> Probability of a transaction resulting in value v is uniform from [0,99].
in reality, most of the transactions that use coins end up conforming to common existing coin combinations e.g. laundromats in US mostly price as multiples of quarters ($0.25)
The $X.99 price thing should be forbidden and I'm deeply disappointed in humanity/customerity that we don't shun them and refuse to deal with them
It's even uglier in jurisdictions where sales tax is not included in the $X.99 price tag. The total amount you need to pay becomes something like $X+1.07 and you end up with a lot of of unexpected change.
Iportant first comment in the blog:
> Just to summarize how commenter, Jeffrey Shallit, addresses the (1, 3, 11, 37) solution: this is the best way to use the Greedy algorithm to select coins. However, (1, 5, 18, 25) and (1, 5, 18, 29) are tied for the actual solutions. [...]
We should better introduce $50, $100, $500, $1000 and $5000 coins. I'd love my entire salary to come in coins and to be able to pay for any purchase in coins conveniently.
And maybe, instead of common metals and assigning them arbitrary value, we could make them out of rare metals (with a little bit of alloying for hardness) and people can trade them for their relative abundance or rarity!
I can only get behind this if there’s a fixed exchange rate between two coinable metals that doesn’t change with their relative scarcity.
You say that, but it used to be a common criticism Americans had of British currency, that large denominations (up to £2) were exclusively coins.
They cited that coins are in compatible with nearly all wallets, being weighed down, and somehow never actually having exact change.
Background: I'm British and live in the UK but have spent a fair amount of time in the US over the years.
I love the dollar bill. I'd really love to have a £1 and/or £2 note in the UK. The moment you need any reasonable number of coins to buy anything they become unwieldy in your pocket and you can carry enough dollar bills to be useful without there being a chunk of metal digging into your leg.
I've hears arguments against relating to durability but those are all predate the new plastic notes we have.
For some reason I get a load of pushback when suggesting that a £1 or £2 note would be nice to have.
On the other hand, coins are pretty neat.
They are also far more durable than bills, specially lower-denomination bills like the $1 note that wears out quickly because it is used more than higher-denomination bills.
I'd love to find your $5000 coin on the sidewalk!
Sounds terrible to me, coins are so much harder to keep track of!
As long as they have prepunched holes in the middle so I can hang them on a chain around my neck like a maester.
perhaps if we reduce these coins to some units of digital currency so we don't have to physically carry them around, like bits, but for coins
How are you going to prevent fraudulent double spending of these digital coins? You'd have to invent some kind of Byzantine Fault Tolerant (BFT) consensus method.
Sure, but then you’d need a way for all participants to agree on which transactions are valid. Maybe like a chain of blocks that hold transaction data, and each block is cryptographically linked to the previous one. Sounds pretty difficult. I doubt that anyone would be able to create anything like that any time soon, if ever.
Few more years of AI investment and we can just ask GPT13 to create and run this model.
That actually sounds more promising than the way most altcoins are operated today. If only Sam Altman doesn't elope with all those GPT13 coins...
And easier to bankrupt yourself because of a hole in your wallet.
Two obvious problems: the fractional part of the price is not uniform over [00..99] and the system has 5 coins, since in 2021 minting for the half-dollar coin was restarted.
Why is a 11-cent coin ridiculous? With nine of them you could pay for these X.99 products and not get a penny in return.
Because X.99 products are pre tax, so you really have to pay X.99 + X.99 * 0.0Y
This made me wonder about the origins of the 0.99 price. I had always thought it was largely to avoid theft, by ensuring the worker had to open the till for change on every transaction. Which makes sense if there's no sales tax, but if there is sales tax then you might as well round everything to the dollar.
Possibly sales tax wasn't a thing when this became a common practice.
Makes the argument for the psychological effect of 0.99 vs 1.00 much stronger these days though I suppose.
In the US, sure, but most of the world display prices inclusive of tax. (at least from my experience in EU and Asia)
Yes, we should totally revamp our coins to suit the needs of retail marketing.
I was curious what the theoretical distribution of digits might be, did not know that there is an extension of Benford's law for later digits which suggests the uniform assumption is quite nearly right: https://en.wikipedia.org/wiki/Benford%27s_law#Generalization...
Of course in real life, 50 cents and 99 cents are way more common.
Most efficient would be to start rounding purchases to the nearest five cents (if is isn't electronic) and get rid of the penny which costs more to produce than the penny is worth.
The coins proposed are all prime, which makes sense to me intuitively. You'll always need a 1 coin. I'm curious if it's generally true that optimal coins for any given range starting at 0 will be primes?
I take issue with the assumption that you always need a 1 coin.
