It's pretty important if you're working in a developing field. The original TPU couldn't do floating point so it wasn't really useful for training. IIRC they also work best with matrices that have dimensions that are multiples of fairly big numbers (128? 256?) with later generations working best with bigger matrices.

That's great for the current focus on gigantic attention matrices but not so great if the next big thing can't be efficiently shoehorned into that paradigm.

I tried to install Platform IO to try it out, but the multi-gigabyte Visual Studio won't work on my old macbook. The Arduino 2.0 IDE isn't exactly fast and efficient, but it at least installs. A plain old text editor is fast, efficient, and installs no problem.

Arduino is powerful because it's a collection of device drivers and other libraries written to a reasonably uniform standard and mostly cross platform too. You can write firmware for an ATMega hooked up to some obscure sensors and an old RS-485 driver then (mostly) have it also run on an STM32, Pi Pico or ESP32.

Lowering prices won't help. That would lower GDP. Raising pay and raising prices would, although raising pay relative to prices is a bit of a double edged sword. The more money you've got the more you're likely to save.

The real answer is that GDP is a pretty shitty measure for this kind of thing.

The GP is not talking about LTE, they're talking about "voice over LTE" (VoLTE). The Bell compatibility checker they linked to seems like a fairly comprehensive list of phones that support it. Very old phones, like the iPhone 4 or original Pixel don't support it because the standard didn't exist when they were manufactured.

This article almost sounds like an ad to get people to buy things to keep the economy rolling rather than a serious discussion.

You've answered your question. "Productivity" in this case is GDP / capita. If an American buys something with American parts from an American retailer then they increase the GDP, which increases the productivity. It doesn't have to increase their personal productivity.

It might not even be necessary to fork much. Genuine Arduino hardware is so expensive most people use clones, lots of people use Platform IO instead of the Arduino IDE, and the Arduino core for the newer microcontrollers is not made by Arduino anyway.

https://kpmg.com/ph/en/home/in...
"The short answer is that the Tax Code enforces a Stock Transaction Tax (STT) on every sale, barter or exchange of shares in a listed company. Under Section 127(A) of the Tax Code, as amended by the Tax Reform for Acceleration and Inclusion (TRAIN) Law, the STT rate is 6/10 of 1% based on the gross selling price or gross value in money of the shares of stock sold, bartered, exchanged or otherwise disposed.
      The burden to pay the STT, as provided in Revenue Regulations (RR) No. 6-08, is imposed on the seller or transferor and remitted by the seller or transferor's broker. The stockbroker who effected the sale has the duty to collect the tax from the seller upon issuance of the confirmation of sale, issue the corresponding receipt thereof, and remit the same to the tax authorities. "

Would such a STT tax in the USA reduce a lot of possibly harmful churn from algorithmic trading? Or would it be extremely harmful to everyone by reducing liquidity? Wondering how that is working out in the Philippines?

Oh, I think I saw that YouTube video!

Generally the "even engineer dads can't make heads nor tails of it" objection is that the engineer dads didn't spend a couple minutes reading the helpfully coloured highlight box in the textbook. There has been a push in math to develop teaching methods that emphasize understanding rather than memorization. Thus 5x3 becomes 5x5x5 or 3x3x3x3x3 instead of "STFU and memorize your times tables."

A better example, also from Internet memes, is a procedure where you add or multiply a pair of larger numbers by breaking them down into component problems. 37 + 55 becomes (30 + 50) + (7 + 5) and some "parent" on Reddit or Facebook with add a comment like "why can't they just do addition like we learned??" Someone sensible will usually point out that people who are good at arithmetic will often use decomposition on harder problems if they're doing them in their head.

The teaching algorithms are pedagogical tools used to increase understanding or illustrate problems from different perspectives, not the final here's-the-algorithm-you-should-always-use".

I said that the 5x3 answer being marked wrong was likely due to a poorly educated teacher. No, primary school children probably won't be multiplying anything non-commutative soon. That was a joke. However, it is important not to instill, and then spend years reinforcing, incorrect facts. You shouldn't tell students things like "multiplication is defined as commutative" because that kind of thing will eventually screw someone up.

Sure. I think the GP's example, if it was correctly described, is probably a sign of a teacher who doesn't understand what they're teaching.

I was pointing out, educationally I hope, that the GP also doesn't really understand what they're talking about, despite claiming it's "simple." Which, incidentally, makes me suspect the anecdote may not be entirely accurate.

Or maybe they want to prepare the kids so they're not shocked when they start Clifford algebras.

Multiplication isn't defined as a commutative operation. It happens to be so when you're multiplying real numbers but in general it is not.

Fractions are difficult for lots of people. You have to understand what a fraction is before "just double the denominator" is simple and obvious. It's not a new thing. There's the story of the 1/3 pounder failing because people thought the 1/4 pounder was bigger. I have a relative who specialized in teaching remedial fractions.

It is kind of shocking that American universities are accepting large numbers of students who can't do basic math, and in programs that apparently involve calculus no less.

I'm not sure about the assertion this is a recent phenomenon when the head of state recently promised to reduce drug prices by a thousand percent.

but also in economics, with the 2008 financial crisis that was caused by a failure of the institutions that are supposed to regulate such things.

Dunno, the institutions who were supposed to regulate such things did a pretty good job here, as they did in most places that weren't the US or a specific bit of shadiness between the UK and Iceland.

It's also unnecessary. The most common alternative to a republic is a constitutional monarchy, and the presence of a figurehead monarch doesn't make a democracy much more resiliant against determined stupidity.