Formal Systems and Applications Thereof (continued)

    The ideas expressed in Hofstadter's first masterpiece, Gödel, Escher, Bach: An Eternal Golden Braid, are powerful, if confusing. However I think he makes them about as accessible as can be expected. He makes humorous use of dialogue in illustrating some of his more far-fetched points. He weaves concepts from mathematics, psychology, philosophy, computer science, and even biology together in a way that draws on one's understandings of some in explaining the others. The beautiful thing, is that the fact he can do that mirrors what the book seeks to explain.

Form and Content

    Central to how any formal system is utilized in a real world setting is the distinction between how it operates and how it is interpreted. How it operates has to do with the axioms upon which it is based and the rules governing the creation of theorems from axioms and other theorems. How it is interpreted has to do with another key word.

Isomorphisms

    What makes a formal system useful, is a powerful isomorphism between the axioms and theorems of the system and some feature of reality. Abstract Algebra is useful in one instance, because if in the real world you have one apple, and someone gives you another, you have two apples. Abstract Algebra does not rely on that fact itself to produce the true statement 2 + 2 = 2, yet in that case and in any similar cases it will produce a theorem that corresponds accurately to our observable reality, given that we interpret it reasonably. The system was specifically developed to so, and is as such an extremely powerful tool in executing all kinds of tasks.

Meta-Mathematics

    Kurt Gödel understood this very well, and so took the path of using a formal mathematical system (number theory) to study itself. By "stepping outside of the system" he used the system itself to prove that it (number theory) was either inconsistent or incomplete.  The more wide reaching implication of Gödel's Theorem is, by the nature of his argument, which can be imported into any sufficiently powerful formal system, that every formal system is by necessarily either inconsistent or incomplete. That is to say it either contradicts itself, or it is not capable of producing every theorem of the system that reality dictates should be true.

The Future of Mathematics in Everyday Life

    We live in an age where technology is developing more rapidly, one might worry, than anyone not directly involved in the development is ready for. The key to maintaining stability, fairness, and equality among our fellow human beings in the coming years will lie in utilizing new technologies reasonably and responsibly. Mathematics plays a critical role in all of this, as every day we find more efficient ways to meaningfully quantify and make use of dimensions associated with economics, engineering, medicine, and psychology, while more and more frequently mathematicians and physicists are found knocking at even philosophy's doorstep. But what of it? Has it not always been the case that scientists are pushing the boundaries of our knowledge to places we have never seen before?

    Absolutely, but lets go over a specific example of a technological area that could become harmful or unsustainable left unchecked, and some that have potential to serve as checks on those. The details tend to hold the truth of a matter, and herein I believe is evidence that we face challenges today that are, by any quantitative measures, beyond the magnitude of almost any we have ever faced as a species. The way I see it, systematic decisions about the distribution of resources in a nation should be made according to scientific realities with the goals of maintaining the health, well-being, and productivity of its citizens and guests. At present no comprehensive system for effectively collecting and aggregating professional opinions in such a way seems to exist.

The Food and Pharmaceutical Industries

    We start with one of the larger problems in the United States as it stands. The free market is almost by definition not supposed to have entirely benevolent intentions towards their customers; companies and corporations are expected to compete for profit above all else. However, a successful free market must be regulated by government bodies that do have benevolent intentions towards their residents, not towards the profits of their corporations. It is not conspiracy that the FDA is controlled by if not entirely run by former executives of the very institutions they are charged with regulating. It is fact. 

Corn

    I introduced this whole topic with the idea of scientific realities. Lets generalize that to quantitatively significant statements. At the expensive of seeming less than scientifically professional, I'm going to use some hash tags to categorize statements without getting any more excessive in my use of headings and subheadings. I am not an expert in many of the areas I tag, but nonetheless I believe my impressions to be accurate-ish. It would be nice to have a system that let me easily find and cite legitimately peer-reviewed sources of information a little more intuitively than Google does now (which is already leagues ahead of the previously best system, the library).

