The Senate is, while not the whole story, a significant part of the reason the government constantly fails to do what is either the desire of the people or what's in their interests. I wouldn't lament losing the Senate.
The US Senate is designed to check and balance the House of Representatives. But that often puts the Congress as a whole in deadlock, meaning it can no longer balance the other two branches.
When they could get anything done they delegated a lot of power to the Executive. Which worked ok, but eventually a "unitary executive" appropriated even more power, and the Legislature is powerless to prevent it.
Unpopular opinion: deadlock is fine. Most legislation is bad. What really matters is the budget. And the rule that failing to pass a budget can automatically force an election avoids the absurd US "shutdown" that isn't a shutdown.
This is now my second favorite idea, after a nationwide ban of first past the post voting schemes.
My third (previously second) is outlawing political parties. The problem with that one is it would be really difficult to implement in a way that doesn't run afoul of freedom of association and freedom of speech. Probably worth figuring out though.
Voting system reform would probably mitigate the worst aspects of political parties.
Egypt after ousting Mubarak held an election where a third of seats were reserved for independents. Most winning candidates were just Muslim Brotherhood affiliated. I suspect the military interim government did that deliberately to justify their later coup.
This is where the intra-party coalitions become important. Every party of significant size has them. Labour is effectively a coalition between a rightwing faction (New Labour/Blue Labour) and everyone else who is more leftwing. The internal and external debate is the question: should they focus "right" (immigrant and queerbashing, welfare cuts) to appease the right wing of the party and try to pick up Reform/Conservative voters, or focus "left" on their base and people who are switching to Green?
On the other hand, voting needs to mean something. If voting doesn't mean anything, because the whole system is held in a vice grip by a sclerotic institution playing power games with itself, then the broader system eventually collapses.
My personal opinion is that Mitch McConnell's intransigence and unwillingness to do anything lest Obama get credit for it led directly to an increased desire for a "strongman"
The Senate was fundamentally from the start a compromise in favor of the slave-owning ogliarchy. You just have to look at free and slave states being admitted in pairs to preserve the status quo of slavery to see how that went.
The Senate gives a rather disproportionate democracy in which the votes of a small number in small states take on disproportionate significance compared to the votes of a large number in populous states.
That still does nothing to refute the parent's complaint about democracy. Lopsided representation is still representation (as opposed to a council of nobles or military generals or whoever).
Also the thing you're objecting to is literally the entire point of the senate from day one. It was intended to give less populous states an equal voice in contrast to the house of representatives. Unfortunately history happened and the house of representatives hasn't been proportional for a long time. But if you're going to complain about something it should probably be the latter rather than the former.
It does not seem fair to say that frequentists do not update their beliefs based on new evidence. This does not seem to accurately capture what the difference between Bayesians and frequentists (or anyone else) is.
I don't like the way it's written, but what they are talking about is completeness in the sense of "Dedekind completeness"; i.e., that given any two sets A and B with everyone in A below everyone in B, there is some number which is simultaneously an upper bound for A and a lower bound for B.
Note that this fails for the rationals: e.g., if we let A be the rationals below sqrt(2) and B be the rationals above sqrt(2).
In school, we talked about “Dedekind cuts” but we never formalized the definition. Kind of disappointed now because your explanation is very simple and elegant.
Note the following comment by Jerry Ling: "The effect goes away if you search properly using the original submission date instead of the most recent submission date. By using most recent submission date, your analysis is biased because we’re so close to the beginning of 2026 so ofc we will see a peak that’s just people who have recently modified their submission."
The last-modified-date effect is even more important, because it can be used to support whatever the latest fad is, without needing to adapt data or arguments to the specifics of that fad.
Not paying attention on the train, even in 2025 girliepop-influencer-Instragram-latte-art New York, is not the smartest. You're probably better off during rush hour, but being aware of your surroundings is never a bad idea, even in "safe" New York.
Suppose, e.g., that you can get $5k/yr in benefits if you make less than $10k/yr in other revenue and $0 otherwise. Unless you have a viable strategy for pushing past $15k/yr it's a strong financial disencentive against actually working, and even then your incremental ROI isn't very good past that cliff (if it takes an extra hundred hours to push to $15.1k/yr, then compared to your $10k/yr option you're only making $1/hr for the extra work).
