The Police, Quakers, and the Satanic Scare

Last Thursday, the Metropolitan police broke into Westminster Friends’ Meeting House to arrest six women members of the pressure group Youth Demand, which ironically probably helps to publicise them and encourages people to join their cause. Although their plans for action are interesting, I want to focus on another aspect of this situation and also compare it to the child abuse allegation farce which took place in the Orkneys at the end of the 1980s CE. Before that though, I want to talk about the place of Friends’ Meeting Houses and the Quakers in my life, mainly the one in Leicester.

The first time I darkened the doors of Leicester Friends’ Meeting House on Queens Road was in autumn 1986. At the time I had recently joined the Green Party and was also involved in hunt sabbing, animal liberation and the university Green group Leicester Environmental Action Force. It was dark and around 7:30 pm on a Thursday evening, and I was walking behind my friend Vicky whom I probably shouldn’t have been behind at that time of night, but you live and learn. At this point, she was for some reason constantly surprised when I turned up to this kind of thing, possibly because her image of me had been dominated by how I’d been over the previous year. Both she and I were on our way to a Supporters Of Greenpeace Leicester meeting, the first of many groups I’d be involved with there over the coming years. Other groups included Friends of the Earth, Leicester CND and, a few years later during the 1991 Gulf War, the Stop The War Coalition. As well as all that, we got married there in a humanist ceremony (well, sort of humanist – long story), went to a complementary medicine taster group, attended Yoga sessions, a parent and toddler group (abortively) and also Leicestershire Education Otherwise. I can’t quite remember, but I don’t think the Green Party or the animal welfare groups I was involved with ever went there, but it was a pretty central part of the alternative scene in Leicester, and particularly Clarendon Park, at the time. It was a venue used by lots of groups, with a tendency towards peace, sustainability, socialism, Green issues and to some extent anarchism. In general, the approaches taken by such groups accords with the Quaker world view. The donkey coöperation cartoon was outside on a board for many years, which seems to me to be pretty much in accordance with these organisations.

There was conflict, even aggressively so, within these groups. In particular the Stop The War Coalition was rife with friction because it involved peace groups and splinter communist groups trying to work together and soon after the end of the first Gulf War it fell apart. That was quite a shouty group, with the overt aggression largely coming from the smaller communist parties. There were members of the main Communist Party of Britain in the group, though, who were generally quiet and in fact didn’t advertise their communism. CND has many of that variety of communists within its ranks, but also people of a more spiritual bent. Supporters of Greenpeace Leicester was merely a fundraising body and in fact we got into trouble for trying to do more, so on the whole the same people worked within Friends of the Earth instead, meeting in the same place. There’s a conversation to be had about this, but not here. FoE also have their issues. Sarada and I concur in the opinion, also expressed by many others, that the more peace and well-being groups could do with being more politically-aware and the more overtly political groups could benefit from being more spiritual. Now I look back on it, the other stuff going on in Leicester at the time didn’t tend to organise from the building, and CND also had its own office, where I was office manager for a while, among other things. Leicester CND was slowly winding down over the whole period I was involved with it, which was from 1991 to about 2011, and was dominated by older people, mainly women. I preferred CND to the other organisations in the ’90s because of their spiritual tendencies. The revolution starts from within. It really helps the world if you become a better person.

That, then, is the kind of group you might expect to meet in a Friends’ Meeting House. Many Quakers don’t have their own premises for various reasons: there aren’t enough of them to afford one or it becomes a case of property ownership in the same way as many churches are saddled with expensive buildings which eat up the money which could be used to benefit the community and the vulnerable in Europe and beyond. That said, it’s a nice thing to have, and although they’re not Quakers themselves there is often quite an overlap in their memberships. In particular, Leicester CND had a lot of Quakers in it, which is not surprising because of the latter’s commitment to pacifism. CND is not a pacifist group although it does contain many such individuals. Quakers also tend to be older, as do members of many religious communities in Britain. Incidentally, I’m talking about Quakers in the “U”K here. What happens elsewhere is probably different. For instance, American Quakers often have what are called “programmed meetings” with singing and they don’t sit in circles.