If we're going to go to such great lengths to minimize the number of coins, even at the cost of making real-life transactions more complicated, we could totally forgo the 1 coin and just have 2 and 5. If an amount ends in 1, you pay 5 and get two 2s back. Those are nice round primes, as far as prime numbers go.
I thought it was going to be about how there was 3700% inflation since coins were actually a useful concept.
It's probably just better to go for eliminating the cent and the nickel and making a 2.5$ coin.
I’d go farther and eliminate all but the quarter.
People need to be able to quickly do the math in their heads to make change. More efficient use of coins but harder for everyone involved is not a functional improvement.
Some of the proposed schemes seem acceptable from that point of view, in particular 1, 3, 10, 25.
Why not just re-index the dollar so that coins are useful amounts of currency?
I think we need a 1337 cent coin!
It's quite surprising to me how the US still has the penny. Like its value is less than the cost of carrying it around.
People are superstitious about math, and fearful that rounding to the nearest nickel, or dime, will result in them getting ripped off. Also, it's an admission that the government has given up on inflation.
This is the country that gave up on the metric system because it involved too much math.
Is any of that still true though?
I think it was 30 years ago. I don't think it is anymore though.
I think people just mostly stopped caring about getting rid of the penny because they use cards and apps for everything now.
On the one hand, I absolutely think we should get rid of the penny. On the other hand, I couldn't care less because I literally haven't used a coin or a bill for a single thing in years.
It's true that things have changed over the passage of time, and I think that people have also stopped caring about the metric system.
Industry has converted. CAD software lets you switch between US and metric with the flip of a switch. Things like the spacing of pins on a microchip are just arbitrary decimal numbers anyway. The car industry has standardized on metric fasteners. Most US households don't even need non metric tools any more.
A few things like building materials are still US, but once again, for industry, they're just decimal entries into a CAD program, and if they need different sizes, they can order custom sizes from the mill.
Some weird units remain, like spark plug threads, but those things are so unique that there's no reason to switch. The only use for a spark plug wrench is to loosen a spark plug.
As an amusing aside, I still use cash, because of my side occupation as a working musician. I often get paid in cash. It piles up in my house and I have to remember to use it. Also, there's an old tradition of drinking establishments letting the musicians have a free drink, so I keep some small bills in my instrument case to tip the bartender.
I'd suspect they rejected the metric system because it would have cost money to change everything over. The argument would presumably have gone something like "we can't have the federal government imposing a cost on the citizens / corporations".
Exactly. It had nothing to do with "too much math" -- I think everyone appreciates metric uses less math, and we all learn it in school anyways for science classes.
It's the cost of change. Replacing every speed limit sign, spending decades where half the cookbooks you own use oven temperatures in °F and half use °C. Years of confusion where someone says they were going 60 and you have to ask if they mean mph or kph.
Not to mention changing the size of every milk container, and so forth...
I'm not sure I buy that excuse. For packaged goods and so on, you don't have to change any sizes of things. Just pick a date and change to a different package design. So nothing in your factory that produces 1 gallon milk jugs has to change except the graphic design needs to start saying 3.8L Milk instead of 1gal Milk. At that point, you can transition to change the physical size of things whenever it is convenient.
For cars, most of them in the US already show mph and kph, so the switch should be easy. Leave old signs alone, but whenever new signs get built, build them in both units for a few years (65mph / 105kph) allowing you to gradually transition to metric.
Repeat for everything else. You can gradually make the switch. Heck, some products (like soda and bullets) are already in liters and millimeters.
I agree with the OOP. We refuse to even take the first steps to switch because of good ol stereotypical American paranoia: "If we switch to metric, all the companies will use it to make everything smaller and rip us off!" as if shrinkflation wasn't already a thing.
> Leave old signs alone, but whenever new signs get built, build them in both units for a few years (65mph / 105kph) allowing you to gradually transition to metric.
Road signs last around a decade. So you're talking 10 years to replace with dual-unit signs (which are more confusing) and then another 10 years to replace again with metric-only signs.
Is it worth it? Is it really that important to change driving speeds to metric? What's the benefit?
And how does it help to say "hey can you pick up 3.8L of milk?" If packaging sizes don't change then we'll still call it a gallon and we won't have "converted" at all.
Conversion is a massive, confusing, expensive effort, and it's reasonable to wonder whether it's actually worth it.
> And how does it help to say "hey can you pick up 3.8L of milk?" If packaging sizes don't change then we'll still call it a gallon and we won't have "converted" at all.
