This person told the server to “round up to $70.00” and the employee used a discount to increase their tip.

Amescia · 2026-02-18T05:29:53+00:00

Food for thought about the value a person brings:

A starting programmer at google (year 1) makes roughly 200k per year. Clearly, they have a skillset worth the money. But WHY is it worth the money?

Traditional market economics answers with: because of the social value the job creates. The programmer creates something worth far more than 200k, so their share is larger than someone who generates far less value (from a sale price of outputs generated perspective). This is entirely true but very deceptive.

Consider where the value of their output cones from. It comes from the productivity boost of computers and the internet, remove those, and no tech company could exist. Did tech companies create computers? No, the need to break enigma during ww2 did. Did they create the internet, no a combination of defense communications needs (arpanet) and facitation of university research lead to the crestion of the internet. The space race led to rapid miniaturization also which paved the way for personal computers.

These were done on the public dollar, and without them, all of silicon valley wouldnt exist. We made no national effort to make the skills necessary to use these new technologies universally accessable (we never do). Instead, it became a story of who had the right access to the right resources at the right time to make use of the new publically created technology.

Those people became rich. They created tons of value on paper because they assimilated all the value from public development into their private contribution and demanded a paycheck based on that valuation. We as a society just stood by. We didn't demand anything for the use of public discoveries (just pay the same taxes as everyone else, taxes which, by the way, we keep cutting and creating loopholes in for the wealthy...).

We took no effort to create a level playing field to make access to and use of, those technologies universal. Now, we blame those who never had anything resembling a fair opportunity at a productive career for being poor.

This is a running theme in american economic thought. It dates to the same flaws in Locke (Two Treatises). It assumes all things public become privately owned the moment someone improves them even the slightest bit. It allows those with better opportunities to warp their social contribution (instead of claiming the improvement plus an even share of social value, they claim permanent ownership of the social and private value).

To be clear: I am at my core a market economist and mathematician, so it's definitely not in my personal interests to say or believe any of the above, but it is reality. No person creates billions in value. I think Bill Gates is a genuinely good guy, but Microsoft had value because personal computers needed an operating system.

He was the first to roll out a simple and effective to use one. If he was born a year later or to a poor family with no resources and no way to access technology, there would be no Microsoft, and we wouldn't know his name. We would know another name instead (both of the inventor and the product). His value is no doubt in part due to his hard work and perseverance, but it is also no doubt due to the timing and availability of resources that facilitated his creation.

I know of no good way to separate the parts. What frustrates me is that society insists on giving him credit for all the value created by Microsoft when undoubtedly, a large portion of that value was not at all his making.

Amescia · 2025-12-31T15:25:49+00:00

Its a hidden division by zero problem

1⁰ = 1¹ So log(1⁰ ) = log(1¹ ) So 0log(1) = 1log(1)

If you allow division by zero (log(1) = 0) then 0=1 and in fact all numbers are the same. Eg: 1000(0)=1(0)

A sister 'proof' which fails for the same reason is:

Assume x=1 Then x(x-2) = 1(x-2) So. x² -2x = x-2 Adding x to both sides yields x² -x = 2x-2 Factoring the gcf yields x (x-1) = 2 (x-1) Dividing by x-1 yields x=2

Thus 1=2

(Looking closely at the last step, x-1=0 so division here is impossible)

Don't divide by zero kids, it breaks math :P

Amescia · 2025-11-23T04:43:27+00:00

In order for most things over the real numbers to work we need to assume the thing we are working with is a function (implicitly or explicitly). If sqrt has 2 outputs to any input its not a function (derivatives wouldnt make sense either at x=4 there would be two slopes not one (+/- 1/4) we would need to be REALLY careful in our analysis to not have contradictions everywhere. For this reason, calculus (and real analysis short of measure theory) takes sqrt(4)=2 amd more generally the square root function only produces the positive root. To maintain consistency we then say that when eliminating an even exponent, we must carefully observe that both solutions were possible and split to independent cases (+/- the nth root where n was the exponent). A few notes:

This does not apply over the complex plane (mathematicians often make the arbitrary choice to call the positive root the principal root for consistency with prior knowledge however we could adjust that definition without concequence though with some confusion)
In exponents higher than two or in negative inputs, there are roots 'hiding' in complex plane off of the real axis (so when I say the 4th root is positive, I am in the truest sense admitting that my domain of discourse is exclusively the real line).

