what's 1+ -1 in yankeeland? bbgod says its not 0 like its in europe.

With my crazy unmathematical skills, I would say it would be 0.

1 + (-1) = 1 - 1 = 0

Does that to me all the time

took about half an hour before that stupid site gave me new captcha.

LOL The beauty of Math is it works the same way no matter what, where, or why you are using it. The answer is 0 and whoever was telling you it wasn't was probably referring to the new "Common Core" process by the Federal Government, where they want 2 and 2 to add up to 5 every time. LOL

3rd bonus site refused to accept 0 as answer to that math question.

The government has adopted the use of statistics as the math of all new sciences and government management. This math ignores individual behaviour and looks at patterns in groups. Its not straightforward like 1 + 1 = 2. It involves tortuous constructs like the imaginary number i and the square root of -1.

It is extremely valuable to managers and policy members because it is complicated enough that the layman can't understand it, and it can be used, since it is imaginary by its nature, to justify almost any lie.

I call upon all anarchists to input incorrect data into the maw of the government data collection machine!

1+ -1
1-1
0

1 minus 1 is an actual equation? thought that that evaluated to 1 plus negative 1. meh. i am getting a bit senile.

hahahahahha

The square root of -1 IS i...

Thanks hawkeyee. That makes me feel much better

edit added after some thought:
I once knew that hawkeyee. It was in the study of statistics in the MBA program at Queen's University that I first considered this. I went to see my professor to discuss it because I had doubts about the whole foundation of statistics at that time. I've since seen statistics used in all sorts of ways. My daughter is about to receive her doctorate in research psychology. All of the effects that she identifies in human behavior are shown to be significant in her research papers through the use of statistics.

So while I have forgotten a lot of statistics, such as the fact that the square root of -1 is i, I have retained my doubts about the entire field of statistics. It is being sold as a hard science but is very often used to support questionable opinions.

I'm confused. Statistics measure real world things. I'm not seeing the connection between statistics and imaginary numbers.

As I recall, the i is used in the mathematical proofs that underlie statistical theory. Not surprisingly google doesn't have a quick search leading to an article on this. My Statistics textbook is long lost.

Also, its not the measurements that I have a problem with, but the design of experiments, the analysis, the conclusions, and the political power wielded using statistics that I question

Could you provide some examples? I'm trying to understand the connection between imaginary numbers and politics...

hawkeyee, I just read through about 20 pages of crap like this:

"I'm always a bit annoyed when people use the phrase "the square root of -1".
i is defined as a number such that i^2 = -1. That makes it a square root of -1. However, it isn't the square root.
When we say "the square root", there either is only one square root (e.g. the number 0, modular arithmetic), or we're talking about the principal square root. However, -1 doesn't have a principal square root.
This isn't just semantics, it actually goes quite deep. Complex conjugation is an R-automorphism of C. Un other words, i and -i are completely interchangable, as seen from R.
Lastly, a few random points:
1. The field of complex numbers is representable using matrices; a+bi can be thought of as the matrix [ [ a b ] [ -b a ] ]. So if "i doesn't exist", then matrices don't exist.
2. According to David Hestenes, every instance of complex numbers in physics actually has a geometric interpretation in Clifford algebra. So in that sense, i doesn't actually exist; it's a simplification for geometric concepts."

Its very tiresome. If only my ex-wife hadn't given all my books to the Goodwill! Not only my text books, but the entire 007 collection by Ian Fleming in ancient paperbacks, and 300 classic scifi books. I'm sorry, but I can no longer give the mathematical reasoning behind my doubts about the validity of statistics as a tool of science.

Getafix:
first my condolences on the loss of your book collection.
Secondly regarding powers: don't confuse real analysis with complex analysis. Although the two follow the same philosophy of mathematics, you end up with completely different outcomes in some cases, as seen by your power example.. division also works differently as does calculus and ultimately measure theory (not going to get into that).

