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#51




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#52




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#53




That's what I keep telling my wife, but...
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#54




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To add to this, because it is not a reason to not adopt SI units but because the implications are important. Floating point is a form of finite mathematics and the distributive law and Associative law for multiplication do not always hold in finite math due to these representation errors. This breaks a lot of assumptions by compilers and programmers. a * ( b * c ) may not equal ( a * b ) * c a * ( b + c ) may not equal ( a * b ) + ( a * c ) These assumptions not holding will lead to compounding inaccuracies well beyond the issues caused by the normal loss of precision with floating point. Decimal based systems, which have intrinsic representation errors can be really problematic because of their nonexistence in base 2 when converting to smaller prefixes. This is why banks and other critical users resort to using computationally expensive decimal data types, and why your online loan amortization tool, phone app or calculator never seems to match your statement. 


#55




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exa E 1000000000000000000 10^18 peta P 1000000000000000 10^15 tera T 1000000000000 10^12 giga G 1000000000 10^9 mega M 1000000 10^6 kilo k 1000 10^3 hecto h 100 10^2 deca da 10 10^1 (none) (none) 1 10^0 deci d 0.1 10^−1 centi c 0.01 10^−2 milli m 0.001 10^−3 micro μ 0.000001 10^−6 nano n 0.000000001 10^−9 pico p 0.000000000001 10^−12 femto f 0.000000000000001 10^−15 atto a 0.000000000000000001 10^−18 Are you really suggesting people don't use the prefixes of the system? Once again, I am not anti SI, but I can go from a mile to an inch and even to a mil with no loss in precision, but I can't do the same for a meter to a centimeter. SI isn't a bad system, but it has very real limitations with very real implications. Last edited by rat avatar; 07122018 at 01:48 PM. 
#56




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So? Yes, we have a name for a 1/12th of a foot. It's called an inch. How does giving 1/12th of a foot a name help us avoid rounding errors? Any decimal expansion rounding error that applies to meters also applies to feet, inches, miles, furlongs, parsecs, light years, chains, rods, yards, leagues, or fathoms. Again, you're not understanding the problem. You can write 4 feet 4 inches, and get exactly 4 and 1/3 feet. That doesn't give you a precise decimal expansion of 4.333333333... feet. It just gives you another way to write 4 1/3 feet. If you need to keep that fraction, then keep the fraction. You can use precise fraction with any unit. One third of a meter. One third of an inch. One third of a yard. One third of a furlong. One third of a light year. The fact that some of these fractional units are equivalent to integer values of other units is completely irrelevant! It doesn't matter that there's a vernacular name for 1/3 of a yard, but no name for 1/3 of a light year. If you absolutely positively must preserve that exact fraction, then preserve that goddam exact fraction. Again, the only way you can preserve those exact fractions in a traditional system is to...preserve those exact fractions, and write them out as fractions, and then give them a special name so that instead of a fraction you've got an integer. Writing six feet four inches is EXACTLY THE SAME THING as writing six and one third feet. Metric has nothing to do with it. Seriously. The only thing is that there are traditional names for some fractions of some traditional units, and there are not such traditional names for metric units. And? The fact that there is no name for one third of a meter is not a problem, just like the fact that there is no name for one third of a chain or one third of a rod or one third of a light year. And of course, all these standardization of traditional units happened by happenstance. Different people used different traditional measures for different reasons, and it didn't matter how many firkens were in a hogshead, because there was no precise definition of a hogshead anyway. Then along came the industrial revolution, and we had to measure precisely how big a hogshead was, and then how many drams that equaled, and maybe we'll fudge the sizes so the relationships are integer multiples of each other. Yes, there is no exact binary representation for 1/10th. There is also no exact binary representation for 1/7th. If those French Revolutionaries would have known that we were going to be using binary, they should have made metric hexadecimal rather than decimal, but they didn't. However, the fact that we have decimal names for things in the metric system doesn't make metric unsuited to binary representation, because traditional measurements have the exact same problem, you can't represent 1/10th of an ounce in binary either. Oh, there's no traditional named unit that's 1/10th of an ounce? And there is one that's 1/6th of an ounce? So what? How does that help? Oh, you can keep track of exact fractions using mixes of two named units and thus get integer representations of fractions? Guess what else gives you integer representations of fractions? Integer representation of fractions. 
#57




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#58




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But yes, like I said up thread, had they ignored the thumbs and been octal, or even duodecimal or hexadecimal some modern problems would be easier to solve. There are some problems like calculating the stable Lagrange points for the asteroid belt with the influences of Jupiter and Mars which are unsolvable in practical compute timelines due to these limitations. JPL has even reduced the precision of their ephemerides due to compute time because they have to use arb precision to get more accurate results which is not hardware accelerated. It may be easy to say just move to another number base, but we have a century of proofs often in nonlinear domains that does not allow for this without a lot of work. But lets be clear, I was responding to people making the claim that there is no reason for someone to use the customary units, but when you are a machinist building an airplane that is a few meters across, and your tolerances need to be within 25.40 μm (1 mil) if you use the customary units your job is a lot easier. As I have stated multiple times that all systems have their limitations, but some systems have intrinsic limitations. So I don't know what your post relates to my claim anyway. All systems have flaws, and this is one of the Metric system, and as I stated before the dollar has similar challenges in modern computer based world.The post I was replying to was pointing out that there are lots of use cases where this loss in precision is problematic, and that it can't just be ignored. Last edited by rat avatar; 07122018 at 02:05 PM. 
#59




