Retirement savings (a rant of sorts)

One of the various and sundry people who provide personal viewpoints on Sunday morning TV delivered an editorial this morning on the necessity of having personal retirement savings. Now I don't disagree with this and I'm pretty well resigned to working until I die because I no longer have any savings for retirement. Why is this? Well....

My late husband had early onset Alzheimer's disease (diagnosed in his early 50's). Neither his job nor mine provided any medical insurance let alone insurance to cover long term care. Once he could no longer be left home alone, I quit working to take care of him. The cost of home care was prohibitive - more than I was earning even with two jobs. His social security disability included Medicare, but medicare doesn't cover home health care, long term care, or prescriptions. Unfortunately he reached a point where I could no longer care for him so that both of us would be safe. Enter the long term care dilemma and using state Medicaid. This was the only way to provide him the necessary care, but excluding the house and including all monthly income, we were allowed....are you ready?.....$2500 in assests. By the time we took his social security income and the value of my car, we were at the limit. Note that any kind of insurance policy or prepaid burial was included in this assest limit. So I have no savings and will most likely not earn enough in the next ten years (theoretical retirement time) to save enough to even consider retirement. And by the way, I still have no medical insurance because I can not afford to pay for it with no access to a group policy. On the other hand I'm very healthy.

The sort of rant? We need to find a way around this kind of idiocy. I don't particularly want to lose half my income to taxes to cover health care and retirement, but the current situation is disastrous for many people. I'm lucky since I'm healthy, prefer working over sitting around getting old, and own my home. But what about the people who aren't as fortunate as I am? Are we going to end up with lots of homeless elderly people who have limited or no access to medical care? There are a lot of people who work hard all their lives, but are not in a position to save for retirement. They're called the working poor. Technically these days, I'm one of them.

That's all. And probably the only time I'll go political here. I much prefer math.

Mathematical "proof" of the existence of God?

Via Bayesian probability here

Is this a sign?

It's raining again - a nor' easter. There are flood watches and high wind warnings out. On my way to school and work this morning the radio played Creedence Clearwater's Bad Moon Rising. Do you think this might be a sign? *snicker*

Tidbits from Ars Mathematica

This past week my favorite math blog, Ars Mathematica, has had two posts that relate to the seminar (Nature & Origins of Consciousness) I'm taking this semester. I doubt the mathematician intended this, but stuff happens. So now I can entertain you with information you never wanted to know about.

On October 19th, this notice appeared: Week 222 of This Week’s Finds in Mathematical Physics is up. If you go to this link, #2 - #5, talk about the idea of singularity - not the black hole math singularity thing, but a point where technological development goes beyond us.

2) Charles Stross, Accelerando, Ace Books, New York. Also available at http://www.accelerando.org/book/

This is one of the few tales I've read that does a good job of fleshing out Verner Vinge's "Singularity" scenario, where the accelerating development of technology soars past human comprehension and undergoes a phase transition to a thoroughly different world. This is a real possibility, and it's been discussed a lot:

One of the things we've discussed fairly extensively in class is what constitutes consciousness and whether an AI machine or a robot is truly conscious. Since I'd never read about this particular idea (singularity), I followed the links to learn some more. Kind of scary when I'm reading that this point in technology is predicted to occur by 2030.

October 23rd's post says "According to a new paper on Arxiv, Goedel’s theorem is false. There you have it." I haven't read the paper, but I'm assuming that it refers to Goedel's incompleteness theorem. One of the more interesting books I've read on consciousness was written by a mathematician (Shadows of the Mind by Roger Penrose, 1994). In the book, Penrose uses Goedel's incompleteness theorem to refute the possibility of creating a conscious machine. Does this mean Penrose isn't buying the singularity idea?

Math and psychology meet on the horizon of physics.

Counting and negative numbers question for all.

In mathematics there is a set of axioms called "Peano's Axioms" which are the basis for proof by induction. These axioms also build the set of natural numbers (1, 2, 3, .......) or counting numbers. There are some interesting studies by psychologists that seem to show that these axioms exist at an unconscious level in children and primates. The psychologists aren't referencing the axioms, it's just something I noticed when reading the papers. It's pretty cool and gives me something to think about when I'm driving.

So....here I am driving down the road and thinking about how we learn to count and when different number concepts were incorporated into arithmetic and mathematics. Which gets me to negative numbers. You can conceptualize the natural numbers and fractions (rational numbers), but how do you conceptualize a negative number? When numbers are thought of as quantities, what is a negative quantity? Any ideas out there?

If you have some uncontrollable desire to read about Peano's axioms, there is a good description here at Wikipedia.