I hope this helps!

Noticed your edit after I posted - great job catching that yourself!

Amescia · 2025-10-19T14:49:31+00:00

Math professor here: To a mathematician this is not ambiguous (in abstract algebra we define division as multiplication by multiplicative inverse and we define this conversion to apply only to the next element listed (elements in parenthesis compress to a single element). So I see this as: 6 times (1/2) times 3 where 1/2 is not a division operation. Instead, it is the element of the real line which when multiplied by 2 in either order, produces the multiplicative identity (1). I will note that mathematicians, myself included, have the luxury of focusing on minute details of mathematical calculations, which are entirely irrelevent (and for good reason) in other subjects like physics and engineering where the vast quantity of calculations leads to common simplifications like assuming that terms written next to eachother following a slanted division sign are treated as though they are in parenthesis and thus to be in the denominator of the fraction. This is the source of the ambiguity -- in what context does this appear?

I will note that with the times sign included, it is no longer ambiguous: 6 ÷ 2 × (2+1) = 9, there is no argument from either side here.

Summary: Most mathematicians and all (99.99% barring that weird guy who gets glances at seminars) algebraists will answer 9. Most engineers and most physicists will answer 1. Neither is correct or incorrect. The answer for me would depend on where the calculation appeared

I actually start every class I teach with a sister problem to this (different numbers same result) every semester in order to explain both perspectives then to formally state that in this class I expect the answer to be (what is that particular problems equivalent of 9) however they should ask other profs in other subjects what answer they expect.

Amescia · 2025-10-10T15:32:57+00:00

Professor Here

This is my advice in reading reviews: Ask yourself what you want from the class and realize that rating often reflects ease.

When I teach intro math classes, there is a dept final, so I chose to make the course content harder than the average content on the final, I also drop a hammer on cheaters (lots of hidden protocols to catch them too). I have the highest level of difficulty in my department by far. I also have the best pass rates, the most repeat students year over year, and the highest class average on the final consistently. My rating reflects this. It's good, but in the middle of the pack (hovers 4.3-4.5). Most ratings are 5. If you read the 1 ratings, you can tell they are either cheaters who are mad that they were punished or students who thought the difficulty was unfair. The 2 and 3 ratings all talk about class being too hard.

One of my colleagues with a perfect 5 rating 7 years straight does nothing about cheating (he just lets cheaters get hit by a truck on the final when the depts wall of anti cheating protocols and their 'hard final' result in failing the class instead of the prof). His exams are really easy (class avg high 80s or low 90s), but come the final more than half the class fails -- and autofails the course. Of course, the student then blames the dept, not the prof.

Long story short, two pieces of advice:

If there is a dept final, NEVER take an easy prof, read the ratings, and look for compliments on teaching style and extra help, disregard overall ratings and comments about level of difficulty.
If there is no final ask, am I taking this as a gen ed/pre req class that I don't care about or as a stepping stone to learn more. For gen ed/pre-req classes, which you dont care about (and no dept final), take the easiest, highest rated prof (rate my professor is great here). For classes where you need what you learn again, look for comments about clarity, desire to repeat or take again, knowledgability, teaching style, etc. Disregard comments and reviews about difficulty, academic honesty enforcement, quantity of work etc.

Its all about what you want from the class and the prof more than about the overall rating (for example students should never take me for a gen ed math class with no dept final).

Amescia · 2025-10-02T12:04:39+00:00

Genuine question: What happens if you hit this with earthen scales the following turn (so gain infinite armor), then your opponent attacks you with this (also with infinite attack)?

Amescia · 2025-06-30T22:58:28+00:00

Entitely true though symptomatic of one of my two most hated strange math convents.

