Actually, mod 2 checks for odd. It returns 1 for odd numbers, and 1 corresponds with true. For even numbers it returns 0 aka false.
FYI, since the inputs are treated symmetrically, there’s a shortcut of only checking one of the (1,0) and (0,1) cases.
Also, here’s something to analyze:
or(x,y) = (x+y+(x+y)%2)/2
Grammar or do you have some other ideas?
Yeah you’re right oops. I don’t think I was thinking about 1 and 0 being true or false when I wrote that, just that you could check for even numbers using mod 2.
(x+y) : sums inputs. 11, 10, 01, 00 → 2, 1, 0
(x+y)%2 : outputs 1 for inputs that sum to odd numbers. 2, 1, 0 → 0, 1, 0
(x+y+(x+y)%2) : increases odd inputs by one 2, 1, 0 → 2, 2, 0
(x+y+(x+y)%2)/2 : 2, 2, 0 → 1, 1, 0
For the last step, it seems like it’s just outputting how many times 2 is contained in the input but that’s what dividing by two does with integers. I haven’t come up with another interpretation. It’s not checking if it’s even, cos 0 is even. It’s not checking if it’s 2 because it would also output 1 if the input was 3.
I don’t have any specific ideas. But something related to grammar/writing sounds good to me.
Another interpretation is compressing or scaling down the numbers.
Oh true! I can see that:
0 / 2 = 0
1 / 2 = 0
2 / 2 = 1
3 / 2 = 1
4 / 2 = 2
5 / 2 = 2
6 / 2 = 3
7 / 2 = 3
8 / 2 = 4
9 / 2 = 4
OK. Summarize what you’ve done in the past. You can mention some things you think you know or don’t know.
Also, do this assignment Eternity Async Tutoring - #446 by Elliot
Oh and for math, another thing you can do is take a function that only takes 2 inputs and maps them to specific outputs. like 3->8, 5->20. And then you can create that function with arithmetic. There are some general concepts you can use to solve these with a repeatable method. Optional but related to recent stuff. It’s much harder with 3 mappings than 2 FYI, so you can create your own practice problems using 2 mappings but I don’t recommend 3. One reason is because you can always draw a straight line through 2 points on a plane, but usually can’t draw a straight line through 3 points which indicates a non-linear solution is needed. Sometimes special cases help like the number 0. like when x+y was 0, 1 or 2, you had to deal with 3 mappings, but you can multiply, divide or remainder without affecting the 0, so the 0 is partially ignorable which can help. @Eternity you might be interested in this too as well as in or(x,y) = (x+y+(x+y)%2)/2 above.
Grammar:
I think I’ve watched all your grammar related YouTube videos.
I’ve read your grammar article
I’ve read and practised grammar as functions
Made a lot of grammar trees
I’ve made core grammar trees
I bought and watched your Grammar and Analysing Text videos and practised some of the techniques. The analysing lies stuff went a bit over my head. I didn’t and don’t know enough about lying yet.
I haven’t studied the use of commas.
I don’t know about making grammar trees of interrogative/declarative/imperative sentences.
I haven’t done the Peikoff Grammar course.
Reading/writing:
I don’t know how to take useful notes while reading
I don’t know how to talk/share about what I’m reading
I made three comments in 60 minutes. It felt a bit forced, and I wasn’t sure that I should say anything. I think my favourite comment was the one on your ‘Human’s Matter’ post (the second one below). With the third one I don’t think I did very well and it was a bit last minute. The topic of ‘food waste’ and ‘waste’ is interesting to me and I don’t have my thoughts together on it.
Something came up at work where I had to re-patch some cabling. I decided to see if I could make a function for the following mapping. It was pretty easy.
2->8
5->9
8, 9 are 1 apart and 2, 5 are even and odd respectively. If I map them to 0 and 1 using an odd number checker ( mod 2) and then add 8 I can map them.
(n mod 2) + 8
(2 mod 2) + 8 = 8
(5 mod 2) + 8 = 9
The mapping in reverse:
8->2
9->5
3n + 2:
0->2
1->5
n mod 2:
8->0
9->1
3(n mod 2) + 2
There’s a general method based on thinking about the gap between the numbers which doesn’t use mod. Using mod like this is more of a special case FYI.
There’s a different way to do this which is much faster and easier. If your friend shows you a 3 minute video clip in person, would you be able to verbally respond with 1-3 sentences and start responding within 30 seconds? I think usually yes.
