Slashdot Mirror

The Unreasonable Effectiveness of Mathematics in the Natural Sciences

Quantum radar will expose stealth aircraft

My son's grade 12 teacher lined the kids up based on how well they did in their last year of high school math class. The top 5 were all girls and 3 more were in the top ten. This is based on a fairly standardized curriculum. Next he lined them up based on their results from the university of Waterloo math contest. 22 kids in the class and the top 8 were all boys. The girls new how to write the tests and give the answers expected but it was obvious that the boys actually understood the math better. (the teacher is no longer teaching)

Here are the math contest results http://www.cemc.uwaterloo.ca/c... you will see a Cynthia on the 6th page of the results. That's the first woman's name I recognized

See here for all the quantum computational complexity classes:
https://complexityzoo.uwaterlo...

I think he is from University of Waterloo in Canada. Here is the statistics https://uwaterloo.ca/engineeri...

Women in Engineering 2016

Women in Engineering # Women % Women

Undergraduate Year One Enrollment 504 29.2%

All Undergraduate Students 1833 25.2%

Undergraduate Degrees Awarded 211 18.6%

All Graduate Students 447 26%

Graduate Degrees Granted 139 23.1%

PhD Degrees Granted 30 20.8%

Professors 49 16.8%

Great university btw

I probably know better than most the mess we're in. I've spent the better part of the last 20 years up to my eyeballs in systems ranging from foreign consular networks, to the innards of various interesting things with blinky lights on nuclear submarines, to the core operations of a couple of dozen Fortune 500 firms. It's all a mess, much more than it used to be, in fact. The first thing you need to realize is this: you shouldn't "just trust" me. You probably also shouldn't trust most of your coworkers/colleagues. If you really want to get down to brass tacks, you also probably shouldn't trust some of your own family members with anything truly sensitive.

It's on you to protect what you value, which means it's on you to educate yourself in the means to do so. There is no magic bullet, but you might start with learning about some of the fundamentals of cryptography. You might also do a bit of research into the backgrounds of folk like Bruce Schneier; you'll find he's rather well published. Heck, you might even strike up some correspondence with him and others like him. It's really all up to you, but don't expect a free ride in any of this. Good luck. -PCP

1) Everyday things like food. What I buy is not decided by advertising, it is decided on trial. Eg, I will try different types of beer and settle on the one I like best.

And how do you know your "liking" doesn't result from harmful components?

I don't, but that is nothing to do with advertising, the topic here.

3) Specialist things like car spares and building materials. What I buy is not decided by advertising, it is decided by what I can find ... who sells the same brand anyway

Here you dodged the question - how did you select the brand in the first place.

By my method (2) in the case of the car itself. With regard to most of its spares there is no choice, even if I went 100 miles for it. Replacement headlamp for a Jeep Grand Cherokee (in the UK) - nearest main dealer for that (the 25 mile away one), and no brand choice. The point I am making here is that for some things there is no choice. Another example is looking for replacement ceramic tiles to replace broken ones installed before my time - had to be certain size and colour. Lucky to find any at all, I don't care about the brand. They don't advertise that sort of stuff anyway, not in the UK.

You did tell an unrelated fact - that the brand you selected is available both 25 miles away and > 100 miles away.

Why is that unrelated? As said above, I didn't "select" the brand; there is only one, the one made for the car. I "selected" the nearest place that sold it.

In spite of knowing that advertisements tell a one sided story, humans still get affected significantly by it.

I havn't time to read that lot, but I can guess what it says. I'm talking about me, and if anything adverts affect me adversly, especially intrusive ones, and increasingly it seems I am not the only one. My reaction to an intrusive advert on my screen is to shout "Fuck off!" and make a mental note never to buy that stuff. Not hard, probably not the type of stuff I am likely to buy anyway.

1) Everyday things like food. What I buy is not decided by advertising, it is decided on trial. Eg, I will try different types of beer and settle on the one I like best.

