The Topology of Epistemology

So I've been super busy with classes this semester but here's a paper that I recently wrote on the philosophy of mathematics (or the mathematics of philosophy?). It has nothing to do with sustainability, but I hope you fine it entertaining.

The Topology of Epistemology

Topology is the study of connectedness, and of the fundamental properties of things that remain despite deformations. “A topologist is interested in those properties of a thing that, while they are in a sense geometrical, are the most permanent – that will survive distortion and stretching” (Barr, 3). Topologically, a doughnut (torus) and a coffee mug are the same object because their surfaces have the same sort of connectedness. They are continuous with the exception of one hole. If they were made of completely malleable materials you could mold either one into the other without poking new holes or making new connections.

A great many things can be considered from a topological perspective, not just solid objects like tori and mugs. Networks can be seen from the topological perspective, analyzing how the different components or nodes of the network are connected to one another. A favorite interest of mine is the use of topological ideas to better understand ecology. In an ecosystem everything is connected, though most of the connections are indirect. Understanding these connections can help us to understand the ecosystems in a new way. More than predator-prey interactions, even the molecules in the atmosphere and the rocks are connected to an ecosystem through nutrient cycles and respiration. These and others are all ways that topology can be practically applied to understand things in our world, but that’s only one aspect of what topology can do.

Of much greater philosophical interest, you can examine the intersection of topology and epistemology. Epistemology is the philosophical study of knowledge and knowing. What is knowledge? How do we acquire it? How can we know if it is true or false? These are all epistemological questions. “None of us is able to get inside the head of another person, to know what that person knows. Even worse, none of us can step outside our own perceptions to determine what something is “really” like” (Mitchell, 226). This sums up what philosophers refer to as the egocentric predicament. This is also where topology and epistemology have their most interesting intersection. Are we connected to each other? Are we connected to the universe? Do we have a direct connection to absolute reality; can we know what things are “really” like? These are still epistemological questions, but now they are topological questions as well.

Plato had an early conception of the egocentric predicament with his “world of forms”, which was a perfect realm that he described containing the most perfect, ideal versions of everything in the universe. For instance, if you were to want to build a table, you would want to build it to be like the perfect table in the world of forms. The problem here is topological, if the world of forms exists then we certainly have no direct physical connection to it. Try as you might, you can only imitate the perfect table from the world of forms. Our connection in this case is through the mind; if you want the perfect table Plato would tell you to go contemplate “tableness”. He believed that ideas from the world of forms could be revealed by getting people to ask the right questions; in fact he believed that all learning was just “remembering” these perfect forms. Mathematical concepts are certainly from the world of forms, as we can imagine perfect triangles and circles and write beautiful equations to express them with infinite precision; however, whatever we draw or construct in physical reality will only be an approximation of the form. A more modern example of this would be the Klein bottle, the form of which certainly exists and can be expressed, but the physical construction of which is literally impossible to make (though we can get close).

Aristotle believed that we were connected to the world that we find ourselves in. If you wanted to build a perfect table, he would suggest that you go look at a bunch of tables and build one with the best qualities of each, and he might tell you that there is no such thing as a perfect table anyways. Aristotle rejected the world of forms on the basis that it could have no impact on the actual world because no direct connection existed. If the world of forms existed at all, Aristotle might use today’s language to say that it is topologically disconnected from our own.

Of course, Plato and Aristotle came along far before formal topology had been developed, so their worldviews were no doubt hindered by today’s standards. Descartes had a much better understanding of mathematics, being the inventor of analytic geometry, and he made things much more topologically interesting. He set out to see if there was anything at all in his mind of which he could be certain. By melting a piece of fresh beeswax he changed its properties in such a way that he no longer recognized it as the piece of wax, but he knew that it must be the original material. Using this example he established the separation between senses and knowledge. His senses told him that the wax was a different thing after melting, but his mind told him that it was the same piece of wax. It appears that there is a connection of some sort between the mind and the senses, but that the two are not entirely continuous. By establishing the discontinuity between the mind and the senses Descartes called into question our ability to know anything at all from our senses and came to the conclusion that the only thing of which he could be certain was his own existence. “I am, I exist, is necessarily true every time I pronounce it or conceive it in my mind” (Mitchell, 230). This philosophical idea is called solipsism, it is the belief that only my mind exists and everything else is just a perception of that mind. Topologically speaking, only one discrete thing exists in the entire universe, my mind, and there is nothing else to even be connected to.

