The following TED video, given by mathemagician and professor Arthur Benjamin (about whom I’ve previously blogged about here), embodies the best idea I’ve heard about math education in a LONG time. Perhaps ever. Just as I recently posted about how games like backgammon embody the 21st century in replacement of games like chess for the 20th, statistics is the central branch of mathematics for the 21st century rather than the calculus centric view of the 20th century. If you’re into math and math education, this will probably be the best 3 minutes you’ll spend today.
Ars Technica has an interesting article today about a paper about to be released in the Proceedings of the National Academy of Sciences (PNAS) about variations to an experiment in Game Theory called the Ultamatum Game. As the Ars article explains,
The basic rules of the Ultimatum Game are simple. One person is given a stack of cash, and told to divide it between themselves and a second party. That second party is then given the chance to accept or reject the offer; if it’s rejected, neither of them get any money. Clearly, any of this free money should be better than nothing, so under assumptions of strictly rational behavior, you might expect all offers to be accepted.
It turns out that tweaking some of the premises of this game leads to some interesting results in terms of human rationality, economic systems, and guilt. I highly recommend reading the article in its entirety. Also, if you’re interested in reading the abstract of actual paper itself, it’s available on the PNAS website here. It also looks like the full paper is available in PDF format if you’d like to read it. Not sure how long it will be available, but it’s there now. Toshio Yamagishi, the lead author, has a website here.
(Photo by cljo)
In 1997, chess champion Gary Kasparov was beaten in a 6-point match against a computer. It was the first time this had ever happened. The computer, named Deep Blue, was developed by IBM after some Carnegie Mellon University graduates joined the company. Here’s what Wikipedia has to say about the hardware computing power of Deep Blue:
The system derived its playing strength mainly out of brute force computing power. It was a massively parallel, RS/6000 SP Thin P2SC-based system with 30-nodes, with each node containing a 120 MHz P2SC microprocessor for a total of 30, enhanced with 480 special purpose VLSI chess chips. Its chess playing program was written in C and ran under the AIX operating system. It was capable of evaluating 200 million positions per second…In June 1997, Deep Blue was the 259th most powerful supercomputer according to the TOP500 list, achieving 11.38 GFLOPS on the High-Performance LINPACK benchmark.
Brute force. That’s how the computer got the job done. Of course, it’s never that simple. But there is one thing that can be said for certain: If you lose a game of chess, it is because you were outplayed. Plain and simple. And I think it’s for this reason that chess became an apt metaphor for modernist notions of intelligence. Stereotypically speaking, if you ask a person the question of what game smart people play, I would guess that chess would be the most common answer in the western world (perhaps Go in the eastern world). The fate of this game is in the hand of the players entirely. There is no chance involved, with the one exception of which player plays first.
As a child, I had a hard time enjoying games that involved a substantial amount of probability. “What’s the point,” I thought, “of playing a game skillfully if it’s possible for me to lose at the last possible moment due to a bad roll of the dice or a badly dealt card?” But as I’ve grown older, I’ve come to enjoy games like this MORE on average than straightforward skill games like chess. Enter backgammon.
For those of you who don’t know backgammon, I suggest checking out the Wikipedia page here. Backgammon has been played for 5,000 years, and has evolved substantially over that time. For example, of the additions to the game, the doubling cube, drastically changed play and was introduced less than 100 years ago. Backgammon is not like chess. In a single game of backgammon, it’s quite possible for a novice to beat a master due to elements of chance. Said another way, it’s possible to play the best possible game of backgammon you can based on your dice rolls and still lose. And this is the aspect of the game that makes it an apt metaphor for the 21st century. While the 20th century dealt with certainty, the 21st will deal with probability.
And this is not to say that games like backgammon are somehow more subjective than games like chess. There are some amazing machine learning techniques used to study the game (e.g. TD-Gammon), and there are quite a few computer programs, such as GNU Backgammon, that use these techniques to outplay human opponents. Poker games like Texas Hold’em also involve an element of probability, and have grown wildly popular over the last many years. And those of you who know poker know that there are rules that govern “right” playing. Though the cards dictate play, there are strategies that maximize gain and minimize risk. The same is true of backgammon. And with the game popping up in popular culture a bit more, like in the television show Lost, I can only see backgammon growing in popularity.