The reason I’m saying all this is to put the incident in Westminster in context. It’s possible that Youth Demand has Quaker members but not inevitable. However, their witness and mission to pursue peace, justice and sustainability accords closely with the Quakers, and they belong under their umbrella. At a guess, Youth Demand probably don’t overlap with membership just because they’re young. Hence it’s an organisation using the centre, with whose aims the Quakers are likely to agree, but it isn’t a Quaker organisation. The situation is therefore that a place of worship hosting a planning meeting by a non-violent group was invaded by the police and their members were arrested.

I may have some of the details wrong but there is a page on the incident here from the British Quakers themselves which is worthwhile for cutting through the verbiage and spin of the mass media, although it has to be said also that the actual mass media coverage is quite sympathetic to the Quakers themselves. There were twenty police officers and six women were arrested for planning a now-criminalised Non-Violent Direct Action. Several aspects of this come to mind. One is the question of whether the police would’ve done the same thing with other places of worship. I heard someone yesterday claim that they wouldn’t have done this with a synagogue or a mosque. I personally think they would’ve done it with a mosque but the fact that synagogues are often guarded and have turnstiles would have made doing it in such a place difficult regardless of how it would’ve looked. I’m pretty sure they wouldn’t have done it to an Anglican, Methodist, Baptist, URC, Roman Catholic or Orthodox church. Regarding gurdwaras, they did actually use a SWAT team in Leicester to my knowledge because they thought the lives of the people within it, who were being held hostage, were in danger. I have no idea how heavy-handed they were. Bearing in mind the direct child abuse and murder which occurs in some churches, for instance when exorcisms have been performed on children, I would expect and in fact hope that they would intervene in such cases. So it isn’t completely out of order to do this, although the provocation would’ve probably been stronger. It’s also not proportionate, and it’s at least interesting that it seems to have been a woman-only group. The implication is that this action would’ve been sufficiently serious and reprehensible to warrant such a response, possibly partly as a deterrent to others.

I mentioned incidents of child abuse within churches. Although this usually calls to mind child sexual abuse, which is indeed a serious problem, I actually had exorcisms in mind. I have actually tried to help someone access exorcism, which they wanted for themselves, and it was difficult to do so due to their lack of association with any particular church. It doesn’t seem easy to get this service within the Episcopal Church. Without this milieu, however, things are sometimes different because some other churches are less reserved or cautious. A fifteen year old boy was drowned during an exorcism in Newham in 2012 and a two-year old was hit fatally in Wolverhampton more recently. It isn’t clear whether either was part of a church-sanctioned process, but these things do happen and the potential victims need to be protected. However, the separate issue of child sexual abuse linked with a general suspicion of Quakers was also called to mind by last week’s events.

This seems to have been almost forgotten today, which may be a good thing except that forgetting history risks repeating it, which in a sense is what’s happened here. You may, though, remember the Satanic panic of the ’80s and ’90s, which is how this was able to take place. I can remember the first time I noticed this in about 1979 when my mother showed me a list of what the London Healing Mission regarded as Satanic activities, including of course Yoga, which I was very keen on at the time. I wish I was still that keen. This initially included heavy metal music and roleplaying games, as in Dungeons And Dragons. Much more recently it included Harry Potter although that’s faded considerably nowadays. By the late ’80s, the focus was on the idea that communities were being infiltrated by Satanists who were engaging in widespread ritual abuse including child murder and sexual abuse. No evidence was ever found, but that didn’t stop a training course for the police being devised. The claim was meanwhile made of fifty thousand murders per year with expert disposal of the corpses. To put this in proportion, this is on the scale of the casualties of a major international war. All this was happening in North America. To quote some of the promoters of these claims, “no evidence can be evidence” and “the most dangerous groups are the ones we know nothing about. . .They are the real underground”. It was eventually concluded that the children involved were being interviewed in a manner which would encourage them to make up stories about being abused due to the poor quality of the questioning techniques, such as closed questions, and in therapy false memories were also created. Because children often deny being abused during interviews, the approach was to keep repeating the question, and it’s fairly simple to recognise even as an adult that that repetition is akin to Hitler’s technique of repeating a lie often enough for it to be accepted as true, a technique currently in use in the US. However, it beggars belief that anyone could have accepted that the process was taking place on such a gigantic scale. It’s the reverse of Holocaust denial in some ways: where are all the relatives of the Roma and Jewish people who were murdered in the Holocaust if they weren’t murdered? Conversely, how could there be tens of thousands of victims of systematic serial murder whose bodies are never recovered and whose absence is never noted by anyone? There were allegations of injuries which would’ve required emergency treatment but no evidence for them either.

