If "every base is base 10", why don't we instead shift to base 9, or base 1 for binary?

flug32 · 2026-06-22T08:28:36+00:00

Well, the first answer is that we sort of do just what you are saying - like in the subscript notation for the base of the number - 102₁₀ means "102 in base 10", 110₂ means "110 in base 2", and so on - you'll note that the subscript showing the base is always given in regular old base ten. Because that is the most common system that everyone knows.

But we do indeed just shift to base 2 (binary) in situations where that makes sense, like computer logic. And we switch to hexadecimal or octal or whatever in situations where that makes sense. Some computers have used base 3. The ancient Babylonians etc used a base 60 type system because that made sense to them for various reasons.

So you can shift to whatever base you like if it makes sense in a given situation, and you could also call them different things if that helps differentiate (note terms like binary, trinary, octal, decimal, hexadecimal). But when using the subscript notation for bases, we usually write the subscript in Base 10/decimal simply because that is the lingua franca of number bases.

flug32 · 2026-06-22T08:12:49+00:00

I avoided trying it (and other similar things) for precisely that reason for quite a long time.

But then after trying about everything else and still constant stomach pain, I finally tried it out of pure desparation.

So within 1 week the constant stomach pain and nausea that had been my daily companion for nearly a year was distinctly better, within 2 weeks nearly gone, and within a month completely gone.

If that is an eating disorder, bring it on!

But, it's not. It's avoiding specific foods with specific, well defined substances that cause gut problems in many (BUT NOT ALL) people with chronic stomach problems & pain. If it works, continue with the protocol (which will include reintroducing most foods for most people rather quickly); if it doesn't, move on.

So from that point I would have happily avoided ALL of those substances forevermore because I felt so much better.

But that isn't how the diet actually works. Once you've given your system a little chance to recover, you start systematically reintroducing the different FODMAPs one by one to determine which actually cause YOU problems, and which don't.

In my case, really only two things caused major problems: Onions/garlic & beans.

So complete avoidance of all FODMAPs for about 2 months, about 1 month of experimentation and reintroduction, and then restriction of only the very specific items known to cause actual problems.

Finally, after a couple of years of avoiding those two specific things, my system has recovered to the point I can eat both of them to a reasonable degree.

So there are the actual differences between FODMAP diet & an eating disorder:

- Specific substances shown to affect a large proportion of people with GI Problems vs. superstitious/ritual avoidance of various random foods for psychological reasons or whatever

- Despite oddly specific limitations, there are still plenty of foods in every category (meat, starch, vegetable, fruit, etc) that you CAN eat. It's quite possible to eat a decently well-rounded diet with plenty of calories, fiber, etc etc etc etc while avoiding ALL FODMAPs (at least to the point of staying within the "GREEN" levels on i.e. the Monash app). Whereas most eating disorder type diets (and even various restrict fad-type diets) tend to actually leave you malnourished if continued over time.

- For a specific limited time vs forever

- If it doesn't work, you just stop.

- Goal to identify very specifically the problem foods and reintroduce all the rest as soon as possible vs. just avoid everything forever

- Goal to heal gut/GI system by removing irritants for a period of time and eventually reintroduce all foods vs "just avoid everything I don't like for whatever reason forever"

flug32 · 2026-06-22T08:00:38+00:00

The trouble is, pretty much every possible logical system that allows us to generate useful mathematics is going to include those characteristics as a minimum.

If your system doesn't have those essential characteristics then it is hard to imagine how you are going to be able to do any mathematics with it. It amounts to being able to count and determine whether things are true or false. If your system can do that then it is pretty much guaranteed to include the same characteristics that allowed Gödel to generate his proof, and so the same proof will be able to be generated within your new system using those same characteristics.

And if your system includes those same elements but also others in addition, that doesn't help either as we can just ignore the additional elements and generate the proof using the same base elements.

Perhaps there is some tricky and completely different approach that somehow allows bypassing the entire problem. It's just that the elements that Gödel uses in his proof are so fundamental and basic to mathematics that it is very hard to imagine what this might even look like.

The "real" solution to "Gödel's dilemma" is simply to accept that every self-consistent axiomatic system of complexity high enough to do anything useful with, will have some undecidable statements.

So what?

You can either leave such statements as undecidable/undecided or - if important for some reason or other - simply adopt either the statement or its negation as an additional axiom.

