i’m enjoying this. going through the questions right now, might do all of them
had a notable experience with one of the early questions:
question: “The battery output voltage, the bottle volume, the digital clock time, and the measure of weight (12 volts; one gallon; 12:36; 1 lb) all have something in common. It is that they are represented by a) one number b) more than one number.”
recollected thought process: apart from the clock time, they all have one number. the time on the clock is also, in my opinion, represented by one number in a non base-n numeral system—the symbols update predictably when the value is incremented, which is all that’s required. i’m not sure if the author intends that interpretation of the clock, though. let’s look for other interpretations.
“lb”—this is a pointer to formulas related to weight/gravity (or more fundamentally, a pointer back to physics/the world). “1 lb” means “1 is the value to pass as the weight variable”. a formula is not itself a number, but can contain them. maybe this is why the clock is included—most would probably consider it to contain two numbers, which would force them to think about how these other three could be ‘more than one number’ as well.
(though it’s down to interpretation, i’ll choose b) more than one number.)
the listed answer is: a) one number. “Each is represented by only one number—the battery by 12 volts, the bottle by one gallon, the time by 12:36 and the weight by one pound. Things described by one number are called scalars. For example: on a scale of one to ten, how do you rate this teacher?” it just restates them and implies in passing that 12:36 is one number, without deriving any insight from the question. *feels disappointed*. (i guess they just wanted to introduce a definition)
FYI I remember being vaguely dissatisfied wth the early exercises in the book, and recommend skipping ahead to somewhere in the middle of the first-half.
i’m enjoying this. going through the questions right now, might do all of them
had a notable experience with one of the early questions:
question: “The battery output voltage, the bottle volume, the digital clock time, and the measure of weight (12 volts; one gallon; 12:36; 1 lb) all have something in common. It is that they are represented by a) one number b) more than one number.”
recollected thought process: apart from the clock time, they all have one number. the time on the clock is also, in my opinion, represented by one number in a non base-n numeral system—the symbols update predictably when the value is incremented, which is all that’s required. i’m not sure if the author intends that interpretation of the clock, though. let’s look for other interpretations.
“lb”—this is a pointer to formulas related to weight/gravity (or more fundamentally, a pointer back to physics/the world). “1 lb” means “1 is the value to pass as the weight variable”. a formula is not itself a number, but can contain them. maybe this is why the clock is included—most would probably consider it to contain two numbers, which would force them to think about how these other three could be ‘more than one number’ as well.
(though it’s down to interpretation, i’ll choose b) more than one number.)
the listed answer is: a) one number. “Each is represented by only one number—the battery by 12 volts, the bottle by one gallon, the time by 12:36 and the weight by one pound. Things described by one number are called scalars. For example: on a scale of one to ten, how do you rate this teacher?” it just restates them and implies in passing that 12:36 is one number, without deriving any insight from the question. *feels disappointed*. (i guess they just wanted to introduce a definition)
FYI I remember being vaguely dissatisfied wth the early exercises in the book, and recommend skipping ahead to somewhere in the middle of the first-half.