[quote]stokedporcupine8 wrote:
<<<<<<<<<<< A VERY long fascinating (sincerely BTW) post >>>>>>>>>[/quote]
Having said that, down here, in the plebeian realm of non “mod 3” addition, where life takes place, 2+2=4.
[quote]Tiribulus wrote:
stokedporcupine8 wrote:
<<<<<<<<<<< A VERY long fascinating (sincerely BTW) post >>>>>>>>>
Having said that, down here, in the plebeian realm of non “mod 3” addition, where life takes place, 2+2=4.
[/quote]
Thanks, I really tried to make it accessible. Going back and reading my post, I realized I never tied it all together, so let me quickly try to do that.
Again, my point wasn’t that 2+2 doesn’t necessarily equal 4, since obviously down in plebeian realm–or really just down in intelligent people realm–this is true. My point was that if you’re looking for the sort of infallible standards of proof that Hedo seems to demand from climatology, you won’t even find those in mathematics (Hence why I centered the whole discussion on the idea of finding a proof for 2+2=4). Even in our most seemingly secure science–the science of numbers–there is still a large bit of speculation and arguing that goes on.
Mathematics gives the appearance that it doesn’t involve this sort of speculation because one can go a long, long, long way in mathematics before having to deal with these sorts of issues. Very few working mathematicians whose specialties aren’t set theory or model theory worry about the nonstandard models in their day to day mathematical research. One can get along perfectly fine in mathematics while ignoring these issues, just like one can get along perfectly fine in theoretical physics by ignoring foundational issues as well. Physicists got along just fine for a few hundred years assuming that ‘F=ma’ was a good way to understand force. Of course in the end it turned out that there are better ways to understand forces, and that ‘F=ma’ isn’t the best. There have been many conceptual revolutions in mathematics over the past 3,000 years as well. Although these changes tend to expand the power of mathematics, basic intuitive truths of naive mathematics like 2+2=4 generally carry over. (There are of course some things that don’t. It used to be thought that all finite quantities were the same size. With the rise of set theory though it’s now well known that this isn’t true, that some infinite quantities are larger then others.)
In any event, if we were to ignore all bits of mathematics that didn’t involve any “speculation”, you’ll lose even seemingly obvious things like 2+2=4.
[quote]stokedporcupine8 wrote:
hedo wrote:
Doubtful. Internet bragging notwithstanding you need to stop falling back on the “I’m the only smart person here” argument. It’s tiresome and boring and is ultimately dismissed by those you are trying to influence. Try a good argument instead. It’s great your a math wiz ,in college. I had a lot of them that worked for me when I was om Wall St. years ago. Nice kids, hard workers, a little one dimensional but they did the job. They were from top schools though.
I’m curious why you think your understanding of mathematics is superior to anyone else when you understanding of the Global warming issue is remedial at best and you have failed to impress me with your superior intellect. People are experts at lot’s of things but it’s better to be called an authority by others rather then self-proclaimed, as your “thing”. It adds to credibility. You created a red herring with an absolute conclusion, therefore proving it false in any instance renders it moot. I kept it simple for you.
Search thru one of your textbooks. You have hitched your belief to a correlation made by others. However proof of that correlation doesn’t exist. Developing broad foundational responses based on speculation by researchers with questionable motives is foolish. Unbiased research performed by independent people is what’s called for.
What does my “remedial” knowledge of climate change have to do with my knowledge of mathematics? I admitted from the start that my understanding of climate change was poor at best, and in fact I never argued for any absolute position on the topic. Anyway, mathematics is my area of research, and in particular foundational work in mathematics. I’m not just some “math wiz kid” whose good with numbers, my entire area of research centers around these very issues.
So with that said, I will explain a little more what I mean when I say that mathematics isn’t the bastion of absolute truth you think it is. Since approaching this issue systematically is well beyond the time and space I have available (you might as well pick up a book on set theory or model theory), I’ll just continue with the example of 2+2=4.
It is true, in a complete ordered field, that 2+2=4. This is generally what people mean when they say that 2+2=4, or when they talk about mathematics at all. Since I assume you have no idea what a field is, or what rings are, or have any knowledge of modern algebra, I’ll try to make this point more simply.