Regarding statistics. You can't use mathematics to completely validate/invalidate the field of science really. Science is deductive reasoning and mathematics (of which statistics is a part) is inductive reasoning. All mathematics is is a tool to help us with various things or in the case of science to reach conclusions.
Pure mathematicians often struggle with more advance statistics as the way of thinking ends up being rather divergent and intuition (if you can call it that) is somewhat different. Part of this is how statistics initially evolved separately of rigorous mathematical theory but was eventually reworked to fit be just as mathematically rigorous using real analysis and measure theory. Unfortunately some of this was done in parallel and independently of the work done on "statistics" in physics. So although ultimately they are one and the same, the approach and definition of concepts is different (ie uncertainty vs probability).

Finally regarding statistical hypothesis testing. It isn't meant to prove/disprove anything in science. It gives you a way to have some kind of quantitative measure of what you observed based on a pre-determined set of scientific and other assumptions. If your initial assumptions about the process is incorrect then you get garbage in/garbage out. Inference is often not well taught to researchers (or economists) and hence gets misused which in turn produces misleading results.

"god does not play dice".. perhaps. But some of the real power behind statistics and statistical inference is the engineering approach that you only need to be "close enough" to build something meaningful (see voice recognition, where if you read up about it in the 1990s, this was supposedly an "impossible" task).

booo stats is not real math fluffem

Thats right FailDiego!

But thanks martian, great essay. You have obviously thought about this and I expect you are a much better mathematician than I.

I know that statistics is a good tool for many things. It certainly helps us to understand the world and make more rational decisions in many fields. I guess my interest in statistics is not so much in the joy of doing the math as in the use of statistics in society to support philisophical or political agendas. If I could cast doubt on the validity of statistics as a tool, it would weaken or destroy the foundation of many an argument!

Thanks also for your kind condolences. Losing your library seems like losing part of your memory. But I have accepted that loss and am moving on without a 26' U-Haul truck to carry all my fluff. (I've lost a few brain cells along the way too :)

Dunno about being a better or worse mathematician. One of my areas of interest is stats which I use for a living as one of several tools. Any tool can be misused as can science. The issue isn't stats per set but rather it being used incorrectly along with some shrewd presentation skills. Same issues exist with people missing other mathematics or the scientific process itself.

I was involved for a number of years in implementing "Lean Manufacturing" at quite a few factories. I have a set of workshops that I teach involving the "Kaizen" approach to improving the production processes. I lead team of 8 or 9 members from from various positions but concentrated in people from the plant floor.

The Kaizen approach relies heavily on getting input from the people who work within the process. They are the experts. By making the team democratic and empowered to make changes the line workers are enabled to make radical improvements.

An alternative approach that companies use to implement production process improvements is six sigma. Six Sigma, (or six std deviations, or 1 defect per million or so) is a top down improvement approach that empowers managers and engineers to find the most effective ways to improve the process using statistical analysis. I learned this method as well and have used it in practice to a limited extent.

My preferred approach is the Kaizen method. I find that the results are more dramatic and less costly than six sigma. By empowering line workers and flattening the hierarchy you create an environment where many small innovations and inventions take place. It pisses off the established middle management and gets huge gains in productivity, quality and morale.

So I feel that I am in a conflict with the statisticians and managers who want to baffle us all with bullfluff, keep us under their thumbs, and ignore our ideas even if they are good. So I guess my battle with the foundations of statistical theory is tied up with my battle for real democracy and freedom, and respect for the workers in the mills and factories.

Getafix, I may need to pick your brain in the near future, assuming I do eventually start down the track of becoming a Certified Quality Technician like I've been considering...


Also, this is barely related at best, but it still feels pertinent to the conversation and speaks on some level to Getafix's concerns with statistics - http://espn.go.com/...-100-facts-2014-preseason

Specifically, in a discussion on fantasy football...

"Getting intel is no longer the concern. There's no advantage because everyone has access to the same information. If you are in any kind of real league in which people are paying attention, the only advantage might be a faster Internet connection or a better smartphone to make a quick pick up in the dying seconds before game time. Otherwise, it's 10 or 12 guys looking at all the same names, numbers and rankings.

The key to winning, then, is parsing that data. Figuring out what to believe and what to ignore. Because, as I'll be the first to tell you every season, stats can say anything you want them to."



