
Math without beauty or truth - ColinWright
http://noahpinionblog.blogspot.com.au/2013/08/a-few-words-about-math.html?m=1
======
HarryHirsch
It's like this: once a system is sufficiently complex it is impossible to
describe with simple models, and one cannot get an intuitive understanding of
its behaviour from staring at two or three equations. Biologists have found
this out - living systems have layers of complexity bolted on layer of
complexity that have evolved in geological time.

It's immediately obvious that economic systems are the same - the simple
models taught to undergrads are simple, elegant - and they don't work to well
in practice, their predictive power is limited. The practice of economy needs
to change, it isn't that we didn't have the data or the computational power to
deal with it.

~~~
pessimizer
>the simple models taught to undergrads are simple, elegant - and they don't
work too well in practice

Also they have been very ideological for a long time.

The idea that real economic behavior will converge on a particular model as
the real actors approach the assumed behavior of the actors in that model is a
good way to think about models. The idea that distance from model behavior in
real actors will smooth out to insignificance over the long term or at a
larger scale is common, but denies the existence of nonlinearities and
feedback effects resulting from the interactions between the differences
between real behavior and model behavior. The effects of those nonlinearities
can (and often do) subsume the model behavior entirely.

Hence, the importance of natural experiments. You can use them to find
important deviations and build a new model. Unless you're from the Chicago
school, in which case deviations are your cue to start hand-waving and
appealing to nature, justice, and the character building nature of hard work.

Some very old and very well established models performed very well during all
of the recent economic shocks. What they couldn't do was compete with a bunch
of cornpone wisdom about spending within your means that was easily understood
by people who have trouble with math.

~~~
temphn
Interesting. What's the best study you have, with scatterplots, that shows
that the "very old" models performed "very well"? Insofar as we have seen
actual quantitative predictive modeling by Keynesians of macroeconomic
quantities, the plots tend to look like this:

[http://affordablehousinginstitute.org/blogs/us/wp-
content/up...](http://affordablehousinginstitute.org/blogs/us/wp-
content/uploads/unemployment_with_arra.jpg)

And the independent variables of course tend to like this:

[http://m.research.stlouisfed.org/fred/series.php?sid=BASE&sh...](http://m.research.stlouisfed.org/fred/series.php?sid=BASE&show=chart&range=max&units=lin)

Neither seem particularly textbook, but you're obviously thinking of
something. Given that people who think differently from you invented Bitcoin
(and thus have at least a glancing familiarity with advanced mathematics, if
the solution of the Byzantine Generals problem means anything) it would be
great to see some plots to the contrary. Not just models, but X/Y plots or
tables in which Keynesians predict something and nail it. It's not hard, after
all to find many examples of Krugman, Bernanke, Goolsbee, or Orszag making
quantitative predictions that turned out flagrantly wrong [1].

[1]:
[https://news.ycombinator.com/item?id=6038790](https://news.ycombinator.com/item?id=6038790)

~~~
pessimizer
It's very difficult for me to figure out what you're trying to say here. The
first graph seems to be about Obama, the second a time series of the monetary
base, and the link in the footnote long statements from random people. Only
the last mentions a model, and only in terms of how well it worked[1].

>Given that people who think differently from you invented Bitcoin (and thus
have at least a glancing familiarity with advanced mathematics, if the
solution of the Byzantine Generals problem means anything) it would be great
to see some plots to the contrary.

I don't know what Bitcoin has do do with anything, or what it is being
presented as an example of.

>Not just models, but X/Y plots or tables in which Keynesians predict
something and nail it.

You're the first person to mention Keynesians, I mentioned economists. If you
want to find something that Krugman nailed, though, try the unemployment rate
from your first graph.

[1]
[http://fraser.stlouisfed.org/docs/meltzer/fisdeb33.pdf](http://fraser.stlouisfed.org/docs/meltzer/fisdeb33.pdf)

~~~
temphn
Ha. Methinks you doth protest too much. But I'll be very precise. Show me the
equations and code that Krugman wrote in 2009 that predicted the unemployment
curve over the last four years. OMB (full of economists!), to their credit, at
least essayed a quantitative prediction. As the first graph showed, it was
completely wrong.

