That’s what math is, except the ‘arbitrary’ part is constrained by the fact it has to be rigorously logically consistent in ways nothing else in life does (because if anything is as logically consistent as math, it is math).
You can say that. You aren’t saying anything interesting, but people say dull things all the time. The rest of us will be over here, playing and doing useful things with modular arithmetic, which is what I described in that post.
Well rebutted, Derleth. I was going to say much the same thing, but you said it better. The “clock” analogy for explaining arithmetic modulos (and thus, indirectly, for exposing the arbitrariness of base-10 and, even less directly, the aribitrariness of lots of things…but therefeore the heightened rigor of wahetever’s left) works quite well for math dunces like myself. Most of us understand that such analogies only work so far, and don’t need to have it spelled out for us what the approximate domain of appropriateness is.
Instead of getting your knickers in a twist, why don’t you enlighten us to what is so useful about that thingy you’re playing with?
Maths is not really about utility. In order to find a use for an area of mathematics that area has to exist beforehand.
Why pick on modular aritmetic though, it’s actually a fairly simple idea that been around for centuries in maths and it has plenty of “real-world” applications.
And to anyone who says it’s arbitary relabelling, i’d say:
a lot of maths is about relabelling as maths is about abstraction and abstarction is pretty much about relabelling in order to capture ideas in their full generality to give them the widest possible application.
This relabelling isn’t arbitary, the “arthimetics” (or to give them their proper mathematical name - rings) formed by congruence classes are different artimetics ) to the arithmetic of the integers (i.e. they are not isomorphic in the catergory of rings except in the degenerate case).
Not to belabor the point, but ID proponents admit that species evolve. Hard for them to ignore all the empirical evidence. They maintain, however, that one species cannot evolve into another species (although there is plenty of evidence for that, too). They refuse to admit that we evolved from lower forms of primates. I once pointed this out in a letter to the editor, and I received an anonymous letter (no return address, of course) that I may have evolved from a monkey, but that he most certainly did not.
Well, he can always hope for his descendants to get there.
Practically all computer arithmetic on integers is modular arithmetic: You only have n bits to represent the value you’re doing math on, so all of your math is done modulo 2[sup]n[/sup]. For example, if you’re writing integer code for a 32-bit system, your integers are 32 bits wide, which means if you have a value one less than 4294967296, adding one to it gets you back to zero. This is equivalent to saying 2[sup]32[/sup] ≡ 0 (mod 2[sup]32[/sup]). (All arithmetic is unsigned; assuming the more common wraparound semantics as opposed to, say, a DSP with saturation semantics.)
(You can use software to get values larger than what you can represent with machine words but, ultimately, you have a finite amount of storage so all computer arithmetic is modular. If the modulus is large enough, you simply stop caring.)
Also, These are my own pants makes wonderful points and, were I a different kind of mathematician, I would mock you quite scornfully for being so artless and ignorant as to imply math should have practical applications.
See, this is where you lose me.
I have no doubt modulo arithmetic has some really fantastic uses.
But when describing reality (i.e. in the universe we live in) we are not restricted to modulo math. We have an infinitely long number line and not a truncated subset of that turned into a circle.
Again, I have two apples and you give me two more apples I have four apples. How does your modulo math get away with saying I have zero apples in that case?
It can’t.
2+2=4
Seems to me even in your example of making it zero there are still four “ticks” or “movements” or “steps” (whatever is it properly called) around your circle. You may land on zero but there were still four iterations to move around that circle that got you there.
Who says math is about describing reality? Sometimes it does, sometimes it doesn’t. It’s interesting either way, and being interesting is what math is about.
It was you that, trying to be smug, started on the whole usefulness road.
Now, binary arithmatic I can grok, also that there might be others and that it can be a ‘fun’ exercise.
I readily admit to be largely ignorant on the matter but my skeptic mind simply had problems with that gauge example.
Always seemed to me that math was the language of the universe.
When prying into the fundamental reality of things the bottom line for doing so is math.
