Objects in C, IR, and ASM--how do you get low-level?: Getting rid of all the crap

Too hung over to work on xen right now so I'll answer your questions:

You can performance or you can have security, you can't optimize for both. There's always a trade-off.

All that 'extraneous crap' is actually quite well designed (at least as far as C/C++ and the POSIX standard goes) and through today's optimizing compilers will generate far more efficient native code than you could ever write by hand.

How do you write secure code? You don't. You leave that to cryptography experts like https://en.wikipedia.org/wiki/Daniel_J._Bernstein

You could spend a lifetime studying side channel attacks (such as caching timing attacks) buffer overruns and specific flaws of one type or another in the numerous instruction sets and hardware implementations of these. This is what cryptography experts do for a living and they achieve excellence at it -- which you never will unless you dedicate your life to it. Not all of them work for the NSA. Djb is quite anti-NSA and has had his elliptic curve cryptography repeatedly rejected from NIST standards because they can't put backdoors in it -- it's too good. Another way you know he's your guy is he releases his algorithms into the public domain -- something only a pure researcher would do. He also sued the US government (and won) to protect his algorithms under free speech laws so they couldn't jail him for exporting munitions. There are people like him all over the world working to make computer security a reality.

Mathematics is not a-priori. This is a made up ex-postfacto justification for it. If you research the history of mathematics you will learn about the foundational crisis and things like naive set theory. In fact mathematics is just an abstraction built from repeatable experiments performed in reality. It is part of the laws of physics. We only have the concept of numbers, counting things, sets etc. because of conservation of mass/energy and spatial exclusivity. Numbers are built by concatenating the logical operator and on spatially-exclusive materially-conserved quantities. Equality is a concept but it's not a baseless concept. Things can have similar or identical traits and we can isolate and signal our recognition of these similar traits. For example the same concentration of and can apply in two different places. We can say in short that the two places have the same number of the entity. We can abstract further and say two sets have the same cardinality.

Quantum theory only works at the quantum level. Once you get to macroscopic "hot" systems the classical laws all apply. Some would argue (including myself) that classical laws also apply to the quantum world and in fact quantum is just a special case of the classical. For example this line of thought is embodied in the causal or pilot wave interpretations of quantum mechanics.

You need to read some reality based philosophy rather than the self-referential infinite regression bullshit taught in mainstream universities. I suggest http://www.amazon.com/Introduction-Objectivist-Epistemology-Expanded-Edition/dp/0452010306

Leibniz's law like most things can be sorted out by just calling things by their proper names. Identical things do not exist in reality due to the law of identity. A thing is itself, it is not also another different thing. Each thing has a single unique identity. When we talk about equality we are comparing a set of similar attributes. Comparison operations are perfectly legal and do not break the law of identity. If we look at post boxes which lack numbers we can say they are all identical in their construction and appearance, but we don't say they are the same postbox. They are made of different atoms and/or exist in difference places or times. If you differentiate concretes from abstractions, you can easily see that concretes follow the law of identity and abstractions don't -- however abstractions aren't real -- their only reality is a series of neurological signals that occur in your brain or a series of electrical or photonic signals that occur in a computer, each set of which is a unique concrete. The law of identity is thus unbroken in making comparisons. All you need to do is differentiate concretes from abstractions.

A function is a recipe. It's not defined by other functions. It's not defined sets or collections or other mathematical constructs. It's defined in terms of the laws of reality. Causality, law of identity and conservation of mass energy is sufficient to define a function: If you perform the same operations on similar inputs you will achieve similar outputs.

Yes we do. Infinity as a concept simply means to go forever and is useful for considering processes that you never intend to terminate. As an actual number (i.e. actual infinity) it is just an assertion brought into mathematics by the axiom of infinity. If you don't accept the axiom, it's not in mathematics. It's not a philosophical axiom (i.e. a statement you can't disprove without first assuming) it's actually just a pure assertion. "Infinity, as a number, exists." Axiom of infinity.

Continuous mathematics is internally inconsistent. You've learned ZFC mathematics which has the conspicuous property of leaving out infinitesimals which provide a logical bridge between discrete and continuous models. This causes a problem because you can never move from one number to another at the fundamental level. If 1.999999 recurring is equal to 2 then a small amount less than 1.999999 recurring is equal to 1.999999 recurring which is still equal to two. Inductively then all numbers are equal to two. And further, whichever number you start with all numbers are equal to that number. This is one of many many internal contradictions in ZFC which you will find if you look for them. In order for mathematics to make sense you need make every actual thing in it finite as in https://en.wikipedia.org/wiki/Finitism This is what reality tell us. Mathematics as it stands has become divorced from reality that's why you have garbage like countable and uncountable actual infinities, etc. It's self referential bullshit that doesn't help you solve real problems. In physics we pick and choose mathematics to suit the problem at hand and we don't bother trying to untangle the mess modern mathematicians have made of it. For example in advanced quantum / perturbation theory we use dual numbers ( https://en.wikipedia.org/wiki/Dual_number ) which give us an infinitesimal to work with while still using the continuous approximation. In other branches we use discrete mathematics, etc.

You use parity bits and checksums. You test your implementation rigorously. You build a conclusion about the device the same way we build conclusions about everything in reality. You test it X number of times and conclude that if X is large and it worked the first X times then it will work the X+1 th time. And the probability that it won't becomes vanishingly small. This is called inductive reasoning. Sometimes you can do better than this and prove mathematically (i.e. deductively) that it won't fail as well. However all deductive reasoning has as premises at some point along the chain of reason some inductively reasoned law (such as a law of physics).

In applications where the risk of hardware/software failure is a great risk to human life, two competing computer systems produced by different teams on different hardware/software to the same set of specifications accept the same inputs and produce the same outputs which are compared and if they differ a graceful failure occurs. This happens in planes.

You can isolate digital systems from ambient noise by Faraday shielding.

A pointer is a memory address and a type: conceptually two pieces of information. When compiled it is just an address: one piece of information. Usually you point to some object or memory on the heap using a pointer stored on the stack. This is logically equivalent to storing a phone number in your address book. If the phone number changes you can always update it in your address book. It gives you a constant place to look for a shifting target. This is one of main fundamental reasons pointers are extensively used in programming. Algorithms rely on moving targets. In fact the processor itself has an instruction pointer which points to the native instruction it is up to. This is how goto works, it just updates the instruction pointer. The instruction pointer is kept in a register which again is a constant place to find a reference to a moving target.

You need to stop trying to apply broken ZFC mathematics to computer science. They are fundamentally different fields. Mathematics gives us short cuts to certain computational results. However most computational results are irreducibly complex and can only be solved by putting it into a computer and doing the calculation. Or putting it into reality and doing the experiment -- the two are not different. What I am saying is that computation is directly part of reality, and every time you write and execute code you are performing a scientific experiment against a hypothesis: this code will do X.

With this mathematical analysis of computing you are putting the cart before the horse. In some cases mathematics will tell you what to expect from your program however this is still just hypothesis forming. The computation itself is the primary, not the mathematics. Mathematics is a set of deductive reasoning and it is not a primary. Mathematics is built from experiment not the other way around.