And how do you know your "liking" doesn't result from harmful components?

3) Specialist things like car spares and building materials. What I buy is not decided by advertising, it is decided by what I can find ... who sells the same brand anyway

Here you dodged the question - how did you select the brand in the first place. You did tell an unrelated fact - that the brand you selected is available both 25 miles away and > 100 miles away.

In spite of knowing that advertisements tell a one sided story, humans still get affected significantly by it.

That's not a terminal. Now THIS is a terminal:

https://cs.uwaterloo.ca/40th/i...

It is presumably an attempt at a joke based on the fact that Forth makes use of RPN.
https://en.wikipedia.org/wiki/...

I for one find Forth to be a fascinating language. The fact that it has been around for a while does not diminish it in any way.

I first heard of it back in the 80's while learning assembler on the 6502. I noticed it again while getting to know FreeBSD (loader stage 3) and decided to finally learn it when I came across some old manuals and software for my newly acquired PET CBM 8032 just a few weeks ago.

Ever since, I seem to notice it mentioned more and more, perhaps partly because of renewed interest in stack machines, but also because it offers an interactive way to boot strap a very small system with minimal resources.

It is available in some form on almost every platform that I know.

Following are some resources that I have found to be of interest. Hopefully those sites will not get badly hurt.

http://www.forth.com/starting-...
http://thinking-forth.sourcefo...
http://playground.arduino.cc/C....
https://www.freebsd.org/cgi/ma...
https://uwaterloo.ca/independe...
http://www.ultratechnology.com...

...

The classic Schneier Applied Cryptography is a great read for anybody who wants a good starting point on the basic concepts and practical considerations. It's technical-ish but conceptual rather than mathematical and leans toward describing what the various crypto pieces do, why they exist, and what they're used for. To get a good intro to some math, try The Handbook of Applied Cryptography. If you have a little bit of number theory and are willing to do some exercises up front, the book is largely self-contained and very well written. It's free for personal use, but nobody I know regretted buying a hard copy.

The University of Waterloo has a Software Engineering program.

I highly doubt all of the people currently holding the job title of Software Engineer here in Canada took an accredited engineering program though. The term Engineer is protected, but I don't know how well.

As for the US, I'm guessing it's not a protected term. They make a complete mockery of it.

Thanks, interesting document, found here. The audio is really bad at the beginning and fluctuates throughout the talk. The interesting bit that you refer to is at 21 minutes from the start.

I'm trying to type in what he said directly from the audio:

The 16-bit design gave us a megabyte of memory. The 8086 has a 20-bit address. It is really a segmented 16-bit data path with segment registers that are really indexes. It is a 1-MB address space. And in this original design I took the upper 384K and tied it to a certain amount to provide for memory video, the ROM and I/O. And that left 640K for general purpose memory. And that leads to today's situation where people talk about the 640K barrier. The limit to how much memory you can put to these machines. I have to say that in 1981 while making those decisions I felt like I was providing enough freedom for 10 years. That is, a move from 64K to 640K felt like something that would last a great deal of time. Well, it didn't. It took only 6 years before people started to see that as a real problem.

Fortunately, there is a reasonable solution. Intel has moved forward with its chips families, the 286 chip introduced in 1984 moves us to a 24-bit address space (mumbles about segmented indirection, being not that good). That is sort of an intermediate milestone. in 1986 we moved up to the 386 where we get a full 32-bit offset to these segments that have been designed in this architecture. So what we have is a machine that can address 4GB of RAM. And I have to say with all honesty, I believe that it will take us more than 10 years to use up that address space.

So he never makes that exact quote, however one can understand why people picked it up. Essentially, BG thought in 1981 640K would be enough for everybody for a long while. Note that he was reasonably prudent regarding using up the 32-bit address space (that ship has sailed now).

Later, regarding memory, he says that computers should have about 1MB of RAM per MIPS. Specifically, he goes on to saying machines with 30-60MB of RAM should be desirable soon (in 1989).