I have been told by physicists (one of my brothers is a physicist) that at the end of the day words fail them when explaining certain concepts and if I really want to understand what is happening I need to understand the math.
Hell, I think that gold record we sent on Voyager to “talk” to aliens if they found it used math to communicate. Obviously an alien will not know English but presumably math is universal and they’d understand that.
Math is WORDS now? Then with my English degree I could be the next Stephen Hawking!
Math is the language we use to describe the universe. The universe doesn’t “care” about math. It’s a human construct.
I studied physics, and I agree. But does that say anything fundamental about the universe itself, or our ability to understand it?
Only in the sense that sentient beings should understand this. Again, the universe just is. It doesn’t “need” math.
I find this interesting but rather than continue what amounts to a hijack (one I started) here I started a new thread to explore this here.
What? I was not trying to be smug. If I were, I wouldn’t merely have tried: I’d have succeeded.
The universe doesn’t have a language. Humans create language.
True, in that math is the only language we have without ‘common sense’, which is the bias inherent in any language evolved or designed for normal human interactions with things like humans and mangoes. ‘Common sense’ is a hindrance when trying to describe photons in a useful fashion, because nothing in our common human experience acts like a photon really acts.
This is also the trait that makes math universal: If you want to describe rocks, you need some language that counts rocks, and arithmetic is the formalized version of that. If you want to describe moving rocks, the calculus is what you must end up with, assuming Newtonian physics works everywhere. And so on.
http://www.washingtonpost.com/blogs/on-faith/post/attention-governor-perry-evolution-is-a-fact/2011/08/23/gIQAuIFUYJ_blog.html
This Dawkin’s article was put in the Elections Threads. It should be here too. Evolution is in line with historical evidence and can be used to predict. It is a fact.
Pretty much this. Describing Evolution as a fact or saying that it’s “just a theory” is conflating how we use the words “fact” and “theory” everyday with how those words are used in science. We use the word “theory” commonly to express something that we think might explain a set of circumstances or might solve a problem, but that concept is much closer to the scientific usage of “hypothesis” than the scientific usage of “theory”. Instead, in science, “theory” is a level much stronger than that and refers to such an explanation that has withstood significant scrutiny and many attempts at falsifying it’s predictions. Similarly, “facts” in science are observations or measurements.
As such, saying evolution is just a theory implies a degree of uncertainty based on common usage that just isn’t there. That it’s a theory doesn’t imply that it the absolute truth, as future observations or circumstances may arise that result in some modifications or a new theory entirely, but there is by no means any uncertainty that the theory is the best explanation we have that best fits the observations.
Similarly, saying evolution is a fact or, for that matter, that gravity or any other widely accepted theory is a fact is nonsensical. The theory predicts what will happen under a certain set of cirumstances, such that when I hold something up and let it go it will fall. When I actually do that and observe it, that is a fact, and it is whether or not it is consistent with the prediction of the theory that adds further confirmation or potentially falsifies its predictions.
So, to answer the OP, in the scientific sense, no evolution is not a fact. But in the way we commonly use the term, then yes.
Nothing in science is ever really proven. Things can be supported, refined or disproven, but not completely proven.
Ptolemy had an effective solar system model by which he could predict planet locations, but it was still based on an erroneous, geocentric paradigm. It is my conviction that evolutionary theory is also based on a false paradigm. I used to accept the possibility of theistic evolution, but now reject it after much study.
The origin of viruses is unknown, apparently by evolutionists or creationists (such as myself), but there is speculation by both sides. They are not considered living, but DO carry nucleic acid information. My speculation is that they served a good purpose once in gene transferrence.
You are conflating evolution with natural selection. Evolution is a fact. We see simpler life in older strata and more complex ones in newer ones. We can look at the genetic information in plants and animals and it corresponds to what we see in the fossil record.
Maybe God was involved in every single new species being created, but life is all made from the same stuff and it is clear that new species appeared over time based on changes to the existing species.