Dr. Escultura Responds

Since our last post about the "secret controversy" wherein Dr. Edgar Escultura claims to have refuted Dr. Andrew Wiles' proof of Fermat's Last Theorem (FLT), Dr. E has returned to the DLMSY comments section. Again, we have no conclusive proof that this is the real Dr. Escultura writing these comments, but the IP address is from the Philipines.

These comments will scroll of the HaloScan system after a few months. Also they're scattered about and rather hard to find, so we have pasted them here in the main blog. There are three comments from Dr. E, which are somewhat duplicative. The first:

For those interested in the countably infinite counterexamples to FLT, here they are:
Let x = (0.99...)10^T,
where T is ordinary integer. y = d*, where d* = 1 - 0.99... called dark number. z = 10^T.
Then, for n > 2, x^n y^n = z^n.

The numbers x, y, z, are called new integers. They consist of d* and numbers of the form N.99..., N = 0, 1, ... They are isomorphic to the ordinary integers under the mapping 0 -> d*, N -> (N-1).99...,N = 1, 2, ... This isomorphic embedding of the oridnary integers into the contradiction-free new real number system as integral parts of the decimals resolves the fundamental flaw of number theory, that the integers have no valid axiomatization at the present time. In other words, until this embedding they were nonsense.

The new integers x, y, z are among the countably infinite counterexamples to FLT that prove this conjecture false. The rest of the countably infinite counter examples to FLT are also countable, the triples (kx,ky,kz), where k = 1, 2, ..., is an ordinary integer, since (kx)^n (ky)^n = (kz)^n.

These counterexamples and their applications are published in over two dozen scientific papers in renowned refereed internatitonal scientific journals and proceedings of international conferences. For details see my websites.

On to the second comment from Dr. E:

For those interested in the countably infinite counterexamples to FLT, here they are:

Let x = (0.99...)10^T, where T is
ordinary integer.

y = d*, where d* = 1 - 0.99...
called dark number.

z = 10^T.

Then, for n > 2,

x^n + y^n = z^n.

The numbers x, y, z, are called new integers. They consist of d* and numbers of the form N.99..., N = 0, 1, ... They are isomorphic to the ordinary integers under the mapping

0 -> d*, N -> (N-1).99...,

N = 1, 2, ... This isomorphic embedding of the oridnary integers into the contradiction-free new real number system as integral parts of the decimals resolves the fundamental flaw of number theory, that the integers have no valid axiomatization at the present time. In other words, until this embedding they were nonsense.

The new integers x, y, z are among the countably infinite counterexamples to FLT that prove this conjecture false.

The rest of the countably infinite counter examples to FLT are also countable, the triples (kx,ky,kz), where k = 1, 2, ..., is an ordinary integer, since

(kx)^n + (ky)^n = (kz)^n.

These counterexamples and their applications are published in over two dozen scientific papers in renowned refereed internatitonal scientific journals and proceedings of international conferences.

For details see my websites.

Perhaps there may be some applications where this system is or will be useful. I simply don't buy Dr. E's assertions that: a) the Trichotomy is false or b) that redefinition of the integers is either necessary or meaningful with respect to FLT or for most of mathematics.

It can be easily shown that 0.999... is neither less than 1 nor greater than 1. The Trichotomy says the only other possiblity is that it is equal to 1. In Dr. E's math universe there is a fourth possiblity, i.e. 0.999... is not less than 1, not more than 1, and not equal to 1, but something else entirely. Something "dark," darker than Hilary's disposition when she sees Bill.

This kind of thing sounds kooky, but it might have some use. The set of imaginary numbers is defined in terms of "i," the square root of -1, which doesn't technically exist. However, imaginary numbers are used for many real world applications, for example in describing the behavior of the NMR signals in spectroscopy (or for "MRI" as it's called for medical imaging).

We don't much care whether or not these alleged counter examples are "countable," and we certainly don't have time to count them. So let's just consider T=1, the first example. So:
x = (0.999...) * 10
y = (0.999...) -1
z = 10

In the integer math of the rest of the world this means x=z=10 and y=0.

Indeed, if any of x, y, z is allowed to be zero, then any positive integer could be used for both of the other two variables. This is trivial, and FLT explicitly requires x, y, and z to be positive integers, and therefore not zero.

Dr. E is free to define 0.999... as different from 1, but clearly even if there were a difference it would be infinitesimally small, approximately zero. This d* would not be a non-zero integer itself under the rules of FLT. Moreover, even if 0.999... were not equal to 1, it would not be an integer either under the rules of the game everyone else is playing by.

And the third comment:

Someone missed the point again. The problem with the argument here is that the set of integers is not well-defined as a mathematical space. It falls short of basic foundational requirements. Therefore, the problem as formulated is nonsense. The only way to fix the integers is to embed them isomorphically into the contradiction-free new real number system as the integral parts of the decimals. Then FLT can be reformulated to make sense in this space.

For more discussion on FLT visit the Digital Mercenary website.