In February 1990, the McEwen family in South Ronaldsay was almost broken apart by a dawn police raid on their home where four children were removed and taken into care on the Scottish mainland. A worker in the NSPCC had made the claim that in Britain four thousand children were murdered through Satanic ritual abuse annually. What had happened was that there had been conferences on Satanic ritual abuse in Britain, notably in Nottingham in connection with a genuine incest case in Broxtowe. Ten adults were jailed for this having been found guilty, but no suggestion of a Satanic element had been made at that time. This connection was made by a group of psychiatrists, social workers and an anthropologist specialising in occult rituals in Afrika. This was happening at a time of growth of evangelical Protestant churches in Britain, which led to the production of a training video called ‘Christian Response To The Occult’. Workers in children’s foster homes and foster parents recorded claims made by the children, which while beginning with accounts of their abuse in relatively prosaic terms tended to veer off into accounts of ritual abuse. There were attempts to explain this in any other way possible, because of the uncanny similarities between the claims. The social workers concluded that they’d uncovered an organised network of ritual abuse in Broxtowe. A checklist was used which contained a large number of non-specific signs of indicators such as bed-wetting, and the foster parents and others had used this as the basis for the interviews, so they’d ended up guiding the process through leading questions. While there was no factual basis for these claims, the fear of not listening to children when they report genuine abuse leads to swinging too far the other way.

By 1994, an inquiry had established that there was no evidence at all for the claims. It’s worth noting that this sounds very like Pizzagate. Now I have a problem. I’ve ransacked the internet for fair accounts of the situation regarding the Ronaldsay Quakers without any success, so I’m going to have to try to reconstruct this from rather ancient personal memories. What I can remember is that someone of national significance among the Quakers was contacted by a worried member of the meeting who expressed her concern that police action was liable to bring the meeting and the wider Quaker movement into disrepute without any firm basis for that. She was reluctant to say more, but in the end she talked about how the police suspected them of Satanic ritual abuse. In particular, she said that the police were suspicious of the Quaker practice of sitting in circles and waiting for the Holy Spirit (as I put it – many Quakers such as atheists and Buddhists would probably disagree with this characterisation but it’s hard to think of a personally authentic way to describe it more diplomatically) to move them to give ministry. This was apparently something the police and many of their associates were unfamiliar with and attributed evil intent to. Putting my evangelical Protestant hat on, something Quakers would disapprove of, I’m familiar with the claim that allowing silence and emptiness of this kind is liable to give Satan a way into the group, and I wonder if this was their take on this. I honestly don’t know what happened in much detail, and I’m finding this quite frustrating right now.

These two incidents, the Westminster invasion and the Orkney Satanic panic, to me both have elements of othering by the authorities, something with which the Quakers will be very familiar as they’ve endured it for centuries. The very heart of Quaker practice, of sitting in circles and waiting to be moved by the Spirit, was attacked by the establishment back in the early ’90s, and last week the general Quaker ethos was attacked in the same way. I’ve long since shed the illusion that the current Westminster government is worthy of being described as Labour and I note the extreme keenness and conformity with which they applied the Tory law introduced in 2022 to enable this kind of thing to happen. But it’s the Tory party which is supposed to be about God, King and Country, and by extension the Anglican church, which is after all also a broad church, much of which would back the actions of the pressure group in question, but the question arises of why a party founded partly by Methodists would decide to persecute Quakers for supporting peaceful protest against the global suicide (yes, it’s a moral crime in this context, but not usually, so it’s “suicide” for the purposes of this paragraph) pact. Why are we in a situation where a group renowned for its non-violence and tireless work for peace is repeatedly treated in this way? And why haven’t we made progress on this since Thatcher’s time in office?

