You’re just not teaching them properly. You have to make it relevant for them, i.e. relate it to the arc that a mouse flies as the cat bats it around, and how to calculate the intercept at any part of that parabola. Also, in terms of numerical simulation of differential equations, cats generally think the Newton-Raphson methods are unsuited to their applications, as they are unable to cope with the complex dynamics and varying simulation step-size necessary to model prey movement. I’ve found that they tend to prefer embedded Runge-Kutta methods, particularly Dormand-Prince and Kash-Carp methods.
Very much so. This is absolutely clear with quantum mechanics; we persist in trying to define behavior in the quantum regime in terms of the classical, quasi-deterministic perspective that works so well for us in everyday life, and it utterly fails us, leaving us with the so-called paradoxes of particle/wave duality and non-locality. In fact, these phenomena are not real paradoxes, as they can be experimentally demonstrated and verified; they just highlight a failure in our language, and therefore our conception of reality, to comprehensively model and comprehend behavior on this level. When you try to deal with this using natural language and philosophy, you end up with glurgage like The Tao of Physics. When you ignore all of the supposed philosophical/theological interpretations and just do the calculations, it works to a very precise degree, as demonstrated by the theory of quantum electrodynamics (often called the “Crown Jewel” of modern physics owning to the high precision in correlation to prediction and experiment).
It is unlikely that we will ever “understand” certain aspects of physics and large-scale complex system intuitively without very fundamental changes to our cognitive structure. As it is, we have to use digital computers running very sophisticated algorithms to simulate phenomena like protein folding, complex network theory, climate behavior, and quantum interactions with any system larger than a single hydrogen atom; these computers act to augment our comprehension (such as it is) of the basic principles with an ability to perform the rapid, synchronized calculations capable of generating any useful predictions.
Or, as Arthur C. Clarke wrote, “Any sufficiently advanced technology is indistinguishable from magic.” What Clarke failed to note is that pretty much any technology more complex than a lever and fulcrum is already “magical” as far as the average person–even an educated and literate one–is concerned. (Just ask your favorite smart person how a block and tackle system works; unless he or she is an engineer or particularly perceptive mechanic, you probably won’t get an intelligible answer.) And even people who are really educated and intuitive about basic scientific principles are generally only conversant in the application to their specific area of discipline; it is a rare electrical engineer who can explain the inner workings of a turbine engine, or a physicist who can speak intelligibly about power distribution systems. Practically no one can explain how something like an iPhone works in fundamental terms; even to a computer engineer it is near-magic that all the computing, communication, and display technologies come together in a way that would have made Stanley Kubrick squeal like a schoolgirl. And this is applied science that is a part of our everyday experience. If we can’t wrap our individual minds around that, what chance do we have of understanding the underlying physics of the universe in a way that is intuitive and useful?
(And if the response is “We will never exhaust the things within our grasp; thus, there will be no end to science”, then arguing that there are things outside our grasp is irrelevant)
We won’t be limited by human cognition forever though. Advances in biotechnology, robotics, nanotechnology, etc. is going to dramatically increase our cognitive abilities someday.
Humans can only walk at about 3mph, and only for a few miles before they get tired. But jets piloted by humans fly at 2000mph for hours on end. The same thing is going to happen with cognition over the next 100 years or so. We will find ways to augment it.
Arguably things like the internet and cell phones have already created first generation cyborgs. A person sitting alone on a park bench with a cell phone or netbook has a device that lets him be in contact with 3 billion people and look up answers to almost any question he has off the top of his head in a few minutes. A person in 1900 who saw that would probably be extremely impressed by the abilities of a person in 2009 with a 3G cell phone. But we just consider it normal.
My gut feel is that someday in the FAR distant future, if we as a race continue to advance our understanding of the universe, then yes, someday we can understand it all.
It’s conceivable at some far, far distant point in the future that we could know “enough” about specific areas of the natural world that additional investigative efforts will be seen to be kind of pointless or overly resource intensive, but as we know more there is (usually) more to know so the overall answer is no. Empirical investigation of the natural world will continue virtually into infinity.
The laws of physics and chemistry may someday be known entirely, but the “stamp collecting” forms of science will never be concluded. There will always be new stars and planets to study, new species of organisms to be discovered and catalogued, etc.
Humanity can understand far, far more than humans can. Most topics in science are studied by breaking them down into pieces, and each scientist then proceeds to study a few of those pieces. When you’re done, you can have a full understanding of a very complicated system spread out over many scientists, even though no individual understands it all. I think that language and writing is the key that makes this possible, such that no species without both (such as cats) can ever go very far in their understanding, but that any species that does have both (such as us) has no ultimate limit.
Aren’t people taking a rather short term view here?
Think of all the progress made over the past century or two in understanding how the universe works. Say that society doesn’t lose interest in science, and it keeps going for 100,000 years.
OK, this makes it clear you haven’t tried teaching the cats calculus. I bought them nice tutoring software, and they just napped on top of the computer. I got Stephen Hawking to come give them a lecture, and they hid under the couch. I set up a ping pong ball about 100 mm above the floor and set the first time derivative of its height to zero, and left it there for them to discover, and they ignored it - then I forgot and erased the equation, and it fell and rolled away, and THEN they were fascinated - you’d think levitating a ball all afternoon would be worth a look, but no. Finally I blew way too much money on a bunch of stuff to demonstrate exponential decay and half-lives, thinking the simplest differential equation in the world would be irresistable, and one of the little buggers sprayed the source housing, and it got all corroded because I didn’t notice until a couple days later, and I had promethium salts wafting all over the guest room to deal with.
Every answer that we get (even when 100% correct, which is fairly unusual) brings up myriad additional questions. And ‘science’ runs the gamut of human experience. We’ll never even run out of questions and answers on this planet, let alone all the other planets out there in the universe. And there there are all the questions about the other dimensions, parallel universes, etc etc.
Our species will die out long before all the questions are answered.
If that happens (humanity keeps on doing science in at least as rigorous a fashion as it’s been doing the last few hundred years) - and I’m skeptical that it will - compared to what we know now, we will either have reached unimaginable levels of understanding and quite probably be at such a point that there is nothing more “natural” to explain, or we will reach a plateau beyond which it is not possible for even the brightest of us to reach further (as Napier said).
Option 1 means we already know “everything”, option 2 means we aren’t intelligent enough. From what I can see at the moment, it seems more likely - if we ever get to that level - that we would be able to genetically engineer our offspring to be more intelligent and hence be more able to understand the natural world. So I’m going with “yes, it’s possible that we will be able to understand everything - at least as far as ‘natural science’ is concerned, as a species at least” with the caveat that I don’t really think it’s likely civilization will last that long.
In addition: it’s quite possible that we won’t know ever, if we’ve reached either level. I am disregarding the option that it is completely impossible for anything to know “everything” as far physics is concerned, but that does not mean that whatever turns out to be the “true law” cannot be unpredictable on at least a small scale - like quantum dynamics, for example.