My take is that pattern-matching is thinking. But it's low-quality thinking. High-quality thinking is logic. And higher still is causality, which is to logic what calculus is to algebra. I.e. if logic studies the relationship between x and y, then causality studies the relationship between dx and dy. And causality is what we actually want, because causality is power. E.g. causality is what lands astronauts on the moon. When folks like Judea Pearl complain that current AI isn't truly thinking, they're complaining that current AI can't reason logically/causally.
The potential to commit violence can be reframed as strength. It's useful because it grants you negotiating leverage, regardless of whether you are the aggressor or defender. Can't defend yourself? Vae victis.
The capability to commit violence might be a strength in a world where violence is an unfortunate necessity, ie for defense of the common good. But unless it's paired with wisdom and reluctance (as the opposite of the willingness noted above and gleefully promoted by adherents to the Spartan mythos) that capability is mostly the tool of tyranny.
> The most energy you can extract from any type of bomb would be if it was converted to energy at 100% efficiency.
Under normal circumstances, a bomb's energy is endogenous. But in the blog's thought-experiment, the energy is assumed to be exogenous. Therefore, your assumption that "the explosion is bounded by the mass of the person" doesn't apply to this scenario. Instead of TNT, imagine a rubberband.
To me, the distinction maps onto the Effectual vs Causal distinction. For some path "A to B", some people prefer to consider their present tools/resources (point A) and work forward opportunistically. While others prefer to consider the end-goal (point B) and work backwards recursively. If the analogy is unclear: a theory is a tool; a specific problem is an end-goal.
I tend to frame this in terms of the Multi-Armed Bandit Problem. It's a trade-off between exploration vs exploitation. It's often impossible to predict beforehand which strategy is optimal for a given environment. Which, I suspect, is why progressive temperments and conservative temperments coexist.
One benefit of markets is price-discovery. But if you're not participating in a market, determining price is akin to shaking a magic 8 ball. It assumes a Just Price, which is a heuristic and a fiction.
Also, quality of living is determined by income, not wealth. Fresh retirees are generally wealthier than other age-groups because they've saved for retirement. But that doesn't mean they consume more. Also, consider the citizens of the Netherlands. They enjoy a comfortable existence while servicing an enormous amount of debt. If wealth were the primary determinant of quality of life, you'd think the Netherlands were as as destitute as Somalia.
The retiree example is intended to demonstrate that a wealth tax is inherently perverse, regardless of who is targeted. Savings are just deferred expenditure and debt is just expedited expenditure. When you tax wealth, you expedite consumption.
Another way of thinking about this: A wealth tax is like inflation, except assets are also devalued alongside your savings. Which means the wisest strategy is to consume now, save nothing, invest nothing.
50 dollars tomorrow may be more useful to you than 100 dollars today if today you'd only buy useless crap for it but tomorrow there is a brilliant investment opportunity.
I tend to think of multiplication as a transformation. "repeated additional" almost makes it sounds like we're merely telescoping an interval within a single dimension. Whereas "transformation" (to me), evokes more of a Cartesian Product or Quadrature sort of mental image.
Suppose your friend Alice arranges your wedding. You ask her to arrange the lawn chairs in an arrangement of 2 rows and 3 columns. But she misinterprets your request as 3 rows and 2 columns. Oops. Now a particular family can't all sit in a single row without rearranging the chairs.
If all you care about is the total number of chairs, the order of operands is irrelevant. but if you care about the structure, "2 x 3" may encode information that "6" does not.
I address that point specifically in my comment. What you say is that the units of the operands matter, which I agree, but the order doesn't. 2rows x 3chairs and 3chairs x 2rows is the same thing.
The point isn't "matrix multiplication != scalar multiplication". The point is "the process of evaluating a reducible expression inherently discards information about the original expression", which is a fact about evalution rather than any specific operator. The fact that "the information discarded is of little consequence to the compressed result" is a quirk specific to scalar multiplication. Thus, the commutative property distracts from explicitly modeling the "AST" so that the student understands what multiplication represents under the hood, beyond the rote memorization of scalar multiplication tables.
Perhaps an analogous situation would be: Suppose a teacher wanted to introduce the notion of limits to a calculus curriculum. "That makes zero sense. The only things a student needs to know are the shortcuts for each parent function, e.g. that (d/dx x^2) reduces to (2x) via handwavey magic." But what if an engineer needs to integrate over an arbitrary curve? Can students solve the problem without being comfortable with Riemann Sums? Maybe 1st-year calc students should rederive the shortcuts from scratch? "Except we're talking about a math course, not an engineering course."
> In particular this bit regarding multiplier/multiplicand makes zero sense to me.
> Isn't 2 rows x 3 chairs the same thing as 3 chairs x 2 rows? It's a bizarre argument.
It's bizarre to simias (and you, I assume) because y'all can't imagine performing the operation without thunking. (Don't get me wrong, I think "repeated addition" is the best method. I'm just attempting to explain the opposite perspective so that it feels less bizarre.)
