Slashdot Mirror
The 23 Toughest Math Questions
coondoggie sends in a Network World post that begins "It sounds like a math phobic's worst nightmare or perhaps Good Will Hunting for the ages. Those wacky folks at the Defense Advanced Research Projects Agency have put out a research request it calls Mathematical Challenges, that has the mighty goal of 'dramatically revolutionizing mathematics and thereby strengthening DoD's scientific and technological capabilities.' The challenges are in fact 23 questions that, if answered, would offer a high potential for major mathematical breakthroughs, DARPA said." Some of the questions overlap with the Millennium Prize Problems of the Clay Mathematics Institute, which each carry a $1M prize.
42
Surely there are enough nerds on slashdot to figure these out. Or are we not as smart as we say we are?
"I don't have to think. I only have to do it. The results are always perfect, but that's old news." - Meat Puppets
The 23 Toughest is Michael Jordan for now
Don't use MS Word.
I also have a challenge for the slashdot janitors: Link to the original source instead of an ad-laden blog.
Do you even lift?
These aren't the 'roids you're looking for.
The portion of the DoD most interested in maths achievements is the NSA, which employs more mathematicians than any other institution in the world (see e.g. Bamford's Body of Secrets ). So when the authors of this list talk about increasing the abilities of the DoD, they really mean increasing violation of privacy and harrasment of anyone thinking too freely.
Does anyone else here feel like we're being asking us to do someone else's math homework for them?
I prefer rogues to imbeciles because they sometimes take a rest.
23
How did the mathematician solve for constipation?
He worked it out with his pencil!
Do you even lift?
These aren't the 'roids you're looking for.
One ever. He will prove that it can be done. But after this is proven, it's quite uninteresting problem.
Bonus question: Is lending a value that is worth 125% of the house it is secured against a good idea? State your reasons why and show your working out.
These are really hard problems and I wonder how does anyone formulate a research grant requests for them.
Physics.
I wonder if it's just coincidence that the number of problems they list is the same as the number of problems David Hilbert listed in his famous address in 1900. And well, the Riemann Hypothesis is there too. A hundred years later, and still no resolution.
Qu'on me donne six lignes écrites de la main du plus honnête homme, j'y trouverai de quoi le faire pendre.
Ha! The subtlety of your sarcasm nearly evaded the grasp of my comprehension. Well done sir!
You just got troll'd!
Say I'm working at N.S.A. Somebody puts a code on my desk, something nobody else can break. So I take a shot at it and maybe I break it. And I'm real happy with myself, 'cause I did my job well. But maybe that code was the location of some rebel army in North Africa or the Middle East. Once they have that location, they bomb the village where the rebels were hiding and fifteen hundred people I never had a problem with get killed.
Now the politicians are sayin' "send in the Marines to secure the area" 'cause they don't give a shit. It won't be their kid over there, gettin' shot. Just like it wasn't them when their number got called, 'cause they were pullin' a tour in the National Guard. It'll be some guy from Southie takin' shrapnel in the ass. And he comes home to find that the plant he used to work at got exported to the country he just got back from. And the guy who put the shrapnel in his ass got his old job, 'cause he'll work for fifteen cents a day and no bathroom breaks. Meanwhile my buddy from Southie realizes the only reason he was over there was so we could install a government that would sell us oil at a good price. And of course the oil companies used the skirmish to scare up oil prices so they could turn a quick buck. A cute, little ancillary benefit for them but it ain't helping my buddy at two-fifty a gallon. And naturally they're takin' their sweet time bringin' the oil back and maybe even took the liberty of hiring an alcoholic skipper who likes to drink seven and sevens and play slalom with the icebergs and it ain't too long 'til he hits one, spills the oil, and kills all the sea-life in the North Atlantic. So my buddy's out of work and he can't afford to drive so he's got to walk to the job interviews which sucks 'cause the shrapnel in his ass is givin' him chronic hemorrhoids. And meanwhile he's starvin' 'cause every time he tries to get a bite to eat the only blue-plate special they're servin' is North Atlantic scrod with Quaker State.
So what'd I think? I'm holdin' out for somethin' better. I figure I'll eliminate the middle man. Why not just shoot my buddy, take his job and give it to his sworn enemy, hike up gas prices, bomb a village, club a baby seal, hit the hash pipe and join the National Guard? Christ, I could be elected President.
How we know is more important than what we know.
