There is no law beyond Do what thou wilt.
@Ioaness said
"...the application of the scientific method to religion. If my understanding is correct in Thelema this method is used to help each individual upon his or her spiritual path. ..."
if 'in Thelema' is not interpreted to mean that it is ubiquitously so used, then you have made a valuable point. the motto of certain proclaimed manifestations of the Great White Brotherhood or Third Order (in particular the A.'.A.'. - "The Method of Science, the Aim of Religion") gives the impression that their intention is to apply the method of science. however, it would be an error to equate Thelema with the A.'.A.'. or any of its possible correlates.
"...hard for me to understand why nearly every Thelemic group has as a requirement to accept the Book of Law without wishing to make changes to it."
adherent conformance in Bible-methodology-laden Western cults is facilitated by the safeguarding against too great a change made to the Magic Book. one need only look to the councils of Nicea and beyond to see what transpired with the Christian cults through the centuries. an oath supposed to gain agreement by the initiate to submit to the cult's selection of the Magic Book is therefore pragmatically helpful to retaining that cult's perpetuation.
the main problem here is the application of the descriptor 'Thelemic' to the term 'group' with the expectation that 'Thelemic' will retain a liberative sense. in fact, enslavement mechanisms utilizing the posture and labelling of 'Thelemic' are not uncommon, and only with a thorough familiarity (through study and insight based on personal discipline, practice, focus, work) of the Law of Thelema will one encountering any cult brandishing oaths for participation in them be able to preserve one's volitional soundness while negotiating a relationship with them.
"If someone tested this for his or herself and found the book would not be of use to him or her, would that not make him or her a Thelemite?"
given the premise that a Thelemite is an initiate to a cult of the Beast that requires these puerile acceptances, that is precisely what it means (that she would not be capable of remaining a member of the cult in good faith). were a different meaning of 'Thelemite' presumed then different conclusions might apply.
"Does not the founding book of Thelema seem {paradoxical} to the nature of Scientific Illuminism?"
not quite. the nature of Scientific Illuminism as an ideal shifts with its expositors and their insight into its character. many of these terms are at issue or have fluctuating referents. if you are familiar with algebra, compare it to asking whether the sum (X^2 + Y^3 + Z^4) yields a specific value. there are too many undefined variables to arrive at a conclusion. the best way to clearly respond to such a question as yours is to provide the variables a firm definition and then solve.
Thelema as a principle of the cosmos (relating to personal volition) wasn't founded on a book. it was given somewhat ambiguous emphasis in book(s) under scrutiny here in the aftermath of works such as that by Rabelais and others.
Scientific Illuminism may proceed by any of a variety of courses as long as the general method is scientific. this might include the use of a Magic Book to effect it, and several cults, even those calling themselves Thelemic or Scientific Illuminates, sport such magic tools.
with each person encountering a religious expression this adds another dimension of possible change to that original by form or interpretation, and in this manner rival factions and vying cults come into being. for the purpose of finding illumination any particular cult might settle on a specific focal object (e.g. a book of their selection) as a fulcrum to attempt its successful result.
certain standards or constraints might assist the group to achieve this with the least trouble and simultaneously encourage individuals within them to self-select against participant disruption. this is in no way paradoxical, it simply sets out an axiom upon which to build theorems in a collaborative enterprise. compare being willing to conform temporarily to the leadership during a group rite so as to make headway in the agreed purpose.
"...you could accept The Book of the Law as {being} false, yet still be considered a Thelemite?"
amongst the more liberated, 'accept' is left ambiguous and the dogmatism of the initiate is allowed (possibly alongside guidance from a mentor) to self-delimit, whereas those whose education and awareness allows need have no notion of the truth or falsity of the illumination object itself. that consistency of referent doesn't qualify so much as one utilizing a law or principle of the cosmos (Thelema) as facilitating participation in a cult ('Thelemic' group).
"Any concept within mathematics could (and most likely would) be changed if deemed false. While this might is extreamly unlikely, if the founding mathematical {principles} were found to be wrong they would be changed. The idea that even if The Book of the Law is well established, the fact that it can't be changed under any circumstances seems to me to be ridiculous."
ignoring for the moment that there is a world of difference between reasoning from simple concepts of number or calculation which are at base axiomatic to conclusions and settling on a Magic Book as one's group's oracular focal tool, you are quite correct that its selection is ARBITRARY.
there are certain helpful characteristics for oracular documents such as imaginative complexity, diversity of language, and obscure references, which make 'peering into them' for bibliomantic enterprises more fruitful. the results, rather than the tool, in this instance, are what will likely constitute a focus in any scientific sense. to require that there be a 'control' as within a strictly materialistic and scientific sense is the effective parallel here. it would be ridiculous if its membership were attempting to export these agreements beyond the cult to Thelema (as a movement or subculture) at large or to the world.
"...why anyone wouldn't attempt to test the theories of Thelema, as this would make them simply mindless sheep. ..."
at issue here is what "the theories of Thelema" are (you can see from my text above that i am already providing to you more than one valence for 'Thelema' in which this would apply). there is a heavy emphasis on results and success (seldom elaborating on how to recognize or measure success, to be noted) within the Crowleyan cultus, and this is one of its positive features.
"...making people accept a book without being able to make any changes, makes scientific testing useless. If the Book of the Law needs no changes why not let people come to this conclusion themselves rather than dictating it as a requirement of Thelema?"
before concluding my response to you, let me compliment you on the acute logic of your queries. based on your premises, your apparent conclusions deserve much attention, and those who encounter you will repeatedly benefit from your philosophic approach. as you can see above, the terms 'accept' and 'Thelema' are given alternative significance to what you seem to be asking here. in some groups sporting the moniker of 'Thelemic' which do in fact require the embrace of a New Bible, your critical assertion is completely proper. they fail as scientific illuminists and are at best illuminists trying to make their way using other methods.
@Knowledge + Deligh said
"Imagine if someone came along and said something like, "Do what thou wilt - but only sometimes." It would be a tainted interpretation of the law. ..."
there is no need to imagine it, you can see it for yourself quite easily. Wiccans and Thelemites say this all the time. 'Do what thou wilt, but only if it is your True Will.' even by religious law: "Do what thou wilt, an it harm none." even Crowley, in his Commentary, issued something similar: 'Do what thou wilt, as long as you're illuminated.'
" ...the end result is an 'alteration of the law'."
only insofar as 'the law' is a set of characters recognized as a book or expression. where it is understood to be a principle of the cosmos, this cannot, in fact, be changed.
"The charge to 'accept without wanting to change' ensures that the original is preserved in full, which is very important for future generations of Thelemites."
it is important for future Crowleyan cultists seeking to use this within their milieu. misunderstanding this and propagating it beyond the cult merits being treated as a centre of pestilence (shunned by reasonable people outside her zealous circle).
Ye are against the people, O my chosen!