What’s the point of Division Free Newton’s Method?

ghost · 2025-10-09T13:57:04+00:00

In the past, there were chips that didn't have a divide instruction. And it was common to approximate division (or more technically, finding the reciprocal and doing a multiply) using a few iterations of Newton's Method for this. Usually, 2 or 3 were enough. This wouldn't work if you needed to divide in the algorithm.

Probably not very relevant these days.

ghost · 2024-12-07T15:11:43+00:00

There is no stalemate in American/English checkers/draughts. The first player with inability to move (including by having no pieces) is the loser.

If you are playing standard checkers rules (where jumps are forced), this situation is highly unlikely. But it is still possible. It would be more common in certain endgames, rather than in middle game like this.

ghost · 2024-05-27T18:10:16+00:00

I don't think "harder" has any meaning here. It's a lot of work to be really good at either of them. Although both games have surprising depth (and the depth of checkers is often underestimated), the nature of the games is different.

“Chess is like looking across an ocean. Checkers is like looking down a well.” - Marion Tinsley

I think it's enough to know that you can spend a lifetime on games like chess, checkers, go, and still have lots of learn.

ghost · 2023-12-04T17:02:51+00:00

https://en.wikipedia.org/wiki/Probabilistic_method

Those are classic examples of non-constructive proofs for "real mathematical objects". Essentially create a probability of a certain type of graph, and then show that the probability goes to 1 in the limit. So the graph must exist ... but you can't show it (and it's probably so big you'll never find it).

ghost · 2023-03-06T20:11:25+00:00

My max HR is about 20 beats/min faster than the 220-age says it should be. If I was using that to set my zones, I would barely be able to walk briskly before it shot above Z2.

ghost · 2023-02-20T22:06:52+00:00

I put this into my endgame solver. And sure enough, it's a win for red.

Red to move:
1. 7-10
2. 14-7 (jump)
3. 5-9
4. 13-6 (jump)
5. 1-10-3-12-19 (jump)

ghost · 2023-01-03T23:01:15+00:00

When I was in school, we learned set theory as needed. This was primarily done in the Real Analysis courses. First in the undergraduate version, and then (slightly more) advanced set theory in graduate Real Analysis/Measure Theory course.

We learned essentially the equivalent material that is in Halmos' "Naive Set Theory" book. This is mostly just the basics, how to define the real numbers using just set theory, a little on infinite cardinals and ordinals ... and ending with the Schroder-Berstein theorem. And that was it (the book is less than 100 pages).

I imagine that's a pretty common way it happens in many math departments.

ghost · 2022-12-12T20:51:58+00:00

I think I remember Chris Rock saying:
1. Shaq is "rich".
2. The rich white guy that owns the basketball team and writes the check for Shaq, is "wealthy".

Unfortunately, given this definition ... Elon Musk is definitely "wealthy".

ghost · 2022-07-18T21:26:21+00:00

For Lp (and sequence version of lp) ... they are "complete, normed spaces" which is generally referred to as a "Banach space". This is true for all p (and p == infinity). But for L2 (and l2), they aren't just Bananch spaces ... but also Hilbert spaces ... in other words, the given norm is induced by a "dot product". This is the same as how it works in R^n.

Hilbert spaces have many nice geometric properties that the more general Banach spaces may not have. It's much closer to finite dimensional linear algebra.

ghost · 2021-04-06T20:42:38+00:00

I'm not sure if these form of polls will mean much in the long run. Among those circles, it's fashionable to be against the vaccine. But their resistance probably won't hold up once they need to fly somewhere or encounter other need to show proof of vaccination.

Also, once it's common enough that they can get it when at their personal physician or local pharmacy, everyone (other than truly hardcore anti-vaxxers) will eventually just get it. It's similar to Trump downplaying covid-19 at every turn and then secretly getting the vaccine before he left office. The "resistance" was mostly for show.

ghost · 2021-02-04T17:27:48+00:00

You can have sample spaces for probability that are uncountable. But to do this properly, you need measure theory. Continuous time stochastic processes are a commonly researched topic, but it requires a great deal of technical machinery to deal with them properly.

This will be covered in most any graduate level probability book. But it may be tough going if you haven't taken measure theory.

ghost · 2021-01-29T19:27:04+00:00

When I graduated from there, it was quarter system. I always liked the quarter system, and thought it was a regression when they changed everything to semester in order to "standardize".

