A Message to My Fellow Bernie Supporters

Tonight, Bernie Sanders confirmed his support for Hillary Clinton at the Democratic National Convention. If you are an ardent supporter of Bernie, like I have been for years (I’m proud to say that, on November 10 2014, I signed a petition for Bernie to run for president), you are surely disappointed.

Unlike Sarah Silverman, I don’t have an condescending remarks for you. If you have supported Bernie Sanders, you are likely progressive, smart, and beautiful. We are dignified human beings worthy of making our own choice about whom we support. If you can’t, in good conscience, vote for Hillary Clinton, don’t. Millions of people have fought and died so that you can vote; do not be cowed into doing something with your vote that you are not comfortable with. Do not give in to fear. There is nothing more inspiring than someone being principled with their decisions, as Killer Mike suggests he will be.

I know that the only person that I have the conscience to vote for is Bernard Sanders. I know that the only person my logical beautiful black mind will allow me to vote for is Senator Bernie Sanders.–Killer Mike

The choice we are faced with is terrible, and on my view, it is the fault of the Democratic Party for putting us here. They pushed a candidate that is weak because they felt she deserved it. Do not let anyone tell you that it will be your fault if Trump becomes president. Blame the party that didn’t have the prudence to go in a direction that would more likely lead to success.

At the same time, if you believe that Hillary Clinton will carry on with some of Bernie’s message (some evidence suggests that she will), then don’t feel ashamed of voting for her to defeat Donald Trump. Bernie is suggesting that we do, and a Trump presidency would be an absolute disgrace.

The good news here is that the presidency isn’t everything and there are many things that you can do to help make Bernie’s beautiful vision a reality.

“What matters most is not who is sitting in the White House, but “who is sitting in” — and who is marching outside the White House, pushing for change.”–Howard Zinn

Make your voice heard; join the movement to elect a brand new congress; volunteer for a local campaign; make calls for Jill Stein (she very likely won’t win, but supporting her campaign doesn’t have to be about her winning); join a march or protest. Just do something. Martin Luther King Jr. was worried about moderates–he said that they are a greater obstacle to achieving justice than extremists who actively seek to thwart our efforts. So, do not be moderate; waiting for justice is a privilege, and many don’t have the luxury of waiting for incremental change. My message to all of you is: stay brave and carry on.

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Want to Produce Better Scientists? Teach them Philosophy.

This week, the statistics blog 538 reposted an article titled “Not Even Scientists Can Easily Explain P-Values” on Facebook. The author suggests that, even though many scientists are able to give the mathematical definition of a p-value, many are unable to explain it to nonscientists in a meaningful way. Commenters on the post were quick to suggest that, really, this isn’t a problem for scientists at all. For example, one writes:

The problem seems to be the demand that p-values be “intuitive” to lay people. They’re not going to be. We don’t go to graduate school for years to learn concepts that are intuitive to lay people. Our intuitions develop far beyond the point where they were at the beginning!

This commenter seems to be suggesting something that several others have echoed: in fact, scientists do know how to define and interpret p-values; the real issues are that (some) scientists aren’t able to explain difficult concepts to nonscientists, and have no obligation to give such an explanation.

If scientists use p-values in their work, do they (1) have an obligation to know their definition? (2) An obligation to know how to give a proper interpretation? (3) An obligation to give a proper explanation to the public? (4) An intuitive explanation? Although I have views on questions (3) and (4), I want to focus on (1) and (2) in this post.

I think we’d all agree that the answer to (1) is ‘yes’, and the 538 suggests that most (or all) scientists asked could give the correct mathematical definition.

A p-value is the probability of obtaining a statistical summary of the data (e.g., the sample mean) that is at least as extreme as the one actually computed, assuming that the null hypothesis is true.

As another 538 post points out that this definition is about as “clear as mud”. Several issues need to be expanded upon, including what “at least as extreme” means, what a null hypothesis is, how we calculate probabilities under the assumption that the null hypothesis is true, and which statistical summaries of data are best in different contexts. All of these expansions are possible given some basic knowledge of probability theory and inferential statistics methodology. But these issues don’t really give a satisfying answer to the question “what does p-value tell me about my statistical and research hypotheses?”

