BIG successes of Lisp (was ...)

[mike420]

In the context of LATEX, some Pythonista asked what the big
successes of Lisp were. I think there were at least three *big*
successes.

a. orbitz.com web site uses Lisp for algorithms, etc.
b. Yahoo store was originally written in Lisp.
c. Emacs

The issues with these will probably come up, so I might as well
mention them myself (which will also make this a more balanced
post)

a. AFAIK Orbitz frequently has to be shut down for maintenance
(read "full garbage collection" - I'm just guessing: with
generational garbage collection, you still have to do full
garbage collection once in a while, and on a system like that
it can take a while)

b. AFAIK, Yahoo Store was eventually rewritten in a non-Lisp.
Why? I'd tell you, but then I'd have to kill you :)

c. Emacs has a reputation for being slow and bloated. But then
it's not written in Common Lisp.

Are ViaWeb and Orbitz bigger successes than LATEX? Do they
have more users? It depends. Does viewing a PDF file made
with LATEX make you a user of LATEX? Does visiting Yahoo
store make you a user of ViaWeb?

For the sake of being balanced: there were also some *big*
failures, such as Lisp Machines. They failed because
they could not compete with UNIX (SUN, SGI) in a time when
performance, multi-userism and uptime were of prime importance.
(Older LispM's just leaked memory until they were shut down,
newer versions overcame that problem but others remained)

Another big failure that is often _attributed_ to Lisp is AI,
of course. But I don't think one should blame a language
for AI not happening. Marvin Mins ky, for example,
blames Robotics and Neural Networks for that.

[Stephen Horne]

On Sat, 01 Nov 2003 17:39:54 GMT, "Andrew Dalke"
<ad****@mindspr ing.com> wrote:

How come then that the sciences have been so uncanningly effective
given that they are such an arbitrary choice within the knowable? The
answer is of course that there are a lot of other possible sciences,
completely unrelated to our own that would have been just as effective
as -or even more effective than- our current sciences, had they been
pursued with equal persistence during the same amount of time over a
lot of generations.
I don't follow your argument that this occurs "of course."

It's not for a dearth of ideas. Humans did try other possible
sciences over the last few millenia. Despite centuries of effort,
alchemy never became more than a descriptive science, and
despite millenia of attempts, animal sacrifices never improved
crop yields, and reading goat entrails didn't yield any better
weather predictions.

;-)

Actually I missed this point in Antons post, being already primed to
be bugged by his last paragraph or two, so I will reply to it here.

The choice was not arbitrary by any stretch of the imagination. We
could not construct the models described by quantum mechanics or
relatively until we had a good understanding of classical mechanics.
We cannot percieve either quantum or relativistic effects directly, so
they could not be the earliest models. We needed sufficient scientific
understanding and practical technology to be able to observe these
effects at all.

I doubt anyone could form a sensible theory of electricity, for
instance, if the only experience of electricity that they could
perceive was of phenomena such as lightning and flames. No wonder it
was all blamed on angry gods!

And yes, even classical mechanics could not have been our first model
for simple commonsense reasons. How often, for instance, did ancient
Greeks get to observe objects moving through a frictionless
environment?
On the other hand, there are different but equivalent ways to
express known physics. For example, Hamiltonian and Newtonian
mechanics, or matrix vs. wave forms of classical quantum mechanics.
These are alternative ways to express the same physics, and some
are easier to use for a given problem than another. Just like a
sun-centered system is easier for some calculations than a "my house"
centered one.
Rather similar to the idea of using different metaphors to explain the
same model, though you are looking at maths rather than language.
On the third hand, there are new theoretical models, like string
theory, which are different than the models we use. But they are
not "completely unrelated" and yield our standard models given
suitable approximations.
Agreed. Just as quantum mechanics and relativity both yield a close
approximation of classical mechanics within certain limits, and just
as classical mechanics yields something close to 'intuitive physics'
within the limits of most peoples everyday lives.
On the fourth hand, Wolfram argues that cellular automata
provide such a new way of doing science as you argue. But
my intuition (brainw^Wtraine d as it is by the current scientific
viewpoint) doesn't agree.
I just love the way that a guy who got rich selling software to do
fiddly maths jobs such as working with systems of differential
equations has suddenly decided that all that fiddly maths is
completely the wrong way to go ;-)

But even if, at some level, the universe is a cellular automata, I
don't see that meaning that the fiddly maths can be abandoned. The
fiddly maths is generally an artifact of removing detail in a sense,
after all - we use the formula for the entire path, for instance,
rather than listing all the points that make up the path. And the list
of points, like the list of states of the cells, lacks explanatory
power.