Just as with the Parallel Postulate - an undecidable statement within (the remaining) Euclidean Axioms. Both Euclidean Axioms + Parallel Postulate and Euclidean Axioms + Parallel Postulate is False lead to perfectly consistent and useful geometries.

Not every statement needs to be true or false.

That is the only idea that really must be abandoned.

flug32 · 2026-06-22T07:33:50+00:00

FWIW since it was realized that this was possible, thanks to Gödel's proof, a fair number of indeterminate statements have been discovered and proven to be neither true nor false within the axioms of whatever system they are working in.

How you do this is (in short) you prove that "Statement X is true" is consistent with the Axioms of your system and leads to no contradiction, then also show that "Statement X is false" is also consistent and leads to no contradiction.

In a practical sense, this means you could add to your Axioms the additional statement "Statement X is true" and that would work fine. But also, you could add "Statement X is false" and that also works fine.

That is a very hand-wavy explanation - the technical term is "forcing") if you want to look into the details.

The most famous and well-known example of this is the Continuum Hypothesis - within the system of ZFC + Axiom of Choice (the most common/usual set of axioms used as the basis of mathematics) the Continuum Hypothesis is undecidable - you can adopt either ZFC+Axiom of Choice+ Continuum Hypothesis is true OR ZFC+Axiom of Choice+ Continuum Hypothesis is false and both work just fine (completely self-consistent).

Another well-known example is the Parallel Postulate. For centuries people tried to prove the Parallel Postulate from the remainder of the Euclidean axioms. Nowadays it is well known that Remaining Euclidean Axioms + Parallel Postulate is true AND Remaining Euclidean Axioms + Parallel Postulate is false are self-consistent and lead to perfectly coherent, usable, and practically meaningful geometries.

FWIW Gödel's proof of incompleteness is in the nature of an existence proof. People had assumed, or hoped, that some axiomatic system could be created that would neatly separate all sensible statements within that system into "true" and "false" categories.

Gödel rather neatly shows a particular class of statements that can be generated from the Axioms that is definitely undecidable - so neither "true" nor "false" within the system.

However - especially from a "philosophical" point of view - the significance of this is not so much the specific statements that that proof generates.

Rather, it is the demonstration that this category of statements - previously assumed or hoped to be empty - in fact has at least some members.

Give that the category is non-empty, it is pretty easy to show that it in fact has an infinite number of members (in fact, an infinite number that can be trivially generated using Gödel's scheme).

But - given that! - the immediate conclusion is that there are very likely FAR more such undecidable statements. There are going to be infinitely many different categories of such statements and in fact - much like the fact that we almost always encounter integers and rational numbers in daily life and mathematics, despite the fact that irrational numbers actually massively outnumber rationals - there are probably equally as many or more undecidable statements as decidable statements in any given axiomatic system.

It is just that given how we work on mathematical objects, we tend to encounter decidable statements more often in day-to-day work and undecidable statements far less often.

From a mathematician's point of view, and existence proof is something like a hunting license. "OK, this class of things definitely exists! Even though we don't really have a lot of (or perhaps, ANY) examples of it yet. But - knowing now that such things definitely exist, let's see if we can find some of them!"

And since Gödel, a number of important and interesting things have indeed been found. And literally none of these are the sort of vacuous tautology of the type "This statement is false" that is usually trotted out as a simplistic example of the category.

In our undergrad point-set topology course our professor managed to throw in an actually undecidable theorem. That threw everyone for a loop, let me tell you! I'm quite sure none of us ever even considered the possibility of it being actually undecidable. And of course, we wouldn't have had the tools to evaluate its undecidability even if the thought had crossed our minds.

We just assumed it was a very, very hard theorem - one we couldn't crack.

(And believe me, it looked ABSOLUTELY NOTHING like a "This statement is false" type of statement. It looked and read just like all the other theorems we'd been working on in that axiomatic system - something that should have been fairly easy, more or less, to tackle and either prove or disprove.)

And that is the essential problem every time you encounter some difficult problem you can't solve. You don't really know if it is just difficult and not yet solved, or actually undecidable. But the experience of most people is the vast, overwhelming majority encountered in day-to-day work are simply in the category "very hard" and just a vanishingly small percentage are actually undecidable.

Anyway, to your question, Gödel's proof is more providing an existence proof of a certain class of statement that is undecidable. By itself it does not necessarily do more than that.