To answer this question, we need to know more probability theory and statistical methodology, but we also need to understand how to think critically and reason carefully. We need to interpret the mathematical definition above in a way that makes no unjustified logical leaps. There is much evidence that doing so is difficult. Misinterpretations of p-values are so common that the American Statistical Association (ASA) has released a statement on their misuse and Wikipedia has a page dedicated to misunderstandings of p-values. Several professional and academic organizations misinterpret p-values in official documents (538 points here, here, here, and here; some extras here, and here).

These links suggest that there are several common misinterpretations. Here are some common ones (note, these are all wrong!):

  • A p-value gives the probability that the null hypothesis is true.
  • A p-value is the probability that the data were produced by chance alone.
  • A low p-value (a “statistically significant result”) means that the finding is practically important.
  • A p-value provides information about replicability (e.g., that one minus the p-value is the reliability of the result).

Given that p-values are widely used in scientific studies–one researcher estimated that p-values have been used in at least three million scientific papers–the fact that academics, scientists, students, etc., have trouble interpreting them is worrisome. It also leads to bad consequences. For example, Stephen T. Ziliak and Deirdre N. McCloskey argue that misinterpretations of p-values leads to a heavy reliance on statistical testing, which can lead to very undesirable consequences.

It seems clear that, contrary to what we may think, many scientists don’t know how to interpret p-values. How might we fix this issue? An important component here seems to be that most of our statistics education focuses on technical aspects, such as important mathematical results and learning how to program. Of course these topics are important, but what makes statistics such a beautiful area of study is that, at once, it is technical, highly theoretical, highly practical, and philosophical. In an age driven by STEM education, it is important that we not overemphasize the technical by not acknowledging the philosophical. As Heidegger would say, thinking exactly might be fashionable, but thinking rigorously is better.* Statistical analyses can be nuanced. Philosophy teaches essential critical thinking and logic skills that motivate us to ask the right questions and seek creative solutions. Philosophy, and especially critical assessments of scientific methodology, such as those studied in a basic philosophy of science course, are wonderful supplements to the standard statistics curriculum.

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“Exact thinking is never the most rigorous thinking, if rigor receives its essence otherwise from the mode of strenuousness with which knowledge always maintains the relation to what is essential in what is. Exact thinking ties itself down solely in calculation with what is and serves this exclusively.”–Martin Heidegger

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My Case for Bernie Sanders

I didn’t become involved in politics until just a few years ago. For so long, I thought that, by not being involved, and by not addressing messy questions about power, inequality, war, economics, ethics, etc., I could somehow stay politically neutral. But, a few years ago a good friend introduced me to the American Historian Howard Zinn. Zinn makes a powerful case for the idea that political neutrality is impossible.

If you think you are being neutral by doing nothing, you are deceiving yourself. You are not being neutral. You are collaborating with whatever forces are dominant in a society, collaborating with whatever trends are already taking place in society. There’s no such things as neutrality in a world which already is subject to many many different kinds of forces, and so many of them malevolent.

So, if Zinn is right, and we can’t be neutral, where shall we start? What sort of political positions should we favor, and what sorts of political positions ought we denounce? My attempt at an answer to this question begins by identifying in what ways a society might be judged. At least according to some, a society will not be judged by how it treats the rich and the privileged, but by how it treats the poor, the marginalized, the underprivileged. In my view, it is how we care for these people that illuminates something profound about our cultural character.

Thus, when I think of who earns my vote, especially my vote for president, I first ask myself whether I think candidate X would represent people on the margins. It seems overwhelmingly clear to me that, of any candidate running for president, Bernie Sanders would represent people on the margins with dignity, character, and authenticity. In what follows, I try to justify why Bernie Sanders has my vote; not because I think that he will be an advocate for me, but because I believe that he will be an advocate for those who need the scales tipped in their favor.

Black people in America have faced and continue to face obstacles on the road to justice. Many are marginalized and disenfranchised by a criminal justice system that treats you better “if you’re rich and guilty than if you’re poor and innocent,” better if you’re white and guilty than if you’re black and innocent.  I don’t like Bernie because I’m white and I think that he has the interests of white people in mind (though, he does). I like Bernie because, if I were black, I would think that he has my best interests in mind.

Why do I think this? Well, consider the following from an interview with Howard Zinn:

The civil rights movement accomplished a good deal by beginning to remove some of the important social barriers. What it did not remove was the barrier of class, the barrier of economic injustice.

