Adrian: I'll deal with your response point by point.
> You're in denial Bill! That remark is both egregious and arrogant, but I'll let it pass. > If they are not units of measure what are they? Dots, pages, pixels, etc. are discrete entities. We count them, but we do not measure them (at least not in the applications so far cited in this thread). In the case of dot pitch, we may measure the distance by which the centers of adjacent dots are separated, but that is not a characteristic of the individual entity. Dots per cm (or dots per inch) is a resolution-based specification that is fairly easily visualized. Traffic engineers use the number of vehicles passing a certain point per hour in planning highway modifications. Does this make a vehicle a unit of measure? Of course not. But a count of the number of vehicles per hour is a perfectly valid and useful piece of information. Again, though, nobody claims that vehicles per hour is a unit of measure. "Per hour," as the inverse (or reciprocal) of hour is the unit of measure, with the figure associated with the vehicles merely being a count (i.e. number of occurrences). (If you are objecting to writing vehicles per hour as vehicle/h, that is simply a writing style consistent with SI practice and containing one SI symbol [h]. ISO does exactly the same thing with bit/s, kbit/s, Mbit/s and Gbit/s. SI does not dictate [either through mandate or prohibition] how we write things that are beyond its scope. However, expressing non-SI information in a manner consistent with SI style/rules makes for clarity -- the very reason ISO does it.) In a later message, you mention the use of liters per flush and gallons per flush. The user, in this context, of the term "flush" is talking about an event, not a unit of measure. The fact that liter is a unit of measure does not make a flush a unit of measure. However, the measurement (or specification) of the number of liters in a flush is very useful. You cannot substitute tank capacity, in liters, for that particular specification. Not all toilets (particularly public ones) have tanks. For compliance with water conservation regulations, it is vital that the designer of a toilet know the number of liters of water used each time the toilet is flushed. [Interesting side note: The conservation-conscious Australians (and, presumably, others) have dual-flush toilets. Pushing one button, of two, yields a full flush. Pushing the other yields a half flush. Pat Naughtin can probably tell us how many liters are allowed to flow in the course of a full flush.] > Can you give me a definition for units of measure? Units of measure are used to measure a dimensional property, such as length, mass, temperature, magnetic flux, and so on. Measurements made using units of measure are, but nature, uncertain (i.e., infinite precision is not possible -- a real world fact). Counts (i.e., occurrences) are usually capable of being certain (i.e., they are discrete and they are integers). > What is the difference between BTU and flushes? The question is incoherent, but I'll try to answer it. A BTU is definitely a unit of measure (albeit an obsolete one). It is the amount of heat it takes to raise the temperature of a pound of water by one degree Fahrenheit. A flush is an event. In the course of that event, a measurable amount of water will flow, but that fact does not make a flush a unit of measure and, until now, I have never met anyone who supposed it did. > I am sorry to say but this thinking is a product of "everything goes" school. I am not trying to be sarcastic or arrogant. I'll accept your word that you're not actually trying to be sarcastic or arrogant. However, your hubris is definitely showing. The thinking is not, of course, a product of an "everything goes" or "anything goes" attitude. There are some things we either cannot or do not need to measure, but which we may very well need to count. > Please try to understand! You actually generated a false unit of measurement dot/cm. Not at all. You have simply made the preposterous claim that dot/cm was a unit of measure. The only unit of measure, there, is the centimeter. We simply count the dots. We don't measure them. Dot/cm is a specification containing a unit of measure. Generically, it's a case of occurrences of something per centimeter. Let me clarify. In California, we separate traffic lanes on the freeways with devices called Botts' Dots (named after their inventor). When Caltrans repaves a stretch of freeway, it has to install new Botts' Dots. Let us say they are repaving 2.5 kilometers of 3 lanes. This will require four lines (lanes are also separated from the shoulders) of Botts' Dots