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Thoughts on the future of math education
This is a guest post by Kevin H. Wilson, a data scientist who usually resides in Brooklyn, but is currently in Chicago as a Mentor at the Data Science for Social Good Fellowship. In past lives he's gotten a Ph.D. in math, worked as a data scientist at Knewton for several years, and continues to oversee programming classes in rural schools for Microsoft's TEALS program. This note comes from that latter work and associated policy work.
Programming is a Tool and Should be Taught as Such
A very popular trend nowadays is to demand that computer science be taught in schools. Indeed, President Obama has started an initiative to bring computer science to all schools in America. Before that, Mayor DeBlasio of New York demanded computer science in all schools in the City by 2025. The Hour of Code is basically a mandatory volunteer activity in many tech firms. And a search for high school hackathons or Capture the Flag on Google reveals huge interest in this topic.
These initiatives seem to miss the broader point about computers: they have fundamentally transformed the way that we interact with the world and school should reflect that. As structured now, high school computer science initiatives tend to build programming courses. These courses tend to focus either on the "cool" things you can do with coding, like building games, or the rigorous implementation details of complicated languages, as in AP Computer Science A. Even the better courses, such as AP Computer Science Principles, often constrain the skills learned to a single classroom.
Programming, however, is simply a tool which solves other problems. Specifically, programming is a tool that allows data to be manipulated. Some of that data is static data, like a business's annual accounts payable and receivable; and some of that data is dynamic streams, like a user's interaction with a game she's playing on the computer. Programming's genius is to abstract these to the same basic paradigm, a paradigm that has made it possible for Google and Facebook and Uber and Blizzard and countless other companies to improve[1] our lives using what, by historical standards, are extremely cheap and accessible devices.
Tools, however, should be taught like tools. To properly teach a tool, it must be used in context and reinforced horizontally (across the school day in multiple subjects) and vertically (across the years as students become more comfortable with more complicated tools). These imperatives have found purchase before, often in the form of encouraging medium- or long-form writing in all subjects,[2] or in the use of (some) math in all science-based courses.[3] But our generally balkanized curricula often lead to a general perception among students (and, as students become adults, among the general populace) that knowledge is a bunch of tiny islands whose inhabitants are called the "Good at Math" or the "Good at English."
I believe that computers and their ability to easily manipulate data offers a chance to truly redefine the mathematics curriculum, to make it more horizontal, and to refocus the tools we teach on what is actually useful and stimulating. Statistics, not calculus, should be the pinnacle achievement of high school, not relegated to box-and-whisker plots and an AP course which is accepted by relatively few universities. Algebra, the math of manipulating symbols, should be taught alongside programming. Calculus, a course which I have heard multiple people describe as "easy but for the Algebra," should be relegated to a unit in Statistics. Trigonometric identities and conics should go away. And earlier math should focus on how and why a student arrives at an answer, and why her procedure always works, not just the answer itself.
The First Bias: Historically Computation was Hard
Why then, if this is such a good idea, hasn't it happened already? Well, in some limited cases, it has. The Common Core math curriculum has brought statistical modeling to the forefront and clarified the balance between learning facts by rote and understanding why procedures always work. There are beautiful curricula like Bootstrap which place Algebra and Computer Science side-by-side. AP History courses have made understanding primary sources and data important to getting an A, and some teachers have gone so far as to incorporate Excel usage into their classrooms.
But there are extremely long-lived biases preventing more radical transformation. Most interesting to me is that historically statistical analysis was hard. Brahe spent an entire lifetime collecting measurements of the solar system, and Kepler spent another lifetime turning those into general rules.[4] And the annals of science is littered with famous insights made possible by introducing nicer notation. For instance, Mendeleev, inventor of the Periodic Table, is considered one of the greatest scientists in history simply because he realized that data on atoms was periodic and there was a compact and insightful way to lay out a bunch of numbers that people already had access to!
Programming allows its user to take means or do t-tests or bootstrap or graph or integrate numerically in an instant. These bread and butter techniques, as central to statistics as long division is to arithmetic, involved days and days of human computation when the curriculum was last revised. Imagine the process in the 1930s for even finding the median of 500 numbers, a task whose first step is to meticulously sort those 500 numbers. Imagine sorting 10 decks of cards into one big deck of cards. And imagine that as a necessary step to understanding. Such a requirement is a fantastic way to miss the point the first few times, and, since sorting 500 numbers doesn't get any faster the 20th time you've done it, it is a severe impediment for providing reinforcement opportunities.
The Second Bias: Measuring Computational Ability is Easy
This leads to a second bias, which is toward the easily measurable. Statistics, like programming, is really a tool that allows its user to answer questions about the world around them. But the world is complex, and there shall never be a procedure as ordered as those in the traditional high school mathematics curriculum[5] which allows the user to easily capture "the truth." If there were, then we people called "Data Scientists" would be out of a job!
This bias toward the easily measurable doesn't just exist in schools. For instance, Kaggle is a platform for "data science contests." Basically, teams compete to "best model" some phenomenon present in real data sets using whatever statistical techniques their hearts desire. Typically, in the end, teams submit some code, and Kaggle runs the code on some data the submitter couldn't see ahead of time and computes a score. The highest score wins.
Any professional data scientist or statistician will tell you this is the easy part. Once you've got a nice CSV filled with data, it's usually pretty clear what the battery of models are that you would probably run on that data. Indeed, there's now a sort of "meta-Kaggle" competition where academics build algorithms that automatically write solutions to Kaggle problems! These typically do pretty well.
The hard parts about statistics and data science is what comes before you even start to model the data. How was it generated? What assumptions does that imply about your data? What does it look like? Does the data look like it reflects those assumptions?[6] And so forth.
And what do you want to do with this data and what does this imply about what metric of success you should impose? If you're Google or Facebook, you want to sell more ads, so likely you want more profit as your ultimate metric. If you're the Chicago Department of Public Health and you're trying to stop children from contracting lead poisoning, then likely your ultimate metric of success is fewer children with lead poisoning. But these are long term metrics, and so how do you translate them into objectives that you can actually train against?
These questions are the hard ones, and proficiency in answering them is much harder to measure than filling in a few bubbles on a standardized test. They must include writing, long form, explaining choices made and why those choices led where they did.[7] Of course, this sort of mathematical and statistical long form writing isn't what we typically think of as writing in schools. Instead we imagine portfolios of fictional stories or persuasive essays. This writing would be filled with tables and math and charts and executive summaries, but its ultimate goal, persuading the reader to accept its conclusions, is a completely familiar one.
To assess these skills, we must teach teachers how to teach a new form of writing, and we must grade it. Of course, long form writing takes much more time to grade than multiple choice answers, and so we must find new ways to grade this writing.
The Third Bias: Learning Happens only in the Classroom
This brings us to a third bias which prevents the curriculum from changing: the troubling view that the classroom is the sole responsibility of the teacher. This view leads to many bad behaviors, I think, but most relevant here is simply the fact that teachers and teachers alone must grade literally everything that students produce in the class. But what if some of the grading could be outsourced, or perhaps "insourced"? What if students could grade each other's work?[8] What if teachers from other schools could grade students' work? What if parents could grade students' work? What if parents could grade students who aren't their children's work? What if members of the community at large could grade students' work? What if somebody from the next state over or the next country over could grade students' work?
This idea is not new. Science fairs are often graded by a "distinguished panel of (non-)experts" and AP tests which involve essays are graded in big hotel ballrooms by college faculty and high school teachers. Students critiquing each other's work is often an integral part of creative writing classes, if not English classes in middle and high schools. In some places, they're even letting community members grade some projects and classes.
Moreover, computers, in their capacity to move data around at will, can facilitate this process greatly. Among other things, I work with TEALS, a program out of Microsoft which helps start programming classes in schools. In particular, I help coordinate and train volunteers who live in big cities to teach programming classes for students in far flung areas of the countries. They rely on systems such as Canvas, Edmodo, and Google Classroom to interact with students on a daily basis and to collect and assess homework and plan classes with teachers.
The Fourth Bias: Teachers Must be Trained
TEALS was built, indeed, to overcome the final bias I'll mention preventing change: teachers know how to teach the current curriculum and teacher training programs are geared toward preparing teachers to teach this curriculum. There are extremely few opportunities for teachers to learn to teach new classes or even for teachers to learn new techniques! Teachers rarely observe, much less critique, other teachers, and the current teacher promotion system typically involves jumping to administration.
This is ludicrous. Every single classroom is a hotbed of experimentation. Each child is slightly different and every area of the United States is inculcated in different norms that affect the way students learn and cooperate. Yet teachers are given very little time to reflect on their teaching, to observe each other, or to, heaven forbid, write about their work in local, regional, or national journals and conferences. It is not at all implausible to imagine a teacher promotion system which includes an academic (as in "the academy") component.