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And the 100ºC also requires distilled water, which isn't normally what's used for cooking. Quote:
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Life ain't peaches and cream, but sometimes it's laughing your ass off when you have no ass.  WhyNot Last edited by Nava; 07122018 at 02:06 PM. 


#60




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And ? 1m = 39.3701 inches = 3.28084 feet. Y'all don't have an exact measure of this specific, arbitrary distance wot my unit system is based on, so yours is pure shite !1!! (I jest, of course, but you get my point, right ?)
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#61




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But 1 foot = 0.3048 meters exactly. As this is GQ, can you please point out where is said the metric system is pure shite !1!!? Or can you provide a cite that shows that my descriptions of the limitations (which all systems have) do not exist? I am quite confident I am being factually correct. I'll bow out of this thread, as I forgot how passionate people are about this subject and it appears that talking about the historical justifications, and limitations of systems of measure is impractical. But an accumulating loss in precision is a very real problem, especially when it is unavoidable by a particular system. Last edited by rat avatar; 07122018 at 02:14 PM. 
#62




Partial repeat, OOT in previous post.
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One of the signs of a bad translator or adapter (which may actually mean a bad editor) is that they've converted temperatures and not used the usual rounding. "He had a high fever, above 38C" in a British edition becomes "he had a high fever, above 100.4F" in the American edition. Because yeah, the decimal is what's sooooo important. Last edited by Nava; 07122018 at 02:14 PM. 
#63




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Don't worry boo, metric cookbook writers still use obnoxiously vague "units" like a pinch, a dash, a sprinkle, a spritz, "as needed" (if I knew how much was needed I wouldn't need to buy a fucking recipe, now would I ?!), a cup (FUCK YOU, that's the whole *point* of using a standardized unit system !), to taste (fuck you, did you put spme in that dish when I ate it in your restaurant or not ?!) and so on. This is because professional cooks are universally assholes who don't want you to succeed and revel in the knowledge that your soufflé is going to be a fucking disaster.
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#64




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In the US we mostly only deal with metric units once in a while. After my daughter lived in Germany for four years she thought in Centigrade temperatures, and know what was hot and what was cold without converting. In chip design we deal in nanometers, and we don't convert from nanoyards. As for computers, it is not hard to write a decimal arithmetic package if needed. IBM1620s from the late '50s, early '60s looked like decimal machines. And people seem to be neglecting that changing from pounds to ounces or cups to pints to quarts requires conversion factors for each step, all incompatible, and none derivable from the name of the unit. 


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#66




I still don't understand how computers can more accurately represent traditional units than they can metric units.
The only way this can be true is if you're allowed to mix units. Feet and inches. Except if your computer system is keeping track of feet and inches as separate values, how are you performing operations on those values? I guarantee you that if you're using traditional units in your computer system, you're picking one unit and staying with that unit for the whole calculation, because otherwise is madness. You might use feet, but you're calculating everything in feet, not switching between feet and inches. If someone inputs 5 feet 4 inches, that's fine. Now multiply that by 3, divide by sqrt(2), and multiply by a constant. You're going to do the math by doing all the operations on 5 feet, and all the operations on 4 inches, and then add the values back together? Dude, if you do that, then go ahead and do the same thing for thirds of a meter, if it's that important. Much more likely you get the input in feet and fractional feet, and do one operation on one value, and output one value. And if so, the length of the unit is arbitrary. 
#67




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I have lots of British recipe books which give both, and either measure works fine. 
#68




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My specific examples did not include "in the 20s", I have no idea where did you read that one. "Twentysomething" and "twentylots" are two different ranges. One is low 20s (21 to 24), the other is high 20s (26 to 29). My apologies if my trying to stick close to the original expressions rather than saying we speak exactly as in English (we don't) confused you.
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#69




Fractional meters are not harder to measure than fractional feet just because they are metric/SI.
Anywho, the decimalized form of metric is appreciated by American surveyors... we just use decimal feet for our measurements. Also, one foot does not equal .3048 meters exactly... it is 1200/3937 meters! For the standard US Survey foot. 


#70




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#71




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In a number with a decimal point, trailing zeros are significant. AND In a number without a decimal point, trailing zeros may or may not be significant. 4 and 4.0 are different by most convention, and that trailing 0 on 4.0 would tend to signify that it is only acculturate to one decimal place, when it would need infinite zeros to capture all of the precision. So I am going to need a cite that an integer is not an exact value, or that 12 /3 !=4 Last edited by rat avatar; 07122018 at 04:57 PM. 
#72




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#73




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#74




You only do the "decile thing" when you use units where 10 units is a convenient range. You don't do it with people's height, for example. You just say "around 5 ft 9".