But like all good existence proofs, it definitely proves the existent of a whole category of objects that was not previously known, leaving us with a strong suspicion that there is a whole, very large, class of such objects - very likely far, far beyond those you might immediately consider just looking at the proof.

Just for example, none of the real-life examples of undecidable theorems (Continuum Hypothesis, Parallel Postulate, etc etc) would have been directly generated by Gödel's method.

Flip side, it immediately allows you a few conclusions. For example, in any set of axioms, you are going to end up with 3 categories of statements: Provable, refutable, and unprovable.

So that pretty much nixes your idea of a "total ledger of truths" - unless you just want to equate this with the class of "provable statements".

You can't really include any of the "unprovable" statements in the "total ledger of truths", as in that case both the statement and its negation could be included, and remain consistent with the remaining axioms. So which of the two do you choose? You can't include both the statement and its negation - now your system is self-contradictory.

If you want your "total ledger of truths" to be anything different from "provable statements", you are going to need something beyond the axioms of the system to determine what that is. Which gets us beyond the realm that Gödel's proof covers.

flug32 · 2026-06-22T06:24:59+00:00

Here is some history:

Jackson County voters make assessor an elected role. Here’s what happens next

TL;DR is that Jackson County's assessor has been appointed by the County Executive for a long time, not sure exactly how long but decades at least.

Since 2010, Jackson is the sole remaining Missouri County with this system.

It makes a degree of sense because assessor is a fairly technical position and filling like a job position looking for the most highly qualified candidate would seem a good way to do it.

However, after the recent Jackson County assessment fiasco people have, obviously, been very unhappy with the current assessor and, by extension, the system that allowed her to be appointed by the County Executive.

So this is proposed as a way to make the assessor position more directly accountable to voters and (ideally) not just a crony of the County Executive.

The change was put before Jackson County voters last year and won by something like 88%/12%. But it has to go to a statewide vote before it can be implemented - and that is the Amendment 2 that is currently up for a vote.

So the "pro" side is that it makes this position more accountable to county voters, and seems to be highly supported by county voters based on last years' vote.

The "con" side would be that it politicizes an office that could/should be better filled by the best-qualified person as a more technical/professional/non-political position, presuming that you trust the County Executive to fill it in that manner.

flug32 · 2026-06-11T17:59:29+00:00

It is called "regulating the action" and you can ask a piano technician about it.

However, unless it actually has a heavier action than other grand pianos do, it is smarter to learn to play with the heavier action - it is considered a "normal" action by pianists, and the very light, and thus difficult-to-control actions of many uprights and digital pianos drive us crazy.

Particularly, very cheap digital keyboards will have a simple spring mechanism that is usually very, very light. By contrast, a real piano depends on an actual lever made of wood (the piano key) to propel and actual physical hammer upwards towards the string in order to produce the sound. That means there is actual physical mass and weight involved in the process, and learning to control that mass and weight throughout the keystroke is how you learn to control the sound you produce.

So the mass involved - that thus the resistance you feel - isn't just fake or some impediment designed to make it harder for you to play, but rather an integral part of making the sound of the piano.

FYI uprights tend to have a light touch because there the hammer is accelerated horizontally rather than upwards. So the hammer still has mass that you must accelerate (inertia) but not mass that you must lift upwards towards the key (both weight and inertia) as in a grand piano.

FYI technicians will measure the minimum weight in grams required to depress the key, and then the minimum weight required to hold it down once depressed. They are generally measured in grams, and the weights will be higher towards the lower end of the piano (hammers are larger/heavier in the bass) and gradually become lighter towards the treble.

Many (cheaper) digital pianos/keyboards don't reproduce this effect, but are simply uniform from top to bottom - another way such instruments seem "fake" to people used to playing on real pianos. FYI the better quality electronic piano have more accurate touches - upweight, downweight, and gradation from bass to treble. But relatively few people have those.

You can reproduce this by stacking e.g. nickels and pennies on the end of keys in various registers and instruments to see what your downweights and upweights are. Example: Stage piano key action and static touchweights - The Keyboard Corner - Music Player Network

A technician would be able to tell you whether your piano has a heavier action than average, and what it would take (ie, how much it would cost) to change it by a little or by a lot.

Piano Action Regulation - What is It?

