Heat vs. Motion

After yes­ter­day’s post, it oc­curred to me that there’s a much sim­pler ex­am­ple of re­duc­tion­ism jump­ing a gap of ap­par­ent-differ­ence-in-kind: the re­duc­tion of heat to mo­tion.

To­day, the equiv­alence of heat and mo­tion may seem too ob­vi­ous in hind­sightev­ery­one says that “heat is mo­tion”, there­fore, it can’t be a “weird” be­lief.

But there was a time when the ki­netic the­ory of heat was a highly con­tro­ver­sial sci­en­tific hy­poth­e­sis, con­trast­ing to be­lief in a caloric fluid that flowed from hot ob­jects to cold ob­jects. Still ear­lier, the main the­ory of heat was “Phlo­gis­ton!

Sup­pose you’d sep­a­rately stud­ied ki­netic the­ory and caloric the­ory. You now know some­thing about ki­net­ics: col­li­sions, elas­tic re­bounds, mo­men­tum, ki­netic en­ergy, grav­ity, in­er­tia, free tra­jec­to­ries. Separately, you know some­thing about heat: Tem­per­a­tures, pres­sures, com­bus­tion, heat flows, en­g­ines, melt­ing, va­por­iza­tion.

Not only is this state of knowl­edge a plau­si­ble one, it is the state of knowl­edge pos­sessed by e.g. Sadi Carnot, who, work­ing strictly from within the caloric the­ory of heat, de­vel­oped the prin­ci­ple of the Carnot cy­cle—a heat en­g­ine of max­i­mum effi­ciency, whose ex­is­tence im­plies the sec­ond law of ther­mo­dy­nam­ics. This in 1824, when ki­net­ics was a highly de­vel­oped sci­ence.

Sup­pose, like Carnot, you know a great deal about ki­net­ics, and a great deal about heat, as sep­a­rate en­tities. Separate en­tities of knowl­edge, that is: your brain has sep­a­rate filing bas­kets for be­liefs about ki­net­ics and be­liefs about heat. But from the in­side, this state of knowl­edge feels like liv­ing in a world of mov­ing things and hot things, a world where mo­tion and heat are in­de­pen­dent prop­er­ties of mat­ter.

Now a Physi­cist From The Fu­ture comes along and tells you: “Where there is heat, there is mo­tion, and vice versa. That’s why, for ex­am­ple, rub­bing things to­gether makes them hot­ter.”

There are (at least) two pos­si­ble in­ter­pre­ta­tions you could at­tach to this state­ment, “Where there is heat, there is mo­tion, and vice versa.”

First, you could sup­pose that heat and mo­tion ex­ist sep­a­rately—that the caloric the­ory is cor­rect—but that among our uni­verse’s phys­i­cal laws is a “bridg­ing law” which states that, where ob­jects are mov­ing quickly, caloric will come into ex­is­tence. And con­versely, an­other bridg­ing law says that caloric can ex­ert pres­sure on things and make them move, which is why a hot­ter gas ex­erts more pres­sure on its en­clo­sure (thus a steam en­g­ine can use steam to drive a pis­ton).

Se­cond, you could sup­pose that heat and mo­tion are, in some as-yet-mys­te­ri­ous sense, the same thing.

“Non­sense,” says Thinker 1, “the words ‘heat’ and ‘mo­tion’ have two differ­ent mean­ings; that is why we have two differ­ent words. We know how to de­ter­mine when we will call an ob­served phe­nomenon ‘heat’—heat can melt things, or make them burst into flame. We know how to de­ter­mine when we will say that an ob­ject is ‘mov­ing quickly’—it changes po­si­tion; and when it crashes, it may de­form, or shat­ter. Heat is con­cerned with change of sub­stance; mo­tion, with change of po­si­tion and shape. To say that these two words have the same mean­ing is sim­ply to con­fuse your­self.”

“Im­pos­si­ble,” says Thinker 2. “It may be that, in our world, heat and mo­tion are as­so­ci­ated by bridg­ing laws, so that it is a law of physics that mo­tion cre­ates caloric, and vice versa. But I can eas­ily imag­ine a world where rub­bing things to­gether does not make them hot­ter, and gases don’t ex­ert more pres­sure at higher tem­per­a­tures. Since there are pos­si­ble wor­lds where heat and mo­tion are not as­so­ci­ated, they must be differ­ent prop­er­ties—this is true a pri­ori.”

Thinker 1 is con­fus­ing the quo­ta­tion and the refer­ent. 2 + 2 = 4, but “2 + 2” ≠ “4“. The string “2 + 2” con­tains 5 char­ac­ters (in­clud­ing whites­pace) and the string “4” con­tains only 1 char­ac­ter. If you type the two strings into a Python in­ter­preter, they yield the same out­put,—> 4. So you can’t con­clude, from look­ing at the strings “2 + 2” and “4″, that just be­cause the strings are differ­ent, they must have differ­ent “mean­ings” rel­a­tive to the Python In­ter­preter.

The words “heat” and “ki­netic en­ergy” can be said to “re­fer to” the same thing, even be­fore we know how heat re­duces to mo­tion, in the sense that we don’t know yet what the refer­ence is, but the refer­ences are in fact the same. You might imag­ine an Ideal­ized Om­ni­scient Science In­ter­preter that would give the same out­put when we typed in “heat” and “ki­netic en­ergy” on the com­mand line.