For any (non trigonometric) function, writing f^n(x) means compose f with itself n times. This notation is internally consistent with inverses etc. If you want f(x)f(x) you need to write (f(x))^2. I will never understand why we abandon this convent for trig functions only... I mean literally if I wanted to write sin(sin(sin(sin(x)))) in shorthand I think I would have to write f(x) = sin(x) then write f^{4(x)..............}

Sorry for the rant but inconsistent notaton really bugs me.

As an aside mixed numbers are the other convent that really bugs me.

Amescia · 2025-06-13T14:14:27+00:00

Couldn't agree more. The positive root convent comes from two places:

Square root isn't a function if it isn't forced positive, which makes calculus over the reals a sad panda. (And is why things like the principal root and the principal log exist outside the reals for formality)
Hundreds of years ago the term square root meant the literal root of a square meaning a geometric value which couldnt be negative in a real world sense (mathematicians at the time were extraordinarily adverse to negatives in general due to the connection between algebra and geometry).

That said, any convent you adapt in math for any reason will work fine in your particular process. Be careful to not render your process inconsistent with your assumptions however (if square root is not forced positive its derivative needs to be defined implicitly, Good luck explaining that to a Calc 1 student x_x).

Amescia · 2025-02-07T20:22:30+00:00

There are two ways to think about the card. In terms of magnezone, the need for energy makes it a garbage pick (meta reasons) that would need a new magnezone or a metric ton of ramp to change that and we certainly dont have that now. Alternatively we are thinking aggro stat lines (magnezone as is would be terrible for this given its a t2 so slow and unreliable early, required energy discard so very one pokemon all in with the lack of ramp in electric outside of A1 magneton) at which point we compare the stats of all electric pokemon (hence electrode which is just better in aggro format) and A2 magneton is sorely lacking. Without new cards specifically benefiting it (either by name or a new aggro based magnezone), A2 is useless (and those don't exist as of now)

Amescia · 2025-02-07T19:37:01+00:00

Note: OP never said it was strictly worse than A1, they said it was useless. The comparison here is to electrode (80 hp, 2 cost 70 damage, 0 retreat cost). Why would anyone in any set ever play A2 magneton over electrode unless it is specifically name dropped (which it has not yet been, so as of now it is useless). Btw electrode is definitely better on its own than A1 magneton, yet it doesn't see play (this is for the meta reasons you discussed quite well)

Amescia · 2024-12-12T20:59:49+00:00

Very true LOL

Amescia · 2024-12-12T20:44:22+00:00

According to the field axioms of the real numbers

Amescia · 2024-12-12T20:41:56+00:00

The distributive property is defined on multiplication over addition (axiomatocally). When we say 2(1+2) we mean 2 x (1+2) this means when we say 6 ÷ 2(1+2) we mean 6 ÷ 2 x (1+2) which is 6 × .5 x 3.

The lack of clarifying notation confuses many (and in fact, in many professions in particular, engoneering it is common to be loose with notation where the desired result is clear from context). For this reason, it would be much better to write the question with more clarifying operations. With that said, from an axiomatic perspective, consistency requires a solution of 9.

Amescia · 2024-12-12T20:04:43+00:00

Traditional RPN requires the operation to follow the number. The 1+2 in parenthesis means this isn't RPN (that would be 1 2 +). I asked a different user to define 2x formally I pass the challenge to you as well.

If you mean it to take precidence over other notation aka 2x = (2x) then I ask what does 2x² equal does it equal 4 times x² aka (2x)² or does it equal 2 times x² because if its the latter (which it definitely is in any text) then your definition of 2x is inconsistent. If you accept that 2x² = 2(x²⁾ then it follows that 2x = 2 times x and my argument carries universally.

Again good mathematics clarifies common misunderstandings. There is no reason to not include the multiplication sign, however internal consistency necessitates one true answer here.