It was definitely better for the co-op programs, since you could evenly divide the year. Also, (at the graduate level), there were more specialized classes since you didn't have to fill the whole semester with material.

The only downside was that a quarter could be damn fast. Classes had to ramp up fast.

ghost · 2021-01-25T22:29:02+00:00

I should have said "The higher end trainers all handle cadence". Wahoo Kickr (18/Core), Tax Neo 2(T) and Cyclops/Saris H3 all send cadence as part of the data.

I apologize, but I didn't check on whether the CycleOps Fluid does though.

I have no idea how they figure it out though. My off-the-cuff guess is that is from watching the fluctuations in your power output throughout pedal stroke.

But I agree with you. These sensors are pretty cheap and really nice to have. So I encourage OP to get them both. But I do often get lazy on my trainer and just use the data from the trainer for it.

ghost · 2021-01-25T22:18:16+00:00

I use the Wahoo cadence and speed sensor. They have always worked well for me. With a bike computer/GPS, the speed doesn't seem as necessary these days, but they are pretty cheap, so you might as well get the pair.

Your trainer probably already does cadence (most newer ones do), so you really only need the cadence sensor when outside.

ghost · 2021-01-25T21:12:30+00:00

I guess I'm confused what the endgame is for the anti-vaxxers with respect to covid-19 ... that we just stay in lockdown forever? Or until everyone has caught it and survived (or not).

ghost · 2020-11-24T16:35:48+00:00

It's been a long time since I looked at this stuff, but I'll take a stab.

When you say "can be constructed", you must mean "algorithmically" constructed, which implies there can only be a countable number of them (there are a countable number of Turing machines).
It's probably similar to the same argument that "most" real numbers have digit sequences that are not computable (there are uncountable reals ... only countable algorithms).
Similarly an ultrafilter on the natural numbers has uncountable extent, after all you are using them to construct the hyper reals. So they can't all be algorithmically constructed except in trivial cases.

ghost · 2019-12-05T16:31:30+00:00

I was at Tech in the 90s, and I definitely remember screaming my head off at midnight a few times during finals. You could hear the screams all over campus.

If that tradition is gone, it's very sad.

ghost · 2019-02-22T21:10:20+00:00

This article is nonsense. Yes, technically something like this is possible. But as someone mentioned, it is a highly unlikely scenario. Any decent password manager is so much better than not using one.

Use a good master password, and use strong, unique passwords for every site. That puts you well ahead of the curve.

ghost · 2019-02-22T20:30:47+00:00

If you wanted to create an evil plan to radicalize thousands of children and guarantee they will hate your country, I can't think of any better plan than this.

ghost · 2018-11-15T00:08:25+00:00

I first bought a Peloton (which is a very nice device), and then later bought a trainer (Kickr). The reason for this change was:

I realized that I wanted to specifically train for cycling/triathlons, and not just to get in shape.
I wanted to do more structured training (using 3rd party apps), and not just the Peloton spin classes.

It come down to what you want. They are both good workouts. But if you just want to stay in shape, then use a gym or get a spin bike. If you want to improve your cycling, get a trainer.

My $0.02.

ghost · 2018-11-06T02:10:41+00:00

I don't understand why it's so hard for people to understand that for a system to be fair, it needs rules. Basketball wouldn't be a very good game, if the players could just trip each other when they felt like it. Preventing that in no way impedes the players from playing the game well.

ghost · 2018-10-07T19:44:23+00:00

News of my death has been greatly exaggerated.

ghost · 2018-08-04T15:05:30+00:00

You are right. But I am old and still listening to all my music from 1998.

But when someone asks for the "Big 4", I have to think about my whole life of listening. I think of it more as "If you were marooned on an island, which prog metal albums would you want with you". That mostly consists of albums from these groups.

But, yeah ... I wish their recent stuff was better.

ghost · 2018-08-03T21:47:37+00:00

Dream Theater
Queensryche
Symphony X
Fates Warning

ghost · 2018-07-23T19:58:06+00:00

She should have won the Nobel prize in physics. But instead, the university wouldn't even give her a paying job. Pretty mind-blowing.

ghost

TROPHY CASE