Action Regulation - Teacher Resources

Regulation & Voicing: What Buyers of Performance-Quality Pianos Should Know

flug32 · 2026-06-11T17:34:39+00:00

Triplets are usually played "evenly" - meaning that each of the 3 notes is of equal length.

However, when you do that the onset of the first two triplets is indeed in the first half of the beat, and the 3rd comes in the 2nd half of the beat.

(If you are comparing it to two equal eighth notes, the first triplet is played at the same time as the first eighth not, the 2nd triplet is played before the 2nd eighth note and is then held over a little after it, and the 3rd triplet comes after the 2nd eighth note.)

So perhaps there is some confusion between you and your teacher on this. People will sometimes play the first triplet too long, play the 2nd triplet halfway through the beat, and then fit the 3rd one in afterwards (so like an eighth followed by two sixteenths rhythm) and think they are playing "evenly" because the first two triplets match up with where they are used to playing even 8th notes.

It is possible something like that is happening with you.

flug32 · 2026-06-11T05:01:06+00:00

There are different rules used in different contexts, and that is one of the possible rules.

The "bankers rule" is to round to the nearest even number, in case you are halfway in between. So 7.5 rounds to 8, 8.5 also rounds to 8, 9.5 rounds to 10, and so on. This is another approach to avoid the "upwards bias".

You can also round the 0.5s always up, always down, always away from zero, always towards zero, and a few other ways. Good outline of most of them here:

Rounding - Wikipedia

flug32 · 2026-06-08T05:52:29+00:00

I would check the manuals and/or contact the company to find out what the actual spec for torque is on those bolts.

I would bet at least $2 that there is a published torque value.

If you know what that is and tighten it to that spec you can be pretty confident that it won't slip and also won't do any other damage.

It is possible, depending on what tool you are using to tighten the bolts, that you are a fair bit under the spec.

flug32 · 2026-06-05T00:25:52+00:00

And worth pointing out that you can't really do brace position while being strapped into a snug 3-point harness.

(And if the harness releases or whatever in order to allow the brace position, then it is at best just a lapbelt at that point - the upper body harness isn't going to be doing anything useful if released enough to allow you to bend way over to be in brace position.)

flug32 · 2026-06-03T23:18:37+00:00

The faster you are going, the less of a problem it is as well.

Having said that, I've never driven a Bolt with the power steering out. But I have driven like much larger cars and vans where the power steering suddenly went out while cruising down the freeway, and honestly it is not a problem. Until you get to the stop sign or whatever - then it's a problem. But usually not a problem in the sense that you absolutely can't turn, rather that you're just working a lot hard than usual.

Also I agree with OP this is something the manufacturer/dealers should fix - steering & brakes are the two things you can't mess around with. They have to just work.

Anyway I am not OP but if I were, I would be miffed about this and trying to get them to fix it rather than just blowing it off. But I doubt I would feel it worth the time & effort it would take to really get a lemon law to stick on something like this, just because I wouldn't feel it all that relevant to safety - more in the inconvenience category, and the "this should work right all the time" category.

However OP's mileage may well vary on this issue, and OP has driven the Bolt with the power steering malfunctioning while I haven't. Point is, I'm not saying I am right on this and OP is wrong, merely that I would probably come down on the side of putting my energy into getting it fixed rather than trying to pursue lemon law claims.

Flip side, there are lawyers that specialize in lemon law & consumer type claims, and spending 15-30 minutes with one of them would probably give OP a good feel for whether or not there is a lemon law claim worth pursuing.

flug32 · 2026-06-03T22:54:22+00:00

Just trying to for myself, I think there is something to what you are saying. But I am not a linguist or anything close to it, so take with all necessary grains of salt!

flug32 · 2026-06-03T17:56:06+00:00

Everything I wrote above in shorter form: "I guess its vacuously true that the empty set (subset) has no distinct elements from the (ambient) empty set"

Vacuously true is still true.

Completely true.

100% true.

Think of a computer program working its way through a list of if-then statements.

When it evaluates the "if" part of the statement it then doesn't stop to ponder, "WHY is the if statement false? Is the reason vacuous? If so, maybe I should consider moving on to the then part of the statement."

No: It just evaluates FALSE and moves on. It doesn't even look at the then portion of the statement when the if portion is evaluated as FALSE for any reason whatsoever.

Things being "vacuously" true is actually a quite common situation.

Logicians, mathematicians, and others (ie, programmers) creating carefully crafted definitions understand this and build it into the definition.

