The proof of the pudding is in the conceiting

(or, it's Maths, Jim, but not as we know it)

Something very strange is happening across the world. We have a (worldwide) official government/Pharma narrative on covid that has more leaky holes than a very large brothel - but half the world can’t see it (or don’t want to).

The other half of the world are desperately trying to get people to see the obvious logical flaws and ask pertinent questions (like those in the meme above). The logic in the above meme isn’t watertight, but it doesn’t have to be - for me, memes are a brilliant way to get people to think a bit.

I would maintain that covid, or the response to covid, hasn’t created this logic-deficit - it has merely amplified it. For quite a while now, the rigorous sciences have been under attack from what I can only describe as third-rate intellects with some kind of serious narcissistic delusions of adequacy.

There is an academic discipline where the logic is watertight - it has to be - and that is mathematics. But the Grand High Clowns of Narcissus are coming for that too.

James Lindsay does an excellent job of dissecting one recent attack here. The team at New Discourses have done a breath-taking job of shredding a lot of the modern Woke-Wooliness. They have read the woke “academic” papers - so you don’t have to (you can do so if you wish - but I really don’t recommend it, because you expose yourself to a very serious risk of losing IQ points if you do).

Lindsay’s essay addresses an article written by an influential “thinker”, - mathematics education activist Rochelle Gutiérrez, who wishes to re-define mathematics and re-shape it into something that is more in line with her feelings and emotions.

I use mathematics a lot, I love mathematics, but I’m not a mathematician as such. I use mathematics primarily as a tool with which to probe the secrets of nature - but it has an astonishing power and beauty all of its own - quite apart from its application to physics. Mathematics is so very much more than its application as a tool in this way.

I want to share a little proof with you so you can get a flavour of how it works. The important thing isn’t the detail of the very simple proof - but what it represents. It’s the big picture of what has been achieved that is critical to understand.

Mathematics often deal with things called “sets”. These are just collections of “objects”. An example of such a set would be the integers
Z = { . . ., -2, -1, 0, 1, 2, . . .}
The three dots here just mean keep on going - so this would be a very big set; of infinite size, in fact. You can make smaller sets - an example might be the integers { 0, 1, 2, 3 } which has only 4 elements in it.

It’s a very natural way of treating a collection of things - and from there you can ask all sorts of questions. Notice how we start with a definition here. A very large part of the art of mathematics is coming up with definitions that are useful. The idea of a “set” is an incredibly useful, and fundamental, one for mathematics.

Now let’s suppose we impose some structure here - some further conditions. Let’s imagine we have a way of combining the elements of a set. In maths terms we might want to write this as a.b = c and the “dot” here represents the operation we use to do the combining. It’s a bit abstract - but it’s easier than it looks. One common way of combining numbers is to add them. In this case we might replace the “dot” with a plus sign, so that we have a + b = c.

Now let’s suppose we have an operation (like addition) - and the result of combining 2 elements of our set gives us another element of our set. So if we have the set of integers then 3 + 4 gives us 7, which is another element of our set.

This kind of operation is a binary operation (we have to call it something). Not all operations on specific sets have this character. If we take addition on the set
{ 0, 1, 2, 3 }
we can see that adding 2 + 3 we will get 5 - which is not in the set. So addition, for this set, isn’t a binary operation. A binary operation always returns another element of our chosen set.

Look at how much time I’ve spent talking about definitions and meanings here. It’s absolutely critical that we get all our starting assumptions pinned down precisely.

We’re going to add another couple of properties to our set with a binary operation defined on it. We will assume that an identity element exists, and we’ll assume that for every element there exists an inverse element. Ouch. But, again, these ideas are simpler than you think.

The identity element just leaves stuff alone when the operation is done. Zero is the identity element for numbers under addition. If I add 2 + 0, I get 2 again - the addition of zero just leaves things alone.

An inverse element just “undoes” things - a way to think about it is to ask “if I add 2 to something, what do I need to add to get back to where I started?”

If you add 2 to something, you have to add minus 2, to get back to where you were. So minus 2 is the inverse of the element 2.

Once you get the hang of the abstract terminology (and it does take some time and effort) you can write all this very quickly. Here we have a set with the following properties

• it has a binary operation

• there is an identity element

• for every element there exists an associated inverse element

This thing (the set and all its properties) is a very special, and important, thing in mathematics and is called a group. Technically, we might say something like “the set of integers forms a group under addition”.

Now for the proof part. Now we’ve got all our ducks lined up in a row we can ask about further properties of this thing we’re going to call a “group”. I’m going to call this the Highlander proof:

Let’s imagine there was more than one identity element in our group - let’s call them e and f. Let’s combine them using the binary operation

e . f is going to equal f because e is an identity (leaves things unchanged) so combining e with f is going to leave f as it was. But we can say the same thing for f too - because we’ve said it is also an identity. So e . f is going to equal e. In shorthand math-speak, what we’ve done here is the following

e . f = f = e

So what we’ve shown is that there can be only one identity element (to properly do the proof you have to also consider f . e - but that follows the same line of reasoning).

