You say to your friend "it's sunny outside". He responds "the sun is just a cloud to me, everything is relative. One man's sun is another man's cloud".
FacePalm. AnythingIsPossible arguments are lame. Is it possible the sun is just a cloud? If everything is relative, the sun might be a cloud... Sigh. Sorry, but EverythingIsNotRelative.
If your planet is orbiting close to Rigel, Earth is nighttime on the sun-facing side in comparison.
We're talking about two people at the same location in the same room looking out the window saying "it's sunny outside, that is a sun". That's a fact, a fundamental thing, which isn't relative.. it's the sun. It's not a cloud, it's the sun.
So you are assuming context. If a Rigelian was around, that assumption would turn out to be "inappropriate".
{All quibbling over perception (and alternative symbology) aside, 2 is not 3, even for unusually large values of 2. This is absolute and not relative. Therefore, not everything is relative. (I'm not sure "everything is not relative", i.e., that there are no relative things, is quite what is intended by this page. There are some relative things, like "big" and "small" for example.)}
[There are some relative things for sure. It is only dark out, relative to where you are on the earth at a certain point in time. But not everything is relative - the sun is the sun, not a cloud. One could argue that the sun is just an electron cloud (or electron clouds) or quantum physics cloud of some kind, but that would be twisting words because what I meant by the sun not being a cloud, is that the sun is most definitely not the same as a white cloud in the sky made of water vapor and water drops. Likewise water is not fire, wood is not stone, and pigs cannot fly, and AnythingIsNotPossible.]
But the more specific you get the more you will need to draw arbitrary (relative) lines in the sand. The sun has no clear-cut boundary. It's energy and influence gradually taper off with distance. Photons from the sun are "in" clouds. You could only draw a hard line if you come up with some arbitrary (relative) definition, such as where the ambient temperature is greater than X, or whatnot. We can talk about clouds versus the sun because we mutually agree upon a UsefulLie for the sake of communication. And life goes on. But if it becomes an issue, such as "what are types", "what is intent", "is Pluto a planet?", etc., then finding a mutual UsefulLie is not so easy.
Everything is relative, but that's not necessarily a problem in many cases. Call it "argument by vote" or "argument by mutual agreement" if you want. It's not the ideal, but allows us to get along and move forward in most cases. It's a useful practice, not necessarily an ideal practice.
Disagree, everything is NOT relative. 2 is not 3. The sun is not water vapor. Pigs cannot fly. Another man's sun is not another man's dog.
Which numbering system? Which planet's atmosphere did you test the pigs in? Maybe God walks his sun in the morning and it barks and poops on the devil's lawn.
ItDepends, WishfulThinking, AnythingIsPossible, maybe there are UFO's floating in my bedroom with aliens opening the UFO doors and sucking paint off the walls.
You can't rule it out. Being 99.999999% certain is not the same as being 100% certain. Your assumption that there are no cloaked & hovering aliens in your bedroom is only an assumption. Perhaps 99.999999% is good enough for "practical" discussion, but that's still not absolute. It's still relative. If you want to say it's "not relative enough for practical uses", I might agree, but technically speaking, even 0.000000000001% relative is still technically "relative". -t
There are absolutes. There is a pencil on my desk, this is absolute. It is there. It's not relative.
Numbers don't exist in reality. They are a mental abstraction.
{Though you can't hold a number in your hand, that 7 is prime is indubitably absolute. So is the fact that a circle's circumference is always greater than its diameter, and plenty of circles exist in reality. The quantity of such absolute truths is likely infinite.}
"Circle" assumes a plane. Perfect planes probably don't exist, and the universe is probably curved in 4D.
{Irrelevant. That absolute truth still holds, as do infinite others like 2 + 2 = 4.}
Not. It's only a model that is "absolute" within a given model, with its subjective assumptions and givens.
{2 + 2 = 4 is an absolute truth, independent of any model and independent of any language used to express it. If you have two things, and bring in -- i.e. "add" -- two more things, you will always have four things regardless of assumptions or laws in effect or not in effect. Even in a universe of pure thought, without anything to count except ideas, two ideas plus two ideas equals four ideas. Mathematical truths are absolute; they are not relative.}
Independent of any model? Integers and human numbering systems are models. They are abstractions we humans created to model and track "reality" as we perceive it.
{Independent of any and all models. Do you genuinely believe there is any circumstance where the notion of a countable quanitity of two things, combined with another countable quantity of two things, is not four things?}
Bullshit. The idealistic model/abstraction in your head doesn't necessarily reflect reality. Approximate it? Perhaps. But it will always involve assumptions. Experiments will give mixed results, as you admitted. And define a "thing" or "object" in an absolute sense. Does the dust "on" it count? A certain percentage of what we often call the "human body" is actually bacteria (some good, some neutral, some harmful). Thus, is a person "one" organization, or billions? Note that some of the bacteria we cannot live without. It evolved as part of our "machinery". Is a brick with a chip still "one" brick? What about a dollar with a corner torn off? You are making yourself the center of the universe. It's a bad habit. Math is merely a UsefulLie.