running for 2.5 km each. Now, the crew installing the Botts' Dots needs to know the separation, in meters, between the dots. However, the purchasing people, in order to buy enough of them, need to know the number of dots per kilometer (either directly or by derivation). So a COUNT of Botts' Dots per kilometer is a perfectly valid and useful piece of information -- and it does NOT involve the invention of a new unit of measure. A Botts' Dot is a discrete entity (a device), not a measurement. > When in fact the correct rating would be the dimension of the pixel in mm, or submultiples. The dimension of a pixel may be interesting. However, it's not a measurement the purchaser usually finds to be of interest. As I already said, the center-to-center distance between pixels (0.28 mm on a typical monitor) is of interest and is a valid measurement. The pixel, however, is an object. As it manifests itself as a finite object, as does a dot (which, in reality, is a tiny disk), it does have dimensions. However, in monitor and printer specifications, those are not the dimensions that interest us. > Do you see what I mean? Is there such unit as dot/cm in ISO or SI? Just the fact that it uses cm does not make it a valid unit of measurement! Adrian. You are the one ascribing to it the property of "unit of measurement." I have not done so, nor, as far as I can see, has anyone else but you. The expression "dot/cm" may very well exist in certain ISO specifications; "bit/s" certainly does, but there is no claim that "bit" is a unit of measure. Again, it's a discrete entity, which we count (in data transmission, in terms of occurrences per second) but do not measure. > I was taught that when I build a tool I classify it by the strength of the material, or by the dimensional characteristics and not by how many holes it can drill per minute. And if I don't know how to characterize it I go and ask the specialists at the national institute for standards. > Rating of a product should have to do with fundamental units of measure hence with fundamental physical properties. I believe Jim Elwell has already given you a perfectly competent answer to that. > By generating a unit (or call it what you want) as "ppm" one does exactly what the cups per minute does or the gallons per flush. Your statement is somewhat incoherent. However, even if we metricationists don't like it, cup is a recognized, non-SI, unit of measure, being equal to 8 fluid ounces. The SI volume of 225 mL is close enough for me and that's what I would prefer to see in a recipe. Now, if you're running an espresso bar, cups per hour might be a very useful standard by which to measure the capacity of the espresso machine -- assuming that a uniform cup of agreed size was used. That said, the expression "cups per hour" would represent a count and not a unit of measure (notwithstanding the fact that the hour is a unit of measure [SI-sanctioned non-SI}). > Creating a fictitious symbol in people's minds that has nothing with physical properties. Nobody is creating symbols, let alone fictitious ones. Dot is a whole word; pixel is an acronym (for picture element); and bit is also an acronym (for binary digit). None is a unit of measure and none is a symbol. If we disregard, for the moment, colored (or grayscale) dots and pixels, all three of these are simply Boolean entities (i.e., each has two states, either 0 and 1 [for a bit] or ON and OFF). The bit is not even real; it's an abstraction. (The device whose state represents the bit's value of 0 or 1 is, of course, real. And, of course, in the aggregate, those states represent real information [also an abstraction if one wants to be really picky].) > The only true UofM in computers is MHz which truly represents the frequency of oscillation of the machine's "clock" which sets the speed for the chip. Well, as I hope I've made clear by now, nobody has actually said that the others are units of measure (your claim to the contrary notwithstanding). However, in terms of true units of measure, with SI symbols and all, aren't you forgetting the physical dimensions of the computer and its components (length, width, height, disk sizes, etc., in cm or mm, mass in g or kg, power consumption and heat dissipation in W, and so on)? Interestingly, vehicles per hour could, in fact, be measured using a pure SI unit -- the hertz. A rate of 3600 vehicles per hour would be a rate (or frequency) of 1 Hz. For the mathematics of traffic planning, that would probably be very useful. As a published statistic, however, it would not convey a great deal of meaning to the layperson. Bill Potts, CMS Roseville, CA http://metric1.org [SI Navigator]
