There are some aspects of software design that are quite difficult to teach and even more difficult to learn. Like elegance in design. I remember helping a colleague with a subroutine to randomly permute a list--just like shuffling a deck of cards. He had this enormous subroutine that generated random numbers then checked them against other numbers. I just shook my head. It's counter-intuitive--at least until you figure it out--but the best way I've found is to generate a list of random numbers, sort them, and then use the shifts so generated to permute the list. In the language we were working with (Interactive Data Language) it's a one-liner.
I don't remember having trouble coming up with this simply because I've worked with simulated random numbers for so long. I've also used sorting for a unique application: calculation of equivalent latitude. Check out the Wikipedia page (which I wrote). I think the algorithm for calculating equivalent latitude is the epitome of elegance and I've discovered a number of very similar tricks for quite different applications.
Not to say that I haven't created my share of bloated code. I remember once writing a piece of code to find local maxima in a gridded, two dimensional field. What I came up with involved dividing the data values into several ranges and using a domain-filling algorithm (not of my own design). Not very accurate and even less fast. A simple, gradient ascent algorithm is faster by far (I know because I eventually rewrote it) or what about just checking for a local maximum in the eight nearest-neighbours?? I recall having tried both at the time, but couldn't get either working. That's the other lesson: sometimes it takes patience to ferret out all the bugs in a piece of code. It also takes confidence in believing that a particular approach will work.
Another particularly embarrassing piece of bloatware I've written involved binning measurement locations from satellite data in the process of interpolating them to a regular grid. The program did work quite well, but I'm pretty sure the binning actually made the algorithm slower. I'm not certain of that since I haven't rewritten it yet. Meanwhile, the indices it generated were gigantic. (I'm still convinced that some type of binning can produce significant speed gains in nearest-neighbour type problems, but I haven't yet been able to come up with the goods.)
Thursday, February 14, 2013
Thursday, February 7, 2013
Stuff that I'm working on
I started this article some time ago, so some of the stuff is already out of date. It's quite long as well, so be warned...
While they should make the software faster and more robust, they are rather routine and somewhat boring improvements. What follows are some more interesting ideas, in order of interest and complexity. Of course, what makes an idea interesting, often also makes it complex and difficult to implement.
Another issue is tolerance of the root. This is exacerbated by the problem just discussed: very low x-tolerances can't be used. If we are using y- tolerances, then for the error function, clearly they must be varied depending on the value of x. For a root-finding algorithm, the idea of "relative tolerance" doesn't have much meaning [3].
This has now been implemented in version 0.9.6.
In the absence of binning, the time efficiency of finding a set of k-nearest neighbours is on the order n, where n is the number of samples. With binning, we can do one of two things: we can either reduce the coefficient, or we can get it down to order klog n.
In the first case, the standard, rectangular binning method in which each dimension is evenly divided into several blocks, would apply. Ideally, the bins should be large enough that most of them contain several samples, but small enough that the number of samples in each bin is significantly smaller than the total. As the number of dimensions increase, the number of bins becomes unmanageably large, while the fraction occupied also gets smaller. I have designed binning routines of this type for application over the surface of the globe. Oddly, they don't provide any speed advantage over simply running through all the samples. Either there is too much book- keeping and overhead, or there are optimizations implemented in the processor, the compiler or both that already provide a similar advantage.
An interesting solution to the multiplication of bins at higher dimensions and the presence of empty bins is to discretize each of the coordinate samples based on the bin size. Each dimension is assigned a rank and the resulting list of integer numbers sorted as you would sort any other integer. The storage requirement is typically no more than double the original. If the bin size is set so that the average number of samples per bin is very low, on the order of one, then we can build up the number of bins to check in a concentrically expanding hypersphere until we have the required number of samples. While this idea looks good on paper, the required amount of book-keeping and overhead is far more than simply searching through each of the samples one-by-one, especially since finding a given bin is now a logn operation.