"You see, I can talk up or talk down anyone; I just have to choose the right stats for the job. Or just ask John Parolin and Zach Rodgers of ESPN Stats & Information to get me the right numbers for the job, as I did at many different points while writing this column. They are both stats studs. Everything you're about to read is heavily researched and thought out -- a 100 percent true, can't be argued with, fully vetted fact.

But they're only some of the facts. The facts that support whatever opinion I have of a player. Listen, there's very little in this world that I am good at, but one thing at which I am truly fantastic? Manipulating stats to tell the story I want to tell. For instance, in a little bit I'm going to use some Scott Linehan stats to talk up Tony Romo's prospects. When I do, I will conveniently leave out the not very impressive numbers from Matthew Stafford's first two seasons and the season Linehan was calling plays for Gus Frerotte.

I'm going to do that because Stafford's first two years were marred by injury, and Gus Frerotte wasn't very good. Caling a lot of passing plays does no good if the guy passing can't make the throws. So I'll leave those stats out because I don't think they are relevant (or helpful) to the point I'm trying to lead you to, which is that Scott Linehan is going to help Tony Romo have top-10 fantasy numbers this year.

If you're having a bit of deja vu, it's because I make this same confession at the top of this column every year. I want to be truthful about everything, so I happily cop to trying to manipulate you because I feel it's important. Extremely important. Throughout this preseason, you will have countless analysts give you all sorts of reasons to draft this guy or avoid that one, so I want you to be aware that every stat thrown at you is really just reflective of an opinion. Your job? Figure out which analysts you trust and whose thinking aligns with yours, question everyone and everything you hear, take it all in, and then make your own call.

Ultimately, that's all any of us is doing: taking a small piece of a big picture and making a call."

Thats very interesting Viceroy. And of course I'd be glad to talk about it with you.

The sports example is a good one. Here is a guy who admits to using whatever stats help his argument. That's often the case I think, though in science and peer reviewed research very rigorous methods are used to ensure repeatability and remove bias.

But in business, and particularly with six sigma programs, statistics is tied right up with applying power. In the six sigma approach, people receive different belts; green belt, black belt, master black belt etc.. It all has a sort of mystical feel to it and is a bit like a religion. In that religion the high priest has all the power. So if the stats say that the quality of the widget coming off the line can be improved by raising the baking temperature by 10 degrees, after a month of experimentation, thats what will be tried. But if Joe, who had been baking widgets for 15 years was consulted he would have told you that, and about how it changes with batches of plastic, the humidity, whether Pete is in die cutting today, etc etc.

I think if statistics could be used in combination with Kaizen that could be a very effective quality program. Statistical analysis is good for finding nonintuitive solutions to problems that no one can figure out. I'm not so much against the use of statistics itself, as its use to give fake cloak of "expert power" to the practitioner.

I'd like to add a bit more, since I'm on a roll here :)

When they send me in to a factory, 90% of the time there is management/ union conflict, the place looks like a bomb hit it and the 25 year plant floor veterans have seen it all, have suggested everything 20 years ago and been ignored and have given up. They put in their hours like zombies.

So they give me general manager power. I can do anything I want and have a good budget. My goal is to create a team that will make and implement change. I am a facilitator, not an expert on their process. When the team, representing employees from across the shop, makes decisions, I provide the power necessary for them to make the changes. I try not to use the power to promote my own agenda. Unlike the existing management, who are heavily invested maintaining the status quo, I am happy to shake everything up and cause chaos.

Suits me perfectly :)

Just one more note. In my example of Joe the widget baker, here is what the Six Sigma managers would do. After forcing Joe to spend a month filling out reports on the brittleness of the widgets at different baking temperatures and determining that the temperature should be 140 degrees and not vary more than 1%, they would take away Joe's temperature adjustment knob and put a control chart on the machine which sent a flashing red alarm to the manager's office that went off if the temperature went off spec. This would make sure that Joe never had any control over the temperature. He would just feed the widgets in, and take them out and pack them.

Then finally Joe would hit his 35 year mark and retire, and finally be free.