Exactly.
Blake, the cite and quote provided by Jovan above suggests (to me anyway) that rather than there being a part of the brain dedicated to multiplication specifically, rather, there’s a part of the brain useful for a general class of problems of which multiplication is just one instance. Do you agree?
In regaurds to the Calculus brain center thing.
Spear throwing relies heavily on calculus. You don’t throw a spear directly at your target. You throw it at a spot above your target because gravity will bring it down. Space is curved, if you throw something in a straight line gravity will bend it’s path. Figuring out how high to throw the spear to compensate for gravity requires predicting how gravity, wind resistance\speed, and throwing speed will make it’s path arc, which requires instinctive use of calculus.
Any chance the brain is making use of, and building on, it’s natural calculus wiring to do formal calculus?
I’m not so sure I’m “doing calculus” in any useful sense when I successfully throw a ball at a target.
Abstracting down a bit, I could probably write a computer program right now that figures out a set of correlations between vectors and points, and a means of interpolating between these correlations, such that after enough practice it does a pretty good job of hitting targets in an environment with gravity, all without the program explicitly “doing calculus.” It would simply have acquired a general “feel” for a relationship between vectors and goal points.
In any case, even if spear throwing is a way to do calculus, the activity is completely divorced from the kind of symbol manipulation done in formal calculus.
I would assume that the process of learning to account for all of the factors to throw the spear properly has more to do with the nature of the brain and how it learns things. Even if it mimics a calculus calculation in the end result, I would be surprised if it used the same facilities that allow us to understand and solve calculus problems in general.
Edit: Didn’t see Frylock’s post
I doubt it. For that matter, I wouldn’t really say that determining the arc of a thrown spear requires calculus; to a reasonable enough approximation, we’re just talking about a parabolic arc which reaches its peak after an amount of time directly proportional to the initial upwards velocity [specifically, that divided by the gravitational acceleration of 9.8 m/s^2], and thus returns to its initial height after twice as much time, the horizontal distance travelled being at any moment proportional to both the time elapsed and the initial horizontal velocity [indeed, exactly their product]. Evaluating such relationships of direct proportionality doesn’t require calculus; you’d only need calculus for the task of abstractly deriving such formulas from first principles.
ETA: Didn’t see anyone’s post. This was in response to The Tao’s Revenge.
Speaking as a primatologist, apes are not monkeys and all the primatologists I know hate it when people call apes monkeys. My teachers and TAs have ranted against it many times. There might be primatologists who call apes monkeys, but I think they are a minority. There’s a joke that you can tell who a primatologist is because they call monkey bars by their ‘correct’ name, ape bars (as in apes have the bachriation complex while monkeys do not).
The thing is ‘ape’ is a taxonomic term that implies common ancestry and relationship, ‘monkey’ is not. DNA testing and phylogenies have shown that Old World Monkeys (Catarrhini) are more closely related to apes than they are to New World Monkeys (Platyrrhini) and calling them both monkeys implies a close genetic relationship. ‘Monkey’ is considered a paraphyletic group in that it contains the most recent common ancestor but not all the descendants of that ancestor (apes). It’s about grade versus clade. Grade is what monkeys and anthropoids are, or, things that were grouped based upon similarity in appearance. Clade, which most of us scientists care about, are groupings that are based on phylogeny rather than appearance.
But why not use the term “monkey” to denote the minimal clade containing both the Old World Monkeys and the New World Monkeys (and thus containing apes as well)? After all, this usage of the term is prevalent throughout so much of ordinary language (that of the “layman”); why cling, then, to a gerrymandered technical definition which both contrasts with this and which lacks the naturality of a monophyletic grouping?
Because they are similar in appearance (convergent evolution) and that can be useful for some things. Think of it this way. Reptiles are a paraphyletic group because it should includes birds to be a true monophyletic group. But we don’t like to always group animals based on evolutionary history.
Fair enough, I suppose, though I still wouldn’t want to call out the layman for departing from this particular codification.
Just in passing, did I have all the families described correctly in my earlier ‘monkey’ post?
Mathematically speaking… this is geometry, not calculus. Practically speaking, it isn’t even geometry, it’s trial and error.
It is safe to say that natural human cognition has absolutely no awareness of relativity whatsoever, nor any need for it.
It may just be because I study it, but I think that we should know more about our close ancestors and our place in phylogeny than less. And aren’t we on a board devoted to fighting ignorance? I always correct people on the issue. It isn’t hard. Gorillas, chimps, orangutans, gibbons, and humans are apes: we can swing from the trees. I don’t mind too much when people call Lemurs monkeys, but I think that the average citizen should be able to correctly distinguish between a monkey and an ape, particularly because we are apes, but I also think that evolution should be a basic course taught in school.
