Workout notes Weights plus a 2.17 mile run on the treadmill (20 minutes; 9:13 pace): 10:09, 8:28 then a little bit more. I kept the incline at 0.5.
Weights: pull ups (5 sets of 10), hip hikes, Achilles, rotator cuff, bench: 10 x 135, 4 x 185, 7 x 170
ab series (3 sets of 10: crunch, v. crunch, twist, sit back), dumbbell military (3 sets of 12 x 50), dumbbell bench (2 sets of 10 x 65), dumbbell row (3 sets of 10 x 65), pull down (3 sets of 10 x 160), curl (3 sets of 10: 60, 60, 65; EZ curl bar).
It sure doesn’t seem like much.
A bit of math
Ok, a mathematician who is known to be brilliant self-publishes (on the internet) a dense, 512 page proof of a famous conjecture. So what happens?
The Internet exploded. Within days, even the mainstream media had picked up on the story. “World’s Most Complex Mathematical Theory Cracked,” announced the Telegraph. “Possible Breakthrough in ABC Conjecture,” reported the New York Times, more demurely.
On MathOverflow, an online math forum, mathematicians around the world began to debate and discuss Mochizuki’s claim. The question which quickly bubbled to the top of the forum, encouraged by the community’s “upvotes,” was simple: “Can someone briefly explain the philosophy behind his work and comment on why it might be expected to shed light on questions like the ABC conjecture?” asked Andy Putman, assistant professor at Rice University. Or, in plainer words: I don’t get it. Does anyone?
The problem, as many mathematicians were discovering when they flocked to Mochizuki’s website, was that the proof was impossible to read. The first paper, entitled “Inter-universal Teichmuller Theory I: Construction of Hodge Theaters,” starts out by stating that the goal is “to establish an arithmetic version of Teichmuller theory for number fields equipped with an elliptic curve…by applying the theory of semi-graphs of anabelioids, Frobenioids, the etale theta function, and log-shells.”
This is not just gibberish to the average layman. It was gibberish to the math community as well.
Here is the deal: reading a mid level mathematics research paper is hard work. Refereeing it is even harder work (really checking the proofs) and it is hard work that is not really going to result in anything positive for the person doing the work.
Of course, if you referee for a journal, you do your best because you want YOUR papers to get good refereeing. You want them fairly evaluated and if there is a mistake in your work, it is much better for the referee to catch it than to look like an idiot in front of your community.
But this work was not submitted to a journal. Interesting, no?
Of course, were I to do this, it would be ok to dismiss me as a crank since I haven’t given the mathematical community any reason to grant me the benefit of the doubt.
And speaking of idiots; I made a rather foolish remark in the comments section of this article by Edward Frenkel in Scientific American. The article itself is fine: it is about the Abel prize and the work by Pierre Deligne which won this prize. The work deals with what one might call the geometry of number theory. The idea: if one wants to look for solutions to an equation, say, one gets different associated geometric objects which depend on “what kind of numbers” we allow for . For example, if are integers, we get a 4 point set. If are real numbers, we get a circle in the plane. Then Frenkel remarked:
such as x2 + y2 = 1, we can look for its solutions in different domains: in the familiar numerical systems, such as real or complex numbers, or in less familiar ones, like natural numbers modulo N. For example, solutions of the above equation in real numbers form a circle, but solutions in complex numbers form a sphere.
The comment that I bolded didn’t make sense to me; I did a quick look up and reviewed that actually forms a 3-sphere which lives in . Note: I added in the “absolute value” signs which were not there in the article.
This is easy to see: if then implies that . But that isn’t what was in the article.
Frenkel made a patient, kind response …and as soon as I read “equate real and imaginary parts” I winced with self-embarrassment.
Of course, he admits that the complex version of this equation really yields a PUNCTURED sphere; basically a copy of in .
Just for fun, let’s look at this beast.
Real part of the equation:
Imaginary part: (for you experts: this is a real algebraic variety in 4-space).
Now let’s look at the intersection of this surface in 4 space with some coordinate planes:
Clearly this surface misses the plane (look at the real part of the equation).
Intersection with the plane yields which is just the unit circle.