Happy Happy Joy Joy

My road is open in both directions! There's still paving and guard rails to go, but I can drive through the much much shorter way. I'm hoping the paving is done before the weekend since the local weather is forcasting heavy rains this weekend.

That's all.

Hypothesis, Theory, and Proof (very long)

One of the classes I'm taking this semester is a senior seminar entitled "Nature and Origins of Consciousness." We've looked at and discussed different historical explanations for consciouness and have now wandered into a discussion of intelligent design vs evolution. Which leads me to the concepts of hypothesis, theory, and proof (and a rant).

I'm finding that scientists, psychologists, mathematicians, and the general population use each of these terms in somewhat different ways. Everyone seems to use hypothesis to denote an unproved idea. A scientific or mathematical hypothesis appears to be a complete idea. It's the theory and proof concepts where problems occur.

For scientists and mathematicians, a theory (or theorem) is an hypothesis that has been proven. For psychologists, a theory is a logically organized set of statements that include definitions of various events or concepts, contain information about relationships between these events, explain the causes of the events where the hypothesis is simpler and more tentative. (I just had to memorize this for a test.)

Psychologists and scientists consider a theory proved when they can show significant evidence for it and when the theory exhibits good predictive validity. Einstein's theory of relativity was considered proven once phenomena predicted by the theory was shown to exist and when phenomena behaved in ways the theory predicted. In psychology proofs of theories are really statistical analyses of experimental data showing that the hypothesis based on the theory has a good probability of being true.

Since people (and the larger world in general) aren't particulary tidy, proof is not a 100% probability, true in all cases, concept for psychologists or scientists. This is also one of the reasons why theories are changed (or thrown out completely). As we learn more and gain more evidence, theories are modified. Sometimes the modifications become so unwieldy that science is forced into rethinking the whole idea. This is how science grows, but this does not automatically invalidate science.

Mathematicians (who are anal retentive) define a proof as a logical and rigourous mathematical argument. Unfortunately exhaustive evidence is not a proof. The mathematician must show that the hypothesis is true for all instances. For example, if I want to show that the sum of the numbers from 1 to n (n is any counting number greater than 1) = n(n+1)/2, just summing all the numbers from 1 to n=2, 1 to n=3, 1 to n=4, and so on for however long I want to go doesn't constitue proof. I could have done the sums a million times and all equaled n(n+1)/2, but that's not a proof. The proof involves an argument that shows this is true for all values of n. (BTW - this has been proved.)

The nice thing about this? Once a theorem is proved in mathematics, it stays proved. Euclid showed a proof of the PythagoreanTheorem that is still valid. The not so nice thing? Hypothesis that appear to work and for which there is a lot of evidence, but no proof. My personal favorite is the Riemann Hypothesis - unproven, but over a million solutions have been calculated and all agree with the hypothesis.

Remember what I said about people not being as tidy as numbers? I have to remind myself of this on a regular basis. Otherwise, I can't look at any psychological theory as proven. I learned the concept of proof in terms of mathematics.

Looking at the arguments "against" Darwin's theory of evolution, it seems that the general population defines both hypothesis and theory as an unproven idea and expects proof to be similar to a mathematicians - 100% true in all cases. The fact that evolutionary theory has significant amounts of evidence and excellent predictive value doesn't appear to convince people of its validity. I end up with a problem though when the counter proposal involves an unknown intelligence for which no evidence is available and a theory with no apparent predictive value.

Of course I also have a problem with the definition of a transcendental number - a number which is not algebraic. Hello, tell me what it is not what it isn't.

Mathematics and Arithmetic

Contagion asked, "What exactly is the difference between mathematics and arithmetic." There's a short answer and a longer answer. Since I live to ramble on about math, this is the longer answer.

Arithmetic is simply the calculation/computational discipline. In terms of my particular interest in mathematical cognition, I consider arithmetic one of the building blocks necessary to mathematics.

Mathworld (a really great online source for short answers to math questions and just fun reading) defines arithmetic as "the branch of mathematics dealing with integers or, more generally, numerical computation. Arithmetical operations include addition, congruence calculation, division, factorization, multiplication, power computation, root extraction, and subtraction. " (http://mathworld.wolfram.com/Arithmetic.html)

Balancing your checkbook is arithmetic. Having a degree in mathematics does not mean that I'm any better (probably significantly worse) at that than the average person.

Mathematics is more difficult for me to define because it covers many areas so back to Mathworld for a definition. "Mathematics is a broad-ranging field of study in which the properties and interactions of idealized objects are examined." (http://mathworld.wolfram.com/Mathematics.html) Things like logic, which is essential to proofs, figure prominently in the study of mathematics.