Martin Luther King recognized this. That’s why toward the end of his life he began working for economic rights for Black people. The trajectory is one which took a very sharp upturn in the 1960s and which then has, you might say, settled down into a situation which is not going to change very much until there’s a change in the economic system of this country. So long as we have an economic system based on profit and corporate wealth, there’s going to be an impoverished class. And so long as there is an impoverished class, I’m talking about the 40 million people who don’t have health care, the 20% of children in the country who grow up very, very poor. So long as we have an impoverished class, Black people will be disproportionately in that class. The trajectory has reached a point where it is not going to go up much further unless we have economic changes which benefit not just Black people but White people, fundamental change in our economic and social system.

It’s no coincidence that Zinn seems to be in agreement with African American leaders like Cornel West and Killer Mike about the fact that Bernie’s economic plans, better than any other candidate’s plans, would carry on the legacy of Martin Luther King Jr. The fight for economic equality is intimately tied to the fight for racial equality. Bernie knows this; sometimes it sounds like he’s reading The People’s History on the campaign trail!

Further, I don’t like Bernie because I’m straight and I think he cares about the well-being of straight people (though, he does). I like Bernie because, if I were LGBT, I would think that he has my best interests in mind. Bernie has been fighting for gay rights since at least the early 70s. There’s nothing wrong with Hillary Clinton (or Barack Obama, or anyone else, for that matter) evolving on the issue of gay rights; it’s better to evolve than to stick to an immoral and oppressive position. But the fact that Bernie has been consistent for so long on gay rights is a testament to his character, his judgement, and his leadership ability. He was for gay people when it was extremely unpopular, because he knew it was the right thing. That’s character. That’s authenticity.

Further, I don’t like Bernie because I’m a male and I think that he has the interests of men in mind. I like Bernie because, if I were a woman, I would think that he has my best interests in mind. Bernie’s record on woman’s issues–from paid sick and maternity leave, to calling for an increase in support to planned parenthood–is about as good as can be.

I mean no disrespect to Hillary Clinton when I say that I think Bernie Sanders will do a better job of representing the interests of the poor, the marginalized, the disenfranchised, and the oppressed. Some might argue that, although Clinton is less progressive, inauthentic to some degree, etc., she is, in a fact, “a progressive that gets things done.” I think this claim is deeply mistaken. It seems to me that the only person that conservatives hate more than President Obama is Hillary Clinton. If she becomes president, conservatives will try to impeach her for the email “scandal” and the Benghazi “scandal” on the first day. They’ve said as much already. Do we have any reason to think that they will work with her any better on anything than they did with Obama? Absolutely not. Bernie Sanders is far less contentious, and has a strong record of working with republicans to best serve the interests of the American people.

Finally, but importantly, the virtues of being a “pragmatic progressive” are, in my view, far overblown. Pragmatism results in slow and careful change–the kind of change that Dr. King deeply criticized white moderates for supporting in the face of oppressive conditions for African Americans in the deep south. Real change is affected by the people committing profound acts of heroism, honesty, protest, etc., not by a “pragmatic progressive” cautious of every next move. Such next moves, as careful as they may be, are likely to be squashed by the flip side of the same power structure coin that elected the pragmatic progressive. As Zinn claims, “What matters most is not who is sitting in the White House, but ‘who is sitting in’– and who is marching outside the White House, pushing for change.” If you want real change in this country–change from our system of capitalist oligarchy, with some democratic representation–you have to be very skeptical about whether Hillary Clinton will conjure up the sort of activism that Zinn is speaking of. In fact, Bernie’s entire platform is based on the idea that, when millions of people become involved in the political process–including people who, up until now, have been fed up with business as usual–we can actually make this country serve the poor and marginalized, rather than the rich and privileged.

That’s why Bernie gets my vote. And that’s why I hope he gets yours, too.

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Cecil the Lion and Eating Meat

Today, Yahoo Health posted an article titled “Why Even Meat-Eaters Are Outraged by Cecil the Lion’s Killing”.  I found this article on Facebook, along with this caption (presumably authored by Yahoo Health’s social media expert): “Why meat eaters can justify what they eat, but are furious over 13-year old lion Cecil’s death.” I knew this was a curious caption, mainly because I know that the vast majority of meat eaters can’t successfully justify what they eat–regardless of what happened to Cecil the Lion. So, I know that this was going to be good. Let’s see what the justifications were.