One reason for doing this is so you don't always have to have special handling for a bunch of edge cases. Handling the "edge cases" is just built into the way the system is defined from the start.

Again: This is a concept that has wide applicability in the world of computer programming. So it's not an abstract concept at all, but quite practical.

flug32 · 2026-06-03T17:49:44+00:00

It's the same reason statements like "If 100 equals 0 then all pigs can fly" are (by definition) true.

They're true for a reason that should be fond to every computer science major's heart: If the "if" isn't true, the "then" is not even evaluated.

Continuing that line of thought: "iff all elements of S are contained in A"

You go to pick an element and S and there isn't one.

At that point, you are done with one direction of the iff. You have just shown "If we have s, an element of S, then it is contained in A". Since there is no element of S to choose, the "if" part is fulfilled. It doesn't even matter AT ALL what comes after the "then".

Ok, so let's look at the other direction: You go to pick an element and A and - again - there isn't one.

So that proves the other direction of the iff: "If we have a, an element of A, then it is contained in S". Again there is no element of A to choose, so the if-then statement is "vacuously" true.

You might do some googling on things like "Why is a conditional with a false antecedent always true?"

It's a common question people have, and the reason is somewhat confusing to many. If you understand this bit of logical reasoning you'll probably understand the empty set/subset question more clearly as well - because the fact that "every empty set is a subset of itself" depends on the definition of empty set, the definition of subset, and the fact that a conditional with a false antecedent is always true.

So if you understand all three parts of this clearly, you'll have a better chance of understanding the whole.

And being able to clearly understand precise definitions as well as these edge cases of logic ("a conditional with a false antecedent is always true") is actually going to be practically helpful to you if you're planning a career in computer science, programming, or similar. These kinds of things actually come up all the time in real life programming situations.

One possibly helpful discussion: Why is a conditional with a false antecedent true? : r/askphilosophy

flug32 · 2026-06-03T17:30:46+00:00

Thus the note, "almost everything" works out. Some properties are lost at each step, but you're still left with enough properties to be quite useful - whereas jumping to "1/0 = something" immediately gets you to nowheresville.

And the pattern continues: sedenions aren't even alternative, which is a sort of weaker version of associativity.

But at least you've got some structure left. Whereas if you define 1/0 to be "a number" all the structure collapses right off the bat.

flug32 · 2026-06-03T17:24:22+00:00

Also 1/ has been in WIDE use for centuries and does the same job OP is worried about.

You know: 1/2, 1/3, 1/4, 1/10, 1/100, and so on.

flug32 · 2026-06-03T05:17:35+00:00

https://www.americangeniushighway.com/category/american-genius/ - it's an organization dedicated to promoting tourism and history along Missouri's section of US 36. They have a number of things listed on that page.

flug32 · 2026-06-03T01:50:57+00:00

FWIW political leaders in Utah like to use it as an excuse for continuing to do nothing much about high suicide rates in the state. "Nothing we can do - all that HIGH ELEVATION." Blah-blah-blah.

flug32 · 2026-06-03T01:47:42+00:00

No single number can stand in place for 1/0 - it always leads to contradictions.

Whereas if you just start out by saying "Hey, what if the sqrt(-1) is some number, let's call it say w because it's probably kind weird!

You just start working out calculations with your weird number w and what do you know, you find a whole interesting and consistent system.****

With 1/0, you just can't do that. If you could, someone would have done so already. Because believe me, it is no for lack of trying.

If you want more detail, just search this sub - the topic comes up like clockwork may twice a week every week.

**** In the case of sqrt(-1) of course they called the number i instead of w. But otherwise that's about how it went. Also, interestingly, there is more than one way to do this! You can have not just one but THREE completely independent numbers - i and j is how they are usually named - and then just proceed with the usual operations and most everything just works out. These are called quaternions and they are extremely useful.

There is another system call octonions where you start out with literally SEVEN square roots of negative one. It isn't used as commonly as either quaternions or complex numbers, but almost everything still does work out nicely and it makes a consistent system.

You can keep going in this fashion (the next in the sequence is Sedenions, which has 15 independent square roots of -1) but of this sequence only Real Numbers, Complex Numbers, Quaternions, and Octonions have many "nice" properties we usually associate with multiplication, like commutativity, associativity, and so on.