#75




A cite, from a book that most people interested in this area probably have access to.
A demonstration on why algebraic properties of floating point are neither associative nor distributive can be found in section 4.2.2 of: The Art of Computer Programming; Volume 2, Seminumerical Algorithms.  Knuth D. (1969) Quote:
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#76




Nobody is arguing that floating point is as exact as integers. We're just saying we never use integers to represent physical quantities like distance/length. Banking is different, a cent is a countable object (or an abstract concept) and not a physical quantity.
Last edited by scr4; 07122018 at 05:20 PM. 
#77




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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. 
#78




I remember back in the late 60's early 70's when I was a kid in school and the push for metrics started in the USA. I was like "you just taught me inches, feet, pounds, etc, now you're telling me to forget that and do this?" So, yeah, I was resistant. But when I got older I realized our system is based on nothing and doesn't really make any sense.
what's really messed up is Puerto Rico. Speed limit signs in MPH, distance signs in KM. WTF?
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I got tired of coming up with lastminute desperate solutions to impossible problems created by other fucking people! William Stranix Last edited by pkbites; 07122018 at 05:24 PM. 
#79




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What does that have to do with the metric system? The fact that there is no exact representation for 1/10th in binary? How exactly does it make doing operations on metric measurements harder? Again, dividing a meter into 10 parts doesn't give an exact representation in binary. Dividing a foot into 10 parts doesn't either. Dividing a foot into 12 parts doesn't either, and neither does dividing a meter into 12 parts. The only fractions that have exact representations in binary are 1/2, 1/4, 1/8, 1/16, and so on. 1/12 doesn't have one. Yes, you can represent 1/12, not as 0.00010101... but as one divided by twelve, or 1/1100, and then you've preserved your exact representation with integer values. But that's not a representation of an exact foot divided exactly into exact inches, that's a representation of one divided by twelve, and if you want to divide a meter into twelve parts you can use the exact same method. Or a meter divided into ten parts. Last edited by Lemur866; 07122018 at 05:37 PM. 


#80




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When you deal with gases : Hydrogen, Natural Gas, Air, Ethylene, Propylene, Oxygen, etc etc they are bought and sold in volumes not weight and their flow is measured in volumes again. So a Natural Gas plant in the US will have a capacity of say 1 Million SCFD (Standard cubic feet per day), while the same in China (or Europe) will be 1116 NM3/hr (Normal cubic meter per hour). Note that it is not just the volume units that need conversion but the reference temperature too. Hope this helps. 
#81




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

#82




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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. https://imgur.com/a/YSTgJgq Is this just user error? Accuracy: closeness of a measured value to a standard or known valueOnce 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. Last edited by rat avatar; 07122018 at 05:50 PM. 
#83




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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. 
#84




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<0 freezing 010 cold 1120 cool 2130 pleasant 3140 hot 41+ stinker or <0 freezing 05 cold 610 also cold 1115 cool but bearable 1620 cool but pleasantish 2125 nice 2630 warm, approaching hot if you are active. 3135 hot 3640 unpleasantly hot 41+ real stinker With personal modifications depending on what you're used to, and what you're doing. 


#85




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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. Last edited by scr4; 07122018 at 06:14 PM. 
#86




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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 toolpaths 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. Last edited by rat avatar; 07122018 at 06:19 PM. 
#87




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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. 
#88




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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. Last edited by bob++; 07122018 at 06:19 PM. 
#89




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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 usecase 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 tradeoffs 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. Last edited by rat avatar; 07122018 at 06:44 PM. 


#90




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So, you retract your statement which lead to all this backandforth: Quote:
Last edited by beowulff; 07122018 at 06:48 PM. 
#91




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I hope that the decimal floatingpoint 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 7542008 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. Last edited by rat avatar; 07122018 at 07:04 PM. 
#92




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#93




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.
https://en.wikipedia.org/wiki/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. Quote:
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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. 
#94




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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 Last edited by rat avatar; 07122018 at 07:53 PM. Reason: Had to do at least one math char 


#95




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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.) 
#96




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

#97




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#98




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. 
#99




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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 midteens, 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. 


#100




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Including Stock market crashes: https://www5.in.tum.de/~huckle/Vancouv.pdf Rocket crashes due to casting a dyadic float to an int http://wwwusers.math.umn.edu/~arnol...rs/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. http://wwwusers.math.umn.edu/~arnol...skeelsiam.pdf Quote:
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) https://github.com/numpy/numpy/blob/...t_financial.py You can also do a google search for: "What Every Computer Scientist Should Know About FloatingPoint Arithmetic, by David Goldberg" https://docs.oracle.com/cd/E1995701..._goldberg.html Quote:
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 ~6.5000000000000004e06. 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 100µm 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. Last edited by rat avatar; 07122018 at 11:02 PM. 
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