But all this is to say that teachers, for all their professionalism and hard work, are given very few opportunities to learn and teach new subjects. And education schools, bound to churn out teachers who can tick off various certification requirements and pass particular exams, find it hard to train teachers in rarely-taught subjects. And if a teacher coming to teach a single new and interesting course is so hard, imagine how hard it would be for them to learn an entirely new curriculum or for an education school to begin to support it!
This is certainly not a theoretical concern. Common Core has gotten so much negative press in part because of an extremely botched rollout plan.[9] Teachers were not trained in it, new textbooks and other materials to support it were not ready, and the tests meant to evaluate progress in the standards were, like all new measurement devices, faulty. And this for a set of standards that, while radical in many respects, still had the same shape as what we have been teaching for a century.
On the Other Side of the Fence: Community-Based Projects
What then would lie on the other side of change if roadblocks like these could be removed? Let's start at what I think would be the best possible end goal: a project that high school seniors would complete before graduation that would serve as the culmination of their years of study. From there we can work backwards.
What I imagine is a project which explicitly uses all the tools students have learned over their years of high school to advocate for change in their communities. This could take many forms depending on the focus the student wants to take. For instance, students focused on writing could write op-eds detailing the history of something that troubles their community and advocating for realistic change. Or perhaps, if journalism is not their cup of tea, they could write a piece of fiction which has at its heart some spiritual conflict recognizable to those in their community.
What most interests me, though, is the sort of work that computers and statistics could open up. Imagine a project in which students identified a potential problem in their community, collected and analyzed data about that problem, and then presented that report to someone who could potentially make changes to the community. Perhaps their data could come from public records, or perhaps their data could come from interviews with community members, or from some other physical collection mechanism they devise.
Imagine a world where students build hardware and place it around their community to measure the effects of pollutants or the weather or traffic. Imagine students analyzing which intersections in their town see the most deaths. Imagine students looking at their community's finances and finding corruption with tools like Benford's law.
Or for those who do not come up with an original idea, imagine continuing a long running project, like the school newspaper, but instead the school's annual weather report, analyzing how the data has changed over time.
All of these projects require a broad range of skills which high schoolers should be proficient in. They require long to medium term planning, they require a reasonable amount of statistical knowledge, they require the ability to manipulate data, they require an understanding of historical trends, and they require the ability to write a piece of persuasive writing that distills and interprets large numbers of facts.
Moreover, such projects have the potential to impact their communities in profound ways. Places like the coal towns of Appalachia are desperately attempting to make their towns more amenable to investment, both in terms of dollars from outside capitalists and in terms of years of life from their progeny. From time to time I have the opportunity to ask kids in Eastern Kentucky whether they planned to stay in their hometowns after their high school graduation, and I have yet to receive a single "yes."[10] Towns who rally around training their students to change their own thinking, I believe, will receive huge dividends.
Of course, we can daydream about these projects' effects, but what sorts of curriculum would actually support them? I won't pretend to remake the entire K-12 curriculum here, and so let's focus instead on the mathematics curriculum. Further, I don't have the space or time right now to completely reimagine the the whole of K-12, nor do I think such a reimagining at all practical, so let's focus on high school subjects.
What Curriculum is Necessary to Support these Projects?
1. Programming and Algebra merge
First, we must teach programming. There is no hope for doing data manipulation if you don't understand programming to some extent. The question is when and how. I believe that algebra and introductory programming are extremely synergistic subjects. I would not go so far as to say they are interchangeable, but they are both essentially arithmetic abstracted. Algebra focuses a bit more on the individual puzzle, and programming focuses a bit more on realizing the general answer, but beyond this, they fundamentally amount to the realization that when symbols stand in for data, we may begin to see the forest and not the trees.
And just how might these two things be interwoven? Well, we have some examples of what might work. The Common Core, for example, emphasizes "computational thinking" in its mathematics curricula for all grade levels, which essentially means encouraging students to learn how to turn their solutions to specific problems into solutions for more general problems.[11] As such we're seeing a large number of new teaching materials reflect this mandate. Perhaps my favorite of these is Bootstrap, which I would highly recommend checking out.[12]
2. Geometry is replaced by Discrete Math and Data Structures
Programming, though, is only a means and not an end, so how will we employ it? Next in the traditional curriculum we find geometry. Geometry is officially the study of space and shapes, but traditionally in America it is the place where we teach students formal logic. We drill them on the equivalence of a statement and its contrapositive, we practice the masochistic yoga of two-column proofs, and we tease them with questions such as "is a quadrilateral whose opposite sides are congruent a parallelogram?"
But there isn't anything particularly special about the SSS and AA rules when it comes to constructing logical puzzles. These sorts of puzzles are simply meant to teach their players how to produce strings of implications from collections of facts. For instance, Lewis Carroll famously constructed nonsensical logic puzzles for his tutees which entertained while abstracting the actual logical process from the distracting influences of reality.
While I find these sorts of logical puzzles entertaining, I don't think they're nearly as useful to students as deriving the facts they will prove themselves. Imagine instead a course in discrete math and data structures. In this course, students would still be asked to construct proofs, but the investigation of the facts would involve programming numerous examples and extrapolating the most likely answer from those examples.
Students would come much more prepared to answer questions in discrete math having essentially become familiar with induction and recursion in their programming classes. Students could also empirically discover that sorting a random list with merge sort takes quasilinear time, and then they could go forth and prove it!
Many of these types of empirical studies would also be the beginning of a statistical education. Plotting times for sorting lists of the same size would introduce the concepts of "typical" and "worst" cases, as well as the idea of "deviance", which are at the very center of statistical conundra.
3. Algebra II begone! Enter Statistics based on Open Data Sets
This then would lead to the next course, a replacement for the traditional and terrible Algebra II. This course, which includes some subset of solutions to systems of (in)equalities, conic sections, trigonometry, and whatever else the state decided to cram in,[13] is generally a useless exercise, where there really is no good answer to the ever-present question of, "Why do we need to know this?"
Thus, I would propose to replace this course wholesale with a course on statistics, expanding on the statistical knowledge that our data structures course laid the foundation for. However, since students have experience in programming and data structures, we can go much, much further than what we traditionally expect from a traditional statistics course. We would still teach about means and medians and z-tests and t-tests, but we can also teach about the extraordinarily powerful permutation test. Here students can really come to understand the hard lessons about what exactly is randomness and what is noise and why these tests are necessary.
Moreover, in traditional statistics courses like AP Statistics, students are usually taught various rules of thumb about sample sizes being sufficiently large and are asked to apply these rules to various fictional situations. But there are a huge number of massive data sets available nowadays, which they could not manipulate without their programming experience. The focus should move away from memorized rules of thumb for small samples to the actual analysis portion and the implications of their explorations for society.[14]
Projects in this course would be multipage reports about exploring their data sets. They would include executive summaries, charts, historical analysis, and policy recommendations. This is a hugely important form of writing which is often not a part of the high school curriculum at all.
4. Machine Learning subsumes Calculus; Calculus becomes a one-month unit
Finally, the capstone class, for the most advanced students, would move away from Calculus and instead into Machine Learning. The typical way this course is taught in colleges nowadays is as an overview of various mathematical and statistical techniques from across the subject, though perhaps the two major themes are linear algebra, especially eigenvectors, and Bayesian statistics, especially the idea of priors, likelihoods, and posteriors. Along the way students would pick up all the Calculus they'll likely need as they learn about optimizing functions.
Indeed, such a course is already being taught at some of the more elite schools in the country, and I have no doubt that anybody who could climb their way to an AP Calculus course, if taught a curriculum like the one outlined above, would be able to approach a machine learning course.
Of course, as mentioned above, the real capstone of this course of study would be the capstone project. The three previous classes contain all that is necessary to be able to approach such a project, though many other classes that students might take could be brought to bear in spectacular ways. History courses could help students put what they learn into the context of the past; biology courses might yield fruitful areas of study, e.g., around pollution; journalism courses might lead to an interest in public records.
And all throughout, the community would be involved. Perhaps they would serve as mentors for these capstone projects, or perhaps they would help grade some of the more specialized projects during the junior year. Or even better, maybe the final exam for the introductory programming course would involve teaching an Hour of Code to community volunteers. And of course the capstone project would focus around the community itself.
Why would this be better? Lessening the linearity of mathematics
One immediate pushback I've gotten when I tell people this story is to ask why I think kids will perform better at this curriculum than the one that we have now. Isn't this one even harder? To which my answer is, yes, but is is both more interesting to students and their communities and begins to help solve the problem of mathematics notoriously linear structure. To understand tenth grade math requires understanding ninth grade math requires understanding eighth grade math and so forth. Moreover, there are very few places where students who somehow fell behind have a place to catch up. This wall persists even into adulthood, with many parents dreading they day they have to tell their kids, "Oh, honey, I never understood that stuff."