There is an art in finding good questions. Hilbert did it in 1900 with his 23 problems or the millenia problems in 2000. Some of the 23 problems stated are too vague. The first example: "Develop the mathematics of the brain". This covers large parts of computer science, artificial intelligence and psychology. What does "mathematically consistent" mean? A mathematical problem can be taken seriously if there is a clear goal and if there is a possibility to determine, when the problem is solved. This is not the case for many of the problems listed on this website.
(Rough quote, probably not quite all the way accurate).
Schiavone: The answer is easy as two plus two!
Heenan: Five!
Schiavone: Two plus two is FOUR, Bobby...
Heenan: Not if you get the deal...
..and most of the challenges have little to do with math. Meanwhile, here's something which could lead to real progress in mathematics (From the Slashdot Firehose):
An anonymous reader writes:
link
Hilbert's problems were stated fairly precisely. The Millenium Prize problems have detailed statements written by experts in the fields involved. Most of these DARPA questions could use some clarification as to what they're asking for. Hopefully that will be forthcoming.
Why?
"Because calculators are a pain in the ass."
Here people seem to think they know everything about anything.
While solutions to any of these mathematical conundrums would be grand, I'm not sure I'd want to do so in the name of DARPA, or even have any association of my discoveries with DARPA.
At the end of the day, DARPA specialises in technology that is designed to benefit the military, and as a result, is frequently designed for either either killing people, or making it easier to do so. Yes, there's the whole "defence" argument; that the technology will be used for saving lives. But this is a half-truth, the lives being saved are almost always select (only lives belonging to a certain state(s) (the US and potentially its allies in this case)), and often at the cost of other lives.
This can of course degenerate into a whole ethics and morality debate on the value of human life, but ideally, I'd rather such findings published through an academic institute, e.g. a university, that doesn't have any ties to military technology, but rather, a persuasion to applying scientific breakthroughs in the advancement of the common good for humanity as a whole.
I know there have been advancements that DARPA has made that have benefited humanity as a whole, such as the Internet, but keep in mind this was not the primary intent. The Internet turned out to have enormous potential outside the military, but it was military benefits that were the primary focus of the project, and they no doubt got them; the military portion of the Internet split from the public domain and is now a highly classified network, possibly with numerous innovations that are not available to the public.
While there are some parallels, the Millenium Prize is a set of Problems. It's a set of specific theorems that are not proven. The challenge is to prove or disprove the theorem (P=NP, Poincare conjecture, Reimann Hypothesis, etc.) It starts with definite propositions that are believed to be true, and challenges proof of those propositions.
The DARPA Challenges is a set of questions that need answering. In a few cases (Reimann Hypothesis, Hodge Conjecture) they overlap. However, the DARPA questions are more typically like: "An Information Theory for Virus Evolution: Can Shannon's theory shed light on this fundamental area of biology?" In the DARPA case, they don't know whether their questions are answerable, or what the answers look like. The challenge is not one of proof, but one of developing new theory.
They are asking the reader to create entire fields! how lazy of them.
Unsure...
:(){
Not as much as using logs.
Only one, but since you need the Axiom of Choice to implement the algorithm, it might not work.
They only want a mathematical model of the brain, a mathematical model of society as a whole, and fundamental laws of biology so they can answer 'why we are here'.
they really are challenged:
"which each carry a $1M prize."
try:
"each of which carries a $1M prize."
Is it mathematician joke time again?
An engineer, a mathematician and an engineer are in separate hotel rooms. They each have a fire in the room when they are asleep.
The engineer grabs his ice bucket, fills it with water, dumps it on the fire and goes back to bed.
The physicist carefully measures how much fuel the fire has, how fast it is spreading and how much oxygen is available for the fire, then calculates exactly how much water he needs and dumps it on the fire.
The mathematician performs the same calculations as the physicist, proclaims "A solution exists!" and goes back to bed.
If a train leaves Chicago at 8:30 headed for Denver traveling at 45 MPH...
Not like the Millenium Prize problems, certainly. They're broad fields, some of which aren't even primarily mathematical and some of which already have some existing answers. That web page appears to be quoting the DARPA .doc precisely, but it reads as if it were a brief summary of a real RFP.
Just looking at the first few examples:
A predictive theory of the brain? That'll be a fantastic biological breakthrough, but I doubt it'll require any new mathematics.
I'm happy to see that "persistence in stochastic environments" is considered a hot topic by others, too, but they could be a little less vague about what they mean by it. The hyperlinked article there seems unrelated.
Foams, suspensions, gels, liquid crystals, etc. can be modeled with the same conservation equations as Navier-Stokes, just with more complex constitutive laws. Getting those laws right sometimes involves new mathematics (e.g. "homogenization") but often just requires getting better experimental measurements of the material you're interested in.