Intersection with the plane yields the hyperbola
Intersection with the plane yields the hyperbola
Intersection with the plane yields two isolated points:
Intersection with the plane yields two isolated points:
(so we know that this object is non-compact; this is one reason the “sphere” remark puzzled me)
Science and the media
This Guardian article points out that it is hard to do good science reporting that goes beyond information entertainment. Of course, one of the reasons is that many “groundbreaking” science findings turn out to be false, even if the scientists in question did their work carefully. If this sounds strange, consider the following “thought experiment”: suppose that there are, say, 1000 factors that one can study and only 1 of them is relevant to the issue at hand (say, one place on the genome might indicate a genuine risk factor for a given disease, and it makes sense to study 1000 different places). So you take one at random, run a statistical test at and find statistical significance at . So, if we get a “positive” result from an experiment, what is the chance that it is a true positive? (assume 95 percent accuracy)
So let P represent a positive outcome of a test, N a negative outcome, T means that this is a genuine factor, and F that it isn’t.
Note: P(T) = .001, P(F) = .999, . It follows
So we seek: the probability that a result is true given that a positive test occurred: we seek . That is, given a test is 95 percent accurate, if one is testing for something very rare, there is only about a 2 percent chance that a positive test is from a true factor, even if the test is done correctly!
Weather and more tornadoes
It isn’t a coincidence that the tornadoes hit after we had some warm spring weather: up to know, we’ve had an unusual cool spring thanks to the jet stream dipping down lower than normal. A side effect was a lighter than normal tornado season. Unfortunately that didn’t last:
Mind: soldiers and brain trauma.
It is no secret that soldiers can suffer a brain injury which doesn’t obviously show. But here is the rub: what if a soldier had a reputation for being a malcontent prior to the brain injury and then gets one. Then:
What happened when he came home is increasingly typical, too. At Fort Carson, the damaged soldier racked up punishments for being late to formation, missing appointments, getting in an argument and not showing up for work. These behaviors can be symptoms of TBI and PTSD, and Army doctors recommended Alvaro go to a special battalion for wounded warriors. Instead, his battalion put him in jail, then threw him out of the Army with an other-than honorable discharge that stripped him of veterans benefits. He was sent packing without even the medicine to stop his convulsions.
“It was like my best friend betrayed me,” Alvaro said at the hospital, his speech as slow as cold oil. “I had given the Army everything, and they took everything away.”
But, what if at least some of this behavior was present PRIOR to the brain injury?
“It’s hard to figure out,” said Maj. Gen. Anderson, who was the final authority for discharging soldiers at Fort Carson. “You are asking young captains, 30-year-old guys, platoon leaders, 25 years old, to decide if this guy is sick or this guy is not sick when the doctors don’t know for sure.”
The uncertainty sets up clashes. The Gazette has uncovered several cases at Fort Carson where doctors and commanders were in direct conflict. Doctors sent one soldier who pointed a gun at the soldiers in his squad to a psychiatric hospital, and commanders pulled him out and put him in jail. Doctors said another soldier who tested positive for marijuana could not be kicked out because he had a brain injury. Commanders discharged him anyway. Another soldier tried to commit suicide by crashing his car into a light pole. Doctors said he had PTSD and depression; commanders discharged him for damaging property.
Several doctors contacted at Fort Carson refused to comment.
It really isn’t easy and clear-cut, is it?
Light weight workout (reduced significantly):
rotator cuff, Achilles, hip hikes, back: full set (PT)
light squats: one set of 5 with 45 (assisted stretching really)
pull ups: 3 sets of 10; tried to minimize unnecessary body movement.
incline press: 5 x 135, 2 x 150, 1 x 165, failed at 175, 1 x 170 (easy!), 8 x 145.
military dumbbell: 2 sets of 12 x 50 lb.
dumbbell rows: 2 sets of 10 x 65 each arm
pull downs: 2 sets of 10 x 160
curls (machine), 2 sets of 10 x 70
It is real; this weekend is going to be hard. Mentally: I am a basket case (more so than normal).
A good aside: I THINK that I solved a math problem that has vexed me for 20 years; I’ll spend the next week or so verifying that I have a solution. I’ve been fooled before.
Some friends thought that I’d like this photo..for some reason.
Here is a nice synopsis on it. Even better: this is a nice reminder that, if you are not a physicist, your “common sense” suggestions of what dark energy might be (or what might replace dark energy as a factor) have been thought of and dismissed.
Woo and evolution Jerry Coyne takes the Chronicle of Higher Education to task for giving woo notions (with regards to evolution) credibility. My guess: even some academics can’t seem to stomach the notion that “you don’t know what you are talking about” IS a valid reason to dismiss an argument in science. Where it is true that, in some cases, it is valid to entertain different points of view (example) that does NOT mean that all points of view have validity.
It is a current conjecture that there are an infinite number of “paired primes”; that is, numbers where and are prime integers. Until recently, no one has come up with any bound for pairs of primes…at all. Evidently, that has changed (note: Annals of Mathematics is the finest mathematics journal in the world):
It’s a result only a mathematician could love. Researchers hoping to get ‘2’ as the answer for a long-sought proof involving pairs of prime numbers are celebrating the fact that a mathematician has wrestled the value down from infinity to 70 million.