Both these examples are using a somewhat naive rectangular binning strategy. A more sophisticated technique would use an adaptive binning strategy that depends on the actual distribution of data. Something like a KD-tree. I still have yet to try these out--coding one up would be far from trivial, while I find I have a distinct aversion to black-boxes so I tend to use pre-compiled libraries rather sparingly. The KD-tree also suffers from an excess of book-keeping as even searching for a single nearest neighbour requires checking every adjacent bin. The number of adjacent bins growing, of course, with the number of dimensions and often lying on very different branches of the tree. Searching fork -nearest-neighbours or all
neighbours within a radius would be even more problematic.
e2=(P/n/hD)2+(h2/n grad2 P)2
calculated respectively, in the limit as the filter width becomes very small and in the limit as it becomes very large. Here, P is the actual density function, n is the number of samples, h is the bandwidth and D is the number of dimensions. The actual density function, P, is of course, not known. But there is no reason why we cannot fit the function through repeated estimates using different bandwidths. Since e=P-f where f is the estimated density we can rearrange the above equation as follows:
n2(f-P)=(1/hD-n2)P2/f + h4 (grad2 P)2/f
Since we have several different samples, we can construct a system of equations by substituting values for f and h. The constant term, P, on the left-hand-side can be eliminated by subtracting different equations in the system:
(1/hD-n2)(1/fi - 1/fj) P2 + (hi4/fi - hj4/fj) (grad2 P)2 = n2(fi - fj)
so in theory we need a minimum of three samples to solve for P and grad2P. In practice, the method should be more stable by taking more than the minimum number of samples and performing a least-squares fit.
I recently took a second look at this project--I've had the method implemented for some time but it didn't work. I've now got it returning reasonable results for the optimal filter width, at least when it works at all, though not if you take the P2 factor from the above equation. Part of the problem is that the matrix is very ill-conditioned--the two variables we are solving for are separated by many orders of magnitude likewise all the different elements of the matrix.
The reviewers were interested first, that the manuscript be fleshed out somewhat, and second, how better to determine the parameters of the method: how many principal components to use and how long of a lead time to use. I am attempting something more general here: to build a simple sparse matrix calculator so that I can perform a series of numerical experiments with the matrices generated by the tracer simulation. I'm hoping that will help me to better understand just how the method works: for instance, how is it possible that you can correlate measurements from before the matrix was integrated and the method will still give good results?
The sparse matrix calculator has already been implemented and has even passed a few very basic tests. I still need to test it with actual, practical matrices like those from the tracer simulation, and of course it needs many refinements and features to make it complete, but the basic idea is there and it's running. At the moment I'm working on refactoring the entire trajectory suite and I'd like to finish that first before continuing with this.
There are two major ways you can divide up the classes: in the first case so that all of the conditional probabilities can be solved for and in the second case so that only the conditional probability of the "winning" class is returned. In the first case, you need at least (n-1)/2 borders--that is, for each border you can write two equations relating the conditional probabilities plus one more for the entire system (they sum to unity.) In the second case, the method is hierarchical: divide the set of classes into two groups, divide each pair of groups into two more and so on. Consider the case of dividing up four classes:
x | o
-----
+ | *
The four classes are x, o, + and *. In the first case, we think of this diagram as representing two borders: one horizontal, and one vertical. In the second case, consider first a horizontal border, and then two vertical borders. It stands to reason that the two methods can also be combined.
[2] Donald Knuth (1998) The Art of Computer Programming, Volume 3: Sorting and Searching, 2nd edition Addison-Wesley.
[3] William Press, Saul Teukolsky, William Vetterling, Brian Flannery (1992). Numerical Recipes in C, 2nd edition Cambridge University Press, Cambridge.
[4] Peter Mills (2012). "Principal component proxy tracer analysis." arxiv:1202.2194
[5] Peter Mills (2006), "The influence of noise on a classical chaotic scatterer." Communications in Nonlinear Science and Numerical Simulation, 11 (8) 899-906.