This mathematical linearity is quite different from traditional humanities curricula. In these curricula, the true emphasis is on practicing the skills of history or the styles of writing or the understanding of culture. And while History has themes and English has great turns of phrase that should be memorized, missing a few for any particular reason does not preclude the student from jumping back into the subject next time around. That great writers spent their youth ignoring their teachers or participating in traditionally educational activities speaks to the flexibility of these subjects to welcome the "late bloomers" into them.
And while the proposed math curriculum does not completely refactor out prerequisites, it does begin to weaken them. This, I think, is a good thing for getting more students on board. The focus shifts from performing specific tasks (like manipulating one trigonometric expression into another) to being able to constantly improve a set of skills, specifically, looking out into the world, identifying a problem, collecting data on that problem, and using that data to help determine means to address that problem.
These skills, identifying problems and supporting the analysis of those problems with facts, is a skill whose importance is paramount. Indeed, the Common Core State Standards for English and Language Arts bring up this point as early as the Seventh Grade.[15] But as data become easier to gather and process, "facts" shall come more and more to mean monstrous collections of data. And being able to discern what "facts" are plausible from these collections of data becomes more and more important.
What next?
There are many obstacles to this dream, even without the status quo biases that I discussed at the beginning. Even the simple job of building materials, much less the community and teacher infrastructure, to support this change is massive and will take years. And though the Common Core standards are reasonable, the move to extreme standardization of the schools does preclude experimentation on the parts of individual schools and teachers with curriculum.
Where next? Immediately, the first order of business is to understand if such a high school curriculum could be built without changing the middle and elementary school curriculum too much, since changing four years worth of curriculum is already extremely disruptive.
Assuming that is the case, then there are several possibilities. One is to take the route of the Bootstrap curriculum and explicitly teach specific skills required by the current curriculum while supplementing them with computer science concepts. This runs into the problem that the school day is already pretty full, especially for high-achieving kids, and adding in new "requirements" would burden them.
Another route is to build a charter or charter-like school around such a curriculum and forsaking the traditional standardized tests. This has the problem of being risky in that if the curricular idea is terrible, then these kids will be disadvantaged relative to their peers.
Whichever way is chosen, the process will be long, involving the hours of many people, not just writing curriculum but also from the community, who themselves by design will be involved in the week-to-week of the courses, and involving the training of many educators in a relatively new type of math curriculum.
- Some would quibble with the word "improve." If, dear reader, you are such a person, I implore you to replace this with "radically transform."
- Well, except often in math, where even though mathematicians have been writing long form proofs for years, students are often stuck with the terrible two-column variety.
- Though, traditionally the "vertical" reinforcement of math has gone off the deep end into the various properties of conic sections and the opaque relationships between trigonometric functions without the aid of complex numbers. Common Core actually does a fair bit to help on this front.
- Though maybe he faked it.
- Long division, taking determinants, solving polynomials, taking formulaic derivatives all spring to mind, though there are many more.
- A piece of advice to aspiring data scientists: If you are applying for a job and they ask you to do a written test ahead of time, there should be at least one plot in your writeup. Unless your solution is brilliant, you aren't getting hired if there's not at least one plot.
- To what I think is its tremendous credit, this sort of writing is integral in the PARCC tests developed for Common Core-aligned curricula in some states. I have not had the chance to review the competing test, called Smarter Balance, but I would expect it would be similar.
- There are actually many teachers who use peer grading, and also quite a bit of research on its effects, some good, some bad. The point here is that we should be open to using novel methods of grading, and especially interested in exploring how computers can facilitate these novel methods.
- What I do not talk about here but which is also an essential problem with any change to the curriculum is that parents play a huge role in their children's education, and so any change to the curriculum that involves reeducating teachers must also, to some degree, involve reeducating parents. Since this piece is about high school, by which time many parents have already "given up" on helping their students with homework because they are not "Good at Math" (a fact I do not have hard numbers for, but I have commonly experienced among my students), I'm leaving this massive issue out of the main text.
- Of course, take this with a grain of salt. I tend to only get to ask this question of kids in computer science classes.
- These solutions often take the form of "algorithms," which are central to computer science, and thus the name "computational thinking."
- Perhaps my favorite aspect of the Bootstrap curriculum is that they emphasize professional development, a woefully underappreciated aspect of improving the curriculum.
- There is no universal definition of Algebra II as far as I know. However, the Common Core has gone a long way to standardizing a definition. The PARCC Model Content Frameworks may be useful for the interested.
- This is not to say that warnings about small samples shouldn't be ingrained into students as well, but here large data sets can help as well. For instance, a simple exercise for the whole class could involve giving every student a randomly sampled set of 20 rows from a very large data set and asking them to run some sort of analysis. In the end, each student would come to vastly different conclusions, and thus, come to learn that sample size matters.
- See CCSS.ELA-LITERACY.RI.7.9, which states, "Analyze how two or more authors writing about the same topic shape their presentations of key information by emphasizing different evidence or advancing different interpretations of facts."
Delete your LinkedIn account
I deleted my LinkedIn account a few weeks ago. I was increasingly getting spammed from solicitors on the site, and all sorts of weird people kept writing to me with bogus requests. Plus the content I saw when I bothered to log in were consistently hyped up crap about magic bullets using big data. I'd had enough, even though I was mildly wistful about the job I'd once landed through the network.
Well, I'm glad I quit, because I just learned that Microsoft has made an offer for LinkedIn for $26 billion. What this means is that all that social data, the professional contacts and so on that people have built up over years and years, is being handed over to a huge and powerful corporation that can change the privacy policy whenever they'd like, it seems. This is data that people protect as personally valuable individually; it is clearly quite valuable more generally.
And I have no personal vendetta against Microsoft, but clearly they have an agenda beyond simply connecting people and suggesting careers. At the very least, they want to expand their portfolio to social networking stuff so they're not still living in the 1990's. I also suspect they'll submit the LinkedIn network to experiments to see how professionals respond to various marketing campaigns. Yuck.
I'm not saying that LinkedIn had motives that were perfectly aligned with its users, but I'm seeing this as a sever drop in alignment. I think it's time to delete your LinkedIn account.
Norman Seabrook is the absolute worst
I'm so glad that guy's been arrested.
For years I've been listening to sports radio, specifically Mets broadcasts on AM710, where Seabrook would have a regular spot – already a sign that the Correction Officers' Benevolent Association has way too much money – and there'd be this awful, deliberate attempt of disgust and fear mongering about the job of a corrections officer.
[Side comment: can someone confirm that Kars4Kids is a scam?]
The ad, which ran way too often and which made me crazy with rage, included the phrase, "We protect you from all the people who'd kill your wife and rape your daughter." See more people complaining about that ad spot and more on this website.
What he was referring to was Riker's prisoners. He was the union boss protecting the Rikers officers who beat those prisoners, including teenagers, when they were unarmed and often had handcuffs on.
And I get it, it's a tough job, and union bosses protect their members. But this guy was on a different level of extreme, both in how far he'd go to protect abusive guards and the extent to which he created a war-like atmosphere between prisoners and guards. He's a bully who leads and protects an army of bullies.
This is a guy who, in order to prevent a prisoner from testifying against one of those officers, had the entire bus system from Riker's shut down. This is a guy who continues to allow prison guards to get away with anything at all, training them to do it behind a curtain or off camera, defending their conduct, and getting rid of investigators he doesn't like or cannot control. This is a guy who told people to "follow the rules" so that they don't have "to sit down at a table and come up with a story that doesn't make any sense."
The actual charges against Seabrook are that he invested his members' pensions in a failing hedge fund in return for kickbacks. I'm guessing that's not the first time something like that happened, and I'm hoping they pin a whole lot more on the guy, and that he's never seen again. I've honestly had nightmares about my sons somehow fucking up and going to Riker's, and I'd like those to end. Maybe with Seabrook gone we can finally reform that god awful hellhole.
Recent talks, useless synopses
I am giving in to the urge to be extremely snarky today. If that doesn't suit your mood, please skip. Just in case it doesn't come through, I really liked two of these talks.
Last week I introduced Carl Pomerance at the Museum of Math for his delightful talk, What We Still Don't Know About Addition and Multiplication. His notes are here.
My synopsis: it's easier to multiply than to factor. Sometimes you can represent numbers as the difference of two squares and factor them pretty fast. And when you can't do that very quickly, you still can do that relatively quickly if you keep track of things.
Yesterday I spent the day at USI2016. I gave a talk in the afternoon but I also went to three talks. Here are my synopses of those talks.
Don Tapscott: Blockchain is a big deal. It will eventually solve inequality. It's a paradigm shift. It's all about getting Dorito customers to make commercials for the Dorito Corporation. Next stop, inequality solved by blockchain.
