Questions re the metric system

[Cugel]

@pkbites

what’s really messed up is Puerto Rico. Speed limit signs in MPH, distance signs in KM. WTF?

Heh, I watch a lot factual TV, some of which comes from the UK. The presenters/writers routinely mix systems in the same sentence

[rat_avatar]

@Lemur866

There is no object in the world that is exactly 4 inches long. There might be objects that are 4.0 inches long, or 4.0000 inches long. But there is no such thing as an object that is precisely 4 integer inches long, because measurements don’t work that way.

Again, 4 is a perfectly legitimate number. It’s my favorite integer. And when I say that I have a 4 inch chef’s knife, is that chef’s knife 4 integer inches long?

Of course not, because even if those knives are manufactured with unearthly precision, they are going to vary by some number of atoms, they’re going to expand or contract based on temperature, and so on.

So 4 is not a precise value for the measurement of a knife. It’s a value that means somewhere between 3.5 and 4.5, not something more precise than 4.000000000000000000.

And again, if you need to keep track of integer values for length for some reason, how does the fact that the knife is in inches or feet make it more precise than if it is in centimeters or meters? Yes, you can divide a foot into 12 inches. You can divide a meter into 1/12th of a meter with exactly the same ease.

I was not making that argument, but are you saying that dividing physical objects into quarters or thirds is not common? Oddly enough I am probably one of the very few Americans who uses a metric tape measure, which I have because it won’t walk away with coworkers or if it does it doesn’t go very far.

Remember to read up thread, where I was discussing the debasement of other systems, not saying the metric system is not very useful.

Luckily for my use case the lack of a line 3.3333333333333333… CM isn’t a huge issue, but I may be reading it wrong so I just took a quick picture.

[Album] imgur.com

Is this just user error?
Accuracy: closeness of a measured value to a standard or known value
Precision: closeness of two or more measurements to each other.

Once again, for people who need to divide physical quantities in portions, have a more difficult time doing so under decimal based systems. Obviously I have no problem with the metric system but I am curious why people are so vehemently defending it when knowing the limitations of a system is also critical to precision and accuracy. Some jobs like machinists are dividing values all day long so fractions maintain both accuracy and precision as defined above.

This is a single example and I didn’t choose the /3 idea, but 333 Millimeters ±1mm is the best you can get in that case, and with that tape measure. There are more factors and options with systems that chose to pick number bases with more factors.

I am not sure why this is so controversial.

[beowulff]

@rat_avatar

I was not making that argument, but are you saying that dividing physical objects into quarters or thirds is not common? Oddly enough I am probably one of the very few Americans who uses a metric tape measure, which I have because it won’t walk away with coworkers or if it does it doesn’t go very far.

Remember to read up thread, where I was discussing the debasement of other systems, not saying the metric system is not very useful.

Luckily for my use case the lack of a line 3.3333333333333333… CM isn’t a huge issue, but I may be reading it wrong so I just took a quick picture.

Imgur: The magic of the Internet

Is this just user error?
Accuracy: closeness of a measured value to a standard or known value
Precision: closeness of two or more measurements to each other.

Once again, for people who need to divide physical quantities in portions, have a more difficult time doing so under decimal based systems. Obviously I have no problem with the metric system but I am curious why people are so vehemently defending it when knowing the limitations of a system is also critical to precision and accuracy. Some jobs like machinists are dividing values all day long so fractions maintain both accuracy and precision as defined above.

This is a single example and I didn’t choose the /3 idea, but 333 Millimeters ±1mm is the best you can get in that case, and with that tape measure. There are more factors and options with systems that chose to pick number bases with more factors.

I am not sure why this is so controversial.

It’s controversial because it’s nonsense.
If you knew anything about machining, you would know that all modern machine tools are programmed in decimal - either millimeters or microns or decimal inches. No CNC system has a fractional scale (although, they may be able to convert factional input to decimal). I design PCB, and I can pick my layout grid as mm or inches, but everything gets converted to the nearest mil (1/1000 of an inch) when it’s output.

[Cugel]

@Orwell

In between, each decile has an easily observable and relatable amount of coolness or warmth. That simply doesn’t happen with the C scale.

<0 freezing
0-10 cold
11-20 cool
21-30 pleasant
31-40 hot
41+ stinker

or
<0 freezing
0-5 cold
6-10 also cold
11-15 cool but bearable
16-20 cool but pleasantish
21-25 nice
26-30 warm, approaching hot if you are active.
31-35 hot
36-40 unpleasantly hot
41+ real stinker

With personal modifications depending on what you’re used to, and what you’re doing.