I'm with you on everything but this. The metric system allows retailers (and/or consumer good manufacturers) to take consumers for a giant ride. I have lived in both USA & EU, and in the USA I just give up entirely on comparing goods in a supermarket. With the metric system there's nowhere to hide, and I can compare all products, whether you use ml or l, mg or g or kg. In the USA different manufacturers will use any odd denominator they can come up with and after about two weeks of normalizing fractions every time I went shopping, I gave up.
Even the little tags supermarkets add to try and help you, aren't enough. Many shops use a different denominator, and even a single shop will vary internally. Something as simple as comparing the price of bacon becomes a middle school math problem.
I hate corporate greed, I am partial to pointless mental exercise like math, and I am very stubborn. I don't want to speak for other people but something tells me I'm not the only one who has given up on this battle. Retail customers have more power in the metric system.
For everything else though yes I agree who cares. Except °F which is actually better. :)
I was thinking 50+50 years, but ok 10+10 years is even better. I mean, if you do it gradually enough, the cost approaches zero, so is it worth "almost zero" to have a standard measurement system across the globe? Maybe?
Nothing stops us from enacting generous legislation mandating the switch to metric by the year 2125 or something. You'd have to have intermediate milestones of course, or everyone would just do nothing and wait until 2124 and then complain endlessly about how the transition is so costly and we can't possibly do it in a year, and so on.
But this is the USA, where we can't seem to do anything that takes longer than a quarter, and our entire country's major priorities change every 4 or 8 years.
There is something to being wary of rounding up. For example when you get food from a drive-through or buy groceries and they ask you to round up to the nearest dollar, with the rest of the exchange going towards a charitable cause. They do that because at scale it's enough for them to get a tax incentive for charitable donations via other people's action. I refuse to help an international corporation cheese tax law.
But for something like me handing the shawarma guy a tenner for an exchange that comes out to $9.39, it's not anything to even care about. It's a rounding error.
That's not how tax law works in the US. See https://taxpolicycenter.org/taxvox/who-gets-tax-benefit-thos...
The corp is acting as a collection agent on behalf of the charity, they don't get to deduct it as a charitable donation. Even if they did, they would have to then count the money as income, which would offset any tax deduction they would get, giving the corp 0 net tax benefit.
...Though they may get some publicity benefit from it, which is why I don't go out of my way to donate using corps as a proxy. If its a small amount that I may not otherwise make, for a good cause, sure. But for my more deliberate giving, I would avoid corp proxies. So I don't give through my employer (unless they are offering to match it with their own funds).
> They do that because at scale it's enough for them to get a tax incentive for charitable donations via other people's action. I refuse to help an international corporation cheese tax law.
This is a myth. They can’t claim this on taxes because they don’t have the associated income. To get that using your money, they’d have to claim your donation as income and pay taxes on it, making moot any tax savings (and committing fraud against you to boot).
What they do use your money for is marketing. All the money goes to the charity but they get to say things like “Our program raised a gazillion dollars for those in need.” Which has the effect of positive associations of a giving company which hasn’t actually given.
Canada gave up on it over a decade ago (https://en.wikipedia.org/wiki/Penny_(Canadian_coin)).
I've said before, I'll say again:
We should have the $0.1 and $0.5 coins and everything should be rounded to that.
There's no reason to have $0.01 or even $0.05 precision. The value of the dollar, these days, has inflated to the point where there's simply no practical difference between $0.01 and $0.03 or $0.08 in everyday life, when dealing with cash transactions.
You could certainly track $0.01 in digital account tracking, but the coin is silly.
And -- with payment processing fees, places dealing with cash or card processing would still see less cost in "rounding down" than paying for card processing.
Prices in America are wired. Bought a beer yesterday waiting for the train. Claimed it was $7, actual price $7.62 (which Amex coincidently converted to exactly £6.00)
If I’d paid in cash I’d have to pay with at least a 2 cent coin (and likely need a 1 or 3 in change), despite the nice round number
Until America changes to advertise things at the actual price rather than a partial price, I don’t see how getting rid of 1 cent coins works.
Does the UK include VAT in all listed prices? I don't recall it working that way in continental Europe, and it certainly doesn't work that way in Canada with our equivalent (nor in the US, as you discovered).
That said, advertised prices are commonly not "round" in the first place. In Canada, we simply round the figure on the bill when paying cash.
It'd cost $7.6 if you pay in cash and $7.62173451123 if you pay via a card?
(and, if I were to pass the "small change" bill, I'd, by fiat, make it so that it'd still be "$7.6" even if it was $7.68 -- and the vendors would still come out ahead because the $0.08 lost from rounding down is much less than the $0.23 in card processing fees that comes with a 3% surcharge from your payment processors.)
Hi Hallo
Hi there. How are ya?