Andrew McAffee: Look at this graph, consumption is no longer going up for Americans if you measure it in a specific way. That means we've entered a new paradigm, especially because I've got a name for it. Also, great news, we rich people no longer need to worry about global warming because technology will solve that like it solves everything else.
Monica Lewinsky: I was the first example of cyber bullying. We need more compassion online. When you click on shame-based news articles, you are training the online clickbait algorithm, and you become part of it. Resist clicking, be nice.
In Paris
Today I'm giving a talk a USI in Paris. It's unbelievably swank, the very first time I've been part of something that is, for example, taking place in the Carrousel du Louvre. I'm also staying at a ridiculous hotel with this view from my balcony:
And yes, it's bizarre to be in such a nice place so I can go complain about how poor people are being surveilled and mistreated. I accept all cries of "hypocrite!" that you might want to throw at me, but know that at least I'm a self-aware hypocrite.
And with that, I wanted to share a few things with you today.
First, did you know there were reparations to slave owners in Britain? Turns out, soon after slavery was abolished in 1836, slave owners in Britain got very seriously compensated, to the tune of 17 billion pounds ($24 billion) in today's money, which was 3.5% of the government's income that year.
Seems to me this should change our perspective on reparations. I learned this just now from the BBC, which is what I watch on TV when I'm in Paris (see also this). There's a new project to map out the slaves and slaveowners that received money all over the world.
Second, thanks to Abe Kohen I found out that Wisconsin's Supreme Court is considering whether recidivism risk scores deny criminal defendants due process and are discriminatory, given that they rely on proprietary source code. Very interested to see how this turns out.
And, yet again, they are relying on the fact that a defendant's score is "one of many factors a court can consider at sentencing." I'm not sure this makes any sense. If there's a shit score, but it's only one of many factors that are used in a process that's supposed to be fair, doesn't that mean the overall process isn't fair?
Finally, I wanted everyone who's interested in what it feels like to be a 40-something old lady rebel to read this essay. An excerpt:
It's partially because I am "old" that I've stopped caring about what's socially acceptable for me to do or wear. I got my first tattoo at 40. This year, I had my hair dyed teal. And you know what? It looks fantastic. My favorite pair of shoes are my Doc Martin boots, and I dare any child on the internet who's probably younger than some of the underwear I own to try to tell me I can no longer wear them.
I mean, my hair is blue, not teal, but yes! Funny and true.
Three Ideas for defusing Weapons of Math Destruction
This is a guest post by Kareem Carr, a data scientist living in the Cambridge. He's a fellow at Harvard's Institute of Quantitative Social Science and an associate computational biologist at the Broad Institute of Harvard and MIT. Formerly, he has held positions at Harvard's Molecular and Cellular Biology Department and the National Bureau of Economic Research.
When your algorithms can potentially affect the way physicians treat their dying patients, it really brings home how critical it is to do data science right. I work at a biomedical research institute where I study cancer data and ways of using it to help make better decisions. It's a tremendously rewarding experience. I get the chance to apply data science on a massive scale and in a socially relevant way. I am passionate about the ways in which we can use automated decision processes for social good and I spend the vast majority of my time thinking about data science.
A year ago, I started working on creating a framework for assessing performance of an algorithm used heavily in cancer research. The first part of the project involved gathering all the data that we could get our hands on. The datasets had been created by different processes and had various advantages and disadvantages. First, the most valued but labor-intensive category of datasets to create had been manually curated by multiple people. More plentiful were datasets that had not been manually curated, but had been assessed by so many different algorithms that they were considered extremely well-characterized. Finally, there were the artificial datasets that had been created by simulation and for which the truth was known, but which lacked the complexity and depth of real data. Each type of dataset required careful consideration of the type of evidence it provided for proper algorithm performance. I came to really understand that validation of an algorithm and characterization of the typical errors were an essential part of the data science. The project taught me a few lessons that I think might be generally applicable.
Use open datasets
In most cases, it is preferable that algorithms be open-source and available for all to examine. If algorithms must be closed-source and proprietary, then open, curated datasets are essential for comparisons among algorithms. These may include real data that has been cleared for general use, anonymized data or high-quality artificial data. Open datasets allow us to analyze algorithms even when they are too complex to understand or when the source code is hidden. We can observe where and when they make errors and discern patterns. We can determine in what circumstances other algorithms can be better. This insight can be extremely powerful when it comes to applying algorithms in the real world.
Take manual curation seriously
Domain-specific experts, such as doctors in medicine or coaches in sports, are generally a very powerful source of information. Panels of experts are even better. While humans are by no means perfect, when careful consideration of an algorithmic result by experts implies that the algorithm has failed, it's important to take that message seriously. It's important to investigate if and why the algorithm failed. Even if the problem is never fixed, it is important to understand the types of errors the algorithm makes and to measure its failure rate in various circumstances.
Demand causal models
While it has become very easy to build systems which generate high-performing black-box algorithms, we must push for explainable results wherever possible. Furthermore, we should demand truly causal models rather than the merely predictive. Predictive models perform well when there are no external modifications of the system. Causal models continue to be accurate despite exogenous shocks and policy interventions. Frequently, we create the former, yet try to deploy them as if they are the latter with disastrous consequences.
All three principles have one underlying idea. Bad data science obscures and ignores the real world performance of its algorithms. It relies on little to no validation. When it does perform validation, it relies on canned approaches to validation. It doesn't critically examine instances of bad performance with an eye towards trying to understand how and why these failures occur. It doesn't make the nature of these failures widely known so consumers of these algorithms can deploy them with discernment and sophistication.
Good data science does the opposite. It creates algorithms which are deeply and widely understood. It allows us to understand when algorithms fail and how to adapt to those failures. It allows us to intelligently interpret the results we receive. It leads to better decision making.
Let's stop the proliferation of weapons of math destruction with better data science!
Sketchy genetic algorithms are the worst
Math is intimidating. People who meet me and learn that I have a Ph.D. in math often say, "Oh, I suck at math." It's usually half hostile, because they're not proud of this fact, and half hopeful, like they want to believe I must be some kind of magician if I'm good at it, and I might share my secrets.
Then there's medical science, specifically anything around DNA or genetics. It's got its own brand of whiz-bang magic and intimidation. I know because, in this case, I'm the one who is no expert, and I kind of want anything at all to be true of a "DNA test." (You can figure out everything that might go wrong and fix it in advance? Awesome!)
If you combine those two things, you've basically floored almost the entire population. They remove themselves from even the possibility of critique.
That's not always a good thing, especially when the object under discussion is an opaque and possibly inaccurate "genetic algorithm" that is in widespread use to help people make important decisions. Today I've got two examples of this kind of thing.
DNA Forensics Tests
The first example is something I mentioned a while ago, which was written up beautifully in the Atlantic by Matthew Shaer. Namely, DNA forensics.
There seem to be two problems in this realm. First, there's a problem around contamination. The tests have gotten so sensitive that it's increasingly difficult to know if the DNA being tested comes from the victim of a crime, the perpetrator of the crime, the forensics person who collected the sample, or some random dude who accidentally breathed in the same room three weeks ago. I am only slightly exaggerating.
Second, there's a problem with consistency. People claiming to know how to perform such tests get very different results from other people claiming to know how to perform them. Here's a quote from the article that sums up the issue:
"Ironically, you have a technology that was meant to help eliminate subjectivity in forensics," Erin Murphy, a law professor at NYU, told me recently. "But when you start to drill down deeper into the way crime laboratories operate today, you see that the subjectivity is still there: Standards vary, training levels vary, quality varies."
Yet, the results are being used to put people away. In fact jurors are extremely convinced by DNA evidence. From the article:
A researcher in Australia recently found that sexual-assault cases involving DNA evidence there were twice as likely to reach trial and 33 times as likely to result in a guilty verdict; homicide cases were 14 times as likely to reach trial and 23 times as likely to end in a guilty verdict.
Opioid Addiction Risk
The second example I have today comes from genetic testing of "opioid addiction risk." It was written up in Medpage Today by Kristina Fiore, and I'm pretty sure someone sent it to me but I can't figure out who (please comment!).
The article discusses two new genetic tests, created by companies Proove and Canterbury, which claim to accurately assess a person's risk of becoming addicted to pain killers.
They don't make their accuracy claims transparent (93% for Proove), and scientists not involved with the companies peddling the algorithms are skeptical for all sorts of reasonable reasons, including historical difficulty reproducing results like this.
Yet they are still being marketed as a way of saving money on worker's comp systems, for example. So in other words, people in pain who are rated "high risk" might be denied pain meds through such a test that has no scientific backing but sounds convincing.
Enough with this intimidation. We need new standards of evidence before we let people wield scientific tools against people.