[scr4]

@rat_avatar

Once again, for people who need to divide physical quantities in portions, have a more difficult time doing so under decimal based systems. Obviously I have no problem with the metric system but I am curious why people are so vehemently defending it when knowing the limitations of a system is also critical to precision and accuracy. Some jobs like machinists are dividing values all day long so fractions maintain both accuracy and precision as defined above.

This is a single example and I didn’t choose the /3 idea, but 333 Millimeters ±1mm is the best you can get in that case, and with that tape measure. There are more factors and options with systems that chose to pick number bases with more factors.

I am not sure why this is so controversial.

I still don’t understand your point. If you are using a ruler and pencil to make a mark, the best you’re going to get is about 0.5mm accuracy anyway. Marking 350mm exactly isn’t any more accurate than 333.33mm using the same tools.

Even if we accept that dividing physical quantities into equal portions is a common operation, you only end up with an integer result in a few special cases. Why would it be more common to divide 1 foot into 3 than, say, 1 foot into 5, or 13.7 inches into 3? My American tape measure doesn’t have a mark at 2.4" or 4.57".

Anyway, I review mechanical drawings all the time, and everything is in decimal inches anyway. You never see “1/2 inch” in a drawing, you see 0.500.

[rat_avatar]

@beowulff

It’s controversial because it’s nonsense.
If you knew anything about machining, you would know that all modern machine tools are programmed in decimal - either millimeters or microns or decimal inches. No CNC system has a fractional scale (although, they may be able to convert factional input to decimal). I design PCB, and I can pick my layout grid as mm or inches, but everything gets converted to the nearest mil (1/1000 of an inch) when it’s output.

Your ad hominem ignores the reality that G Code directives often have to be corrected for spring, tool parameters and that for critical applications the end product has to be tested to see if it is within spec.

I am not claiming to be an expert at all but I have fought the G4* codes enough to know that job shops can’t ignore variables like cutter radius compensation.

But you most likely ship your designs off to a PCB service, and the programs are working with well known footprints and designs. FYI, I built a 3 axis milling machine for mechanical etching of PCBs from scratch, used Voronoi tool-paths and could still get away with a hot plate for a L6470. Have you ever CNC etched a board for a simple solder paste using expensive chips like HTSSOP28? It is a real bummer when they don’t float to the right place.

Thats why talking about the facts tends to be a better idea than ad hominems.

You don’t have to worry about it because someone else is doing QA for you, and circuit boards are fairly easy to do most QC anyway with just calibrated cameras. But that has only been true for the past couple of decades and takes a lot more then traditional machinist tools. And not many applications are that simple.

[Lemur866]

@rat_avatar

This is a single example and I didn’t choose the /3 idea, but 333 Millimeters ±1mm is the best you can get in that case, and with that tape measure. There are more factors and options with systems that chose to pick number bases with more factors.

I am not sure why this is so controversial.

It’s controversial because you’re bouncing around.

Do you stand by your assertion that traditional measures are easier to represent on computer systems? Or not?

Yes, it’s a tragedy that there’s no exact marker for 1/3 of a meter on a metric tape measure. There’s no such exact marker on a traditional tape measure either.

If you have something that’s a foot long, it’s easy to divide it in half, or thirds, or fourths, or sixths, or twelfths using a traditional ruler. Just line it up and mark every six inches, or four inches, or three inches, or two inches, or one inch.

But what if the object you want to divide isn’t a foot long? If it’s 14 inches long?

If you have an object of arbitrary size that you want to divide closely into fractions of 1/2, 1/3, 1/4, or whatever, you aren’t any better off with a traditional tape measure, because one third of 12.234 feet isn’t any integer value.

Also, if you’re dealing with real world objects, the preciseness with which you can measure and the preciseness with which you can cut start to overwhelm your mathematical round errors. Oh, you don’t have an exact 333.33333… millimeter spot on your tape measure? Yeah, but the line that marks 4 inches on a ruler is wider than a tenth of a millimeter anyway. You can’t mark precisely 4.0000 inches with a pencil, because your pencil won’t make lines that small. And you can’t saw at exactly 4.0000 inches because your saw blade is wider than 0.00001 inches.

If you need that much precision, you can’t use a regular ruler and a pencil and a saw, you have to use better tools.

