I guess the math stands out to me more because I care about it.
And so much of it isn't debatable in any reasonable sense.
I guess the math stands out to me more because I care about it.
And so much of it isn't debatable in any reasonable sense.
Fundamentally I agree, although I will try to be nicer about it. Mostly because I think there are barriers (often barriers that serve the powerful) that keep people from learning these things.
And no matter how old you are or how late it is if you are willing to try to get it I'll help. I will forget the resentment I feel about it.
So, when you point out innumeracy I think you should explain it with patience. Explain it understanding that some people who may be well informed and intelligent in other matters might not understand why, for example, decreasing by more than 100 percent is nonsense.
(100 percent is all of something. A 50 percent decrease is half. '100 percent decrease means' it's zero. Decrease by more than 200 percent? means it's less than zero, negative. Negative prices make no sense. )
Often we will pick out some instance of the president making a mathematical error. Abusing percentages, confusing billions and trillions... a lot of people nodding along pretending they agree and understand that he's making no sense... don't really know what we're so mad about. And they don't want to admit that since we make it so clear we think everyone who doesn't get it is hopelessly ignorant.
And perhaps there is something pretentious, anxiety inducing, something deeply nerdy and off putting about knowing your way around numbers. Speaking about them with care.
That's our fault, mathematics teachers. We can't keep traumatizing the youth and alienating people from mathematical reasoning.
It opens a door for some people to be seduced by the comforting notion that things that you don't understand can't possibly be important.
Mathematics is a language. But innumeracy is also a language and our president is fluent.
It's not just that he exaggerates, lies, and says things that make no sense when talking about numbers "often" no this is something deeper.
He is deeply committed to *never* speaking about any statistic or numerical fact in a way that would suggest that it's important to understand how basic math works, or even that it exists at all.
This isn't just ignorance or laziness, it's one of his core values.
The whole idea of the lesson, which I'm very passionate about is making irrational numbers like root two and root three seem... real. Both as "real numbers" but also as ... real numbers, physical distances that make as much sense as 4 cm or 1/3 of an inch.
In fact I will take these to school and make it THEIR problem. I have a whole box of materials and notes for possible future lessons, and if I put them all in one place I'll be more likely to get them written up and ready to go so other teachers might use them.
I've told the other math teachers about how we should do this and they sort of nod along but I suspect they have no idea what I'm talking about.
But if I show them a ruler with root two on it it'll be clear enough I think. 
THIS is why cleaning is so difficult. I bought these blank ruler-sized pieces of wood six years ago. I have an idea for a lesson where students use a compass to create a ruler, including irrational numbers, such as square root of two I should write the lesson up and make the sample ruler **or** throw these away. I will write myself a note about this and put them in the “soon trash” box. I need to be ruthless!
Let's say you want to draw a hypocycloid (spirograph) with a turtle. I use a parametric equation for each of the circles and combining them to find the x and y position of the points on the curve then telling the turtle to goto(x,y)
This works fine, however it is NOT in the intended "spirit" of drawing with a turtle. Drawing with a turtle is about "relative" navigation. Consider two ways to draw a circle:
for 0<t<2pi:
goto(rcos(t), rsin(t))
repeat 100:
forward 2
right 2
*angry old lady noises*
"For a long time we thought they were like trees. After all, humans are very large."
"And you can climb on them!"
"And you can lick nectar off of them!"
"I've never heard of THAT. Anyway. We realized we were wrong. Humans are not intelligent like trees. Trees will warn each other of danger. Trees don't destroy their environment and die in huge numbers."
"But don't we ants die in huge numbers in our wars?"
"That's TOTALLY different."
"But what if humans have wars?"
"Preposterous!"
"He burned our libraries. Why did he do that? It's so destructive. Can you think of anything more evil?"
"I can, child. There is something worse than burning a library."
"How!"
"It happened long ago, this was a time when books were not rare as they are today. Everyone had hundereds of books."
"Hundreds! No!"
"Thousands."
"Oh!"
"So, the new kings realized they couldn't possibly destroy all of the books. They would always miss a few."
"What did they do?"
1/
The other reason I'm skeptical is ants have very poor vision with a few notable exceptions. I don't know if ant would react to a mirror at all. I will try this with "the girls" later today and see what happens. Will post about this again.
Here is the paper. It was widely discussed ... on reddit for a long time I didn't think it was real.
Ants are painted with dots that match their exoskeletons, some are painted with blue dots. The ants are observed interacting with a mirror.
I've seen this experiment mentioned as a reason why calling the mirror dot test a "test for self awareness" is flawed: a lot of people really don't like this result.
Still, the journal gives me pause. What do you think?
https://www.journalofscience.net/showpdf/MjY4a2FsYWkxNDc4NTIzNjk=
There is a really crazy paper where they did the "mirror dot" test for self recognition on ants. BUT. It's in the "Journal of Science" which isn't "Science" ... and it's odd to have an insect paper not in an insect journal.
And this is their webpage:
Listen I just want this paper to be real, but it's kind of out there and the journal IDK.
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