You’re making it harder by choosing longer stuff and then trying to write high quality, important comments.
For articles, a lot of people actually write comments (e.g. tweets) based only on the headline (sometimes they also view the subheading and/or the article’s first image). Although that is problematic in various ways (it’s often undisclosed and the comments are often just approval or disapproval based on whether the headline is good or bad for their tribe), it’s actually also a good skill to have to be able to have thoughts about a small amount of information. A good practice activity is actually to write thoughts on a headline, then read the rest of the article and see if you change your mind. It’s important that you don’t never change your mind given more information (that shows bias and tribalism), but also don’t frequently change your mind (that shows low accuracy at guessing the missing information that wasn’t in the headline and avoiding beliefs that have much chance to be contradicted in the article).
Try it again with short, easy comments. But just stop if you’re stuck/blocked; don’t force yourself if it’s notably hard.
@Eternity relevant for you too. and commenting on a headline then checking if you got it right is something you could try now if it sounds good but is totally optional.
I made four comments in about an hour (I forgot to time it, but thats my estimate.) I was trying to imagine I was just being sent a video by a friend and try to quickly register what comes to mind. I enjoyed making these more than my last comments.
ok make 3 sentence grammar trees at 3 significantly different levels of difficulty.
These are all from George Reisman's Blog on Economics, Politics, Society, and Culture: 140th Birthday Tribute to Ludwig von Mises (I got think link from your post here)
Level 1
Von Mises was not primarily anti-socialist.
Level 2
Von Mises demonstrated that competition under capitalism is of an entirely different character than competition in the animal kingdom.
Level 3
He argued with unanswerable logic that the economic causes of war are the result of government interference, in the form of trade and migration barriers, and that such interference restricting foreign economic relations is the product of other government interference, restricting domestic economic activity.
I think that the difference between level 2 and level 3 could’ve been greater. Level 3 included participles which I was getting wrong up until last time I practised grammar though. Apart from that it’s only really the size of the sentence that makes it harder. I’m going to try and find one that is quite hard for me. I think I’ll look at sentences by another writer because I’ve done a lot of Reisman and he’s got a consistent style.
All these trees were quite quick for me. The level 3 i estimate took less than 10 mins to do. The others were less.
I looked at the trees. 2 and 3 look good but I think 1 is incorrect. Give it a second look.
Hmm. Ok. I can think of two other plausible options that I can’t decide between.
One is that perhaps ‘not’ is modifying primarily, and not ‘was’?
The other is that perhaps ‘primarily’ modifies ‘anti-socialist’. Like in the sentence:
He ran a primarily anti-socialist campaign
Like how in the fragment ‘an entirely different character’ in my sentence 2 ‘entirely’ modifies ‘different’.
Hmm maybe a third option, a combination of the two, works? In the sentence fragment ‘the not primarily anti-socialist Von Mises’ I think ‘not’ is modifying ‘primarily’ and ‘primarily’ is modifying ‘anti-socialist’ which is modifying ‘Von Mises’.
I kind of feel better about this third option than my previous two options, maybe cos the presence of the alternative of either of the first two options seemed like a criticism of each other? And this is both of them.
I’d look at the meaning not just the grammar here. Can you brainstorm some things the sentence should and shouldn’t mean? What does each modifier need to do, mean or apply to in order for the sentence to have the right meaning? What are some applications of modifiers that would definitely give the wrong meaning?
what should it mean?
Von Mises was anti-socialist but not primarily. Meaning: to describe him as anti-socialist would be true but it would be misleading or inadequate; that his intellectual works and goals were broader than just anti-socialism; or that his anti-socialism was a part or a detail or perhaps a consequence of his more primary intellectual concerns.
what shouldn’t it mean:
That Von Mises was socialist; that Von Mises was not anti-socialist; that Von Mises was primarily anti-socialist; that Von Mises was just not pro-socialist; or that primarily, Von Mises wasn’t anti-socialist.
Hmm my first sentence diagram seems like it means this last thing I thought it shouldn’t mean:
primarily, Von Mises wasn’t anti-socialist.
I think I’d diagram that sentence like my first tree e.g like:
was
Von Mises
not
anti-socialist
primarily
If so, then perhaps:
Von Mises was, not primarily, anti-socialist.
Having ‘not’ modifying the adverb ‘primarily’, as a kind of parenthetical, does mean the correct thing?
like:
was
Von Mises
primarily
not
anti-socialist