[bob_2]

@Cugel

Heh, I watch a lot factual TV, some of which comes from the UK. The presenters/writers routinely mix systems in the same sentence

Which is how it is here. Shopping list:

1 doz eggs
4 pints milk
½ litre cooking oil
500 grams sugar
6 botts beer (330ml)

I drive 2 miles to buy 50 litres of petrol in a car that does 25mpg.

A new baby’s weight will be recorded as 3.8kg and the parents told they have an 8lb 6oz baby.

[rat_avatar]

@Lemur866

It’s controversial because you’re bouncing around.

Do you stand by your assertion that traditional measures are easier to represent on computer systems? Or not?

Yes, it’s a tragedy that there’s no exact marker for 1/3 of a meter on a metric tape measure. There’s no such exact marker on a traditional tape measure either.

If you have something that’s a foot long, it’s easy to divide it in half, or thirds, or fourths, or sixths, or twelfths using a traditional ruler. Just line it up and mark every six inches, or four inches, or three inches, or two inches, or one inch.

But what if the object you want to divide isn’t a foot long? If it’s 14 inches long?

If you have an object of arbitrary size that you want to divide closely into fractions of 1/2, 1/3, 1/4, or whatever, you aren’t any better off with a traditional tape measure, because one third of 12.234 feet isn’t any integer value.

Also, if you’re dealing with real world objects, the preciseness with which you can measure and the preciseness with which you can cut start to overwhelm your mathematical round errors. Oh, you don’t have an exact 333.33333… millimeter spot on your tape measure? Yeah, but the line that marks 4 inches on a ruler is wider than a tenth of a millimeter anyway. You can’t mark precisely 4.0000 inches with a pencil, because your pencil won’t make lines that small. And you can’t saw at exactly 4.0000 inches because your saw blade is wider than 0.00001 inches.

If you need that much precision, you can’t use a regular ruler and a pencil and a saw, you have to use better tools.

I looked through my past posts, I am bouncing around answering straw-men reply’s. Which I admit is always a bad idea.

My message has been consistent.

1. The avoirdupois pound mass, and the wine gallon are useful in some domains, and were superior previous the the industrial revolution in a context of limited technology.
2. In some domains these systems are still easier to use but that is use-case dependent.
3. In general a unified form of measurement is better and SI is the best bet.
4. Neither decimal nor factorable systems are good or bad in a black and white fashion, both have trade-offs with real implications.
5. Do not confuse the Imperial based fluid measurements, which are an artifact of British currency with the US system which was based on Queen Anne’s older rules.
6. It is mildly amusing to be having this conversation using hexadecimal, when the main point everyone seems to have is that ‘customary units are bad because decimal is good enough’
   Added:
7. I obviously am forced to deal with massive changes in scale more then the average dope user.

[beowulff]

@rat_avatar

I looked through my past posts, I am bouncing around answering straw-men reply’s. Which I admit is always a bad idea.

My message has been consistent.

1. The avoirdupois pound mass, and the wine gallon are useful in some domains, and were superior previous the the industrial revolution in a context of limited technology.
2. In some domains these systems are still easier to use but that is use-case dependent.
3. In general a unified form of measurement is better and SI is the best bet.
4. Neither decimal nor factorable systems are good or bad in a black and white fashion, both have trade-offs with real implications.
5. Do not confuse the Imperial based fluid measurements, which are an artifact of British currency with the US system which was based on Queen Anne’s older rules.
6. It is mildly amusing to be having this conversation using hexadecimal, when the main point everyone seems to have is that ‘customary units are bad because decimal is good enough’
   Added:
7. I obviously am forced to deal with massive changes in scale more then the average dope user.

Those are all reasonable points.
So, you retract your statement which lead to all this back-and-forth:

SI becomes problematic with computers (not SI’s falt) as an example

???

[rat_avatar]

@beowulff

Those are all reasonable points.
So, you retract your statement which lead to all this back-and-forth:
???

Nope, see points #4, #6 and #7
I hope that the decimal floating-point unit of IBM’s POWER cpus takes off, but as half precision is faster and good enough for sigmoid funcitons in ML I doubt it will. decimal128 may be in IEEE 754-2008 but I’ll have to deal with relativity poor performing software implementations for now.

Feel free to provide a cite that I am in error about a large portion decimals haveing infinite representations in binary, and division by powers of 10 is one of them. I provided a cite, but for my current needs I can’t even use the entire mantissa in the 8087 era FPUs because I have to avoid the count by two change in the binary number line too.

I will not concede that FP doesn’t have it’s very well known problems, including numbers that do not exist in binary like .1, .01 … without evidence.

