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Technology Stocks : Rambus (RMBS) - Eagle or Penguin -- Ignore unavailable to you. Want to Upgrade?


To: Investor2 who wrote (30588)9/24/1999 9:17:00 PM
From: Bilow  Read Replies (5) | Respond to of 93625
 
Hi Investor2; Mathematically, there are an infinite number of real numbers between 98.0 and 102.0, for instance, which might describe the capacitance of a capacitor, for instance. This infinity is referred to as "Aleph-0", which is generally thought to be the smallest infinity.

Since a single design has a finite number of capacitors & what not, the total parameter space for those parts is something like (Aleph-0)^N, where N is the number of parts. This is still just Aleph-0, according to the usual mathematical theory.

A higher order infinity would be represented by all the possible functions that map an interval to another interval, for instance, and that is the kind of order that might describe a noise function.

Even applying a frequency limit on those functions (and, therefore, a continuity requirement), wouldn't reduce that infinity, which the mathematicians call Aleph-1.

For more information on the various infinities, look up the Continuum Hypothesis in theoretical math books.

The upshot of all this is that modelling all the possible conditions that can beset a computer in real life is so far beyond impossible that it isn't even conceivable. Machines have to be designed conservatively, otherwise the spirit in the machine will gain life, and make the computer do something that its designers did not intend.

Engineers refer to errors in computers as "bugs." This is more descriptive than is realized by most people, because bugs are a form of life. Machines are supposed to be fully controlled things, free of any hint of soul or free will. That is what consumers want, machines that are predictable, not machines that sometimes do odd things.

Life is an incredibly strong force, and to hunt down every bug and kill it is what makes engineering a difficult thing. All living things guard their life with defenses, that is a consequence of evolution, and the defense best used by computer bugs is complexity. The safest and easiest way to avoid bugs in designs is to make sure that there is sufficient margin that the bugs are unable to squeeze through the cracks in the (hopelessly finite and human-error prone) simulations. This is what Rambus has not done.

Does this explain better? I love electronics design. I always feel great when I have hunted down and butchered another bug. Other engineers would describe it in some other way, but I see the perfection that is achievable in engineering design to be as close as I, a finite, frail, constantly dying, limited and stupid human, can come to the perfection of God, who can see all infinities simultaneously. Engineering is a way of forcing the purity of mathematics onto the imperfection of a world of blood, feces and mucus, it is the most exquisite thing in the world, short of mathematics itself.

I see the Rambus design the way a big game hunter would see an African veldt. A lot of places for a lot of dangerous game to hide, mate, kill, eat, die, live. A lot of places for a big game hunter to get hurt. A place where there are likely to be big game left, even after the hunter thinks he has gotten them all.

-- Carl