Skipping to learn long division by hand because you'll always have a calculator (or better a smartphone at hand) is like going to a gym with a forklift. It is faster to lift the weights, but it kinda defeats the purpose.
Learning to do long division by hand trains the mind. It prepares you to understand polynomial division. It teaches you the deep connection of division and subtraction. So, mastering it should be part of the curriculum. As soon as it is truly mastered, it should be allowed to use a calculator.
I think there is also an argument for general numeracy as a life skill. Lots of people I run into just have no intuitive sense of how numbers work and how to calculate roughly.
The number of people that cannot calculate a tip in their head, or have a basic grasp of how interest works is constantly shocking to me. Yeah, we all carry calculators around, but you should be able to reason about numbers enough to know when an entry error has been made on a calculator
(Shrug) Every time a higher level of abstraction becomes available, a lower one loses importance. That's how it's worked for humanity since the dawn of recorded history. As others have pointed out, the ancient Greek scholars had the same baseless fears.
I don't think I've ever had to do polynomial division by hand. It comes up in control theory and a few other subfields, obviously including mathematics itself, but for me it's always been handled by software. It's safe to say that any given clanker will have better odds of doing it right than I will.
People love to cite the Phaedrus (although usually they just cite Plato) as a reason for why we should discard the warnings or fears about the cognitive effects of new technology as baseless.
But I think that this is foolish. Firstly, the fears weren't baseless! There's no question that the replacement of an oral culture by a literate culture meant the loss of certain cognitive skills for some people.
But more importantly, even if those fears were baseless, a fear in the past being baseless does not mean a similar one in the present is baseless. From our vantage point we can see the benefits of a literate society, but are we confident that what comes next will be as beneficial? Maybe it will be far more beneficial than literacy was, or maybe it will heighten inequalities to feudal levels. Either way, it's moving at a much more rapid pace than the spread of literacy, so we have much less time to reflect. It pays to be prudent here.
The point I tried to make wasn't that we still need to be able to do everything by hand. My point is more that we need to develop our brains. And for that we need training excercises. Similar to excercises in the gym. I doubt anybody encountered a barbell in real life outside the gym. Yet it is good tool to develop muscles. Math is an excellent tool to develop certain aspects of the brain.
I am wondering why people are so hyped about Ghostty? I gave it recently a try coming from kitty. And I had to configure stuff that worked out of the box with kitty, like Ctrl-Enter support and other key combos for agent harnesses. I like the development model of ghostt. And the developer really cares about creating great building blocks, e.g libghostty. But I am a bit underwhelmed.
I feel like the ghostty hype make more sense as excitement around the direction of terminal infra than a claim it is the one true terminal. Kitty's fine and if you are happy with it there's probably no good reason to switch.
Tangentially I also kind of feel like there is some level of deification of Mitchell's products but that's a diff topic.
Does anybody know why it wasn't implemented in a backwards compatible manner?
One could wrap a whole merkle-tree with an additional extension tree, that just adds the new hashes. That way both kinds hashes could be used to traverse all data. The new hashes could be used to check the consistency, the old hashes would still be there to use in UIs or old release documentation. The downside being that you introduce more nodes in the overall data-structure which will have to be supported basically forever. And if SHA-256 is to week a third layer would need to be introduced. But the point is, it could be done. Albeit it would loose some of the elegance of the data structures involved.
Allowing both hash algorithms is, from a security standpoint, equivalent to just using the less-secure hash algorithm.
All repos need to end up using SHA-2 exclusively by the end. All tools that speak only SHA-1 need to be made incompatible intentionally. If the SHA-1/SHA-2 hybrid approach could allow that to happen, then it would be useful. If not, then it would just be a waste of time.
The way you would do that generally is to make it backwards compatible, then adding warning to legacy tools, then turning SHA-1 off by default, then removing it entirely.
Doing it in a backwards incompatible way creates a chicken and egg problem, can't convert repo to sha-256 because some tool doesn't support it, tools don't have an incentive to be updated because no repositories.
The point I'm making is that "backwards compatibility" cannot rely on SHA-1 support being around forever. At some point, all uses of SHA-1 must go. This includes not only the interfaces between Git and external tools, but also Git's internal data structures. Past a certain point in the near future, there cannot be a two-tier Merkle tree system anymore; the SHA-1 tier has to be removed before long.
No, that argument misses the point. Cryptographic hashes enable you to trust, that I only have to review the changes since the last trusted commit. That is more important for the developers and maintainers of the software and less for the users.
In order to work for the users, a thing first has to work for its makers.
There are a lot of tools where the lines blur between “for the users” and “for the development team” because the users benefit from some things that make the developers’ lives easier.
Interesting, but I've read for a long time, that our humanoid predecessors at some point figured out how to get to bone marrow with tools. That provided the energy dense food as well an evolutionary impetus to develop larger brains to build better tools and handle them better. Fire and the capability to cook were developed much later.
While meat was definitely a caloric bonanza for early humans, recent primate studies offer evidence that sugary fruits continued to be a critical “brain food.” A 2017 paper looked at 140 primate species and compared their brain sizes with their diets.
“What [that study] showed very clearly was that the fruit-eaters, the frugivores, had 25 percent bigger brains, on average, than the folivores, the leaf-eaters,” Brand-Miller says. The fruit-eaters also had bigger brains than the omnivores, which ate meat.
But the Inca lived to late for this discussion. They already had advanced agriculture. For evolutionary terms, the time before agriculture and the time of the predecessors of homo sapiens are more relevant, because that time span was larger by orders of magnitude.
Learning to do long division by hand trains the mind. It prepares you to understand polynomial division. It teaches you the deep connection of division and subtraction. So, mastering it should be part of the curriculum. As soon as it is truly mastered, it should be allowed to use a calculator.
reply