blueollie

My take on Birthdays

Now, if there is some omnipotent deity that knows when you will die, this is correct. But as someone else points out: we die via a “bathtub curve” function.

That is, given our current age, say $x$, we have an “expected time left to live $l(x)$ and as we age, the quantity $x + l(x)$ increases, even though, after the risk of early death is over, $l(x)$ is a decreasing function of $x$.

Of course, $l(x)$ is changed if there is a war, famine, pestilence, etc.

September 16, 2014

Calculus gets dissed by Burl….

Note: if you haven’t followed Julie Larson’s comic strip Dinette Set, Burl is, well, not the world’s most intellectually minded character. Neither are Timmy’s grandparents. :-)

Ironically, I see such attitudes displayed by people…posting their thoughts on the internet via a computer or smart phone. The irony doesn’t even occur to them.

August 25, 2014

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. :-)

August 6, 2014

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.

July 31, 2014

The National Review “disses” Differential Equations

[...]One part insecure hipsterism, one part unwarranted condescension, the two defining characteristics of self-professed 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.

July 30, 2014

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 non-technical people.

This is one reason discussing issues with people outside of math, science and engineering departments is so difficult for me.

July 29, 2014

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.

July 22, 2014

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 not-water.
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: $\frac{1}{.02} = 50$ 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 $\frac{49}{50} = .98$ 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).

July 15, 2014

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 $f$ from $[0,1]$ 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.

July 12, 2014

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 e-mail 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:

June 5, 2014