try #2:

one aspirin shared amongst every human being who has ever lived (estimated at 106 billion) is still more concentrated than a 30C homeopathic remedy

My suggestions, which entirely avoid numbers (might be an idea - many people are not so hot on maths, including me).

This might disqualify me on the "accuracy" count ... so be it.

"Homeopathy is so dilute that ..."

1. "... if you take all of the bottles of homeopathic medicines ever made and put them in a giant (and very clean) tank, and then you looked at this tank with the most powerful microscope you had, you would be extremely lucky to find anything except water."

2. "... if you analysed the water going into a homeopathic factory (water deliveries) and the water coming out (in bottles), you would find no discernible difference."

3. "... if you bought 10 bottles of one sort and 10 of another from Boots, switched the labels around and took them back, Boots would be unable to tell the difference."

4. "... every time you buy a bottle, you are essentially being charged for the same bottle."

5. "... if you took a bottle and filled it with tap water and compared it to a bottle of homeopathic 30C Arnica remedy, you'd have a better chance of finding a molecule of Arnica in the tap water."*

*I think the maths would back me up on this, and this claim is rock-solid for mineral-based remedies (cf. sulphur for example).

Just some ideas... :=)

If you take all the water on Earth (in seas, lakes, rivers, ice caps, underground currents...) and dissolve a single baby aspirin in it, you will have roughly a 15C aspirin dilution. Now try to cure a headache with a few drops of it...

Preparing a homeopathic remedy creates lots of waste water, itself a stronger dilution of the eventual remedy. Those dilutions are poured away and are then diluted into earth's drinking water supply, making all drinking water on earth a homeopathic remedy.

This ordinary drinking water is more likely to contain an active ingredient than a correctly prepared homeopathic remedy made with pure water.

Ben Goldacre, on his blog, has described the level of dilution in the following way:

"Diluted, so extremely, that it equates to one molecule of the substance in a sphere of water whose diameter is roughly the distance from the earth to the sun."

That's the one that stuck with me.

Dr. Park has noted that to expect to get even one molecule of the "medicinal" substance allegedly present in 30X pills, it would be necessary to take some two billion of them, which would total about a thousand tons of lactose plus whatever impurities the lactose contained.

From here.

The allowable level of arsenic in US drinking water is 0.01ppm, equivalent to an 8x (4C) homeopathic dilution. Homeopathic preparations are often 30C or more, so take that ppm figure and add more than 50 zeros in front of that 1. We're no longer talking parts-per-millions, but parts-per-gobsmackingmindbogglingjawdroppingillions. If a 4C preparation of arsenic is safe as drinking water, then how the hell is a 30C preparation going to do anything at all?

Tweaked from Wikipedia:

On average a 30C dilution would require giving two billion doses per second to six billion people for 4 billion years to deliver a single molecule of the original material to any patient.

In order to take even one molecule of medicine in 30C Homeopathic pill form, you'd have to swallow a pill with a volume of 3,000,000,000,000,000,000,000,000 (septillion) square miles.

The chance of winning the jackpot on both the wednesday and saturday national lottery draws each week for a month is 6.84x10^-58.

The chance of a sample of homoeopathic remedy being something other than water: 1.00x10^-60.

I once wee-wee'd in a swimming pool. Given that the water in any homeopathic remedy you take came from this planet, the quantity of ATOMS of the original product you imbibe will be indistinguishable from the quantity of atoms that passed through me (as well as Sir Isaac Newton, Shakespeare and Adolf Hitler)

Taking Homeopathic remedies is akin to taking an aspirin and expecting it curing the the headache of you great-great-great-great-great grand child.

Maybe a bit of a leap scientifically and mathematically, but you get the idea.

I have to run the numbers, but... what about comparing it with treating all the people in the world with a single aspirin?

In any case I think that examples with more "mundane" things (water in the seas, people in the world, pennies in National Budget...) are a lot easier to grasp than talking about stars or universes.

a good one from the times

"You can try imagining Wembley Stadium completely filled with people, all drinking pints of medicine at the rate of two an hour. For just one of these people to eventually consume one molecule, you would need a million Wembley Stadiums all at full capacity with people who have drinking pints constantly since the Earth formed 4.5 billion years ago. Oh, and you’d need 737 million such Earths."

http://timesonline.typepad.com/science/2010/01/homeopathy-by-the-mindboggling-numbers.html

For a 20c solution, the amount of 'medicine' to the amount of water is about like the mass of one bacterium compared to the mass of the Planet Earth. Spreadsheet with other useful examples here: http://ow.ly/11Rcs please add to!

Let's say you take a gram of some agent, such as silica, and dissolve it in a Liter of water to make your initial solution - your mother tincture. Let's just say, for the purpose of argument, that you've ground it down fine enough to suspend it evenly in solution. I've run the numbers with common beach sand as the agent. SiO2.

Remember that the more dilute something is, the more rounds of dilution you need to take it to. 200C is supposedly much more potent than 30C.

