(no subject)

finest-quality reblogged your post “real orthogonal matrices do rotations”

The way I learned the definition of orthogonal, the reflection A= [-1 0; 0 1] is orthogonal because A transpose = A inverse

Yup. That’s a reflection, and it’s orthogonal.

My reasoning was incorrect, because

v . w = ||v|| ||w|| cos(θ)

and

Av . Aw = ||Av|| ||Aw|| cos(-θ) = ||v|| ||w|| cos(θ) = v . w

So, while I was right that the angle between them “reverses” in a certain sense--you turn one direction to get from v to w, and another direction to get from Av to Aw--I was wrong that this flips the sign of the dot product. In fact it doesn’t, because the dot product has the cosine of the angle, and cos(-θ) = cos(θ).

(no subject)

my dad I think has some vague spiritual beliefs involving reincarnation; I could be wrong, he doesn’t really talk about it. My mom, after she got lupus, started going to the Chabad center and keeping kosher and such. And driving to schul on Shabbat, but parking kind of far away so nobody could see that she had driven in.

My mom started raising us Jewish, and my brother was to have his bar mitzvah, and my dad allowed all this but drew the line at tefillin. Nobody’s putting leather straps on his kid. No way my mom was going to win that argument. But it was what she was supposed to do; her son was supposed to start putting on tefillin after his bar mitzvah.

She was talking about this with my paternal grandfather. He took out his father’s tefillin, tried to put them on, couldn’t remember how to do it. Later, he was talking to an Orthodox jew that goes to his gym, who was going to Israel. They ended up agreeing, this orthodox guy would pick up some kosher tefillin in israel, and my grandfather would buy them from him. My mom didn’t put him up to this, it was an independent idea.

So he did, and gave me and my brother tefillin as bar mitzvah gifts, and my dad couldn’t say anything to that, and of course all the lubavitchers at my mom’s schul were saying it was divine providence.

(no subject)

hebrew school was a good way to learn jewish mythology which is important for understanding the influences on the western literary tradition. They teach greek mythology in public school but not jewish and christian, so sunday religious education was a good way to pick that up.

(no subject)

c² = 2 a²

thinking of each number as a bag of prime factors.

c², being a square, must have an even number of factors of 2.

2 a² must have an odd number of factors of 2.

So the equality is a contradiction.

(no subject)

fnord888 reblogged your post and added:

Not a contradiction, just a and c can’t be integers (I think can’t be rational, but that’s not a proof of that).

Also, any number that’s not itself perfect square is the same, right?

Yeah, it’s a contradiction under the assumption that a and c are integers.

And yeah, that’s true, it works not just for 2 but any number that is not itself a perfect square.