Mise said:
To a man with a hammer everything looks like a nail. I particularly like your 18th century French scientist hypothetical.
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To a man with a hammer everything looks like a nail. I particularly like your 18th century French scientist hypothetical.
madviking
north american scum
Spoiler dummy engineer solution :
Do you believe numbers exist?
IdiotsOpposite
Boom, headshot.
That depends on what you mean by "existing". There are many people who believe "existing" means that it has some sort of physical presence, that is, that there is something that we can point to and say "that is two" or some such. If that's the definition you're using, I'd say no. Numbers are a mathematical reality, not a physical reality. They're a mental construction that happens to coincide well with what we experience around us.
Oh, and as for the string thingy, I did manage to figure it out.
Spoiler :
Is it possible that an alien intelligence would have a completely different idea of numbers, and therefore a completely different set of mathematics?
I understand that much of mathematics is more formally expressed as logic - are there other logics out there in the same way that Euclidean Geometry isn't the only Geometry?
I'm always reminded of the ad hoc nature of layman math when other bases come up - base 2, base 8, base 16 etc.
Does e retain its properties across bases? This is something i've never grasped...
IdiotsOpposite
Boom, headshot.
Personally, I'd call it unlikely. However, I wouldn't rule it out.
Yes, many. I'm not sure if I could provide examples for you, though.
Of course it does - the base of a number doesn't affect the properties of the number itself. A base is just a representation of the number. pi in base 3 has exactly the same properties as pi in base 10.
GhostWriter16
Deity
What does the number 1E99 mean?
(That's the highest my calculator will go, but I have no idea what it means.)
(That's the highest my calculator will go, but I have no idea what it means.)
IdiotsOpposite
Boom, headshot.
The E is a calculator shorthand for "times ten to the". So this literally means "1 times ten to the 99", or 10 to the 99th power.
SS-18 ICBM
Oscillator
1 followed by 99 zeros, essentially.
Anyway, question. What do you think of duodecimal advocacy? The main argument seems to be that there are more divisors of 12 than 10 (2,3,4,6 as opposed to 2,5), leading to easier multiplication/division and less cumbersome fractions to deal with. They also argue that the divisors of 12 are more useful than those of 10 (yes, I am aware that 5 is common, but that may be due to the demands of base-10).
Anyway, question. What do you think of duodecimal advocacy? The main argument seems to be that there are more divisors of 12 than 10 (2,3,4,6 as opposed to 2,5), leading to easier multiplication/division and less cumbersome fractions to deal with. They also argue that the divisors of 12 are more useful than those of 10 (yes, I am aware that 5 is common, but that may be due to the demands of base-10).
madviking
north american scum
Even some would argue that base 2 is needless. Why do you need anything more than base 1? 
GhostWriter16
Deity
That makes sense. I had wondered why it wasn't "10E99." Now I know why
Another question: What's the point of imaginary numbers? If they aren't even real, why do we need to understand them?
ParadigmShifter
Random Nonsense Generator
That makes sense. I had wondered why it wasn't "10E99." Now I know why
Another question: What's the point of imaginary numbers? If they aren't even real, why do we need to understand them?
10E99 isn't normalised (all scientific notation has the mantissa (part before the 'E' between 1 and 9.9999...)
Imaginary numbers enable you to solve x2 = -1
And it turns out you don't need any "more" numbers to solve all polynomials in real (or complex) numbers either, so they are the algebraic closure of the real (and complex) numbers.
They also have nice geometric properties (multiplication by a complex number is a spiral enlargement) which is very useful for describing physical properties (come up in the equation for solving motion of an oscillating spring, A/C current, etc.).
madviking
north american scum
Imaginary numbers are numbers, too. By extension, imaginary answers are answers, too. How else are you supposed to solve sqrt(-1)? They just exist on a different set of axis than real numbers. The real-imaginary plane allows you to plot all kinds of crazy imaginary numbers and allows you to get some pretty crazy relationships, e.g. e^(pi*i) + 1 = 0.
More generally, imaginary numbers enable electricity to get to your house, as a lot of electrical engineering deals with imaginary numbers. A few other fields, such as differential equations, numeric analysis, and some other stuff more mathematically-inclined people can tell you about, also deal heavily with imaginary numbers.
More generally, imaginary numbers enable electricity to get to your house, as a lot of electrical engineering deals with imaginary numbers. A few other fields, such as differential equations, numeric analysis, and some other stuff more mathematically-inclined people can tell you about, also deal heavily with imaginary numbers.
Mise
isle of lucy
I was about to say that imaginary and complex numbers are mathematical tricks to make physics easier, but then, all of maths is just a trick to make physics easier.
IdiotsOpposite
Boom, headshot.
Well, what base a number is in doesn't actually affect mathematics that much, especially since a number in base 10 is still just as valid a number as a number in base 12! However, based purely on convenience, it would have been a lot nicer for civilization if we had developed using a base 12 number system, yes. Much more convenient to have that many divisors. (This is actually one of the reasons why the Babylonian's base 60 is so useful: it has divisors 2, 3, 4, 5, AND 6!) Alas, God/Nature/Evolution gave us ten fingers, and humans love to use their fingers for things.
Really, it's unfortunate that imaginary numbers were termed "imaginary". This term was given to the number system by a detractor, much like other scientific concepts, including the "big bang" (which wasn't a bang at all). Imaginary numbers are VERY real, and have very real uses. The most common you hear about is in the field of electrical engineering, and they are useful there, but they're also instrumental in simply and easily solving the differential equation, for example, y'' + y = 0. Now, this equation COULD be solved for y without using complex numbers, but it's easier if you use them (along with the general method for solving ordinary differential equations with constant coefficients) to find the solution.
GhostWriter16
Deity
I have a feeling I won't understand the answer anyway, but how does the concept of square-rooting negative one make sense, when any number squared is positive? In other words, how CAN the square root of negative one exist when it breaks other mathematical rules?
ParadigmShifter
Random Nonsense Generator
It doesn't break any rules.
You just make up a number, i, and say that i2 = -1. (-i)2 is -1 as well, of course
We did the same thing when we made up negative numbers...
You just make up a number, i, and say that i2 = -1. (-i)2 is -1 as well, of course
We did the same thing when we made up negative numbers...
IdiotsOpposite
Boom, headshot.
You're close there. Any "real" number squared is positive, and that's still true, by the definition of what "real" means in mathematics. (Hint: It's not the same as what it means in real life! This trips people up!) However, i, referred to as the "square root of negative one", which is kind of an arbitrary thing, is not a real number, and so doesn't have to conform to this rule. Then we say, okay, so we got these numbers that aren't "real", but they make real numbers when you perform a certain operation on them. We'll call them "imaginary" numbers then.
ParadigmShifter
Random Nonsense Generator
I'd best not mention quaternions then, with their 3 distinct (but related) square roots of -1
Those are used all the time in 3d graphics of course, since they don't commute in exactly the same way that 3d rotations don't
Those are used all the time in 3d graphics of course, since they don't commute in exactly the same way that 3d rotations don't