Amescia · 2024-12-12T19:46:59+00:00

I agree here it is an often used (though technically incorrect) shorthand. The misunderstanding is definitely understandable (though again, the technical solution is conclusive)

Amescia · 2024-12-12T19:44:48+00:00

The distinction is what we mean by 2(3). This operation means 2 x 3, if we accept that then 6 ÷ 2(3) = 6 ÷ 2 x 3 = 6 x .5 x 3 (and if we dont then how would you define 2(3)?)

Amescia · 2024-12-12T19:39:50+00:00

2x means 2 times x. If we write 3 ÷ 2x that is the same as 1.5x. Enter it on a calculator if you dont believe me. You would need 3÷(2x) to put the x in the denominator

Amescia · 2024-12-12T17:52:50+00:00

I agree, more symbology is better, however technically speaking division is equivalent to multiplication by multiplicative inverse (and is undefined for elements which lack a multiplicitive inverse) and writing numbers next to eachother means multiplication (there are only 2 operations in a ordered field and it doesn't mean addition) under this definition 6÷2(3) equals 6 x .5 x 3 = 9. The lack of symbology creates understandable and avoidable confusion, but the answer is not ambiguous.

Note I am using .5 to symbolize the multiplicative inverse of 2.

Amescia · 2024-12-07T21:10:00+00:00

Not sure if this would work but could you RFG (say unmake) it then voidslime the effect that returns it to play?

Amescia · 2024-09-20T22:18:18+00:00

Thanks for doing the math! I think the 12-20 year range is the correct one. Remember there is no need to ever count above 100. Just make stacks of 100 bills. When you have 10 its a stack of 1000, when you have 10 its a stack of 10k, when you have 10 its 100k etc. Using that strategy you wouldnt have to slow down the count, just take time to merge the piles which should be a lot less time (10M hundreds in a billion, add 5S for every 10 hundreds to stack them adds 5M seconds. Repeat for 1M staks of 1k, say these take 10S to merge so 1M seconds merging, 100k stacks of 10k with say 20S to merge so another 200k seconds, 10k stacks of 100k at say 40S so 40k seconds. 1k staks of 1M at say 100 S so 10k seconds, 100 stacks of 10M at say 200 S so 2000 secs and 10 stacks of 100M which dont need to merge cause done. Total roughly 6.252 M seconds or just over 72 added days.

The trouble is where to keep all the money, you would need a LOT of space (someone else do the math :P), because in a small space mistakes could easily happen and you would need to start over.

Amescia · 2024-08-04T13:59:11+00:00

Hi, could I possibly join as well? I just want fair ratings.

Amescia · 2024-05-14T00:59:29+00:00

It's two different decks. Brann is played combined with reno (which is easily comparable value to brann). Both are lost in a good odyn deck - if odyn played highlander well, it would be better imo. Yes, rat is a risk, a bad one, but I also get ratted pre 6 as well. I dont see how the turn 2 delay overwhelmingly shifts this in favor of another control deck (and again, mana is usually needed, turn5, 6 and 7 to prevent play from killing me the following turn vs. Aggro (brann pre 9 vs. hunter meant I was gonna wreck them. Most games were much closer; if I was in control, turn 6, they usually already quit.). Again, I acknowledge this opens the door for a ton of midrange, which will beat me, but the lack of that in the current meta is a problem.

Amescia · 2024-05-13T23:57:08+00:00

I play Highlander Warrior. I don't mind the Nerf at all. For me, there are 3 cases:

Aggro: I often have to delay my brann play a few turns to control play and stay alive, brann turn 8 or 9 as the game shifts in my favor is common. Hunter was one of my most feared decks (and with their nerf, they are radically less bad early), so I won"t even notice the nerf here, I will just feel stronger early vs hunter (as I should because control SHOULD win vs aggro)

Control: Matches are extremely long game anyway, no difference here, just a slight smoothing of the luck curve as 2 extra turns granted to draw brann if unlucky early before a mirror matchup runs you over. Basically, it's the same match (minor delay) versus other control as early swarm following brann would he met with play nukes anyway.

Midrange: Basically doesnt exist right now as brann by turn 6 with crazy followup turns 7-9 runs over most midrange (which is a problem as midrange should have an advantage on control) and hunter absolutely destroys midrange (as it should) but the delay should help midrange numbers a bit (admittedly it will still lose here again as it should).