But there’s more.

Quakers seek to see the spark of God in everyone, and they mean that in a positive way which anti-theists may find hard to perceive. I think it was Viktor Frankl who said that the line between good and evil runs down the centre of the human heart. We all have within us the potential for peace and violence in his view. I’m not sure I’d go that far, but the fact remains that this situation is likely to provoke anger in those who have been persecuted, directly and indirectly. There is a potential antidote to this, because the very police officers and social workers involved in these incidents are human, and as such there’s that of God in them too.

It reminded me of two other incidents, and again I’m having to rely on somewhat shaky memories. One is of an incident regarding the peace movement and the police, possibly on Menwith Hill or Faslane – it’s vague. A group of people were trying to project peaceful and healing energy to the police force involved in this conflict. The metaphysical basis for this may be questionable but bear with me. One of the male police officers involved in protecting the base burst into tears in this incident, and it was found later that he’d been at Hillsborough, where the fatal crush had happened in the football ground and after which South Yorkshire Police spread false stories criticising the fans, as did the Sun newspaper. Whatever his involvement in that, he had been emotionally traumatised by what he witnessed because guess what, police officers are also human beings. The other incident was much more recent and involved another police officer who was guarding a fossil fuel facility of some kind – I’m having to dredge my memory here, sorry about any mistakes. One of the protestors mentioned to her that Just Stop Oil, if it was them, were among other things trying to protect her children’s and other descendants’ future, and once again, she was in tears. I don’t know the details of this incident. It could’ve been to do with a family tragedy, some other experience or maybe the interpretation given is correct. It was in any case a remarkable incident, once again revealing what might be called the humanity of police officers. Because there is that of God in everyone.

But there is also a police officer in everyone. By this I don’t mean a “bobby on the beat”, although maybe there is, but someone more like a member of the Special Patrol Group or the Carabinieri. We all have an inner fascist boot boy too, and we need to be conscious of it.

I was sitting in a sociology lecture once about the 1981 inner city riots, and suddenly had the thought that the police were not just Thatcher’s Army but also ordinary human beings with romantic relationships and families, and the thought had such a profound affect on me that it literally gave me vertigo. It made my head spin. I feel bad about that incident because it clearly means I was seriously objectifying the people concerned, but of course it’s true. When the Met broke into the Friends’ Meeting House in Westminster the other day, what they did was reprehensible and bizarre, but after it they presumably went home to their families, read their children bedtime stories, did the vacuuming, made love to their spouses and watched telly with them. They are also human. It shouldn’t need saying, but we need to have the mental reach to recognise the temptation to other and behave like them in ourselves and condemn and work against that in us as well as in them, and also to do what we can to see their divine nature, and this is very difficult.

I feel like this is a bit of a platitude, sorry.

Bigger On The Inside

Will be removed on request

“Dimensionally transcendental” was initially a cool-sounding phrase mentioned by, I think, Susan Foreman in the first episode of ‘Doctor Who’. It meant “bigger on the inside”, and definitely sounds like technobabble. TARDIS stands, as we all know, for “Time And Relative Dimensions In Space”, but even in the Whoniverse this is probably a backronym because why would something from Gallifrey have an English initialism? I think most people who think about it would probably say that Susan came up with the abbreviation, which probably explains why it doesn’t make much sense.