"Biological Quantum Field Theory" sounds like another "we've got the right algorithms but just need more biological data to scale them up with" situation, but maybe this is a case where the algorithms don't yet scale optimally?
"Duality in Mathematics" includes still-developing fields... but the answer to "Can it be extended to develop principled computational techniques where duality and geometry are the basis for novel algorithms?" is "Yes, and it has been for at least a decade or two."
1 Eat
2 shit
3 die
Or, if you are an underpants gnome:
1. Eat, shit, die
2. ???
3. Profit
And to answer the question above it:
Settle the Smooth Poincare Conjecture in Dimension 4. The Poincare Conjecture in Pantene's new Dimension 4 shampoo smooths out all stubborn theories in cosmology to unlock the secret of "dark energy" and give a depth to your space-time.
it is only after a long journey that you know the strength of the horse.
Nothing about a northbound train leaving at 10:00?
Or, maybe, Alice can't sit next to Bill, Charlie is wearing a red shirt, Dale won't eat vegetables, Elroy has incontinence issues, and Frank sucks at photoshop. Based on this, which one is left handed?
There must be some kind of analogue to Godwin's law here...
Fuzzy Math
Not as much as using logs.
They are a bit too heavy. I use paddle pop sticks instead.
Don't be apathetic. Procrastinate!
Now I know what to do this evening.
I'd like to be the top travelling salesman in the world, damnit!
I hear what you're saying, I just don't get why it's a problem.
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
How Much Wood Could A Wooodchuck Chuck If A Woodchuck Could Chuck Wood?
Granted, DARPA gave us the internet, but this being military it will more likely be used more for evil rather than good.
People contribute if their greed or jingoistic patriotism (some might call it sense of duty) trump their humanity and wisdom.
this is mental!
I take my children to see Madonna(..), but I never for once ever thought I was in the same business.Chris Rea.
I had the answer to some of the these questions just by using Google, but IE crashed on me. Question (24) How to create an operating system that doesn't suck!
As always /. brings us old news: The n-category cafe carried a lively discussion of this business back in December. The response from the small sampling of mathematicians represented there was highly skeptical at best. Now who knows whether or not this program will be good for DARPA in the long run. However, there should be no doubt in anybody's mind that the proposer of these problems is no David Hilbert...
For any result greater than 3 the answer is 'A suffusion of yellow'
A learning experience is one of those things that say, 'You know that thing you just did? Don't do that.' - D. Adams
-777.68
By the process of elimination of the gravitons and graviolies, the electron must taste like grape-aid.
Go back to art school, you posers!
23 = 6
Man, I'm so smart!
Spork.
P.S. Spork.
Just in case anyone is late to this discussion, let's be very clear about one thing: "These are not homework problems!"*
*Thanks to George Dantzig this is now a requisite warning whenever people talk about lists of difficult problems.
EvilCON - Made Famous by
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Here's the list:
* The Mathematics of the Brain: Develop a mathematical theory to build a functional model of the Terminator that is mathematically consistent and predictive rather than merely biologically inspired.
* The Dynamics of Networks: Develop the high-dimensional mathematics needed to accurately model and predict behavior in large-scale distributed networks that evolve over time occurring in communication, biology and the Matrix.
* Capture and Harness Stochasticity in Nature: Address Mumford's call for new mathematics for the 21st century. Develop methods that apply extrodinary rendition to persistence in stochastic environments.
* 21st Century Fluids: Classical chemical warfare and the Navier-Stokes Equation were extraordinarily successful in obtaining quantitative understanding of shock waves, turbulence and solitons, but new methods are needed to tackle complex fluids such as foams, suspensions, gels and liquid crystals.
* Biological Quantum Field Theory: Quantum and statistical methods have had great success modeling virus evolution. Can such techniques be used to model more complex systems such as biological warfare agents? Can these techniques be used to control the battlefield?
* Computational Duality: Duality in mathematics has been a profound tool for theoretical understanding. Can it be extended to develop principled computational techniques where duality and geometry are the basis for novel weapon systems?
* Occam's Razor in Many Dimensions: As data collection increases can we "do more with less" by finding lower bounds for surveiling each and every citizen on the planet? This is related to questions about entropy maximization algorithms.
* Beyond Convex Optimization: Can linear algebra be replaced by algebraic geometry in a systematic weapon guidance system?