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Jingo (Discworld Series #21)by Terry Pratchett
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It isn't much of an island that rises up one moonless night from the depths of the Circle Sea -- just a few square miles of silt and some old ruins. Unfortunately, the historically disputed lump of land called Leshp is once again floating directly between Ankh-Morpork and the city of Al-Khali on the coast of Klatch -- which is spark enough to ignite that glorious
It isn't much of an island that rises up one moonless night from the depths of the Circle Sea -- just a few square miles of silt and some old ruins. Unfortunately, the historically disputed lump of land called Leshp is once again floating directly between Ankh-Morpork and the city of Al-Khali on the coast of Klatch -- which is spark enough to ignite that glorious internationalpastime called "war." Pressed into patriotic service, Commander Sam Vimes thinks he should be leading his loyal watchmen, female watchdwarf, and lady werewolf into battle against local malefactors rather than against uncomfortably well-armed strangers in the Klatchian desert. But war is, after all, simply the greatest of all crimes -- and it's Sir Samuel's sworn duty to seek out criminal masterminds wherever they may be hiding ... and lock them away before they can do any real damage. Even the ones on his own side.
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Product Details
- 9780061807695
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- Publication date:
- 10/13/2009
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Read an Excerpt
It was a moonless night, which was good for the purposes of Solid Jackson.
He fished for Curious Squid, so called because, as well as being squid, they were curious.That is to say, their curiosity was the curious thing about them.
Shortly after they got curious about the, lantern that Solid had hung over the stern of his boat, they started to become curious about the way in which various of their number suddenly van-ished skyward with a splash.
Some of them even became curiousvery briefly curiousabout the sharp barbed thing that was coming very quickly toward them.
The Curious Squid were extremely curious.Unfortunately, they weren't very good at making connections.
It was a very long way to this fishing ground, but for Solid the trip was usually well worth it.The Curious Squid were very small, harmless, difficult to find and reckoned by connoisseurs to have the foulest taste of any creature in the world.This made them very much in demand in a certain kind of restaurant where highly skilled chefs made, with great care, dishes containing no trace of the squid whatsoever.
Solid Jackson's problem was that tonight, a moonless night in the spawning season, when the squid were especially curious about everything, the chef seemed to have been at work on the sea itself.
There was not a single interested eyeball to be seen.There weren't any other fish either, and usually there were a few attracted to the light.He'd caught sight of one.It had been making through the water extremely fast in a straight line.
He laid down his trident and walked to the other end of the boat, where his son Les was also gazing intentlyat the torch-lit sea.
"Not a thing in half an hour," said Solid.
"You sure we're in the right spot, Dad?"
Solid squinted at the horizon.There was a faint glow in the sky that indicated the city of Al-Khali, on the Klatchian coast.He turned round.The other horizon glowed, too, with the lights of Ankh-Morpork.The boat bobbed gently halfway between the two."'Course we are," he said, but certainty edged away from his words.Because there was a hush on the sea.It didn't look right.The boat rocked a little, but that was with their movement,not from any motion of the waves.It felt as if there was going to be a storm.But the stars twinkled softly and there was not a cloud in the sky.
The stars twinkled on the surface of the water, too.Now that was something you didn't often see.
"I reckon we ought to be getting out of here," Solid said.
Les pointed at the slack sail."What're we going to use for wind, Dad?"
It was then that they heard the splash of oars.
Solid, squinting hard, could just make out the shape of another boat, heading toward him.He grabbed his boat-hook.
"I knows that's you, you thieving foreign bastard!"
The oars stopped.A voice sang over the water.
"May you be consumed by a thousand devils, you damned person!
The other boat glided closer.It looked foreign with eyes painted on the prow.
"Fished 'em all out, have you? I'll take my trident to you, you bottom-feedin' scum that y'are!'
My curvy sword at your neck, you unclean son of a dog of the female persuasion!"
Les looked over the side.Little bubbles fizzed on the surface of the sea.
"Dad?" he said.
"That's Greasy Arif out there!" snapped his father."You take a good look at him! He's been coming out here for years, stealing our squid, the evil lying little devil!"
"Dad there's"
"You get on them oars and I'll knock his black teeth out!"
Les could hear a voice saying from the other boat "-see, my son, how the underhanded fish thief"
"Row!" his father shouted.
"To the oars!" shouted someone in the other boat.
"Whose squid are they, Dad?" said Les.
"What, even before we've caught them?"
"Just you shut up and row!"
"I can't move the boat, Dad, we' re stuck on something!"
"It's a hundred fathoms deep here, boy! What's there to stick on?"
Les tried to disentangle an oar from the thing rising slowly out of the fizzing sea.
"Looks like a ... a chicken, Dad!"
There was a sound from below the surface.It sounded like some bell or gong, slowly swinging.
"Chickens can't swim!"
"It's made of iron, Dad!"
Solid scrambled to the rear of the boat.
It was a chicken, made of iron.Seaweed and shells covered it and water dripped off it as it rose against the stars.
It stood on a cross-shaped perch.
There seemed to be a letter on each of the four ends of the cross.
Solid held the torch closer.
"What the"
Then he pulled the oar free and sat down beside his son.
"Row like the blazes, Les!"
"What's happening, Dad?"
"Shut up and row! Get us away from it!"
"Is it a monster, Dad?"
"It's worse than a monster, son!" shouted Solid, as the oars bit into the water.
The thing was quite high now, standing on some kind of tower ... "What is it, Dad! What is it?"
"It's a damned weathercock.
There was not, on the whole, a lot of geological excitement.The sinking of continents is usually accompanied by volcanoes, earthquakes and armadas of little boats containing old men anxious to build pyramids and mystic stone circles in some new land where being the possessor of genuine ancient occult wisdom might be expected to attract girls.But the rising of this one caused barely a ripple in the purely physical scheme of things.It more or less sidled back, like a cat who's been away for a few days and knows you've been worrying.
Around the shores of the Circle Sea a large wave, only five or six feet high by the time it reached them, caused some comment.
Meet the Author
Sir Terry Pratchett, OBE, was the author of more than 70 books, including the internationally bestselling Discworld series of novels. His books have been adapted for stage and screen, and he was the winner of multiple prizes, including the Carnegie Medal. In January 2009, Pratchett was knighted by Queen Elizabeth II in recognition of his services to literature. Sir Terry, who lived in England, died in March 2015 at the age of 66.
Brief Biography
- Hometown:
- Salisbury, Wiltshire, England
- Date of Birth:
- April 28, 1948
- Place of Birth:
- Beaconsfield, Buckinghamshire, England
- Education:
- Four honorary degrees in literature from the universities of Portsmouth, Bristol, Bath and Warwick
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Of course when that happens you may suddenly realize, "I'd be better off if I were some where else." Some times it's not about winning, it's about how you go about losing that counts, at least it is in "Jingo," and of course the New Testament Gospels -- not that I'm comparing "Jingo" to the Bible. I'm amazed how Terry Pratchett can translate current events (whether they've happened or not) into a Diskworld story, capturing the reality, stupidity, and ultimately salvation.
My name is bloodkit
Hi, Im Larksong. Im not here to join, but Hollyfur told me that she is locked out. If someone needs to speak to me, I am at information booth any res. Okay? Bye! ~Larksong
Im going to be singing in front of a bunch of people. Its my first time singing in front of people solo
He licks her ear. Hello~Racoonclaw
Mudkit frowned. "Its not that boring."
Hailstar carries an unconsious small black odd-eyed tom into camp. The tom is horribly ingured and his body is red from blood.
If you adopted Sunkit and Opalkit up top write to Firegazer.
A tiny meteal cage is tbrust in. In it are two waling kita that slides on their soft tummies on the meatl flors all around the cage. They have metal collars that pinch. They mew pitfully with flat ears for milk pain and fera
Scarletpaw paused outside the barrier. she could hear cats laughing and talking, being happy on this fine day. Scarletpaw made amove to go in but shied away. Her haunted past was too horrible- they would never let her join. Im not called scarletpaw for nothing, she thought grimly with a touch of sadness. She padde slowly away.
Another gem, funny and witty til the end some nice summer reading.
Vetinari at his best, even when he has left office.

subset: commoncrawl


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another name for jr (see jr)
and his eye color
his eyes are amazing
and his eye color
his eyes are amazing
blue-green is the most wonderful color in the world. hands down dont argue with me.
av JRFan 1. juli 2007
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Bible contradiction proof + Citations
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So now I have to wonder if all the people down rating this thread are more evidence that a believer only accept things about their beliefs that make them look good and then damn everything that makes them look bad even if both sides of the coin are true. Again, this behavior would be very predictable from the faithful as their belief system is there to give them a sense of self confidence and often little more. So anything that threatens that self confidence must be bad and must be eliminated and treated as the enemy. Although this is in general and exists on a spectrum, as some do indeed try to embody those good qualities as opposed to just talking about them.
I mean I'm not a professional licensed psychologist or anything but hey observations are observations and data is data and patterns are patterns.
