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This book lists, in ascending numerical order, things of which there are this many. Not all of them, just some that work well as examples.
If you're trying to make a number clear to a lay audience, you could look it up there, and talk about "water molecules in the Atlantic ocean" or "the number of
ping pong balls that would fit into the Metropolitan Opera".
I wouldn't be surprised to find that such a thing already exists, but I did a superficial search and didn't find it - anyone?
[Kudos to phundug for his "Amazing Equivalence Calculator" and to simonj for the "Worth Your Weight In..." index - I hope this is different enough in focusing on the numbers themselves - half such a device, if you want.]
innumeracy
http://www.innumeracy.com/index.htm
OK, it's a Hofstadter thing [globaltourniquet, Nov 25 2007]
here's a great book
http://www.amazon.c...dy3Q%3D#reader-link
about it - I knew I had seen this somewhere. I've actually read this one, and forgot all about it :) [globaltourniquet, Nov 25 2007]
Adam Spencer's Book of Numbers
http://www.amazon.c...82897/ref=sid_av_dp
Covers 1-100. Going by the detailed review, it's easy to slip into irrelevance. [jutta, Nov 25 2007]
Orders of Magnitude
http://en.wikipedia...itude_%28numbers%29
Some great source material here. [st3f, Nov 25 2007]
Worth Your Weight In Index
the_20WYWI_20Index
Somewhat related [simonj, Nov 26 2007]
Charles and Ray Eames' "Powers of Ten"
http://www.gofish.c...gfp?gfid=30-1025863
More a display of scale, than numerics - but a classic all the same. [zen_tom, Nov 26 2007]
The Principle of Computational Equivalence
http://www.wolframs...ce.com/prizes/tm23/
Just an interesting dissertation on how any system (number) may be represented by like units in a limited number of states, e.g. golf ball, back side of a golf ball, innner vs. outer golf ball in a golf ball cage. [reensure, Nov 27 2007]
Winston Churchill
http://www.wsu.edu/...rors/churchill.html
''...up with which, I will not put" [xenzag, Nov 27 2007]
unit conversion calculator
http://futureboy.us...#SampleCalculations
An actual working equivalence calculator, sort of [gtoal, Nov 28 2007]
Online standards converter
http://www.theregis...ards-converter.html
1 mile = 11495.5742 linguine, 174.5721 double-decker buses, or 11.6381 brontosauruses [angel, Nov 28 2007]
[link]
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Just to be clear - I meant illustration in the sense of a verbal example, not in the sense of drawing. (Edited idea text to avoid confusion.) |
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Although some drawings or photographs would actually be cool. But it wouldn't be the main focus. |
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"Innumeracy" (a term I forget where I first heard, but retrofit it to "illiteracy" and you get what it means) is a huge blight on my country. It is a major source of superstition, religious nonsense, and general lack of understanding. Something like this would certainly help. |
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It was about to get published under this
title: "What is the weight of Jupiter in
dandruff?" :-) |
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I like the idea, but there's still a
difficulty in really getting to grips with
big numbers. If I say "1 billion -
population of the US" (or whatever it is),
I'm not sure that that helps me to form
a mental image of either the size of the
US population _or_ the size of a billion.
In other words, "a billion" is difficult to
conceive as a number, and difficult to
conceive as a concrete representation,
so equating the former with the latter
may not help. If you tell me that
"there are ten to
the 46 water molecules in the Atlantic
ocean", or that "there are as many
people in the US as ping-pong balls
needed to fill the Metropolitan Opera"
what does that actually help me to
understand? |
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I think that, to begin to grasp big (or
indeed very small) numbers, you need
more graphic examples. For instance, a
picture of 1000 people, 1000 birds or
1000 coins might help me get to grips
with "a thousand". A well-constructed
series of photographs might enable me
to visualize a million, and maybe more.
I think that "understanding" a billion in
any real sense is very difficult. |
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//I think that "understanding" a billion in any real sense is very difficult.// |
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Grains of sand are a useful way of imagining large numbers. For example, there are roughly a billion grains in 30 litres of sand. |
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//For example, there are roughly a
billion grains in 30 litres of sand.//
Yes, and maybe that works for some
people - I guess people think in
different ways. Personally, if I look at
30 litres of sand, I see 30 litres - it
doesn't really help me imagine the
number "one billion". In fact, if you'd
told me there were 100 million or 10
billion grains of sand in 30 litres, I'd
quite happily have believed that. |
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I think the problem (for me at least, but
I suspect for most people) is that you're
just equating one unimaginable number
with another. |
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If I wanted to visualize, say, a million,
then I think I could do it by laying out a
million pieces of gravel on a 1000 x
1000 square: it would be possible to
see all of them at once and appreciate
how many there were. A billion would
be harder - I think I'd need to see a
series of images, zooming out from a
square with a million items, then seeing
that there were a thousand such
squares. |
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When you think of 30 litres of sand,
[xavier], do you really get a good grasp
of "a billion" as a number? |
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There is a fascinating article in this months' Discover. It's an interview with Steven Pinker about how he believes human brain is hardwired to be able to grasp language.
The role that metaphor plays in basic understanding, if applied to numbers would make mathematics much simpler for children who don't learn linearly to "get". |
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//For example, there are roughly a billion grains in 30 litres of sand.//
But are these, say, coarse grains like you might find on a Devon pebble beach, or the fine coral sand (aka "parrot fish shit") you might find in the Tropics?
