I often hear cooks discuss that idea that if you are multiplying, say, a recipe for 4 to be a for 32, that you shouldn't multiply some herbs, spices, or salt. I've never understood any reason why this should be true. Maybe something to do with surface area to volume ratios, or cooking times? Does anyone have a real explanation, or is this nonsense?
The notion that salt or spices specifically don't scale linearly sounds like nonsense to me. In any recipe involving salt and water, the salt is dissolved, so all that matters is the concentration, and that concentration is going to be the same with linear scaling.
Scaling in general is problematic when scaling more than 2x or 4x. When you take into account that:
Recipes targeted at home cooks are imprecise to begin with and often use volumetric measurements that are sensitive to heat, humidity, and other environmental conditions, so the imprecision is magnified at larger scale;
Larger portions of food may get cooked less evenly and/or at less consistent temperatures due to the volume/surface area ratio; that part is correct, but it has nothing to do with salt, it has to do with your equipment. On the stovetop, most of the heat is coming from the bottom of the pan unless you use induction, and even in an oven you've got one or two heat sources radiating heat in a specific pattern.
Cooking times are also going to vary due to changes in things like rates of evaporation. The total amount of heat you're able to deliver at any given time generally does not increase as quickly as the amount of heat you need to deliver, so very often you need to increase cooking times.
I'm sure you probably already know all this, but the reason I'm pointing it all out is that I'm pretty sure that this odd-sounding assertion about non-linear salt/spice scaling is due to some mutation or misunderstanding of general scaling issues.
Probably, salt and spices are typically present in very small quantities in most recipes, and those quantities are already wild guesses much of the time, so the effect of compounding all this wild inaccuracy, especially with volumetric measurements, is actually pretty noticeable at large scale. Scaling sucks with these ingredients because the initial quantities and scaling method are both nonsense.
Assuming you have a precise recipe that gives weight measurements, and you scale by weight, then you're not going to have any problems as long as you either cook it in batches or adjust your cooking time/temp accordingly.
I suppose I could be wrong, but I spent 20 minutes digging for some evidence to contradict my claims above and came up dry; you'd think that somebody would have presented some evidence if the claim were true.
Most strong spices and/or herbs have a lot of flavor that gets put into any dish that they are associated with, and because they are an extraction or an infusion, the flavor that moves into the dish varies by time, method of extraction and quantity. All of those factors will affect the "spiciness" of a dish. The amount, in most non-commercial recipes, is not necessarily exact. An additional variation is the strength of the spices themselves. Fresh ground cinnamon is much more pungent than a dusty bottle of ground cinnamon at the dollar store.
That means that if you double everything including the spices, you may have too much in the way of spices, you may not. However, if you multiply the recipe times 8, as in your example, if the original recipe spice amount is off a little bit, will be off a lot. This can make a huge difference in the final taste.
In addition, a multiplied recipe may take longer to bring to a simmer, say, so your spices will be in contact with the extracting liquid for a longer time.
There are a couple of options to make larger recipe amounts. Your best bet if you need to go large, is to use recipes from a commercial cookbook. These are generally oriented towards batches for 50 and tend to be more accurate. Cutting a recipe for 50 back to 32 is, mathematically, much less of a change than multiplying a recipe for 4 times 8.
A second choice would be to do 8 batches of whatever you are prepping. Yes, it's more work, but depending on the dish, if you are plating individually, this could work to your benefit.
If neither of these options works for you, a decent rule of thumb is to start with 1/2 of the multiplied spices amount and then adjust. So in your example, you are multiplying times 8, I would only multiply the spices times 4 and add to the recipe. Taste and see where you are. Add more if it needs it. There are even cuisines where you add the same spice at the beginning and the end of the dish to get different flavor profiles so you may very well make this a better dish.
And, by the way, salt would fall into the same category. Go light. You can always add more, but you can't take it out.
I find dissolving flavorings like salt tend to be the worst offenders for linear scaling, making the dish unpalatable. They don't need to be reduced by half, I found 1.5 salt/strong spices for a doubled recipe, to about 6.5 for making ten times the original recipe's amount.
I use this primarily in making large batch soups/stews/chilis/stir-fry for freezing portions. Of course most of the time dissolving ingredients aren't a worry outside of baking you can still adjust to taste very easily (you always have a tasting spoon handy).
Baking is a whole different can of worms when it comes to scaling anyways; that's where going in batches is an especially good idea.