This is really quite profound. We’ve been able to show that IF we have an object called a group, then it can only have one identity element.

This doesn’t depend on what day of the week it is, how much melanin you have in your skin, whether you’d rather have sex with people or squirrels, or whether you believe in Odin or not.

It’s an unavoidable and unassailable consequence of there being something we can call a “group”.

Notice how long it took me to set things up and how careful I had to be in doing that (and proper mathematicians will, even then, doubtless shiver in horror at some of the corners I cut). Even if you can’t fully follow things (it does take a while to get into this way of thinking) I hope you can appreciate the power of the result we obtained.

At the end of the process we’ve achieved a result that we can rely on. It’s true, and will always be true - if we have a group.

Notice how pure and clean this is. There’s no room for considerations of feelings or politics. The societal power of the mathematician in the context of a classroom is utterly irrelevant. The fact that a white European man first proved this is of no consequence whatsoever - that’s just an accident of history.

But this is where these woke pillocks want to take us.

Let’s have a look at what Rochelle Gutiérrez, this influential educational “thinker” is proposing in her article.

Not only must we: a) be conscious of the ways mathematics can dominate and b) constantly question what counts as mathematics and who decides, we must also c) think about how we, as living beings, practice mathematics as we interact with others and ourselves. As we begin to reimagine mathematics, we have the opportunity to reimagine the mathematician—who is considered a mathematician as well as how are mathematicians influenced by the mathematics they do?

To see just how preposterous her assertions are here, just replace ‘mathematics’ and ‘mathematicians’ with ‘brain surgery’ and ‘brain surgeons’.

There is precisely nothing of any value, to mathematics, in what she writes here. She’s talking about feelings and power structures and re-defining what mathematics IS to suit her own particular ideology.

She’s not happy with the reality of mathematics, so she wants to re-shape that reality in order to fit in with her particular set of ideological, political and emotional suppositions. She just makes assertions without any shred of evidence.

Hmmmm. I wonder where we’ve seen that during the last 20 months?

But it gets worse. Here’s another quote from the article:

Combining the views of In Lak’ech, reciprocity, and Nepantla allows us to raise new questions about a vision of practicing mathematics that might move past previous notions of Western versus other mathematics, past an idea of mathematics as either oppressing or liberating, beyond a mathematics that is either discovered or invented, towards an idea that allows us to deal with today’s complexity and uncertainties. Towards that end, I am calling for a radical reimagination of mathematics, a version that embraces the body, emotions, and harmony.

What a complete load of bollocks. You don’t have to be a technically-minded person to see just how mind-bogglingly idiotic her ideas are here. These buffoons talk about different “forms” of mathematics - you’ll see she picks on “Western” mathematics here. What the fuck is “Western” mathematics? I have no idea.

Maths doesn’t depend on geography or ethnicity or whether you’re a non-cis-gender-fluid lunchbox on Tuesdays.

Notice also how, for her, there is an idea of mathematics being liberating or oppressing. This is something she’s bringing in - it’s her own external supposition that she is imposing on mathematics. It doesn’t exist in mathematics itself. One does not, normally, think about how many people one is oppressing by solving a differential equation.

The important considerations, for her, aren’t about truth, but about feelings and power-dynamics and emotion. I suspect she’s calling for a “radical reimagining” because she’s crap at maths.

And it gets even worse:

Current versions of what count as “beautiful” in mathematics tend not to reflect the diversity in our world. Instead, they tend to relate to truth, implying universals rather than uniqueness/expression that would align with performance or a plurality of epistemologies. If we can recognize that cultural theses of modes of living are aesthetic choices and some aesthetics are not superior to others, then the means for controlling or dominating is lessened.

The fact that mathematics (as it actually IS and not as she supposes it to be) is independent of “diversity” or “ideology” or “culture” is deeply anathema to her. She wants to be relevant - but for her, relevance is defined in terms of nebulous ideas like “diversity”.

Look at how she rails against truth here - she sees individual expression and performance and plurality as being higher goals.

These people pretend to be intellectuals. Their nonsense is everywhere. One of the Chief High Priestesses of Batshit Buffoonery, Judith Butler, wrote this:

The move from a structuralist account in which capital is understood to structure social relations in relatively homologous ways to a view of hegemony in which power relations are subject to repetition, convergence, and rearticulation brought the question of temporality into the thinking of structure, and marked a shift from a form of Althusserian theory that takes structural totalities as theoretical objects to one in which the insights into the contingent possibility of structure inaugurate a renewed conception of hegemony as bound up with the contingent sites and strategies of the rearticulation of power.

This is the work of a decidedly third-rate intellect trying to sound impressive. It’s meaningless gibberish dressed up as profundity.

This is the intellectual milieu, the backdrop, against which covid emerged. And, my, haven’t we reaped the benefits of this severe loosening of our pursuit of academic rigour and truth over the last 20 months or so?

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