Talk:Where Mathematics Comes From
the quotes were already in fair use on the page of reviews of Lakoff and Nunez referenced at the bottom - I presumed (perhaps wrongly?) that this means that they were cleared for quotation. Only the Santa Fe one seemed to be long, but it's quite specific, and justifies the claims int he rest of the article, so I'm not sure the scope of this is very clear without it... but I'll go with consensus, obviously.
It's significant to the article that "counting up to four" and moving along a line are empirically observed cognitive phenomena. Does it really make sense without that?
The Sigma Xi review is of the first edition which had technical errors.
My careful read of the other reviews, which include some pretty prominent journals and institutes, didn't make note of those errors, and the reviews have been up for some time, so presumably they'd object if they thought the overall theory was wrong.
Nonetheless, it speaks to the care of the authors that the technical errors be mentioned by some neutral party, so the Sigma Xi review belongs there - maybe with a note to the effect that these errors don't seem to have caused the other later reviewers to give up on the theory.
OK- scratch that - I see there's now a link to their "warning" about this.
Removed this from the article:
- It may well be that turning mathematics into an empirical science will involve a great deal of animal testing, to determine what's shared - and what is merely a widely shared human bias, arising out of our over-complex brains.
Many things may be, but this is unlikely to be one of them. Who says this? Other than you?
The objection is legit, thanks, but when you changed it you said this was deleted for being "surreal" - I admit it's speculative, but what's "surreal" about empirical testing of a cognitive science thesis, to see what we say share with apes and what is uniquely or bizarrely human?
Most of anthropology and primatology recently seems to be testing what things apes can do, what they can't, where we share a foundation ontology with them, where we don't. For instance how do they see 'family', or 'friend', or etc..
I also can't be the first person to call the human brain "over-complex"... I thought it was kind of a crack on the whole community arguing this stuff, as well... many wouuld just say "mathematics works" and leave it at that...
But the article is controversial enough without this suggestion of a path to validating... I'll actually see if I can get a quote out of Lakoff or find the material on chimps being tested to determine who real "number" is to them - saw this being done in a lab in Japan - on the Discovery channel - as usual the credits scroll by too fast adn the researchers name is too Japanese. ;-) But I'll dig it up.
"Clearly, when a man shoots a bear it is not only the man whose experience of the bullet is defined by "F=MA"."
This was actually the exact sentence (in private converation) that convinced me that mathematics could not be wholly a human invention...
The bit about nuclear weapons seems to be totally unrelated to the topic in the first and second sentences of that paragraph. The article as a whole is a little confused and poorly organised - perhaps a re-write is in order? As to animal testing... You mean experiments conducted using animals which is an different kettle of fish. -- The Ostrich
No, both topics are related, and if that's not clear, I'll fix it. Tell me if it makes more sense to you this way. Lengthy but clear:
1. if mathematics is a system that arises from constraints in the cognitive makeup of humans, then we cannot know what is "human delusion" and what is "objectively real" without some non-human animals to test mathematics on. Scientists in Japan are presently testing chimps to see how much of math they can master. If it turns out that they can master all the basic traits like "counting up to four", then this cognitive science of mathematics must apply to them as much as to humans - and we ought to be able to discuss it with them, or jointly agree with them on concepts like "whether this is four coconuts or not". This amounts to a primate testing of mathematics itself.
It is certainly an experiment, and it is certainly conducted using animals, and it is being done now. It's a glaring and obvious issue with the L&N claim that somehow mathematics is "uniquely human" or that we "can't know how much of it is objectively real" - we can at least know how much is shared with near cousins.
2. more difficult, the physics question. Addressed somewhat in particle physics foundation ontology. Tom Siegfried's objection is different, that what scientists see in a particle accelerator can be modelled using math - although Dirac had to invent a different notation I think that's a side issue.
If mathematical models such as those in physics are shared only by humans, and it's not clear that the "reasons why we believe there is a new particle" can be shared beyond humans, i.e. the chimps don't know what we're talking about, and when they look at the charts they just scratch their heads like any untrained human, then the reality of these theories are on shaky ground.
If it's only highly trained humans saying that they saw this particle and that this math is therefore "real", well, we start to be on shaky ground... Siegfried's assertion may well be more controversial than any by L&N here.
3. most difficult, the ethics question. The use of nuclear weapons and particle accelerators are restricted by a lack of opportunity to test the theories. WE CANNOT SIMPLY TEST ALL THEORIES OF WHAT WILL HAPPEN EQUALLY - therefore we have a lack of objectivity in experiments the same as we (might, if you accept this cogsci of math stuff) may lack such objectivity in notation.
This is very closely related to the argument about censoring science distorting it, and the Precautionary Principle which says you should not test a theory if one of the conceived outcomes of the test is destroying something you can't replace. Probably this is too complex to bring up in this entry, but:
We have ethical obligations not to destroy the planet to see if nuclear winter will happen, and there is a limited amount of particle acclerator time for which scientists compete fiercely. So inter-human politics absolutely deterines what theories get tested, which tends to determine what theories get discussed, which is in turn going to guide what theories get proposed.
This is also called "the paradigm problem" - when do we give up on some infrastructure, and tell the scientists who were "improving" it or using it "to test a theory" to go home, and that they aren't needed any more....
Extreme form of this argument: nuclear weapons aren't needed since they lead to more trouble than they're worth. Therefore, particle acclerators aren't needed since they are likely to shed light only on more ways to get big bursts of energy and blow up more stuff at once, or make black holes to suck up the Earth. Therefore, particle physicists aren't needed, etc...
If you accept the cogsci of mathematics as real, then all this stuff that was built assuming that the mathematical models were "real" and could be validated by simulations (purely mathematical) or complex webs of assumptions about the observer infrastructure, becomes very very doubtful.
So, it's one of the objections to this, that the cogsci of math is just one of those politically motivated theories that gets in the way of "real science"
I wanted to deal with that objection, which isn't possible without laying it out a bit.
Whew.
OK, now I need a beer.
I think the "bear line" and the "primate testing" line really get across the point. However, it would be nice not to have to lay out ALL the details of the objection and debate as above.
I also still think that without the Santa Fe quote, no one is going to really understand the scope of this, or how limited it really is - making it feasible to test - even on chimps.
OK, I see what you mean about the nuclear weapons thing, it wasn't clear that this is a view of Zerzan and Waring rather than Wigner. Now it is, and there's some bridge there.
I also mentioned the relationship with the Precautionary Principle - and the common theme of limiting trust in human constructed mathematical models, and deliberately choosing "not to go there" as a consequence of nuclear standoffs.
I could have mentioned climate change too, but that's not generally seen to be something that can destroy all cognitive beings - just make us war more...
Lakoff is a highly political commentator so it's not really right to avoid the politics of his conclusions. Although he carefully quotes in his reviews people from technical communities who agree with him, his overstatement of the degree to which "mathematics is human" is a clear sign of a certain bias.
Mathematics, to the degree he's talking about it, which is not very far, is just as well understood by chimps, and probably by dolphins, horses, and dogs.