The central question for the author, Korin Miller, is: “why is there such outrage over the death of an animal we’ve never met — outrage that seems to be shared by vegetarians and meat-eaters alike?” This is a very sensible question. In fact, there are actually two related but very different questions here: (1) a descriptive question about why some meat eaters are outraged by the death of Cecil, and (2) a normative question about whether a meat-eater is inconsistent in demanding justice for Cecil while participating in a system of misery and injustice for millions of farm animals that have roughly the same capacity for suffering as lions.

Miller only attempts an answer at (1). She asks psychologists, and these psychologists give answer like “[the killing of Cecil] touches on our cultural and societal beliefs around themes of injustice and victimization — and these beliefs are certainly not limited to people,” or

“Killing an animal to eat feels much more ‘just’ in our minds than killing an animal for a trophy…many people consciously or unconsciously disassociate the bacon on their plates from the pig they see in a field [but are] able to feel OK about it knowing that the animal died for a reason (i.e. to feed us), rather than sport.”

Psychologists may be good at giving answers to questions about descriptive morality. What does culture X participate in practice Y? That’s a great question for a psychologist, sociologist, or anthropologist. But, as the caption to this article hints at, this is not the only question being asked. We also care about how meat eaters might justify their meat-eating, and still be outraged at the Cecil murder.  This is a question that we (or at least me and the social media expert) want answered as well. But Miller didn’t interview any ethicists of philosophers to try and answer this question. This fact is telling; culturally, we seem to respect the views of psychologists because psychology is, in some sense of the word, a science (although psychology, like a few other sciences, is having a tough time with certain scientific gold standards like reproducibility and disinterestedness). Perhaps we don’t interview ethicists because philosophy isn’t a science. But, no matter what Sam Harris says, the simple fact is that science alone does not decide questions about right or wrong. David Hume taught us long ago that just because X is the case (e.g., it is the case that some countries in Africa practice genital mutilation) doesn’t imply that X ought to be the case (e.g., that it is morally permissible to practice genital mutilation). To answer the question about whether meat-eaters are justified in their outrage over Cecil while at the same time eating meat, is a question about oughts–and it’s a question for an ethicist.

The arguments against eating meat–especially meat from factory farms, where the vast majority of meat in the US comes from–are spectacularly good. I won’t restate them here. But I will note that the psychological answer above clearly don’t answer the ethical question (question (2), above). Just because we happen to disassociate the bacon on our plates from the pig we see in a field says absolutely nothing about whether that disassociation is justified on ethical grounds. What is morally relevant, according to ethicists, is that (a) pigs feel pain, (b) they are basically tortured everyday on factory farms, and (c) the vast majority of us have plenty of other healthy (and tasty) food options. Given these facts, our disassociation is not at all justified. Just because we don’t want to admit that a certain atrocity is happening doesn’t imply that it’s not actually happening.

And then there’s this video of a presidential candidate cooking bacon with a machine gun. If you are calling for Dr. Walter Palmer to be brought to justice for his actions, what shall we do to Ted Cruz?

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Reflections on Teaching Workshop

This week I’m attending a summer teaching workshop at the University of Colorado, Boulder. Today, we discussed learning objectives and student assessments. One theme that seemed to run through both of these discussions is the concept of measurability. When writing learning objectives for a demo lesson (to be given later in the week), we were instructed to make sure that the objectives could be measured in some way. Using Bloom’s Taxonomy, one may write a learning objective for a given “level” of knowledge that uses a measurable verb. For example, consider the following learning objective:

At the end of the lesson, students will be able to restate the Intermediate Value Theorem.

This learning objective is not objectionable (at least I don’t think it is!) because it uses the measurable verb restate. One can measure to what extent the learning objective has been met by measuring to what extent the theorem has been correctly restated. Often in these conversations, measurable verbs are contrasted with the paradigm example of a non-measurable verb: understanding.

I found this discussion of measurable verbs, and particularly the relegation of understanding, really striking. It reminds me of Heidegger’s distinction between exact thinking and rigorous thinking:

Exact thinking is never the most rigorous thinking, if rigor receives its essence otherwise from the mode of strenuousness with which knowledge always maintains the relation to what is essential in what is. Exact thinking ties itself down solely in calculation with what is and serves this exclusively.