Descartes worked around this by using the idea of a perfect God who would not deceive him to explain reality. He separated reality into two substances, or realms. The realm of matter is unthinking and extended (it takes up space), and the realm of the mind is thinking and unextended (it occupies no space). This allowed him to escape persecution by the Catholic Church by leaving the soul in their realm while delegating the realm of matter to scientists, but it introduced a significant topological problem, the mind-body problem. If mind and matter are two different fundamental things, how can they possibly be connected? How do they interact? They appear by definition to be completely disconnected from one another. Descartes never addressed these issues.

David Hume did address the mind-body problem, by completely throwing it out. He was a radical skeptic who believed that all knowledge came from impressions of reality and descriptions of the world, which were imperfect and uncertain. The only knowledge that we could be certain of, things like mathematical ideas, could not tell us anything meaningful about the world. Absolute knowledge of reality is forever unobtainable, because our minds are only indirectly connected to the universe through our senses. Bertrand Russell goes further down this path, questioning our senses and maintaining the disconnection of our mind from true reality. We only have our sense data and the mathematical reasoning that we can apply to it. Russell argues that rather than discard all knowledge as uncertain rubbish we should just recognize that we are largely separated from reality and from each other and we should just accept what works as being “true enough”.

Russell’s conclusion seems to be the basis for all of science and mathematics. We generally have a list of assumptions and exceptions to any mathematical process. Pure mathematics does not mirror reality because pure mathematics is itself disconnected from reality. You can prove incredible things in pure mathematics, and you can describe the most amazing objects, but they tell us very little about reality. We take math and make up sets of rules that allow us to apply it to model certain physical situations to some degree of accuracy. We match it to our sense data as best we can and continue to use it as long as it is useful. We are connected to reality only indirectly and can never experience “true” reality. All of our ideas are based on uncertain impressions of the universe that we find ourselves in yet find ourselves disconnected from. The best we can do is to ensure that our worldview is consistent. If the collection of sense data and ideas that we have is continuous and all makes sense, then it is true enough. As long as we continue searching for ultimate truth about reality we will continue to get closer to it, but we must accept that we may never actually attain it.

In Euclidian space it would be difficult if not impossible to produce a picture that adequately expresses our topological relationship to the universe. There is certainly a “neighborhood” with which we can become somewhat familiar, and that is defined by our curiosity and how hard we try to learn something. If I want to go learn about ecology I can go read a book on it, and extend my neighborhood of knowing to the information in that book. The difficulty is that our neighborhoods are not smooth. Due to the limitations placed on us by our relations to our senses it seems that every point of our neighborhood is a boundary point. Nothing from the outside world can ever really be brought within; we can only touch on it. I can go learn more about ecology by reading more about it or performing research, extending my neighborhood to new boundaries, but the first points of contact are still boundary points as well. This is why a picture of our relationship with the world would make little sense. All of the points are boundary points, yet each is connected to our unextended mind. Modeled in 3-space our relation to the universe would be an incredibly complex and somewhat discontinuous surface with every point connected to the point of the internal mind, which could only be expressed in this case as being a 4th dimensional quality of the surface. The human quest for knowledge then becomes a quest to ensure that this surface is as smooth and continuous as possible, by always looking for new observations and discontinuities, and endeavoring to use the tools of mathematics and logic to determine what “is not” and what “probably is”.

