Really? https://www.mathvalues.org/masterblog/of-course-2-2-4-is-cultural-that-doesnt-mean-the-sum-could-be-anything-else, Cathy O’Neil, Mutant Algorithms Are Coming for Your Education, https://www.bloomberg.com/opinion/articles/2020-09-08/mutant-algorithms-are-coming-for-your-education, Cathy O’Neil, Weapons of Math Destruction. The symbols “+” and “=” came centuries after “2” and “4”. Take this to extremes, and you find 2+2=4 to be a statement that’s not about the world at all, but about how the mind perceives and categorizes. It might seem as sophomoric as dorm-room arguments about solipsism (“How do we really know anything?
Let's start with something uncontroversial: a valid mathematical assertion like 3+3+3=9 can be "wrong" if it's been dragged into a situation in which it just doesn't belong. And if you know that Peano didn’t actually define 2 as 1+1 but rather defined 2 as “the successor of 1”, and similarly for 3, 4, etc. A problem of legendary difficulty first created by Pierre de Fermat in 1637, it attained its first proof centuries later in 1994.
Meanwhile, Galton’s account is suspiciously omniscient; in particular, I’m struck by the phrase “his mind got hazy and confused”. We may think that truth is a butterfly and language the net that captures it, but too often truth is a rabbit and language is a mound of jello that we throw at the rabbit, and some of the jello sticks to the rabbit but most of it falls off when the rabbit runs away, and we look at where the jello is and argue about what it tells us, but the jello landed mostly where we threw it, as it was inevitably bound to do, and the rabbit is long gone (and doesn’t eat jello anyway). For all their education, modern urbanites in the English-speaking world usually lack metacognition about their ability to be fooled when their short-term memory is being overtaxed. I talked about how the story of the equation 2+2=4 intersects with the story of commerce and capitalism and then I talked about how it intersects with racism, eugenics, and genocide.
Some of them try to find contexts in which 2+2=5, but it always involves subverting the common shared meaning of 2+2=4 (a subversion that they sometimes admit to and sometimes don’t). For instance, a female sheep is probably worth more than a male (as we might say in symbols nowadays, F > M), but two female sheep are probably worth less than a breeding pair (F + F < M + F), which is a mathematical contradiction if we assume value is additive. How we test gear. The curves have been redrawn but no fruits have been harmed or moved. I’ll take ideology over bigotry any day.
Regardless of whether you think capitalism is “good” or “bad” (I think it’s both), it’s important to recognize the economic aspect of 2+2=4 as part of its social history. One of the points Barany makes is that we never get to hear the shepherd’s side of the story.
For instance, it’s absolutely true that if we round the numbers in the equation “2.3+2.4=4.7” to the nearest whole number, we indeed get “2+2=5”. To read what Keith Devlin has to say about this, Of course, in saying that both kinds of thinking are needed to help us make sense of the world, I’m presupposing there’s a world for us to make sense of, and this brings us to another philosophical take on 2+2=4, which is that the formula reminds us that, Take this to extremes, and you find 2+2=4 to be a statement that’s not about the world at all, but about how the mind perceives and categorizes.
It makes me think harder about what knowledge my students bring into the classroom.
I really enjoyed this essay.
“Now, I’m no expert or anything,” said Nasrudin, “and please don’t take this the wrong way-but tell me this: Doesn’t it take nine months for a woman to go from child conception to childbirth?”, “You men are all alike,” she replied, “so ignorant of womanly matters.
Consider that, for a shepherd, a flock is a collection of individuals, more like 1+1+1+1 than 2+2 or 4. The value of a sheep as measured in sticks of tobacco might vary from sheep to sheep. Guess who tends to benefit from these algorithmically-driven decisions: those who already have lots of social privilege or those who don’t? And now you know that I think both are right. I’m unmoved by slogans like “Western mathematics is a tool of cultural imperialism”, though I’m sympathetic to concrete critiques of specific teaching practices that I believe are the wellspring of the math-as-imperialism ideology voiced by some math educators.5 At the same time, I’m aghast at the sort of sexist and racist tropes that have been flung at proponents of critical theory by self-proclaimed defenders of “objectivity” when the proponents are women or people of color or both. Both agreed that Bob’s negative balance was a problem, but Bob insisted that to set things right it was Lenny who needed to make up the negative in Bob’s capital account. So we’re not on purely mathematical turf anymore, and you can imagine how battles over 2+2=4 could happen on social media as a proxy for battles over real-world issues. Even smart people can be fooled by the con, and more importantly, most people are unaware that they can be conned in this way. Mathematician Kevin Buzzard warns that the field of math could be full of nonsense, as many prominent researchers don't double-check others' proofs. The mercantile-capitalist-technological civilization that gave us the mathematics of the modern era has done wonderful things and terrible things. Everyone can be successful in math when presented with opportunities to succeed, an open mind and a belief that one can do math.
So where did the story come from, since SV’s proposed budget increase was nowhere near 21%?
You could have a fire!”. “I realized the computers would only accept inputs in a very precise form, which is my favorite way of thinking about math,” Buzzard tells Vice's Motherboard.
All that’s changed is the way I’m compartmentalizing things.
Now It's Scrap. So if the guests originally handed over $30, what happened to the remaining $1? And how can math be wrong?
Maybe someone should write an article called “‘As’ As Multivalent Signifier”?
I’m unmoved by slogans like “Western mathematics is a tool of cultural imperialism”, though I’m sympathetic to concrete critiques of specific teaching practices that I believe are the wellspring of the math-as-imperialism ideology voiced by some math educators. We need to find better ways of dealing with difference, cooperating, and sharing.
If a prominent researcher cites a mathematical proof in their work, others may assume it’s true without actually checking for themselves.
That Doesn’t Mean the Sum Could be Anything Else. Perhaps he should be hailed as the patron saint of diversity.
The original physical key, his memory of the key, and his son's conception of the key all existed on a plane of degrading memory, which occurred "as the idea moved around," Buzzard says on a slide.
I mentioned before that a big advantage of the algorithms introduced in Europe in the late Middle Ages was their auditability.
Our prejudices get in the way, and categories of thought that seem neutral in themselves can subtly affect our interpretations of reality.
The equation is seen by some as a touchstone for objectivity and truth and by others as a manifestation of a repressive social system. I have done so, and seen a man first put two of the sticks apart and take a sight over them at one of the sheep he was about to sell. In comparison, that shepherd could be viewed as a metacognitive sophisticate, wisely separating two transactions rather than trying to combine them! We can and must try to do better, but that doesn’t mean we throw away what we’ve learned. The reason I’m bringing this up is that over the summer Twitter saw a lot of discussion of the equation 2+2=4. Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. When I was young, the word “algorithm” meant a procedure for operating on numbers (think: long division), and later on when I studied computer science, some of the basic algorithms I got to know were procedures for sorting numbers, with cute names like QuickSort, HeapSort, MergeSort, and BatchSort. ( Log Out / Self-styled champions of the concept of “objectivity” (you can often recognize them because of the way they hype “2+2=4” and say things that amount to “Ha ha, I’m objective and you’re not”) all too often are championing their convictions about what’s true, ignoring all the ways in which their experience is partial, their interpretations biased, and their statements couched in language that’s vague and subject to multiple interpretations.
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