It quite a stretch to throw out Trichotomy while claiming this system is "contradiction free" and traditional math is "nonsense."

In plane geometry two lines must intersect in a single point, all points, or not intersect at all. Change the system to spherical geometry and the lines could intersect in two points, one, all, or not at all. One cannot establish that a theorem in plane geometry is false by using the rules of spherical geometry or vice versa.

This is what Dr. E is attempting to do with FLT, as he admits in saying, "Then FLT can be reformulated to make sense in this space." Reformulating FLT into his system, where he has an extra zero to play with, makes it a completely different (trivial) problem. So what? This has nothing to do with Dr. Wiles' work.

How many legs does a dog have, if you call the tail a leg? It has 4, because calling a tail a leg doesn't make it one. The dog's legs are countable. You might say it has 3.999... legs, and we wouldn't disagree. We're not ready to go over to The Dark Side, though.

Dr Escultura's web site is here, if you really can't get enough of this stuff.

Technorati: Andrew Wiles, Fermat, Edgar Escultura, mathematics, hoax, press misconduct, Manila Times

Anti-Semitism in France

In Nazi-occupied France the Vichy government cheerfully rounded up extra Jews for deportation to the death camps. There's a French streak of anti-Semitism that goes back a long way, and it's on the rise again. A few years ago Ariel Sharon provoked French ire by publicly suggesting that French Jews consider emmigrating to Israel for safety's sake.

Like their blindness at the failed "Integration Model" for French Muslim immigrants, denial by the French of French anti-Semitism is practically the state religion. While the US was pre-occupied with the riveting tale of Dick Cheney's hunting accident a particularly nasty kidnapping and murder occurred in France. The target: a young, French Jew. The kidnappers: a gang of French Muslims.

Nidra Poller at OpinionJournal:

PARIS--Two weeks ago a 23-year-old man initially identified as "Ilan" was found by a passerby stumbling in a field near the railroad tracks in the Essonne region south of Paris. Handcuffed, naked, with four-fifths of his body covered with bruises, stab wounds and serious burns, Ilan died in the ambulance on the way to the hospital.

Soon after, police provided more details. The victim had been kidnapped Jan. 20 and held for 24 days by a gang from the banlieues, the poor suburban projects that ring the French capital, who eluded capture while repeatedly contacting Ilan's family with ransom demands. The police suspect the group was involved in other kidnapping attempts in the past two months that used young women as bait. Several of the targeted men worked, as Ilan did, in the small cell phone shops along Boulevard Voltaire in the mixed 11th arrondissement of Paris. In another case, a suspicious father replaced his son for a meeting with a girl who claimed to be a singer, and fell into the hands of masked men who tried to capture him but ran away when someone called the police.

Throughout Ilan's disappearance, the police handled his case as a straightforward kidnap for ransom. The discovery of his body, bearing signs of barbaric torture over an extended period of time, raised serious doubts about this hypothesis. Later, a policeman admitted to the press that he and his colleagues were baffled by the gang's erratic behavior. Ransom demands went up to 400,000 euros, dropped to 100,000 euros one day, 5,000 euros another. The kidnappers called off several pickup arrangements, acting like amateurs, but were highly sophisticated in using untraceable emails and cell phones.

Yet one detail was consistently played down by the investigators and missing from the early media reporting on the killing. The victim, whose full name is Ilan Halimi, was Jewish. Most of the men targeted in other kidnapping attempts were Jewish. Most members of the gang who allegedly carried out the crime are Muslims, whose families come from the Maghreb or sub-Saharan Africa and live in the very sort of neighborhoods that went up in flames during three weeks of nationwide rioting last fall.

You'll want to read the rest. Even though the killers tortured him on the phone as they taunted the family with anti-Semitic remarks and passages from the Koran, the police didn't see any evidence that a hate crime was in progress. And:

No longer able to deny or play down the racial motive, the investigation is entering a new phase. One of the most troubling aspects of this affair is the probable involvement of relatives and neighbors, beyond the immediate circle of the gang, who were told about the Jewish hostage and dropped in to participate in the torture.

Fortunately Islam is a Religion of Peace. Otherwise just imagine how nasty this might have been. We paean Allah and Mohammed for these works of their devoted disciples.

Update: From Jihad Watch. The "mastermind" of the murder, Youssouf Fofana, has been returned to France from the Ivory Coast where he fled. Lots more information including this:

Twenty-one people have already been arrested, nineteen are behind bars, several big goons are still on the run. Police think that an even wider circle of people knew about the hostage and the torture, and kept silent. Some may be charged with "non-assistance to an endangered person."

Straight Shooting Woman on Al-Jazeera

Here's a great video from MEMRI of Arab-American Psychologist Wafa Sultan on Al-Jazeera TV. She doesn't pull any punches, as she takes the Islamic world to task for the "Clash of Civilizations." (H/T UnklB) Maybe someday Muslims who live in Muslim countries will be able and willing to speak as frankly as she does. We can hope. In the meantime, I'm pleasantly surprised and a little impressed that Al-Jazeera actually aired this.