Bibliography
Russell, Bertrand. The Problems of Philosophy. Simon and Brown, 2011. Print.
Barr, Stephen. Experiments In Topology. New York: TThomas Y. Crowell Company, 1964. Print.
Mitchell, Helen Buss. Roots Of Wisdom. Wadsworth Pub Co, 2009. Print.

Getting Arrested for Environmental and Social Justice

Tar Sands Action is now keeping a tally of the number of people arrested while peacefully protesting the Keystone XL pipeline and tar sands oil on their website. The group that I was arrested with today brings the total to 220, and counting.

Yup, that's me. The officer was quite friendly. But how did I end up in handcuffs? Funny story.

It's legal to walk across the sidewalk in front of the White House. It's also legal to stand in the street there, which is closed to vehicle traffic. But it's illegal to stop moving on the sidewalk. We have permits to march by each day, but once we stop it's three warnings and then off to jail. So this morning we all met in Lafayette Park, lined up, walked up to the fence, held up some banners, and stopped moving. The police were expecting us and the area was already covered with police officers and vehicles. They even had the bike rack style fence all stacked up and ready to deploy, as well as a tent set up ahead of time for processing. The police ordered us to leave, we stood our ground. Dozens of supporters and tourists gathered outside of the cordoned-off area and shouted out their support to us. One man started yelling "Drill baby drill!" in an effort to get a counter-chant going, but after a few minutes realized that he was literally the only person doing it, and was promptly drown out by the chanting supporters of stopping the pipeline and breaking our addiction to oil.

Three warnings later (and a healthy amount of chanting and singing on our part) they started arresting people. It was an entirely peaceful affair. They just pointed us out one at and time, told us we were under arrest, and we walked out and presented our arms to be cuffed. It took about half an hour just to cuff everyone.They took my mug shot and loaded me into a paddy-wagon for the drive to Anacostia Precinct. Despite the cuffs and the cramped hot paddy-wagon we kept up good spirits the whole time, telling stories about why we had come out. I've been to a number of marches and rallies (though this is my first arrest) and I was quite pleased that this was the most normal group of people that I had ever run into while being politically active. We were all just normal Americans, Canadians, and Native Americans (and one Irishman) who cared about the kind of world that our descendants will inherit.

After getting to the jail they unloaded us, removed the cuffs, searched us, and wrote us our tickets for "failure to obey a lawful order". We were offered the option to "elect to forfeit", which out lawyers explained as essentially a legal bribe. We payed a $100 fine each, and that was the end of it (though they keep a record and it is an official arrest).

Here's where it got really interesting though. While my officer was filling out my papers in the jail, the earthquake hit. No one had the slightest idea what was going on at first. It's certainly the first quake that I've ever been in. Right after it stopped one of the police just shouted "That was an earthquake! Any of you guys from California?". Within seconds alarms were going off in the building and the police radios started crackling to life, and about half of them ran out responding to emergency calls. While my officer was filling out my papers he said to me "That was AWESOME!" I can't stress how friendly the police were during this whole ordeal (though they still took their jobs seriously, as my sore wrists can testify).

They finished processing us and turned us all loose. On the way to the Metro station we walked by a National Park Ranger and had an interesting exchange:
Park Ranger: "Hey, are you guys from the tar sands protest?"
Us: "Yes"
Ranger: "Congratulations, thanks you guys. Keep up the good fight!"
Us: "Wow, thank you!"
Ranger: "No seriously. Thank you!"

And then I fought post-earthquake Metro traffic for over an hour to get back to my car. All in all, it was a pretty awesome day.

The above photo was taken by Tar Sands action and is available, along with many others, on their flickr.