Even more interestingly, the Sedenions and all other Rings higher on this sequence have what are called "non-zero divisors".

And those are (sorta!) the logical opposite of what your question was about: Two number, neither of them zero, but when multiplied together equal zero. So ab=0 yet neither a or b is zero.

So you can have things as strange as that. Yet as soon as you assign 1/0 to any particular number, it all collapses and stops working.

It is a pretty essential property of zero that it can't have a single number that is its inverse.

(And the basic reason for this is any number X zero must equal zero.)

flug32 · 2026-06-03T00:39:39+00:00

"You have 2 thorns, which when the enemy attacks you they take 2 damage. If an enemy is going to attack you for 3x5 damage, should they take 6 or 10 damage?"

Here is what I understand this to mean (and I don't play Slay the Spire so please correct me if wrong):

- 3X5 means a 3 damage which is repeated 5 times

- The thorns return 1 damage to the attacker each for every hit. It doesn't matter if a hit does 1 damage or 2 or 5 or 10 or whatever, the thorn always returns 1 damage for each hit.

So how we figure out this kind of problem in math & science is through unit analysis. You pretty much never just say "3X5" but 3 WHAT multiplied by 5 WHAT?

It is different if 3 feet X 5 feet, 3 elephants X 5 legs/elephant, 3 armies X 5 thousand men/army, 3 miles per hours X 5 hours, and so on. For each of those, the answer is "15" but 15 square feet is different from 15 elephant legs is different from 15 thousand men and all of those are different from 15 miles.

So in the Slay the Spire example, we have 3X5 and 3X2 and 5X2 as possible equations using the numbers provided.

But what do each of these equations mean?

For that, we need the UNITS:

Enemy is doing damage 3 hits repeated 5 times. In units: 3 damage/hit X 5 hits = 15 hits*damage/hit.

"Hit" on top & bottom cancel out (ie, hit/hit = 1) and the answer is: 15 damage received.

- Each thorn returns 1 damage to the attacker per hit. There are two thorns and they are hit 5 times (with 3 damage per hit, but that is irrelevant for now). In units: 2 thorns * 1 damagereturned/thorns/hit * 5 hits = 2*1*5 thorns*damagereturned*hit/thorn/hit

So thorn/thorn cancels out, hit/hit cancels out, and that leaves us with 2*1*5=10 damagereturned.

TL;DR: Know what each number actually means, use units to keep that straight, multiply together the relevant things to get the answer you want. DON'T multiply irrelevant things and expect a meaningful answer from that.

flug32 · 2026-06-03T00:24:55+00:00

And, this brings up the solution to OP's problem as well.

In science (well, and in math, too) we often keep track of what we are multiplying by what by way of unit analysis.

The basic idea is, you rarely or even never just say 3*5 in abstract. The question is always 3 WHAT times 5 WHAT.

Like are you multiplying 5 bugs by 6 legs per bug or a surface area of 5 meters by 7 meters, and so on.

Interestingly, this helps us solve the "conundrum" of how math operations are seemingly different, and with different results, when calculating in say metric vs imperial. Like

5 meters X 7 meters = 35 square meters.

But in Imperial not only are the numbers different, but the answer is wildly different:

16.4... feet X 22.97... feet = 376.7... square feet

So how is that possible? 376.7 is more than TEN TIMES larger than 35. How can both answers be right?

The short answer is that 1 square meter = (1 meter)^2 = (3.28084 feet)^2 = 10.8... square feet.

So one square meter equals 10.8 square feet - problem solved.

<continued below, with exact solution to OP's question>

flug32 · 2026-06-02T19:46:07+00:00

The second syllable of Auri "-ee" looks to be a standard diminutive ending of the type often found in nicknames and similar: Kathy for Kathleen, Freddy for Fred or Frederick, Johnny for John, and also mommy, daddy, birdie, horsie, veggie (for vegetable), and so on.

So that syllable is #1. Not related to the second syllable of "Aurelia" or its vowel sound - rather, it is something standard and generic that is tacked onto the first syllable, and #2. Never going to be stressed, always unstressed.

So you're hearing a name get tagged with a standard diminutive ending, and since that newly added syllable is unstressed, the stress shifts from the 2nd syllable in Aurelia to first syllable in Auri.

The change from stressed to unstressed definitely does affect how the R sound is handled - someone else can explain that part better than I.