“That’s only [a factor of] 35 million away” from the target, quips Dan Goldston, an analytic number theorist at San Jose State University in California who was not involved in the work. “Every step down is a step towards the ultimate answer.”
That goal is the proof to a conjecture concerning prime numbers. Those are the whole numbers that are divisible only by one and themselves. Primes abound among smaller numbers, but they become less and less frequent as one goes towards larger numbers. In fact, the gap between each prime and the next becomes larger and larger — on average. But exceptions exist: the ‘twin primes’, which are pairs of prime numbers that differ in value by 2. Examples of known twin primes are 3 and 5, or 17 and 19, or 2,003,663,613 × 2195,000 − 1 and 2,003,663,613 × 2195,000 + 1.
The twin prime conjecture says that there is an infinite number of such twin pairs. Some attribute the conjecture to the Greek mathematician Euclid of Alexandria, which would make it one of the oldest open problems in mathematics.
The problem has eluded all attempts to find a solution so far. A major milestone was reached in 2005 when Goldston and two colleagues showed that there is an infinite number of prime pairs that differ by no more than 16. But there was a catch. “They were assuming a conjecture that no one knows how to prove,” says Dorian Goldfeld, a number theorist at Columbia University in New York.
The new result, from Yitang Zhang of the University of New Hampshire in Durham, finds that there are infinitely many pairs of primes that are less than 70 million units apart without relying on unproven conjectures. Although 70 million seems like a very large number, the existence of any finite bound, no matter how large, means that that the gaps between consecutive numbers don’t keep growing forever. The jump from 2 to 70 million is nothing compared with the jump from 70 million to infinity. “If this is right, I’m absolutely astounded,” says Goldfeld.
In a nutshell: Zhang has proved that there exists infinitely many prime numbers where . Seriously, until now, we had no upper bound at all.
Economy: job growth continues to be weak:
We remain in the gravitational pull of the Great Recession. The Labor Department reports that 165,000 new jobs were created in April – below the average gains of 183,000 in the previous three months.
We can’t achieve escape velocity. Since mid-2010, the three-month rolling average of job gains hasn’t dipped below 100,000 but has exceeded 250,000 jobs just twice.
This isn’t enough to ease the backlog of at least 3 million (estimates range up to 8 million) job losses since 2007, just before the Great Recession began. (And as I’ll point out in a moment, 2007 wasn’t exactly jobs nirvana.)
Moreover, most of the new jobs now being created pay less than the ones that were lost.
First, government is doing exactly the opposite of what it should be doing. It raised payroll taxes in January (ending the temporary tax holiday), thereby reducing the incomes of the typical family by about $1,000 this year.
More damaging, government cut spending through the damnable sequester – thereby reducing overall demand for goods and services. (Direct government employment dropped another 11,000 in April.)
There’s also a deepening structural problem. All the economic gains from the recovery have gone to the very top, leaving the middle class (and everyone aspiring to join it) with a shrinking portion of the pie.
Consumers are still spending, but tentatively at best. And much of the spending is coming from the rich, whose stock portfolios have grown nicely. (The wealthiest 10 percent of Americans own 90 percent of all shares of stock.)
But the rich don’t spend as much of their earnings as everyone else. They save and speculate around the world wherever they can get the highest return.
We have a demand problem; businesses won’t hire unless there is demand to warrant it.
And no: we don’t always call for more spending; spending is for bust times; austerity is for boom times.
Every so often, someone announces that they have solved a big problem. What happens: mathematicians check the solution…and the vast majority of the time: it isn’t a correct solution. This recently happened with the claim:
On August 6, 2010, a computer scientist named Vinay Deolalikar published a paper with a name as concise as it was audacious: “P ≠ NP.” If Deolalikar was right, he had cut one of mathematics’ most tightly tied Gordian knots. In 2000, the P = NP problem was designated by the Clay Mathematics Institute as one of seven Millennium Problems—“important classic questions that have resisted solution for many years”—only one of which has been solved since. (The Poincaré Conjecture was vanquished in 2003 by the reclusive Russian mathematician Grigory Perelman, who refused the attached million-dollar prize.)
A few of the Clay problems are long-standing head-scratchers. The Riemann hypothesis, for example, made its debut in 1859. By contrast, P versus NP is relatively young, having been introduced by the University of Toronto mathematical theorist Stephen Cook in 1971, in a paper titled “The complexity of theorem-proving procedures,” though it had been touched upon two decades earlier in a letter by Kurt Gödel, whom David Foster Wallace branded “modern math’s absolute Prince of Darkness.” The question inherent in those three letters is a devilish one: Does P (problems that we can easily solve) equal NP (problems that we can easily check)? [...]
