The thing with brewing is that you are at the mercy of a colony of little organisms... think of it this way:
You create a brand new 23 litre ecosystem with (hopefully, if you've got your sanitation right!) no inhabitants whatsoever and a LOT of food.
You introduce a miniscule number of inhabitants (your little 3g packet of yeast). Now, I'm not entirely sure of the biology of dried yeast but I would imagine to ensure it has a good shelf life it will actually not be dried yeast cells but "spores" - basically radically "cut down" cells where all the cytoplasm (the sort of gooey stuff that fills them out and spaces out all the important bits) is reduced to a minimum. Those spores have to firstly activate and grow themselves into full yeast cells, then start to multiply...
Wiki is suggesting that they double in 1.25 - 2 hours @ 30 degrees (not optimum for brewing but is for scientists). Our 20ish degrees will slow that down, lets say 3 hours.
18 hours is therefore only 6 doubling cycles. 1->2->4->8->16->32->64 times the number you started with. Not a lot really... another 24 hrs...
64->128->256->512->1024->2048->4096->8192->16386 times the number you started with. Now we're talking!!! :party:
Not 100% correct there...When you add dried yaest to a brew the first thing that happens is that the coating of the dried yeast is broken down releasing the yeast cells inside. The yeast will then consume all the dissolved oxygen in the wort (this is why we ariate at this stage). Once the dissolved oxygen has been depleted it will start to consume to the sugars. There are now two by-products, alcohol (not exactly true) and CO2. Every strain of yeast has a optimum temp to work at its best, as brewers we want that to be as quick as possible, so we ferment at the optimum temp for that strain of yeast. We need to set the correct temps and conditions for the yeast to do its job
This is also why, in some circumstances (my brewing is still lagging behind my biology and maths here so someone else will tell us why...) it is best to make a starter colony first and chuck that in. If you start doubling in your wort from 16386 times the number of viable cells in the packet then you are going to start fizzing pretty quick!!!
The other way to think about it is to imagine the tiny little packet that comes with your kit, then imagine how many times bigger the pack of sludge at the bottom of your FV is after fermentation is complete!!!
All of which is just the biological and mathematical reasoning behind the fundamental rule of brewing...
...have patience and you will be rewarded with good beer! :