BB(n) isn't computable, even given unlimited computational resources.
Running all n-state machines won't work, because you may have some machines that continue indefinitely, but without repeating. (Remember that while the number of states is finite, the tape is infinite.) No matter how long you run them for, you can't be sure whether they are going to terminate at some point in the future, or if they'll continue forever without halting.
This is why computing BB(n) for arbitrary n is equivalent to solving the halting problem.
Princeton's COS 226 covered this topic quite well when I took it. It was a good intro to both algorithms and DS content, as well as practical skills for leetcode style questions.
You can check out the Syllabus for the course as taught at Princeton here[0], or take the Algorithms I and II courses on Coursera[1] which cover ~2/3 of the content but have video lectures.
The point of the tax is not that the revenue will be used to reduce waste. The point is that it will increase the cost of producing waste for the polluter, ideally exactly to the point where it matches the cost to society of that waste.
The purpose isn't to make people stop polluting entirely, but to make it so they will only do so when it brings them a benefit larger than the societal cost of the pollution.
Right, but if the public wants to reduce X, and makes a tax on X a big contributor to city revenue, a city can improve their finances by increasing X, i.e. doing the opposite of what the public wants.
Why spend $$$ promoting and supporting recycling if a landfill tax is paying your wages?
It seems incorrect to conclude the public wants to reduce X when it taxes X.
The minimally logical conclusion (to me) is the public doesn’t want to pay for the externalities of X. Taxing X—assuming the tax levied is an appropriate amount to cover the externalities of X—makes actor Y who is doing X pay for X and its externalities, alleviating the burden on the public while avoiding taking an actual stand and/or engaging an effort to reduce X. Y does X? Y pays for it, not the public.
How much taxes on X adds to public revenue is mostly irrelevant, so long as it is enough to cover the costs of dealing with X without shifting that burden onto the general public via other taxes. If the revenue from X is enough to cover the costs of X’s externalities and also pays for wages and/or other public needs, that’s a net win for the public. You likely won’t see a city starting up a campaign to increase undesirable thing X just because it’d increase revenues.
Now, if the public really wants to reduce X by means of taxing X, it will likely choose to levy heavy, punitive taxes on X as doing X increases/continues, hoping to make it financially painful to those doing X to have to pay for X—for example, look at cigarette taxes. That can only go so far, though, before you encounter those for whom the added punitive tax is not a sufficient deterrent. Then it’s either a choice between more increases to get X to zero, or some other type of concerted public or legal effort to curtail X.
The act of taxing X isn’t enough of a signal to conclude the public is using the tax as a reduction effort. But it’s certainly a signal that the public doesn’t want to pay for X via standard revenues—and the public absolutely should not bear the burden for the negative externalities of any X. There’s no doubt a built-in hope that, assuming the costs of X’s externalities are known, taxing Y to pay for X will encourage reduction because—especially if Y is a company—Y wants to keep their expenses low, and really doesn’t want to pay for X. A city levying such taxes, assuming it is even moderately well-managed, will hope to see that the tax revenue for X will hit zero in tandem with X itself hitting zero—the success state[0].
[0]: I’m going to ignore the real-world chance that revenues from X get allocated to previously non-existing programs that then need to find a new source of revenue—but that’s a different problem.
The example I was thinking of is [1] - "Revenue-hungry cities mess with traffic lights to write more tickets [...] cities and towns shortening yellow lights spike the number of tickets, and thereby increase revenue. The profits come at a social cost, as shorter yellow light times have been associated with an increase in car accidents."
In that case, X=car accidents - any public red-light-camera advocacy will say they reduce X.
Of course, you're right to say that a tax on X doesn't prove people dislike X - a tax on income doesn't mean citizens hate income. You could even argue a tax on alcohol means citizens like alcohol too much! But a subset of taxes, such as fines and some sin taxes, are presented in the public discourse as about reducing X rather than making money.
I’d agree that some taxes are presented in public discourse as at least partially being about reducing some X—though fines shouldn’t be lumped in with taxes. Fines are worth considering as a different thing with their own reasoning and goals that often make them distinct from taxes—particularly because fines are punitive and come after known legislated/regulated behavior has occurred.
That worked really well for cigarettes and alcohol. Time to face the truth: these type of taxes are a way to profit off of people's behavior for the sake of the politically connected.
Not married, but in a long-term relationship living with my partner. I listen to them while commuting to work or while doing household chores, and consistently get through 4+ hours/week of podcasts.
I don't find my listening habits change that much when I'm alone, as either way I tend to only listen to them while I'm engaged in some other activity. (When I have completely free time I prefer more interactive activities like games or music.)
If you do get around to reading CA: AQA, you can follow along with this Coursera course (it's taught by the professor I had when I took it at Princeton, and he does a great job teaching it): https://www.coursera.org/learn/comparch
I don't have enough patience for courses. I sort of scan the material for what I really need or want to learn and ignore what's not interesting to me. I can make consistent A's with the benefit of Adderall, but I don't feel comfortable with that.
Your recommendation was very useful and interesting to me, and I bought the paperback. I was surprised that it was cheaper to buy a used paperback than to rent it via Kindle for a month.
It seems like there's an obvious solution to the problem of how to crack down on the types of bot your AI tries to detect, without removing legitimate boots:
Give users the ability to designate their account as a self-reported bot. Accounts designated this way would be identified as a bot in the Twitter UI, and would be exempt from captchas.
I would assume that there was a special policy in place for people working on teams with a requirement for that amount of RAM.
I interned on Chrome in 2013, and at the time all Chrome engineers got a computer with an SSD (which I was told wasn't standard at the time), since they had to build Chrome on their desktops (whereas most other engineers could use Google's distributed build system).
I empathize with that feeling! I recently "automated" washing dishes by upgrading to an apartment with a dishwasher, and it's an amazing quality of life improvement!
I think the parent was saying that they would buy parcels of land where they planned to build stations, and then profit when that land appreciated due to the presence of the station.
The term they're using in Australia when politicians waffle on about an East Coast high-speed rail system that's never going to happen is "value capture".
I haven't used Kotlin, but glancing over their comparison page the one that jumped out to me was that it (almost) eliminates the possibility of null pointer exceptions: https://kotlinlang.org/docs/reference/null-safety.html
Running all n-state machines won't work, because you may have some machines that continue indefinitely, but without repeating. (Remember that while the number of states is finite, the tape is infinite.) No matter how long you run them for, you can't be sure whether they are going to terminate at some point in the future, or if they'll continue forever without halting.
This is why computing BB(n) for arbitrary n is equivalent to solving the halting problem.