the Cifas scheme
Would they let her know what details of hers the scammers had used (they wouldn’t do this on her phone call with them in August “for data protection reasons”)
We also said that as the scammers had tried to contact her by phone and by email we’d prefer any response to be via snail mail.
The first thing we were going to learn is that all communications with the loan company have to age for 10 days before anybody sends a response. The second thing was that nobody was spending those 10 days reading what was written. Here’s the first response…
Let’s just take a moment to appreciate the full beauty of that response. In reply to an email saying that scammers applied for a loan in her name, using a false email address, the loan company are saying that they can’t respond, because the email hasn’t come from the email address they have on record.
The one the scammers setup and operate.
The one they wouldn’t tell us, for data protection reasons.
Still, there was the possibility of contacting them through their secure online portal. That seemed to be an avenue worth exploring.
The initial page of the online portal requires three pieces of information, (i) the loan agreement number, (ii) your postcode, (iii) your date of birth. Once you’ve put those in it gives you a message saying that the information does not match that held on record, and won’t proceed any further. What’s more, as the arrears notice contains both the loan agreement number and our postcode we could be sure that we were in-step with the loan company on those two items, so the erroneous piece of information must be the date of birth used.
The scammers hadn’t even used my wife’s correct date of birth. We emailed back, explaining this, and adding to our list of questions for some sort of explanation as to how even an incorrect DoB hadn’t raised some sort of red flag. Once again, we made it clear that we’d prefer to receive a response by post.
The 10 days to their next reply simply flew by. This one said that as our case sounded like fraud the case details had been passed to the fraud team.
All that happened for the next 3 weeks was that the loan company added another missed payment to my wife’s credit report. We decided to raise a complaint with the loan company and sent them all the details, and our list of questions, again.
This time it only took 4 days for us to get another reply from the customer services team, telling us that, As you have explained in your email that you have had suspicious emails from others in relation to this, we will contact you by letter with any updates.
Woo-hoo! Now we only had to wait 10 days (+2 days to allow for postage) to get an actual physical letter through the post. It acknowledged that we’d raised a complaint, told us it was being investigated, and reminding us that whatever our complaint we must continue to make repayments.
My wife, a defeated woman by this point, left drafting the reply to me.
My wife, perhaps wisely, refused to put her name to this, and we cut it down to a rather boring 2-liner, asking them not to add any more late payments to her credit report.
This time somebody competent seems to have been involved, as inside a week the loan was flagged as “Disputed” on my wife’s credit record, and no further late payment was added.
Then, finally, a flurry of activity, and two letters from the loan company in the space of a couple of days. The first was a baffling one, both address to my wife and also referring to her in the third-person. Dear Mrs R, it opens, We’re writing about your request to cancel the agreement with Mrs Lisa R. In case that wasn’t confusing enough, it continues, I’m happy to say that Mrs Lisa R has given their permission to cancel the agreement.
Mrs Lisa R, who has never had an agreement with the loan company, was delighted to hear that Mrs Lisa R has kindly agreed to cancel that agreement, and agrees that the agreement was most disagreeable.
The second letter was more understandable and informed my wife that the investigation had concluded and, more than 2 months after the arrears notice landed, and a full 5 months after her initial contact with the loan company, had decided that fraud had taken place.
There was a certain finality to that letter. A real feeling that things are sorted now, so let’s just draw a line under the whole experience.
My wife, who had contacted the loan company at 9am the day after the money appeared in her account still has 2 missed payments on her credit record for a loan she never took out.
The loan company have not answered a single one of the questions she raised.
If they don’t soon then this blog will be edited, to name them.
What would you do if you received an email tomorrow morning, telling you that your £4,500 loan has gone through, the money would be in your account today, and that somebody from the customer care team would be in touch shortly to check that the process had been smooth and hassle free?
You might think of it as a nice customer services touch. After all, you’ve probably got plans for that money; a new car, a family holiday, home improvements, or just filling a bin-bag with Haribo and eating until you die of Insulin, whatever.
What, though, if you hadn’t applied for a loan, and this was the first you were hearing about it?
In that case you’d probably just write the email off as spam, especially if you looked at the reply-to address and noticed it was from a domain called protonmail.com, which provides secure, end-to-end encrypted, and untraceable email accounts. Into the trash, spammer!
Then, an hour later your phone rings, and it’s the customer services guy from the loan company, all preppy and cheerful, asking how the loan process went and could you answer a few questions, for their customer feedback survey. “What?”, “Who the fuck are you?”, and “I didn’t ask for a loan, why are you calling me?” might be among your first questions. The preppy loan guy is shocked by your potty mouth, but is a pro, and calmly tells you that the £4,500 was paid into your bank account in the last 24 hours. He tells you to go and verify this and gives you a number to call him back on.