In order to turn this mother tincture of sand/water into a vial of 200C, 200 serial dilutions are done. Take 10mL of the tincture and 990mL of pure water to create the 1C dilution. Do that from the 1C to create the 2C, again and again.

If we were to make the entire batch of the final 200C step from that little tiny bit of sand, how much would we have? Thousands of Liters? Enough to fill one of the North American Great Lakes? Enough to raise the sea level by a couple meters if poured into the ocean? No. You would have 10^400 Liters of homeopathic remedy. How much is that?

Imagine a sphere centered where you are right now. Stretch the radius of that sphere out at the speed of light for a FULL EARTH YEAR to describe a sphere that has a diameter of TWO LIGHT YEARS across at its widest point. Start filling that sphere with your 200C potion.

When you're done, you will have been able to squeeze in only 3.5 * 10^51 Liters into this massive sphere.

Two light years across, and can't even hold the whole thing.

Think about that for a second.

Now, keep adding bubbles of the same size, light years across, and keep filling. When you have all these huge orbs that would take life times for you to cross (let alone fill with water) in a sub-light-speed ship... remember, that first little gram of sand only had 3 x 10^22 atoms in it, and they stand a good chance of having been eliminated from the solutions well before this final remedy has been created.

This is based on an article I wrote with some of the numbers wrote out with all the zeroes and did a lot of math that I think is right;

http://www.skepticaldog.com/2007/07/02/diluting-homeopathy/

10^60 = 2^200 (roughly - actually 2^199.3)

Half life of caffiene = about 6 hours

6*200 = 1200 = 7 weeks, 1 day roughly.

Ergo - When you take a homeopathic remedy, there's more active ingredient left from the cup of coffee you had nearly 2 months ago than there is in the pill in your hand.

(this was a good idea in my head until I did the maths. Perhaps exponential decay wasn't a good idea)

Topical this time:

"It's like solving the whole recession, across the whole world, with one millionth of a penny. And having enough left over to make every man, woman and child on earth a millionaire."

(and having enough to do it all over again, a million times)

Sources:

• Total cost of recession $4 trillion (IMF figures)=£2.5trillion
• Dilute 10^30
• =2.5e-18 pounds = 2.5e-16 pence
• 1 millionth of a p = 1e-6 pence (ie overkill by a factor of 4 billion = 1e-6/2.5e-16)
• This gives us 4billion x 2.5 trillion pounds to play with (minus a couple of trillion for the recession)
• Population of world roughly 6.6bn = 1.52 trillion pounds each.

Gah, my earlier answer used 10^30 (which is a 15C dilution) and not 10^60 like it should.

"It's like solving the whole recession, across the whole world, with one atom of a penny. And having enough left over to make every man, woman and child on earth a millionaire."

(and having enough to do it all over again, more than a million/billion/whatever you want really times)

Sources:

• Total cost of recession $4 trillion (IMF figures)=£2.5trillion
• Dilute 10^60
• =2.5e-48 pounds = 2.5e-46 pence
• 1p = 3.56 grams
• atomic weight of constituents = 55-65 mostly (copper, iron) but some carbon(12) (they make them from steel now!) so call it 50 for ease
• 2.5e-46 * 3.56g = 8.9e-46 grams
• 8.9e-46 / 50 * 6.022e23 = 1.1e-23 atoms required (Avogadro/10:23 appears!)
• so, with a whole atom we've overkilled by a factor of 10^23 which leaves (2.5trillion x 10^23 = 2.5e35 pounds left)

• 2.5e35 pounds is more than enough to give everyone on earth a million (=6.6e12 pounds) and still leave a factor of over 10^22 to cover the financial crisis being worse than the IMF figures (which do look a little low). And to do it over a few times.

  • don't lose the atom of penny though

This is a fun game...

It's like dropping a single molecule of oil in a river in New Zealand, picking up a single drop from the sea in Brighton, and selling it as glue.

(volume of all world's water about 1.5 x 10^21 litres, oil molecular weight in the region of 300 depending on type, so volume of one molecule = 1/3 / (6x10^23) = 5x10^-25 assuming roughly a kilo per litre. So that's really only a 23C dilution and perhaps wouldn't make the strongest glue unless you asked a homeopathist to dilute it further for you)

Well the scaling example I will set out probably wont get as far as a 30C but it should lead them to 10C or beyond - and it can have props for the first 2C.

For the example take a sugar lump and let on its a perfect cube of 1cm each side, colour/paint it some colour other than white. This coloured cube will be your homeopathic drop.
01C Now place it in a 10cm square with 99 white sugar lumps

02C Add more sugar lumps until you have a square made up of sides 1m

03C Change your 1m square into a 1m cube

04C Extend your 1m cube so it becomes a 100m*1m*1m meter long cuboid

05C Extend you cuboid so it is now a 10km*1m*1m long cuboid

06C Extend the cuboid now so it now 1,000km*1m*1m long cuboid (about the distance from London to Prague)

07C The cuboid is still 1m*1m and can go around the earth about 2.5 times

08C It now stretches to the moon and back and to the moon again

09C OK if you wanted to walk to the moon and back and there again 1m wide isn't very wide, so we will make the 1m high walkway 100m across.

