|José Argüelles was not a scientist, and was not a Mayanist scholar, but rather was a believer in the mystical / New Age belief system called Mayanism|
José Argüelles (January 24, 1939 - March 23, 2011) held a Ph.D. in Art History and Aesthetics from the University of Chicago. He is remembered primarily for his role in the Harmonic Convergence event, and his various mystical/new age books.
- (1975). The Transformative Vision: Reflections on the Nature and History of Human Expression. Shambhala Publications.
- (1987). The Mayan Factor: Path Beyond Technology. Inner Traditions/Bear & Company. ISBN 0939680386.
- (1988). Earth Ascending: An Illustrated Treatise on Law Governing Whole Systems. Inner Traditions/Bear & Company. ISBN 0939680459.
- Argüelles, José; Miriam Arguelles, Chogyam Trungpa (Foreword) (1995). Mandala. Shambhala. ISBN 1570621209.
- (1996). The Call of Pacal Votan: Time is the Fourth Dimension. Altea Publishing. ISBN 0952455560.
- (2002). Time and the Technosphere: The Law of Time in Human Affairs. Inner Traditions/Bear & Company. ISBN 1879181991.
Ideas and claims
Argüelles has had some very unusual ideas over the years.
Arguelles claimed that he was the "heir of the legacy of Pacal Votan and the instrument of his prophecy, Telektonon" . He called himself "Valum Votan" which he claims means "Closer of the Cycle".
The use of the word 'Votan' is interesting, because the name "Pacal Votan" is not one that comes from legitimate mayanist sources. "Votan" and "Pakal" are two different figures: one mythological, and one historical. The story of Votan in Mexico dates back to the late 17th century, and it refers to a mythological 'founder' or ancestor of the Chiapas region. K'inich Janaab' Pakal, on the other hand, was the ruler of Palenque in the Late Classic period. It is only in sources associated with the mystic/new-age mayanism movement, and notably Arguelles' account and derivative accounts, that 'Votan' becomes associated with 'Pakal'.
Arguelles had some very odd ideas about time and space. For example:
By uncovering the Mayan codes, Arguelles discovered the telepathic nature of time. He also realized that the human species is living in artificial time, which is disrupting its planetary environment and destroying its civilization1.
This is only one of the claims made by Arguelles with regard to time. He also claimed that time is telepathic in nature, that it is faster than light, and that he can travel through it.
Another strange idea was the proposal of the 'Dreamspell' calendar, which was somehow going to cure the ills of the world. He issued an ultimatum to the effect:
If the human race does not reject the current twelve-month Gregorian Calendar and replace it by the new Thirteen Moon 28-Day Calendar by July 26, 1995, it will very soon bring about its own self-destruction.
Changing calendars by this date is a planetary ultimatum. The Thirteen Moon Calendar Change is the spearhead of a peace plan that calls for a universal cease-fire on July 25, 1995 to observe the historically unprecedented calendar change and a five-year follow-up program, Pax Cultura Pax Biospherica.
In order to implement their program, the Autonomous People's Planetary Moral Emergency Committees of the Thirteen Moon Calendar Change Movement are serving world leaders notice in the form of a "Biospheric Oath" to uphold the calendar change. Leaders who receive this Oath are given until July 24, 1995 to publicly affirm their support of the calendar change. After this date, if they do not agree to the Oath, they will be publically known as "enemies of the biosphere."
Through diplomatic channels the first world leaders to receive notice of the calendar change and Biospheric Oath are Pope John Paul II, Chief of State of the Vatican, and Boutros Boutros Ghali, Secretary General of the United Nations. 
When that didn't work out (apparently he received a polite refusal from an undersecretary who apparently was not concerned with being labeled "an enemy of the biosphere") he announced that he was putting the United Nations on trial . Other than this proclamation, I can't find any reference to this 'trial' or whether a verdict was ever rendered, and by whom.
Law of Time
His current website goes by the impressive title "The Galactic Research Institute of the Foundation for the Law of Time". On that site he made the following claim:
By 2012, according to the Law of Time, we must be ready for this shift, the unparalleled transition into the next stage of our evolution, the noosphere. This signifies the attainment of a unified field of planetary consciousness.
To change human consciousness, one preliminary step is to change the human macroprogram - the calendar. The most practical application of the Law of Time is the Thirteen Moon/28-day calendar. With this elegant tool, the Law of Time lays the foundation for the reformulation of the human mind - the coming of the noosphere. But this is only the beginning of the adventure in time. 
Argüelles (or as he called himself "Valum Votan, Closer of the Cycle" ) also asserted his "Law of Time" is expressed as "T(E) = Art, Energy factored by Time equals Art" and that this "accounts for the intrinsic elegance of all natural phenomena", and that "time is faster than light" which "accounts for telepathy and various paranormal phenomena" 
Therefore, it appears that his first prediction was for 1995. 14 years later Argüelles was making essentially the same claim, with a new date. So, the question becomes: "What evidence does José Argüelles show to support his assertions?". As far as I can tell, none, other than more assertions by himself.
Preparing for the transformation
As far as was known at the time of authorship of this biography (2009), Argüelles was living in New Zealand, trying to "prepare humanity for its shift into galactic consciousness" by sponsoring projects such as the "Circumpolar Rainbow Bridge Project, the goal of which is to telepathically connect the two auroras of Earth’s poles by 2012." 
José Argüelles passed away on 23rd March 2011, aged 722.