Can anyone explain the maths in the blackboard scene?
Are there any maths postgrads reading this who can explain the maths in the blackboard scene...to someone who didn't do advanced maths at school?
Thanks.
Some equations look like variations on Euler's formula (the real & imaginary components of a complex phaser, possibly with some amplitude or phase modulation). Other equations look like 2x2 matrix math/linear algebra (solving 2 equations with 2 unknowns) with rather elaborate expressions for the elements of those matrices.
Nevertheless, none of these equations has the slightest meaning whatsoever, because neither Armstrong nor Lindt define what problem (what aspect of Ballistic Missile Defense) they are trying to solve. i.e., What, exactly, "isn't working" is never stated.
Furthermore, the script makes a major blunder by several times identifying Armstrong as a Nuclear Physicist, yet the big project he was working on was Ballistic Missile Defense . . . . . a field that has zero use for Nuclear Physicists.
In fact, Ballistic Missile Defense -- then as now -- is mostly an engineering problem, not a scientific one. The challenges are
(1) improving range & velocity resolution of ground-based radars. The DSP and pulse-doppler radar technology needed to do that were just getting started in the mid-60's.
(2) increasing the bandwidth of the feedback control loop that . . . .
(2a) receives the ground-based radar's range & velocity data about the incoming warheads
(2b) distinguishes dummy warheads from real warheads (based on small velocity differences)
(2c) predicts future positions of the real warheads
(2d) and then directs in-flight SAMs (surface-to-air missiles) to correct their flight course to intercept those real warheads
. . . . which really just boils down to Moore's law (number of transistors per unit area on an integrated circuit doubles every 18 months) which has driven the whole explosion in computer processing-and-communication speed (and reduction in size) that we've seen in the personal computer (and now tablet & smartphone) for the last 35 years.
Many thanks, that's an excellent answer. In fact it's so good that I'll throw another question at you:
What are "finite absolutes"?
If you have ever seen the sf film "Colossus: The Forbin Project", released in 1970, there is a scene in it where the Colossus supercomputer starts showing human observers in the room on a tv screen what it is learning and how its learning power is rapidly increasing.
At one point, Forbin says, "This is way beyond me...it is deep into Finite Absolutes."
What are "finite absolutes"?
Here's the link, it's great fun...
https://www.youtube.com/watch?v=5iwq0Tu8Ss8
Many thanks,
Paul Murphy,
London, UK.
Can you tell me approximately when (__:__:__) this dialogue occurs? I've seen the movie before -- and enjoyed it -- but I don't have time to re-watch the whole thing.
Offhand, though, the phrase "finite absolutes" doesn't ring a bell with me. But maybe hearing it in context will help, so let me know if you can narrow-down the swath of time in the film where it occurs.
Maybe you should also run this question by Matt Damon. He played a math genius in Good Will Hunting, but has taken that role so literally, he now thinks he should pontificate on many issues he knows nothing about! (Just kidding)
It's at 26:40 to 26:50 in the clip I sent you. Thanks so much. I only did literature and history at college, I know nothing about maths!
shareNo, I can't tell you anything more about "absolute finites" than the nothing that I could tell you before.
But the whole exchange does bring up an interesting idea: when an "advanced" computer system starts spitting out data/claims/conclusions/results that are unintelligible to it's human operators, that presents a fascinating problem of intellectual detective work for the humans to verify whether those data/claims/conclusions/results are true or if they are in error . . . . . and if in error, where is the error?
(a) dynamic (transitory) errors in memory (cosmic rays can flip a 1 to a 0 and vice-versa). There are ways of combating this (ECC = error checking & correction), but they are statistical in nature, not absolute cure-alls.
(b) static errors in the software
(c) recursive errors in self-modifying software (i.e., like fractals: non-linear equations with SDIC = sensitive dependence on initial conditions; read James Gleick's 1987 book "Chaos")
By the way, I haven't seen Colossus: The Forbin Project in years, but don't the Russian & American supercomputers threaten mankind with nuclear annihilation if the humans don't carry out some particular orders that the supercomputers issue? I know the film takes pains to point out that the supercomputers have independent power supplies (humans can't pull the plug), but look to see if the film's dialogue suggests whether the supercomputers were designed to be nuclear-hardened (nuclear bomb bursts greatly attenuate transistor gain, rendering most electronics in-operable). i.e., By nuking humans, the supercomputers may also be nuking themselves.
One has to spend a great deal of time with that sequence before it dawns into one's mind as to its full meaning . . . and, no, it has nothing to do with what's been posted above . . .
shareThanks very much for your reply. I've researched Finite Absolutes online and asked other people about them. No one knows anything, so I've come to the conclusion that they may well have been something invented by the scriptwriter and never existed at all!
Yes, I agree with your observations about nuking. And no nuclear power plant, either inside a giant supercomputer or outside in a conventional nuclear power station, could ever be run completely automatically, without any human crew, so the whole premise of the film is nonsense, really. But I still enjoyed every moment of the film, and it's a hundred times better than the special effects addled rubbish that we're served up today by Hollywood sf producers.
Thanks again,
Paul.