* What are the Physical Consequences of Perelman's Proof of Thurston's Geometrization Theorem?: Can profound theoretical advances in understanding three dimensions be applied to construct and manipulate structures across scales to fabricate giant robots?
* Algorithmic Origami and Biology: Build a stronger mathematical theory for isometric and rigid embedding that can give insight into protein destruction.
* Optimal Nanostructures: Develop new mathematics for constructing optimal globally symmetric structures by following simple local rules via the process of nanoscale self-assembling armor plates.
* The Mathematics of Quantum Computing, Algorithms, and Entanglement: In the last century we learned how quantum phenomena shape our world. In the coming century we need to develop the mathematics required to blast the quantum world into little tiny pieces.
* Creating a Game Theory that Scales: What new scalable mathematics is needed to replace the traditional Partial Differential Equations (PDE) approach to android targeting systems?
* An Information Theory for Virus Evolution: Can Shannon's theory shed light on this fundamental area of biological warfare?
* The Geometry of Genome Space: What notion of distance is needed to disintegrate biological utility?
* What are the Symmetries and Action Principles for Biology?: Extend our understanding of symmetries and action principles in biology along the lines of classical thermodynamics, to include important biological concepts such as robustness, modularity, evolvability and head mounted laser beams.
* Geometric Langlands and Quantum Explosives: How does the Langlands program, which originated in number theory and repres
What is that, like, a C? I was never able to do percentages.
A time series like the S&P500 can currently bring all statistical models to their knees. Unlike an earlier poster, I gladly admit that I only work for the money so that I can afford a certain lifestyle I want to lead. If I can use my skills to be to accurately predict tomorrows closing price on the S&P500, then I'll have accomplished a great mathematical achievement for the world (when I reveal it), and in the process make alot of money for myself. Two moral, ethical, and legal goals.
As if there were no better organizations to work for as a mathematician...
1 billion.
But now the Iraqui's* suffer occupation and devastation, which we soothe with the infusion of billions of dollars we don't have....
(Iraquians, whatever)
the significance of a signature is insignificant
Here's what they don't tell you in that joke:
The tradesman was at the same convention, in the same hotel, but didn't have a fire in his room because he kept the vendor swag from "spark throwing alarm clocks inc." and "oily rags inc." apart.
It's been a long time.
The trick with these problems is to ask the right questions. I think they'd have a lot more right answers if they made the problems multiple choice.
For being about math problems, it's kind of ironic they would use bullet list on the questions rather than a number list.
Kind of hard to count up to 23 on the list is my whole point I'm trying to get at.
Answers:
1. No. But read the fine print and you'll discover that you are giving more than 700 bilion.
2. Nothing, it is being wiped out by stock invertors' ineptitude. (Or are you asking how much was lost by financing idiotic CEO's? That is a toughter question.)
3. With a bailout, near US$800 bilion. Without it, they'll be out of the job by the year's end.
Rethinking email
Strange. I don't see the one about the train leaving Chicago at 6:00...
-Loyal
I aim to misbehave.
That knowledge will be used against us... That's why I'm not telling them the answers...Please don't insist.
Yay for the DOD.
Why do they need all of that? What does wikipedia have to say? :
DARPA was established in 1958 in response to the Soviet launching of Sputnik in 1957, with the mission of keeping U.S. military technology ahead of the nation's enemies. From DARPA's own introduction[1]:
DARPAâ(TM)s original mission, established in 1958, was to prevent technological surprise like the launch of Sputnik, which signaled that the Soviets had beaten the U.S. into space. The mission statement has evolved over time. Today, DARPAâ(TM)s mission is still to prevent technological surprise to the US, but also to create technological surprise for our enemies.
to create technological surprise
They exist to invent The Transformers.
OK, I finished the test. Whew, that *was* a toughy! I think I might have gotten one of them wrong, but where do I send my answers?
"They said I probly shouldn't fly with just one eye," "I am Bender. Please insert girder."
How about we use the correct term and call it what it is: legislation.
...and yes, I expect to get modded down just because the video is clearly pro-McCain.
Congress didn't "encourage" subprime lending. They required it. (please excuse the McCain propaganda in this video...not meant to be political but it has some very relevant facts to the question at hand)
Doesn't anyone remember "redlining" mortgages from the 80's and 90's? Here is some background info. Read the part about mortgages.
Congress reacted to this by legislating subprime lending and requiring banks to provide X% of their loans to people who probably should not have gotten them.
1) Take a Finnish student
2) ???
3) Here's the unanswered part: how do you get a profit?