Say someone asked you to prove that 2+2=4. How would you do it? In order to prove that 2+2=4, what you need is a set of rules, or axioms, that roughly define how numbers act under certain operations like addition (thereby indirectly defining addition). Once one establishes some set of axioms that define how numbers are to act under operations like “addition” and “multiplication”, one can then go on to explicitly define what the numbers are, and then show that for 2 and 4 so defined, 2+2=4. Now, if one goes about taking the definition for a complete ordered field as our axioms that describe how numbers act under addition, then if we can appropriately define the numerals ‘2’ and ‘4’, or basically the second and fourth successors of zero, we will find that indeed, 2+2=4. Of course we rely on our intuitions about numbers to guild us as we set out the axioms, and if we do a good job we get the results we want.
There is a fundamental problem though. Just as in geometry where we can develop alternative axioms systems, we can in another way develop alternative sets of weaker or strong axioms for numbers. Under loser or tighter axioms systems, the objects which the numerals ‘2’ and ‘4’ designate need not be so that 2+2=4. It might be that in some of these other systems, 2+2=5 or 2+2=1 (The former is a bit hard to explain, the latter is true under addition mod 3). The big problem is that there is no reason to pick one of these axiom systems as THE REAL description of the numbers, just like there is no reason to pick out one type of geometry as THE REAL description of points and lines.
Now, you may argue that this is all well and good, but that it doesn’t amount to much–that it’s just a bunch of games or something. While this would be s serious misunderstanding of algebraic structures, I’ll even play along and grant you that we all, being reasonable and smart people, can agree to one axioms system that corresponds to our intuitions best. In algebra we would naturally pick the definition of a complete ordered field, whereas if we wanted something a bit more fundamental we might pick the peano axioms, which are generally taken to be a description of what we intuitively mean by “natural numbers”.
Even if all this is granted to you, and we ignore the problems of selecting some one axiom system as THE description of numbers, we still run into problems when we arbitrary pick the most seemingly natural axioms systems. The problem is basically this, say we pick the peano axioms as the description of number, and we appropriately define our numerals in it and define addition. It is true that if we do this, we will naturally find that we can prove that 2+2=4 (As we have originally set out to do). Nevertheless, all is not well… even though we find some good results, like our proof of 2+2=4, we will find (as mathematicians have) that our best attempts to axiomatize the numbers still lead to bad results. One common made result is that we can also prove that there exists a largest number, which is seemingly something we should not be able to prove. Other bad results are that we find that some seemingly well-formed statements about numbers have no truth value at all–they are neither true nor false (This one REALLY drives mathematicians crazy). It gets even worse… we find that there are some seeming truths of numbers that cannot be proved… The problems go on. All these problems ultimately stem from the fact that even in our best attempts to rigorously describe numbers–to make explicit our seeming intuitions about them–lead to what are called nonstandard models. The existence of nonstandard models of number theory is well known and well studied, in fact there are conferences on the topic.
Now, you might find several objections to all of this. First you might object that these attempts to formalize number theory, mathematics, etc., fail simply because we haven’t found the right axiom system. You may try to argue that if we did in fact find a correct axiom system, then we would do away with all the problems I’ve listed. The problem is if you thought this you would be wrong. There are vigorous proofs that show that NO axiom system can so uniquely specify number theory (You’ll have to trust me on this one, cause gee, this is my area of research, and the proofs are long and complicated). You may admit this point, and further object something like “well, that’s all fine, but intuitively, we know what we mean by “numbers”, and intuitively we just know that 2+2=4, it’s absolutely true and we don’t need a proof of it”. If you did object in this way though, I would first respond by saying that most mathematicians would disagree with you… There is a point to algebra and set theory. I would also say that such an objection is naive. Relying on our intuitions about the absolute truth of mathematics and the truth of basic mathematical propositions like “2+2=4” is just begging the question, no?
To conclude, I’ll give you some things to look up if you wish. Most of the wiki articles on these topics aren’t TOO bad, so they’re ok. There should be an article on “nonstandard models of arithmetic”, and the major relevant theorems about these problems are Godel’s incompleteness theorem, the compactness theorem, and lowenheim-skolem theorem. There are other important things, but even a brief search for these things will show you I’m not talking out my ass…
EDIT: I did some googling for you, so you can see I’m not talking out my ass. This is a tiny sample, just some of the better stuff that popped up on the first and second pages of the search.
http://www.springerlink.com/content/l102867674663721/
http://www.columbia.edu/~hg17/nonstandard-02-16-04-cls.pdf
http://www.jstor.org/pss/20014690 (In case the other link doesn’t work)
http://en.wikipedia.org/wiki/Compactness_theorem[/quote]
Hey your really good at cutting an pasting too. Good work. Try taking a look at some of the public information on Global warming and educate yourself.
