No. 65: Liquid Cooling & Overclocking

10 July, 2012 1:59 AM / 1 Comment /

Hey everyone,

A while back I wrote about a Linux server I set up in order to do statistical work remotely from other computers. So far, I haven’t done much with it other than learn R and LaTeX, but recently I’ve discovered that it would be a great tool to document some of the algorithms I’ve developed through my modeling projects at work in the event that I would ever need to use them again (highly likely). Back in January, I wrote that I was concerned about the CPU getting too hot since I left it on at home while I was away at work. Since I leave the AC off when I’m gone, the air going into the machine would be hotter and would hinder the cooling ability of the server’s fans.

Original setup with stock AMD fan + heatsink

I could leave the AC on, but that wouldn’t be environmentally friendly, so I’ve been looking for other solutions to keep my processor cool. One of the options I decided to try was liquid cooling – which I heard was more energy efficient and better at cooling than traditional air cooling found on stock computers. Moreover, I had seen some really creative setups on overclockers.net – which encouraged me to try it myself. To get started, I purchased a basic all-in-one cooler from Corsair. This setup isn’t as sophisticated as any of the custom builds you’d see at overclockers, but it was inexpensive and I thought it would give me a basic grasp on the concept of liquid cooling.

The installation was pretty easy – all I had to do was remove the old heatsink and screw in pump/waterblock into the CPU socket. Then, I attached the 2 x 120 mm fans along with the radiator to the back of the case:

New setup with Corsair H80 system installed

However, one of the problems with these no-fuss all-in-one systems is that you can’t modify the hose length, which might make the system difficult or impossible to install if your case is too large or too small. As you can see, I got lucky – the two fans along with the radiator barely fit inside my mid-tower Antec 900 case. If it were any smaller the pump would have gotten in the way and I would have had to remove the interior fan to make it fit. Nevertheless, I’m really satisfied with the product – as soon as I booted up the machine I was impressed by how quietly it ran.

Naturally, I decided to overclock the processor to test the effectiveness of the new cooling system. I increased the clock speed of the CPU (AMD Phenom II) from 3200 MHz to 3680 MHz and ran all 4 cores at 100% capacity to see how high temperatures would get. Here are the results below:

Overclocking at 3680 MHz

You can see that the maximum temperature was just 46 C – that’s pretty cool for an overclocked processor. I only ran the test for a few minutes because I had been steadily increasing the clock speed little by little to see how far it could go. The test ran comfortably at 3519 MHz, but as soon as I reached 3680 MHz the computer started having issues with booting up. I was able to reach 3841 MHz by increasing the voltage to 1.5 V and 3999 MHz by increasing the voltage to 1.55 V. I was somewhat disappointed because I couldn’t get the clock speed to surpass 4 GHz (as the Phenom II has been pushed to much higher clock speeds with more sophisticated cooling techniques). At this point I couldn’t even run mprime without having my computer crash, but I was able to continue the stress testing by using BurnK7:

Stress testing with BurnK7 at 100% load – 3999 MHz

You can see that the core temperature maxed out at 60 C, so I’m pretty sure I could have pushed it a little further. However, the machine wouldn’t even boot up after I increased the multiplier, so I called it a day. I contacted my friend Daniel Lin (who had been overclocking machines since middle school) with the results, and he responded with his own stress test using an Intel Core i7 quad core:

Daniel Lin’s machine at 4300 MHz

The impressive part is he was able to reach 4300 MHz using nothing but stock voltages (1.32 V) and air cooling. He told me that I had an inferior processor and I believe him (then again, you get what you pay for – the Intel i7 is three times more expensive). If he had liquid cooled his computer he probably could have pushed it even further. Anyway, Daniel told me that you can’t be sure if an overclock is truly stable unless you stress test it over the span of several hours. So, I decided that my next task would be to get Ubuntu’s sensors to output its readings into a text file while I run mprime over the course of 24 hours. I’d also like compare temperature readings depending on whether or not the AC is turned on while I’m away at work. I’ll have the results up next week (hopefully).