New software release and planned improvements
The Peteysoft Foundation has released a new version of the libagf software and the libpetey scientific library required by it. Changes are fairly minor, but nonetheless important. The Runge Kutta integrator now has a thread-safe version. The function pointer passed to this routine is compatible with the GSL. New routines have been introduced including a symbol table class and a "smart" pointer class. More significant improvements are detailed in the next two sections, while many exciting planned new developments follow.k-least algorithm
The kleast subroutine selects the k smallest elements in an array. Past versions of this algorithm were based on a binary tree and have a theoretical average time efficiency of O(n log k), although tests suggest that the actual running time is slightly better, closer to n+k log k [1]. This is the theoretical best efficiency for a k-least algorithm that sorts the resulting output, necessarily true for a binary tree. According to Knuth, if the output is not sorted, the efficiency can be as good as O(n) [2]. This can be acheived through a modified quicksort algorithm, but not one based on a heap which again, sorts the output. A new, faster k-least algorithm based on a quicksort has been implemented and applied to the libagf library to pre-select the data and to find the k-nearest- neighbours.Solving for the filter width
The old algorithm for solving for the filter width while holding the total of the weights, W, was based on repeated squaring of the weights until the total passed the target value. The final result was found by exponential interpolation between the final value and the previous value. The purpose of this excessively clever method was to reduce the number of computed exponentials--the number is fixed at two per weight. Unfortunately, it was quite finicky and improper initialization or certain sample distributions (such as duplicate samples) would cause the method to hang. To address these issues, it was replaced with nothing more than a root-finding algorithm, although a fairly sophisticated one. This is the same as used for searching out the class borders: a third order interpolation method which brackets the roots. I call this root-finding method, "supernewton". [1]While they should make the software faster and more robust, they are rather routine and somewhat boring improvements. What follows are some more interesting ideas, in order of interest and complexity. Of course, what makes an idea interesting, often also makes it complex and difficult to implement.
The inverse error function and the superNewton algorithm
The inverse error function is quite useful since it tells you for a given integrated probability and Guassian statistics, how far from the centre of the distribution you need to be. So for instance, if you have n normally distributed random samples, you can use the inverse error function to figure out approximately where the most distant sample should lie. Unfortunately, most math libraries don't include a numerical implementation of it. I figured, no problem, I'll use my powerful numerical inverse method "superNewton" to implement my own. Rather than giving me a simple, efficient math function in record time, it revealed to me some rather striking limitations in the algorithm as it is currently implemented. Most importantly, it tends to get stuck always re-bracketing the the root on the same side. This could probably be fixed quite easily, but at the cost of some extra book-keeping. Simply track how many times the estimated root has landed on the same side of the actual root as well as the relative distance between the previous left and right brackets. If these values are too high, the estimated root can be shifted so that it's now on the opposite side of the actual root. I would suggest doubling the difference between the estimated root and the closest bracket.Another issue is tolerance of the root. This is exacerbated by the problem just discussed: very low x-tolerances can't be used. If we are using y- tolerances, then for the error function, clearly they must be varied depending on the value of x. For a root-finding algorithm, the idea of "relative tolerance" doesn't have much meaning [3].
Cross-validation of PDF estimates
Cross-validation or n-fold cross validation are simple and reliable ways of testing the accuracy of a supervised statistical classification algorithm. Something similar would be nice to have for probability density function (PDF) estimates as well. Unfortunately, unlike that for a classification problem, actual values of the PDF are not contained in training data for a probability estimation problem and the underlying PDF is frequently not known. This can be solved quite readily by adding an extra step. A new dataset with the equivalent distribution as the existing training data is first simulated using the same method as a metropolis Monte Carlo [3]. This dataset is not used for PDF estimation, but rather the original dataset is randomly split up, PDFs are calculated for each portion at the locations in the simulated dataset and then compared, e.g. through cross-correlation. Note that the parameters used (k for KNN, W for AGF) will need to scaled up in proportion (i.e. by n if this is considered a form of n-fold validation) when using the full dataset.This has now been implemented in version 0.9.6.
Binning
There are so many applications for an efficient, multi-dimensional binning algorithm, I don't even know where to begin. For instance, in the surgery step of contour advection with surgery, a nearest neighbour search must be performed for every pair of points to check if they are too close or not. Kernel estimators are more efficient if the samples used are restricted to a subset near the centre of the kernel function. Binning can also be used for collocation routines used for the purpose, for instance, of creating satellite inverse methods.In the absence of binning, the time efficiency of finding a set of k-nearest neighbours is on the order n, where n is the number of samples. With binning, we can do one of two things: we can either reduce the coefficient, or we can get it down to order klog n.