If I posted information on say how to drive a tank, at night, on a battlefield, would it have a practical application to the discussion of global warming.
You post was foolish and boring and I still ask why do you think high level mathematics is over my head? Silly kid.
[quote]stokedporcupine8 wrote:
Tiribulus wrote:
stokedporcupine8 wrote:
<<<<<<<<<<< A VERY long fascinating (sincerely BTW) post >>>>>>>>>
Having said that, down here, in the plebeian realm of non “mod 3” addition, where life takes place, 2+2=4.
Thanks, I really tried to make it accessible. Going back and reading my post, I realized I never tied it all together, so let me quickly try to do that.
Again, my point wasn’t that 2+2 doesn’t necessarily equal 4, since obviously down in plebeian realm–or really just down in intelligent people realm–this is true. My point was that if you’re looking for the sort of infallible standards of proof that Hedo seems to demand from climatology, you won’t even find those in mathematics (Hence why I centered the whole discussion on the idea of finding a proof for 2+2=4). Even in our most seemingly secure science–the science of numbers–there is still a large bit of speculation and arguing that goes on.
Mathematics gives the appearance that it doesn’t involve this sort of speculation because one can go a long, long, long way in mathematics before having to deal with these sorts of issues. Very few working mathematicians whose specialties aren’t set theory or model theory worry about the nonstandard models in their day to day mathematical research. One can get along perfectly fine in mathematics while ignoring these issues, just like one can get along perfectly fine in theoretical physics by ignoring foundational issues as well. Physicists got along just fine for a few hundred years assuming that ‘F=ma’ was a good way to understand force. Of course in the end it turned out that there are better ways to understand forces, and that ‘F=ma’ isn’t the best. There have been many conceptual revolutions in mathematics over the past 3,000 years as well. Although these changes tend to expand the power of mathematics, basic intuitive truths of naive mathematics like 2+2=4 generally carry over. (There are of course some things that don’t. It used to be thought that all finite quantities were the same size. With the rise of set theory though it’s now well known that this isn’t true, that some infinite quantities are larger then others.)
In any event, if we were to ignore all bits of mathematics that didn’t involve any “speculation”, you’ll lose even seemingly obvious things like 2+2=4.[/quote]
You need to brush up on the verbal “realm”.
The point, which like common sense, is lost on you, is that a theory needs to be proven before an economy is destroyed, based on that theory. Perhaps you could diagram that sentence to help you understand it better. Accept the fact that 2+2=4, it would be a breakthrough for you.
Good article that lays out some of the results of cap and trade legislation. You should be able to grasp it. The pages are numbered in an ordered fashion. However they are in ascending order and it will go 1, 2, 3, 4, 5. The larger number will always follow the smaller one, on this planet at least, maybe not yours. Should help you to read the article in order.
http://article.nationalreview.com/?q=YTc1MmVhMGYxY2UzNzAwMTJlODBjZjg2NDJjNmM2MWE=&w=MA==
[quote]PB-Crawl wrote:
hedo wrote:
lou21 wrote:
hedo wrote:
stokedporcupine8 wrote:
hedo wrote:
The point I did make is the cornerstone of global warming rests on a model.
You literally have no idea what you’re talking about. I mean NONE, at all.
Unfortunately typical for a believer of Global Warming. Actually observation is the basis of the scientific method. Should have been in the first chapter of your textbook. If the experiment cannot be replicated then the theory is a belief not a legitimate theory.
Clearly based on this thread it is you who don’t seem to have a grasp on the basics of the argument. Your point is that you are the only one “smart” enough to understand, unfortunately you have been able to prove your case by anything you posted.
Try this on for size: The total percentage of carbon right now in the atmosphere is about 370/1000000. The increase in the last 100 years, or so of the industrial age has added about 10 - 20 parts per million. A HIGH estimate of the effect of mans effort would put it at 0.000025% added. This small increase according to the believers affects the other 99.999975%. It affects it so much that we must cripple our economy based on the speculation that it does and that this minute increase in temperature is a bad thing, despite the evidence throughout history that it has been a benefit to mankind.
