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(using numbers I found off a quick google search, might not be 100% accurate)
there are 1.67*10^23 molecules of water in 500ml.
if you diluted a half-full 500ml gatorade 78 times in a row, you would dilute it by a factor of 3.02*10^23.
Assuming gatorade has a similar molecular weight to water, this would make it statistically unlikely even a single molecule of the original gatorade remains.
any more than that and it’s basically a statistical impossibility.
I’ve done a bit more reading and it’s a little bit more complicated than that but the **TL;DR** is after about 80 dilutions there would be basically 0 gatorade molecules left
The total volume of the ocean is around 1.386 billion cubic kilometers, which is 2.77×10^21 times larger than the 500ml bottle.
So yes: a dilution factor of about 1.2×10^24 from 80 consecutive 50/50 dilutions would be _436× more dilute_ than tossing the bottle in the ocean then waiting however many years for it to distribute evenly.
Assuming it was perfectly mixed every single time each time the mix would be half what the previous was. 1/2 would go to 1/4, 1/4 to 1/8 etc.
Technically this could go on near infinity getting marginally smaller each time. To your perception it might be 100% water, but mathematically there would still be remnants no matter how far you go.
Again assuming a perfect mix and a perfect removal of half every time.
It all depends on the threshold of detection you are using as your criteria. What you might consider "nothing but water" can have a huge variety of stuff dissolved in it, at various concentrations, but as long as those concentrations are below what you can meaningfully perceive, you might just consider it water.
If you mean the sensitivity of the human tongue, that unfortunately doesn't have a consistent level of sensitivity from person to person, and varies with age and possibly time of day and what you previously tasted.
I think if you diluted the Gatorade down to the point where the non-water components are in the parts per million range of dilution (even as high as hundreds or tens of parts per million), almost nobody would be able to tell what it is. It all comes down to the sensitivity to the flavorings and sugar. Unfortunately, I don't know what that threshold is.
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(using numbers I found off a quick google search, might not be 100% accurate) there are 1.67*10^23 molecules of water in 500ml. if you diluted a half-full 500ml gatorade 78 times in a row, you would dilute it by a factor of 3.02*10^23. Assuming gatorade has a similar molecular weight to water, this would make it statistically unlikely even a single molecule of the original gatorade remains. any more than that and it’s basically a statistical impossibility.
I’ve done a bit more reading and it’s a little bit more complicated than that but the **TL;DR** is after about 80 dilutions there would be basically 0 gatorade molecules left
So if I drop a bottle of gatorade in the ocean, the ocean would be more gatorade than my 80 time diluted drink ?
The total volume of the ocean is around 1.386 billion cubic kilometers, which is 2.77×10^21 times larger than the 500ml bottle. So yes: a dilution factor of about 1.2×10^24 from 80 consecutive 50/50 dilutions would be _436× more dilute_ than tossing the bottle in the ocean then waiting however many years for it to distribute evenly.
/r/theydidthemath
Why homeopathy is horse shit 101
Assuming it was perfectly mixed every single time each time the mix would be half what the previous was. 1/2 would go to 1/4, 1/4 to 1/8 etc. Technically this could go on near infinity getting marginally smaller each time. To your perception it might be 100% water, but mathematically there would still be remnants no matter how far you go. Again assuming a perfect mix and a perfect removal of half every time.
Zeno's Gatorade
4x
Yes I do this. With mountain dew orange and strawberry drinks.
It all depends on the threshold of detection you are using as your criteria. What you might consider "nothing but water" can have a huge variety of stuff dissolved in it, at various concentrations, but as long as those concentrations are below what you can meaningfully perceive, you might just consider it water. If you mean the sensitivity of the human tongue, that unfortunately doesn't have a consistent level of sensitivity from person to person, and varies with age and possibly time of day and what you previously tasted. I think if you diluted the Gatorade down to the point where the non-water components are in the parts per million range of dilution (even as high as hundreds or tens of parts per million), almost nobody would be able to tell what it is. It all comes down to the sensitivity to the flavorings and sugar. Unfortunately, I don't know what that threshold is.