{Beware of letting yourself be distracted by pseudo-philosophical arguments. You can attempt to divert the issue by quibbling about what a "thing" is, but that does nothing to disguise the simple fact that if you count to two, and then count two more (i.e., you add two to two), you get four. This is true independent of model, environment, or universe. Thus, 2 + 2 = 4 is an incontrovertible, indisputable, inarguable, absolute truth.}
...relative to the number model being used. In another number model, 2 + 2 = 7. We use the "usual" number model because it approximates reality relatively well, or at least most people mutually agree that it models reality "good enough" and mutually agree to use it as a common reference model. We simplify life by agreeing on reference models, but that doesn't make the model a universal truth.
Similarly, most engineers agree to use Newtonian physics even as they realize it has known flaws (relativistic effects, etc). However, the economic cost of using alternative models is judged as too great for organizations or domains such that Newton is the agreed-upon reference standard for most.
Complex/imaginary numbers is a case where a different number model is used because it better fits the domain (electronics) than "regular" arithmetic. It's a different UsefulLie. Thus, we already have multiple different number models in use and neither is a universal truth. Humans are economic animals and readily use and switch to different models that (are perceived to) maximize commerce as needed. Oracle and IBM chose to use "bags" instead of "sets" in their relational engines because they felt it was the better economic path at the time, not necessarily because bags were considered the "best" or "cleanest" model. -t
{You are conflating a language people use to represent numbers with numbers themselves. When I say "2 + 2 = 4", I don't mean the symbol with the curvy top and the flat bottom plus the symbol with the curvy top and the flat bottom always equals the symbol with the peaked roof, legs and a tail. You can replace "2" and "4" with any arbitrary glyph you like, as long as they represent the appropriate counts of things. Using counts of (for example) sticks (represented with a |), I mean (count with me, here) || plus || always equals ||||. That is an absolute truth. It is not relative.}
Symbols are how we communicate back and forth. It's the only way so far, even. The only "real" numbers are in people's heads. But, that's not "real", at least in the normal definition of "real" ("real" is relative too ;-)
As far as sticks, we are right back to the "chipped brick" kind of problems. What if a stick breaks in half while doing the counting? Or termites softened them so that they merge together after a rain? The number system approximates sticks, or at least we mutually agree it can be used to approximate or simulate sticks, or at least some ideal head-model of sticks that never break or rot. Again, you appear to be mistaking your ideal head-model of sticks for reality. If I change my head model to work with brake-able sticks such that 2 sticks + 2 sticks equals 5 sticks, it no longer matches your head model, but is not necessarily wrong. (A probabilistic kind of math may be a better for working with break-able sticks.) If I agree to use "regular" arithmetic to match the model you agreed to, it simplifies life, but is not necessarily the universal "right" way to do anything.
Math is in the head. Each head is different. The only known way to compare between heads (communicate) is with symbols. What these symbols "mean" is in the head, and each head is different, etc...
{I already pointed out that the symbols are irrelevant. Numbers are what is important, not the symbols used to represent them. Numbers are the first rung on the abstraction ladder, where physical notions like broken sticks are irrelevant, but where the abstraction that a number represents is clearly applicable throughout the physical world. Two apples plus two apples is always four apples. That an apple has been half eaten by a worm doesn't matter -- it's still four apples. Two people plus two people is always four people, even if one of them is missing an arm. Two somethings plus two somethings is always four somethings. One, two... Three, four. Always. That simple abstraction, 2 + 2 = 4, is always true -- and obviously true -- independent of viewpoint, inclination, perception, political leaning, philosophy or intelligence.}
Re: "Two apples plus two apples is always four apples. That an apple has been half eaten by a worm doesn't matter -- it's still four apples."
Because you say so doesn't make it true. If I'm at the market and ask for another apple, but get the worm-eaten apple yet am charged for it, I will complain. To my "wallet head" that apple is NOT an apple and I feel it should not be COUNTED as an apple (at least a whole apple) for commerce purposes. Scope matters and scope is relative.
And Newton's Laws are still "applicable throughout the physical world" because parties agree that they are "good enough" among themselves. Yet Newton's Laws have known shortcomings. Being useful and being accurate or objective are not necessarily the same thing.
Further, "viewpoint, inclination, perception, political leaning, philosophy or intelligence" is what we use to mutually (or forcefully) agree upon models (UsefulLies). The ideal model(s) you have in your head is JUST in your head. The person above shopping for apples does not have to use your model of what a "whole" apple is.
All models are flawed and make assumptions. Which model and which assumptions are kept and tossed involves the list you gave (viewpoint, politics, etc.). The assumption that integers are a sufficient model for counting apples is an assumption. In classroom or textbook setting, we may live with a good many assumptions in order to simplify the model for teaching purposes. But the grocery market setting will use different assumptions than the classroom.
And being a simpler model is not the same as the "righter" model nor the more "universal" model (unless maybe popularity is the metric).
You seem to be implying a formula such as:
g = u / cWhere g=goodness of model, u = utility (such as prediction accuracy), and c = complexity. I will agree that integers and real numbers have a high score under this, but does that make them "universal" or One True or "fundamental"?
