ergman wrote:Mmm. Everything is relat
edive. For example: every way we have of giving directions becomes arbitrary at a certain point. Left and right are relative to the direction you're looking, north south east and west are planet specific, as are up and down. Is there some universal three dimensional grid of dimensions that people use to chart space, or is that relative too at some point?
Quite so. Even assuming universal agreement on three perpendicular axes, the location of the origin, the distance that each unit (amount of "one") equals, and the direction of the first axis are completely arbitrary. After that the direction of the second axis is partially confined but you still have a 360° range to choose from, and two choices for the third axis. Einstein also reminds us that all frames of reference are relative, so this is actually a very important tenet of science.
Eternal Density wrote:Interestingly, while cryptography (i.e. hiding information in a form that only specifically limited agents are able to obtain it) doesn't exist in nature, coded information systems do exist throughout all life, to the point that they are a sign either of life or the products of living beings.
Indeed, because sometimes "code" just means you've written something down for you or someone else to read later and doesn't always imply that you've applied an obfuscation method that must be reversed by the reader.
charlie_grumbles wrote:I don't think mathematicians think like that. Mathematics isn't (in our view) inherent in anything except the human mind. We "see" order in the universe, but it is an order imposed by how we think of it, not, precisely speaking, how it is.
Math is "pure mind stuff" (I think I'm quoting a badly remembered source here).
I'm pretty sure that physicists feel the same way. Physical theories aren't inherent in nature, but explanations of nature imposed by the way we choose to think. Both mathematicians and physicists build models of things and we have a bias for simple models (Occam's Razor). So, we say the earth follows an elliptical path around the sun, but that is far from accurate. It is just an approximation. The reality is that there is lots of wobble.
So, I think you have the understanding of the relationship between math and the universe just backwards; not an uncommon view. It isn't that there is math in the universe. It is that, in math (and somewhat differently in physics) we build models that help us understand, in a simple way, the complexity of the universe. But the math is in us.
I think I'm on pretty solid ground above, so I'm going to speculate a bit here. I've gotten some push-back on the following in the past, and physics is not my main study. But I'll make the bold claim that Atoms don't "exist". Neither do quarks and muons and all the rest. Those are just explanations, thought up by smart people to try to explain the complexity of the small. They are a mental model from which we can predict phenomena pretty accurately (not exactly). The reality is more complex than the model. Physicists, however, speak of quarks as if they "exist", but I think that really what they mean is that there are some phenomena that are "well explained" by the idea of quarks.
So, in this view (my story, and I'm stickin' to it), the universe isn't "built up" from small things like quarks. It just IS. We use quarks as a way to get a simple (hmmm) way to think about that complexity. Neither does it embody mathematical principles. People think those up themselves. But math is also used to build "sensible" models (i.e. predictive models) of how it all hangs together.
Again, I'm mostly speaking off the cuff and we're not really in disagreement on things, I think.
Elliptical orbits are there because they work
. Planets don't decide to move in an elliptical path rather than a circular one, and they don't sit down with a calculator and run the figures, they just settle into a path that keeps them around the sun or they fly off into space. It's quite mathematical (though as you say, not with 100% precision) because there's a definite consistency there, but the formulas describing it exist because humans were curious and wanted to know why.
As far as the difference between the theory and reality, especially on the atomic scale, yes, the purpose of science is to describe and predict within a desired amount of precision and on a particular scale. Newtonian physics describes things wonderfully at a macroscopic level but disintegrates on the atomic scale. But what about the reverse? If all movement of particles can be alternately described as waves, does a thrown baseball have a waveform? The answer is yes, but it's so damn small compared to the baseball as a whole that it's not worth bothering with.
If you look at the history of knowledge about the atomic and sub-atomic scale, each new theory explained things that were known at the time. As we get better at investigating the quantum world, we find new things that existing theory doesn't fit, and so we refine the theory in a way that includes the new things but doesn't change the way that the older model fit with all the things we knew about before.
It's kind of like this comic http://www.xkcd.com/435/
again. If you are looking at behavioral mannerism you don't spend a lot of time thinking about how cells work. If you are looking at cells you don't spend a lot of time thinking about how atoms and molecules work. If you are looking at atoms and molecules you don't spend a lot of time thinking about how quarks work. And if you are looking at behavioral mannerisms you certainly never spend time thinking about quarks. It's all down there, or rather something that roughly corresponds to the descriptive theory is down there, but each theory is suited to the thing it's describing on the appropriate scale.
SBN wrote:I've got some domesticated wolpies here that very much understand hours. I must arise each day at 6:00 am. Breakfast is to be served precisely at 8:30 am, and dinner exactly at 5:00 pm. Bedtime is 10:00 pm. Any deviations from these times are met with severe disapproval, and the occasional paw-smack. They do not appear to understand days of the week, though, so this schedule is adhered to even on the weekends. The humans in the household do not have anywhere near the regularity the dogs have. (Other than that enforced by the dogs.)
My meowlpies seem to understand time as well, though I am not sure how. They get off track during time changes (well, so do I), so instead of trying to get me up at 6:25 a.m., they were trying to get me up at 5:25 a.m. But then they seemed to figure it out when, despite their efforts, I refused to get up to feed them and they would not hear my alarm for another hour. By the way, their attempts to wake me up are consistently 10 to 5 minutes before my alarm goes off, so I know they are not basing their actions on my alarm. Also, it is a similar ritual at night. They start to gather around at 11:50 p.m. because they know that I will be feeding them at midnight. Again, during time changes, it takes them a week or two to adjust, but they do finally get it. Their schedule, like my own, revolves around specific hours of the day, and not just external cues that I may be providing.
How interesting! They must have very accurate circadian rhythms. Although this is somewhat Pavlovian, they only expect to be fed at a certain time because they learned that food would be given to them at a certain time. If these were not domesticated animals they would not have that luxury. I wonder if zoo animals, despite being not very far removed from the wild as a species, can develop a similar sense of when "feeding time" will be.
And yes, your cats getting you up are basing their actions on your alarm, but in anticipation of it rather than reaction to it. That's why the daylight savings change throws them off but then they are able to readjust.
Edit: spelling error fixed