The BBC, and also Terry Nation’s estate, are quite protective about their intellectual property with respect to ‘Doctor Who’, which has led to a couple of disputes over the use of the likeness of police boxes and the word “Tardis”. Therefore I’ve posted a picture of a Portaloo up there instead of a Tardis or police box. In 2013, the portable toilet hire company Tardis Environmental came into dispute with the BBC over the use of the word, which was registered as a trademark by the Corporation in 1976. The BBC claimed that the company might end up seeming to be endorsed by them, to which they responded, “we don’t roam the universe in little police boxes from the 1930s, we actually hire out portable toilets and remove waste.”. I think we can all be grateful to them for clearing that up. I suppose it does make sense that the taboo against human excrement is not a positive association for this word. There was also a dispute with the Met. In 2002, after six years, the BBC won a case against the Metropolitan Police who took them to court over their use of the police box in ‘Doctor Who’ merchandise because they claimed that since they were responsible for the original boxes, it rightly belonged to them. I think I’ve seen two or possibly three police boxes, in Glasgow, Bradgate Park and London, this last being the one I’m least confident about, and I don’t think any of them look very like the Tardis. The one in Bradgate Park I’ve seen on a regular basis, and looks like this:

This is a listed building and is apparently still in use. It doesn’t look like a Tardis to me really but it’s a nice shade of blue. It’s 9 646 metres from where I’m sitting right now. The one in Glasgow is rather further away. It was the Met against which the BBC won the case, but the Tardis props are clearly wooden, a different shade of blue and have different windows, at least compared to the one I’m familiar with, so it seems a bit unfair. To be honest I don’t understand why this dispute even happened. It was between two publicly-funded bodies, I think, and seems to be a bit of a waste of money and time. Even if it was BBC Worldwide or BBC Enterprises, the Met was still involved.

Anyway, this is not what I came here to talk about today, but the concept of dimensional transcendentality. I’ve previously mentioned the fact that extremely large spheres are appreciably larger on the inside than their Euclidean volume because space is non-Euclidean – parallel lines always meet, at a distance of many gigaparsecs. This is possible because Euclid’s Fifth Postulate is based on observation rather than axiomatic or deduction, and the observation turned out to be incorrect. A sphere whose radius is equivalent to that of the Universe’s has a volume of five thousand quintillion (long scale) cubic light years, but if it were to be considered a sphere in Euclidean space, its volume would be only four hundred and twenty quintillion cubic light years, a difference of a dozenfold. This is quite counter-intuitive and I’ve ended up checking the calculation about five times to ensure it’s correct, but it starts to indicate how very confounding to the human mind higher dimensions really are.

I want to consider three cases of curved shapes in hyperspace to illustrate what I mean. Well, actually one of them is rotary motion rather than a literal curved shape, and I’ll go into that first. Here’s a circle with a dot in the middle:

(I’m drawing all of these in a ZX Spectrum emulator because Chromebooks rule out the use of more sophisticated graphics programs as far as I know). The circle can be rotated around the dot, so in a sense that dot is the “axis” of rotation of that circle. Now consider this as a cross-section down the middle of a sphere:

This is an axis of symmetry and also of rotation. Spinning the sphere through which this is a cross-section would lead to it turning round this line, which would be the only stationary part of the sphere just as the point is the only stationary part of the circle. Geometrically speaking, these are infinitely thin and infinitely small, so it’s rather abstract, but in the real world the closer you get to the centre of a spinning circle or sphere, the less you’d move.

Now consider the hypersphere, i.e. a four-dimensional version of a sphere: that which is to a sphere as a sphere is to a circle. If that rotates, doesn’t that mean its “axis” is a circular portion of a plane bisecting it? Can we even imagine something rotating about a two-dimensional axis? Also, just as two-dimensional objects have lines or points of symmetry and three-dimensional ones lines or planes of symmetry, surely that means that four-dimensional ones can have solids of symmetry? A hypersphere could be divided into two hemihyperspheres along a central sphere touching its surface, and since it’s symmetrical in that way, just as points on or in a sphere describe circles when they spin, doesn’t that mean line segments on or in a hypersphere would describe spheres? I find this entirely unimaginable, but is that a failure of my three-dimensional imagination or a flaw in the idea of hyperspace. It’s probably the former but this brings up a surprising recent finding about the nature of the human brain, which is that small cliques of neurones form which are best modelled topologically in up to eleven dimensions. No, I don’t really understand that either.