In this talk he talks about many things, most are pretty insightful in fact: OS design, multitasking, parallelization, multi-processor designs, dynamic linking, object-oriented design. Funnily he talks at length about OS2 in a very positive way. This was before Windows 3 of course. He compares OS2 and Unix, saying that OS2 will take over the desktop and Unix the servers, and all other OSes will die out. He talks about the FSF, saying its task of creating a free Unix-like OS is doomed.

Some interesting comments on that talk here.

This is the equivalent of ray tracing in graphics - nice effect, but very heavy on the computation.

With graphics, rasterization is faster, and the reason is that it can be characterized as "a bunch of cheats that happen to look good". Can we identify some similar cheats for sound?

Yes, I think so. Here's a paper I wrote 16 years ago outlining one possible, very simple, basis for soundscape generation.

https://ece.uwaterloo.ca/~vrml...

Unfortunately, I didn't get to progress with it as VRML faded out pretty quickly after 1998.

It's like there's some strange black hole of information available on the internet that only happens around the super specific topic the Ask Slashdotter is interested in. I'm pretty sure all of these folks are the ones that were our best horses in Keener Bingo:

http://www.mathnews.uwaterloo....

...Radio is slower than light even in a vacuum...

It takes about 5 seconds of googling to disprove this statement.

http://imagine.gsfc.nasa.gov/docs/science/know_l2/emspectrum.html

http://www.science.uwaterloo.ca/~cchieh/cact/c120/emwave.html

Er, "strongly conjectured to occur" should be "strongly conjectured to *not occur*. Need to proofread more when using preview. Also, as long as I'm replying to myself, note that the set of problems which can be solved easily by a quantum computer is BQP http://en.wikipedia.org/wiki/BQP, but it is likely that for many practical applications, one will want the set of problems where a quantum computer can quickly convince a classical computer that it really has a solution, and this set, ZBQP, is likely much much smaller https://complexityzoo.uwaterloo.ca/Complexity_Zoo:Z#zbqp. Factoring lives in this smaller set because the classical computer can check the quantum computer's work essentially by just multiplying together the factors given by the quantum machine.

Once sucrose is cleaved in to fructose and glucose a few ms after hitting the stomach,

Wrong.

there is no chemical difference between HFCS and Sucrose.

Wrong again. HFCS is high-fructose corn syrup. The ratio of fructose to glucose is higher in HFCS than in sucrose. That's why it is called "high fructose".

The problem with HFCS is that it first bypasses the metabolic pathway that sucrose must go through, thereby creating a rush as the simple sugars are directly absorbed by the blood. Second, it puts a stress on the liver where fructose is metabolized, which causes more fructose to be converted to storage forms since there is more available at one time than can be used. The rush of glucose also stresses the glucose regulatory systems and can lead to diabetes and near-diabetes.

Gary Taubes has dealt with the "HFCS is just sugar" myth in his books. He points out that the common factor in aboriginal peoples who adopt a western diet and earn an obesity epidemic with it is the use of HFCS and other processed carbs. They eat fats and sugars in their natural diet and do fine. It's when they pick up the HFCS and white bread that they start to bulk up.

This stuff about HFCS being just like sugar is marketing hype by the people who make HFCS products, aimed at people who are ignorant of the metabolism of sugars. "HFCS is just like sugar" is about as true as saying "drinking from a firehose is the same as sipping a glass of water through a straw."

