[FOM] f.o.m. documentary 1

Harvey Friedman friedman at math.ohio-state.edu
Sun Feb 12 23:16:49 EST 2012

Harvey M. Friedman
February 10, 2012

I am planning to author a multipart documentary entitled


Here are the steps I want to take in creating this documentary.

1. Extensive presentation/discussion on the FOM, of the content of the  
lecture notes.
2. Working with a variety of scholars and laypeople in and out of  
academia testing the effectiveness of 1 for a wide audience.
3. Videotaped lecture series by me based on 1. Internet dissemination.
4. Working with a variety of scholars and laypeople in and out of  
academia testing the effectiveness of 3 for a wide audience.
5. Designing the visuals needed for greatly enhanced dissemination.
6. Obtaining funding for implementing 5.

The core intellectual work is done in 1, with major upgrades expected  
from what I learn in 2 and 4.

Of course, I have control over 1-4, which would leave 3 as a finished  
product. Generally speaking, Universities will cooperate with 3.

There is a very natural flow of ideas emanating from CAN EVERY  
MATHEMATICAL QUESTION BE ANSWERED? that touches on most of the iconic  
events in the foundations of mathematics.

This flow of ideas is remarkably accessible as long as the copious  
technical material needed to do research are suppressed.


So what is a "wide audience"?

I am greatly encouraged by looking at the remarkable inventory of  
videos documenting state of the art work on scientific issues of  
compelling interest. I.e.,

Big bang.
Star formation.
Black holes.
Gamma ray bursts.
Space and time travel.
Creation of elements.
Relativity, space, time.
Quantum nonlocality.
Molecules and elements.
Mass extinctions.
Origin of life.
Search for life.

These hundreds of high quality video documentaries, airing frequently  
on public and cable television stations, and generally available for  
purchase, feature highly credentialed experts on these topics.

There seems to have emerged a generally acceptable and useful standard  
for discussing state of the art work in these areas in remarkably  
accessible terms. In each video, there appears to be a proper balance of

i. recent developments - at least towards the end.
ii. compelling understandability.
iii. intellectual validity.

I have compared some of the material presented in these videos with  
what appears on the Wikipedia, and there is considerable common  
material and common language. There is probably considerable overlap  
also in the people involved in pitching in on Wikipedia and in these  
videos. However, Wikipedia is now being taken pretty seriously as a  
kind of serious exposure for scientific topics, and I regard the  
considerable matchup between Wikipedia and the videos as lending  
credibility to the videos, and the idea that state of the art advances  
in at least considerable portions of science can be made widely  
accessible under a consistent standard.

These science videos are generally rather professionally done, with  
substantial budgets. Most of them are part of series of videos on  
related topics. I would be surprised if any of these series were  
produced in much under, say, 5 million dollars. I will try to find out  
more about this.

Here is some subscription or circulation information I have found  
browsing the Internet. What I found is vague on the issue of  
subscription versus circulation, which needs to be taken into account.

1. According to Scientific American, fewer than 10% of their  
readership are scientists.
2. Circulation of Scientific American: 476,867.
3. Circulation of New Scientist: 137,605.
4. Discover magazine: 716,079
5. American Scientist: 72,959
6. Science News: 140,000
7. Astronomy: 106,647
8. Popular Science:  1,302,472
9. Sky and Telescope: 77,382
10. Astronomy Now: 30,000
11. BBC Focus:  73,600
12. Cosmos (magazine): 28,000
13. New Scientist: 892,347

It is not so easy to get the sizes of viewing audiences for the high  
quality science videos. If someone knows such figures, I would  
appreciate hearing about them.


The mathematics presence in this arena seems to me to be relatively  
minor. And what mathematics there is, in this arena, generally appears  
in terms of its usefulness for *something else*. I.e., *something  
else* that is of compelling interest - not the mathematics itself.

The weak mathematics presence in this arena feeds into a general  
cultural perception that mathematics is interesting as far as it is  
useful for *something else* that is interesting. This is the general  
perception within the applied mathematics community - although the  
applied mathematicians, having generally won various resource fights  
with the pure mathematicians, will not openly express this view, so as  
to avoid accumulating enemies without purpose.

My own view is that mathematics is - or at least can be - interesting  
independently of whether or not it is useful for *something else* that  
is interesting. This is because mathematics sometimes directly  
addresses matters of great general intellectual interest. However, it  
is not the norm that mathematics directly address matters of great  
general intellectual interest.

The research agenda of pure mathematicians does not appear to be  
influenced by the addressing of issues of great general intellectual  
interest. Instead, they appear content to operate under a largely  
unanalyzed and unarticulated value system(s) that is far too subtle to  
be appreciated outside their own community.

But I have no doubt that there is some coherence in the implicit value  
system(s) in pure mathematics, and that great things would come from a  
detailed analysis and explication of it. There do seem to be a handful  
of quite incompatible value systems in operation. This causes  
considerable friction - all the more reason to have detailed analyses  
and explications of them.


Foundations of mathematics (f.o.m.) has in the past had a special  
status among mathematical subjects.

Note that I have chosen the category "mathematical subject" instead of  
"areas of mathematics". Some of the highest profile mathematicians  
today - and previously - have not regarded f.o.m. as a legitimate area  
of mathematics, or at least not a significant one. However, at least  
in my own experience, there is clear acknowledgement that f.o.m. is a  
"mathematical subject". And when I push the point, there is  
acknowledgement that f.o.m. is, or at least has been, a "mathematical  
subject of unusually wide interest outside mathematics".

As a high profile example, I have heard on good authority that Carl  
Ludwig Seigel did not think that what Kurt Goedel was doing properly  
belonged in the mathematics division of the IAS. Von Neumann thought  

That f.o.m. has, at least historically, special status among  
mathematical subjects is to me completely evident from its content,  
which I know well. Moreover, I can point to indications of this, that  
may be persuasive to people who know little about f.o.m..

Specifically, the high profile of Kurt Goedel. Not nearly as high as  
Albert Einstein, to be sure. But high enough to be on the very  
credible list of "100 most influential people of the 20th century",  
under the subdivision "(20) great minds of the century", published by  
TIME-LIFE at the end of the 20th century. In fact, there are as many  
as three figures in f.o.m., or I would say, 2 1/2 figures in f.o.m.,  
being Goedel, Turing, and Wittgenstein. Russell was mentioned as a  
runner up, and Wittgenstein being on the list rather than Russell  
reflects unstable trends in the philosophy community.

Note that no mathematician - pure or applied - is on that list  
(outside of f.o.m.), which was compiled via surveys among leading  
intellectual figures, by TIME-LIFE. Bear in mind, that we are talking  
about *general intellectual interest* here. And note that leading  
intellectual figures and others have had time to reflect on the 20th  

The Wright Brothers
Albert Einstein
Ludwig Wittgenstein
Sigmund Freud
Leo Baekeland
Alexander Fleming
Philo T. Farnsworth
Jean Piaget
Kurt Goedel
Robert Goddard
Edwin Hubble
Enrico Fermi
John Maynard Keynes
Alan Turing
William Shockley
James Watson & Francis Crick
Jonas Salk
Rachel Carson
The Leakeys
Tim Berners-Lee

It is generally acknowledged that the 1930s represented a Golden Age  
in f.o.m.

But what about since?

I will take this up in the next posting.

Harvey Friedman

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