3 of the things on that list are Math questions: the ones that start with "Settle the ____ [conjecture/hypothesis]"
The rest are at best areas of study, and only a few of those are areas of study in Mathematics.
It is asking too much for the mathematician that he explain what a hell means each variable in giant formulas does he do? Without this, is just a bunch of letters and symbols.
Religion: The greatest weapon of mass destruction of all time
That number 2:
The Dynamics of Networks: Develop the high-dimensional mathematics needed to accurately model and predict behavior in large-scale distributed networks that evolve over time occurring in communication, biology and the social sciences.
Was based on Psychohistory?
Why is 6 afraid of 7?
I will not do the government's homework nor will I ever produce anything of mathematical significance for a governmental agency.
I counted 24. Man, this thing is tough before you even start.
The answer is 17.
Geeks like to think that they can ignore politics, you can leave politics alone, but politics won't leave you alone.-rms
Captain Clark welcomes you aboard.
[-- Trust the Monkey --]
Yes! I read that too. Most of the problems seem truly mathematical in nature, but the first two especially seemed Orewellian:
Emphasis mine...the second one is worse.
They want to quantify every aspect of human existence and be able to predict with high accuracy every potential human behavior. Just re-read that sentence once and ponder if you really want the government to be able to do that, given what we've seen them do to people in the War on Terror (TM).
The worst part is, human behavior is never, repeat: NEVER going to be able to be predicted on that level. Sure there are tendencies, but correlation is not causation, and the best we can do in the predictive sense is observe tendencies. If the DoD's goal is to have total predictive awareness of an individual's thoughts and actions, they will eventually come up with something...whether it works or not!
That's the root of it...they can't do it, but they're spending so much money trying that eventually they will have to come up with some BS system (polygraph combined with brain imaging and psycological profile) and call it a predictive system.
Their goals may seem innocuous at first (and I don't want to insinuate evil intentions on any one individual, save Dick Cheney)...the old "national security" but we know how that evolves into just maintaining power over the citizenry.
Humans behavior will NEVER be quantifiable enough to do what the DoD and DARPA want.
Thank you Dave Raggett
Ok, here's my bid: An engineer and a mathematician were trying to each fence off the largest field possible using a set amount of fence. The engineer calculated out the optimum position of the perimeter and fenced off a field. The mathematician made a tiny fence around himself and said "I'm on the outside".
I am officially gone from
I hope he used paper as well.
I've seen this list before and I really dislike it.
* The Mathematics of the Brain: Develop a mathematical theory to build a functional model of the brain that is mathematically consistent and predictive rather than merely biologically inspired.
This isn't an issue of mathematics. Sure, when we come to the stage when we can model brains we'll be using mathematics. But the question of how to model brains isn't itself mathematics.
* Biological Quantum Field Theory: Quantum and statistical methods have had great success modeling virus evolution. Can such techniques be used to model more complex systems such as bacteria? Can these techniques be used to control pathogen evolution?
This is highly suspect stuff. There isn't really a subject called "Biological Quantum Field Theory" and I doubt that anything similar to QFT has been used to model virus evolution.
* Computational Duality: Duality in mathematics has been a profound tool for theoretical understanding. Can it be extended to develop principled computational techniques where duality and geometry are the basis for novel algorithms?
These are just empty buzzwords. There are already countless things called "duality" all the way through computer science.
* An Information Theory for Virus Evolution: Can Shannon's theory shed light on this fundamental area of biology?
I'm ambivalent about this one. People were interested in this decades ago and I read a good chunk of the literature. But nothing real has come out of it. Maybe something could. But biological systems are inherently messy and I'm not sure that new mathematics is the solution.
* The Geometry of Genome Space: What notion of distance is needed to incorporate biological utility?
This simply isn't mathematics. I worked in a similar field years ago. But this wasn't really a subject that would push forward mathematics, it was just creative use of mathematics in a new domain. There's no deep mathematics to be found here.
* What are the Symmetries and Action Principles for Biology?: Extend our understanding of symmetries and action principles in biology along the lines of classical thermodynamics, to include important biological concepts such as robustness, modularity, evolvability and variability.
This is a bit off the wall. The person behind this list clearly sees some kind of analogy between quantum mechanics and biology (eg. biological QFT above). Wacky ideas are all well and good, but making some 'official' list from one person's hobby horse seems very strange to me.
* Settle the Smooth Poincare Conjecture in Dimension 4: What are the implications for space-time and cosmology? And might the answer unlock the secret of "dark energy"?