You are nearly there. Agonisingly close but still missing the point. The levels of CO2 in the atmosphere now are geologically associated with very much warmer climates. As I recall (my degree was a couple of years ago now) the rise over the last century is from 280 ppm to 370ppm. So anthropogenic contributions are of the order of one third of the total atmospheric CO2 present today. The rise over the last 100 years is the same as that associated with a mass extinction event at 55Ma (Paleocene�??�?�¢??Eocene Thermal Maximum).
Now I don’t know if the high CO2 cause the PETM or the PETM caused the high CO2. What I do know is that a similar event would probably be rather damaging to the economy you prize so highly. Of course the construction industry would probably boom as billions of people would be displaced and need new homes built…
So if I take your numbers at face value, then a 1/3 rise in CO2 have caused a rise in temperature of 1 degree C and this increase in carbon levels was caused by man. What caused the event 55M ago? Keeping in mind that the term average is a misnomer and highly suspect to manipulation, haven’t generally warmer periods been associated with periods of great prosperity for mankind during history? Is 1 to 2 C within the normal temperature ranges of the planet?
Shouldn’t the date for the past say 200 years be able to be plugged into the model and have it spit out the correct results for the last 20 years of the experiment? If it cannot do that why trust the model to speculate on the climate 100 years form now?
no, temperature changes have not been this high in the past 1k years, check out a temperature anomaly graph.
2 degree change in C, are you kidding? You really have no clue what youre discussing, you should back away slowly, dont look it in the eyes.[/quote]
Really? The earth has always had a fixed temperature that doesn’t vary? Do you think mankind has prospered and grown during warming or cooling periods? Or do you think that has never happened? What instruments were used to take precise measurements in 1009 and how were they recorded. Lot’s of questions, let’s derail the economy just to be sure…
[quote]hedo wrote:
Hey your really good at cutting an pasting too. Good work. Try taking a look at some of the public information on Global warming and educate yourself.
If I posted information on say how to drive a tank, at night, on a battlefield, would it have a practical application to the discussion of global warming.
You post was foolish and boring and I still ask why do you think high level mathematics is over my head? Silly kid.[/quote]
Your stupidity is astounding. First I don’t understand why you are, again, ignoring everything of substance that I’ve said regarding mathematics and bringing up irrelevant points about global warming. As far as being a “cut and paste job”, hardly… What I wrote brought up general issues beyond what is discussed in any of the links I provided. There certainly was no literal cut and paste going on, nor was my post just some rewording of the links I gave.
I had prepared a long response explaining why I thought you had little understanding of mathematics (I even had a cute quiz), but since I know that will only encourage you to ignore the real issues and to slam me back, I ask you this. WHY was my post foolish and boring? Just what did I say in my long post that was incorrect? Where did I err?
Since I assume that contra what I previously thought you are indeed well versed in algebra and set theory, please tell me where I went wrong. Curiously enough, there were some ambiguities in my post that could be called out as being misleading. I can defend these of course and explain why I put things the way I did, but I want to hear your actual criticisms first. Why was my post foolish? What did I say that was wrong?
[quote]hedo wrote:
The point, which like common sense, is lost on you, is that a theory needs to be proven before an economy is destroyed, based on that theory. Perhaps you could diagram that sentence to help you understand it better. Accept the fact that 2+2=4, it would be a breakthrough for you.
[/quote]
The point, which is lost on you, is that if one applied the same standards of proof to mathematical propositions like 2+2=4 that you want to apply to climatology, then even those mathematical propositions wouldn’t be “proved”. The point is not whether or not 2+2=4, which I never contested, but what sort of standards we should hold for theory.
There certainly is evidence for made-man climate change, just as there is evidence for the mathematical proposition 2+2=4. Of course there is far more evidence for the mathematical proposition, but if you require absolute unquestionable proof then even the mathematical proposition fails. (Obviously I’m using “evidence” loosely here, since the sort of evidence backing up mathematical propositions isn’t empirical.)
Clearly you know anyway, that as a point of logic, a theory can never be confirmed, but only falsified, correct? So seemingly the best any empirical science can ever do is to gather support for its claims, not proof.