Who Really "Knows" E8 ?

On the Impossibility of Knowing It All And What That Means and The Faith Based Rejection of Science

When the E₈ figure constructed by a team of mathematicians using linked computers was announced it was kind of thrilling, if you find that kind of thing thrilling.  The sheer size of the effort to describe such an imaginary object in eight dimensions is stunning.  If I recall correctly, one of the more informed newspaper stories I read said that if printed out the paper required would be bigger than the island of Manhattan, or maybe it was twice the size.   At any rate, it would take more paper than I ever used in all of the math courses I took by a considerable amount.   In this "narrative" account  by David Vogan, a leader of the group,  of how it was done, if you wade through the stuff that I had to pretty much skim (with time taken out for my mouth to drop open at the size of the numbers involved in the effort) you'll come to this

So how big a computation is this character table for split E8? Fokko's software immediately told us exactly how many different representations we were talking about (453,060); that's also the number of terms that could appear in the character formulas. So the character table is a square matrix of size 453060. The number of entries is therefore about 200 billion, or 2 x 1011.

But, not to worry because he continues:

Fortunately the matrix is upper triangular, so we only need 100 billion entries

Reading even this narrative, for me, is like looking at the shadow of a reflection of the E₈ figure at a great distance, through a gauze.   I can gather enough of the achievement to be very impressed but I really can't even understand the terms in the first paragraph.   My friend who teaches mathematics at a quite decent land-grant university and who publishes several papers a decade told me that she doesn't understand much more of it.   I don't think she's just trying to make me feel better, she's admitting the same thing that Richard Lewontin did more generally. 

First, no one can know and understand everything. Even individual scientists are ignorant about most of the body of scientific knowledge, and it is not simply that biologists do not understand quantum mechanics. If I were to ask my colleagues in the Museum of Comparative Zoology at Harvard to explain the evolutionary importance of RNA editing in trypanosomes, they would be just as mystified by the question as the typical well-educated reader of this review.*

As soon as I read the size of the effort of constructing the model of the E₈ figure my first question was if anyone, even the most well informed members of the group could meaningfully claim to understand it or how confident they could really be in the tightness of their results.   No one could possibly master more than a small part of the topic and there is not really any such thing as knowledge that is held collectively, not without a great deal of faith in all of the other members of the group.  Perhaps in the efficacy of the computers and the intellectual architecture of the attempt.  Faith would, obviously, be a requirement of even a mathematical or scientific "fact" of  even less daunting dimensions.   Short of many minds being joined as the computers could be, the fact is that no one can really "know" much of anything about even that many dimensions.  The holding that what is "known" about it is actually known stretches the meaning of the word.   That word is similarly stretched even further to cover the entirety of what is included in science. 

While the obvious connection of this issue of faith in science with religious faith are there, those aren't what I'm interested in addressing in this post.   I'm interested in, once again, addressing the annoying and arrogant superstition among the obnoxious scientistic fundamentalists that is getting steadily worse.    Yes, I've been looking at the trash filtered out from my in-box, again. 

Everywhere since the inception of the "Skepticism" industry and especially since Sam Harris and Richard Dawkins have instituted the new atheist fad, the internet has been plagued with masses of these scientistic fundamentalists, many of whom are far more ignorant of even very simple math and science than, for example, I am.   It's not uncommon to find them making baroque and elaborate arguments about, most typically, religion on the basis of string or M-theory that involves speculations about more than eight dimensions, all while appearing to not be able to solve a linear equation, never mind a quadratic one.  As can be seen in the series I did about James Randi  et al. it is possible for a total ignoramus in matters scientific, to be revered as an oracular figure of science by a large number of acolytes.   And not only the quite ignorant of science but popular figures who are actual scientists.  One person I encountered recently said, well, yeah, Randi doesn't have any training in science but he spent a lot of time with Carl Sagan.   I noted that Carl Sagan spent a lot of time with Ann Druyan but that didn't make him a woman.    What is clear about this is that even such a figure of the church of scientism as Carl Sagan must have known that Randi is a complete non-entity in science but they were OK with the effort to sell him as a representative of science.  

The reason for that is ideological and political,  Randi shares a faith in materialism with Sagan and other actual scientists in the promotion of scientism.  That shared faith is enough for them to, not merely overlook the dishonesty of the effort, but often to participate in Randi's PR promotion.   The sheer dishonesty of Randi and the widespread acceptance of his self-generated career as a spokesman for science by scientists who know it is a total fraud, is certainly a scandal.  I would say it is a scandal big enough to do actual harm to science.  But that is the price that lots of scientists are willing to pay.  I think it's as clear an example of the corruption of science as it is alleged to be as opposed to the ideology that it has become in far too many cases. 

On The Faith Based Rejection of Science

As creationism and climate change denial shows, science can't only be accepted on the basis of pre-existing faith but it can be rejected as well.   I would have to say that it is in the materialists' faith-based rejection of science and other ideas that is the most basic aspect of their religion.   That is an aspect of "Skepticism" that is too little addressed.   I will point out, again, that several of the pseudo-scientific "voices of science" such as Randi and Penn Jillette, have extended this practice of "Skeptical" denial to climate change science. 

Dr. Dean Radin has posted a linked index of peer-reviewed studies in psi and related phenomena.  Many of the papers lay out quite impressively careful and controlled experiments which have yielded results of far, far more than sufficient statistical evidence than is generally required by science.   I can understand quite a bit of the math in some of them so I don't have to take that on faith.   I know the "Skeptics" provide a level of oversight that almost certainly guards against lapses in methodology and attention, I have even more faith in the internal critics and referees in that area.  I would say that someone who is even more knowledgeable of statistics than I am would not need as high a level of faith in the results of that science than need to either accept or reject it.  Though they would be even more aware of the necessary effort required to SCIENTIFICALLY challenge the reviewed results that are reported.   Requirements that are often not practiced by the "Skeptics".  I don't think anyone who hasn't even read the abstract of a paper can reject it on the basis of anything but faith.  I'll bet not one in 200 of the blog "Skeptics" could do even that. 

*  Richard Lewontin addresses the problem of the fact that we are all at the mercy of an inevitable reliance on authority, and the choices of even very sophisticated scientists will often be less than universally accepted by those with more knowledge than they have.

Third, it is said that there is no place for an argument from authority in science. The community of science is constantly self-critical, as evidenced by the experience of university colloquia "in which the speaker has hardly gotten 30 seconds into the talk before there are devastating questions and comments from the audience." If Sagan really wants to hear serious disputation about the nature of the universe, he should leave the academic precincts in Ithaca and spend a few minutes in an Orthodox study house in Brooklyn. It is certainly true that within each narrowly defined scientific field there is a constant challenge to new technical claims and to old wisdom. In what my wife calls the Gunfight at the O.K. Corral Syndrome, young scientists on the make will challenge a graybeard, and this adversarial atmosphere for the most part serves the truth. But when scientists transgress the bounds of their own specialty they have no choice but to accept the claims of authority, even though they do not know how solid the grounds of those claims may be. Who am I to believe about quantum physics if not Steven Weinberg, or about the solar system if not Carl Sagan? What worries me is that they may believe what Dawkins and Wilson tell them about evolution.