You go and check your online banking and, sure enough, last night £4,500 that you weren’t expecting fell into your account, delivered there by a genuine loan company. Your phone rings again, it’s the world’s brightest customer services guy, phoning back because he’s concerned that the loan was news to you. Maybe this is some kind of scam, but he just can’t understand it. Why would someone scam you with a loan paid into your bank account? That makes no sense.
Never mind, if it’s a scam then it’s a stupid one. The loan company are very apologetic, but this is easily sorted. Just repay the loan to the bank account given in the email you received this morning and the whole thing will be cancelled and chalked up to “WTF?” What, you accidentally deleted that email? Never mind, here’s the account details. Repay the money and the loan company will do a thorough investigation into what happened. Tap, tap, tap, sorted. On with the rest of your day.
In case you’re wondering where this story came from, it happened to my wife, back in August.
Her interaction didn’t play out quite as above as, purely by chance, she’d checked her bank account on the evening of 10th August and seen the unexpected £4,500 in there, so by the time the email arrived she’d already spoken to the loan company and established that although they’d had an online application from someone using her name, address and bank account details, and that the mobile number and email address they held for her were not hers (the email was courtesy of our friends at protonmail.com again).
This meant that when the happy customer services guy rang her, and claimed to be calling from a company who she knew didn’t have her mobile number, he got told to fuck off in no uncertain terms. Likewise for the calls that followed – from the same number, from blocked numbers, from Spain, from a hotel in Biarritz (!). As the calls shifted geography they also shifted tone, from happy and helpful through to threatening legal action before reaching their final destination of just threatening.
In case you’re not following how this scam is working, it plays on three factors:
Getting a loan on-line is pretty easy and very low-risk. The details you need about the target aren’t exactly secret; their name, address, email, mobile number and bank account number. With a common factor, like an email address, you can pull these details together from multiple sources fairly easily, but…
Loan companies baulk at paying the loan into an off-shore numbered account, or depositing it as a carrier-bag full of fifties next to a bin in Hyde Park, so you need a way to get the money from the victim’s account to your own, and bank accounts are harder to hack into, but…
Most people, having found themselves the recipient of an expected loan, will want to do the right thing and repay the money. If you can convince them that they are doing this, while they are actually sending the money to where you want it, then you’re home and dry.
Even step 6 here is uncertain. Depending on your circumstances, and how tight a rein you keep on your finances, it might be a while before you even notice that the lender has set up a direct debit on your account, and start asking them why they’re still taking payments for a loan you repaid.
It’s a low-risk crime, with a nice long getaway time built into the back end. The police seemed uncertain what crime had been committed. They doled out a crime number, sent an email saying they’d call me wife back at time she was at work, and then never got in touch again. I think we can safely assume they’re not staking out that Biarritz hotel right now.
What we’ve learned from this is:
If you get an email saying your loan has been approved then do not ignore it.
Be sure that the people you’re talking to are who they say they are. Phone the lender yourself, using the details from their website, don’t trust that anybody claiming to be them is who they say they are.
Let the loan company and your bank sort out the money being reclaimed, don’t go making payments to a bunch of numbers passed to you over the phone.
As we’ll see when I write part 2 of this story, don’t assume that just because you get steps 1-3 right that your problems are anywhere near over.
Remember #MeToo? How about #BelieveHer? Remember when, for a brief moment, it looked and felt like the world was committed to finally banishing the four horsemen, who have plagued every women to ever try reporting sexual assault?
My, how far we’ve come from there, as the Wi Spa incident shows.
Who’d have thought that in those days when we finally seemed about to let daylight into the murky world of male sexual aggression towards women that we were only a few years away from women being told they were bigots for being made uncomfortable or that they were siding with Nazis in wanting it to stop? Who’d have believed that the people saying that define themselves as feminist, or that they claim, straight-faced, that those who disagree with them are, by definition, not feminists.
Wi Spa has been a tremendous victory for the men who want to women to keep quiet about sexual violence, because it has perfectly demonstrated that all of the old weapons are oiled, loaded and in full working order, and that new arms have been added to the arsenal. Every woman has got to see that, even there, where the case turned out to be as cut and dried as one could hope for in such matters, the cost to the woman at the centre of it was terrible. They can all vividly imagine how things would go if their own case was even a little more marginal.
#MeToo felt like the start of the end of the easy ride for male abusers, instead they can now cite feminist scholars, saying that their accusers are no better than racists. Women were angry then, the best of them – the ones who understand how men have learned to use ideology to not only wound women directly but also to cut them adrift from feminist support – are furious now. Come and see.