[beowulff]

@rat_avatar

Nope, see points #4, #6 and #7
I hope that the decimal floating-point unit of IBM’s POWER cpus takes off, but as half precision is faster and good enough for sigmoid funcitons in ML I doubt it will. decimal128 may be in IEEE 754-2008 but I’ll have to deal with relativity poor performing software implementations for now.

Feel free to provide a cite that I am in error about a large portion decimals haveing infinite representations in binary, and division by powers of 10 is one of them. I provided a cite, but for my current needs I can’t even use the entire mantissa in the 8087 era FPUs because I have to avoid the count by two change in the binary number line too.

I will not concede that FP doesn’t have it’s very well known problems, including numbers that do not exist in binary like .1, .01 … without evidence.

Please, just answer one question - what makes this precision problem worse for the metric system?

[rat_avatar]

I finally found the term ‘dyadic rational’ deep down in the recesses of my grey matter, and the first google hit is Wikipedia of course. Which while always a questionable source due to their desire to simplify over accuracy has the most accessible description I can find.

Dyadic rational

Note the image on the top of the page, and how it looks exactly like a USC ruler or tape measure, then note this statement in the opening block.

These are precisely the numbers whose binary expansion is finite.

And the statement on use in measurement

The inch is customarily subdivided in dyadic rather than decimal fractions; similarly, the customary divisions of the gallon into half-gallons, quarts, and pints are dyadic. The ancient Egyptians also used dyadic fractions in measurement, with denominators up to 64.

Hopefully this will help explain why I am having what seems like a debate in GQ.

Dyadic rationals are finite in floating point because floating point is made up of dyadic rationals. You still have problems with the epsilon, small values and large values but USC units are less impacted by cumulative FP errors in computers due to the very structure.

My claims are not made as an opinion, and I apologize for failing to remember the correct term.

[rat_avatar]

@beowulff

Please, just answer one question - what makes this precision problem worse for the metric system?

As I didn’t see this post with my last reply,

Addition, multiplication and subtraction of dyadic fractions always results in another dyadic fraction. And while division doesn’t always end up being a dyadic fraction it is far more likely to do so then decimal to floating point.

Customary units are dyadic and floating point is dyadic and many numbers that are finite in decimal representations are not finite in dyadic form so you have rounding and representation errors.

UTF8 doesn’t have good symbols for set theory and the dope doesn’t support mathtex or other tools that would help so…

∴ math

[DavidwithanR]

@Orwell

Exactly. I would have no problem with the metric system for lengths, weights and volumes, and would actually prefer it for some applications like wrenches and kitchen measurements. But not temperature. Yeah, I get the scientific rationale for 0=freezing and 100=boiling, but that means little in everyday life as we live it. Fahrenheit is much more intuitive and useful for weather and indoor and outdoor temps.

There is absolutely nothing intuitive about Fahrenheit or any other temperature scale. Nothing. You’re just used to it - it really is that simple.

I just invented the one and only truly intuitive temperature scale. Comfortable is zero. Way too hot is +10; way too cold is -10. THAT’S intuitive. (And basically useless.)

[Isamu]

@Surreal

Wrong. People prefer to use units of measurement that they’re already familiar with, and the only real advantage of SI units is that the conversion factors (10X, 1000X, etc.) are simpler if you don’t have access to a computer.

Wrong. Show me one person educated in a metric system who is an advocate for change to inches.

[beowulff]

@rat_avatar

I finally found the term ‘dyadic rational’ deep down in the recesses of my grey matter, and the first google hit is Wikipedia of course. Which while always a questionable source due to their desire to simplify over accuracy has the most accessible description I can find.

Dyadic rational - Wikipedia

Note the image on the top of the page, and how it looks exactly like a USC ruler or tape measure, then note this statement in the opening block.

And the statement on use in measurement

Hopefully this will help explain why I am having what seems like a debate in GQ.

Dyadic rationals are finite in floating point because floating point is made up of dyadic rationals. You still have problems with the epsilon, small values and large values but USC units are less impacted by cumulative FP errors in computers due to the very structure.

My claims are not made as an opinion, and I apologize for failing to remember the correct term.

Yeah, that’s all well and good in La La land, but I would like you to give me one (1) example where a change to a different measurement system was required to cope with the disastrous loss of precision in a computer program caused by the metric system.

[Lemur866]

I still don’t understand why it is easier to represent traditional measures using computers compared to metric measures.