Not exactly, Polycarp.
Order Primates is divided into Strepsirrhines which are Cheirogaleidae, Lemuridae, Lepilemuridae, Indriidae, Daubentoniidae, Lorisidae, and Galagidae.
Haplorrhines are tarsiers, Catarrhini and Platyrrhini.
In Catarrhini
Families: Hominidae (humans, chimps, gorillas, orangs; otherwise known as the great apes), Hylobatidae (gibbons and siamangs [lesser apes which people who study them hate calling them]), and Cercopithecidae (Old World Monkeys).
In Platyrrhini (New World Monkeys)
Families: Cebidae (marmosets, tamarins, squirrel monkeys, capuchins), Aotidae (owl monkey), Pitheciidae (titis and sakis) and Atelidae (woolly, howler, and spider).
I had a primate evolution class where I had to be able to draw all these out and give at least one species example for each of these families. If we ever meet, I can draw out all the trees which is far easier to understand! I did a google image search to try to find a good tree with all the details but couldn’t.
But it’s not knowing more or less about our close ancestors to decide whether or not to use the term monkeys to denote a full clade or just a paraphyletic group; it’s purely a terminological convention, for us to set one way or another. And if the layman decides, for whatever reason, to employ this term in an evolutionarily natural way which just happens to depart from technical jargon which focuses less on evolutionary history and more on current similarities, well, that doesn’t indicate ignorance about evolution, just about an arbitrary linguistic standard.
Sure, if anyone ever were to call a rhesus macaque an ape, call them out; the apes clearly form a clade which excludes the rhesus macaque, a grouping which is quite natural to speak of. But if one calls a chimpanzee a monkey, well, they’re just using a heterodox, but historically common and in some ways more natural, definition of “monkey”, as a clade rather than a paraphyletic grouping. They’re actually being more focused, whether they know it or not, on evolutionary relationships.
That is, you want monkeys and apes to be disjoint classifications. But why? Why not have apes constitute a strict subset of the monkeys, just as humans constitute a strict subset of the apes? [Why not let “monkey” be used synonymously with “simian”, at least in ordinary language, where it clearly often is? It betrays no evolutionary ignorance.]
Of course, there are those of us who, when we refer to “reptiles”, do include birds. Perhaps once the idea that birds are dinosaurs has sufficiently filtered into the lay-world, the concept that birds are necessarily reptiles as well won’t seem so foreign.
Actually, just to make sure no one misreads: mathematical skill is an expression of specific skills that are useful for other things than mathematics but are not general problem solving skills either. You can count, compare and estimate quantities. You can remember facts. You can follow a set of instructions. You can see and imagine shapes. Etc.
Right. But I don’t think anyone thought otherwise; the concept of a single generic “You can solve problems!” skill isn’t really all that coherent, I would think. Presumably, any time anyone has referred to general problem-solving skills, they’ve just meant, as you did, “Skills which are wider in scope than specifically mathematical”.
That should have been your main point. Because that’s what it boils down to, really.
Humans are, by human accounts at least, the most stupendous killing machines out there. We’re very good at it, apparently. Also, we unilaterally hate those effing crawling pests. They’re gross, they’re creepy, they’re disgusting and we kill them on sight. We have for hundreds of years. We have developped intricate and downright Machiavellian strategies to deal with the Cockroach Problem. Killing them (and rats) is among the top list of homeowners priorities.
They’re still around. The rats, too.
The thing is, like some other terms, the distinction between monkeys and apes is an ex post facto one made by scientists. In non-technical English, the terms are interchangeable, and in my opinion it is pedantic to chastise someone for calling a chimp a monkey. In ordinary English, it’s perfectly valid to call a chimp or a gorilla a monkey.
“Ape” is the older term, originating before the 12th century, from Old English apa; monkey entered English in 1530, probably indirectly from the Romance languages. Originally monkeys were considered to be just a sub-category of apes. Gradually apes became considered to be a subset of monkeys, those without tails. And it wasn’t until the great apes became known, much later, that scientists began to make the technical distinction that now exists. But this is a quite artificial one and entirely arbitrary one considering the original English usage.
It’s a bit ironic now, since scientists have been insisting for a century or more that apes and monkeys were distinct, that according to modern cladistic classification that is quite false. As has been said, apes are simply a subset of monkeys. So if you want to make a technical distinction, the best you can do is say that all apes are monkeys, although all monkeys are not apes.
Yes, that’s what I meant by the phrase “a general class of problems.” I didn’t mean all problems in general, rather, I meant a class of problems more general than just (say) multiplication.