In the context of learning objectives, I think what Heidegger is getting at is this: what we really care about understanding, thoughtfulness, reflection, etc.–what Heidegger calls rigorous thinking. These are qualities that separate humans from everything else (other animals, computers, and inanimate objects). But understanding is not measurable, and thus, we cannot assess whether our students actually understand anything. So, instead, we assess things that are measurable, like whether they can restate, apply, or prove a theorem–examples of what Heidegger calls exact thinking But in the switch from rigorous to exact thinking, one loses something essential. As John Searle convincingly argues, the fact that an entity (e.g., a computer program) can restate, translate, apply, or even prove a theorem is not sufficient evidence that the entity actually understands the theorem.

I wonder then, if, in stating measurable learning objectives, we are aiming at the wrong target–albeit an easier target to hit. Perhaps those who object to learning objectives are really pointing at something profound: that real thinking (rigorous thinking) can’t always be measured, and that’s OK. This raises all sorts of questions about how we might keep students accountable, how we might assign grades, etc. But these questions shouldn’t stop us from thinking clearly about what, in many cases, we really want students to do: understand!

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Toughen Up

But even when one is dead and gone
It still take two to make a house home
I’m as lonesome as the catacombs
I hear you call me name and no one is there
Just a feeling in the air

‘Cause you and I both know that the house is haunted
Yeah you and I both know that the ghost is me
You used to walk around screaming, all slamming all ‘dem doors.
Well I’m all grown up now and I don’t scare easy no more —Shakey Graves

Here’s an interpretation of this song…

The people we lose (to death, or for other reasons), if we love them, haunt us after they are gone. But really, what haunts us is the fact that we allow ourselves to continue to think of them. That is, we allow ourselves to “scare easily”. The word “allow” implies that there’s an individual choice involved here. We can, if we want, “grow up” and not “scare easy no more”. Ya know, like toughen up, and join the real world where pain happens, and where we devise mechanisms to cope with this pain.

I get that, for our own health, we need to devise such mechanisms to cope with the pain of losing someone, but something irks me about it. If these losses are really haunting (and they are), then “growing up” just sounds like abandonment or the suppression of an important, painful, and very real feeling. Is suppression the right response? Is toughening up the right response? Maybe. I don’t know. It seems to me that, in general, we’re already tough enough, and that often, we’re too indifferent to pain and suffering. Maybe the world needs less toughness.

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A Place for Philosophy

In 2004, the city of Memphis celebrated the “50th Anniversary of Rock ‘n’ Roll,” attributing the roots of rock to Elvis Presley’s 1954 recording of That’s All Right. Some have rightly taken issue with this; black artists were playing what sounded like rock music for years before Elvis. Perhaps the origin of rock music is better attributed to Jackie Brenston’s Rocket 88, recorded in 1951. This event seems to be just one in music history where white artists capitalize on the talent of lesser-known black artists. Still today, some argue that white artists are more successful at pushing boundaries simply because they are white.

Just as the achievements of black artists sometimes go unacknowledged, philosophers are often not acknowledged for their past and ongoing contributions to furthering knowledge (scientific or otherwise). Moreover, scientists rely on philosophical thinking in their work but often don’t acknowledge it as such. In what follows, I hope to convince the reader that philosophical thinking has a central place in modern science and academia and that we ought not marginalize philosophy in favor of pure scientism.

Science as we know it today developed out of philosophy. Galileo and Isaac Newton were known as “natural philosophers.” It was not until the modern period that science began to separate from philosophy. Even after this separation, there was plenty of interaction between the two disciplines. The formalization of calculus was occasioned by a philosopher and many philosophers made contributions to modern mathematics.  However, science does not just owe a tip of the hat to philosophy for its origins; many modern scientific theories, such as string theory, rely on reasoning that goes beyond physically observable phenomena–what I think of as philosophical reasoning.

