[FOM] f.o.m. documentary 1

[Abolfazl Karimi]

Hello everyone,

I believe it's a great idea to produce a documentary on foundations of
mathematics. I'll explain my case as an example of how a documentary can
inspire someone to pursue a particular field of research.

In high school, I enjoyed technology and engaged in amateur building of
robots, electrical circuits and computer programming. These led me to
choose software engineering in school of ECE in University of Tehran for
undergraduate studies. In those years I realized that my cognition is
developing to a deeper state: I could not accept the validity of the
formulas which have originated in sciences such as mathematics and physics
until I had verified them myself. Because in engineering more emphasis is
placed on how to use formulas rather than their proof, I decided to switch
to computer science for M.Sc. degree which is offered in the faculty of
mathematics. In my graduate studies, I enjoyed the meticulous attitude of
mathematicians and computer scientists, building their theories from
scratch and proving every single proposition. But I realized that something
is missing: I was interested in an all-encompassing and unifying theory
which would reveal limits of human knowledge and its foundation and most
basic axioms, rather than specializing in a narrow and secluded area of
research.

So after my graduation, I initiated an extensive research to find out in
what discipline my goals are pursued. When I was a B.S. student, I had
watched "The Elegant Universe" which is a documentary on the foundations of
physics, describing early and modern efforts to unify all of physics into
one coherent and consistent theory. It seemed to me that physics is based
extensively on mathematics (apart from experimental data), but mathematics
seemed to be independent of any other theory. Also, mathematics is more
extensively used in other sciences than physics. So I wasn't inclined to
convert to physics. Therefore, I decided to investigate whether some
unifying theory exists in mathematics. I started searching some keywords
such as "unification in mathematics" or "a theory for everything in
mathematics" until I found Gregory Chaitin's article: "Omega and why maths
has no TOEs". I read some relevant sources and was exhilarated when I knew
that all of mathematics can be embedded in set theory and also surprised by
the incompleteness results. FOM is appealing to me because it includes both
philosophical motivations and mathematical rigor. Now, it's almost a year
that I'm reading introductory textbooks and papers on Foundations and
Philosophy of Mathematics and Logic and I'm considering to continue my
studies in this field.

Best wishes for the documentary,
Abolfazl Karimi

On Mon, Feb 13, 2012 at 7:46 AM, Harvey Friedman <
friedman at math.ohio-state.edu> wrote:

> PLANS FOR A DOCUMENTARY
> by
> Harvey M. Friedman
> February 10, 2012
>
> I am planning to author a multipart documentary entitled
>
> CAN EVERY MATHEMATICAL QUESTION BE ANSWERED?
>
> 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.
>
> AUDIENCES FOR STATE OF THE ART SCIENCE.
>
> 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.
> Supernovas.
> Black holes.
> Gamma ray bursts.
> Space and time travel.
> Creation of elements.
> Relativity, space, time.
> Quantum nonlocality.
> Molecules and elements.
> DNA.
> Evolution.
> Mass extinctions.
> Origin of life.
> Search for life.
> etcetera.
>
> 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.
>
> 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.
>
> SPECIAL STATUS OF FOUNDATIONS OF MATHEMATICS - HISTORICALLY.
>
> 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 otherwise.
>
> 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 century.
>
> 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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