If Deolalikar’s audacious proof were to hold, he could not only quit his day job as a researcher for Hewlett-Packard but rightly expect to enter the pantheon as one of the day’s great mathematicians. But such glory was not forthcoming. Computer scientists and mathematicians went at Deolalikar’s proof—which runs to dozens of pages of fixed-point logistics and k-SAT structures and other such goodies—with the ferocity of sharks in the presence of blood. The M.I.T. computational theorist Scott Aaronson (with whom I consulted on this essay’s factual assertions) wrote on his blog, “If Vinay Deolalikar is awarded the $1,000,000 Clay Millennium Prize for his proof of P ≠ NP, then I, Scott Aaronson, will personally supplement his prize by the amount of $200,000.” It wasn’t long before Deolalikar’s paper was thoroughly discredited, with Dr. Moshe Vardi, a computer-science professor at Rice University, telling the Times, “I think Deolalikar got his 15 minutes of fame.”
As Lance Fortnow describes in his new book, “The Golden Ticket: P, NP and the Search for the Impossible,” P versus NP is “one of the great open problems in all of mathematics” not only because it is extremely difficult to solve but because it has such obvious practical applications. It is the dream of total ease, of the confidence that there is an efficient way to calculate nearly everything, “from cures to deadly diseases to the nature of the universe,” even “an algorithmic process to recognize greatness.” So while a solution for the Birch and Swinnerton-Dyer conjecture, another of the Clay Millennium Prize problems, would be an impressive feat, it would have less practical application than definitive proof that anything we are able to quickly check (NP), we can also quickly solve (P).
For a “quick and dirty” of P versus NP, read this. Basically, the “P” stands for “polynomial time” and things that can either be checked or solved in polynomial time are more tractable. A problem is “P” if it can be solved in polynomial time and a problem is “NP” if a solution can be verified in polynomial time. Now it is “common sense” that it should be easier to check if a solution is correct than to come up with the correct solution to begin with, but as of right now, we don’t have a proof of this assertion.
To see what I am talking about: suppose you have a graph with nodes (think of this as a collection of cities in, say, a state with the roads between the cities being the segments of the graphs. If you want to find the shortest path in a graph from one vertex to another (say, find the shortest distance to get from Peoria to Chicago via roads), that is an example of a P problem; it can be readily solved in a reasonable amount of time.
On the other hand, if you wanted to solve the “travelling salesman problem” (find the shortest path to travel to ALL cities, hit each city only once and then return); that problem is “NP complete”: it might not be solvable in a reasonable amount of time in all cases.
I didn’t sleep well (Mexican meal too heavy last night?)
I got up early and walked 4.47 miles in 1:06 (14:52 pace) doing roughly the same course I did yesterday, minus a .7 mile out and back and a .3 out and back near the soccer fields.
It was in the 40′s and crisp; I got to see the sun rise.
Talks: the morning talks were good but tough; still I managed to pick up techniques at every one of them.
Several people said that they would have to leave prior to my talk; I expected that (4 pm slot). Some might still be there and I owe them a professional effort; I practiced my talk twice.
Campus: very pretty
I am in the background, near the rear of the room (white beard).
This is a small group, but the speaker and many that you can see are among the world’s best topologists.
It was a different story at my hotel room:
5.7 mile run over lunch; 57 minutes.
Going to research meetings is always eye-opening. On one hand, I often learn something and pick up techniques and ideas that I can use.
On the other hand: I am seeing people who, for the most part, research and direct graduate students for a living. This is very different from what I am used to (teaching moderately talented undergraduates relatively elementary things).
The blunt fact is that the researchers are not only the best that graduate school graduating classes have to offer (I wasn’t) but they are also people who do it full time; if you teach a 11-12 hour load (with administrative duties to boot) you are NOT going to research at that level. But it is easy to forget that if you don’t take in one of these from time to time. Those who don’t: often lose perspective.
Yes, this is a Salon article and the title is misleading. But it does raise a point:
The heads and hearts of atheists may not be on precisely the same page. That’s the implication of recently published research from Finland, which finds avowed non-believers become emotionally aroused when daring God to do terrible things.
“The results imply that atheists’ attitudes toward God are ambivalent, in that their explicit beliefs conflict with their affective response,” concludes a research team led by University of Helsinki psychologist Marjaana Lindeman. Its study is published in the International Journal for the Psychology of Religion.