The effectiveness of the current natural sciences is a perceptual
artifact caused by our biased history. From a lot of different
directions messages are coming in now, all saying more or less the
same: "If asking certain questions, one gets answers to these
questions in a certain way, but if asking different questions one gets
different answers, sometimes even contradicting the answers to the
other questions".

This might seem mystic or strange but one can see these things
everywhere, if one asks that kind of questions :-)

Or it means that asking those questions is meaningless.

I wouldn't go so far. No model (at least none we have yet) is perfect,
so different models are bound to contradict each other - particularly
when you push them beyond their limits. Extrapolation is always less
reliable than interpolation, so it is best not to use a model to
extrapolate beyond the range where experiment has shown it to apply.

But there is clearly a baseline reality which these models are seeking
to approximate.

As I mentioned earlier, when a primitive person tries to understand
how your car works, the engine does not turn into a demon. The
technology based on our current scientific understanding works,
whatever you personally happen to believe.
For a simpler case .. what is the center of the universe? All locations
are equally correct. Is it mystic then that there can be multiple
different answers or is simply that the question isn't well defined?
Hmmm - I suppose this depends what you mean by center. If you mean
'origin' in the graph-plotting sense, then you are right, of course.

But my understanding is that the universe, so far as anyone can tell,
is either an infinite space or finite without bounds. In either case,
there is no such thing as a center.

I find the 'infinite' theory dubious - if the expansion rate has
remained finite since the big bang, then how can space have grown to
become infinite? The only way I can understand it is if space was
always infinite. That wouldn't necessarily mean it can't 'expand',
just as it isn't necessarily impossible to multiply infinity by two.

I guess 'expansion' relating to the universe is a metaphor too, really
- after all, the universe isn't an object within some other space. The
'expansion' is really just rewriting of the scale factors on the
dimension axes of the universe, I suppose. That being why the speed of
light isn't a problem in inflation - nothing is actually moving faster
than the speed of light, even though the distances between things is
expanding faster than the speed of light.

Hmmm - I wonder if 'expansion' or 'scale' is a continuous value in
space-time, like curvature? Well, I guess it must be really - just
write the model in those terms and hey presto - but what I mean, I
guess, is "is there a function that can define that 'scale' in terms
of local physics to explain things we don't currently have an
explanation for?".

One example would be the role the observer plays in quantum mechanics,
but something closer to a programmer would be the way static or
dynamic typing influence the way one thinks about designing a computer
program.

<snip>
And I don't see how the reference to QM affects the argument. Then
again, I've no problems living in a collapsing wave function.

I suspect this is the 'conscious mind has special role as observer'
thing again. And as has already stated, there are other explanations
of waveform collapse that don't require consciousness to take a
special role. Explanations that make more sense, as the observer never
had any control over how the waveform collapses - it is a mechanical
process that follows clearly defined non-mystical rules.
--
Steve Horne

steve at ninereeds dot fsnet dot co dot uk

[Andrew Dalke]

Me:

(Eg, QCD could be used to
model the weather on Jupiter, if only we had a currently almost
inconceivably powerful computer. Running Python. ;)
GrayGeek:

Weather (3D fluid dynamics) is chaotic both here on Earth and on Jupiter.
As Dr. Lorenz established when he tried to model Earth's weather, prediction of future events based on past behavior (deterministic modeling) is not
possible with chaotic events.
Weather is chaotic, but you misstate the conclusion. Short term predictions
are possible. After all, we do make weather predictions based on
simulations, and the "shot in the dark" horizon is getting more distant.
We're even getting reasonable models for hurricane track predictions.
Orbital mechanics for the major planets are also chaotic, it's just that the
time frame for problems well exceeds the life of the sun. (As I recall;
don't have a reference handy.)

