The Kervaire invariant is a property of an "n-dimensional manifold", so the paper is likely about 126-dimensional manifolds. That in turn has a formal definition, and although it's not my specialization, I think means it can be locally represented as an n-dimensional Euclidean space.

A simple example would be a circle, which I guess would be a 1-dimensional manifold, because every point on a circle has a tangent where the circle can be approximated by a line passing through the same point.

So they're saying that there are these surfaces which can be locally approximated by 126-dimensional Euclidean spaces. This in turn probably requires that the surface itself is embedded in some higher-dimensional space such as R^127.

The second paragraph has what you want. From the article:

> The App Tracking Transparency (ATT) framework used by Apple on iPhones and iPads since 2021 makes the use of third-party applications too complex and hurts small companies that rely on advertising revenue ... The system harms "smaller publishers in particular since, unlike the main vertically integrated platforms, they depend to a large extent on third-party data collection to finance their business," the agency said.

Is there another way to interpret this than that the agency wants to protect advertizing and data collection practices by small businesses?

Personally I'm trying to watch less youtube. When I want a break from work, I try to go read a book for a while instead of taking the "mental junk food" option. I can't provide an objective report on whether measures like this help, but they do feel better.

In practice, science requires balancing multiple criteria. Does a model have the right level of simplicity and complexity? Can I convince my peers that it's correct? Should I trust the results of a crank over the results of someone who has a long history of excellent work, and how much onus is there on my me and my research group to reproduce every single published result?

Keep in mind, no one expects to be responsible for a revolution, so you get an effect similar to "poll herding" -- it is desirable to have a consensus, and as consensus emerges around a theory for how to describe some new observations, you get people going along with it even if they maintain personal reservations. In fact, it has been clear to many physicists that dark energy is just an ad hoc explanation, and there has been serious contention about what better model could exist, and there have been several competing models. But every model had its flaws. It's possible that the timescape model will also have flaws that cause it to be re-evaluated.

I recommend a book called "What is this thing called science?" by Chalmers [1]. When I was an undergrad it gave me a more nuanced understanding of the Philosophy of Science.

[1] https://en.wikipedia.org/wiki/What_Is_This_Thing_Called_Scie...

Or FLACs, if you can get them, which you can on bandcamp. I've got a terabyte of music in my offline playlist. It takes a few months to cycle through everything, then top it up with any new discoveries and latest releases before the next cycle starts.

Yeah, that was a great blog post. As someone who started in mathematics but ended up in computing, I read it and realized, hang on, he is talking about taking a devops approach to mathematics. It definitely struck me that this is the way of the future: mathematics transformed from almost a humanities-like discipline into an engineered enterprize.

The reason is, there are some skills which are highly in demand, and few people are strong in those skills. In particular, I am thinking of HPC engineering and cloud computing infrastructure engineering. Companies and institutions own large server fleets, we're talking hundreds or thousands of servers. They want whatever is running on those fleets to have high performance, security, and zero downtime.

This kind of work requires strong Linux systems administration and programming skills, an understanding of enterprise networking and storage technologies, confidence with at least one orchestration stack such as OpenStack or Kubernetes, and strong CI/CD and IaC skills (look up GitOps.) As a junior, you don't need to tick all these boxes, but people should be able to see that you're able to learn whatever you're missing.

These skills don't usually come directly from a computer science degree. However, a computer science degree is the primary way to get your foot in the door with building those skills. If you want a junior job in cloud computing and are cold-calling because you don't know anyone yet, then it will help if you have good marks in a computer science degree (although it's possible to prove your chops in other ways, like having a history of strong contributions to open source.)

Later, after you build some experience, and you prove that you can keep learning, you get the job done, and you can get along with people, you'll eventually have recruiters chasing after you, and companies willing to listen to whatever income you pitch to them.

Regarding cannon vs canon, the way I remember it is that "you need a double-n for a cannon to be double-barrelled." I have no idea whether that's useful to anyone else.

Etymologically, they are both related to "cane", so it's pretty much a historical accident that we now spell them differently to each other, or that it's not the other way around.

I remember in one dream, it started off on a nice beach, when awareness hit me. I looked around and marvelled at how real it all looked. I was near a wooden railing and touched it, wondering how could I ever tell the difference between a dream and reality, since it all looked and felt so solid and vibrant. Then I noticed a truck parked nearby, levitated it with my mind, and hurled it hundreds of meters down the beach.

The frequency of lucidity subsided after a while. I don't know why my brain only switched on lucid dreaming for just one phase of my life. I did have another lucid dream a week ago, the first in about four years. I was flying over a landscape and entered a surreal city, and once again marvelled at how real everything all looked.

I'm with a couple of the other commenters in this thread. It's nice to have experienced lucid dreaming at some point, and it's fun when it happens again. However, it's also kind of pointless. A healthy attitude is to appreciate restful sleep instead of craving for some useless thrill.

If you think it would be fun, maybe you could expose different algorithm choices for how to allocate the blocks?

Eg, I don't necessarily need to maximize the block lengths, but would like the holidays to be more evenly spread through the year. At the moment, it gives me a huge block around the easter period and another one week block later in the same month. And then, there are no holidays for an entire six months from the end of May to the start of November, despite several public holidays in between! I suggest an alternative algorithm would seek fewer one-week blocks and more long-weekend blocks, with some sort of pressure which penalizes blocks for being too close together?