The mention of "dark energy" here is completely bogus. I guess it's a scheme to raise funding or something by trying to link some pure mathematics to a hot topic.
* What are the Fundamental Laws of Biology?: This question will remain front and center for the next 100 years. DARPA places this challenge last as finding these laws will undoubtedly require the mathematics developed in answering several of the questions listed above.
Again, "Fundamental Laws of Biology" sounds like one person's hobby horse than any serious trend in biology. And anyway, this isn't mathematics. We already have a Fundamental Law of Biology, it's called "Evolution by Natural Selection". Just about everything else slots into that framework and we explain almost everything in biology in terms of this. Sure, it'd be nice to extract some solid numerical predictions from evolution, but that's not a problem for mathematics.
Doesn't it make you feel good to know that our freedoms are protected by politicans, lawyers and journalists.
Prove that the questions above are the world's 23 toughest math questions.
So if you have ever wanted to settle the Riemann Hypothesis, which I won't begin to describe but it is one of the great unanswered questions in math history, experts say. Or perhaps you've always had a theory about Dark Energy, which in a nutshell holds that the universe is ever-expanding, this may be your calling.
I can't really call it a sentence, because somehow it turned into two of them... and it doesn't really work like that.
Alexander Peter Kristopeit bought his basement from his mommy for one dollar.
did anyone else notice in the article:
"Settle the Riemann Hypothesis: The Holy Grail of number theory."
where, "the holy grail" linked to the monty python wikipedia article..... good work....
"If you have one bucket that holds two gallons, and another bucket that holds five gallons, how many buckets do you have?"
What was the source of your video? It has been pulled by Warner Music Group. I don't want to sound like a member of the tin foil hat brigade, but this is not the first time in recent days I have been sent to youtube to watch a video about political scandal only to find it pulled by a media company. Am I alone in this, and just being paranoid, or is something else going on?
But things like "the brain" is not a mathematical object and thus has no place in the formulation of a mathematical question.
Let's see how quickly you can formulate a mathematical question after having your brain eaten by a zombie.
"If a nation expects to be ignorant and free in a state of civilization, it expects what never was and never will be."
It's over 9000!
Can you explain what was in the video, now that it has been pulled?
DARPA = military attempts to get help through open source.
It's okay so long as they are imaginary.
GAAH! MY PRINTER IS ON FIRE!!! PUT IT OUT! PUT IT OUT!
I write this with tongue slightly in cheek, but there is also a serious point...
I think there is a whole class of problems missing that if solved could have an immediate impact on every day life. I'm thinking of underspecified problems where you have made an 'investment' that looks like it might fail and you have to decide whether to bail out:
1. You are waiting for a bus but the bus is late. How long should you keep waiting before giving up and looking for an alternative? You don't know how often buses run on this route or whether the bus you are waiting for has been cancelled or is just late. You want to arrive as soon as possible, but trying to find an alternative mode of transport will take a long time.
2. You are in a checkout queue. The one to your right seems to be moving faster. Should you switch?
3. You have invested in shares that are on a downward slide. Do you bail out, or hold on in the hope that they recover?
The problem with all of these is you don't have any estimate for how likely the 'investment' is to succeed. With the waiting for the bus example, the probability of it arriving in the next minute ought to increase the longer you wait, but the longer you wait the greater the 'cost' if it doesn't arrive at all.
You may argue that if you can't estimate the probability then the problem has no solution. I'd just argue that this makes it a 'hard' problem ;-)
Am I reading this wrong, or do they actually want mathematicians to invent Asimov's Psychohistory?
One items mentions the "Holy Grail" with a link... to a wiki page about a Monty Python movie :-)
is on the minds of MANY people including the Manhattan project scientists. The fear is that they would get the bomb before any one else. It was a well founded fear.
GWB is only the latest proponent of deregulation and the view of 'government is the source of all problems' which you perhaps subscribe to.
As for the Community Reinvestment Act, it was intended to reduce discrimination in bank lending. These was NO requirement to lend specific kinds of products to specific groups of people. In fact, prudent lending was required. See a nice historical summary in this congressional testimony:
http://www.federalreserve.gov/newsevents/testimony/braunstein20080213a.htm
Where GWB is most culpable is in the lax (intentional?) enforcement of existing regulations. Fundings for many regulatory agencies were cut. Anti-regulatory heads of departments were appointed, etc..
Of course, I DO agrees that the prime drivers were private enterprises that loaded up too much risk without adequtae compensation.
How about: Requiring someone to do something stupid, doesn't change the fact that it's stupid :).