Posted in: Logs / Tagged: , , ,

No. 64: Player Piano

3 July, 2012 2:21 AM / Leave a Comment /

Hey everyone,

I started reading Kurt Vonnegut’s Player Piano after I passed C/4 last month. The plot centers around an engineer named Paul Proteus and takes place in an alternative post WW2 era, in which machines have have displaced almost all of human labor. The only jobs left are for engineers, business managers, and hairstylists. As the story progresses, the machines get so good even the engineers end up losing their jobs – hence the title, Player Piano (a Piano that plays music without the need of a human performer). I guess you can see where I’m going with this…I wouldn’t want to spoil the rest, and I haven’t finished the book myself though I’m just 20 pages shy of finishing. Anyway, I became interested in the novel when I was searching the web for articles on post-scarcity economics. The basic idea is that classical economics stems from the conflict between unlimited human wants and limited natural resources. These wants are satisfied through the exchange of goods and services – two or more parties mutually agree to exchange resources – and this is done by valuing one party’s resources against another party’s resources. However, if a society were to achieve the ability to costlessly produce goods and services, the system of exchange and valuation breaks down because you’d no longer be able to value one good relative to another, which makes it impossible for two parties to come to an agreement on how to exchange goods. Some people believe such a system would be more egalitarian since people would no longer have to fight over limited resources. On the other hand, others have hypothesized that such a system would lead not to equality, but to a society dominated by an elite few – the original owners of capital (this is where post-scarcity economics overlaps with Marxist economics).

I’ve thought about such a scenario many times (maybe every other day) but I haven’t been able to reach any solid conclusions over the outcome of this situation. First of all, companies can save costs by automating manual labor and firing workers whose skills have become obsolete. This would result in short term gains because the company would be able to gain market share over its competitors by offering lower prices. However, in order for the company to make money, people would have to be willing to pay for its products. But if such automation were to occur on a large scale, you would end up in a paradoxical situation in which companies would be able to produce goods at no cost – but people wouldn’t be able to buy these goods because they don’t have jobs and aren’t earning wages. Moreover, if these workers aren’t buying goods, then the company won’t make any money. Thus, despite the economy’s ability to produce unlimited goods and services for its people, these people aren’t made any richer because there’s no longer a way to allocate these goods amongst themselves.

Historically, this sort of doomsday scenario hasn’t occurred because automation created more jobs than it destroyed. However, you don’t want to be too careless and assume that automation will continue to create jobs indefinitely just because it has in the past, since there’s no guarantee that this trend of job creation will continue. Perhaps, it might be possible that machines become so effective that they can replace all of human labor…or maybe we’ll eventually get to the point where we can costlessly create humanoid robots that are superior to their biological counterparts, rendering humans obsolete. On the other hand, it might be the case that a post-scarcity society is impossible to achieve. I noticed that in my previous paragraph that the inability to equitably allocate resources amongst a population represents scarcity in service (or scarcity in capital, if you want to take the Marxist point of view). So, while we might not reach post-scarcity, there could be some kind of scenario like “post-human labor”, which would present similar problems.

Anyway, Player Piano is somewhat similar to Zamyatin’s We, and Vonnegut himself said that he “cheerfully ripped off the plot of Brave New World, whose plot had been cheerfully ripped off from Yevgeny Zamyatin’s We.” I read We during the Summer after high school and now that I’m almost done with Player Piano, I can see that the basic structure is similar between the two books, though Vonnegut’s book contains more humor and has a more playful tone than Zamyatin’s. Vonnegut’s book was published in the U.S. after WW2, whereas Zamyatin’s book was written in 1920, suppressed by the Soviets during the Cold War, and later published in 1988. I’d recommend reading both as you’d get to compare the different perspectives between the Soviet Union and the United States, both before the War and afterward.

Posted in: Logs / Tagged: , , ,

No. 63: St. Petersburg Paradox

26 June, 2012 1:32 AM / Leave a Comment /

Hey everyone,

Work has kept me busy, as I’ve spent the last three weeks catching up on the tasks I pushed back while studying for my exam. I didn’t have any time to work on anything creative, so I decided to pull up an old project I had done a year ago on the St. Petersburg Paradox. The St. Petersburg Paradox is a famous problem in mathematics, proposed in 1713 by Nicolas Bernoulli in a letter to fellow mathematician Pierre Raymond de Montmort. The problem consists of a game where the player continuously flips a fair coin until it lands tails. The payout is equal to 2 raised to the number of consecutive heads obtained. For example, if the player gets 1 head, he receives a payout of 2. If he gets 2 heads in a row, he receives a payout of 4. If he gets 3 heads in a row, he receives a payout of 8, and so on and so forth. More formally, we can express the expected payout as:

$latex displaystyle mathrm{E}[mbox{payout}] = sum_{i=1}^infty (mbox{payout for }imbox{ consecutive heads})timesmathrm{Pr}(imbox{ consecutive heads}) $