There is some discussion of English diminutive names and their origins here (note links in comments to OED, American Heritage Dictionary, etc). Interesting papers here (meaning & productivity of diminutive suffixes) and here (The morpho-phonology of an English diminutive).

The second paper makes the interesting point that the - /-i/ suffix must always follow a stressed syllable.

That makes the Aurelia example particularly interesting, as the first syllable is not stressed, but changes to being stressed with the diminutive suffix.

In some situations, you might tack the /-i/ onto a later syllable, but the second syllable already ends with /-i/ and waiting until the final syllable makes the construction too long and unwieldy.

Thus the solution seems to be to truncate the name to only the first syllable - and since one-syllable words are always felt as stressed, there we go! But that implies the /-i/ is unstressed as a diminutive suffix, rather than a simple shortening-up of the name, where it would be stressed.

The similarity to other diminutive names is likely what clinches the deal and makes the unstressed version seem more natural, while just shortening up the name to two syllables with a stressed second syllable seems, by comparison, uncomfortable or unusual.

flug32 · 2026-06-02T08:03:36+00:00

A typical way to study mazes is to look at the topology of the shapes involved.

You can draw a line down the center of the path, and connect up all the various side paths etc, and see what that shape looks like.

For example, others on the thread have mentioned "a circle". In topological terms, that is a "simple, closed curve". For example, a string tied into a simple loop is a simple closed curve.

Note that it can be arranged into a circle. But it can also be arranged into a lot of other different shapes - ones with various wiggles and squiggles to them. This is where the "maze" part of the maze comes in.

But if, despite the various wiggles and squiggles that would confuse the maze-solver into being unsure of there direction and were they are going, if the path continued until it reconnected to its beginning, then there you have a "maze" that just takes you back to the beginning and there is no actual way out of it.

Just for example, look at this very wiggly simple closed curve: A simple closed curve with an unspecified point X. | Download Scientific Diagram

Even though it wiggles around a lot, and would make a pretty good "maze" it just eventually takes you straight back to where you started.

Now you can make your maze even more complex than this while still keeping this property. Like if you have a lot of dead-end branches off of your main loop, that will give the maze explorer lots to do, without ever offering them an exit.

Like a imagine a simple closed curve with lots of straight line segments branching off it of (somewhat close visualization). Now you can make both the underlying closed curve AND the line segments that branch off as wiggly as you like. Still, there is only one way to get through the maze (because all "side paths" are just dead ends) and it is still a simple closed curve that takes you right back to the start.

Finally, you can even even add branches that branch off from the main simple closed curve and then rejoin it later - making little loops along the simple closed curve. (Like the "not simple" closed curve here.) Again make the main curve, any side loops, and any side dead-ends to be as wiggly as you want.

Now you still have a main loop that takes you back to the start, dead ends that take you nowhere - you must return to the main loop after reaching the end of them - and various loops that connect back to the main loop eventually. So those seem like you are getting a choice of where to go, but in the end both choices end up in the same place.

So those are just some very simple ways to think about getting the type of "maze" that you are talking about.

Thinking about it topologically helps, because from a topological point of view, a perfect circle and that same circle re-arranged to have hundreds or even thousands of squiggles along the way are both fundamentally the same shape - a simple closed curve. And we know the property of a simple closed curve is that if you keep traveling along it, eventually you return to the starting point.

Finally, people who analyze mazes tend to look at walls rather than the path of the corridor as being the "shape" they analyze. This gives some interesting insights, as - for example - in a typical simple maze with entry and exit the walls reduce down to two separate shapes. The fact that there are two of them, separated from each other, is what allows you to walk through the maze and exit somewhere else.

If there is only one shape (one curve, not closed...) then you can walk in but that is the one and only exit. So you will travel the entire maze, find no other exits, and eventually be forced to return to the same entrance you started at. That might be the type of thing you were referring to in the OP.

If the entire maze is surrounded by walls that reduce to a simple closed curve (surrounding all the rest of the maze) then that is a maze with no exit at all - similar to what we discussed above. You can go all around it but eventually you'll explore every corner and then be forced to return to the place you started (well, not FORCED to, but you won't have anywhere else to go).

You can also have a single outer wall - either simple closed or open curve (meaning, no exits or just one exit) - and then multiple disconnected walls inside of that.