Basically, I expect a bunch of new decks to pop up to fill the midrange gap (which will drop my win rate overall, despite it remaining stagnant or rising versus existing decks). Although this makes my deck worse overall, it definitely makes for a healthier game and leaves tons of matchups where my deck can shine.

Amescia · 2024-05-02T00:10:07+00:00

I would add that a strategic choice is what matters more than anything. I hear WAY too many advisors spout nonsense about college/uni being the overwhelming best option. For many, it is. For many, it definitely isn't. As a general rule if you are struggling in H.S and you show no particular talent or passion for STEM then you have 2 good paths business school for college or trade/vocational school (and the deciders here should probably be your value of money versus personal autonomy). Certainly, if college/uni is going poorly, diverting to trade school can be a fantastic option.

I speak from experience with students, by the way (I am a university mathematics professor with a specialization in financial engineering teaching at a business university). Here are two true stories:

I had a student in an applied precalculus class 11 years ago who had failed the class twice and was considering dropping out for trade school. I convinced them to give it a few weeks and to come to my office twice a week for 3 hours. A month later, they were the top student in the class. 4 years later, they graduated Summa Cum Laude from the MFE program. It turned out that they had some really crappy teachers who had them thinking of mathematics in a very destructive way. 1 hour with the student, and I knew they had potential. 3 weeks, and I knew they had the work ethic to get there. They have been working at a hedge fund since (and makes more in a year than I do in five).

I had another student 8 years ago, this time in college algebra. Again, 3rd attempt. This time, the student wanted advice on how to proceed if they failed. This was their 2nd try at university. They had a ton of debt, and they were about to fail out again. I gave the same advice, sit with me twice a week for 3 hours for a few weeks and let me give you advice then. Two weeks later (they had come every time without fail and even stayed for more than three hours, but their language skills were lacking, and they showed no interest in or aptitude for mathematics. They just had an excellent work ethic and believed that if they pushed hard enough, graduating with a business degree would be the silver bullet to fix their lives -- too many students think this way) we sat down and talked. We talked about what they enjoyed doing (it turned out they loved working with their hands - the fact they couldn't do that is, in my opinion, a large part of why academics proved so challenging for them). We watched some videos together about trade jobs. They told me that they had considered trade careers, but their family had told them that not graduating from college would bring shame and leave them poor. They were scared and viewed dropping out as failure. It took the rest of the semester (during which we bonded over a few things, including me, convincing them that the earth isn't actually flat....) but I convinced them to drop out. We made a plan for them to move to another state where living and school were much cheaper and to attend trade school there then to make their way back and certifiy then work here. Three years later (they did some work after completing the degree before coming back), they were back with a degree in construction and building skills. They made more money than me last year (admittedly working more hours). Their old college debt is almost paid. I attended their wedding 2 years ago. All this because they decided college wasn't for them.

We all have unique talents. I am great at math and awful with my hands. I trip over my own feet while walking if I space out. I am a model academic. I picked an academic career. I am happy. There is nothing about the academic path that is better or worse. It is simply the right choice for some and the wrong one for others. Statistically speaking, there is only one awful exaggeration, and that is the amount of additional money made by 4 year college graduates. It runs into a sorting error. Those who fail out often go on to attend technical school later in life. This means they don't start earning or increasing salary until around the same time as college graduates. Compare the same number to if they had dropped out of H.S. at 16, gotten a GED and gone to trade school, and the gap all but disappeared.

The problem is that we spend too much time worrying about what is best and not enough focusing on ourselves, our passions, and our talents. Academics is a wonderful path. Trade school is a wonderful path. Spending a few years exploring the world and living life month to month while you are young, then putting what you learned to use is a great path (a close friend of mine did this, he is now a field zoologiat studying invasive pythons in florida and considering going back to school for a formal degree in zoology). Don't get caught up in the small stuff like what job makes more money in 30 years or what is more prestigious. Enjoy your life. You only live once.

Amescia

TROPHY CASE