$latex displaystyle mathrm{E}[mbox{payout}] = sum_i^infty 2^i (.5)^i $

$latex displaystyle = 2timesfrac{1}{2} + 4timesfrac{1}{4} + 8timesfrac{1}{8}cdots $

$latex displaystyle mathrm{E}[mbox{payout}] = 1+1+1cdots = infty$

As you can see, the expected payout is infinite. So, how much would the typical person pay to play this game? It turns out that you might be able to get a person to pay $1 or $5 to play, but once the fee gets into the double-digits, people start getting reluctant. Why is this so? Shouldn’t a rational person be willing to put down any finite amount of money to play the game? That’s why the problem is called the St. Petersburg Paradox. Even though the expected payout is infinite, most people aren’t willing to gamble a large sum of money to play the game.

Intuitively, this makes sense. If you’ve ever tried flipping a penny over and over again, you’ll notice that getting just 5 heads in a row is a rare event. Even then, the payout is just 32. The odds of getting a payout of 1024 is just under one out of a thousand. So, unless you have something better to do than to flip coins all day (and flip them really fast), you’re better off flipping burgers if you want to make a living wage (keep in mind you have to pay each time you play).

I wrote a couple of VBA subroutines to simulate the problem and posted a video of the execution on YouTube, a little more than a year ago (I believe I used a payout of 2^(i-1) instead of 2^i for this simulation):

[youtube=http://www.youtube.com/watch?v=QAizn9gqhO8]

Here, I allow the user to set some values for the simulation, like the game price, starting balance, and number of games. In addition, I added a progress bar, data bars, and sparklines to test out some new features in Excel 2010. The subroutine runs much faster without these features (like a thousand times faster), since the computer gets interrupted each time it has to update the progress bar and spreadsheet features. The columns to the right compare the theoretical distribution to the empirical distribution obtained through the simulation. As you can see, large payouts are very rare, and the player spends most of the time with a negative balance. The important lesson to glean out of this is that it would take a ridiculously large number of games to get a large payout, and relying on expected payouts alone would be a foolish choice to make in a business situation (especially in insurance).

Posted in: Logs, Mathematics / Tagged: , ,

No. 62: The Dowry Problem

19 June, 2012 2:30 AM / 1 Comment /

Hey everyone,

Let me introduce you to a famous problem in mathematics. Suppose you’re looking for someone to marry. In order to find that special someone, you, like most people, go on a series of dates, and then pick the best candidate amongst those whom you’ve dated. Unfortunately, while you have the ability to rank the suitors in retrospect, you have no way to determine if your ultimate choice will have been the best one out of all the available options. For example, if you were to pick the 8th person whom you’ve dated as your lifelong partner, until death do you part, you would be able to rank that person amongst the 7 previous candidates, but you would have no idea if anyone better would have come along had you rejected that 8th person and kept looking instead. Hence, the dowry problem. (Also called The Secretary Problem, The Fussy Suitor Problem, The Marriage Problem, The Sultan’s Dowry Problem, The Gogol Game, and The Best Choice Problem).

More formally, suppose you have 100 rankable suitors whom you will date one at a time, in succession. After each date, you have the choice to either reject or accept the suitor. If you accept the suitor, you cannot date anymore candidates and are stuck with that person for life. If you reject the suitor, you will not have the chance to date that candidate again and will move on to the next suitor. With each additional suitor, you have the ability to rank that suitor unambiguously amongst your previous suitors. The process continues until you either accept a suitor, or reject all 100 suitors and doom yourself to a life of lonely bachelorhood or spinsterhood.

So, how do you maximize your chance of selecting the best candidate? It turns out the solution to the problem is to employ an optimal stopping rule. This means you date X number suitors, rank those suitors, and then choose the next suitor who is at least as good as those X suitors. In this problem the optimal stopping rule is to date 37 candidates, and then choose the next suitor who is at least as good as the best of the 37.

It turns out the problem has an elegant solution when n suitors are involved. Generally, the optimal stopping rule is to date n/e (where e is Euler’s constant) candidates, and then choose the next candidate that is at least as good as the the first n/e candidates. This means you should date about 37% of the candidate pool, and then choose the next person who is at least as good as the best of that 37%. So it works no matter how big n is:

100: date the first 37 candidates
1,000: date the first 368 candidates
10,000: date the first 3,679 candidates
100,000: date the first 36,788 candidates
1,000,000: date the first 367,879 candidates

And so on.

