Re: [Phys-L] Lord Of The Flies + eyeglasses + burning glass + phase space + soft fail

[John Denker <jsd@av8n.com>]

On 05/18/2017 04:49 AM, Anthony Lapinski wrote:

> This came up the other day while I was teaching optics -- when Jack takes
> Piggy's glasses to start a fire on a sunny day (Chapter 2, Fire On The
> Mountain). I've always heard (and there's plenty of info online) that the
> story is flawed because Piggy is NEARsighted and thus wears diverging
> lenses which could not be used to start a fire. However, the text reads:
>
> *...Give 'em back. I can hardly see...*
>
> *...Jus' blurs, that's all. Hardly see my hand....*
>
> This implies that Piggy is actually FARsighted and thus wears converging
> lenses.
>
> Am I missing something here?

Three comments:

1) The story is implausible (to say the least) before we even
get to the bit about starting the fire.

Being so nearsighted *or* farsighted that you can "hardly see"
your hand would be exceedingly unusual.

You can do the experiment as follows:
 -- To experience uncorrected farsightedness, borrow eyeglasses
  from somebody who is nearsighted.  Put them on /over/ whatever
  eyewear you usually use, if any.  I predict that you will be
  able to see your hand and count your fingers.  You will be able
  to walk around just fine.  You won't be able to read books,
  but that's not what the story was talking about.
 -- To experience uncorrected nearsightedness, borrow eyeglasses
  from somebody who is farsighted ... or just use dollar-store
  reading glasses.

Maybe Piggy is exaggerating, but even that strikes me as implausible
or at least unwise from the character's point of view.  Farmers have
a saying: "A sick goat is a dead goat" because animals go to great
lengths to conceal any ailment or disability.  That's because the
weak get picked on by their peers ... not to mention predators.
This seems relevant, because the expression "Lord of the Flies"
is practically synonymous with "law of the jungle".

===============

2) It pays to do the burning-glass experiment.

       Wear eye protection.
       A couple layers of good-quality
       sunglasses should suffice.

 I predict you will find it rather difficult to start a fire using
 ordinary (rather strong) +3 diopter reading glasses in the obvious
 way.  There are some interesting physics reasons for this, as
 discussed below.

 HOWEVER, you can use *two* pairs of reading glasses.  Or you can
 pop the lenses out of a single pair (at which point Piggy is
 much more unhappy, for good reason).  Make a compound lens.  You
 should be able to start a fire this way:
   https://www.youtube.com/watch?v=JSW0UNBfwYs

===============

3) It is amusing to discuss the previous item in terms of /phase space/.
 This is not the chemistry phase space (as in Gibbs phase rule)
 but rather the physics phase space, as in
  -- Liouville theorem
  -- brightness theorem
  -- 2nd law of thermodynamics
  -- Heisenberg uncertainty principle
  -- unitarity of the equations of motion
  -- symplectic integrators
  -- Feistel networks
  -- etc. etc. etc.

 You can understand this qualitatively as follows.  Imagine you
 are located at the tinder, looking up at the burning glass.
 The glass subtends /some/ of the solid angle above you, but
 not very much, only a fraction of a percent (assuming a +3
 diopter lens with an eyeglass-sized diameter).

 In accordance with the brightness theorem, the glass looks
 /at best/ like a black body with a temperature equal to the
 photosphere of the sun (6000 K).

 Hypothetically, if you consider only radiation in and radiation
 out, this might be enough.  You can do the calculation based on
 the black-body formula:

   power in = power out (in equilibrium)
   A1 T1^4 = A2 T2^4

   A = area   T = temperature
   A1 = the lens
   T1 = photosphere temperature
   A2 = the entire hemisphere above you
   T2 = tinder temperature

 I mention this because it is an authentic example of something
 that was discussed recently, namely, a /soft fail/.
 We tried to use the T^4 radiation law to prove that a non-compound
 eyeglass lens can't start a fire, but we failed.  However, we
 didn't know it would fail until after we had done most of the
 calculation.  (We kinda suspected, because that fourth power
 is brutal, but it was still worth doing the calculation.)

 We still wish to explain why using the non-compound lens is
 difficult if not impossible.  We learned that the radiation
 law is not sufficient;  we have to consider other things such
 as thermal conductivity (through the air and/or through the
 tinder itself) ... things that go like temperature to the
 first power, not fourth power.  With sufficient engineering
 you might be able to work around the conductivity issues, but
 children on a desert island would have a hard time.

 This is a 100% authentic example of how physics is done.  It's
 like exploring a maze.  You poke your nose into the simplest
 and most universal possible explanation, and if that doesn't
 work out, you go looking for another explanation.
   https://www.av8n.com/physics/glorpy-maze.html

 Because of a somewhat-understandable publication bias, failures
 (soft and otherwise) are severely under-reported.  This contributes
 to gross misunderstandings about how science is done.  Textbooks
 paint a wildly unrealistic picture of the history of science.
 Kuhn discussed this in his famous book.



 Compounding the lens cuts the f/stop in half.  It brings the
 lens twice as close to the tinder.  The lens now subtends
 *four* times as much solid angle, so the tinder gets a *lot*
 hotter.

 BTW this is related to why typical versions of the Archimedes
 death ray don't work:  In addition to various practical details
 (aiming et cetera), at any reasonable distance the mirrors don't
 capture a very big fraction of the phase space.  If you had
 ranks /and/ files, arranged horizontally and vertically on a
 tall hillside, you might have a better chance.

----------

More generally:

I find it odd that the concept of phase space gets covered
so little and/or so late.  Students might encounter it for
the first time in upper-division or even graduate-level
courses.

Phase space is about as fundamental as anything you can
think of.

For example, a lot of people imagine that quantum mechanics
evolved from classical mechanics by way of the Hamiltonian
and quantization of energy.  HOWEVER, almost every word of
that is wrong.  Energy is not necessarily quantized, but
let's not even worry about that.  Originally QM evolved
from thermodynamics by way of phase space.  Planck's constant
is the quantum of /action/ not energy.  It measures area in
phase space.