70 Arrested at White House for Civil Disobedience

The Tar Sands Action peaceful sit-in started today in front of the White House, with the goal of convincing President Obama to keep his campaign promises and to prevent the Keystone XL pipeline from being built. Within minutes police issued warnings to move along, and at 11:30am the arrests began. Tar Sands Action has made the following statement:

On a phone call late this afternoon, U.S. Park Police told organizers of the sit-in that the jail time was expressly intended as a deterrent for future participants.The Park Police were especially concerned that sit-ins would continue during the week of events beginning on August 28 surrounding the dedication of a new memorial to civil rights leader Martin Luther King Jr., one of the greatest exponents of creative nonviolence.In multiple phone calls and in person meetings before today’s sit-in, the Park Police had previously assured organizers that participants in the protest would be facing a “post and forfeit” situation, meaning they would pay a $100 fine and be released the same day. While participants in this morning’s sit-in were trained the evening before to prepare for the worst, many were operating on the “post and forfeit” assumption due to police assurances.

Despite these efforts to deter us, volunteers will be showing up in front of the White House every day for the next two weeks because we understand how vitally important it is that our society stops using fossil fuels and moves to renewable energy. I'm not deterred, and I'll be in DC on the 23rd, peacefully sitting in front of the White House.

"Gasland" director Josh Fox made the following video to help explain why the Keystone XL pipeline must be stopped.

Sen. Sanders Opposes Keystone XL Pipeline

Senator Bernie Sanders has recently come out in support of Tar Sands Action (video)and joined them in opposition to the proposed Keystone XL pipeline. Today he wrote a great article on Daily Kos. Here are some of the best excerpts (in my opinion):

We need to move aggressively as a nation toward energy efficiency and sustainable energy to reduce carbon pollution, reduce dependence on foreign energy sources, and create good jobs here in the United States.

Big Oil, with record profits of $1 trillion for the top five oil companies over the last decade, is trying to keep us hooked on oil, even using tobacco industry tactics to confuse the public about global warming. The science is clear however. The U.S. Global Change Research Program, which includes top scientists at the Departments of Defense, Health, Agriculture, Energy, Transportation, Commerce, Interior, State, as well as NASA, the EPA, and the National Science Foundation, has stated that “warming of the climate is unequivocal…due primarily to human-induced emissions of heat-trapping gases…mainly from the burning of fossil fuels.” We have a national and global imperative to move away from fossil fuels, which pollute our air, imperil our planet, enrich hugely profitable corporations, and make America less secure.

There are many...ways to reduce our reliance on oil. We can make our buildings and homes that heat with oil more efficient. We can move to renewable heating sources like geothermal, solar, and biomass. We can develop and use truly clean and advanced biofuels like cellulosic ethanol. We can move aggressively to mass transit, high-speed rail, and plug-in hybrid and electric vehicles. But even if we simply look at the opportunity from fuel economy standards, I have to ask a question: why in the world would we ever consider approving a new Big Oil pipeline to carry dirty fuel and keep America addicted to oil, when we could save money, create jobs, and reduce our dependence on foreign oil by moving to stronger fuel economy standards?

I could not have said it better myself, and I encourage you to read his entire post. Senator Sanders is a great American and one of the handful of people in congress who really listens to the science when it comes to political decisions.

Biopunk Book Review

I read a lot of non-fiction books (and even a few novels from time to time) and every so often I'll be posting book reviews.

I just finished reading "Biopunk" by Marcus Wohlsen. It's all about the new and growing DIYbio movement / subculture. It begins with a very interesting quote:

Bill Gates recently told Wired that if he were a teenager today, he would be hacking biology

From the DIYbio website:

DIYbio.org is an organization dedicated to making biology an accessible pursuit for citizen scientists, amateur biologists and biological engineers who value openness and safety. This will require mechanisms for amateurs to increase their knowledge and skills, access to a community of experts, the development of a code of ethics, responsible oversight, and leadership on issues that are unique to doing biology outside of traditional professional settings.

The book offers a fairly objective look at the movement, covering its history and development, a number of people in the movement, the promise of DIYbio, and the potential dangers of it as well. You would think that people with a genetic engineering lab in their garage could be pretty dangerous, but it turns out that the science isn't nearly that advanced. Only the best minds in the world in the best labs could design new, unstoppable pathogens. Even then it would be tough.