{You are wandering in vast halls of irrelevance. Given the number two, add the number two. The result is always the number four. That is an absolute truth. Unless, of course, you wish to engage in some absurd denial of counting, addition, and numbers.}
Denial? I didn't deny it. You are putting words in my mouth. I'm only saying it's not absolute. Perhaps you are saying WITHIN a given model, absolute truth exists. Maybe, maybe not, but my scope of discussion is usually the "real world". -t
{I didn't say you are engaging in some absurd denial of counting, addition, or numbers. It's only if you deny that adding the number two to the number two always results in the number four -- and is therefore unconditionally absolute -- that you're effectively engaging in some absurd denial of counting, addition, or numbers.}
Where is this "adding" taking place? In the real world? In your head? A simulation? It matters.
Nowhere. Seriously, it's nowhere. Addition doesn't actually "take place". It might help you to understand to consider that when we add it is us modelling addition and not the other way around.
{Indeed. Furthermore, where "adding takes place" doesn't matter at all. It need not ever take place for it to be absolutely true that if it takes place, adding the number two to the number two will result in the number four. It is not relative to anything.}
For now, I can tentatively agree that "adding" is absolute within a given model. But it's relative in terms of its relationship with reality. Deal? -t
{"Relative in terms of its relationship with reality" doesn't make sense, and there is no model. Adding the number two to the number two equals four, unconditionally. It is unconditionally absolute.}
You are saying it's nowhere yet also absolute? Hmmmm. -t
{Mathematical relationships, like 2 + 2 = 4 (and infinite others), hold true whether or not there is anyone or anything to hold them. They simply are. Mathematics is.}
Mathematics is not a property of the physical universe. It's a human artifact that exists only in our heads. The abstractions in our heads are not reality. You can dream about playing drunken leapfrog with supermodels all you want, but that doesn't make it reality.
{The language of mathematics, its symbols and expressions and how we invent and use them, is certainly a human artifact. However, we use that language to express relationships that transcend perceived reality. This is not a statement of numinosity, but one of ultimate, and ultimately simple, reality. 2 + 2 = 4 is an inviolate and absolute truth, independent of anything else. It simply is.}
You are anthropomorphizing the universe. Math is no more real or "absolute" than that supermodel in your wet-dreams. She "transcends reality" also because no real supermodel would touch your grumpy ass.
{Do not confuse mathematics with one of its sub-fields -- computation and/or calculation. This is a common source of misunderstanding. Humans and machines compute or calculate, but mathematics is ultimately about relationships, not calculations per se. Calculations are merely the steps humans (or machines) can follow to discover mathematical relationships that already exist. So: Imagine there is nothing in the universe but two atoms over there and two more atoms over here. There is nothing else in the universe. How many atoms are there in total? Is the result any different whether a human calculates it or not?}
There are probably boatloads of assumptions made in that vision of such a universe in your mind, such as that there are no multiverses involved that may have more or fewer atoms, etc. You assume a "regular" human perspective that doesn't fork etc. In other words, it's relative to a manufactured human perspective, a "cartoon" universe.
{But none of that matters -- that was my point. Even if it did, the number two plus the number two is the number four. Regardless of perspective, universe ("cartoon" or otherwise), multiverses or monoverse, fewer atoms or more, the number two plus the number two is the number four, no matter what. It is, therefore, absolute.}
1: 2+2 [Given] 2: 0^^+0^^ [1 and definition of 2] 3: 0^^^+0^ [2 and definition of +] 4: 0^^^^+0 [3 and definition of +] 5: 0^^^^ [4 and definition of +] 6: 4 [5 and definition of 4]Notice that the entire proof depends only on the definitions of 2, 4, and +. "2+2" is just another name for 4.
{Further explanation, in case you're unfamiliar with the notation: n^ is short for S(n), where S the successor function under the Peano axioms. n^^ is therefore short for S(S(n)), so S(S(0)) is 0^^ or 2. See http://en.wikipedia.org/wiki/Peano_axioms }
You haven't connected it with reality.
{Mathematics transcends reality. Again, you are conflating measurement with mathematics.}
See above.
Why do people insist on being wrong just to continue an argument? Intentionally misunderstanding the topic of discussion is not clever, and gains you no points. Just because you can come up with a sentence where something is true does not mean that it is even possible. The topic is not debatable, because there absolutely are absolutes.
ArguingForTheSakeOfArguing. Some top minds have bottom minds.
Projection, my friend.
Also, being "relative" and being "possible" are different issues. I don't understand why you are mixing them.
It's also a mistake to conflate `arbitrary` and `relative`.
Let me add some actual history to this.
The idea that "everything is relative" supposedly comes from Einstein's theories of General and Special Relativity. Many people incorrectly boil these theories down to those three words. Einstein said no such thing, and specifically refuted it.
He said that velocity and position are relative, that there is no coordinate system that you could use to measure where you are or where you are going with respect to the universe. You always have to measure these things relative to some other object. On the other hand, C, the speed of light in a vacuum, is constant, and is specifically not relative to anything, especially not relative to your position or velocity.
I've heard people say that the "everything is relative" lie leads to moral relativism and, eventually, to an "if it feels good, do it" mentality. I don't know how true this is.