In the first case, the standard, rectangular binning method in which each dimension is evenly divided into several blocks, would apply. Ideally, the bins should be large enough that most of them contain several samples, but small enough that the number of samples in each bin is significantly smaller than the total. As the number of dimensions increase, the number of bins becomes unmanageably large, while the fraction occupied also gets smaller. I have designed binning routines of this type for application over the surface of the globe. Oddly, they don't provide any speed advantage over simply running through all the samples. Either there is too much book- keeping and overhead, or there are optimizations implemented in the processor, the compiler or both that already provide a similar advantage.
An interesting solution to the multiplication of bins at higher dimensions and the presence of empty bins is to discretize each of the coordinate samples based on the bin size. Each dimension is assigned a rank and the resulting list of integer numbers sorted as you would sort any other integer. The storage requirement is typically no more than double the original. If the bin size is set so that the average number of samples per bin is very low, on the order of one, then we can build up the number of bins to check in a concentrically expanding hypersphere until we have the required number of samples. While this idea looks good on paper, the required amount of book-keeping and overhead is far more than simply searching through each of the samples one-by-one, especially since finding a given bin is now a log
Both these examples are using a somewhat naive rectangular binning strategy. A more sophisticated technique would use an adaptive binning strategy that depends on the actual distribution of data. Something like a KD-tree. I still have yet to try these out--coding one up would be far from trivial, while I find I have a distinct aversion to black-boxes so I tend to use pre-compiled libraries rather sparingly. The KD-tree also suffers from an excess of book-keeping as even searching for a single nearest neighbour requires checking every adjacent bin. The number of adjacent bins growing, of course, with the number of dimensions and often lying on very different branches of the tree. Searching for
Optimal AGF
The current version of Adaptive Gaussian filtering is quite useful and has a reasonable justification. We can, however, write an expression for the error of kernel density estimator as a function of the bandwidth. There are two terms, a variance term and and a bias term:e2=(P/n/hD)2+(h2/n grad2 P)2
calculated respectively, in the limit as the filter width becomes very small and in the limit as it becomes very large. Here, P is the actual density function, n is the number of samples, h is the bandwidth and D is the number of dimensions. The actual density function, P, is of course, not known. But there is no reason why we cannot fit the function through repeated estimates using different bandwidths. Since e=P-f where f is the estimated density we can rearrange the above equation as follows:
n2(f-P)=(1/hD-n2)P2/f + h4 (grad2 P)2/f
Since we have several different samples, we can construct a system of equations by substituting values for f and h. The constant term, P, on the left-hand-side can be eliminated by subtracting different equations in the system:
(1/hD-n2)(1/fi - 1/fj) P2 + (hi4/fi - hj4/fj) (grad2 P)2 = n2(fi - fj)
so in theory we need a minimum of three samples to solve for P and grad2P. In practice, the method should be more stable by taking more than the minimum number of samples and performing a least-squares fit.
I recently took a second look at this project--I've had the method implemented for some time but it didn't work. I've now got it returning reasonable results for the optimal filter width, at least when it works at all, though not if you take the P2 factor from the above equation. Part of the problem is that the matrix is very ill-conditioned--the two variables we are solving for are separated by many orders of magnitude likewise all the different elements of the matrix.
Sparse matrix calculator
I have recently put out a paper that describes a powerful dynamical tracer reconstruction method called principal component proxy analysis [4]. The method is based on decomposing a matrix representation of the tracer dynamics using principal component analysis (PCA). Each PC is then regressed with a series of (typically sparse) tracer measurements and the entire field thus reconstructed. The manuscript was sent to Atmospheric Environment but was unfortunately rejected.The reviewers were interested first, that the manuscript be fleshed out somewhat, and second, how better to determine the parameters of the method: how many principal components to use and how long of a lead time to use. I am attempting something more general here: to build a simple sparse matrix calculator so that I can perform a series of numerical experiments with the matrices generated by the tracer simulation. I'm hoping that will help me to better understand just how the method works: for instance, how is it possible that you can correlate measurements from before the matrix was integrated and the method will still give good results?
The sparse matrix calculator has already been implemented and has even passed a few very basic tests. I still need to test it with actual, practical matrices like those from the tracer simulation, and of course it needs many refinements and features to make it complete, but the basic idea is there and it's running. At the moment I'm working on refactoring the entire trajectory suite and I'd like to finish that first before continuing with this.