I talk about the Science In­ter­preter to em­pha­size that, to derefer­ence the poin­ter, you’ve got to step out­side cog­ni­tion. The end re­sult of the derefer­ence is some­thing out there in re­al­ity, not in any­one’s mind. So you can say “real refer­ent” or “ac­tual refer­ent”, but you can’t eval­u­ate the words lo­cally, from the in­side of your own head. You can’t rea­son us­ing the ac­tual heat-refer­ent—if you thought us­ing real heat, think­ing “1 mil­lion Kelvin” would va­por­ize your brain. But, by form­ing a be­lief about your be­lief about heat, you can talk about your be­lief about heat, and say things like “It’s pos­si­ble that my be­lief about heat doesn’t much re­sem­ble real heat.” You can’t ac­tu­ally perform that com­par­i­son right there in your own mind, but you can talk about it.

Hence you can say, “My be­liefs about heat and mo­tion are not the same be­liefs, but it’s pos­si­ble that ac­tual heat and ac­tual mo­tion are the same thing.” It’s just like be­ing able to ac­knowl­edge that “the morn­ing star” and “the evening star” might be the same planet, while also un­der­stand­ing that you can’t de­ter­mine this just by ex­am­in­ing your be­liefs—you’ve got to haul out the telescope.

Thinker 2′s mis­take fol­lows similarly. A physi­cist told him, “Where there is heat, there is mo­tion” and P2 mis­took this for a state­ment of phys­i­cal law: The pres­ence of caloric causes the ex­is­tence of mo­tion. What the physi­cist re­ally means is more akin to an in­fer­en­tial rule: Where you are told there is “heat”, de­duce the pres­ence of “mo­tion”.

From this ba­sic pro­jec­tion of a mul­ti­level model into a mul­ti­level re­al­ity fol­lows an­other, dis­tinct er­ror: the con­fla­tion of con­cep­tual pos­si­bil­ity with log­i­cal pos­si­bil­ity. To Sadi Carnot, it is con­ceiv­able that there could be an­other world where heat and mo­tion are not as­so­ci­ated. To Richard Feyn­man, armed with spe­cific knowl­edge of how to de­rive equa­tions about heat from equa­tions about mo­tion, this idea is not only in­con­ceiv­able, but so wildly in­con­sis­tent as to make one’s head ex­plode.

I should note, in fair­ness to philoso­phers, that there are philoso­phers who have said these things. For ex­am­ple, Hilary Put­nam, writ­ing on the “Twin Earth” thought ex­per­i­ment:

Once we have dis­cov­ered that wa­ter (in the ac­tual world) is H20, noth­ing counts as a pos­si­ble world in which wa­ter isn’t H20. In par­tic­u­lar, if a “log­i­cally pos­si­ble” state­ment is one that holds in some “log­i­cally pos­si­ble world”, it isn’t log­i­cally pos­si­ble that wa­ter isn’t H20.

On the other hand, we can perfectly well imag­ine hav­ing ex­pe­riences that would con­vince us (and that would make it ra­tio­nal to be­lieve that) wa­ter isn’t H20. In that sense, it is con­ceiv­able that wa­ter isn’t H20. It is con­ceiv­able but it isn’t log­i­cally pos­si­ble! Con­ceiv­abil­ity is no proof of log­i­cal pos­si­bil­ity.

It ap­pears to me that “wa­ter” is be­ing used in two differ­ent senses in these two para­graphs—one in which the word “wa­ter” refers to what we type into the Science In­ter­preter, and one in which “wa­ter” refers to what we get out of the Science In­ter­preter when we type “wa­ter” into it. In the first para­graph, Hilary seems to be say­ing that af­ter we do some ex­per­i­ments and find out that wa­ter is H20, wa­ter be­comes au­to­mat­i­cally re­defined to mean H20. But you could co­her­ently hold a differ­ent po­si­tion about whether the word “wa­ter” now means “H20″ or “what­ever is re­ally in that bot­tle next to me”, so long as you use your terms con­sis­tently.

I be­lieve the above has already been said as well? Any­way...

It is quite pos­si­ble for there to be only one thing out-there-in-the-world, but for it to take on suffi­ciently differ­ent forms, and for you your­self to be suffi­ciently ig­no­rant of the re­duc­tion, that it feels like liv­ing in a world con­tain­ing two en­tirely differ­ent things. Knowl­edge con­cern­ing these two differ­ent phe­nom­ena may taught in two differ­ent classes, and stud­ied by two differ­ent aca­demic fields, lo­cated in two differ­ent build­ings of your uni­ver­sity.

You’ve got to put your­self quite a ways back, into a his­tor­i­cally re­al­is­tic frame of mind, to re­mem­ber how differ­ent heat and mo­tion once seemed. Though, de­pend­ing on how much you know to­day, it may not be as hard as all that, if you can look past the pres­sure of con­ven­tion­al­ity (that is, “heat is mo­tion” is an un-weird be­lief, “heat is not mo­tion” is a weird be­lief). I mean, sup­pose that to­mor­row the physi­cists stepped for­ward and said, “Our pop­u­lariza­tions of sci­ence have always con­tained one lie. Ac­tu­ally, heat has noth­ing to do with mo­tion.” Could you prove they were wrong?

Say­ing “Maybe heat and mo­tion are the same thing!” is easy. The difficult part is ex­plain­ing how. It takes a great deal of de­tailed knowl­edge to get your­self to the point where you can no longer con­ceive of a world in which the two phe­nom­ena go sep­a­rate ways. Re­duc­tion isn’t cheap, and that’s why it buys so much.

Or maybe you could say: “Re­duc­tion­ism is easy, re­duc­tion is hard.” But it does kinda help to be a re­duc­tion­ist, I think, when it comes time to go look­ing for a re­duc­tion.