This hints the nature of hyperspace is very counter-intuitive, which isn’t that surprising really. Another issue is that of the torus. This is a Clifford Torus:

And this is a flat torus:

By Claudio Rocchini – Own work, CC BY 2.5, https://commons.wikimedia.org/w/index.php?cur
id=1387006

Travelling across the surface of a torus, one would find oneself disappearing off the top or bottom of a map and appearing on the bottom or top of it, or doing the same at the right and left hand sides. This is not like a cylindrical map projection of a planet, where the poles are either at an infinite distance or one would traverse horizontally exactly half way across the map and appear 180° of longitude away vertically but do the same as on a torus horizontally. With a four-dimensional torus, one would be in an apparently three-dimensional warped space forming the analogue of its surface, which you might think of as a cube with linked opposite faces, but the faces could be linked in different ways. One of the dimensions could be like a spherical map, with the concomitant traversal near the faces, or two of them could be, so there seem to be at least two different four-dimensional toroidal analogues. I confess at this point that this may not be what the above two animations represent.

The third problem relates to what ‘Doctor Who’ calls dimensional transcendentality, and it’s this which I’ve only recently heard about, from Numberphile. To illustrate this, I’ll go back to the Spectrum:

These are supposed to be four circles fifty pixels in radius touching each other. Now the question arises of what the biggest circle fitting among those four would be. The answer is quite straightfoward because squares can be drawn around each circle whose diagonals touch at the centre of these four circles. If you think of each circle as having a radius of one, the diagonal of the containing square has a length of the square root of 22 +22, or roughly 2.8. The radius of the circles is one, so subtract that from 1.4, or half the length of that diagonal, and you have 0.6. In other words, the square root of two is involved.

If you then extend this into three dimensions and imagine eight spheres stacked together in a similar manner, there’s a bit more room. The hypotenuse of a right angled triangle from the centre of an outer sphere to the inner one’s is then the square root of the sum of the squares of the three sides, which is root three, so the radius of the inner sphere is just over 73% of the outers’. This makes sense intuitively, for the last time, because it’s easy to understand that the diagram above shows a cross-section of the equators of all the spheres and therefore the minimum space between them, so a larger sphere is possible than one with the same circumference as the central circle in two dimensions.

The radius of the hyperspheres at the centres of analogous arrangements in higher dimensions is always going to be one less than the square root of the number of dimensions involved. At four dimensions, the central hypersphere’s radius is one less than root four, also known as 2-1, which is one, so rather surprisingly perhaps, it’s possible to fit seventeen equally sized spheres into a hypercubic arrangement. At five dimensions, the central “sphere” is actually 23% larger in radius, as root 5 minus 1. This is actually nearly three times the size in terms of a five-dimensional “bulk”, if that’s the right word. At nine dimensions, even the radius is double that of the surrounding hyperspheres, which makes it five hundred and twelve times larger altogether. There’s no limit to the increase in radius at all. I find this highly counterintuitive.

Moreover, these sphere analogues don’t even occupy the whole space. What does is a peculiar pointed shape which starts off like a square with concave sides in two dimensions (whose bottom point I’ve accidentally cut off) and a kind of inwardly-curved octahedron in three. In three, it has to be greater than the area of the largest circle in six different directions. In four, it resembles a concave version of a cross polytope, which is the higher-dimensional counterpart to the octahedron. Cross polytopes always have twice the number of vertices as they have dimensions, whereas measure polytopes, also known as hypercubes, always have twice the number of faces as dimensions.