I decided to use VBA to run some simulations on this problem to see if I could confirm what we have seen here. Unfortunately, I was not successful, but after looking more carefully, I think I found the problem had to do with the built-in random number generator, as well as the shuffling algorithm I employed to randomize the order of the suitors. I basically generated an array of 100 integers from 1 to 100, shuffled them, applied the stopping rule from 1 to 100, and repeated the procedure to see if the optimal  stopping point (deterimined by the maximum empirical probability of success) matched 37.

As you can see, as the number of iterations increases, the curve approaches that of the true distribution.

After many thousands of iterations I discovered the optimal stopping point centered around 60, and I spent about an hour trying to correct the issue without success. Then I tried counting the proportion of iterations in which the best candidate (integer 100) wound up within the first 33 indices of the array. It turned out that best candidate ended up in the first 33 only 17%-20% of the time, when it ought to be 33%. This would explain why the optimal stopping point for this distribution ended up being further to the right than 100/e. From here I concluded that the shuffling algorithm I used was not shuffling the array uniformly. Here is the code below:

Sub ShuffleArrayInPlace(InArray() As Variant)
''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''
' ShuffleArrayInPlace
' This shuffles InArray to random order, randomized in place.
''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''
Dim N As Long
Dim Temp As Variant
Dim J As Long

Randomize
For N = LBound(InArray) To UBound(InArray)
J = CLng(((UBound(InArray) - N) * Rnd) + N)
If N <> J Then
Temp = InArray(N)
InArray(N) = InArray(J)
InArray(J) = Temp
End If
Next N
End Sub

I obtained the shuffling algorithm from Chip Pearson’s VBA page. I’m willing to give the problem another shot with one that shuffles the array more uniformly, so if anyone can help me out that would be great!

Posted in: Logs, Mathematics / Tagged: , , , , ,

No. 61: Pass

5 June, 2012 3:48 AM / 2 Comments /

Hey everyone,

I’ve got some good news – I passed exam C/4! In retrospect, it felt like one of the most difficult exams I’ve ever taken, if not the hardest. I sacrificed three weeks of training and pretty much studied nonstop until I walked into the testing center for my sitting. The exam was a computerized test – the questions were drawn randomly with the passing score calibrated based on the difficulty of the questions. That means a test with easy questions will on average have a higher passmark than a test with hard questions. I must have gotten unlucky this time around because almost all of my questions were hard…there weren’t many questions I knew how to do right away, and I had to skip several when time ran out. I just felt relieved when I found out I had passed after submitting my answers.

I won’t get my score until mid-July, but my preliminary passing result has a 99.9975% chance of matching my final result. The one (or two) exams in the history of computerized actuarial exams whose preliminary results didn’t match the final results were due to human error in handling the scores. So, I’m confident that I passed…maybe barely. In my opinion didn’t study very well – I didn’t follow through with my plan to memorize every single definition and theorem from Loss Models. I did however, put in the recommended 300-400 hours, which is probably more than what most people did, but I think at my level, the efficiency of study was somewhat lacking. I ought to have improved over last time, but I didn’t get rid of the bad habit of holding off until the last two months to study…I kind of got away with it since I’m really familiar with the way standardized tests work. The raw probability of any one individual passing 4 exams in a row is only 2.6%…I ought to consider myself lucky for having a smooth path so far, but I aim to make my next pass based off hard work.

There might have been a slight improvement over the last sitting as I was seriously looking at the material at least two months ahead of time, compared to 6 weeks before the exam date last time and 4 weeks the time before that. Those are merely rough guesses, though, so for my next test, MFE/3F, which I’ll be taking in November, I’ve made it a point to start early (I started studying the day after I passed), to record each day what I’ve studied, and to use linear interpolation to predict when I’ll finish the material. I suppose in this sense I shouldn’t expect a miraculous improvement in studying…if I can just do one thing better than I did last time (like memorizing all of the definitions) for each of the next 6 exams, the cumulative effect of these small improvements should pay off over time.

I’m working on some interesting things – I’m currently designing some simulations on the dowry problem that I’ll write about next week. But for now I’m pretty tired. I finally got around to reading The Cyclist’s Training Bible and I’m almost a third of the way through it. There are a lot of things I learned from that book, and I’m looking forward to building a new training program in the coming months. It looks like I’m too out of shape to participate in the summer races, and I think I might have sacrificed too much of my fitness to target the late-season races…then again, I wouldn’t be able to race at all if I didn’t make the income to support it, so in the end I think it was worth it.

By the way, it looks like I finally broke my New Year’s resolution. I managed to update this blog 18 weeks in a row but I stopped because of the exam. Now I’m back.

Posted in: Logs