# Is this usage of "up to" ambiguous?

I was inspired by What is the meaning of “one-half meter”? to ask this follow-on question.

The article at the following link uses the phrase "up to" in a possibly ambiguous way.

https://arstechnica.com/science/2017/03/inside-nasas-daring-8-billion-plan-to-finally-find-extraterrestrial-life/

And Clipper will provide an amazing set of eyes, flying to within 25km of the surface in long, looping orbits and returning images with a resolution of up to one-half meter per pixel. By comparison, even the best images of Pluto captured by New Horizons were about 70 meters per pixel.

I believe that the intended meaning is that the resolution of the images will be at best 0.5 meter per pixel. Therefore, no images would have a resolution of 0.1 meter per pixel, but some images might be at 1 meter per pixel.

However, a literal interpretation could be that "up to" refers to "one-half meter". Therefore, 1 meter per pixel could not happen but 0.1 meter per pixel could happen.

Is the article poorly worded, or is this a correct usage of "up to"?

---------- EDIT ----------

I thought of an example that I think suffers from the exact same ambiguity, but that doesn't have the complexity of the technical meaning of "resolution" confusing things.

From an ad - Each of our products are on sale this week at amazing prices of up to 70% of retail. Compare these prices to our competitor's prices of 90% of retail.

Based on that ad, could there be a sale price of 60% of retail? How about 80% of retail? I don't think that the second sentence of the ad removes the ambiguity.

Maybe I'm just being too literal though.

• "up to" is used to say that something is less than or equal to but not more than a stated value, number, or level. So, the possibility is between and including '0.1 and 0.5', not more than 0.5 meter per pixel. Mar 8, 2017 at 15:49
• @In the context of [image] resolution, we'd normally follow up to with some referent where bigger = better (for example, number of pixels). Consequently the cited usage looks a bit strange, but the apparently more appropriate down to simply wouldn't work very well in that exact context. But it's fine in contexts like This microscope can resolve [images] down to nanometer scales (where smaller = better). Mar 8, 2017 at 16:22
• Virtually every usage of "up to" is ambiguous. It's a relatively imprecise terminology that typically is only used when better precision is unnecessary or would be deceptive. As such it's a useful term, since a knowledgeable reader/listener knows it implies a degree of imprecision. Mar 10, 2017 at 13:07

"Up to" means "less than or equal to", or "at most".

The claim "a resolution of up to one-half meter per pixel" would be ambiguous without further qualifications, but since further qualifications are provided, ("up to one-half meter per pixel. By comparison, even the best images of Pluto captured by New Horizons were about 70 meters per pixel."), it's an accurately approximate way of describing one of Clipper's abilities.

"Up to" without further qualification is ambiguous and is sometimes abused. "Up to" therefore shows up in lists of weasel words, it sounds positive, but might be nothing at all. Example:

• With NetZero you will be able to surf the web up to five times faster.

Which means NetZero might not have been faster at all, (i.e. if the data was already compressed.)

Even vaguer is "Up to __% -- or more!", which can be said of any unknown ratio.

Both of the weasel word variants of "up to ___" exploit a form of cognitive anchoring, in which the first, (and perhaps only), number mentioned induces listeners to somehow infer higher probabilities must be assigned to that first number and its neighbors -- even when they know the first number is selected at random:

...in a study by Dan Ariely, an audience is first asked to write the last two digits of their social security number and consider whether they would pay this number of dollars for items whose value they did not know, such as wine, chocolate and computer equipment. They were then asked to bid for these items, with the result that the audience members with higher two-digit numbers would submit bids that were between 60 percent and 120 percent higher than those with the lower social security numbers, which had become their anchor. -WP

Another point of confusion is that ratios given in "meters per pixel" and "kilometers per pixel" are inconsistent with the usual pixel density notations based on reciprocal ratios, such as PPI, (Pixels Per Inch), and PPCM, (Pixels Per Centimeter).

"PPK", (Pixels Per Kilometer), would be a more standard ratio. The Clipper quote, after converting the units, is equivalent to: "up to 2000PPK. By comparison, even the best images of Pluto captured by New Horizons were about 14PPK."

• @AndyT: Are you referring to the quote in my question? Consider the following two ranges of resolutions: A) 0.3--0.5 meters per pixel B) 0.5--0.7 meters per pixel. Which one (or both) do you think the quote in my questions could be describing? Mar 8, 2017 at 18:37
• @James - Yes, the quote in your question. It clearly means 0.5 to (say) 0.7 meters per pixel, when you take it in context the with following sentence which says it is better than New Horizons which achieved 70 meters per pixel. Mar 9, 2017 at 9:21
• @AndyT, Thanks, changed ambiguous to approximate.
– agc
Mar 9, 2017 at 14:11
• @AndyT: Please see the edit at the bottom of my question. I'm curious whether you think that the example ad is ambiguous or not. Mar 10, 2017 at 12:37
• @James - Is it ambiguous? - No, it's clear that their prices go as low as 70% of retail. Is it grammatically/logically correct - No. Mar 10, 2017 at 13:00

The phrase is ambiguous in isolation because you can parse it in either of the following ways:

1. with a resolution of (up to one-half meter) per pixel; or
2. with a resolution of up to (one-half meter per pixel).

The first applies up to to one-half meter. Since 0.1m is in this range, a resolution of 0.1m/pixel qualifies. By the same token, 1m/pixel does not qualify. Hence statement 1 claims a resolution of that range (0m to 0.5m) per pixel.

In the second interpretation, the resolution is given an upper bound of 0.5m/pixel. Since 0.1m/pixel is a higher resolution, it does not qualify. Likewise, 1m/pixel qualifies because it is a lower resolution. Hence statement 2 claims a resolution of (0.5m or any higher distance) per pixel.

However, as noted elsewhere by @AndyT, the context continues with:

By comparison, even the best images of Pluto captured by New Horizons were about 70 meters per pixel.

This forces the phrase in question to take on interpretation #2.

So to answer your question: no. Although the immediate phrase containing "up to" is ambiguous in isolation, it is disambiguated by its context.

The sharpness of imaging is improving, as shown by amazing.

amazing set of eyes ... with a resolution of up to one-half meter per pixel

Instead of each pixel squeezing in 70 meters of the original view, with Clipper each pixel holds a finer view. Fewer meters into a pixel makes a better picture.

The words up to mean as good as, or reaching the fineness of such resolution. Yes, to be literal this direction is down, as in narrower, but the Clipper is reaching up to a better picture, in achieving (up to) a crisper resolution.