| --- Log opened Sun Oct 04 00:00:08 2020 |
| --- Day changed Sun Oct 04 2020 |
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| 05:46 | <&McMartin> | Woo |
| 05:46 | | * McMartin gets a runnable hello world program on the TRS-80 |
| 05:46 | <&McMartin> | I also note that there is a TRS-80 podcast called "Trash Talk" and this is great |
| 05:49 | <~Vornicus> | that is a good name |
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| 06:47 | <@sshine> | I'm trying to model the set of cocktails as a monoid in Haskell. |
| 06:49 | <@sshine> | initially I represent a cocktail as a 'Map Ingredient Natural' (a dictionary mapping ingredients to the number of parts in the cocktail recipe). |
| 06:50 | <@sshine> | I also define mix :: Cocktail -> Cocktail -> Cocktail by simply adding the parts together, so if 'gintonic' is {gin:1,tonic:1}, then 'mix gintonic gintonic' simply becomes {gin:2,tonic:2}. the problem with that is that trivially, 'gintonic /= mix gintonic gintonic', which reflects that I've not actually modelled the *recipe* but the *drink*. |
| 06:51 | <@sshine> | surely a twice as big gin-tonic is not the same, but recipe-wise, only the ratio between the parts matters. |
| 06:51 | <@sshine> | I realize that what I *probably* want to model is the recipe. |
| 06:51 | <@sshine> | at least, the recipe forms nicer equivalences for this nicely structured monoid that I'm trying to form. |
| 06:51 | <@sshine> | so... really... since there is no point to this, I'd rather model the thing that expresses a nice property. |
| 06:54 | <@sshine> | so I need to normalize the parts somewhere |
| 06:55 | <@sshine> | I could either do it in the constructor for Cocktail, since then equality testing can be a simple check for structural equality. |
| 06:56 | <@sshine> | but the drawback is that I won't be able to have these helper functions: parts :: Natural -> Ingredient -> Cocktail, e.g. 2 `parts` Gin. |
| 06:56 | <@sshine> | since 2 `parts` Gin would immediately get reduced to 1 `parts` Gin. |
| 06:57 | < Pinkhair> | It seems that not including the glasses could lead to some issues. |
| 06:57 | <@sshine> | or I could do it in the Eq instance ('==' operator), which means I can actually have recipes that say "5 parts X" and that's it... maybe that's kinda funny even though it is, normalized, equivalent to 1 part X. |
| 06:58 | <@sshine> | one drawback of normalizing when comparing is that it's a bit more expensive if comparing often. |
| 06:59 | <@sshine> | another drawback is that eventually I'll need to go and fix the Ord instance ('<=' operator), not because there is any obvious way to order drinks, but because in Haskell it is *very* nice to have some unambiguous, structurally derived ordering relation for practical purposes such as stuffing cocktails inside dictionaries. |
| 07:00 | <@sshine> | I think this suggests that the normalization must happen in 'mix' which is going to be the monoidal composition operator. |
| 07:02 | <@sshine> | and... argh... that'd mean 1 `parts` Gin /= 2 `parts` Gin which, I guess, is what I'm arguing for, even though... yeah, I guess if you ever go to a bar and one person says they'd like plain gin and you'd say you'd like two parts plain gin, you probably get served twice the alcohol. |
| 07:02 | <@sshine> | so... the drink 2 `parts` Gin is distinct from 1 `parts` Gin, and then (1 `parts` Gin) `mix` (2 `parts` Gin) can't become 1 `parts` Gin, that's just silly... |
| 07:03 | <@sshine> | OK, clearly I'm being inconsistent here. the distinction of ordering says "cocktail the object", not "cocktail the recipe". |
| 07:03 | <@sshine> | I have to stick to one interpretation at a time. |
| 07:04 | <~Vornicus> | free commutative monoid |
| 07:05 | <@sshine> | cocktail, the beverage, is a free commutative monoid. |
| 07:05 | < Pinkhair> | I am reminded of the example from i7 |
| 07:06 | <@sshine> | i7? |
| 07:07 | < Pinkhair> | 'Any given liquid can be expressed as a vector in N-space, where N is the number of available ingredients and the length of the vector depends on how much of each ingredient is used; then we find the recipe that best describes the liquid by taking the dot product of our liquid vector with a bunch of sample vectors and selecting the one with the largest result.' |