So: what "very old" models performed "very well"? You must be thinking of
something here. I'm not talking about a Krugman blog post where he says the
stimulus was too small. I'm talking about an actual scatterplot, a time series
prediction with the X axis as time, the Y axis as the dependent variable, and
actual empirical measurements plotted vs. the predictions of theory.

Here is another example from a different field:

[http://www.nature.com/news/climate-change-the-forecast-
for-2...](http://www.nature.com/news/climate-change-the-forecast-for-2018-is-
cloudy-with-record-heat-1.13344)

[http://www.nature.com/news/499139a-i2-0-jpg-7.11335?article=...](http://www.nature.com/news/499139a-i2-0-jpg-7.11335?article=1.13344)

You can see the graph halfway down the page, with theoretical predictions as
the red line and actual empirical measurements as the black line. The Nature
article admits they don't match well. But in other fields they do match well.
For example:

[http://physics.info/projectiles/practice.shtml](http://physics.info/projectiles/practice.shtml)

In ballistics the predicted time series match experimental results very
closely. So I ask again: what "very well established models" in economics
performed "very well"? Which of them nailed the curve?

------
juanre
I took Caltech/Coursera class "Principles of Economics for Scientists" this
winter. I was struck by how lean and clear the concepts are once you bother to
write them down mathematically. Much better than the hand-wavy explanations I
had heard before.

I also took it a step further, and wrote them down as code. When you can
explain something to a computer you know you have understood it; and you may
even end up with something that other people can understand and play with. I
believe something along the lines of what I ended up with
([https://github.com/juanre/econopy](https://github.com/juanre/econopy)) might
be profitably used to teach economics to CS-type students.

As far as economics math not representing reality: I think it's obvious enough
that humans don't behave the way these equations assume. However, they are a
great framework from which to think about how humans actually behave.

~~~
HarryHirsch
_As far as economics math not representing reality: I think it 's obvious
enough that humans don't behave the way these equations assume. However, they
are a great framework from which to think about how humans actually behave._

There's a problem: the only reason you would build a model is to predict
things from it. If the model can't do that for you what you are doing has
stopped being science and had turned into something else. Again: if the
"framework from which to think about how humans ... behave" can't predict how
humans behave in actuality looking at such frameworks is an exercise in
futility.

~~~
juanre
A classic example of irrationality is mental accounting. Say you are going to
the theater. You have a $100 ticket and a $100 bill, and on the way to the
theater you lose the ticket. Would you spend your $100 to buy another one?
Most people wouldn't, because they would be assigning a $200 cost to the
theater department.

Now imagine that you only have a $100 bill with which you are going to pay the
ticket, and you lose it on the way to the theater. Would you take out your
credit card and pay for the ticket anyway? Most people would.

We know that if people were rational the two scenarios would be identical. But
they differ, and this is interesting because we have a framework from which to
look into it, and we can see it doesn't fit the framework, and therefore we
can infer new and unexpected facts about the economic agents. Models inform in
interesting ways how we go about trying to understand reality, even when they
are poor predictors.

~~~
hypersoar
But those aren't identical. If I lose the $100 bill, I'm out those hundred
bucks whether I buy a ticket or not. Whereas if I lose the ticket, I get to
keep the money if I don't buy a replacement.

~~~
FaceKicker
Scenario A: The setup is (1) lose $100, gain 1 ticket (current state is -$100,
+1 ticket); (2) lose 1 ticket (current state is -$100, 0 tickets). The choices
are (a) lose $100, gain 1 ticket (yields state -$200, +1 ticket) or (b) do
nothing (yields state -$100, 0 tickets).

Scenario B: The setup is (1) lose $100 (current state is -$100, 0 tickets).
The choices are the same as above.

The final 'state' at the end of each setup is the same, and the choices are
the same, so the argument is that a rational actor would make the same choice
in both situations. Maybe there's an argument that the state should include
more than just $ and tickets though?

~~~
hypersoar
Ah, indeed! That'll teach me to think myself exempt from cognitive biases.

------
tsiki
Lately I've developed a distaste for thinking of math as simply a
representation of "something real", I'd rather think of it as a language in
its own right. I'll just link this here because it explains the point way
better than I could: [http://onfoodandcoding.blogspot.fi/2013/04/completely-
reliab...](http://onfoodandcoding.blogspot.fi/2013/04/completely-reliable-
conclusions.html) (the first 5'ish paragraphs especially)

~~~
paganel
> Lately I've developed a distaste for thinking of math as simply a
> representation of "something real", I'd rather think of it as a language in
> its own right.