Lindeman and her colleagues describe two small-scale experiments. The first featured 17 Finns, recruited online, who expressed high levels of belief, or disbelief, in God. They read out loud a series of statements while skin conductance data was collected via electrodes placed on two of their fingers.
Some of the statements were direct dares to a deity (“I dare God to make my parents drown”). Others were similarly disturbing, but did not reference God (“It’s OK to kick a puppy in the face”). Still others were bland and neutral (“I hope it’s not raining today”).
The arousal levels of the believers and non-believers followed precisely the same pattern: Higher for both the God dares and otherwise unpleasant statements, and lower for the neutral ones.
Compared to the atheists, the believers reported feeling more uncomfortable reciting the God dares. But skin conductance data revealed the underlying emotional reactions of the two groups were essentially the same. This suggests that taunting God made the atheists more upset than they were letting on (even to themselves).[...]
The second experiment was designed to test that hypothesis. It featured 19 Finnish atheists, who participated in an expanded version of the first experiment. It included 10 additional statements—variations on the God dares which excluded any mention of supernatural forces. For example, in addition to “I dare God to turn all my friends against me,” they read out loud the statement: “I wish all of my friends would turn against me.”
The results: The atheists showed greater emotional arousal when reading the God-related statements than while reading the otherwise nearly identical sentences that omitted the almighty. To the researchers, this indicates that “even atheists have difficulty daring God to harm themselves and their loved ones.”
Note: the “n” is rather low.
The article goes on to make conjectures as to why this might be so. I’ll make mine:
my position of atheism is NOT so much an emotional one as an intellectual one. I see no evidence of divine intervention in human affairs and the idea that there is a “interested in human events” deity in such a large universe with billions of galaxies and billions of stars per galaxy makes no sense to me. I just don’t believe it.
But I WAS raised Catholic; my dad wasn’t a religious man but believed in a deity of some sort; mom believed in “magic tricks” of a deity (one that intervened). So I was raised that way and I have the resulting emotions. I sometimes ask a non-existent deity to eternally condemn inanimate objects when they break or spill (or when I break them ).
But emotions and emotional actions are hard to turn off.
I’ll give an example: I know that my stuffed frogs are inanimate objects. But I’d feel bad if, say, they burned in a fire and I’d get very angry if someone “mistreated” them. That is an emotional, irrational reaction. I’d have the same about religious stuff even though my mind knows better.
This is only for my records: last night saw me getting up a LOT and a LOT of pink bismuth. Otherwise, I don’t feel that bad; I was told by my spouse (who lovingly gave me this bug ) that this should “pass” in a couple of more days.
I might walk again today and try something approaching a full workout tomorrow.
So, just a bit of humor:
- 2008 Election
- 2010 election
- 2012 election
- Aaron Schock
- affirmative action
- Agricultural Commisioner
- alternative energy
- April 1
- Barack Obama
- barback obama
- Barbara Boxer
- big butts
- bill maher on mosque
- bill richardson
- blog humor
- blood donation
- Bobby Jindal
- business & economy
- Cheri Bustos
- civil liberties
- Claire McCaskill
- climate change
- college football
- d k hirner
- dark energy
- dave koehler
- Dick Durbin
- Dick Morris
- dk hirner
- draw Mohammad day
- draw Muhammad day
- Fox News Lies Again
- free speech
- glenn beck
- glenn hubbard
- green news
- ground zero mosque
- gwen ifill
- haunting songs
- health care
- Herman Cain
- High Speed Rail
- hillary clinton
- human sexuality
- if rich people have to pay taxes
- immigration. racial profiling
- internet issues
- Intrade Prediction
- jan brewer
- jim lehrer
- Joe Biden
- John McCain
- jon stewart
- Judicial nominations
- knee rehabilitation
- laughing at myself
- michelle bachmann
- Mid Life Crisis
- Middle East
- Mike Huckabee
- mike's blog round up
- Mitt Romney
- national disgrace
- Navel Staring
- Newt Gingrich
- north america
- north carolina
- Olympic Spandex
- Personal Issues
- Political Ad
- political humor
- public policy and discussion from NPR public radio program Science Friday with host Ira Flatow. Science Videos
- rebulican party
- republican party
- republican senate minority leader
- republicans political/social
- republicans politics
- rick perry
- rick santorum
- Rush Limbaugh
- sarah palin
- Science Friday teachers
- Science Friday teens.
- shoulder rehabilitation
- Spineless Democrats
- stem cells
- stephen colbert
- tax cuts
- the colbert report
- Tim Pawlenty
- time trial/ race
- war on drugs
- weight training
- wise cracks
- world events