Also, knowledge of history does help. Chaotic systems are still
subject to energy conservation and other physical laws, so
observations help predict which parts of phase space are accessible.
And if the system is only mildly chaotic (eg, Lyapunov exponent is
small enough) then an observation which is "close enough" to the
current state does help predict some of the future.
In a chaotic system changing the inputs by even a small fractional
amount causes wild swings in the output, but for deterministic
models fractional changes on the input produce predictable outputs.
To be nit-picky, that should be "... amount eventually causes arbitrary
differences in the output .. " (up to the constraints of phase space).
The two values could swing wildly but still track each other for some
time.
The charge of an Electron is a case in point. Okkam's Razor is the
justification for adopting unitary charges and disregarding fractional
charges. But, who justifies Okkam's Razor?
Quarks have partial charges, and solid state uses partial charges
for things like the fractional Hall effect.

The justification is that without Occam (or Ockham)'s razor
then there is no way to choose between theories with the same
ability to describe observed data.

In a simple case, consider
x y
-----
1 1
2 2
3 3
4 4
5 5

This can be modeled with y = x or with the osculating

y = 1*(x-2)*(x-3)*(x-4)*(x-5)/( (1-2)*(1-3)*(1-4)*(1-5) ) +
2*(x-1)*(x-3)*(x-4)*(x-5)/( (2-1)*(2-3)*(2-4)*(2-5) ) +
3*(x-1)*(x-2)*(x-4)*(x-5)/( (3-1)*(3-2)*(3-4)*(3-5) ) +
4*(x-1)*(x-2)*(x-3)*(x-5)/( (4-1)*(4-2)*(4-3)*(4-5) ) +
5*(x-1)*(x-2)*(x-3)*(x-4)/( (5-1)*(5-2)*(5-3)*(5-4) )

(Hope I got that all correct. BTW, I remember this as the
an osculating function, because it wobbles back and forth
so much it 'kisses' the actual function. However, the term
'osculating curve' appears to be something different and the
term 'osculating function' is almost never used. Pointers? )

Both describe the finite amount of data seen. Which
do you prefer, and why?
Me: For a simpler case .. what is the center of the universe? All locations
are equally correct. Is it mystic then that there can be multiple
different answers or is simply that the question isn't well defined?

"All locations are equally correct" depends on your base assumptions about
the Cosmological Constant, and a few other constants. Event Stephen
Hawkings, in "A Brief History of Time" mentions the admixture of philsophy
in determining the value of A in Einstein's Metric.

I was refering to my earlier statement that I could designate my house
as the center of the universe and still have all my calculations come
out correct. I somewhat overstepped that when I made the above
statement.

I looked in my copy of ABHoT but didn't see mention of "A".
It's been about a decade since I last looked at Wheeler, and I
never took a GR course, so I don't recognize the term. Web
searches don't find anything relevant. (Do you really mean
"a Lorentzian manifold whose Ricci tendor R_(ab) in the
coordinate basis is a constant scalar multiple of the metric
tensor g_(ab)."? Perhaps you mean the Robertson-Walker
metric, which appears to meet that definition. But there
doesn't appear to be an A term in the formulations I found.
Perhaps it's the a in the cosmic scale factor of the Friedmann
equation?)

How does the cosmological constant affect things? I don't
recall that having an implication on isotropy and homogeneity.

In any case, you are refering to the observed large-scale
isotropy and homogeneity of the universe. There is a bit in
ABHoT on that, but it's pre-COBE, and definitely pre-brane and
the statements of Hawking are more of a "this may explain things
but it's untested." Then again, that's about the current state of
the art too. ;)

So it's still pretty safe to say that my house is the center
of the universe.

Andrew
da***@dalkescie ntific.com
P.S.
When you quote someone else's post, please take care to
trim the paragraphs you are not responding to. That makes
it easier to find the text you added.

[Stephen Horne]

On 1 Nov 2003 22:19:11 -0800, mi**@pitt.edu (Michele Simionato) wrote:

most current theory is so
abstract that the explanations should be taken as metaphors rather
than reality anyway.
True.

Thank god - someone actually understood that bit!!!

Except you could have agreed with your own misunderstandin g of what I
meant, I suppose - but lets agree to ignore that option ;-)
According to the old school of Physics, there is a large distinction
between fundamental (somewhat microscopic) Physics and
non-fundamental (somewhat macroscopic) Physics. The idea
is that once you know the fundamental Physics, you may in principle
derive all the rest (not only Physics, but also Chemistry, Biology,
Medicine, and every science in principle). This point of view, the
reductionism , has never been popular between chemists of biologists, of
course, but it was quite popular between fundamental physicists with
a large hubrys.
I think I understand what you mean.