Multi-class classification with AGF borders
If you have a discrimination border, this is only good for discriminating two classes. If you want to be more discriminating, you need more than one border. This is something I've been planning for a long time, but made very little progress on. The problem is: there is no one-size-fits-all solution. You can divide up the classes in many different ways and still get usable results and the best way to divide them may be highly problem-dependent. For instance: in the case of a discretized continuum variable, you'd probably want to make sure that all the borders only separate "adjacent" classes, that is, ranges that are next to each other in the discretization scheme. On the other hand, if there are four classes, but they can be reduced into two overlapping sets of two classes, then that right there tells you how to divide them up.There are two major ways you can divide up the classes: in the first case so that all of the conditional probabilities can be solved for and in the second case so that only the conditional probability of the "winning" class is returned. In the first case, you need at least (n-1)/2 borders--that is, for each border you can write two equations relating the conditional probabilities plus one more for the entire system (they sum to unity.) In the second case, the method is hierarchical: divide the set of classes into two groups, divide each pair of groups into two more and so on. Consider the case of dividing up four classes:
x | o
-----
+ | *
The four classes are x, o, + and *. In the first case, we think of this diagram as representing two borders: one horizontal, and one vertical. In the second case, consider first a horizontal border, and then two vertical borders. It stands to reason that the two methods can also be combined.
References
[1] Peter Mills (2011) "Efficient statistical classification of satellite measurements." International Journal of Remote Sensing, 32 (21): 6109-6132.[2] Donald Knuth (1998) The Art of Computer Programming, Volume 3: Sorting and Searching, 2nd edition Addison-Wesley.
[3] William Press, Saul Teukolsky, William Vetterling, Brian Flannery (1992). Numerical Recipes in C, 2nd edition Cambridge University Press, Cambridge.
[4] Peter Mills (2012). "Principal component proxy tracer analysis." arxiv:1202.2194
[5] Peter Mills (2006), "The influence of noise on a classical chaotic scatterer." Communications in Nonlinear Science and Numerical Simulation, 11 (8) 899-906.
Thursday, January 31, 2013
Bias in drug trials
I just came across this talk and I think it is very important. It deals with the tendency for journals and researchers to publish only positive results while either ignoring or rejecting negative results. The problem exists not just in clinical medicine, but in every area of science. Science is a very competitive business and positive results often herald a "new discovery." By contrast, we tend to think that a negative result says very little, thus it's in scientists' own best interests to publish only positive results, assuming that the journal will even accept the negative ones.
From my own experience, I have seen scientists not only picking the best exemplar from a series of experiments and publishing only that one, but also essentially cherry-picking the data by using some creative averaging. I also know that I am not immune from this myself.
From my own experience, I have seen scientists not only picking the best exemplar from a series of experiments and publishing only that one, but also essentially cherry-picking the data by using some creative averaging. I also know that I am not immune from this myself.
Sunday, January 13, 2013
The known and the unknowable
While I was still an undergraduate at the University of Waterloo, I attended a lecture by the Canadian philosopher William Hatcher detailing a logical proof of God. Having recently had something of an existential crisis, thoughts of God and spirituality were very much on my mind. Here was something that I could really sink my teeth into: in contrast to the blind dogma fed to me by the fundamentalist Christians I was hanging out with at the time, Hatcher took more of a scientific approach.
At the same time, I was taking a philosophy course on science and religion. As soon as I heard the talk, I just knew I had to write an essay on it. What I came up with, which can be found here, turned out to be rather critical. At first I was extremely impressed with the simplicity of the argument, but soon discovered the hole--detailed in the essay.
Hatcher has written others essay that attempt to apply the tools of mathematics to metaphysical problems such as "A Logical Solution to the Problem of Evil" which can be found in "Logic and Logos: Essays in Science Religion and Philosophy." While I don't believe either example is entirely successful, the approach is nonetheless greatly appreciated. Sadly, Prof. Hatcher is no longer with us and passed away in 2004. His legacy, however, is alive and well and his estate is attempting to compile his work online: http://william.hatcher.org/.
The point I wanted to make with this essay was not about God, nor about the problem of evil, it was rather about knowledge itself. I have looked at a number of other proofs of God, and while they are all interesting and ultimately quite audacious, none of them is really commensurate with more useful proofs in science and mathematics. What if certain questions, such as, "Is there a God?" simply cannot be answered?