It's not really a matter of appearances.
I couldn't care less what you think of me because I believe what the bible says and I believe in JESUS.
From what I can tell, the entire purpose of this thread is to try to make Christians look bad,(and it's a fail.)
There are things that seem to be contradictions, but as a person presses on and studies prayerfully, it comes together.
I know that you don't believe that because you've never done it... as you stated in the original message, (you don't own a bible.)
Perhaps before you make unfounded accusations you would do well to seek and search it out for yourself. It's not just a matter of reading it, it's a heart matter...that's all I will say on that.
Jesus said this:
Matthew 7:13 Enter ye in at the strait gate: for wide is the gate, and broad is the way, that leadeth to destruction, and many there be which go in thereat:
Matthew 7:14 Because strait is the gate, and narrow is the way, which leadeth unto life, and few there be that find it.
Anonymous Coward 1553081
I've been doing my searching. That's how I've come to the conclusion that there's only a scant few real christians out there who actually practice teh teachings. The rest just want to feel special and they're the problem. And of course it becomes a bigger problem for everyone when there's confusion about what christianity actually is. If the majority of alleged christians are just the douchebags who want to feel special then all of christianity gets viewed that way. So basically what I've been doing is making observations of people to see what they're really like and what they really believe. And so far I've found that only a scant few "christians" actually are real christians. Same goes for other belief systems. This assumes that a real christian or whatever truly wants goodness for all and all that nice stuff.
So far however most of the christian responses to this thread come from christians who are only christians in name only. Its just more observational data for me and that's all.
I spent so many years looking at the overall attitude of Christians that I didn't want any part of Christianity. I justified my turning away based on the things I saw Christians do or say, and never bothered to examine my own ways. If I had I would have realized long ago that I had no right to make such judgments because I myself am imperfect.
But I do trust that Jesus is faithful to finish the good work that HE has started in me.
We all fail in one way or another....(myself...I believe I've failed more often than most.) I learned to consider my own shortcomings when I want to point the finger at other believers. As far as applying the word to my life, I still fall short, but I do try, and I won't give up. As the bible says, "Be doers of the word and not hearers only deceiving your own selves."
Don't turn away because of what others are doing, and don't deny yourself the opportunity to know Jesus.
It's a poor excuse when you really think about it, and I tell you that from my own personal experience.
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- News tagged "microsoft"
Friday, 14 Jun 2013
Microsoft Rolls Out Office Mobile for iPhone
Microsoft has released Office Mobile for the iPhone. Compatible with iPhone 4, 4S, and 5, as well as iPod Touch 5th gen, the Microsoft Office Mobile allows you to access, view, and edit your Microsoft Word, Excel, and PowerPoint documents from anywhere.
Thursday, 13 Jun 2013
Xbox One to Launch in Asia Only in Late 2014
According to a Microsoft executive, the Xbox One will only launch in Asia in late 2014. There's no word yet on when Japan will be getting the Xbox One.
Monday, 10 Jun 2013
Rumor: Windows 8.1 to Ship August 1
According to Paul Thurrott, Windows 8.1 will ship on August 1. The question is: Will the OS update also appear on the Windows Store on the same day?
Friday, 7 Jun 2013
Windows 8.1 to Bring Outlook 2013 RT to Windows RT Devices (Update)
Microsoft has announced that Outlook 2013 RT will be coming to Windows RT devices through the upcoming Windows 8.1 update. And the Acer Iconia W3, the world's first 8-inch Windows 8 tablet, will come pre-installed with Office Home & Student 2013.
Wednesday, 5 Jun 2013
AMD Drops Exclusive Windows OS Support; Ready for Android and Chrome OS
It seems like AMD will be supporting Google's Android and Chrome platforms, instead of exclusively sticking to Windows OS, as the company aims to be more outstanding on the market of tablets, low-cost PCs, and smartphones.
Tuesday, 4 Jun 2013
Microsoft Details Business Features in Windows 8.1
Microsoft has just shared some of the upcoming business features of Windows 8.1. And for the first time, we've confirmation that Windows 8.1 lets you boot directly to the desktop.
Friday, 31 May 2013
Microsoft Reveals More Details on Windows 8.1
Microsoft has revealed more details about the upcoming Windows 8.1 update. It packs features galore, including more personalization options, more powerful search, greater cloud connectivity, more ways to use apps side-by-side, Internet Explorer 11 with tab syncing across devices, and a Windows Logo Start 'tip'.
Tuesday, 28 May 2013
Microsoft Surface Pro Available in Singapore on 3 June from S$1198
Microsoft's much awaited Surface Pro notebook will soon be available in Singapore from 3rd June at 20 major Challenger Stores around Singapore, as well as selected Harvey Norman and Newstead outlets. Both the 64GB and 128GB editions will be available with their accessories, so check out the full details after the jump!
Wednesday, 22 May 2013
NVIDIA Announces PhysX Support for Microsoft Xbox One
Hot on the heels of Microsoft's announcement regarding their next generation gaming console, the Xbox One, NVIDIA has announced that the product will support their popular NVIDIA PhysX and NVIDIA APEX software development kits.
Wednesday, 15 May 2013
Microsoft Confirms Windows 8.1 Will Be a Free Upgrade
At JP Morgan's Technology, Media & Telecom Conference, Microsoft's Windows Division CMO and CFO, Tami Reller, confirmed that the upcoming Windows 8 update, previously codenamed Windows Blue, has now been given the official release name Windows 8.1, and will be a free upgrade for all Windows 8 users.


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Help please answere.
If you mean you want to cancel your listing with the Broker and be free to list elsewhere - that's not so easy to do. You'd need the Broker to agree to give you an "unconditional release" , which would then allow you to move forward with another company. You'd need to work this out with the agent and Broker.
If you mean cancel a SALES contract that you have entered into with a buyer..........that depends on the contract, and what contingencies there are that have not been satisfied.
Ask your agent where you stand, or better yet.............check with a real estate attorney to see what legal rights you have.
Best wishes!
cancellation there is always the issue of "EXPOSURE" ! The
other party dosn't need to prevail to cause a problem-all that
needs to be done is create a "cloud on the title " and you are in
place for your "worst nightmare ". Carefully consider what you are
trying to acheve then get good legal advice as to how cancellation
wil help you! Best of Success! Get good Legal opinion before making
any moves!
Bob Brubaker Highlight Realty Palm Beach County Fl. 561-876-6649
Nicole Marks Mason, Realtor
A very interesting question and a topic I had not too long ago with an attorney who only deals with real estate. Her take on your question was it would be very difficult to find a judge who would rule favorably on any specific performance lawsuit, especially if any case was properly presented on the plaintiffs behalf. While it seems crazy if I take this literally it would mean a seller could essentially say a couple minutes prior to closing that they changed their mind and if properly represented the ramifications would be minor.
If you are in a situation where you need legal advice please consult a capable lawyer who will be happy to assist you.
The very best of luck to you and I hope this information is helpful but if you need anything additional please do not hesitate to give me a call.
Always at Your Service,
Tom Priester e-PRO
"Results Driven Real Estate"
Keller Williams Realty
561 308-0175
Are you talking about your listing agreement with your listing agent's brokerage to market and sell your home, or are you talking about the real estate contract you signed with a buyer?
Two very different contracts....
There is in most cases always a way, depends on the reasons and what the terms in the contract or agreement say, therefore it is more a legal question ...... you can ask your listing agent's opinion based on the contract terms and then get more detailed legal advice from a good real estate attorney if that becomes necessary.
We cannot really give you any legal advice here and we do not know the terms in your contract either
@Properties North Shore, 30 Green Bay Rd. Winnetka Il. 60093
Edith always works in the very BEST interest of her clients Buyers, Sellers and Investors alike,
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EcoTools, Loofah Bath Sponge
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- Loyalty credit is equal to 10% of the value of your order, excluding shipping charges.
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Shipping Weight:?0.27 lbs (0.12 kg)
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- Product Code: ECT-07119
- UPC Code: 079625071191
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- Dimensions: 1.3 x 3.5 x 6 in, 0.05 lbs (0.02 kg)
- Eco-Friendly Beauty
- Reveal Radiant Skin with Exfoliating Loofah
- Buff & Exfoliate
- Expands When Wet
Look beautiful and live beautifully every day with the Loofah Sponge.
Suggested Use
This large loofah bath sponge expands when wet and exfoliates for smooth skin.
Loofah's are wonderful ways to soap up in the shower, as they really get your circulation going. This particular loofah stays quite hard, even when wet, so it doesn't suds up a lot and it can feel a bit clumsy when you scrub your body with it. I find it makes for a very nice DRY scrubber. Hop in the shower and, before you get wet, scrub over your entire body (not your face!) with this loofah. You'll remove dead skin cells and get your circulation going (very good for ladies with cellulite problems). Be sure to rinse it really well, then hang it up to dry. It's a great addition to your bath time routine. If you've got dry skin, you might want to add a very nice goat milk shampoo-soap to your order: Tierra Mia Organics, Raw Goat Milk Skin Therapy, Lime in Coconut Shampoo Bar. Your skin will feel like silk.