I am aware of the idea, though I haven't really considered what it
implies. Certainly we haven't discovered any fundamental layer of
physics yet (AFAIK) and we may never do. And even if we do discover a
baseline level, it may be that we can never express the higher levels
deterministical ly in baseline level terms (as Goedel says, there are
relations that can never be proven or disproven - the incompleteness
theorem).

If forced to take a position, I would say that the key requirement is
that each model be consistent with all other models at all layers of
abstraction over the range where all are applicable. A higher level
layer may have features that cannot be derived from the lower level
layers, but they cannot contradict each other unless you go outside
the scope where one or more of the models is applicable.
Now, things are changing. Nowadays most people agree with the effective
field theory point of view. According to the effective field theory approach,
the fundamental (microscopic) theory is not so important. Actually, for
the description of most phenomena it is mostly irrelevant. The point is
that macroscopic phenomena (here I have in mind (super)conducti vity or
superfluidit y) are NOT simply microscopic effects en mass: and in
certain circumstances they do NOT depend at all from the microscopic theory.
OK - but if you are describing superfluidity as a single macroscopic
effect then you must describe it within a macroscopic framework. At
which point it has nothing to do with quantum effects because it isn't
within a quantum framework - it is just that the macroscopic
phenomenon called electricity (distinct from electrons moving en
masse) is not subject to the macroscopic phenomenon called resistance
(distinct from energy loss through the electomagnetic interactions
between electrons and atoms en masse) when the macroscopic phenomenon
called temperature (distinct from the kinetic energy of atoms en
masse) is sufficiently low.

There is nothing wrong with this per se - it is the limit of most
peoples (mine included) understanding of superconductivi ty - but it
has nothing to do with the framework of quantum mechanics.

The quantum framework may give an explanation, of sorts, for why
superconductivi ty occurs (or perhaps Goedel has put his veto on this)
but I do understand why explaining something less abstract to our
perceptions in terms of something even more abstract might seem
counterproducti ve ;-)
That's life, but it is more interesting this way ;)

Agreed ;-)
--
Steve Horne

steve at ninereeds dot fsnet dot co dot uk

[Andrew Dalke]

Stephen Horne:

We cannot percieve either quantum or relativistic effects directly, so
they could not be the earliest models.
[In general I agree with your post. Just some comments.]

What about superfluid helium?
And yes, even classical mechanics could not have been our first model
for simple commonsense reasons. How often, for instance, did ancient
Greeks get to observe objects moving through a frictionless
environment?
Every clear night.
I just love the way that a guy who got rich selling software to do
fiddly maths jobs such as working with systems of differential
equations has suddenly decided that all that fiddly maths is
completely the wrong way to go ;-)
Excepting that he spent 10 years on that book :)
But even if, at some level, the universe is a cellular automata, I
don't see that meaning that the fiddly maths can be abandoned.
I liked the scene in one of Brin's novels (from the Brightness Rift
trilogy). Alien civilizations are the result of a several billion years
old lineage. Nearly all knowledge is found in the Library.
Computer simulations are based on automata theory. But Earth
isn't part of the culture ("wolflings" ) and developed this bizarre
math using infinitesimals which was sophisticated enough to make
pen&paper(&abac us) predictions of certain events which were
hard to simulate.
I wouldn't go so far. No model (at least none we have yet) is perfect,
so different models are bound to contradict each other - particularly
when you push them beyond their limits.
True. But some questions are meaningless. "Wave or particle?"
"Where is the center of a black hole?" "What would happen if you
were driving at the speed of light and turned the headlights on?"
Hmmm - I suppose this depends what you mean by center. If you mean
'origin' in the graph-plotting sense, then you are right, of course.

But my understanding is that the universe, so far as anyone can tell,
is either an infinite space or finite without bounds. In either case,
there is no such thing as a center.
Michele is a better one for this topic. My point was just that many
different answers doesn't necessarily imply a mystic explanation.
I find the 'infinite' theory dubious - if the expansion rate has
remained finite since the big bang, then how can space have grown to
become infinite?

There's also the Oblers' paradox, but that also requires infinite time.

I read a popular account of "branes", membrane theory, which
was interesting. I don't know enough to describe it, other than
that the universe was created from high-dimensional membranes
hitting each other.

