Integration: just think about driving somewhere in your car. How long it takes you to get there depends on how fast you’re going as well as the total distance you need to travel. This is easy to figure out if you’re going exactly one constant speed for the entire trip.

But what if you’re driving in the city and you’re speeding up and slowing down all the time? Maybe sometimes you even need to go in reverse which takes you further away from the destination! So the problem you have is that your speed is changing throughout the trip (sometimes even going negative when you’re driving in reverse) and you still want to somehow figure out how long it takes.

Perhaps you might have thought of a straightforward (albeit tedious) way of getting the answer: record your current speed and the current time in a notebook every so often and then multiply each speed by the time interval to get all these small slices of distance travelled, then add them all up at the end. Congratulations, that’s the idea behind integration!

There’s one problem though: your speed might be changing throughout each time interval so the answer you get has all these mistakes that just add up to give you an inaccurate result! Solution: make all the time intervals smaller! This way each time interval includes a more accurate speed, so there will be less errors when we add them all up. Thus the theory of integration is that we can make the intervals arbitrarily small (as small as we want) to get an answer as accurate as we want all the way down to infinite intervals of infinitesimal length which ought to give us the exact answer (and it does)!

Differentiation (calculation of derivatives): the opposite of integration. This takes an entire trip in the car and gives us the ability to calculate our exact speed at any instant in time. Unlike how we might calculate an average speed by looking at the total distance travelled over a time interval and dividing it by that length of time, a derivative gives us the exact speed at a moment in time!

Anyway I hope those two rough explanations help illuminate things a bit for you. Integration and differentiation (calculus) are actually way more useful than just for calculating speeds and distances. For example, the same ideas can be used to calculate the area of an irregular shape (divide it up into squares and add them all up, making the squares smaller helps reduce the errors around the edges) or the volume of an irregular container! Or the slope of a hill at any point on its surface! Or perhaps the lowest point of a valley (using a technique called gradient descent).

That last one is actually very commonly used in artificial intelligence as a training technique. There you’re trying to find the minimum point in some higher dimensional data, according to some rules you have. With gradient descent you use differentiation to find the slope and then you take a small step along the slope towards that minimum point, then repeat!

Love integration! Much more fun than derivatives!

Neither in Canada nor in the US do you need to pay a service to file taxes. All you need to do is get the forms and fill them out. People use these services because the forms are very long with many things to figure out, most of which don’t apply to most people.

I dunno about the US but in Canada you can download the completed form at the end before submitting it to the tax agency. Using this completed form can show you what you need to fill out yourself next year, assuming your circumstances don’t change.

All spiders are little mechs to me! Their legs are powered by hydraulics!

Nice! I’m a long-time fan of Shattered Pixel Dungeon! Even @[email protected] is a Lemmy user and he often posts updates over on [email protected].

The game is very easy to get into, with fairly simple (for a traditional Roguelike) mechanics. However don’t let the simplicity fool you! The game is incredibly deep with layers and layers of rich strategy and very high run-to-run variety.

Some highlights:

• 6 unique character classes, each with 2 subclasses
• a unique talent tree for each class, with a high degree of synergy between talents and items found in the dungeon
• a simple, intuitive upgrade system where scrolls of upgrade can be applied to weapons, armour, rings, wands, or throwing weapons
• a fun and interactive item identification system, including deduction-based mechanics (an item that can identify something if you correctly guess what it is) as well as environmental clues that help you narrow down an item’s identity without knowing exactly what it is
• an ultra-deep crafting system called alchemy which allows you to re-purpose the many consumables you find (seeds, scrolls, and potions) into a much larger variety of runestones, exotic scrolls, (exotic) potions, elixirs, brews, and even consumable spells. The alchemy system alone is so powerful that a skilled player can win many of the game’s toughest fights using alchemy alone
• a very interesting (but not excessively large) dungeon with many special features, traps, puzzle rooms, floor varieties, quests, and boss battles, divided up into multiple chapters with a storyline you uncover over multiple play-throughs
• an extremely well-made UI that was originally designed for mobile but is equally at home on a PC. The game has a very intuitive help system for getting information about everything you might want to know about: character classes, talents, items, enemies, dungeon features, debuffs, alchemy recipes, and many more. This information is available through context-sensitive pop up windows as well as a comprehensive journal system which automatically fills out as you identify things over multiple runs
• an excellent achievement system in the form of badges which are fun to unlock and help you to learn more about some of the strategic ways to play the game
• a challenge system that unlocks after your first victory which allows you to enable up to 9 different challenge settings in any combination you choose. Expert players who find the default (0-challenge) setting too easy can continue to find interesting difficulty all the way up to the full 9 challenges, which deeply test your knowledge of the game
• a very nice high score table which allows you to view all the components that go into your score calculation as well as see a summary of the equipment and talent choices you made for that character
• a random seed system that allows people to share seeds and try their hand at the same dungeon as others. A daily seed feature allows you to compete against the community for high score with the same seed for everyone!

Also known as kicking the can down the road.

If you don’t fail a kid in elementary school they’re gonna fail in high school. If you don’t fail them in high school they’re gonna fail in university or in life in general.

Life has consequences for making mistakes and not learning from them. If we try to shelter children from their mistakes and bad habits then we raise adults who are poorly equipped for handling the challenges of life.

When I was in first year of university I met so many nice, seemingly-well-adjusted people who hit a brick wall with their coursework. I believe around a third of my peers failed to graduate at all in their programs. Many dropped out or transferred to other departments or other universities.

But here’s the thing: my peers had already been subject to a rigorous selection process to get in (only about 10% of applicants were admitted). If you had put all applicants through the rigours of the coursework far more would have failed.

