h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

http://www.mensa.org/workout2.php

Why does Mensa rely so heavily on mathematics as a measure of intelligence?

In my experience numbers are an artifice, a man-made construction. Numbers bear little relationship to reality except as a neurotic (yay, psychotic) projection or a displacement or transference mechanism.

Like, in E=MC2, the value of the speed of light depends on whether you calculate in km/sec or mph. In other words, the number is variable according to your cultural environment. Conclusion: culture matters more than numbers.

Ask yourselves, would you rather be a calculator or an mp3 player. Which would rather have with you on a desert island.


~jwf~

Do I take it you didn't score well?

I don't know about fun; it's pretty easy. 29/30 for me.

B

I did it yesterday for fun, but can't remember what I scored. Wasn't paying that much attention to the result, because before I had surgery a couple of years ago I had to do some similar tests and came out with an IQ of >120.

They're not so much looking at the maths using the numbers, more like can you see the relationship between them. I personally found that the numeric ones were tougher, while the graphic and spacial ones were fairly easy.

"Like, in E=MC2, the value of the speed of light depends on whether you calculate in km/sec or mph"

What's that supposed to prove?

The speed of light is the speed of light. It doesn't matter whether you calculate it in mph, km/sec or furlongs/fortnight. All that matters is that your units of velocity are consistent with your units of mass and energy. The equivalence is NOT a human construction. Any given arbitrary set of units for measuring it is.

You might just as well say the height of Mt. Everest is different depending on whether you measure it in feet or metres. Well, yeah, the NUMBER would be different, but the height is exactly the same in either case.

You haven't measured the time it takes to climb Mount Everest.
But furlongs per fortnight might be a reasonable scale.

>> Well, yeah, the NUMBER would be different...<<

And when you square it that difference increases disproportionately.

So whatever 'number' you get for the square of the speed of light will change the answer you get when you multiply it by M.


~jwf~

>> Do I take it you didn't score well? <<

I just didn't score. No point. The answer would just be a number.

In fact it would be a fraction, worse than just a number because
it depends on the relationship between two numbers which is like
defining a word by using the same word. If a dictionary just said
that a turkey is a turkey or a ball is a ball you'd still not know what they were.


~jwf~

>>And when you square it that difference increases disproportionately.

So whatever 'number' you get for the square of the speed of light will change the answer you get when you multiply it by M.<<



jwf, you're getting into quite a mess. The speed of light in a vacuum is exactly the same whether you measure it in miles per hour, metres per second or feet per year. The numbers might differ but will be exactly equivalent.

Multiplying it by itself doesn't change anything except the units. An energy change measured will be the same number of joules regardless of what units the velocity or mass is measured in.

Did the quiz, got 26/30. The question about primes had an error in that it missed out 4.

No time for the quiz (started, but noticed clock) 4's not a prime number, though, because it's divisible by 2 (so the only even number that can be a prime is 2 itself)--a prime number is only divisible by itself and 1.

jwf, I refer you to http://xkcd.com/54/

I suppose that you're probably playing devil's advocate again anyway.

~ jwf ~
<>> Well, yeah, the NUMBER would be different...<<

And when you square it that difference increases disproportionately.

So whatever 'number' you get for the square of the speed of light will change the answer you get when you multiply it by M.>

This is incorrect. When carrying out calculations using formulae one has to ensure consistency in your units.

Typically, SI. units or imperial units.

E=MC2

In SI units(i.e. using mass=kg, length= m and time=secs):

E=energy in joules i.e. kg·m2/s2

m=mass in kg

c=speed of light in m/s

to make the equation 'work' you need to ensure that everything you muliply on the right hand side of the equation is in in SI units.

You *could* have the mass in pounds(lbs)

but then your energy would be given as lb.m2/s2. While this is 'a number' it makes absolutely no sense at all because a) you are mixing SI and imperial and b) no-one will be able to use the 'number' as no one else works in that unit...one might as well say:

1 jwf = 1 lb.m2/s2

Congratulations you have a unit of energy named after you...Noble prizes all round.

i.e. you have to insert the *unit* into the equation not a 'number'.

Of course, it's simple to convert 1jwf into joules as

1joule= 2.2jwf

You need to tink about units rather than numbers.

I have a hangover.

~*~I don't know about fun; it's pretty easy. 29/30 for me.~*~

Were you following the time-limit rule?

What can I say? It was far too early for a Sunday morning when I attempted it

"So whatever 'number' you get for the square of the speed of light will change the answer you get when you multiply it by M."

The NUMBER will change. What that number MEANS, will not. Watch:

First, for simplicity, SI units.

Consider a mass of 1kg. How much energy is that mass equivalent to?

E=mc^2.
m = 1 kg
c = 3x10^8 m/s

Multiply them together, and you get E, which we find to be
1x 3 x 10^8 x 3 x 10^8 kgm2/s2

1 kgm2/s2 is the definition of the SI unit called the Joule, the basic unit of energy.

So: 9 x 10^16 J

Big number. A LOT of energy.

Now, for comparison, let's do it in old fashioned units, like this:

Consider a mass of 2.204 lbs. (Hint: the mass is the same this time round.)

Lightspeed is 671,080,887 mph. (Hint: the speed is the same this time round.)

First we need to convert to units which are consistent within the system, so we need to convert lightspeed to feet per second, which comes to: 984,251,968 feet/second.

So now our calculation becomes:

2.204 x 984,251,968 x 984,251,968 lb ft2/s2

Or 2.14 x 10^18 lb ft2/s2.

What the hell kind of unit is lb ft2/s2?
Well, a "poundal" is 1 lbft/s2, you could say that what you've got there is foot poundals. Not a commonly used unit.
But there's a conversion possible: 25031 foot poundals is 1 Btu. So you've actually got E=8.4x10^13 Btus.

That's also a big number. It's a different number, though.

So we've got two "different" answers.

Except if you go to any online conversion utility, and convert 8.4x10^13 Btus into Joules, guess what you get? 9 x 10^16 Joules.

So yes, whatever number you get for the square of c DOES change the answer you get when you multiply it by M.

That's not an insight. It's just an observation that if you pose the question in different units, you >SURPRISE< get a different answer, because the answer is in whatever units you asked the question in.

But whatever number you get, whatever set of units you use, the ANSWER is the same. You merely choose to express that answer in one way or another. The actual amount of energy you calculate is exactly the same.

Oh, and 13 minutes for 30/30.

Clever bar steward.


Here's a little teaser I found:

http://pics.livejournal.com/avva/pic/0001qddx

is f the right answer?

assuming that you are meant to finish the pattern?

<>

Well, once you crack the pattern you won't have to ask: you'll be 100% sure which the right answer is.