| 07:07 | < Pinkhair> | Inform |
| 07:07 | < Pinkhair> | Inform 7 that is |
| 07:07 | <@sshine> | cocktail, the recipe, is a quotient subgroup of the free commutative monoid of cocktail, the beverage... I think? |
| 07:08 | <@sshine> | Pinkhair, ah :) I know of Inform 7. played with it briefly some years ago. was impressed, yet couldn't concentrate on making use of it. |
| 07:08 | <@sshine> | Pinkhair, yeah, so a cocktail recipe is like an N-vector except scaled down to the unit vector. |
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| 07:09 | <@sshine> | i.e. recipes don't care about quantities, only ratios. |
| 07:10 | <@sshine> | so to form the monoid over recipes, I have to scale down the quantities of each ingredient. |
| 07:10 | <@sshine> | so scaling *has* to happen while mixing. |
| 07:10 | <@sshine> | OK, I just derailed myself a little, but here comes my actual question: |
| 07:12 | <@sshine> | if a cocktail (one drink) is easily modelled as a dictionary mapping ingredients to quantities, how do I normalize the sum of two cocktails? |
| 07:13 | <@sshine> | e.g. {gin:1} + {tonic:1} = {gin:1,tonic:1}, so if there's no overlap, the parts are preserved. |
| 07:13 | <@sshine> | but {gin:1,tonic:2} + {gin:2,tonic:1} = {gin:1,tonic:1} |
| 07:13 | < Pinkhair> | I dunno if they actually only care about ratios. |
| 07:13 | <@sshine> | I guess one thing I can do is divide by the GCD of every multiplicity. |
| 07:14 | <@sshine> | Pinkhair, I think mixologists care about a lot of things that are incompatible with this simplistic understanding of what a cocktail is. for example, real cocktails aren't actually commutative. i.e., order of pouring matters. |
| 07:17 | <@sshine> | and yeah, I think they don't actually just care about the ratios, as in, you can't make an a drink with an actual gallon of vodka, unless you call it a punch. :-D |
| 07:18 | <@sshine> | so 100 `parts` Vodka isn't just a plain vodka, it's a bad idea. |
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| 07:52 | <@sshine> | when I add two cocktail recipes, I have to make sure that I scale them according to their common ingredients. that was the part I had a hard time articulating, I think. |
| 07:53 | <@sshine> | when you combine recipes you have to choose between scaling or not scaling, and I think... I don't even know if it makes sense to always pick one, since such cocktails probably end up pretty bad, anyways. |
| 07:54 | <@sshine> | so {gin:1, tonic:1} + {gin:2, lemon:1} = {gin:2, tonic:2} + {gin:2, lemon:1} = {gin:4, tonic:2, lemon:1}... is one possible way to add recipes. |
| 07:55 | <@sshine> | but wait, what if there isn't a natural scaling between all ingredients. this is getting ridiculous. I'm clearly over-complicating things. |
| 07:58 | <@sshine> | {gin:1, tonic:2} + {gin:2, tonic:3, lemon:1}; now there's no obvious factor between the two. so the only trivial way to add two cocktail recipes is to just combine the verbatim ingredients list. then if I want to normalize that, that is clearly an interpretation in my own imagination of what a cocktail recipe is, since I've made so many assumptions that are not real. |
| 08:02 | <~Vorntastic> | Mixology is not exactly abstract algebra |
| 08:17 | <@sshine> | also, normalizing recipe quantities when mixing breaks associativity. |
| 08:26 | <&McMartin> | Well, this didn't end well. https://imgur.com/a/pXMuJNn |
| 08:58 | <&McMartin> | Nothing like having your board cells be 1 2/3s characters tall because that's the largest that fits and the smallest that still lets you distinguish solid from outline. |
| 09:05 | <~Vorntastic> | Yikes |
| 09:26 | <@sshine> | McMartin, maybe only have the letters at the bottom? |
| 09:30 | <@sshine> | Vorntastic, ah, so what I ended up with *was* a free commutative monoid, and the thing I *tried* to make didn't respect the monoid laws. :) |
| 09:31 | <~Vorntastic> | Yes |
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| --- Log closed Mon Oct 05 00:00:54 2020 |