Hint: you can have half a meter and it is represented in binary as 0.1. Same as half a foot. Yes, it is true that there is no traditional name for the half meter, but there’s no traditional name for half a mile, or half a furlong. OK, we could call half a foot six inches instead. But if you’re calculating using a computer algorithm and switching back and forth between feet and inches, you’re doing it wrong.

[Kiwi_Fruit]

@bob_2

Which is how it is here. Shopping list:

1 doz eggs
4 pints milk
½ litre cooking oil
500 grams sugar
6 botts beer (330ml)

I drive 2 miles to buy 50 litres of petrol in a car that does 25mpg.

A new baby’s weight will be recorded as 3.8kg and the parents told they have an 8lb 6oz baby.

That is Britain’s not very sincere attempt to use metric measurements. My shopping list for the same things would be:

1 doz eggs (but some packs are in tens rather than dozens)
2 or 3 litres of milk (probably 2 as that is a standard size container)
500 ml cooking oil
500 grams sugar
6 stubbies of beer (330 or maybe 355 ml)

I drive 3 km to buy 50 litres of diesel in a car that does 6 l/100km.

The baby’s weight thing repeats here though. Official weight might be 3800 gm but all parents seem to say the lbs and ozs thing. Weird as nothing else is measured in lbs/ozs so how do you do the comparison? Only to every other baby, I suppose.

I weigh myself in kg, even though my scales can be switched between that, lbs, and stones/pounds, and I grew up using stones and pounds.

Temperatures are always Celsius. Today is in the mid-teens, yesterday was in the low teens. Summer is low to mid twenties, sometimes high twenties. In a way, that is a narrower range than the deciles used in Fahrenheit.

[rat_avatar]

@beowulff

Yeah, that’s all well and good in La La land, but I would like you to give me one (1) example where a change to a different measurement system was required to cope with the disastrous loss of precision in a computer program caused by the metric system.

Strawman, but I already offered a few cases where ignoring this very real math problem causes issues.

Including

Stock market crashes:

Vancouv.pdf

Rocket crashes due to casting a dyadic float to an int

http://www-users.math.umn.edu/~arnold/disasters/ariane.html

Or the failure of patriot missiles to hit it’s target due to the binary expansion of 1/10 that is the same issue.

Patriot-dharan-skeel-siam.pdf

A 24-bit representation of 0.1 was used to multiply the clocktime,
yielding a result in a pair of 24-bit registers.

Here is another example where a very popular python package numpy, has a test using the software Decimal implementation because of the implications for financial transactions (same decimal vs float problem)

numpy/numpy/blob/b8e8a6ee1f032474a0119fa0c0a6dfb51355abd6/numpy/lib/tests/test_financial.py

You can also do a google search for: “What Every Computer Scientist Should Know About Floating-Point Arithmetic, by David Goldberg”

https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html

Floating-point representations have a base (which is always assumed to be even) and a precision p. If = 10 and p = 3, then the number 0.1 is represented as 1.00 × 10-1. If = 2 and p = 24, then the decimal number 0.1 cannot be represented exactly, but is approximately 1.10011001100110011001101 × 2-4.

That paper is pretty much the “here let me google that for you” answer to the huge number of stack exchange questions that come in about the problem.

As you are an expert, or at least your ad hominem claimed before, it is worth your time understanding this just in case. Eagle, Proteus ,or Altium Designer or what ever you use will take care of it where tolerances matter like standard footprints, but it is important if you also write code.

But it is less likely in your case, DIP packages were spaced at 2.54mm because they were originally 0.1". The choice of 2.54cm == 1 inch was intentional due to the need to consider dyadic issues. Even the choices of ball pitch on BGA is intentional thus 0.40, 0.50, 0.65, 0.75, 0.80, 1.00mm. At 1mm, where there may be errors the size of panels at manufactures limits the impact, and for the smaller sizes they chose values on purpose that wouldn’t lead to issues.

0.65/100 will be ~0.006500000000000001 as an example but even 0.65/100000 which is bigger then you have to worry about is ~6.5000000000000004e-06.

Be glad you are in an industry where you don’t have to deal with this, it is not an easy problem to deal with. I guess you may work with UHF needs, but even with 100-µm conductor line the critical dimensions tend to deal more with the relative error, and routing will typically push out dimensions more based on bigger issues like min distances manufacturing tolerances etc. Meaning that the hard parts like via placement is relative and the error won’t accumulate like with banking errors or missile trajectories. As the scale of panelization is typically limited by panel size of the manufacture it is just something you can ignore as long as the vias are where they need to be and the pick and place can get close enough.

Not all needs are as lucky.