Right now, computational complexity classes for quantum computing fall into a variety of different categories. BQP is the set of problems where a quantum computer can efficiently solve them with high probability , but we don't have a good way of verifying that a given solution is correct. It is suspected that this class is strictly larger than the set of problems which can be easily solved on a quantum computer and the solution can be checked on a classical computer, which is ZBQP https://complexityzoo.uwaterloo.ca/Complexity_Zoo:Z#zbqp. (There are some slight technical issue here in terms of distinguishing programs which just answer yes or no and programs which can give more than 1 bit of data out.) So for example, factoring, is in ZBQP because a classical computer can verify the result by just multiplying the factors together (as well as checking that they are prime, which can be done in polynomial time).

t this point, we can't prove that P != BQP, let alone that P!=ZBQP or that ZBQP!=BQP (since P is contained in ZBQP which is contained in BQP, either of the second two statements would imply the third). Worse, we can't even prove the much weaker statement that P != PSPACE (essentially that there are things you can do with polynomial memory that you can't do in polynomial time).

What this work does is suggests is that thinking in terms of ZBQP may not be that important in practice, since it may be easy to verify quantum computations with other quantum computers in a reliable fashion.

I strongly recommend that people interested in this subject first read Scott Aaronson's book "Quantum Comptuing Since Democritus" which discusses a lot of the relevant issues and provides a decent primer on the subject. (Assuming only some decent familiarity with linear algebra and a little calculus). Note that TFA like many articles about quantum computing for the popular press has statements that are not strictly speaking true to the point where they border on being wrong. The most egregious error in TFA (which is a very common one) is the claim that "Because each qubit can embody so many different states, quantum computers could compute certain classes of problems dramatically faster than regular computers by running through every combination of possibilities at once." - This is wrong. Quantum computers don't work by checking every combination at once- if they could they'd be able to handle a lot of problems they (probably) can't.

I did read a paper not so long ago about the Ozone layer being regulated to a large degree by cosmic rays, over the Antarctic.

And by the way, moderating dissenting voices "troll" is totally beyond the pale. Science is about skepticism. Physicists are highly skeptical of each other's results. When it comes to Earth Sciences, why is it that people crowd the paradigm like it's a sacred tome? Debates here would be far more interesting if they were actually allowed.

The formula input and formatting is much more like Tex than MS Word too, which is really handy for all sorts of scientific and math input.

Are you using a recent Word version?

The syntax used for euqations in Word 2007 and later is probably best described as "LaTeX without curly bracers" (granted there are some annoying differences but the commonalities are overwhelming) and the rendering is very close in quality, too.

The pity is that almost nobody seems to have any clue how to use linear mode in the Word 2007+ equation editor. Here's a decent guide in case you are looking for one.

I mean, we would be ecstatic to have people contribute in any way! That could even just mean learning the framework and the software and using it in your own research. We have lots of tutorials, and we'd be happy to help if you want to make your own models. The software itself is pretty good, but it's academic software, and certainly we'd welcome anyone's contributions to the software! We're pretty responsive, either at any of our emails, or by making a github issue if you need any assistance.

Unfortunately, I don't know if we have a lot of "low hanging fruit", things that we need done but are just too lazy to do so. Though I'm sure we could come up with some of those tasks if desired, as we're certainly lazy.

Hey, I'm still figuring out the copyright rules as to what I can post, but there are plenty of things already available:

This paper on Spaun specifically
Some background on how Spaun is built
Some background (with code) on the theoretical framework used
The actual code for Spaun

I'll let you know if a pre-print goes up!

We do use Python scripting to interface with our simulator, Nengo. See the last link for the actual script we use for Spaun.

You know, you could have just done a simple web search. There are university degrees in Software Engineering. Example: http://uwaterloo.ca/software-engineering/home

store-bought PC

sudo apt-get install firefox

'sudo' is not recognized as an internal or external command,
operable program or batch file.

wget http://mirror.csclub.uwaterloo.ca/ubuntu-releases/lucid/ubuntu-10.04.1-desktop-i386.iso

'wget' is not recognized as an internal or external command,
operable program or batch file.

Any store-bought PC not made by Apple will include Windows as its only installed operating system, and I'm not aware of a command-line HTTP downloader client shipped with home versions of Windows.