Posted by 5228203886868083145 on Jun 09, 2016
a big pc of loofah
It's okay
Posted by 5316041887926119916 on May 03, 2016
It's okay.
Posted by Yes0Yes0 on Feb 19, 2016
I didn't think it would be quite scratchy. It gives you the smooth skin that you want, though it didn't completely exfoliate my skin as a whole. Remember not to overdo it 'cause it will leave your skin with few redness (but nothing serious). The product has good qualities like how it is eco-friendly so it's okay! (:
Posted by 5505560129250870570 on May 01, 2015
Il gomme bien le corps, quand je l'utilise avec mon gommage, j'ai l'impression qu'il fait beaucoup de bien à ma peau. Le prix est vraiment petit et vaut vraiment le coup.
Posted by DameBridget on Apr 15, 2015
First and foremost - since this product is not available for purchase in my country, I love that it comes non-expanded to save shipping costs, which allows me to order more than one (and thanks to iHerb save even more money!). Now for the loofah itself - I have atopic dermatitis, mostly on my calves, shoulders and back so I have been searching for something that is gentle on the skin yet does it's job when it comes to exfoliating and this product is exactly what I was looking for! I whole heartedly recommend it to anyone and everyone! Keep in mind though - the first few times it's still a bit too rough so my suggestion is don't put your body wash the first few times directly on the sponge and lather yourself up, instead use your hands and then gently go over the areas of your body with the loofah as needed. A few times of doing this the sponge will become more softer and then you can put your body wash directly on it. Bottom line - I will mostly definitely be restocking this as it has become my favourite loofah!


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March 24, 2013
I am from India, living In Dubai for past 1 year.
Using different shutter speed and manual operations in the camera.
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No, but I worked in T.V industry back in Mumbai so have little knowledge about lighting and good angles.
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"Melodramus is a band worth checking out, especially for fans of progressive metal/rock that bears a likeness to Dream Theater. The music leaves an impact for both its range and ambition, with thoroughly outstanding songwriting that manages to transcend genres."
"Melodramus is well on their way to receiving four highly coveted laminated, all-access, backstage passes for their laudable rock & roll accomplishments."
"Melodramus created a tune that is Grammy worthy..."
"4/4 rating. There is no reason this band shouldn't be all over the radio and piling up multi-platinum sales."
"With 'Black And Grey' appearing on the newly released 'Speed Racer: The Soundtrack'- things are definitely looking up for Melodramus as a band to watch."
"The caliber of musicianship and vocal prowess displayed on this record is dumbfounding and it is pride inspiring to know that they're a homegrown act. There is absolutely nothing that sounds like this in Utah. If you dig modern progressive rock/metal, seek this one out."
"One of the "Top 100 Unsigned Artists for 2007"


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Satin Sheets Romance Review of "Highland Healer" by Willa Blair - Strong secondary characters, including a mentor, a maternal healer, and Toran's jealous former lover, Coira, and intense lines such as:'"What should I do with so beautiful, so valuable, a prize?" he murmured, almost to himself. His deep blue gaze ensnared Aileana as completely as his hands.' make this a rich, enjoyable read. Easily 4 satin pillows. (Really liked it! Will share with friends.)
From the Author
In my award-winning debut novel Highland Healer, the first in my Highland Talents series, I take you to the Scottish Highlands of the early 16th century, where the old ways (and old talents) can still be found.
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Top Customer Reviews
Highland Healer skillfully blends an exciting plot with the personal stories of Aileana and Toran, two very appealing characters. If you love an action-packed and sensual historical romance, you'll love this book.
I am not 100% sure, but I believe this was a debut effort and it shows in the writing. There must have been some scenes that didn't make the final edit, but dialogue later doesn't reflect those edits. There were quite a few scenes that I read and said "whoa, when did that happen?" Being the compulsive freak that I am, I had to then scan back through the book to see where I missed these revelations, only to find that I hadn't missed them because they were not there. I blame the editor for that - not the author.
I also found the heroine Aileana to be incredibly stupid. Not just in a silly ,flighty young girl way but in a "OMG you are a moron" sort of way. I don't want to spoil anything so suffice it say if I had her "talent"( yes talent not gift), I would not have been a captive for 2 years. Just saying.....
The hero, Toran was a good hero. He was a bit wishy-washy at times, but I contribute most of that to the aforementioned editing issues.
All in all, I believe that Ms. Blair has a great deal of potential and I am willing to give her next book a try. I can't say that I would recommend this book, but I think with a better editor I could have.
My heart has been swept away in this heartwarming Highland story. The visionary words had me picturing myself amongst the clans themselves within the mountains behind their keep. The characters Toran and Aileanna chemistry sizzled between each other and their sweet nothing teasing whispers had me grinning and laughing at how hot the scenes were. I read this smooth writing story within a day and couldn't believe I was done so quickly, this was one of those stories I wanted to last forever.
Laird Lathan is a man of honor, a fierce fighter, a gentle lover, and caring lord over his clan, and of course the sexiest man every woman would dream of. His actions and tenderness swept me away immediately. The story in itself showed his strength when one moment he was captured yet yielded his demeanor until he could be rescued. Once rescued his charisma melted into my soul as he lead his clan and protected them along with his own captive rescue of the Healer Aileanna from the brutal rogue lowland army leader.
I really didn't gain any feelings towards the Healer Aileanna until the end of the book. However, she was a character who was a bit standoffish due to her gift of healing, she was scared of her own feelings and what might happen to herself if she failed. It was a relief and enjoyable to see how she grew within the story, how she gains a back bone and shows grace and forgiveness to those who would speak out against her.
At the end I did get angry with Aileanna because of her foolish actions in her thinking but the story is bitter sweet and I found my heart melted. I had happy teary eyes knowing that Aileanna and Toran would be together forever and a day with three blessings on the way.
Awesome Read!
Most Recent Customer Reviews
This was a great book to read. I truly enjoyed it very much. I laughed and cried through out this. Looking forward to the next book in this series.Published 2 months ago by Kindle Customer
I have wanted to read this book for a long time. It was well worth the wait! Willa Blair doesn't disappoint and this first book in the Highland talents series is a great beginning... Read morePublished 3 months ago by DKBRICK
The dialect was a bit difficult, but I really enjoyed the entire story, strong, faithful characters!Published 3 months ago by Kindle Customer
I skimmed through this a second time while on vacation. This author could have left out the explicit sex because her scenes leading up to the act were so beautifully descriptive... Read morePublished 4 months ago by maria
It was okay. Not the best and not the worst. Definitely predictablePublished 4 months ago by gretchen n
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Seattle Coffee Gear offers a selection of customer-accessible parts and tune-up kits to help keep your machine in tip-top shape! If your coffee or espresso producing apparatus is in need of a little more TLC, our tech crew offers a variety of professional tune-up and repair services.
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The Nature of Difference: Sciences of Race in the United States from Jefferson to Genomicsby Evelynn M. Hammonds
View All Available Formats & Editions
Pub. Date: 01/23/2009
Publisher: MIT Press
The Nature of Difference documents how distinctions between people have been generated in and by the life sciences. Through insightful commentaries and a wide-ranging selection of primary documents by the editors, it charts the shifting boundaries of science and race through more than two centuries of American history.
The documents, primarily writings by
The Nature of Difference documents how distinctions between people have been generated in and by the life sciences. Through insightful commentaries and a wide-ranging selection of primary documents by the editors, it charts the shifting boundaries of science and race through more than two centuries of American history.
The documents, primarily writings by authoritative, eminent scientists intended for their professional peers, show how various sciences of race have changed their object of study over time: from racial groups to types to populations to genomes and beyond. The book's thematic and synthetic approach reveals the profoundly diverse array of practices--countless acts of observation, quantification, and experimentation--that enabled the consequential categorizations we inherit. The documents--most reproduced in their entirety--range from dictionary definitions of race published between 1886 and 2005 to an exchange of letters between Benjamin
Baneker and Thomas Jefferson; from Samuel Cartwright's 1851 "Report on the
Diseases and Physical Peculiarities of the Negro Race" to a 1950 UNESCO
declaration that race is a social myth; from a 1928 paper detailing the importance of the glands in shaping human nature to a 2005 report of the discovery of a genetic basis for skin color. Such documents, given context by the editors' introductions to each thematic chapter, provide scholars, journalists, and general readers with the rich historical background necessary for understanding contemporary developments in racial science.
Evelynn M. Hammonds is Professor of the History of
Science and Professor of African and African American Studies at Harvard University.
