It isn’t “j” it is “i”!
If you get the comment/joke at 30:30 to 31:05, you are probably my kind of person. :)
Throwback Thursday
This photo is both painful and joyful for me. This was taken in May, 1981, when I graduated from the Naval Academy. My mom was my current age at that time.
Of note: I am at the age when most of my peers have lost or are losing their parents. It is merely the “bathtub curve” in action:
(not to scale for humans). This curve is used in reliability engineering. When a piece of equipment is put in place, there are some “early failures” (e. g. defective components) and as time goes on, there comes a point when the equipment fails due to wear and tear on the various components. And for humans, it looks a bit like (this is the U. K.):
This lists the “likelihood of dying” by age and sex. (From here)
Note: if this looks linear past the local minimum, look at the scale on left. It is a log scale, hence the linear appearance. It really is a bathtub curve.
The National Review “disses” Differential Equations
[...]One part insecure hipsterism, one part unwarranted condescension, the two defining characteristics of selfprofessed nerds are (a) the belief that one can discover all of the secrets of human experience through differential equations and (b) the unlovely tendency to presume themselves to be smarter than everybody else in the world. Prominent examples include [...]
(emphasis mine).
Oh noes! I love differential equations! :)
Yeah, I am just having fun with the quote; what really sticks in the craw of people like this is that many of us reject the idea that humans are the focal point of some deity and claim that “supernatural” explanations are really no explanation at all. :)
Keep in mind that the National Review is supposed to be their “intellectual” magazine; in fact, it probably ranks alongside Salon.
Politics: emotional issues robs us of abstract reasoning ability…
Good Vox article here. Moral (for me): mathematical and statistical reasoning really disciplines our thinking, BUT does not convince nontechnical people.
This is one reason discussing issues with people outside of math, science and engineering departments is so difficult for me.
Scientists figure out a bit about a toad’s brain (observation, hypothesis, experiment, model, predction)
First a bonus: Jerry Coyne’s website has a post about mayfly emergence showing up on radar!
Toad Brain Activity
A friend alerted me to this post, which is about how a toad reacts to stimuli which mimics prey in the wild. There was a bit of a “ha, ha, watch the stupid toad get “owned”” but the videos are quite interesting and illuminate how science works.
First, there is the observation (toad hunting a worm).
(photo: Heidi Carpenter)
Then some conjectures are made: “what type of stimuli elicits a “hunt” response”?
Then there is an series of “experiment followed by a refined conjecture”; here we see what “looks like” prey to the toad and what doesn’t, and what sort of response does the toad make? Then we look at the signals in the toad’s brain.
It turns out that there are a couple of receptors involved: one if the “predator” sensor is activated, it sends a signal which cancels the “hunt maneuver” response. How is this verified: one can disconnect the “canceling signal” pathway.
Then the whole lot is modeled by a neural network which elicits the predicted response. Yes, there is some mathematics that underlies this, which includes signal theory, neural networks, probability and possibly fuzzy set theory as the “predator/prey” sets appear to be fuzzy.
The videos total 30 minutes but are worth watching.
How even elementary math tricks our brain…
This simple example shows how a political campaign (or an advertising team) can use our intuitions to trick us, while remaining completely factual.
Suppose we ship 100 pounds of watermelons. At the start, each watermelon is 99 percent water (by weight).
The shipment arrives, and upon arrival, we find that some of the water has evaporated. Each watermelon is 98 percent water. There is no other change.
How much did the shipment weigh upon arrival?
Now our intuitions don’t handle things like percentages very well. Seriously.
So, what is the answer?
Start: the watermelons weigh 100 pounds: 99 pounds water, 1 pound notwater.
Finish: the 1 pound of “not water” is the same and comprises 2 percent of the arrival weight (arrival: 98 percent water).
So the finishing weight is: pounds.
Yes, going from 99 percent water to 98 percent water involves a loss of 50 pounds?
Don’t believe me?
99 pounds water + 1 pound not water = 100 pounds.
49 pounds water + 1 pound not water = 50 pounds, and which is 98 percent.
Imagine how this could be used in a political ad.