This past week, I attended Denver’s third Nerd Nite. Kayla Knopp, Rachel Miller, and Lane Nesbitt, clinical psychology students at the University of Denver, spoke about the way in which both biology and culture influence our understanding of sexual behavior. Although they didn’t state their conclusions explicitly (more on this below!), I take one of their main conclusions to be that (C) the set of all morally permissible sexual activities is larger than the set of all culturally accepted sexually activities. After what I think was an honest assessment of their talk, I took the argument for (C) to be the following:

P1. In nonhuman animals, there exists a set of sexual activities that our culture would find unacceptable if practiced by humans (e.g., one member of this set is deer threesomes!).
P2. We have evolved to enjoy (some) activities in this set.
P3. Since these activities are part of our natural evolutionary heritage, we ought to explore them (i.e., they are not immoral).
C. The set of all morally permissible sexually activities–i.e., the set of culturally acceptable activities plus the set of “natural-yet-culturally-unacceptable” activities that we ought to explore–is larger than the set of all culturally accepted sexually activities.

To be clear, I agree with (C); it is the argument for (C) that I take issue with.The problem with this argument–as many philosophy students may pick up on–is that P3 is fallacious: just because an act is natural doesn’t mean that that act is right, moral, or ethical. There are many examples that illustrate this fact. For one, we have evolved to eat meat—i.e., it is natural—but it’s not at all clear that eating meat is ethical; there are very strong arguments that support the claim that eating meat is unethical. To consider a more relevant example, sex between adult and juvenile animals occurs naturally among certain types of weasels and primates. But, among humans, such acts are considered immoral by most (and for good reason, since these relationships in humans often cause significant harm to at least one party, they are often non-consensual, etc.).

I notice this fallacy often in scientific discussion, and it is sometimes made by scientists. But philosophers have been warning us about making this mistake so much that they’ve given it a name: the appeal to nature fallacy. Generally speaking, my (admittedly anecdotal) experience suggests that philosophers are more careful with the form of their reasoning than scientists are. As further evidence for this claim, philosophers are notorious for writing their arguments and conclusions explicitly and very carefully; they sometimes even number their premises in the way that I did above. Philosophers follow this practice because they think it removes a lot of potential ambiguity and misinterpretation. Scientists follow this practice less often but I think that, in many instances, doing so would make their work more clear. After all, if explicitly outlining arguments was a standard scientific practice, then I wouldn’t have had to create my own (possibly misinterpreted!) outline of the sex-talk argument above. The point here is that, in so far as scientists use arguments in their work, they are doing philosophy in some sense, and that scientists may have something to learn from philosophers about how to present their arguments more effectively.

This week’s Radiolab provides another example of how philosophical thinking fails to get the credit that it deserves. It’s worth looking at the description of the episode:

The “mind” and “self” were formerly the domain of philosophers and priests. But in this hour of Radiolab, neurologists lead the charge on profound questions like “How does the brain make me?”

The connotation here (if I’m not being overly sensitive to the science-philosophy tension) seems to be that, for centuries, philosophers have spun their wheels with the question of personal identity, but that no serious work has been done until brain scientists caught on to the question. This kind of thinking is problematic for a number of reasons. For one, in an incredibly complicated area such as personal identity, just formulating the right set of questions is difficult. In many areas, philosophers deserve credit for formulating the right questions. Second, as philosopher Alva Noë has argued, neuroscience operates under the philosophical assumption that consciousness and the self are cognitive phenomena that are to be found by studying neural activity in the brain. This assumption is not empirical or “scientific”; it has roots in Cartesian philosophy (and I don’t think it is at all obviously true). Noë’s position, which builds upon work by Martin Heidegger and Maurice Merleau-Ponty, is that we are missing something of fundamental importance if we do not try to understand the self in terms of our embodied existence. Finally, the idea that discoveries in neuroscience (and many other disciplines) are reliable has been called into question by epidemiologist John P. A. Ioannidis. Ioannidis, in the celebrated paper, “Why Most Published Research Findings Are False,” argues that, in “hot” fields where there are small studies, small effect sizes, or great financial interest, many findings are likely to be false (arguably, neuroscience falls into each of these categories). While Ioannidis is not a philosopher, his arguments attack the (poor) statistical reasoning of some scientists. Since statistics is really a formalization of inductive reasoning, it can be understood as a sub-discipline of philosophy. Thus, I think Ioanidis’s criticism of scientific findings is largely a philosophical criticism.

There are many other examples of the importance of philosophy in scientific practice: disputes in the foundations of statistics, the interpretation of probability in modern physics, the definition of life in biology, and the understanding of measurements and mathematical models are all inherently philosophical. We ought to  acknowledge that philosophy place such an important role.

 

 

 

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