Andrew
da***@dalkescie ntific.com

[Stephen Horne]

On Sat, 01 Nov 2003 18:55:18 GMT, GrayGeek <jk********@FIS Hneb.rr.com>
wrote:

Weather (3D fluid dynamics) is chaotic both here on Earth and on Jupiter.
As Dr. Lorenz established when he tried to model Earth's weather, prediction
of future events based on past behavior (deterministic modeling) is not
possible with chaotic events. Current weather models predicting global or
regional temperatures 50 years from now obtain those results by careful
choices of initial conditions and assumptions. In a chaotic system
changing the inputs by even a small fractional amount causes wild swings in
the output, but for deterministic models fractional changes on the input
produce predictable outputs.

Very true for predicting weather, but the 50 years hence models are
predicting climate. That is a different layer of abstraction, and not
necessarily chaotic (at least on the same timescales) as shown by the
fact that the real world climate only changes relatively slowly -
despite some quite random inputs such as sunspot activity which have
nothing to do with chaos in the climate model.

Whether these models are actually accurate (or rather which, if any)
is, of course, a whole other question. I guess we'll find out in 50
years time ;-)

So "objectivel y" science gains more knowledge, but
relatively speaking (seeing it as a percentage of that what is
currently known to be not known, but knowable in principle) science is
loosing ground fast. Also an even greater area of the universe is
supposed to exist that we will not even have a chance *ever* to know
anything about.

Exactly. Even worse, the various peripherals of Physics and Math are
getting so esoteric that scholars in those areas are losing their ability
to communicate to each other. It is almost like casting chicken entrails.

There are just too many too abstract fields to be studied, I guess -
at some point, we'll need more specialists than the entire human
population!

Better start working on them AI systems ;-)
--
Steve Horne

steve at ninereeds dot fsnet dot co dot uk

[Andrew Dalke]

Michele Simionato:

I would qualify myself as an expert on renormalization theory and I would
like to make an observation on how the approach to renormalization has
changed in recent years, since you raise the point.
Feel free. I started a field theory course in '93 but didn't finish it
as I decided to do computational biophysics instead. So not only is
my knowledge dated but it wasn't strong to begin with.

(Plus, I was getting sick of SHOs ;)
only seems similar). Now, one can prove that the arbitrarity is
extremely small and has no effect at all at our energy scales: but
in principle it seems that we cannot determine completely an observable,
even in quantum electrodynamics , due to an internal inconsistency of the
mathematical model.
How small? Plank scale small?
Yes, and still a lot of science is done without computers. I never
used a computer for my scientific work, expect for writing my papers
in latex ;)

Whereas I went into computer simulations. Then again, I
wrote my first simulation program in ... 9th grade? .. for simulating
orbits, and tested it out by hand. Too bad I didn't know that I
should decrease the timestep, as my planets jumped all over the
place, and I didn't know about using a symplectic integrator,
nor about atan2, nor ...

Andrew
da***@dalkescie ntific.com

[Stephen Horne]

On Sun, 02 Nov 2003 08:36:09 GMT, "Andrew Dalke"
<ad****@mindspr ing.com> wrote:

Stephen Horne:

We cannot percieve either quantum or relativistic effects directly, so
they could not be the earliest models.
[In general I agree with your post. Just some comments.]

What about superfluid helium?

Superfluid helium is a macroscopic phenomenon - it may be explained in
terms of QM effects, but that doesn't make it a quantum effect in
itself any more than more everyday macroscopic effects (which can also
be described in QM terms). If superfluid helium is your only clue, it
will tell you no more about quantum effects than e.g. lightening tells
you about the properties of an electron.

Besides, you need the science and technology to achieve very low
temperatures before you can observe superfluid helium. It may be
pretty cold in the winter, but even so we don't often see superfluid
helium laying around ;-)

And yes, even classical mechanics could not have been our first model
for simple commonsense reasons. How often, for instance, did ancient
Greeks get to observe objects moving through a frictionless
environment?

Every clear night.

Yes, but they mostly thought the planets obeyed different laws to the
things that could see up close. Besides, with an Earth-centric model,
it is pretty hard to see the simple patterns of motion - and of course
even if they did, gravity is still confusing the issue. Don't forget
that it was actually quite a big leap of understanding when Newton
realised that the planets followed elliptical orbits because of the
same force that made apples fall from trees - it is only from the
perspective of having been told this since the age of 12 that it seems
obvious.