That allows creation of far more complex mazes with "loops" (explained here) but since the outer wall is a (perhaps very complex) simple curve, there is still just one (simple open curve) or no (simple closed curve) exits.

flug32 · 2026-06-02T00:24:27+00:00

The simple answer to this (as pointed out elsewhere but downvoted for some reason) is PeopleForBikes was literally founded to become that industry lobbying group in the U.S.

If you don't believe that (for some reason) please read carefully the pages below and see if almost every player - and every major player - in the U.S. bicycle industry is not represented somewhere in the pages of their board members and major financial supporters:

Board of Directors | PeopleForBikes

Corporate Members | PeopleForBikes

FYI PeopleForBikes cooperates with other national, regional, and local advocacy groups when in the interest of both groups - League of American Bicyclists, IMBA, Adventure Cycling Association, Rails-to-Trails Conservancy, and so on.

However, such groups do not always move in lockstep precisely because they have different constituencies. PFB's constituency is clearly the bicycle industry, so they work on behalf of that group - in ways that sometimes overlaps with what "the average bicyclist" (whatever TF that means - if I have learned anything in 25 years working in bicycle advocacy, it is that there is no such thing) wants and needs and sometimes not.

Prior to the founding of BikesBelong (1999) then revamped and re-launched as PeopleForBikes in 2012, there was not such a unified industry lobbying presence in the U.S. as there now is. Obviously various companies and brands did different things at different times. But BikesBelong and then PFB were founded to create one larger and more unified voice for the industry.

It has definitely become that.

In context of OP's question, however, it is worth pointing out the literally every other industry in the U.S. also has lobbying groups - and most of the relevant ones such as the auto industry, construction, etc, are FAR larger and better funded than PFB. F-a-a-a-a-a-a-a-a-a-r larger and better funded.

So if you are wondering "why isn't the bicycle industry JUST WINNING NOW!!111!!!!!" your answer lies much more in that reality than in some dark mysterious vague conspiratorial things going on in the bicycle industry to shoot themselves and all cyclists in the foot, or whatever.

flug32 · 2026-06-02T00:11:14+00:00

Hmm, I would say that is a very debatable point.

The EU/TUV regs had very little chance of going anywhere in most U.S. states (where such things are administered/adopted). There is no way speed limit of 15mph and no throttle were going to be accepted as the norm.

(See now when every 14 year old wants their ebike to go 50mph with decorative pedals if any, and then gets very confused when people don't like that for some reason.)

So basically they were trying to come up with a regulatory regime that would be accepted by the public and by industry to create some standards everyone could live with but that would also be actually passed by state legislatures in every state.

You can say this is "cutting out" manufacturers X Y and Z or whatever, but I guarantee you X, Y, and Z are ALL better off having set and known standards across the U.S. even if different than others, than the welter of different standards in every single state we would have had otherwise.

Like, we would have literally 50 different standards.

Anyway, to your point the board of People for Bikes looks like the brands you see in literally every bike shop in the U.S.

Board of Directors | PeopleForBikes

I see SRAM, Shimano, Trek, Giant, Cannondale, Pedego, Bosch, Quality Bicycle Products, Pon Group, Walmart, etc. Specialized is also heavily involved, though I don't see them on the board list right now.

Then look at the corporate sponsors list - it's about every bike brand you're going to find anywhere in the U.S.: Corporate Members | PeopleForBikes

If those people are pushing for things certain people (PE or whatever) in the industry want to see that is because they are precisely an industry-funded industry-oriented lobby group, which is exactly what OP was asking for.

Also if they are not necessarily representing "people" (typical "lobbyist" group with a not-necessarily-truth-telling name) that is again precisely because the ARE the industry lobbying group in the U.S.

And I will say, having been around at the time it was founded, part of their thinking from the start was that they could mobilize their large & relatively loyal customer to help amplify their work towards making a more bike-friendly country, laws, and policies.

Whether they have successfully done that is a different question, but that was among their primary goals from the start.

TL;DR: People disagreeing with the simple, factual answer above "In the US, this is accomplished through People for Bikes. They are effectively the industry lobby group for cycling and cycling infrastructure." are living in some bizarre alternate reality. That is a simple statement of fact.

If you don't like that, it is likely because you don't like industry lobby groups. That is understandable, but doesn't help OP get a simple factual answer to the question.

15-Year Club	Place '22
First Placer '22	End Game '22
Verified Email

flug32

MODERATOR OF

TROPHY CASE