25-35 is a great time. I moved cities and changed careers in my late 20’s, and pivoted again in my early 30’s, and it was a good reset to build on lessons learned and undoing past mistakes, while having the youth and energy to really enjoy myself and actually choose a path I was going to have fun with.
I’m enjoying my 40’s a lot, but I look back fondly on that 25-35 period as being both fun in itself and setting me up for a good 30’s and 40’s (and possibly further).
I can’t answer for dual numbers, but I can answer for imaginary numbers in circuit design.
Imaginary numbers are those that include an imaginary component, that squares into a negative number. Traditionally, i^2 = -1, but electrical engineers like to use j instead (I tends to be a variable used to describe electrical current).
Complex numbers, that include a real component and an imaginary component, can be thought of as having an “angle,” based on how much of it is imaginary and how much of it is real, mapped onto a 2-dimensional representation of that number’s real and imaginary components. 5 + 5j is as real as it is imaginary, so it’s like having a 45° angle. The real number 5 is completely real, so it has a 0° angle.
Meanwhile, in alternating current (AC) circuits, like what you get from your wall outlet, the voltage source is a wave that alternates between a maximum peak of positive voltage and a bottom trough of negative voltage, in a nice clean sinusoidal shape over time. If you hook up a normal resistor, the nice clean sinusoidal voltage also becomes a nice clean sinusoidal current with the exact same timing of when the max voltage matches up with the max current.
But there’s also capacitors, which accumulate charge so that the flow of current on the other side depends on its own state of charge. And there are inductors, that affect current based on the amount of energy stored magnetically. These react to the existing current and voltage in the system and manipulate the time relationship between what moment in time a peak current will happen and when the peak voltage was.
And through some interesting overlap in how adding and subtracting and delaying sinusoidal waves works, the circuit characteristics line up perfectly with that complex angle I was talking about, with the imaginary numbers. So any circuit, or any part of a circuit, can be represented with an “impedance” that has both an imaginary and real component, with a corresponding phase angle. And that complex number can be used to calculate information about the time delay in the wave of current versus the wave of voltage.
So using complex phase angles makes certain AC calculations much, much easier, to represent the output of real current from real voltage, where the imaginary numbers are an important part of the calculation but not in the actual real world observation itself.
So even though we start with real numbers and end with real numbers, having imaginary numbers in the toolbox make the middle part feasible.
Set phasors to “confuse”
New In Town came out in 2009, 16 years ago.
IT’S A BEAR DANCE
Those are called pancrepes I think
To quote The Good Place:
There’s something so human about taking something great and ruining it a little so you can have more of it.
It’s not about work ethic. It’s an openness to new things, and a willingness to coordinate and plan things.
And seeing “moving away” as a huge sacrifice, to where you’d tend to describe it as “uprooting your life,” is a particular worldview that you’re entitled to, but one you should be aware that many other people don’t share.
You’re attributing a lot of unspoken values in that comment that I don’t really think are there, and I suspect it’s because you place a much higher value in staying close to home than the typical person does, and because you seem to elevate the purpose of a career to primarily be maximizing one’s own money.
So take a step back. Reread that comment with the revisited assumption that some people choose careers for reasons completely different from money, and that people don’t feel a strong need to stay in the same city where they grew up. It’s just career advice at that point.
There’s more to careers than just money. The distribution of jobs in different industry sectors, job specialties, etc. aren’t going to be uniform throughout the world, so many types of jobs will require people to move.
It’s not even about money. It’s about wanting to work in something specific that isn’t as easily available in the town you happened to be born in.
that’s insanity
makes me feel sick
That’s a pretty strong reaction to the simple idea that maybe living your entire life within a 30 minute drive of where you were born isn’t the best way to experience this life. You don’t have to want it, but is it that much to ask to simply understand that some other people want it?
My hometown is, like, fine. I could’ve stayed. But its state government is insane, the dominant local industries and companies don’t really fit my moral framework, and the social aspect pushes people into a car-based lifestyle that I’m not particularly interested in. I left for a job, but I also was just looking for a reason to leave.
Lazard is a pretty respected analyst for energy costs. Here’s their report from June 2024.
In the U.S., peaker gas plants that are only fired up between 5-20% of the time, the levelized cost of electricity (LCOE) is between $110 to $230 per MWh. The levelized cost of storage for utility scale 4-hour storage ranges from $124-$226 per MWh, after subsidies. Before subsidies, that 4-hour storage costs $170-$296.
Residential storage, on the other hand, doesn’t come close. That’s $882 to $1101 before subsidies, or $653 to $855 after subsidies.
So in other words, utility scale storage has dropped down to around the same price as gas peaker plants, in the U.S., after subsidies.
And yet, people do.
Should we just ignore the dynamics of that system, and pretend it doesn’t exist? Or can we make observations about that system, and analyze its effects?
This comment section is all people missing the point.
The point of the post is that a particular job will generally stabilize at a particular pay. If it’s a tipped position, then the employer will pay less, so that the overall income is roughly at that stable income for that position, including the overall average tip.
So people who tip less than the average are free riding off of the people who tip more than average, where that worker will make an average tip overall, which comes more from the generous tippers than the stingy tippers. Thus, it effectively transfers money from generous tippers to stingy tippers, on net, in the long run.
The merits of this system, whether servers deserve to be paid more, whether we should push for reforms so that this isn’t the system, is besides the point. The post is making an observation of how things actually are, not advocating for how things should be.
It’s just that I don’t have any expectation of the girls in the picture being shocked
That’s the joke.
Yeah, people are working on it.
The EIA estimates that there’s about 30 GW of battery capacity in the U.S., mostly in storage systems that are designed to store about 1-4 hours worth.
That’s in comparison to 1,200 GW of generation capacity, or 400 times as much as there is storage.
It’s coming along, but the orders of magnitude difference between real-time supply and demand and our capacity for shifting some of the power just a few hours isn’t quite ready for load balancing across a whole 24 hour day, much less for days-long weather patterns or even seasonality across the year. We’re probably gonna need to see another few years of exponential growth before it starts actually making a big impact to generation activity.
I’ve heard of nigging but I’ve never heard of this.
Um I hope you mean negging
“Mogging” as a term originated in the early 2000’s and went mainstream-ish in the late 2000’s when the “pickup artist” community started getting attention in places like the New York Times. The people who originated it are probably like 45-50 years old now.
Quick etymology: comes from these pseudoscientific douchebags trying to name the phenomenon where a man tries to subtly belittle another man in front of women, establishing that he’s the AMOG (alpha male of group), eventually became a verb amogging or mogging, and then various specific types of this behavior earned prefixes: heightmogging, etc.
The fact that it has this kind of staying power, 20 years later, is the surprising part.
It sounds like the thesis to David Epstein’s book, Range. When I read it, it was a game changer for me.
If I recall correctly, the main examples were Roger Federer (who played a lot of sports and didn’t choose to specialize in tennis until much later than the typical tennis pro), jazz legend Django Reinhardt, Vincent Van Gogh, and a bunch of other less famous, but much more typical examples.
Sampling is important, and has value beyond just the things they sampled and abandoned. The act of trying many different things is itself helpful.
Van Gogh wouldn’t have become the artist he became if he didn’t fizzle out of multiple career paths beforehand.
David Epstein’s Range really explores this idea and puts forth a pretty convincing argument that sampling and delaying specialization is helpful for becoming the type of well rounded generalist whose skills are best suited for our chaotic world.
Some daals are spicy, and could arguably be considered British?
ew