Depends on your frame of reference. When traversing the surface of a globe, your described concept of a straight line isn’t intuitive.

Ah shit. Reading is hard sometimes.

A pint is 568ml.

Edit: the extra 30ml might be accounted for with the patented Guinness widget, a little ball of nitrogen gas that ruptures and forms a foamy head when the can is cracked.

GPT4 is wrong and it doesn’t require a price per litre comparison to prove it.

4 cans at 440ml cost £4.50. Therefore 12 cans at 440ml cost £13.50, £1.50 less than 12 cans at 330ml.

This is a great observation. I just generally think a world that poses questions such as “why haven’t wizards fixed this” is more interesting than a world with arbitrary precision measurements and walk-in cancer curing services in every hamlet.

Some good points. I’m just going to continue this discussion because it’s interesting and it helps me prepare my games to consider these things.

1: Universal answers don’t necessitate universal acceptance, and it can make for more interesting lore when that’s the case. As an example: in the lore of Legend of the Five Rings, it’s common knowledge in the Empire that the official map of the Empire has a massively inconsistent scale, with journeys of similar charted length having up to a threefold difference in travel time. Savvy travellers know to plan accordingly, but no one would ever question Imperial doctrine, as the charting of the Empire was an act of a very real and tangible living god. This is where I got my praying at every temple comment; it’s common for people to avoid accidentally badmouthing the Empire by saying “I took longer than expected as I took every opportunity to honour my ancestors at every shrine on the road.”

1b: The pantheon of the Forgotten Realms is ever expanding and there are gods in that pantheon that are opposed to Mystra, as well as luddite gods who are oppose the gods of innovation such as Gond. Gondians certainly promote the advancement of science, and Mystrans and Oghmans promote the advancement of magic to a very certain extent, but there are gods in the pantheon who would task its worshippers with direct opposition of these missions, if for nothing else than to piss off their rival god.

2: This comes back to point 1. Different states will have their own standards of measurement, often using the same name, and the usage of these standards are very often more political than logical. A famous example from history is Napoleon’s height. Napoleon was “5 foot 2 by the French measurement and 5 foot 6 by the English measurement,” which made him a French adult man of average height. It was a common political tool to report him in the British Press as 5 foot 2, thus implying that he was short of stature.

Imagine the compounding issue of different species interacting in the Sword Coast. A human-majority patriarchal city state may define an inch as the average length of the the second knuckle of an adult human male’s middle finger, while an elvish-majority patriarchal enclave may define it exactly the same but for an elf’s finger. These slight discrepancies aren’t an issue until they can be exploited for political gain; an elvish embassy may be established at a distance no closer than a mile to the Palace of the Magistrates, but there’s roughly a 10 human-yard difference between an elvish mile and a human mile.

If someone casts a spell asking for a measurement and they are told “10 miles,” is that 10 miles from their perspective, 10 miles from the perspective of whoever invented the measurement spell, 10 miles according to some third “universal” perspective, or something else entirely?

3: Again from my previous comment, the precise limitations of spells are assumptions and generalisations made for the purpose of codifying into a game. In the actual fiction, spells are quite variable dependent on the caster and their abilities. The only general assumption we can actually make is that a set of repeatable actions yield roughly the same result: if you rub a glass rod with a bolt of fur and sing the chorus of Tubthumping backwards, lightning appears. The reason that in the current edition of the game we have somewhat concrete descriptions of spells is that we as the players require a certain level of abstraction in order to play the game; The GM shouldn’t need to have an idea of wind speed, the aerodynamics of the flier, and all other forces in order to make a quick decision to determine how the flier flies. Some randomness of outcome is still evident on the modern game rules, such as the damage from spells being random and spells like sleep affecting a random number of creatures. Older editions were a lot more meticulous with this.

Edit: specifically tackling Wish, assuming even a perfect casting would not yield a perfect map. Check out the Coastline Paradox for a real world example of how natural bodies such as coastlines fail to have well-defined length. No amount of arbitrary precision measurement is going to change the facts that coastlines and waterways have fractal dimension.

4: At least in 5e rules as written (and I dislike this and usually houserule it when forced to play D&D), with the exception of protection scrolls, reading a spell scroll requires caster to have the given spell on their spell list.

There are a couple things that need addressing in this line or argument.

First is a certain assumption of rigour in logic; rigour in proof was a very nebulous thing until concrete efforts to codify rigour in the 19th century. We used to simply assume Euclid’s Elements was true because it was old, reasonably argued, and some easier results were verifiable. There’s no guarantee that Forgotten Realms wizard, who lives in a magical late renaissance analogue, would hold a scientific philosophy similar to our modern philosophy, rather than having a scientific philosophy similar to that of a renaissance scientist.

Supplementary to the first point, there is also the question of religion. Given how much the Catholic church impeded scientific progress that challenged their worldview, we could expect the many churches of the FR pantheon - many with opposed views to one another - to interfere with scientific progress.