(Here I describe where I got the answer from; no I did not give the answer on this blog as that blog’s audience should have no difficulty solving this problem).
Fooling yourself to think that you are smarter than you are….
I just had a case of this on a professional level.
Though I teach college mathematics for a living, I have a modest publication record. (Example) But my research is in pure mathematics, and I am far from being elite…
So don’t even think about hitting me up for a loan. There is a reason I vote Democrat. :)
So, back to research….I am studying something called “wild knots” and “wild arcs“.
If you’ve had some calculus: roughly speaking, an arc can me thought of as the one to one image of a map from into 3 space. For example, think of a piece of string that isn’t allowed to intersect itself.
Arcs that come from differentiable functions are very well understood. What can be challenging to understand are arcs that are merely the image of continuous functions; for example:
.
This arc has no well defined tangent at the rightmost end point (where all the stuff curls up).
One known fact is: all arcs that have at most ONE point that doesn’t have a tangent (called a “wild point”) have a certain property called “being cellular”. It is a technical property; an implication of this property is that the set complement (everything in three space that is NOT on the arc) is “homeomorphic” to the complement of a smooth arc; that is, there exists a one to one, onto continuous map with continuous inverse, between the complement of this arc with a wild point to the complement of an arc that doesn’t have any wild points.
I was reviewing this fact and tried to produce a proof. I was able to and when I looked at my proof, it was the same proof that famous mathematician R. H. Bing produced in his book.
HA! I figured I was hot stuff for having been able to do what Bing did. Then I remembered: “who did you have your first graduate topology class from”? (yep, it was him). Where did you learn your topology from? (yes, from the University of Texas, where he had a major influence). OF COURSE I’d approach the problem in a similar way…it would have been strange if I didn’t.
The real genius is to be able to come up with new techniques on my own…and I didn’t do that. :)
Bottom line: those who we’ve studied and have talked to greatly influence what we are able to do; this is one reason that “closed” societies that didn’t have much contact with other societies didn’t progress nearly as much as those which did.
Some humor (intentional and unintentional)
The ankle is still slightly sore, so I’ll do a run on the treadmill and walk outside. I’ll write more later in the day; I am closing in on finishing some revisions for a paper.
You need a bit of math background to get the joke; hint: the sigma in the picture doesn’t stand for “sigma”.
(photo taken from a “wedding photo fails” collection): My guess that the above is an inside joke of some sort; perhaps it relates to an incident in the bride’s life? Something like this happened to my 8’th grade English teacher in class while she was walking around, checking student’s work at the desks. And, unlike these women, she was wearing hose but no underwear.
Rihanna takes a stand against visible panty lines.
Conservatives
This is the type of thing that your crazy email forwarding uncle is getting so worked up about:
Picky, picky, picky
A right wing US Senate candidate in South Dakota was charged with election fraud. Reason: she signed a statement that she personally witnessed people signing petitions to get her on the ballot. At the date of signing: she was actually overseas. Ooops.
Climate Change: that is Jesus getting angry with us:
Reading comprehension
I get a negative impression of conservatives because, well, the ones I encounter can’t understand what they read:
A bit of mathematics: discrete log problem
This is an interesting post about mathematics (“applied number theory”) and applications to cryptography.
Here is the discrete log problem: if one wants to solve, say, where is a positive real number and is a positive real number, then we know or, equivalently, where is the natural (base ) logarithm.
Now a field is a system of objects that can be added, multiplied where the usual distribution properties hold and each object, save the additive identity (the “zero”) has a multiplicative inverse; the usual examples are the real numbers, the rational numbers, the complex numbers, and the integers modulo a prime number).
A finite field is a field that has only a finite number of elements (say, the integers mod a prime number). Finite fields always have characteristic where is a prime number.
The discrete log problem is to solve where are known elements of the field. This problem doesn’t always has a solution even if the field is of characteristic .
Example: if we work “integers mod 7 ” and we wish to solve the solution does not exist. Why? therefore . The problem: the set of units mod(7) with multiplication from a group of order 6, and 2 generates a subgroup of order 3. Note that “4” generates a subgroup of order 2.