I remember reading a SF story some time ago (forgot its title and author)
where maths is the language of choice between us, humans, and the passengers
of an alien ship who had just landed on Earth.

I also dream of other realities (call them parallel universes or whatever)
where maths is just different, like for example the real numbers being one and
the same as the natural number. It could still be called "maths" even though
totally different from "ours", the same as the Basque language is totally
different from a "classic" Indo-European language but they serve the same
purpose.

~~~
arnsholt
You might be thinking of Carl Sagan's _Contact_. There a set of construction
instructions are constructed from first principles using mathematical
notation.

------
nooron
Noah's spot on about the tedium and emotional frustration of studying
macroeconomics-- of staying up to late hours to learn something that not only
may not correspond to real-world behavior, but demonstrably doesn't.

I'll point out that at the University of Michigan, where I believe Noah was
before Stony Brook, there's exactly one class available on the philosophy of
modeling and economics. And it's for upperclassmen and grad students.

I happen to think this really sucks and that the methods of model construction
and model-oriented thinking should happen much earlier in economics study. Is
it different any where else?

------
CurtMonash
As Dave Kollat told me way back in 1974, "Micro is trivial and macro is
wrong." I went on to study a bit of economics anyway, attending some graduate
seminars at Harvard. On one occasion, some grad student held forth "It is
axiomatic that ...", whereupon I retorted "It may be axiomatic, but it happens
to be incorrect."

My life would actually have been easier had I respected economics. I jumped
from math all the way to business or public policy (I wound up as a Kennedy
School post-doc); the only assistant professorship I was ever offered was at a
B-school (Kellogg); I went to Wall Street instead; and have been in the
business world ever since.

~~~
dnautics
easier != worthwhile

Sometimes something is not worthy of your respect! Something I thought was
interesting is that the article is basically a rehashing of the Austrian
criticism of modern macro. Although the austrians superimpose their own
theology as well.

------
j2kun
The only way that mathematics should be used to signal intelligence is if you
can explain a mathematical idea in a way that makes it completely obvious and
trivial. The kind of "signalling" that the author describes in macro (by
obscurity and complexity) is the opposite, and it makes me sad.

~~~
cynicalkane
_The only way that (X) should be used to signal intelligence is if you can
explain an idea in a way that makes it completely obvious and trivial_

This is the opposite, unfortunately, of academia in general, not just
economics.

~~~
j2kun
I think mathematics at least strives to achieve that goal. But then when I say
obvious and trivial I mean it in a mathematical sense: it's obvious and
trivial if you understand all of the obvious and trivial groundwork needed to
understand how obvious and trivial the idea at hand is.

------
Mikeb85
The problem with economic models isn't that they don't work, or that they're
made up.

The problem is that economies, especially on a global scale, are so complex,
they can't possibly be modeled with a few equations. To keep things reasonably
simple, you need to make assumptions that may or may not be BS.

There's a reason economists, quantitative analysts, and people who come up
with economic/financial algorithms often make a ton of money, why the
algorithms are very closely guarded secrets, and why hedge funds and banks go
to such lengths to develop their models.

Another thing to keep in mind, is that applying math and programming to
something so dynamic as human behaviour on a macro scale is very difficult.
Scientists and economists employ massive supercomputers, and entire teams of
researchers to test their models. Not something that can be taught in an
undergrad economics class...

------
omn1
I'm surprised that he compares the quality of economic models with those from
physics. No matter the discipline it's still just a _model_ \-- with all their
strengths and weaknesses. If he liked the rigor of physics in school, why not
pursue a career in mathematics with a stronger focus on _concepts_? I get the
feeling that he would enjoy the purity of it. If that lacks practical
benefits, theoretical physics might be a good choice.

------
xanth
So no psychohistory yet :(

~~~
tunesmith
It's worth remembering that even psychohistory was "wrong". It's a good
example of a model that was "usefully" right but not mathematically true.