10C you cuboid is now just taller than big ben, goes to the moon and back and to the moon again and is 100m wide.

..

14C the volume of your cuboid just went to 10times the earth (still think you can find our coloured sugar lump?)

..

17C the volume of our shape is now 7 times the volume of the sun

..

27C your shape is back cube but now has sides approximately 1 light year(LY) in dimension (1Ly = 9,460,730,472,580.8 km)

..

30C your cuboid is now approx 1,000,000 LY* 1 LY * 1 LY. Given the approx width of galaxy is approx 100,000 LY, I for one wont be volunteering to look for our coloured lump in a box that size

For one molecule of the original substance to actually be present in a 30C dilution would need a ball of water bigger than our solar system.

My preferred example (also mentioned here about two minutes in) is diluting a strong spirit - preferably whisky, as it is initially coloured.

Since most people are familiar with the idea of the strength of drinks, and that diluting them makes them weaker, this one has an obvious "reality power".

If you do this as a demonstration, I would suggest you should raise a glass of the initial libation and toast:

"The Mother Tincture!"

• Then dilute one to a hundred (even one to ten will do)

• Then do same again.

Take a small drink, raising glass to audience, at each stage.

"That'sh shrtrong shtuff"

"Packsh a punch"

etc.

You can also keep telling them:

"Wait for it, we've only reached 6X - LOTS more diluting to go 'til it getsh REALLY medicinal"

You can also tell them it works with antifreeze, or car screen wash, as well.

• The standard pay-off line is to ask people to guess how large the last glass of water would have to be to find, on average, a single alcohol molecule if the dilution is "30C" (10^60).

• The answer is a spherical droplet with a diameter that approximates to the distance from the earth to the sun.

If you took the prize of a LIMITED EDITION t-shirt and turned it into homeopathic clothing for the whole planet we would all be naked.

Looking for the active ingredient in a homeopathic remedy is like dropping a stone into the ocean, pulling it out, then sifting through the water looking for pebbles.

(The solution is to ignore the stone and the ocean and instead listen to the person standing next to you wearing an enormous sign that reads: "I'm a doctor, my medicine is based on proven science, and I want to help.")

On the basis that 10^60 water molecules is about 15000 solar masses, and the Eagle Nebula is about 12000 solar masses, I'd suggest:

http://en.wikipedia.org/wiki/File:Eagle_Nebula_from_ESO.jpg - This is the Eagle Nebula. If you had enough 30C homeopathic remedy to have a molecule of the original ingredient still in it, you'd have more matter than is shown in that image.

edit: Actually, it's also about the same number of visible stars in the sky - there's maybe 6000 visible stars to the human eye in the best conditions, so it is fair to say that "If you took all the matter in all the stars you can see with the naked eye on the darkest night, you still would not have enough to make a 30C remedy with some original ingredient left in it."

If cups of tea were homeopathic, the overdose would render our urine toxic to life on all known planets.

I liked the lottery example, so I thought I'd try to expand on it:

If there was a homeopathic lottery in which tickets were drops of 30C homeopathic water, and the winning ticket was a drop containing at least one molecule of the active ingredient, you would need to buy approximately 4.28 x 10^21 (That's 428 followed by 29 zeroes) tickets just in order to have the same chance of winning as a standard lottery.

You'd better hope the ticket prices are diluted by the same amount!

The all important working:

I may have made a few errors in my calculations/facts as this isn't really my area so I'm happy to have someone correct me on the details.

First, I found after making assumptions that an average drop of water was 50mg that the number of molecules in a single drop of water is 1.67 x 10^21.

Next, I took it that a 30C remedy is diluted to 1 molecule of active ingredient per 10^60 molecules of water (is this correct?)

Therefore, 10^60 divided into drops of 1.67 x 10^21 ought to give a number of tickets in an amount of water containing one molecule of active ingredient (and, therefore, one winning ticket.) This makes the chance of picking a winner approximately 1 in 5.99 x 10^38.

Finally, I simply divided this number by the chance of winning a standard 6 numbers out of 49 lottery, (1 in 13,983,816) to see how much more unlikely winning a homeopathic lottery would be, and this gave me the figure that approximated to 4.28 x 10^21. Therefore you would need to buy that many tickets to reach the same probability as a normal lottery.

Did I go wrong anywhere?

Playing with marbles using one marble in a schoolyard the size of the visible universe. (No wonder skeptics think homeopaths have lost theirs.)

I absolutely suck at math, so give me a hand with this:

Had to go with 12C since i couldn't make 30C work.

12C 1 * 10^24

1 light year 9,4605284 * 10^15 m

A marble: 0,014 m

The visible universe 14,000,000 light years

Size of the visible universe in meters: 14 000 000 * 9,4605284 * (10^15) = 1,32447398 × 10^23

Number of marbles you van fit in the visible universe: (1,32447398 * (10^23)) / 0,014 = 9,46052843 × 10^24

Rounding off a bit to make it catchier.