This doesn't sound monotonic. This sounds like a mapping from pre-benefit income to post-benefit income which sends just under $10k/yr to just under $15k/yr, but sends just over $10k/yr to just over $10k/yr. So it sends a larger input to a smaller output.
I think I see the definitions we're disagreeing on. I'll lay out what I meant and then address your thing.
1. A couple levels up, the function somebody requested being continuously differentiable was the "benefits." You seem to be looking at the total post-benefit income instead.
2. It's not totally clear, but you _might_ also be using "monotonic" to refer to "monotonic increasing" or "strictly monotonic increasing" instead (the total income function in my example isn't even monotonic, so this is just me reading between the lines in the wording of your reply).
The cliff issue still exists though (and still exists in the differentiable version -- you want bounds on the derivative ideally to prevent the cliff issue, and for unrelated reasons you probably want other properties like the benefits not increasing as a function of pre-benefit income). Suppose you have a strictly monotonic increasing function mapping pre to post benefit income. That function can still, e.g., have a long region with a high slope, followed by a long region with a low slope, and some curvy thing connecting those. It's still continuously differentiable and strictly monotonic increasing, but the incremental value of work in the low-slope region is low (by definition). You might make a dollar in pre-benefit income and $0.10 in post-benefit income, so at minimum wage you're back to a <$1/hr situation unless you can make enough money to push substantially past the right side of that low-slope region (which we're assuming exists, else it basically says you have a 90% tax rate if you make too much money, and in-context "too much" would be near poverty levels, so even people wanting that sort of thing for the ultra rich wouldn't think that to be a good idea).
I'll go further and say what we probably want is for the derivative of net income as a function of earned income to be monotonic increasing but max out less than 1. So that there aren't ranges of income where you are receiving very little per dollar earned and then after some point start receiving more per dollar.
But solving benefit cliffs really just means having earned=>net income strictly increasing with the marginal rate reasonable, say at least 30 cents more net income per earned income. Under that constraint, you could have ranged where net income grows slower until you hit some higher dollar amount of earnings, but imo that should also not be desirable.
Not GP, but … because the overwhelming majority of programming is done in support of businesses selling things?
I’m not just talking about people who program for a living. The majority of academic CS chooses its research directions because of what limits people are running into for business; even privacy-focused software has been commoditized by many business; a large amount of OSS development is by (and often paid for by the employers of) people working for money; heck, after Linus’s initial “just a hobby OS” period even Linux’s contribution base was primarily driven by business needs (even if those needs influenced it via “contributor had a problem at work and committed a solution for it upstream in spare time” as often as “paid contributor upstreamed a change on behalf of their employer”).
Yes and no. Most of the big new languages today are created to support the business of selling things because languages are expensive to make, they don't generate any profit themselves, so the only people who have enough money to fund their development are mega corporations, who act in self-interested ways.
But look at historical languages and why they were created:
Algol - to explore writing algorithms
Fortran - to help scientists write programs using typical math formulas
Matlab - to help write programs in linear algebra
Haskell - to explore lazy program evaluation
ML - to explore how to reason about proof automatically
C - to build an OS
Python - to interface with an OS
LISP - to formalize symbol processing
APL - to explore programs defined over arrays
LOGO - to help young kids to program computers
Prolog - to create a language around the idea of formal logic.
Smalltalk - to create an entire programming system, not just a language
(I've left out C++, Java, and JavaScript because I feel like those languages are mostly about serving business interests)
Pretty much the entire computing landscape over the past 50-70 years has been defined by people writing languages for reasons other than "this is for a business to use to make more money". So if we let business-driven interest dictate the future direction, we will have missed out on all the things that could have been. Would Haskell ever have been invented if businesses interests were the only concern for researchers?
Fortran compilers were historically implemented by hardware vendors in order to sell their hardware, and this still largely holds true across the surviving implementations with the exceptions of GNU Fortran (obviously) and nagfor (commercial s/w product). There's a good reason that Cray Research's software group was initially part of its marketing department.
The fact that there is a precise analogy between how Ax + s = b works when A is a matrix and the other quantities are vectors, and how this works when everything is scalars or what have you, is a fundamental insight which is useful to notationally encode. It's good to be able to readily reason that in either case, x = A^(-1) (b - s) if A is invertible, and so on.
It's good to be able to think and talk in terms of abstractions that do not force viewing analogous situations in very different terms. This is much of what math is about.
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