Now consider a nine-dimensional stack of hyperspheres intersecting with our three dimensional space at one of its equators, with the centres of the hyperspheres aligned at the vertices of a nine-dimensional measure polytope. This would appear to be a stack of eight spheres, so this can be simplified by cutting off the outer spheres and converting them to hemidemisemispheres, if that’s the word, stacked together. Similar slicing could occur in hyperspace. So, it’s converted to a cube, then you put a door in the middle of one of the faces of the cube and find that it opens into a space which is quite a bit larger than the volume of the cube. The trimmed cube is only an eighth of the volume of the original, but it contains a “sphere” which is four thousand and ninety six times larger. With a mere four dimensions this becomes a mere eight times the size. This is starting to sound very like dimensional transcendentality.

The term has two words in it. “Dimensional” is fairly straightforward if one sticks to a simple definition instead of the non-integral dimensions used with fractal geometry. “Transcendental” brings to mind transcendental meditation, which is probably one reason for using it along with the fact that it was also used to refer to a particular set of numbers. What, then, are transcendental numbers?

A transcendental number is defined as a number which is not the root of a non-zero polynomial of finite degree with rational coefficients. The numbers e and π are both transcendental. All such numbers are irrational, that is, they cannot be expressed as the ratio of two whole numbers, since all rational numbers can be expressed in the way transcendental numbers can’t. Π is sometimes approximated by such values as 22/7, but these are not accurate values of the constant in question. Since the value is in fact involved in calculations of these volumes and hypervolumes, there might be a way of including the word “transcendental” in the description of this property of being “larger on the inside”. The square root of two is involved in two dimensions, but that’s merely irrational and not transcendental because it can be expressed using algebra – it’s a square root. This also means that the method of calculating the volume of a central sphere within a stack of hyperspheres is not transcendental either, so a good bet for including the concept would be to use π instead.

Although I can see that π is useful in calculating the surface area of the shape between the spheres, I don’t know what this thing is called. There’s a gallery of similar shapes here but they don’t include this one. I find it hard to believe this thing neither has a name nor has been extensively studied. I can assert various things about it. Its volume is greater than the largest sphere it can contain. It’s also greater than six times the spheres which can be placed touching the equators of the spheres it can occur within. I don’t know if the central sphere overlaps with its neighbours in the points. Each of its eight curved surfaces has an area equal to ½(πr2), meaning that its total surface area is equal to a sphere whose diameter is equal to the length of its largest diameters. Similar criteria apply to its higher dimensional friends. Hence I could perhaps be allowed to say that it’s dimensionally transcendental because its volume or hypervolume, or the volume of its hypersurface in higher-dimensional space can be calculated using the transcendental number π. And it can be, as I will now show.

Up until now I’ve been describing the central spheres and hyperspheres as if they’re three dimensional, and it is possible to lodge three dimensional spheres in there if you want, although it would be rather a waste of space. However, the actual volume of a four-dimensional space is not its bulk but its surface. I’m going to consider this nameless shape as having a length of two units, which is the same as the cube it’s found inside. The surface area of a sphere is 4πr2 and the circumference of a circle is 2πr. If it just carries on like this, it makes the volume of the hypersurface of this shape in four dimensions 8πr3 (spot today’s deliberate mistake with the volume of a sphere half the size of the Universe, incidentally). This means the volume of this shape is a bit more than twenty-five cubic metres, which is equivalent to that of a cube 2.9 metres on a side. For a nine-dimensional version, this would be over eight hundred cubic metres, which is a nine-metre cube. That’s about the size of a three-story house.

The TARDIS is of course bigger than that, although as far as I can remember Nu-Who has never shown its real internal size. If the door was located at a point where it was at the end of one of the projections and located in three-dimensional space, it would be accessible to a three-dimensional being. In fact it could have up to six such doors, though if it had there’d be one in the roof and another underneath it, and there could also be two other doors opening into four-dimensional space. If, however, it had nine dimensions, it could have a total of eighteen doors, only a third of which would be accessible from normal space and the majority of which wouldn’t even open into four-dimensional hyperspace.

I think it makes more sense for the police box to be closer to a cube than just a cuboid, for the sake of neatness, so maybe the chamæleon circuit should’ve got stuck on the Bradgate Park police box after all, with two secret trap doors and two hypersecret doors for which there is no name because they’re ana and kata 3-space.