(Photo by Jeephead)
As an artistic diversion, I decided to search Flickr for the words “mathematics”, “math”, and “probability” on Creative Commons licensed photographs. The results were wonderful. Some of my favorites are below. Click on the photos to see explanations from the authors or to see more of their work!
Klein bottle (procrastination), by Pragmagraphr
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Love & Mathematics, by Lost Archetype
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Vegetable Meets Mathematics, by anroir
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n(n+1), by Jan Tik
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Torus with pairs of Villarceau circles, by Seb Przd
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Railroad Math, by Adamcha
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The Portrait of Conditional Probability, With A Third Ear Maybe, by DerrickT
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One in a billion, by Micah Sittig
I’ve spent some time over the last week looking at resumes. I’ve had about 100 or so cross my email inbox from a variety of job posting sites, and I was reminded of a few quirks that people tend to fall into that are not at all helpful for getting yourself a job. I’ve been on both sides of the hiring manager divide, and I thought I would relate some resume writing tips. There are a few examples given below that are IT-centric, so feel free to fill in your own examples as you’re reading.
- Do not include an objective section: Objective lines are always generic; they say nothing that differentiates you from others who are applying. I would much rather that a person has an overview section that includes your career highlights or technical capabilities. Telling me that you’re “interested in using your skills in an innovative and challenging environment” says nothing and wastes precious space. Rather, tell me that you “have 5 years experience in data warehousing technologies, including the deployment of 3 large scale data cubes.” The former is a statement that tells me nothing specific. The latter gives me a much better idea of who you are professionally and what you’re capable of accomplishing.
- Proofread: Your resume is the first piece of work you’ve created that I see. Do you really expect me to trust your level of conscientiousness if you’re not capable of adequately proofreading your public facing professional document? The answer should be no. This includes not only spelling and grammar, but consistent formatting.
- Do not use a generic resume template: Again, when a hiring manager is looking at stacks of resumes, differentiation makes a difference. If your resume blends in with 50 others, it’s a safe bet that I’m not going to remember yours. It’s worth your while to spend some time planning out the formatting of your resume for uniqueness.
- Tell me what you’ve done; tell me what it accomplished: Most people do the former, but few do the latter. I oftentimes read resume blurbs like “program effectively in C#.” A sentence like this relates to me your skill set, but it doesn’t tell me what you’ve done with this skill. A blurb like “programmed a replacement CRM system in C#, increasing application performance and saving the company $50K over the previously licensed CRM system” not only relays your skills, but it tells me what your skills have accomplished.
- Use white space: White space is capable of focusing the attention of the reader on particular pieces of the resume. More often than not, I receive what I refer to as “machine gun” resumes. These are resumes that use 8 point font, have 0.15in margins, and have full lines of text on every line. The thinking here seems to be that if you’re able to throw every possible thing you’ve ever done or read about (or whatever) at the manager, they’ll be impressed. Actually, it’s quite the opposite. If it’s difficult for me to focus on your resume, and there’s no indication of what pieces of the document you’d like for me to focus on, sensory overload takes over and it’s nearly impossible for me to remember anything about your resume.
- Do not refer to yourself in the third person: It sounds ridiculous, but I’ve seen this in a lot of resumes. You cannot vouch for yourself. By referring to yourself in the third person you sound silly. Do not do this.
- No images: Please don’t include any images. I’m sure some people will disagree with this one, but I don’t think that it’s appropriate. For tech resumes, I understand that people are sometimes interested in including graphics that represent certain received certifications. While these certifications should certainly be listed in the resume, please exclude the graphics. There have been several times where people have included graphics for certifications that have NOTHING to do with the position they’re applying to. And this tells me that they’re simply blanketing job sites with resumes rather than to tailor their search to specific positions.