So, this is an interesting and difficult problem to solve, in general, at least in a “reasonable mount of time”.
Note: this is one branch of mathematics where it makes sense to do some experimentation, even though mathematical results require proof; an experiment with lots of data doesn’t cut it.
For more:

Archives
 August 2014 (60)
 July 2014 (112)
 June 2014 (92)
 May 2014 (78)
 April 2014 (91)
 March 2014 (94)
 February 2014 (80)
 January 2014 (79)
 December 2013 (81)
 November 2013 (66)
 October 2013 (86)
 September 2013 (81)

Categories
 2008 Election
 2010
 2010 election
 2012 election
 2014 midterm
 Aaron Schock
 Ad
 affirmative action
 Agricultural Commisioner
 aircraft
 Alabama
 alternative energy
 america
 April 1
 arizona
 astronomy
 atheism
 Barack Obama
 barback obama
 Barbara Boxer
 basketball
 bicycling
 Biden
 big butts
 bikinis
 bill maher on mosque
 bill richardson
 biology
 blog humor
 Blogroll
 blogs
 blood donation
 Bobby Jindal
 books
 boxing
 brain
 bushera
 business & economy
 butt
 Cheri Bustos
 civil liberties
 Claire McCaskill
 climate change
 college football
 comedy
 cop
 cosmology
 creationism
 d k hirner
 dark energy
 dave koehler
 deadline
 Democrats
 Dick Durbin
 Dick Morris
 disease
 dk hirner
 draw Mohammad day
 draw Muhammad day
 economics
 economy
 education
 edwards
 energy
 entertainment
 environment
 evolution
 extension
 family
 flu
 football
 Fox News Lies Again
 free speech
 Friends
 frogs
 geese
 glenn beck
 glenn hubbard
 green news
 ground zero mosque
 gwen ifill
 haunting songs
 health
 health care
 Herman Cain
 High Speed Rail
 hiking
 hillary clinton
 history
 hsr
 huckabee
 human sexuality
 humor
 if rich people have to pay taxes
 IL17
 IL18
 Illinois
 illness
 immigration. racial profiling
 injury
 internet issues
 interviews
 Intrade Prediction
 islamophobia
 jan brewer
 jim lehrer
 job
 Joe Biden
 John McCain
 jon stewart
 Judicial nominations
 knee rehabilitation
 lahood
 laughing at myself
 liars
 marathons
 mathematics
 matter
 mccain
 media
 michelle bachmann
 Mid Life Crisis
 Middle East
 Mike Huckabee
 mike's blog round up
 mind
 Mitt Romney
 money
 moron
 morons
 movies
 music
 nanotechnology
 national disgrace
 nature
 Navel Staring
 NBA
 neuroscience
 newshour
 Newt Gingrich
 NFL
 north america
 north carolina
 NSFW humor
 obama
 obesity
 Olympic Spandex
 Olympics
 Peoria
 Peoria/local
 Personal Issues
 photos
 physics
 Political Ad
 political humor
 political/social
 politics
 politics/social
 poll
 poor
 poverty
 public policy and discussion from NPR public radio program Science Friday with host Ira Flatow. Science Videos
 pwnd
 quackery
 racewalking
 racism
 ranting
 rebulican party
 recession
 relationships
 religion
 Republican
 republican party
 republican senate minority leader
 republicans
 republicans political/social
 republicans politics
 restaurants
 resume
 rich
 rick perry
 rick santorum
 running
 Rush Limbaugh
 sarah palin
 sb1070
 science
 Science Friday teachers
 Science Friday teens.
 SCOTUS
 shinkansen
 shoulder rehabilitation
 sickness
 social/political
 space
 spandex
 Spineless Democrats
 sports
 statistics
 stem cells
 stephen colbert
 story
 summer
 superstition
 swimming
 tax cuts
 taxes
 technology
 the colbert report
 Tim Pawlenty
 time trial/ race
 training
 trains
 Transportation
 travel
 ultra
 Uncategorized
 walking
 war on drugs
 wealth
 weight training
 whining
 wise cracks
 workouts
 world events
 WTF
 yoga

RSS
Entries RSS
Comments RSS