You could easily be an order of magnitude out.
[boysparks] My teacher used to use a similar analogy based on the height of the Empire State Building, which would've been understandable had it been that the class lived in or near the Empire State, and not Lancashire. |
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Whatever next? Decimal - Binary Phrasebook? |
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Chapter A: 0 to 1023
0 - 0;
1 - 1;
2 - 10;
... |
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Chapter D: Two's complement, -511 to 512
... |
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See Stanislaw Lem: One Human Minute, in which all human activity is numerically quantified. |
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I've often wanted something like this for dollar amounts. When newscasters talk about the cost of a new building or a new initiative, they invariably speak the word "million" or "billion" as if it were italicized and bold-faced. E.g. "fifty MILLION dollars". But I still don't know if $50 million is cheap or expensive for a building, and for all I know, $1 billion is a small amount of money for this type of initiative. I don't have a good benchmark for the true size of $1 billion. |
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//I don't have a good benchmark for the true size of $1 billion//
Imagine spending $1903 every single minute of every hour of every day for a whole year.
Or nearly $32 every second for the same period. |
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On the thirteenth day of Christmas my true love sent to me
Thirteen cessationist colonies
Twelve tribes of Israel
Eleven rubbish footballers
Ten stone Commandments
Nine solar planets
An eight-legged spider
Seven ancient wonders
Six degrees of seperation
A Soviet five-year plan
Four Chinese gangsters
Three Mile Island
A double-barrelled shotgun
With a cartridge loaded for me.
Blackadder: "If I have two beans and I add two more beans, what does that make?"
Baldrick: "A very small casserole." |
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A dictionary of regular numbers might start getting repetitive after a while. Perhaps this dictionary should have Prime Number chapter headings, or a Fibonacci index. |
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And what about irrationals? Or perhaps this is just a dictionary of integers. |
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On pressing a secret catch in the spine, you could have a pole that sticks out perpendicular to the book-cover that has all the values of i marked out along its length, with little flags denoting all the imaginary things of which there are that many e.g. 325 Unicorns in Hyperborea, 119 Pixies in Mu, and 11 Bo Peepses in Fairyville etc. |
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//Imagine spending $1903 every single minute of every hour of every day for a whole year.// |
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Sorry, I can't. Probably the easiest examples would concern not oceans and molecules or arbitrary repititions of things that normally don't repeat, but rather the human body or visible objects, e.g. the number of pores on your body or the number of ants in America. |
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How many fingers am I holding up? |
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Wow, you must be a teradactyl. |
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New Scientist frequently posts examples of these that they've seen in print (usually with a wry comment as to how exactly someone knows how many elephants are equivalent to a double-decker bus...) |
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I guess with this they'd stop wondering how people know these obscure equivalences! |
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Or in terms of lengths/heights of double-decker busses. |
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Anything to do with jelly beans gets my vote + |
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A number is, among other things, every other number. |
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//How many fingers am I holding up? //
Grammar (ending with preposition). How many upwardly held fingers do I have? |
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[vincevince] When the preposition is part of a compound verb, it is allowed. It is not a preposition in this case, actually, it is an adverb. |
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Be careful when you back the car up. |
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These grammar problems do me in. |
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Put that kinetic sculpture down. |
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When the preposition requires an object, it must not be the thing with which we end the sentence: |
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Around which building were we supposed to run? |
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The boy does not know the man with whom he is flinging bricks. |
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God won't tell us with which planets and stars he is playing marbles. |
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While "up" in "holding up four fingers" isn't a preposition ("up four fingers is not an adverbial phrase to "holding"), the prohibition against ending sentences with prepositions is wrong is a myth, born from a 17th-century misconception about how language works. |
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Pedantry is one thing up with which I will
not put. |
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+ if only we knew how many holes it take to fill the Albert Hall...oh, now we know. |
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"Which building did he climb up?" is very different from "Which bank did he hold up?" |
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In the former "up" is a preposition, in the latter it is not. There is a King's English rule against ending the sentence with a true preposition, though we do it colloquially. The former is more properly "Up which building did he climb?" but to our ears this sounds austere, so we change it. Language is malleable. Incidentally, in most European languages this is still a hard rule. For instance, I am sure you would never hear even the "lowest" of German speakers say "Welches Haus ist er versteckt unter?" while we will happily say "Which house is he hiding under?" |
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At the time where Dryden claimed that ending sentences with a preposition was bad, the practice was already common and correct. The rule was bogus even then. |
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Make it online and hypertext all the objects. Go from an ant with all the ant stats below: |
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1 million ants fit in a bathtub..... |
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1 million bathtubs fit in lake superior... |
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and so on. Nonetheless [+] |
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//to our ears this sounds austere, so we change it. //
Unless we like austerity, in which case we maintain it. |
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//Language is malleable.//
However, the more frequently it's malleted, the less able it is to convey complex and/or unfamiliar ideas intelligibly. The ultimate colloquial language would convey "I belong to this group", "you don't", and no other ideas at all. |
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I'm reminded of a long, rambling tale told by my grammar school English teacher in which a primary school child is instructed by his mother to choose a book from the shelf for his story-telling session. The child returns with "Lady Chatterley's Lover" (or somesuch) and the mother asks "What did you get a book like that to be read out of to for?" |
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