There are a lot of other recommendations I could give, but others have already done a great job of this. Please check out these other resume tip sites:
Resume Tips from Taos
44 Resume Writing Tips from Daily Writing Tips
12 Important Resume Tips (YouTube)
Photo by woodleywonderworks
Computers were created in large measure to solve problems. And the programs that run on computers are designed to solve these problems. And those programs generally run to do exactly what we tell them to do. And much of what we tell them to do is straightforward in the sense that the problems they solve follow the law of non-contradiction, i.e. an answer provided by a computer for a specific problem is either true or not true, but never both simultaneously.
I can program a computer to answer for me the question, “What is three factorial?”
The answer provided, hopefully “six”, is either true or not true, but is quite obviously not both.
I’m ignoring some gray areas here, particularly in the places where problems are solved by computers learning, a la genetic algorithms in the case of Roger Alsing’s EvoLisa program or neural nets in the case of GNU Backgammon. But even in these arenas, computers are programmed to perform specific tasks that solve (or approximate) particular problems. For the rest of this post, I’m generally referring to the simpler class of problems, though I will touch on how decisions made within the financial sector over the last several years have in part caused our current global economic situation based on solutions to incomplete mathematical models.
I really started thinking about this issue in relation to the now famous Verizon Math site and associated videos that show just how hapless humans can be when we depend entirely on computers to return the correct answer. What I’m saying here is that we’ve more or less reached the point where we believe that computers will always return the correct answer, and forget that while computer programmers aim to have their programs answer on the “true” side of the law of non-contradiction, sometimes this unfortunately isn’t the case.
If you’d like a poignant example, please watch this video, where several Verizon employees fail to recognize how their computer system has overcharged the customer on the phone. I don’t bring this video up to pick on Verizon specifically, but this is an issue that has gained a lot of attention over the last several months:
Now, here’s the point: Though Verizon is in the wrong, the employees are not willing to recognize the error. And why is this the case? I can think of several reasons.
- Verizon employees are used to hearing customers complain about how they have been mischarged, and generally speaking the customer is wrong.
- These Verizon employees do not understand the math being explained to them by the customer.
- These Verizon employees are trusting what their computer system is telling them without fail.
And I think that all three issues played a part in the lack of understanding of the employees. But the issue that bothers me the most is the third, that the employees infallibly trust their computer system. What bothers me most about this story is that even in the face of blatant mathematical reasoning, the belief of the employees was to side with the answer provided by the computer. And the computer was incorrect. Due to a variety of circumstances, the math provided by the computer program did not match the price quote delivered by Verizon. And rather than viewing the computer as the product of human intellict, they viewed the computer as the objective arbiter.
Using the computer as an objective arbiter is a dangerous business for a variety of reasons, including most notably that the program returning the answer can be incomplete or incorrect. In the case of the recent financial meltodown, at least part of the blame can be placed on mathematical models that viewed sets of risk transactions (e.g. credit default swaps) as indepdent events. As it turns out, these events were NOT independent. Here’s an article about this. But an assumption of the program was to treat them independently. So was the computer wrong? Practically speaking, in retrospect, yes. But I don’t think that’s the right way of looking at it. The computer was answering the question based upon the programmer’s intent. And it was answering the question correctly in that sense.
What’s the moral of the story? Basically, it’s that computers answer problem in EXACTLY the ways they are programmed to do so. No more and no less. Computers are designed to be “right”, but it doesn’t mean that it will always pan out this way. Treating them as flawless objective arbiters is farming out your intellect. And while I’m certainly not saying that computers and their programs can’t be trusted (hell, it’s what I do for a living), I’m also saying that it’s a good idea to treat them as if they’re a product of humanity.
I’ve seen Craig Damrauer’s New Math pictures across a bunch of different places on the web, and they always make me take pause. A lot of them are downright hilarious, while others are more thoughtful. Check this one out:
I actually laughed out loud the first time I saw this. And then I thought about pirates in recent news history. And then I thought about Pirates of the Caribbean. And then I realized that in my brain there was a giant chasm between these two impressions.
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