A more obvious example would be certain more extreme claims in the interpretation of quantum mechanics such as, "The moon truly isn't there when we aren't looking at it." That is, when something is not being observed, it no longer exists. Such an assertion is clearly absurd because the only way we ascertain existence is through observation and hence, unanswerable.
Multi-valued logics have a long and somewhat chequered history, culminating in the current, slightly controversial extreme of "fuzzy logic." In fuzzy logic, it's not that there are more than two truth-values, rather truth exists on a continuum between 100% false and 100% true, but nonetheless it is in the same spirit.
My own contribution is somewhat more modest (and likely not original). I propose adding a single extra truth value, namely that something cannot be known. Here are the truth tables:
AND
0 1 X
0 0 0 0
1 0 1 X
X 0 X X
OR
0 1 X
0 0 1 X
1 1 1 1
X X 1 X
NOT
0 1
1 0
X X
Here, X denotes that a proposition "cannot be known" and functions somewhat like an NaN or Inf in floating point arithmetic in the sense that once one creeps into a calculation, the tendency is for it to propogate itself throughout.
As I've gotten older, I haven't lost my interest in questions of God, metaphysics and spirituality, although I try now to take them a bit less seriously. If you want to waste a lot of time, log onto one of the discussion boards debating the existence of God. The same tired arguments are brought up again and again and the same tired counter-arguments brought up in response.
One development that interests me is the current crop of fervently atheist authors such as Richard Dawkins. Part of their argument against God and religion is that science has become so powerful in explanatory ability that faith has lost any purchase it might once have had. My own belief is the exact opposite: science and faith actually complement one another perfectly. That being said, we should guard against having a "God of the gaps" wherein we attribute to God and spirituality whatever it is that science has yet failed to conquer, hence the domain of spirituality becomes smaller and smaller. Once we acknowledge, however, that certain things cannot be known, we now have an enormous zone wherein faith and spirituality can thrive. I like to think of the boundary between the known and the unknowable as a "jumping off point."
At the same time, I was taking a philosophy course on science and religion. As soon as I heard the talk, I just knew I had to write an essay on it. What I came up with, which can be found here, turned out to be rather critical. At first I was extremely impressed with the simplicity of the argument, but soon discovered the hole--detailed in the essay.
Hatcher has written others essay that attempt to apply the tools of mathematics to metaphysical problems such as "A Logical Solution to the Problem of Evil" which can be found in "Logic and Logos: Essays in Science Religion and Philosophy." While I don't believe either example is entirely successful, the approach is nonetheless greatly appreciated. Sadly, Prof. Hatcher is no longer with us and passed away in 2004. His legacy, however, is alive and well and his estate is attempting to compile his work online: http://william.hatcher.org/.
The point I wanted to make with this essay was not about God, nor about the problem of evil, it was rather about knowledge itself. I have looked at a number of other proofs of God, and while they are all interesting and ultimately quite audacious, none of them is really commensurate with more useful proofs in science and mathematics. What if certain questions, such as, "Is there a God?" simply cannot be answered?
A more obvious example would be certain more extreme claims in the interpretation of quantum mechanics such as, "The moon truly isn't there when we aren't looking at it." That is, when something is not being observed, it no longer exists. Such an assertion is clearly absurd because the only way we ascertain existence is through observation and hence, unanswerable.
Multi-valued logics have a long and somewhat chequered history, culminating in the current, slightly controversial extreme of "fuzzy logic." In fuzzy logic, it's not that there are more than two truth-values, rather truth exists on a continuum between 100% false and 100% true, but nonetheless it is in the same spirit.
My own contribution is somewhat more modest (and likely not original). I propose adding a single extra truth value, namely that something cannot be known. Here are the truth tables:
AND
0 1 X
0 0 0 0
1 0 1 X
X 0 X X
OR
0 1 X
0 0 1 X
1 1 1 1
X X 1 X
NOT
0 1
1 0
X X
Here, X denotes that a proposition "cannot be known" and functions somewhat like an NaN or Inf in floating point arithmetic in the sense that once one creeps into a calculation, the tendency is for it to propogate itself throughout.