It was quite a revelation to discover that the physics of the cosmos
were actually the same physics we experience on the ground.
True. But some questions are meaningless. "Wave or particle?"
"Where is the center of a black hole?" "What would happen if you
were driving at the speed of light and turned the headlights on?"
Absolutely.

"Wave" and "particle" should be seen as metaphors, each describing a
subset of the properties of subatomic particles. The 'duality' is an
artifact of the metaphors.

The centre of a black hole exists, in a sense, but we can never
observe it because it is inside the event horizon, and as time itself
stops at the event horizon (from the perspective of any outside
observer) there is even good reason for claiming that the space inside
the event horizon doesn't exist.
Michele is a better one for this topic. My point was just that many
different answers doesn't necessarily imply a mystic explanation.
Yes, sorry - I was just following a random tangent.
I read a popular account of "branes", membrane theory, which
was interesting. I don't know enough to describe it, other than
that the universe was created from high-dimensional membranes
hitting each other.

I read a book about string and brane theory some time ago - I guess
possibly the same one, though it has vanished into book-borrowing
space as all the best books do so I can't tell you the title.

Lots of theory about possible geometries and topologies of many
dimensional space-time and how they could change from one another.
They didn't address the issue of how they could change at all, given
that time existed within the geometry rather than outside of it, and
for that among other reasons my impression was that it was a
fascinating read that nevertheless left me with no more clue than I
had to start with.

I would at least have appreciated a definition of supersymmetry,
rather than the usual 'its too abstract for your puny mind' copout.
--
Steve Horne

steve at ninereeds dot fsnet dot co dot uk

[Stephen Horne]

On Sun, 02 Nov 2003 08:12:09 GMT, "Andrew Dalke"
<ad****@mindspr ing.com> wrote:

Orbital mechanics for the major planets are also chaotic, it's just that the
time frame for problems well exceeds the life of the sun. (As I recall;
don't have a reference handy.)

Are you sure?

I know that multi-object gravitational systems can be chaotic in
principle (and I believe that the orbits of some of Jupiters moons are
a case in point) but I thought the orbit of the planets around the sun
had been proven stable. Which implies that you needn't worry about
chaos unless you are worried about the minor deviations from the
idealised orbits - the idealised bit can be treated as constant, and
forms a very close approximation of reality no matter what timescale
you are working in.

It was one of the big successes of the Laplace transform, IIRC. But I
could be mistaken.
--
Steve Horne

steve at ninereeds dot fsnet dot co dot uk

[Michele Simionato]

Stephen Horne <st***@ninereed s.fsnet.co.uk> wrote in message news:<4e******* *************** **********@4ax. com>...

I have just been through the same point (ad nauseum) in an e-mail
discussion. Yet I can't see what is controversial about my words.
Current theory is abstract (relative to what we can percieve) and we
simply don't have the right vocabulary (both in language, and within
the mind) to represent the concepts involved. We can invent words to
solve the language problem, of course, but at some point we have to
explain what the new words mean.

Thus, as I said, "most current theory is so abstract that the
explanations should be taken as metaphors rather than reality anyway."

The point being that different metaphors may equally have been chosen
to explain the same models - presumably emphasising different aspects
of them - and such explanations may work better for people who can't
connect with the existing explanations. The model would still be the
same, though, just as it remains the same even if you describe it in a
language other than English. The terminology changes, but not the
model.

Read very carefully, and you will note that I said the EXPLANATIONS
should be taken as metaphors - NOT the models themselves.

Dunno who was "attacking" you via e-mail, but FWIW, I fully support
your point of view and I am sure a lot of other people in science
would agree. The time where one could have a fully intuitive or
visual understanding of physical models is long past.

Nice discussion, BTW.

Michele

[Anton Vredegoor]

Stephen Horne <st***@ninereed s.fsnet.co.uk> wrote:

Oh dear, here we go again...
No, we don't :-)

[..]
I have just been through the same point (ad nauseum) in an e-mail
discussion. Yet I can't see what is controversial about my words.
Current theory is abstract (relative to what we can percieve) and we
simply don't have the right vocabulary (both in language, and within
the mind) to represent the concepts involved. We can invent words to
solve the language problem, of course, but at some point we have to
explain what the new words mean.

Probably this e-mail discussion -which I didn't have any part in- has
caused a lot of irritation, some of which has ended up on my plate,
but I just want to make clear it's not my piece of cake :-)

Anton