Is it just me, or are phrases like "3x cheaper" hard for other people to grok too? For some reason they always require me to pause and try to sort it out. Like, is the price being reduced by 66% or 75% or something else? What would "1x cheaper" mean?
For the opposite word, "expensive", it all depends on the word before it: "as expensive" or "more expensive".
"100 widgets cost $100. Unit price is $1."
They are now twice _as_ expensive -> they now cost $200. Unit price is now $2.
"100 widgets cost $100. Unit price is $1."
They are now two times _more_ expensive -> they now cost $300. Unit price is now $3.
But How do you do this with the word "cheap"? Does "cheaper" clearly mean "3x as cheap" or "3x more cheap" (which even sounds a bit wrong)? I guess it means "more cheap" means "cheaper".
Better to avoid the problem and say "They are now two times the cost, or half the cost". Which is much clearer.
> For the opposite word, "expensive", it all depends on the word before it: "as expensive" or "more expensive".
Frustratingly, I find this isn't always true in practice. Lots of people use "x times as y" and "x times more y" interchangeably. To avoid ambiguity I try to only use the former in any context where precision is useful.
That reminds of the sign "Buy one, get one".
Does that mean you pay for an item and you get that item, or you pay for an item and you get another item for free? I expect the meaning to the be the second one, but my brain parses it to be the first one.
That’s because it they have left off the word “free” - it’s just an odd shortening of the less ambiguous “buy one get one free”, probably made by someone who is very familiar with seeing “buy one get one free”
It not really all that odd in retail. “BOGO” (pronounced bo-go) is quick to say on the floor and is less awkward than “BOGOF” which sounds like either a franken-portmanteau of “beef” and “stroganof [sic]” or an amateur spy’s attempt at a cover identity.
It’s also used more generally for buy one get one X% off sales and you’ll see lots of “BOGO50” promo/coupon codes. Then marketing jumped on the bandwagon and started plastering “BOGO” all over marketing material so consumers are used to the lingo now
I know what you mean. 1x cheaper would be same price. 3x cheaper means “the new price times 3 equals the old price.” However this is easier than percents or fractions. 100% cheaper means free. Do you want something 67% cheaper, 2/3s cheaper or 3x cheaper?
Let's say you have a product for sale at $32. Then you have a sale to boost name recognition, and have a coupon for $32 dollars off (limited time offer). Or equivalently, that would be $32 cheaper. So the net price is free ($0). $32 cheaper = 100% cheaper = 1x cheaper. Likewise, 25% cheaper = 25% less expensive, or doing the math $32 - 0.25*$32 = 0.75*$32 = $24.
That’s precisely why it’s confusing, yes. You can’t equate 100% cheaper with 1x cheaper. 99% cheaper is sensible. 200% cheaper is not. 2x cheaper is. I’d love a cogent reason to explain this convention.
> I’d love a cogent reason to explain this convention.
"cheaper" isn't a defined operation except for "a is cheaper than b".
So the statements "6% cheaper" and "2 times cheaper" are shorts for "it is cheaper, it costs 6% less" and "it is cheaper, you get 2 times more for the same amount of money".
No, it isn't sensible, and is certainly confusing, and that is why you should commit to never using that phrasing from this day forward. It isn't like there is a hardship you have to overcome when using precise language. There are plenty of alternative ways to state the desired objective that are clear and unambiguous:
- The product is now half-priced!
- The item costs half as much!
- The unit comes with a 50% discount!
No, it's not just you. When you "times" something it is multiplication, not division. The phrasing is a logical impossibility, where the reader has to guess the intent of the author - of which there are several interpretations. The key here is that this is a language "thing" only and certainly not a construct of logic or math.
In the headline of this page, it wouldn't have taken but a moment to write a phrasing that would be understandable to all readers of the page. It could read, "GPT-3 will be Two Thirds Less," or, "GPT-3 will cost One Third the Price."
This example from a non-native English speaker shows the difficulties of having several possible interpretations, at least three! [1]
To open.ai's credit, I don't see that text anywhere on the page or in the page title. The only info I see on the page about the price change is.
> We’re making our API more affordable on September 1, thanks to progress in making our models run more efficiently.
If you visit the page the price change is pretty clear, they show the before and after. 1k tokens will be anywhere from 1/2 to 1/3 the current price depending on which model you're using.
It probably means that it has 3X better value. If I spent $1 previously to do X, I can now do 3X for the same $1.
I think this is more intuitive for most people than using percent difference for the same reason using a raw ratio (speed up) is better for expressing performance improvement.
I usually read that as "new price = old price / X" where X = "3" in this scenario. In my head, "1x cheaper" would mean "new price = old price / 1", so no reduction, I guess.
For me, I tend to think of "3x" and "cheaper" as separate operations. So "3x cheaper" sounds like you're saying new_price = price - 3*price.
That (usually) makes no sense, so I assume people mean something else when they say it, but I never have any clue what. Is it a third of the original price? Is it two thirds (new_price = price - price/3)?
Percentages also work this way. If I say "10% cheaper", most people understand that I mean the price is 90% of what it was previously. Although percentages get weird when increasing the price.
e.g. if it was a flat doubling, I would say that as "200% of the price" (new_price = price*(200/100)).
However, I take "200% more expensive" to mean new_price = price + price*(200/100). To me, the "more" implies addition specifically.
One of my former colleagues who was always in charge of publishing our team's performance testing results was a complete hardass on the rest of us for using proper language around multipliers and superlatives. It's well worth the clarity to avoid precisely this situation.
It's hard to understand because "cheaper" only makes sense as a relative comparison.
Assuming that if, say, the service was 25% cheaper than the nominal price last month, it is now 0.25 * 3 = 75% cheaper than the nominal price. However, it would make more sense to advertise that as a 75% discount over nominal price, so probably that's NOT what they meant.
That's the only explanation that makes sense arithmetically, I believe. There cannot be another interpretation of "3x cheaper" unless you reinterpret the word "cheaper."
10x is literally the difference of an order of magnitude.
An order of magnitude is an exponential change of plus or minus 1 in the
value of a quantity or unit. The term is generally used in conjunction with
power-of-10 scientific notation.
Order of magnitude is used to make the size of numbers and measurements of
things more intuitive and understandable. It is generally used to provide
approximate comparisons between two numbers. For example, if the
circumference of the Sun is compared with the circumference of the Earth,
the Sun's circumference would be described as many orders of magnitude
larger than the Earth's. [1]
An order of magnitude is an approximation of the logarithm of a value relative to some
contextually understood reference value, usually 10, interpreted as the base of the
logarithm and the representative of values of magnitude one. [2]
Yes, an order of magnitude literally means 10x. But in my experience, in common speech it's often used to convey an approximation. i.e. 'Changing this will decrease performance of that endpoint by an order of magnitude', when it's really somewhere around 10x. If someone said 'decrease performance by 10x' that seems much more concrete to me.
From my copy editing days, it's drilled into me to never write "n times less" -- I get that it means "1/n" and that's how I'd rewrite it, but yes, it's notoriously confusing, or at least imprecise.
Consider “cheapness” to be the reciprocal of price; thus, something that costs $30 has a cheapness score of 1/30 antidollars.
For this item to become 3x cheaper would mean for its cheapness score to be multiplied by 3, thus 1/10 antidollars. Thus “3x cheaper” means the same thing as “price multipled by one third”.
I like this hypothesis; however, if that was indeed the original meaning, it would have more sense to advertise it as a 33% discount, or as slashing the price by 1/3. "3x cheaper" seems to be aimed to the average Joe shopping for shoes, not to a developer who knows arithmetic.