Corn is among the most subsidized agricultural products in the United States #policy

Cows are often fed a stock of almost all corn, #foodIndustry

regardless of the fact that cows are evolved to eat grass, not corn #biology

I'm fairly certain growing nothing but corn is bad for the dirt itself, fertility-wise #agriculture

Corn contains very simple carbohydrates,  #chemistry

and is most commonly refined into pure glucose #foodIndustry

This corn syrup is in almost everything. #theGroceryStore

The human body is not evolved to process anywhere near the levels of pure glucose an average American consumes #biology

The risk of diabetes for an average American is and has been growing #publicHealth

Obesity is a leading cause of death and a driving force behind rising health care costs in the US #publicHealth

Those health risks are most prevalent among minorities and low-income families, who presumably eat more of the products that government subsidies render inexpensive. #I could go on, but I hope I have made a point by now.

    What I mean is this: if the people in charge (of this specific area and others besides) were taking into account the actual numbers, that correspond to actual reality, they would not make the policy decisions they make. It's easy to blame financial interests and greed in this situation. It is more difficult to move people to do anything about it. First, someone has to make them listen, then understand the problem. Even then we are left the arduous task of convincing them that they can do anything to help, and then guiding them through the process of actually doing what they can to help, i.e. nominating and then voting for officials who will enact the necessary policy changes. Scientists are busy people. They need help with this stuff. This corn example is simply meant to illustrate one area in which rigorous discussion could be started from general tagged comments, if there were a system designed to link quantitative results to those tagged statements ad hoc.

Genetically Modified Organisms

    I believe that the scientifically literate opinion on GMO's in general is simple: they are a profound agricultural breakthrough that should be exploited energetically, but carefully. Furthermore they should be created with altruistic, not profit-based goals in mind. There is an enormous problem when it comes to the way genetic modification is being conducted. We are killing all of the bees! The enormity of that quasi-fact is more than present enough to warrant treating it like a fact when it comes to corn that is genetically modified to naturally contain pesticides. But I digress.

Social Media

    A never-before-seen power for solidarity and free distribution of critical information is present among the hoards of kitten videos and relationship advice columns we find on sites like twitter and facebook. However, the machinery is not doing all it can do yet, and won't be until it is purposefully nudged in the right direction. 

Big Data

    Scientists have been making use of the huge data pools that come out of social media sites for a while now, but at this point advertising agencies seem to have more fun with it. I posit that this can change, and moreover that it needs to change. I believe that the scientifically, mathematically, and statistically literate can make a push for expanding that literacy through social media, to the benefit of all. I believe that people need to be aware that they are, in addition to being a human being, a data point. It feels dehumanizing, and to some extent it is. However, it is the reality we live in and to make the best of it, we could for instance maybe find ways to make racist data points see themselves in the context of the whole spectrum of racial awareness.

Quantitatively Transparent Media

    The whole point of my corn rambling was to illustrate a portion of government policy that I find reprehensibly idiotic.  I think that we as human beings are at a point in our evolution where we can make clear statistically at least when something reprehensibly idiotic is in fact, reprehensibly idiotic. If only there was a way to broadcast the truth of such things to everyone in the world in a way that all could understand and believe... it seems no one tries because they don't think it possible. I think all we need are much more interactive systems that allow people to record their thoughts and beliefs relationally to see how they integrate with each other and with scientific evidence.

Where are the p-values?

    I know that most people don't understand what a p-value is, but that doesn't mean they shouldn't have some awareness of what one is. The news of the future is customizable to the viewers knowledge and interests. There must be ways to make it clear that if people want the truth they need to see the p-values. This is shooting a little high, I know, but any movement in that direction would be good movement. I started this blog with a discussion of how numbers may or may not lie. Well, they have a lot less motivation than human beings to do so. That much is certain. The key to defeating corruption in government policy is not to make lying more difficult. It is to make telling the truth easier. To do so will require advancements in education and user interface design, all of which are well within reach.