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Are you telling me that you do math with a pen and paper in binary? everything is decimal. Computers aren't, but almost everyone tries to paper over that fact a
by smabie 6y ago
Are you telling me that you do math with a pen and paper in binary? everything is decimal. Computers aren't, but almost everyone tries to paper over that fact as much as possible.
- enriquto 6y ago> Computers aren't, but almost everyone tries to paper over that fact as much as possible. Do you realize that many entire fields of scientific computing (i.e., computer vision, fluid mechanics, solid mechanics, signal processing, numerical partial differential equations, computational chemistry, climate modeling, and dozens of other things) couldn't care less whether the inner representation of floating point numbers is decimal or binary? If binary can be made just a little faster, so be it.
- smabie 6y agoI'm not saying anyone thinks we should have computers process numbers as decimal. I'm just saying that no one thinks (like the brains internal representation) in decimal binary, that's it.
- enriquto 6y agoI don't think about real numbers as decimals either (for one, the decimal representation is not unique). For many people real numbers are points on a straight line.
- smabie 6y agoI'm not sure why I'm replying, but let's say someone asks you to square 1.2 in your head. You think about points on a line?
- enriquto 6y agoSure. The square (or more generally the product) of two segments is the area of the corresponding square (or rectangle). Given a unit measure you can also put the product as the length of a new segment built by triangle similarity.
- vbarrielle 6y agoThis representation is useful to reason about products in general, but I don't see how it can be used to compute a specific product.
- enriquto 6y agoThis is wildly offtopic now, but greek geometry (thales, euclid, etc) pretty much starts with the construction of a segment whose length is the product of those of two arbitrary given segments. It can be done with compasses and ruler. We've been doing effective and precise computations with numbers thousands of years before the decimal notation was even invented.
- vbarrielle 6y agoYou're completely right, I had forgotten about constructive geometry. Thanks for pointing it out!
- laumars 6y agoI think you're conflating two things: formulas and numbering systems. Ancient Greeks still operated in decimal albeit they'd use the Greek alphabet (since dedicated glyphs for numbers didn't exist) but those letters followed a base-10 system. They would have done the same finger counting we did as kids. The difference between then and now is their calculations were geometric instead than algebraic, rather than them not thinking in decimal. In that regard your argument is a little like saying kids test question such as "Jennifer has 3 apples and gives one to Bob and Terry, how many does she have left" isn't decimal because the calculation is written in English rather than as a "number sentence" (as schools call them). But clearly the kids are still thinking about those numbers as decimal even if the question is not phrased as a mathematical equation. Whereas some other cultures used base-12 or base-60 (https://en.wikipedia.org/wiki/Sexagesimal https://en.wikipedia.org/wiki/Sexagesimal) which, incidentally, are also believed to originate from finger counting much like base-10 was. I believe the Romans also thought about things in decimal despite their numerals being logarithmic. However their numerals do follow the decimal orders of magnitude.
- laumars 6y agoEven if that were true (and I highly doubt it is), when you then need to transcribe those points on a line for future reference you'd do so using decimal. You wouldn't have number lines on a shopping list against items you need multiples of any more than you'd hold up different lengths of string to bar staff when ordering a round of drinks. The reason being is because decimal is the base system people learn when growing up. It's also widely speculated that one of the origins of decimal is around the number of digits (it's not an accident I've chosen that ambiguous term) on our hands: 10 fingers and thumbs. You might mentally map that to number line when trying to assess the distance between numbers or visualise formula but ultimately these would be mental models you generate on top of decimal rather than in place of.
- jfkebwjsbx 6y agoPrices aren’t real numbers. They aren’t even fractional. They are integers with a fixed point, which is an entirely different domain.
- laumars 6y agoYou put quantities on shipping lists, not prices. Prices go on the receipt. They would be integers rather than real numbers. edit: you've now edited your post to repeat a lot of what I put above. Though I doubt intentional (probably a race condition of us both posting at the same time). Anyhow, I'll keep what I posted as it's still relevant.
- jfkebwjsbx 6y agoYeah sorry, I added more because leaving it at the first sentence could be misunderstood. It is true that in home shopping lists there aren’t prices. I was thinking more about company ones (like parts).
- laumars 6y agoEither way your point is valid :)
- bregma 6y agoMy slide rule isn't even digital, let alone decimal or binary.
- rurban 6y agoTotally wrong. So why do you think languages defined the floating point type "real", not inexact or approximate? Because they are more real than base 10 rationals. Math is either calculating with exact numbers (without any floating point nor overflow, or bigrat. ie symbolic), or inexact approximations (floating point types). Nothing is decimal, but those folks counting with their fingers, or financial folks who cannot afford to work with exact numbers. Decimal is just to minimize errors on the decimal representation side, nobody else does decimal. It's either binary or exact.