She is the author of Childhood's Deadly Scourge: The Campaign to Control Diphtheria in New York City, 1880-1930. Rebecca M. Herzig is Associate Professor of Women and
Gender Studies at Bates College and the author of Suffering for Science: Reason and
Sacrifice in Modern America.
Product Details
- 9780262582759
- Publisher:
- MIT Press
- Publication date:
- 01/23/2009
- Edition description:
- New Edition
- Pages:
- 400
- Product dimensions:
- 6.90(w) x 8.90(h) x 0.90(d)
- Age Range:
- 18 Years
Table of Contents
Introduction xi
1 Dictionary Definitions of "Race" 1
Introduction 3
1.1 A Complete Pronouncing Medical Dictionary: Embracing the Terminology of Medicine and the Kindred Sciences, with their Signification, Etymology, and Pronunciation (1886) J. Thomas 4
1.2 A Practical Medical Dictionary (1911) T. L. Stedman 5
1.3 Gould's Medical Dictionary: Containing All the Words and Phrases Generally Used in Medicine and the Allied Sciences, with Their Proper Pronunciation, Derivation, and Definition Based on Recent Medical Literature (1928) G. M. Gould 5
1.4 Dictionary of Anthropology (1956) C. Winick 6
1.5 A Dictionary of Scientific Terms (1957) I. F. Henderson W. D. Henderson 6
1.6 Dictionary of the Biological Sciences (1967) P. Gary 7
1.7 A Dictionary of Anthropology (1972) D. M. Davies 7
1.8 McGraw-Hill Dictionary of the Life Sciences (1976) 8
1.9 Macmillan Dictionary of Anthropology (1986) C. Seymour-Smith 8
1.10 International Dictionary of Medicine and Biology (1986) S. I. Landau, ed. 8
1.11 Dictionary of Genetics and Cell Biology (1987) N. Maclean 9
1.12 Glossary of Genetics: Classical and Molecular (1991) R. Rieger 9
1.13 Encyclopedia & Dictionary of Medicine, Nursing, & Allied Health (1992) B. F. Miller 10
1.14 A Dictionary of Genetics (1997) R. King 10
1.15 The Cambridge Dictionary of Human Biology and Evolution (2005) L. L. Mai M. Young Owl M. P. Kersting 10
2 Anatomical Observations 13
Introduction 15
2.1 "Laws" (Query XIV) (1781-1782) Thomas Jefferson 19
2.2 "Letter to the Secretary of State" (1791) Benjamin Banneker 33
2.3 Thomas Jefferson's reply to Banneker (1791) 36
2.4 "The Effect of Circumstances upon the Physical Man" (1854)Frederick Douglass 37
2.5 "Peculiarities in the Structure and Diseases of the Ear of the Negro" (1887) T. E. Murrell 42
2.6 "The Deformity Termed 'Pug Nose' and Its Correction by a Simple Operation" (1887) John Orlando Roe 52
2.7 "The Hair and Wool of the Different Species of Man" (1850) 58
2.8 "On Some of the Apparent Peculiarities of Partuition in the Negro Races" (1875) Joseph Taber Johnson 59
3 Immunity and Contagion 61
Introduction 63
3.1 "Report on the Diseases and Physical Peculiarities of the Negro Race" (1851) Samuel A. Cartwright 67
3.2 "The Plague Spot" (1878) Mary P. Sawtelle 87
3.3 "Consumption Among the Indians" (1887) Washington Matthews 89
3.4 "Does Pulmonary Consumption Tend to Exterminate the American Indian?" (1887) Thomas Mays 95
3.5 "The Study of Consumption Among the Indians" (1887) Washington Matthews 100
4 Evolution and Degeneration 103
Introduction 105
4.1 "The Impossibility of Acclimatizing Races" (1861) 113
4.2 "Vital Statistics of the Negro" (1892) Frederick L. Hoffman 116
4.3 "The Influence of Environment and Race on Diseases" (1910) C. W. Birnie 129
4.4 "How to Improve the Race" (1914) Alexander Graham Bell 135
5 Techniques of Measurement 145
Introduction 147
5.1 Investigations in the Military and Anthropological Statistics of American Soldiers (1869) Benjamin Gould 151
5.2 "Some Recent Criticisms of Physical Anthropology" (1899) Franz Boas 155
5.3 "Observations on the Sweat Glands of Tropical and Northern Races" (1917) Elbert Clark Ruskin H. Lhamon 161
5.4 "The Color-Top Method of Estimating Skin Pigmentation" (1930) H. A. Bowman 168
5.5 "Race and Runners" (1936) W. Montague Cobb 179
6 Glandular Differences 195
Introduction 197
6.1 "The Gland As a Clue to the Mystery of Human Faces" (1920) 201
6.2 "Man and the Endocrines: With Stress on the Female" (1921) G. K. Dickinson 205
6.3 The Glands Regulating Personality: A Study of the Glands of Internal Secretion in Relation to the Types of Human Nature (1921) Louis Berman 210
6.4 "The Relation of the Endocrine Glands to Heredity and Development" (1922) Lewellys F. Barker 223
6.5 Endocrinology in Modern Practice (1939) William Wolf 231
7 Hybridity and Admixture 235
Introduction 237
7.1 "Effects of Race Intermingling" (1917) C. B. Davenport 241
7.2 "Biological and Social Consequences of Race-Crossing" (1926) W. E. Castle 245
7.3 "Racial Fusion Among the California and Nevada Indians" (1943) S. F. Cook 255
7.4 "The Physical Characteristics of the Hybrid" (1944) Louis Wirth Herbert Goldhamer 266
8 Toward Genetics 277
Introduction 279
8.1 "The Race Concept in Biology" (1941) Theodosius Dobzhansky 281
8.2 "Rh and the Races of Man" (1951) William C. Boyd 287
8.3 "On the Non-Existence of Human Races" (1962) Frank B. Livingstone Theodosius Dobzhansky 296
8.4 "The Genetic Basis of Human Races" (1968) Bentley Glass 302
9 The End of Race? 307
Introduction 309
9.1 "Statement on Race" (1950) UNESCO 313
9.2 "Statement on Biological Aspects of Race" (1996) American Association of Physical Anthropologists 319
9.3 "Statement on Race" (1999) American Anthropological Association 322
9.4 "Categorization of Humans in Biomedical Research: Genes, Race, and Disease" (2002) Neil Risch Esteban Burchard Elad Ziv Hua Tang 325
9.5 The Importance of Collecting Data and Doing Social Scientific Research on Race (2003) American Sociological Association 346
9.6 "Zebrafish Researchers Hook Gene for Human Skin Color" (2005) Michael Balter 358
9.7 "SLC24A5, a Putative Cation Exchanger, Affects Pigmentation in Zebrafish and Humans" (2005) Rebecca L. Lamason Manzoor-Ali P. K. Mohideen Jason R. Mest Andrew C. Wong Heather L. Norton Michele C. Aros Michael J. Jurynec Xianyun Mao Vanessa R. Humphreville Jasper E. Humbert Soniya Sinha Jessica L. Moore Pudur Jagadeeswaran Wei Zhao Gang Ning Izabela Makalowska Paul M. McKeigue David O'Donnell Rick Kittles Esteban J. Parra Nancy J. Mangini David J. Grunwald Mark D. Shriver Victor A. Canfield Keith C. Cheng 360
Index 369
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Health care: Big differencesOctober 24,2013
Health care: Big differences
Many people commenting on Vermonts health care reform have confused the federal Affordable Care Act and our states universal health care plan that has yet to be implemented. It is important that Vermonters understand these are two different programs, based on two very different approaches to health care and health care financing.
The ACA takes effect in 2014. The recently opened exchange is a requirement of the ACA, which employs insurance as the device to pay for our health care. The ACA does not cover everyone.
Vermont has already enacted but not yet implemented a universal health care plan. It is scheduled to take effect in 2017. It does not use insurance as a device to pay for health care costs; instead it is publicly funded and, best of all, it covers everyone.
Any confusion between these two very different programs is likely to be used by opponents of universal health care to sow discontent in the period between implementation of the ACA in 2014 and implementation of universal health care in 2017.
The Vermont Workers Center is sponsoring a series of forums around the state in an effort to keep our universal health care system on track. A partial list of these forums: Burlingtons Main Street Landing train station, today from 5 to 8 p.m.; the Fox Room of the Rutland Free Library, Monday from 5 to 8 p.m.; Church of the Good Shepherd in Barre, Dec. 3 from 5 to 8 p.m.
Lodiza LePore
BenningtonMORE IN LettersI believe that Matt Dunne has the energy, experience and creativity to lead Vermont, as our... Full StoryI am writing in support of Sue Minter for governor. Full StoryIm voting for Phil Scott for Governor on Aug. 9. You should too. Phil Scott listens to Vermonters. Full Story
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