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It doesn't take a ton of mental capacity, but even though I have a good education in math, I still find myself doing the heuristics of assuming that larger digits means larger number. Using fractions for comparing sizes can flip these heuristics. And I think a lot of people are like me, and also that they won't spend a lot of time reading each item on the menu.
Where I'm from, burger sizes are just given in amount of grams, which makes it a lot easier to compare.
Even though fractions makes sense for accuracy in a mathematical point of view, I see no benefit in a practical application.
Fractions are easier to do calculations in your head or on paper than trying to do the same stuff in decimals. E.g. half of 1/2 is 1/4, half of 1/4 is 1/8, half of 1/8 is 1/16, half of 1/16 is 1/32 etc. In decimals this would be 0.5 -> 0.25 -> 0.125 -> 0.0625 -> 0.03125. When building stuff, I find it useful to be able to do that kind of stuff in my head easily.
The problem occurs when you have a 1/4 pound burger for $1 and a 1/3 pound burger for $1.25. Is it worth it?
If only using fractions in powers of 2 1/2, I understand that it's simpler. A carpenter is happy to meassure 3/16s of an inch, since the tools have notches or marks for that. But when you include other fractions, it becomes messy.
How much more is 1/3 than 1/4? Instead of handling digits, you have to find the lowest common denominator to perform the subtraction. I.e. 1/3 - 1/4 = 4/12 - 3/12 = 1/12.
And at this point, I believe the relationship to the units are lost. Do you have any direct sense to what 1/12 of a pound is?
The 1/3 pound burger is (1/3)/(1/4) times the size of the 1/4 pound burger. So the burger is worth it if $1*(1/3)/(1/4) is greater than $1.25. We arrive at $4/3 which we want to compare to $1.25. Now, since we are relating units which use fractions to units where fractions are unusual, we have another problem. (Yes, we can easily see tha 4/3 = 1.333..., but we wanted to use fractions, right?). So to compare the numbers, we can see that 1.25 = 125/100, which we can simplify to 5/4. So in the end we are left with the simple problem of finding which is bigger between 4/3 or 5/4.
To summarize, I agree that fractions are nice when you have them in a vacuum and don't have to relate them to numbers of other units.
Tell me you're American without telling me you're American.
:) I think British woodworkers also use fractional units.
why use decimals when you can use the... you know, actual weight of the thing?
How is saying “this weighs .25 kg“ not using the “actual weight of the thing”?
I get what you mean, but its adding a useless complexity layer.
If the thing always is smaller than, for example, a kilogram, just use the next measurement unit, a gram. 100g, 200g, 500g, etc.
It's true the other way around, if the thing is always bigger than, for example, a kilogram, use it as is. 1kg, 1.5kg, 4kg, 6.2kg.
For ease of comparison, always use the most significant unit.
Interesting.
But we use fractions a ton here in the US. For example, you can buy milk in a half gallon or a gallon. When you measure, you use 1/4 cup or 1/2 cup. In metric, you rarely use fractions and instead just change the unit (e.g. 250ml or 1L).
Since it's so common here, it's honestly nuts to me that anyone here would be confused at whether 1/4 lb or 1/3 lb is bigger, because we use fractions so often here. If you've ever cooked anything in your life (incl. macaroni and cheese from a box), you've dealt with fractions in real life. I probably do more fraction math than decimal math, especially since I buy everything with my credit card, so when I see a decimal, I round it to the nearest convenient fraction (e.g. I bought 4.5lbs of meat recently for a dinner party, and I communicated that as 4 1/2 lbs). If you ask me how many ounces are in a 1/4 cup, I'd have to stop and think. But if you ask me how many 1/4 cups are in a cup, I'd have the answer for you on the spot.
So I could see this happening in areas where fractions aren't common, but in the US, it's something everyone deals with, pretty much daily. Oh, btw, we have one of these at my local dump:
)heuristics of assuming that larger digits means larger number
That's not heuristics, it's mental laziness or smoothbrain. You shouldn't say you have a good education in math and then say that...
It's indeed a form of mental laziness because the mind is designed to approach some concepts with a non-perfect optimization. That's heuristics. Yes, I can very easily see which number is the largest if I put my mind at it. But scanning over a fast food chain-sized menu, seeing numbers for 2, 4, 8, 12 piece nuggets, prices on different items and a 1/3 pound burger next to a 1/4 pound burger, I could easily see my mind skip the math and mess up the size comparrison.
Don't use language you don't understand, mate. Heuristic
I'm all up for being corrected if I'm wrong in my laguage somehow, but that article seems to be 100% in line with my understanding. What do you find to be wrong?
Like the article says in the first sentence, heuristics "is any approach to problem solving that employs a pragmatic method". Looking at fractions and assuming that the big number is larger is not a pragmatic method, it's a completely smoothbrain approach. I can't even comprehend how you think that's a good approach to fractions. It's just flummoxing.
I think we just disagree on the level something has to be to be considered "pragmatic". Almost all numbers we deal with in a daily basis are not fractions, so it's very natural to develop a shortcut to quickly look at digits to compare numbers. That is a practical approach.
Now, if you don't get too stuck on the word "pragmatic" but actually finish the sentence, you might find it to be more applicable.
Or maybe even look at the wikipedia page for heuristics from a psychological perspective:
Yes, I disagree that looking at a fraction and thinking "bigger number = larger number" is heuristic. It's just really extremely dumb and I can't even.
That's it. There's no argument, although you seem to think there is.
That's exactly it: heuristics are mental shortcuts. It's about avoiding the thinking part. No, I don't think that larger digits mean larger numbers in every case. But when scanning over multiple numbers without putting thought into it, it is a shortcut which works most of the time.
It's not fully logical. It might even be considered dumb. But that doesn't mean it doesn't fit the description of the word. That's just not how words work.
You seem to be ignoring the problem solving part. If it doesn't provide a response in the ballpark of the true solution it is not heuristic, it's just wrong line of thought.
No, it's the correct line of thought in most cases, as most numbers we work with on a daily basis are not fractions. This might be skewed differently in the US, but it's a solution which works in most cases. Heuristics are not necessarily perfect solutions and additional considerations need to be applied when they fail.
If somebody uses a heuristic that’s flat-out wrong, is it no longer a heuristic?
I believe that's the jist of it. Heuristic is a way to get a roughly correct answer to a specific problem. If it doesn't provide a response that stays in the same ballpark of the real solution to the problem it's not heuristic, it's just a wrong train of thought.