The second point comes from the measurement units used in the rulebooks of the game. Unless we’re accepting that FR society independently came up with the imperial system or a measurement system that translates rather cleanly to the imperial system, we can assume that the measurements in the game book are approximations for the purpose of ease of use to the player. I doubt a wizard in canon is calling a distance “about 10 feet” and Ed Greenwood is just doing the common fantasy thing of “translating their language and measurements to a form understandable by earthlings.”

The third point is the Wish issue. The Wish spell is undeniably the strongest spell in the canon and requires a wizard of tremendous power to cast. Given the hubris of powerful wizards in the Forgotten Realms and fantasy in general, it’s doubtful that a wizard would use their one 9th level spell per day to either altruistically progress the knowledge of the realm or to improve mapping methods to sell a better map. If a wizard were to use their strongest spell for something as trite as monetary gain, That same knowledge gained from a Wish could be hoarded and exploited for substantial personal gain.

Finally, there’s the time commitment. You mentioned using Find Familiar to measure distances but that still requires a wizard in the field, essentially using a sentient trundle stick. Mapping requires a ridiculous level of effort from a huge team of surveyors, and is almost always backed by a government. The Sword Coast, where all the main plot happens in FR canon, is a handful of city states and frontier towns in a wild region. The Open Lords of Waterdeep would probably have hired a set of wizards to accurately calculate the acreage of farmers fields in the immediate vicinity. For something like the distance from Baldur’s Gate to Elturel, distances would be approximate, about 200 miles or 10 days travel with time to pray at every shrine.

That’s what I’ve been saying. I’ve only ever been calling bad things bad. I was saying that fish and chips from a take away is bad and shouldn’t be recommended as some exemplar of British cuisine

Sure, if you insist. Though the barrier for “nice” is really low. If you like beer that isn’t Stella or Carling, you’re not calling beer trash in general.

I like fish and chips from an actual restaurant or homemade. With the exception of the Magpie in Whitby, which is a restaurant with an attached take away, every take away fish and chips I’ve had has been flavourless chunks of varying textures.

It’s fine now but some “staples” of our cuisine are trash. If you value your low blood pressure, don’t go into threads about people asking for food recommendations while visiting Britain. It’s just full of people recommending actual garbage like fish and chips from a take away. Are people delusional? I’ve been to dozens of chippies across the country, and save one meal at the Magpie in Whitby, I’ve never had a chippy tea that’s lived up to expectations.

Recommend a good haggis or something rather than the bland meme food.

Sorry if you’ve seen this already, as your comment has just come through. The two sets are the same size, this is clear. This is because they’re both countably infinite. There isn’t such a thing as different sizes of countably infinite sets. Logic that works for finite sets (“For any finite a and b, there are twice as many integers between a and b as there are even integers between a and b, thus the set of integers is twice the set of even integers”) simply does not work for infinite sets (“The set of all integers has the same size as the set of all even integers”).

So no, it isn’t due to lack of knowledge, as we know logically that the two sets have the exact same size.

The niche story/support communities were a real staying power for me until they started taking a nosedive ~5+ years ago. Suddenly power-users were showing up, posting their creative writing exercises in all tangentially related subs, and it got ate up because over the top drama is more entertaining to some than true (or at least very plausible) stories.

It began with users policing others. You called out a fake story and you got half a dozen people playing devils advocate asking how you knew the story was fake. The poster being a serial poster who has dozens of box-ticking ragebait stories (per week) across multiple subs isn’t a clear enough indicator that this is a creative writing exercise for them.

Before long, subs were seeing much more engagement due to copycats and drama seekers; suddenly the rules prohibited calling out fake stories. Suddenly your support subreddit for offloading about your abusive parents has turned into the personal playground for creative writers with 58 part epics about their mother getting arrested for the fifteenth time for brandishing a knife at a baby at the family dinner.

I’ve already unsubbed from a community on Lemmy because I’ve seen one creative writer is cross-posting to Lemmy under the same name.

I admit the only time I’ve encountered the word utility as an algebraist is when I had to TA Linear Optimisation & Game Theory; it was in the sections of notes for the M level course that wasn’t examinable for the Bachelors students so I didn’t bother reading it. My knowledge caps out at equilibria of mixed strategies. It’s interesting to see that there’s some rigorous way of codifying user preference. I’ll have to read about it at some point.

Actually, the commenter is exactly right. The real line does contain the open interval (0,1). The open interval (0,1) has the exact same cardinality as the real numbers.

An easy map that uniquely maps a real number to a number of the interval (0,1) is the function mapping x to arctan(x)/π + 1/2. The existence of a bijection proves that the sets have the same size, despite one wholly containing the other.

The comment, like the meme, plays on the difference between common intuition and mathematical intuition.

Yes, there are infinities of larger magnitude. It’s not a simple intuitive comparison though. One might think “well there are twice as many whole numbers as even whole numbers, so the set of whole numbers is larger.” In fact they are the same size.