So I take it the only way to win IE is not to play. In that case, how does one start with a store-bought PC and download something better such as Firefox,

sudo apt-get install firefox

Chrome,

sudo apt-get install chromium-browser

or a whole different operating system, without playing?

wget http://mirror.csclub.uwaterloo.ca/ubuntu-releases/lucid/ubuntu-10.04.1-desktop-i386.iso

Unless everyone forgets: http://crysp.uwaterloo.ca/courses/cs458/F08-lectures/local/www.acm.org/classics/sep95/
Reflections on Trusting Trust by Ken Thompson

Actually, the hole isn't inexplicable. There's a strong correlation between ozone depletion and cosmic rays. It's possible the CFC theory is a load of old baloney, based on a few years worth of data and not very much actual understanding. But, well, I guess I'll get down-modded for making the point :).

If you want to know what's causing the depletion, you can find out. What you'll want to avoid is sources that come from industry. You can bet they'll be skewing research to keep the status quo for business. If you want the answer to anything, just follow the money. If there's money involved, you can bet there's going to be some propaganda to sift through. I don't know anything about a cosmic ray theory, but you can bet if it's a buisness backed theory, it's bullshit. About like climate change denial...total corporate propaganda.

Actually, the hole isn't inexplicable. There's a strong correlation between ozone depletion and cosmic rays. It's possible the CFC theory is a load of old baloney, based on a few years worth of data and not very much actual understanding. But, well, I guess I'll get down-modded for making the point :).

What I'm saying is it would be inexplicable to the propaganda fodder (fox, cnn viewers) CFC hole denialists that would exist if industry had its way. Do you get that? I know the fucking hole is easily explained. I'm saying business doesn't like change and if duping a few suckers will stop change or slow it to another business cycle, that's exactly what business will do. That's exactly what's happening with climate change; problem is, it's a matter of human survival this time, not just some smog hanging out over LA or needing some extra sunblock. This stuff is getting serious and it's time the propaganda fodder wised up.

Actually, the hole isn't inexplicable. There's a strong correlation between ozone depletion and cosmic rays. It's possible the CFC theory is a load of old baloney, based on a few years worth of data and not very much actual understanding. But, well, I guess I'll get down-modded for making the point :).

Try http://cscircles.cemc.uwaterloo.ca/ and http://thinkcspy.appspot.com/build/index.html the latter is an interactive version of the famous "thinkpython" book. They both have structured curriculum and interactive exercises starting from ground[0].

Well, Bogo sort can be done in O(n)

http://www.mathnews.uwaterloo.ca/Issues/mn11103/QuantumBogoSort.php

I used to work at the Institute for Quantum Computing (http://iqc.uwaterloo.ca) in Waterloo, ON, Canada.

They offer a summer program called QCSYS for deserving high school students. You should check it out: http://iqc.uwaterloo.ca/conferences/qcsys2012

This could be used as an efficient implementation of the quantum bogosort

That is the most cretinous argument I think I've so far read. Notwithstanding the fact that recent papers showed the hole in the ozone layer is caused primarily by cosmic rays (I don't expect you to have read it), the total amount of CFC emitted by the world's asthmatics is so tiny compared to the size of the ozone layer that its effect can only be but a tiny pin prick.

This kind of over-regulation based on the flimsy evidence of politically motivated activists is destroying not only our economies, but public trust in science and the scientific method.

maybe something like this SOHCG-7.pdf
  "Self organizing and Self Healing Certificate Authority"

There is a lot of research going into mental health gadgets as well. It's just that they're a bit tougher to make since they involve a lot of stuff related to machine learning and artificial intelligence. One of my Professor's at the University of Waterloo has been working on a system using off the shelf parts to help Alzheimer's sufferers be more independent in their home and thus help lessen the burden that typically falls on their children to care after them. I'm talking things such as reminding a sufferer a step in the hand washing process if they forget it. Of course, everyone has different patterns and has varying levels of "annoyance" thresholds, etc. which makes fine tuning the system hard, hence the machine learning part.