Mathworld's main index lists the following topics and serves as a fairly good example of what is included in mathematics: Algebra, Applied Mathematics, Calculus and Analysis, Discrete Mathematics, Foundations of Mathematics, Geometry, History and Terminology, Number Theory (my personal favorite), Probability and Statistics, Recreational Mathematics, and Topology. No arithmetic. The foundations of mathematics section includes axioms, logic, set theory, and theorem proving. Again, no arithmetic.

If you look at the history of mathematics, different maths were developed to serve the needs of people. All mathematics through calculus were application driven and strongly tied to arithmetical calculations. Early in the 19th century, math went crazy (probably too much math happy juice) and new maths were developed for their own sake. It happens that many of these "pure" maths have applications in today's world, but the applications came later and are only of interest to applied mathematicians (or scientists, engineers, etc.) using them.

Have I put you to sleep yet? LOL If not, here's one of my favorite math quotes - A mathematician is a machine for converting coffee into theorems.

The Bad Example Family has a black sheep

Check out my welcome -

It's a Girl

Reality Check

I got out to work and school today. One of my friends from school was evacuated early Sunday morning. She's been allowed back to her house to start cleaning up, but has lost quite a bit of stuff. Another student in one of my classes got caught in a flash flood on her way home from the library on Saturday. Her car, her text books, her notebooks, her computer, and her bike are toast. I know that I came out of this with little more than inconvenience.

If you want to see pictures and video from the area, check out the online coverage from the local TV station at www.theWMURChannel.com

And more rain (possibly 3 - 5") with flash flood warnings are up for Wednesday evening into Thursday.

It Rained

And then it rained some more. My road did not make out too well. If I make a right turn out of my driveway, this is what I find.

This is an issue for me because until it’s fixed my drive to work goes from 12.5 miles each way to 22.5 miles each way. Since I go from home to work to school, I’m ending up with way more driving than seems reasonable for a part-time job. Oh well. It’s just a temporary job and I’ll probably end up looking for something else soon since I’m in week 18 of a 6 week job. LOL

If I make a left turn and drive about 2 miles, this is what I find.

Around noon today, the town filled in this little hole enough for my housemate to get out and buy food for the birds (chickens, ducks, and geese – oh my!). But my road is now on the list of road closures on the TV, so who knows what tomorrow will bring.

On the bright side, my house is intact and dry.

Arithmetic and numerical processing are NOT Mathematics!

I recently purchased a relatively expensive book titled "Handbook of Mathematical Cognition" (2005). In the preface the editor defines mathematical cognition as "...the field of research concerned with the cognitive and neurological processes that underlie numerical and mathematical abilities." In the next paragraph, he says that the book is "a collection of twenty-seven essays by leading researchers in the field, and constitutes a comprehensive survey of state-of-the-art research on important facets of mathematical cognition."

Now, turn to the table of contents. Of the twenty-seven essays, eighteen are strictly number or arithmetic based papers. One definitely deals with mathematics. The remaining eight papers may or may not be about mathematics since I can not be sure just from the titles.

I had a number of reasons for buying the book and I'm not disappointed. Just from the research I've been doing the past two years, this was more or less what I expected.

I have a degree in Applied Mathematics which means that I spend way too much time explaining that I am not a good candidate for a job in accounts payable/receivable/payroll, etc. A math degree does not equal "good at and likes doing arithmetic." Arithmetic is one of the skills that provide a foundation for mathematics. It is not mathematics. Arithmetic and mathematics take place in different areas of the brain - they're neurologically different. So, everyone repeat ten times a day until you've learned it - arithmetic is NOT mathematics!

I'm Surprised

I didn't really expect anyone to wander off and read this let alone offer a welcome. Of course I haven't said anything yet that will cause you to enter a comatose state. Once I do, you all will remember Teresa's greeting (*** Sending over a bottle of Drambuie to start you off right - THAT should certainly be interesting - drunk blogging at its finest! *grin*) and beg me to hurry up and drink the Drambuie. The good news there - it only takes one drink and I'm toast. *snork*

Thanks to all of you who welcomed me to the family. *grin*

Just because there should be more than one post.

Tentative classes for the spring semester

1. Psychology of Learning

2. History & Systems of Psyc

3. Honors Seminar

4. Honors Research Project

5. Ethology (maybe)

Anybody who is foolish enough to ask what the research project is will be answered.

The stupid thing ate the first post. It was very important, so I will repeat.

This is here just so Snakeypoo can have a blog offspring who is a left of center math deviant geek.