Sunday, April 5, 2009

Unanswered questions

One of the things I really enjoyed about being a high-school teacher was being able to ask the Science teachers all manner of interesting questions. One of the things I love thinking about are extremes, for example:

  • The highest mountain (Everest 8,848m)
  • The deepest ocean trench (Mariana Trench, 11,000m)
  • The smallest particles (subatomic particles)
  • The distance at which the Earth's atmosphere ends (outer edge of the exosphere 190,000 km, half way to the moon, where the remaining atmospheric particles are overwhelmed by the gravitational pull of the solar wind)
However I still have lots of outstanding questions, for example:
  • The largest known object in the universe?
  • Is it possible to have a coldest possible theoretical temperature, what would be the limits?
  • Can disorders like say Autism occur on a spectrum and if so what's the name for non-medically treated part of the spectrum?
  • Are Bell curves the only types of 2D curves for data?


Radagast said...

The coldest theoretical temperature is "absolute zero", −273.15°C, and I believe people have gotten quite close to that in the lab.

Physicists often measure temperature in "kelvins" which are degrees that start counting from absolute zero. If you do that, a whole lot of mathematics comes out nicely, such as the fact that the amount of energy emitted by an object at temperature T will be T to the fourth power.

Autism indeed occurs on a spectrum, and people speak of "autism spectrum disorders".

There are suggestions that mild autism trails off into the behaviour of perfectly ordinary engineers. Interestingly, autism is more common than average in the families of engineers, physicists, and mathematicians.

Bell curves are not the only 2D curves for data, but they are very common because they result when many small and independent differences add up, as in, say, the heights of adult men. When two or more large differences get thrown in, you can get "two-humped" bell curves. When differences are not independent, you can get various different kinds of skewed curves, such as the famous "long tail."

Luke said...

Cool, thanks Tony.

RE: the coldest theoretical temperature. Would lower temperatures occur in space? If so would there be a point at which they simply level out and it doesn't get any colder?

RE: Autism spectrum disorders. I presume this is the same for other disorders that super mild forms exisit in the majority of the population.

RE: Other data curve

Luke said...


RE: Other data curves. I'd be interesting to survey the vareity that can exisit.

Thanks again.

Radagast said...

"Would lower temperatures occur in space?" No, zero kelvins (−273.15°C) is the absolute limit. Intergalactic space is a warm and balmy 2.7 kelvins (−270.5°C).

"RE: Autism spectrum disorders" -- I don't know. People do speak of the "gift of autism", and I imagine other ways of thinking that differ from the "average" can also be viewed as gifts. I would want nuclear power plant safety to be checked by people who are fairly obsessive about details, for example.

"RE: Other data curves." These include lognormal, power law ("long tail", as in the sales of different books, with a few bestsellers and millions of low-volume sales), and bimodal (two-humped).

Radagast said...

Re "absolute zero", one way of looking at this is that there is no such thing as "cold", but only an absence of heat. When you suck all the heat out, that's as far as you can go, and that's "absolute zero".

There are theological parallels here with the idea that evil is simply the lack of good, rather than anything positive.

By the way, they're knocking down a large apartment complex a few blocks from my place. I keep wanting to take a photo of the ruins against the sunset sky, but I keep forgetting.

Luke said...

So what would be the maximum theoretical temperature or is it always subject to revision? Maybe another way of asking of all the known stars, or space events there must be a maximum temperature for them?

It's interesting that really temperature is a heat spectrum not a ying-yang of hot and cold. (Interesting about evil like cold being a privation.)

Thanks for the other graphs. Is the reason the bell curve is so popular is because it shows the one thing with multiple variations? So would for example test results of students always fall into a bell curve or they could also go into the long tail or the Camel one?

Radagast said...

I don't believe there's a maximum theoretical temperature in quite the same way, although there are presumably practical limits on how hot things can get. For one thing, hot objects produce radiation, which carries some of their heat away.

The interior of the sun is about 15,000,000°C (compared to 5,500°C for the surface), but some other stars are much hotter at their core.

The bell curve is popular because when lots of small independent differences add up, a bell curve is always what you get. That's a mathematically provable fact of life.

As a teacher, I found exam marks always fitted a "two hump" curve. The students divided into two quite distinct groups ("lazy" and "studious"), so I got two bell curves joined together.

Radagast said...

This ball dropping demo shows how a bell curve is built up. The key is that the direction of each "bounce" is (a) independent of the others and (b) has a small effect on the final position.

Large effects produce multi-humped curves, and non-independent effects produce skewed curves like lognormal or long-tail.

Radagast said...

I believe Shiloh has answered the "size" question?

Radagast said...

On Autism, Google have been running a project aimed at the visual skills of autistic children. See their blog.