You can check out some of his work here: http://www.cs.uwaterloo.ca/~jhoey/research/coach/index.php

Not all universities make students and professors sign away their work. University of Waterloo policy is that the creators retain all rights, presumably because the university likes to brag about students who started companies based on work done in their research or as design projects. It's easier for students to form companies to brag about if you stay out of the way and let them do the heavy lifting if they want to. I wouldn't be surprised if you could find other schools with similar philosophies.

I beg to differ. It doesn't take much effort to find Lilypond versions: http://www.google.com/search?q=goldberg%20variations%20filetype%3Aly leads quickly to this set of scores with copies here and here, all of which provide the score as Lilypond files, as well as PDFs and MIDI.

So it seems worth asking again: what is the new thing that this project is bringing to the table?

As some other commenters have noted, C++ and its plethora of features give something comparable to a write-only language like COBOL (remember that debugging is part of reading the code).
I wouldn't retrofit things like polymorphism onto C, if I were to start over (something the guys at digital mars probably agree with). IMHO, you end up with kludginess without the brevity (sometimes called "elegance", but that's a bit debatable) of perl. Hey, we could be doing worse---at least it's not PL/I! *g*

I'm just surprised nobody has parroted the oft-quoted "obscenity is the crutch of inarticulate motherfuckers" yet ;)
captcha: innuendo

Software engineering is a systematic and disciplined approach to developing software. It applies both computer science and engineering principles and practices to the creation, operation, and maintenance of software systems.

At the University of Waterloo, Software Engineering is an independent, interdisciplinary program supported by both the Faculty of Mathematics and the Faculty of Engineering. Graduates of this program will earn a Bachelor of SoftwareEngineering (BSE) degree.

There is a reason that one of the most highly regarded engineering AND computer science schools in the world sees the need to have separate programmes for both computer science and software engineering. It's because they are different. They are similar, but not identical.

If you think that the term "software engineering" is a meaningless, self-appointed term, then you're right. It's because, in most of the US at least, "engineer" is not a regulated professional term whereas maybe it should be. Generally, I'd say that most people calling themselves software engineers are not software engineers. That doesn't mean that it's not a valid profession with valid differences from being a computer scientist or a programmer. We just need better ways of weeding out the people who like to call themselves software engineers from those who actually are.

Only diploma mills issue software engineering degrees? The University of Waterloo is hardly such: http://www.softeng.uwaterloo.ca/

if you resubmit your own work, it's not plagiarism.

My university begs to differ.

How does one even redo a very similar assignment when you have the same thought process? There is bound to be similarities that their plagiarism detector would flag.

Students graduating from the University of Waterloo's Math Faculty are invited to make one or more graduating pledges to support U(W). One of those pledges is the Dean's Prime Number Club, which confers upon you your very own Prime Number.

As others have noted, the binary sequence is a palindrome prime number in base 2. David Johnston is U(W)'s out-going President. It's likely that the Math Dean's Office has awarded him his very own Prime Number as an honorific (or for completing the pledge!) and he has chosen to incorporate it into his personal Coat of Arms.

I am unable to find the Prime Number registry online or in fact any mention of it at all, U(W) web pages about pledges aside. Digging out my old papers I see that the letter awarding one's Prime Number merely says "Here it is in the box at the bottom. Congratulations!" Perhaps the Dean's Office will confirm tomorrow.

...Stu, hopefully not the only member of the Dean's Prime Number Club reading Slashdot...

Students graduating from the University of Waterloo's Math Faculty are invited to make one or more graduating pledges to support U(W). One of those pledges is the Dean's Prime Number Club, which confers upon you your very own Prime Number.

As others have noted, the binary sequence is a palindrome prime number in base 2. David Johnston is U(W)'s out-going President. It's likely that the Math Dean's Office has awarded him his very own Prime Number as an honorific (or for completing the pledge!) and he has chosen to incorporate it into his personal Coat of Arms.

