Great, Nick. Hadn't thought of the triangle. Neat way of getting at it. So the relation is real but not yet as a concrete number. The triangle example says that the ration of the hypotenuse to the side is sqrt(2) :: 1, but it doesn't give us an actual number as a "real" thing. (I hesitate to use "real" since I'm not about to define what that means. I'm certainly not pushing a Platonic view of mathematical entities.)
You wrote: I don’t think Eric and I are committed to the proposition that imaginary numbers aren’t real. They are signs that stand in a rigorous, systematic, and extensively confirmed way for a vast collection of mathematical relationships. If you could show me that the idea of subjective mind is embedded in a structure of experimental experience as rigorous as that which embraces the square root of two, I would concede the argument. (I'm assuming you meant irrational numbers, but imaginary numbers raise a similar problem) I find myself confused about what you mean when you say they are "signs that stand in a rigorous, systematic, and extensively confirmed way to ... mathematical relationships". A sign is not (in your view) a thing (other than itself) is it? I would have thought that a sign it's a reference to a thing. The thing itself is only brought to mind (in the mind) when looking at and thinking about the sign. And mathematics itself is only confirmed by what people say. It's a very conceptual discipline. It's not an empirical discipline. So let's say we take a paint color strip and ask people to select from a list of five color words (along with non-of-these as an option) the best match to the color experience they have when looking at the strip. Let's say there is essentially universal agreement. Is that good enough to confirm that they all have the same color experience? That sounds more empirical than mathematics and should satisfy your requirement for an experimental experience -- although I'm not sure what you mean by "experimental experience". On Thu, Mar 3, 2016 at 10:33 PM Nick Thompson <nickthomp...@earthlink.net> wrote: > Well, Russ, now, I think you might be ready to see (be the only one to > see?) the force of my making an analogy between the first derivative of a > function and the motivation of a behavior. > > > > One can see and touch increasingly accurate approximations to it, but one > can never see and touch the square root of two itself -- at least not as a > concrete number. > > > > Funny I wonder what the mathematicians on this list will say about this > statement. It seems to be that the problem of the square root of two is > the reverse of how you have it. You can touch it any time. Just lay out a > unit isosceles right triangle and touch the hypotenuse. The problem is > that you cannot measure it using a unit ruler. The square root of two is > concrete; it’s just the ruler that measures it is abstract. > > > > But I don’t think Eric and I are committed to the proposition that > imaginary numbers aren’t real. They are signs that stand in a rigorous, > systematic, and extensively confirmed way for a vast collection of > mathematical relationships. If you could show me that the idea of > subjective mind is embedded in a structure of experimental experience as > rigorous as that which embraces the square root of two, I would concede the > argument. > > > > Nick > > > > Nicholas S. Thompson > > Emeritus Professor of Psychology and Biology > > Clark University > > http://home.earthlink.net/~nickthompson/naturaldesigns/ > > > > *From:* Friam [mailto:friam-boun...@redfish.com] *On Behalf Of *Russ > Abbott > *Sent:* Thursday, March 03, 2016 10:09 PM > *To:* The Friday Morning Applied Complexity Coffee Group < > friam@redfish.com> > *Subject:* Re: [FRIAM] Subjectivity and square roots > > > > Since Glen missed the square root analogy, I'd like to repeat it. > > > > Nick and Eric seem to be saying that there is no such thing as subjective > experience since only things that can be seen and touched are real. > > > > I said that such a position seems to deny the existence of the square root > of two. One can see and touch increasingly accurate approximations to it, > but one can never see and touch the square root of two itself -- at least > not as a concrete number. > > > > One can also see and touch Newton's algorithm for computing the square > root of two. But again, not the number itself. > > > > So does that mean from Eric' and Nick's perspective there is no such thing > as the square root of 2? > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com
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