As the book explains, biotechnologists are trying to turn biology into something more like engineering, where you decide what you want to have and then you build it from off the shelf parts. There are a few problems though. No one yet knows how the parts will interact with each other. You can isolate a gene for a particular protein, such as the protein that glows under fluorescent light. You could then put that gene into something else, like a bunny. It's fairly easy to plug in single genes. When you go to build something from scratch, even something as simple as a bacterium, it's much harder. Even worse, you can't try different parts like you can when working on your car. Building the genome for your organism is a continuous process, you can't swap different parts halfway through, and you have to finish before testing. In other words, there's not much to be concerned about.

There does seem to be a lot of potential to the movement though. They want biology to be open source and accessible to everyone. To reach that goal, they are innovating to make everything cheaper. One person mentioned in the book developed a way to test for a genetic disease that runs in her family that costs a fraction of the cost of the regular test. Many people are working on chips that you can plug into your smartphone that will allow you to test for specific pathogens, with the goal of making diagnoses available in developing countries.

That's just a little of what this book offered. If you're interested in the nuts and bolts of getting involved with this yourself, this isn't a how-to book (though it might be a good place to start, and has an excellent notes section of 209 citations). If you're interested in science in general, biology, medicine, or just emerging trends in our society then I definitely recommend this book. I admit that I'm biased though. While not fighting cancer in my kitchen, I am pursuing studies in biotechnology. Many people think that biotech will be to the next several decades what the computer was to the past several decades, and I happen to be one of them.

Robinson Nature Center

I attended the last blogger/blog reader party at the Stanford Grill and I definitely had a great time. I got to know a few people a little better than I did, I met new people, and I ran into an old acquaintance that I hadn't seen in over a year. I'm definitely an introvert so it's a bit hard to get me talking to people, but I'm already looking forward to the next event.

Of particular interest was one of the new people that I met, Jeff. He writes the Green Floss blog under the personal section of HocoBlogs. Turns out he's a green building professional and is volunteering over at the Robinson Nature Center, which is set to open September 10th. It sounds like it'll be a pretty awesome place, they're shooting for LEED Platinum certification. When you build a LEED building you get points for sustainability improvements in different categories. More points = higher LEED certification. Jeff explained to me that there was an innovation category, and that the Robinson Nature Center was getting a LEED point for having etched glass windows, which reduce bird strikes. Of course, it will also have a geothermal heat pump, a green roof, and a lot more. I can't wait for it to open, and I plan to blog about it again.

Our Nation's Priorities

I'm watching a recent episode of Real Time with Bill Maher. One of his guests is Dr. Neil DeGrasse Tyson, noted astrophysicist and director of the Hayden Planetarium. Many people consider him to be the modern Carl Sagan. Bill just pointed out that the cost of the James Webb Space Telescope (still facing the budget ax) is about equal to the cost of keeping our people in Afghanistan for a month. Dr. Tyson responded by pointing out the rather disturbing fact that the $850 billion TARP bill, the bank bailout, is greater than all 50 years of NASA's operating budget combined.

It's no wonder that our nation finds itself in the situation that we're in when we're willing to consistently under-fund and scrap the programs of one of the only government agencies that gives us real reason to dream of a better future. Back in the Apollo era there was common talk of the amazing future that humanity could look forward to. I have a children's book from the 60s that I picked up at a garage sale, "You Will go to the Moon!". I've seen dozens of these types of books, and as a child they taught me to dream of a better world. I'm still working toward that world, pursuing my studies and staying active in the community.

It's too bad that our nation's leaders, for many years now, have been more concerned with the next election than with the actual future that lies ahead. If we only focus on maintaining the status quo, we will achieve nothing and lose everything. In order to make this a better world, we have to actively invest in it. According to the White House website, only 1.2% of our tax dollars are going to science, space, and technology programs. Only part of that is NASA. 26.3%, on the other hand, goes into the military. It's past time to stop focusing on tearing the world apart and to actually start dreaming again and start the serious work of building the future.