The really tragic part of this whole story is when you factor in the degrees of the consequences for failure. In elementary school the consequences for failure would be very low. Children who are older than their peers tend to outperform them anyway. In university, however, the consequences for failure are very high (thousands of dollars wasted on failed courses that need to be repeated).

The consequences for failure outside of school (real life as they call it) are even higher: unemployment, homelessness, incarceration, and even violence and death.

They did mention being a driving instructor. Driving (and teaching students to drive) all day every day is going to put a lot more wear on the tires than a typical driver.

When the right goes too far, they’re ascendant in politics. They’ve won the election and they’re enacting some seriously bad policies.

When the left goes too far they fragment into a million pieces. No coalition can be built because everyone is too caught up in fighting over the details.

What I described is water filtration: biological filtration. Runoff from farms is organic in nature: manure and fertilizer, for the most part. Filtering it with traditional water filters (which need to be regularly replaced) is a huge waste of materials and a source of plastic waste that needs to be disposed of. It’s spending more money in order to fill up landfills needlessly.

Furthermore, it doesn’t even make sense from an infrastructure perspective. Artificial water filters are designed to be installed in pipelines. The water runoff on farms is not contained in a pipeline. It’s caused by rainfall and snowmelt on fields and running downhill (as well as sinking into the ground, soil permitting) over a large area. To filter it artificially you’d need to collect all that water into a pipe which would require enormous infrastructure to construct.

It’s so much easier, so much more economical, and so much more environmentally friendly to do minimal landscaping and allow water to collect in a basin located downhill where the water was flowing anyway. Some of it may need to be diverted for one reason or another, but that’s nothing compared to the cost of full collection and water treatment. Plus all those native wetlands plants that uptake the excess nutrients provide a habitat for native wetlands wildlife. It’s a win-win!

I’d prefer if they dumped Danielle instead and elected a non-traitor premier.

Fixing the runoff problem is just a matter of proper landscaping. Establishing an artificial wetland or preserving a natural wetland can go a long way towards reducing nutrient loads in the water that drains from a farm.

It’s all about having a basin to store water so it doesn’t drain off the farm too quickly and allowing native aquatic plants to take up nutrients to filter them out of the water.

Yes, in order to talk to his closest ally, the United States!

I love this. I am a big fan of the use of colour, the small details, the little spires in the distance. So evocative! Beautiful!

Which is not always the best thing, admittedly. I watch a lot of repair videos that get me thinking I can repair anything from vintage computers to old tractors and old radios. If you yourself are not looking for such a hobby then you’ll probably want to avoid such repair videos.

Compressor could probably also use some service. Cleanup inside, fresh oil, and check the bearings to see if they’re still good.

Even chess feels the inevitability of carcinization! We might as well start calling it like it is: the 4th law of thermodynamics.

Look at the gold line then. That’s the effective tax rate which incorporates all of the different bands (right now there are only 2 bands anyway).

Why are you so ardent to defend taxing billionaires?

Please, be more charitable than that.

My argument is not that we shouldn’t make wealthy people pay their fair share. It’s that tax avoidance isn’t a trivial problem to solve. It’s actually very complicated because people are smart in general and they generally always try to minimize the taxes they pay.

This is half of the reason the entire accounting profession exists (the other half in auditing)! When one tax loophole is discovered, an accounting firm can put it to work for all of their clients.

What I suspect you’re identifying is the loophole whereby wealthy individuals hold on to stocks to avoid taxable events. They then take out a loan with the stocks as collateral. The bank charges a small % because the risk to them is tiny. Thus it’s far cheaper for the individual than simply paying the capital gains.

Yes, though it’s not just billionaires who do this. Regular people do this as well. And they don’t just do this with stocks and bonds, they do it with real estate. Reverse mortgages, home equity lines of credit, rental properties, etc!

If you own a million dollars worth of stocks and bonds you can use that as collateral for a loan to help you make the down payment on a new mortgage. Then you can convert that property into a rental and use the rental income to pay off the loan as well as make mortgage payments. Or you could use the loan to help you start a small business.

There’s just so much people can do when they have access to capital. Our whole economy is based on it.

Capital gains taxes only need to be paid when the gains are realized; that is, when stocks or bonds are sold for a profit or when dividends are paid. Capital gains taxes are not owed if you’re just holding a stock as it rises in value over time.

If you look at the history of capital gains taxes in the US, you’ll see that when capital gains taxes are high people don’t realize their gains because they don’t want to pay the tax. Instead they’ll hold on to their investments until a later time when taxes are low again:

Source: Wikipedia

As you can see with the “taxes paid on capital gains” line in the graph, lowering capital gains tax can actually increase the total amount of taxes you collect.

Most wealth isn’t in the form of houses and luxury goods, it’s in the form of capital. Ownership of businesses, stocks, and bonds.

Trying to seize all that wealth in the stock market is even more difficult than seizing a car or a boat. As we’ve seen, the stock market can drop by billions and trillions of dollars within seconds. The truth is, that wealth doesn’t really exist in the same way that a rock or a tree exists. That wealth is based on people’s perception of value. It’s literally a figment of our imaginations and it can vanish in an instant if people come to believe it has.

Imposing a large wealth tax on people’s stocks and bonds would crater the market far worse than the Great Depression. It would trigger bank runs and total chaos.

Even if you announced a plan to gradually phase it in over several years, you’d have people phase out their market holdings faster than that. They’d switch to buying tankers full of oil or other hard commodities that they keep off-shore. And they’d use it to hold the country hostage as everyday living costs skyrocket.