Two most commonly used in mathematics are countably infinite and uncountably infinite. A set is countably infinite if we can establish a one to one correspondence between the set of natural numbers (counting numbers) and that set. Examples are all whole numbers (divide by 2 if the natural number is even, add 1, divide by 2, and multiply by -1 if it’s odd) and rational numbers (this is more involved, basically you can get 2 copies of the natural numbers, associate each pair (a,b) to a rational number a/b then draw a snaking line through all the numbers to establish a correspondence with the natural numbers).

Uncountably infinite sets are just that, uncountable. It’s impossible to devise a logical and consistent way of saying “this is the first number in the set, this is the second,…) and somehow counting every single number in the set. The main example that someone would know is the real numbers, which contain all rational numbers and all irrational numbers including numbers such as e, π, Φ etc. which are not rational numbers but can either be described as solutions to rational algebraic equations (“what are the solutions to “x^2 - 2 = 0”) or as the limits of rational sequences.

Interestingly, the rational numbers are a dense subset within the real numbers. There’s some mathsy mumbo jumbo behind this statement, but a simplistic (and insufficient) argument is: pick 2 real numbers, then there exists a rational number between those two numbers. Still, despite the fact that the rationals are infinite, and dense within the reals, if it was possible to somehow place all the real numbers on a huge dartboard where every molecule of the dartboard is a number, then throwing a dart there is a 0% chance to hit a rational number and a 100% chance to hit an irrational number. This relies on more sophisticated maths techniques for measuring sets, but essentially the rationals are like a layer of inconsequential dust covering the real line.

There’s no problem at all with not understanding something, and I’d go so far as to say it’s virtuous to seek understanding. I’m talking about a certain phenomenon that is overrepresented in STEM discussions, of untrained people (who’ve probably took some internet IQ test) thinking they can hash out the subject as a function of raw brainpower. The ceiling for “natural talent” alone is actually incredibly low in any technical subject.

There’s nothing wrong with meming on a subject you’re not familiar with, in fact it’s often really funny. It’s the armchair experts in the thread trying to “umm actually…” the memer when their “experience” is a YouTube video at best.

I like this comment. It reads like a mathematician making a fun troll based on comparing rates of convergence (well, divergence considering the sets are unbounded). If you’re not a mathematician, it’s actually a really insightful comment.

So the value of the two sets isn’t some inherent characteristic of the two sets. It is a function which we apply to the sets. Both sets are a collection of bills. To the set of singles we assign one value function: “let the value of this set be $1 times the number of bills in this set.” To the set of hundreds we assign a second value function: “let the value of this set be $100 times the number of bills in this set.”

Now, if we compare the value restricted to two finite subsets (set within a set) of the same size, the subset of hundreds is valued at 100 times the subset of singles.

Comparing the infinite set of bills with the infinite set of 100s, there is no such difference in values. Since the two sets have unbounded size (i.e. if we pick any number N no matter how large, the size of these sets is larger) then naturally, any positive value function applied to these sets yields an unbounded number, no mater how large the value function is on the hundreds “I decide by fiat that a hundred dollar bill is worth $1million” and how small the value function is on the singles “I decide by fiat that a single is worth one millionth of a cent.”

In overly simplified (and only slightly wrong) terms, it’s because the sizes of the sets are so incalculably large compared to any positive value function, that these numbers just get absorbed by the larger number without perceivably changing anything.

The weight question is actually really good. You’ve essentially stumbled upon a comparison tool which is comparing the rates of convergence. As I said previously, comparing the value of two finite subsets of bills of the same size, we see that the value of the subset of hundreds is 100 times that of the subset of singles. This is a repeatable phenomenon no matter what size of finite set we choose. By making a long list of set sizes and values “one single is worth $1, 2 singles are worth $2,…” we can define a series which we can actually use for comparison reasons. Note that the next term in the series of hundreds always increases at a rate of 100 times that of the series of singles. Using analysis techniques, we conclude that the set of hundreds is approaching its (unbounded) limit at 100 times the rate of the singles.

The reason we cannot make such comparisons for the unbounded sets is that they’re unbounded. What is the weight of an unbounded number of hundreds? What is the weight of an unbounded number of collections of 100x singles?

In short, yes.

This kind of thread is why I duck out of casual maths discussions as a maths PhD.

The two sets have the same value, that is the value of both sets is unbounded. The set of 100s approaches that value 100 times quicker than the set of singles. Completely intuitive to someone who’s taken first year undergraduate logic and calculus courses. Completely unintuitive to the lay person, and 100 lay people can come up with 100 different wrong conclusions based on incorrect rationalisations of the statement.

I’ve made an effort to just not participate since back when people were arguing Rick and Morty infinite universe bollocks. “Infinite universes means there are an infinite number of identical universes” really boils my blood.

It’s why I just say “algebra” when asked what I do. Even explaining my research (representation theory) to a tangentially related person, like a mathematical physicist, just ends in tedious non-discussion based on an incorrect framing of my work through their lens of understanding.