As I've gotten older, I haven't lost my interest in questions of God, metaphysics and spirituality, although I try now to take them a bit less seriously. If you want to waste a lot of time, log onto one of the discussion boards debating the existence of God. The same tired arguments are brought up again and again and the same tired counter-arguments brought up in response.
One development that interests me is the current crop of fervently atheist authors such as Richard Dawkins. Part of their argument against God and religion is that science has become so powerful in explanatory ability that faith has lost any purchase it might once have had. My own belief is the exact opposite: science and faith actually complement one another perfectly. That being said, we should guard against having a "God of the gaps" wherein we attribute to God and spirituality whatever it is that science has yet failed to conquer, hence the domain of spirituality becomes smaller and smaller. Once we acknowledge, however, that certain things cannot be known, we now have an enormous zone wherein faith and spirituality can thrive. I like to think of the boundary between the known and the unknowable as a "jumping off point."
Friday, November 23, 2012
Super-efficient motor-assisted bicycle: first baby steps
But before I get into the details of how this thing will eventually work, I want to discuss a more pressing issue. When I get this thing completed, it will be highly illegal on Ontario roads, a situation which concerns me and which should concern anyone interested in improving the environment. Politicians say that they want improve the environment, but the current state of the Ontario Highway Traffic Act proves that they are not serious. The definition of a power-assisted bicycle or "e-bike" is an electrically assisted bicycle (it must have pedals) which is limited in power to 500 W and a top speed of 32 km/h. This is a joke. They are legal for anyone over the age of 16 to ride (without a license) but why anyone would want to is beyond me. I regularly pass these things on my (unassisted) pedal bicycle despite lungs blackened by years of abuse with cigarettes.
The standard argument is that the absurd speed and power limitations are for safety. This is easily debunked. If this is the case, why are Porches and other super-cars that are mostly engine still allowed on public roads? For that matter, why is any car? My parents' bottom-end sedan could easily be driven at two to three times the posted limit on most roads. It is up to the operator to exercise discretion in the conduction of their vehicle. In fact increasing the top speed of these things will actually make them safer as they can now keep up with traffic. As a long-time cyclist, I have always felt safer on tight and busy roads when I am moving at the same pace (or faster) than the surrounding traffic.
The definition of a motor-assisted bicycle (or mo-ped) is a gasoline assisted bicycle (again, it must have pedals) whose engine has a maximum displacement of 50 cc and a top speed limited to 60 km/h. This is a bit more reasonable. Ontario, however, has recently changed the rules regarding who can drive these vehicles; a driver's license used to be sufficient. Now you need either a full-on motorcycle license or an emasculated motorcycle license good for only this type of vehicle. Way to make driving efficient vehicles sexy!
I remember once boarding a ferry in Schleswig-Holstein. Shortly after me came two scruffy motor-cyclists riding custom-style bikes with engines big enough to power a
The final death knell to the moped as a useful and efficient vehicle (at least in Ontario) comes from this further limitation: "It must not have a hand- or foot-operated clutch or gearbox." Anyone who's ridden a bicycle knows that under-powered vehicles need lots of gears to be efficient. This means that in order for the bike to have gears at all, it must be equipped with either a continuously variable transmission (CVT) or some kind of torque-converter, both of which are notorious for robbing power. On a vehicle that is 1. under-powered to begin with and 2. supposed to be efficient, this makes no sense whatsoever.
Lets be honest here. Any competent engineer could design a motor-assisted bicycle at least as good as what I am building. In fact the technology to create such a device has existed a lot longer. A similar situation, it could be argued, existed in the eighteenth century in regards to bicycles. The technology was sufficient to create them, but there was no demand because of prevailing social conditions. For that, we had to wait until the nineteenth century with the rise of the middle class, who demanded cheap and efficient transportation despite not being able to afford horses. Today, I would argue that the reasons good motor-assisted bicycles are all but forbidden are two-fold:
1. to restrict the poor from having access to cheap and efficient transportation
2. because of the power wielded by the oil and automotive companies
The first, at least, is held only semi-consciously. The second may well be due to overt lobbying by powerful corporate interests.
I'll step off my soap-box for now. Stay tuned for the next installment which will discuss the more technical aspects of this creation: design considerations and how I intend to actually build it. The next installment can be found here.
Thursday, October 25, 2012
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