I am unable to find the Prime Number registry online or in fact any mention of it at all, U(W) web pages about pledges aside. Digging out my old papers I see that the letter awarding one's Prime Number merely says "Here it is in the box at the bottom. Congratulations!" Perhaps the Dean's Office will confirm tomorrow.

...Stu, hopefully not the only member of the Dean's Prime Number Club reading Slashdot...

Students graduating from the University of Waterloo's Math Faculty are invited to make one or more graduating pledges to support U(W). One of those pledges is the Dean's Prime Number Club, which confers upon you your very own Prime Number.

As others have noted, the binary sequence is a palindrome prime number in base 2. David Johnston is U(W)'s out-going President. It's likely that the Math Dean's Office has awarded him his very own Prime Number as an honorific (or for completing the pledge!) and he has chosen to incorporate it into his personal Coat of Arms.

I am unable to find the Prime Number registry online or in fact any mention of it at all, U(W) web pages about pledges aside. Digging out my old papers I see that the letter awarding one's Prime Number merely says "Here it is in the box at the bottom. Congratulations!" Perhaps the Dean's Office will confirm tomorrow.

...Stu, hopefully not the only member of the Dean's Prime Number Club reading Slashdot...

Students graduating from the University of Waterloo's Math Faculty are invited to make one or more graduating pledges to support U(W). One of those pledges is the Dean's Prime Number Club, which confers upon you your very own Prime Number.

As others have noted, the binary sequence is a palindrome prime number in base 2. David Johnston is U(W)'s out-going President. It's likely that the Math Dean's Office has awarded him his very own Prime Number as an honorific (or for completing the pledge!) and he has chosen to incorporate it into his personal Coat of Arms.

I am unable to find the Prime Number registry online or in fact any mention of it at all, U(W) web pages about pledges aside. Digging out my old papers I see that the letter awarding one's Prime Number merely says "Here it is in the box at the bottom. Congratulations!" Perhaps the Dean's Office will confirm tomorrow.

...Stu, hopefully not the only member of the Dean's Prime Number Club reading Slashdot...

I'm currently at the University of Waterloo doing a PhD in the Electrical and Computer Engineering department. It's in Canada, so it's not a big 10 school, but it has a solid reputation as a pretty decent school, especially in engineering. For our program, it's expected that a grad student maintains at least a 78% average with 75% being a pass. This means that if you're running a grad course, and you think that a student should pass the course, you basically have to give them at least a 75%. The end result is that if you graduate from the program, you're almost guaranteed an A average.

The requirements are listed here: http://ece.uwaterloo.ca/Graduate/PhD/

Since nobody seems to have mentioned it yet: Reflections on trusting trust.
Note that he already mentions planting exploits into microcode, which is already quite close to the hardware. Do you know for sure there's no exploit planted in the microcode of your CPU? Maybe someone manipulated the compiler for the microcode? The compiler on which the compiler for the microcode was compiled?

But even with the actual hardware, that's possible: Just as you can place an exploit in the C compiler, you can also place an exploit in the VHDL compiler. Then the VHDL code will be unsuspicious, and run correctly in the simulator, but the actual chip will still be modified. Again, several levels are possible.

OK, is there anything which can protect us? Well, on one hand it's getting more complicated with each intermediate step. But then, there's also another protection: Exactly the fact that not everything isn't done by the same company! And this even applies for the simple case mentioned in TFA: A company which is asked for a component which, say, adds up a bunch of numbers, doesn't know how it's combined with the other blocks, or what the other blocks actually look like. Therefore he likely cannot tell how you could actually trigger the bad behaviour in the complete chip, or how to do something "useful" on that condition. The same is true on all the other levels: The chip developers will not write their own VHDL compiler, and the VHDL compiler writers have no clue what the chips which will defined with them will look like. The microcode developers likely don't write the microcode compiler, and the microcode compiler people probably don't have access to the microcode source code.

Would be pretty simple using quantum bogosort also.