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Panos Ipeirotis
Works at New York University
Attended Columbia University, New York, NY, USA
Lives in New York, NY, USA
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Panos Ipeirotis

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+TANIA IPEIROTI Γύρω στο 9, αλλες φορές πάνω, άλλες φορές κάτω. Γενικά, μέχρι στιγμής έχουμε ήπιο χειμώνα. (Ειδικά σε σχέση με πέρισυ που μας είχε τρελλάνει στα -10C με -20C)
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Interesting hypothesis on how the way that a calculator works (yes, a calculator) can influence how you think when doing math. Worth reading till the end.
 
My 16-year-old daughter has just finished her mathematics GCSE (an exam that people in England take at that age), which means that she can now give up the subject and concentrate on other subjects that interest her more. She told me before the exams that she found functions difficult, so I gave her a bit of help with them, which was quite revealing. A standard type of question is to be given two functions and asked to compose them. So I tried out a couple of questions of that form on her. What follows is an account that won't be fully accurate in its details (because I can't remember precisely how our conversations went), but accurate enough not to be misleading. 

I began by asking her something like "If f(x) = x^2 and g(y) = y+1, then what is g(f(x))?" I thought I was making things clearer by saying that g was a function of y, so that one could substitute y=x^2 rather than substituting x=x^2. This, however, was a mistake and led to her making statements like, "Well, y must be x^2 -1," which I couldn't really do much about given that I couldn't talk about quantifiers.

Actually, I tried to talk about quantifiers without explicitly mentioning them, by saying things like "f takes any number and squares it, while g adds 1." But it didn't really help. When I gave up and said "f(x) = x^2 and g(x) = x+1," she was no longer confused, even though in some sense she ought to have been confused.

Well, I say she wasn't, but then a new problem emerged, which was that she consistently composed functions the wrong way round. So I'd ask her what g(f(x)) was when g(x)=x+1 and f(x)=x^2 and she would say (x+1)^2. I tried hard to think what could possibly be going on in her mind, which was difficult when I find the notation g(f(x)) utterly transparent: obviously you rewrite f(x) as x^2 to get g(x^2), and then since g(x) is x+1, g(x^2) must be x^2+1. But somehow she wasn't seeing it like that. 

Writing this, I now think that perhaps she read the g and thought "OK, that gives me x+1," then read the f and thought "That's x^2, so I must square the x+1," ending up with (x+1)^2. In other words, she was simply doing the functions in the order they were written. So she wasn't reading g(f(x)) as "Do g to f(x)". Rather, she was reading it as "Do g and then f to x". 

At some point in the conversation I discovered something that suddenly shed light on the situation. When I was her age, if I had been told that f(x) = sin(x+30) and had then been asked to work out f(10) on a calculator, I would have had to type in 1 0 + 3 0 = SIN. Similarly, if I had had to work out exp(sqrt(log 20)) I would have had to type in 2 0 LN SQRT EXP. But she had been issued with a calculator where you simply type in the expression as it is written on the page. So for those examples, she would have typed SIN ( 1 0 + 3 0 ) = and EXP ( SQRT ( LN 2 0 ) ) =. The result: without being conscious of it, I was internalizing the way functions worked, every time I used my calculator, while she could simply switch off her brain and copy expressions directly from the page, with no need to consider what they meant. This calculator, by the way, is the standard one that everyone in the country taking the exam is supposed to use.

The end of the story is that she did in the end get the idea and did her functions questions without any problem. So this post is not about her but about the way she, and presumably hundreds of thousands of others, have been taught mathematics.
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My Peer Grading Scheme
One of the components that I use in my class is student presentations.  While I like having students present, I had always a hard time grading the presentations. Plus, many students seemed to target the presentation to me, trying to sound too technical and ...
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Very nice !!
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LED-lit solar panel roads could power all of our electricity needs.

Learn more: goo.gl/ahTJa9
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Yet another idea on how computers and humans will work together...

"...The stray object in the path that might once have immobilised a robot won't immobilise it if the robot can ring up tech support and informed that it's just a stray object, go around dummy...[...].... It's very hard to design a machine that can improvise when confronted by the unfamiliar or reason its way through most difficulties—just as it's rare to find a human who can seamlessly navigate his way across all of America's public roads, large and small, without some sort of guide. But just as any regular joe with access to Wikipedia can do a passable impression of someone with enormous intellectual powers, the extended mind of the cloud could lead to impressive improvements in robot capabilities."
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The pain of being the only engineer in a business meeting (or being a computer scientist in a business school :-p)
The pain of being the only engineer in a business meeting is perfectly illustrated in the comedy sketch, "The Expert." The sketch was written and directed by Lauris Beinerts and is based on the (Ru...
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The class Mining Massive Data Sets looks fantastic. Not only does it have an all-star cast (Jure Leskovec, Anand Rajaraman, Jeff Ullman), but also the production quality looks quite high and content appears to be very good (at least from the first week of lectures and the syllabus). It just started at Coursera and is free.
Mining Massive Datasets is a free online class taught by Jure Leskovec, Anand Rajaraman and Jeff Ullman of Stanford University
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that looks great, please check out Billpayadvisor.com
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Soliciting truthful reports, while preserving anonymity:

A school wanted to ask students if they have ever taken drugs (yes or no). The survey was anonymous, but school was still worried that students will not report drug use.

So they introduced randomness to help. Each student was asked to flip a coin (privately) before answering. Heads, the student would have to say "yes". Tails, they would have to say the truth.

So, students could safely select “yes, I have taken drugs” and even if personally identified, the answer could be justified as the coin telling them to do so.

If no one had been taking drugs, 50% of the final result would be positive for drug use (those who got heads), and 50% would be negative (those who got tails).

In practice, it was something closer to 60%-40%, which meant about 20% of students had been taking drugs.
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While it's clear from what Chris Ferrie says that the idea wasn't original to me, I proposed it in a blog post once as a mechanism for having secret ballots in parliament while retaining a party system. The aim was to allow people to vote on issues on their merits without incurring the wrath of the party if they go against the party line, while not allowing them to do something like pretending to belong to one party while secretly always voting against it. The idea is that your voting record would be made public, except that each vote would have a certain probability, such as 10%, of being switched the other way. Then consistent anti-party voting would be detectable, but not the occasional rebellion.
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Importing Web Data into Google Spreadsheet

Did you know you can import tables available online directly into +Google Drive? That can be done using the ImportHTML function on  Google Spreadsheets and will save you a lot of time. The image below shows how to do it (source goo.gl/19mojE).
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The panorama stitching + HDR was done automatically by Google, after uploading my raw images in Google Drive. I am getting increasingly impressed by the features that are silently introduced by Google in its products.
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omg!
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"In the United States you have shareholder capitalism, in which shareholders will pressure a company for short-term profits. Japan and Germany have a stakeholder system, which lets companies invest in workers who are better trained, more loyal and more informed."
From a department store's elaborate welcoming rituals to a hotel's nearly uncanny sense of its guests' needs, one writer explores the Land of the Rising Sun's comprehensive service culture.
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The Informative Herd: why humans and other animals imitate more when conditions are adverse

Decisions in a group often result in imitation and aggregation, which are enhanced in panic, dangerous, stressful or negative situations. Current explanations of this enhancement are restricted to particular contexts, such as anti-predatory behavior, deflection of responsibility in humans, or cases in which the negative situation is associated with an increase in uncertainty. But this effect is observed across taxa and in very diverse conditions, suggesting that it may arise from a more general cause, such as a fundamental characteristic of social decision-making. Current decision-making theories do not explain it, but we noted that they concentrate on estimating which of the available options is the best one, implicitly neglecting the cases in which several options can be good at the same time. We explore a more general model of decision-making that instead estimates the probability that each option is good, allowing several options to be good simultaneously. This model predicts with great generality the enhanced imitation in negative situations. Fish and human behavioral data showing an increased imitation behavior in negative circumstances are well described by this type of decisions to choose a good option.
Abstract: Decisions in a group often result in imitation and aggregation, which are enhanced in panic, dangerous, stressful or negative situations. Current explanations of this enhancement are restricted to particular contexts, such as anti-predatory behavior, deflection of responsibility in ...
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Sadly, this model seems to extend to explain the success of fearmongering. By influencing people's perceptions of outcomes -- and, in particular, increasing their fear of the negative outcomes -- the model would seem to predict that you can move them as a group to a particular decision.
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Associate Professor
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  • New York University
    Associate Professor, 2004 - present
  • Computer Technology Institute, Patras, Greece
  • Columbia University, New York, NY, USA
    1999 - 2004
  • Microsoft Research, Cambridge, UK
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New York, NY, USA
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Greece - Serres, Greece - Patras, Greece - New York, NY, USA - Cambridge, UK
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44 West 4th Street, Ste 8-84New York, NY 10012
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Introduction
Panos Ipeirotis is an Associate Professor and George A. Kellner Faculty Fellow at the Department of Information, Operations, and Management Sciences at Leonard N. Stern School of Business of New York University.
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  • Columbia University, New York, NY, USA
  • University of Patras, Greece
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just go there for the crepes!
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