Stupid Questions September 2016

If money is not an issue, wireless headphones is probably at the top of my improve my life for less than $50 list.

You don't have to worry about untangling, putting away or unplugging.

I recommend the ones that sit on your neck like these

While being aware of various ways to solve this problem. Mine is to fold the cable in half, then half again, then half again until it's small enough to go into a pocket. Then store it somewhere where it will not get moved around very much, and be encouraged to tangle. The only disadvantage is that this doesn't always suit the twist of the cable, so the cable will sometimes twist around itself a few times, but never form a knot (in my experience).

You might find that owing to manufacturing process, multicoloured cables are a bit of a pain to make. We usually make very long rolls of wire with identical sleeves. Then cut down the wire to make relevant size pieces. This idea would require doing things differently.

That's an interesting idea and yes, I think it would help. It seems you can find cable sleeves in this style, though I'm only seeing them in bulk.

1 The mental image I have, which may or may not be helpful to anyone else, is of a row of the LH matrix sliding over and rotating clockwise until it matches a column of the RH matrix.

2 If you don't mind working it out from scratch and have a more "algebraic" than "geometric" brain, the following considerations may help:

• Matrices are indexed row first, then column (think "reading order": if you think of the indices as numbers, then as you read along rows like reading a book they increase monotonically).
• When you multiply matrices, what happens is that "middle indices match": element (i,k) of the product is sum over j of left[i,j] right[j,k]. See how the j's match up and "cancel out".

3 The product matrix is an array of inner products of rows from the LH factor and columns from the RH factor.

I make no guarantee that any of those will help, but if any of them seems to be heading in the right direction but not getting there I'm happy to try to adapt further...

Low confidence that this will help, but my approach: I mentally move the right-hand matrix up, so that the space "in between" them (right of the first, below the second) is the right shape for the result. Each value of the result is the dot product of the vectors to the left and above it. (I don't have a trick for dot products, I just know how to calculate them.)

. . . . g h i
a b c * j k l
d e f . m n o

"becomes"

. . . g h i
. . . j k l
. . . m n o
. . . -----
a b c|S T W
d e f|X Y Z

and e.g. S is (a b c) dot (g j m), Y is (d e f) dot (h k n).

Perhaps explicitly thinking of them as systems of equations (or transformations on a vector) would be helpful.

As an example, suppose you are asked to multiply matrices A and B, where A is [1 2, 0 4, -1 2] (the commas represent the end of a row) and B is [2 1 0, 3 1 2]. Start out by taking the rightmost matrix (B in this case) and converting it into a series of equations, one for each row. So since the first row is 2 1 0, the relevant equation will be 2x + 1y + 0z. Assign each of these equations to some other variable. So we now have

X = 2x + y

Y = 3x + y + 2z

Now do the same thing with the matrix on the left, except this time use the new variables you've introduced (X and Y), so the three equations you end up with (one for each row) will be

X + 2Y

4Y

-X + 2Y

Now that you have these formulae, substitute in the values of X and Y based on your earlier equations. You get

(2x + y) + 2(3x + y + 2z)

4(3x + y + 2z)

-(2x + y) + 2(3x + y + 2z)

Simplifying, you get

8x + 3y + 4z

12x + 4y + 8z

4x + y + 4z

The coefficients of these equations are the result of the multiplication. So the product of the two matrices is [8 3 4, 12 4 8, 4 1 4].

I'll admit this is not the quickest way to go about multiplying matrices, but it might be easier for you to remember since it doesn't seem as arbitrary. And maybe once you get used to thinking about multiplication this way, the usual visual rule will start making more sense to you.

Maybe this will help

https://www.chilimath.com/algebra/advanced/matops/images2/ex2.gif

These videos are really good: https://www.khanacademy.org/math/linear-algebra/eola-topic

It's a 50-50 arbitrary convention.

I suggest physically tracing through the matrices with one finger from each hand. As you would multiply If you do it the right way enough times, doing it the wrong way will feel weird.

Also, the canonical example is y=Ax, with A a matrix, and x,y as vertical vectors. If you can at least remember that one goes vertically, and one horizontally, Ax will show that it is the one on the right that goes vertically.

As a person who has read 100% of the Sequences, I would also prefer if there would exist a shorter version. But, as far as I know, it doesn't exist yet. Someone would have to make it. Someone other than Eliezer, because this is not at the top of his priority list.

Would I be losing anything if I didn't need to be convinced, I just want to know the pointers?

You would be probably more likely to forget them. In general, longer text requires you to spend more time focusing on the idea. If someone would convert the Sequences into a PowerPoint presentation of 20 pages, a week later you probably wouldn't remember anything.

I realize how what I wrote here conflicts with my desire to have a shorter version of the Sequences, and... I don't know. Perhaps the shorter version should use other techniques for easier memorization, e.g. funny pictures.

Rationality is about not simply taking up believes unfiltered but evaluating claims of other people before you believe in them. Not doing that would seem to miss the point on a general level.

I think you can't add images to comments. As far as posts go, I think it's html tags.

What's the recipient using, and did they previously use something else? If they switched from iPhone to not-iPhone, there's a bug with Apple's iMessage that could prevent them from receiving texts. https://support.apple.com/en-gb/HT204270