Amaton

Maybe not so bad. [math]H(\pi,\tau)=\dfrac{2}{\frac{1}{\pi}+\frac{1}{\tau}}=\frac{4}{3}\pi=\frac{2}{3}\tau[/math]. Ah! Let's denote this constant [math]\eta[/math]. The volume of the space enclosed by a sphere is [math]V=\eta r^3[/math]. Now where's my Nobel Prize?

Repainting the Mona Lisa seems a bit easier... Okay, how about the harmonic mean of [math]\pi[/math] and [math]\tau[/math]? Love and peace, right guise?

Thank you.

True. This discussion isn't really exclusive to mathematical aesthetic. What do you say about pedagogy? Public school students in the US begin learning trigonometry and radian geometry in high school (freshman year at the earliest AFAIK). There has always been some initial confusion with learning radians in multiples of pi, having to wrap one's head around pesky factors that seem almost extraneous. For most students in accelerated curricula, this almost never turns out to be problematic later on, but it is a slight pedagogical issue nonetheless. Do I think it merits a complete overhaul of which constant to use? Certainly not -- but it's still something to consider. It's more of a literary device than a serious, objective statement. The author did not intend anything "stupid" by saying that and indeed elaborates on it.

Coming from a confused introductory chemistry student... My problem began while I was reading over the chapter on aqueous reactions. Rather than go into chronological detail about my confusion, I'll just ask the more fundamental questions first to see if there's a root misconception involved. 1) Okay, so when a compound is said to be molecular, it contains covalent bonds. (so, "covalent" and "molecular" are, in a sense, interchangeable) Correct? 2) Ionization vs dissociation: An ionic electrolyte dissociates in aqueous solution, while a molecular electrolyte is said to ionize. Is this right? I'm not sure if the terms are somewhat interchangeable or if they're even precise, but it seems to make sense... A molecular compound consists of covalently bonded atoms, so when such an electrolyte breaks up into ions, it changes i.e. ionizes. On the other hand, ions are already present in some form with an ionic compound, so there's not really any "ionization" going on -- the component ions simply need to separate, i.e. "dissociate". Am I picking this up correctly? Or is there no hard-cut distinction between the terms? 3) Are acids ionic or molecular compounds? And what of bases?

To no one in particular... I can see why this inquiry might seem a bit unnecessary, but I'm trying to show and discuss the blurriness in terminology concerning belief systems and practices. So what would you call it?

They are not perfect rhymes, but they are rhymes to a degree (and rhymes nonetheless). More precisely, these follow a pattern of imitating the vowel, just with different consonantal sounds. I forgot the literary term for "words with the same vowel sounds".

I'm aware that many members of this forum are non-religious (and atheistic to a greater depth). Generally, this group regards religion as uncorroborated claims and silly rituals. However, I had a thought, and so I ask, is it possible (from the secularist view) for there to be a reasonable religion? And can / will people like us willingly take part in it? Let's say an alien species makes contact with us, one that is relatively advanced both biologically and technologically; they are incredibly capable beings. The species intends no hostility or invasive harm, but it does hold some desire of sovereignty. They give us advanced technology, essential resources, longevity, and protection. Now, imagine if this species arrived at a time of great human hardship and turmoil: lack of resources, war, global famine, suffering. And now, these almost supernatural beings have become our salvation. A "cult of the personality" like image has come to fruition in humanity's collective mentality, as we worship in wonder and thanksgiving to our superiors. Even rationalists and former secularists are enthralled in their almost-supernatural semblance. The masses gather at localized congregations to give thanks and praise to their ubiquitous image. We build monuments to them. Worship becomes a central aspect of our lives; etc. So I ask, would one consider this religion? If most of society understands that these beings are not above the laws of nature, and that they are simply very progressed technologically, then in intention we are not worshiping gods, per se. There is no doubt to evidence and rational skepticism, as is the problem with today's major religions. However, in this scenario, humanity is essentially idolizing them in ritualistic veneration, just as devout adherents to a faith would: bowing down, giving thanks, venerating symbols and images, etc. One might argue that this is more similar to a "cult" rather than a religion, with the major exception of it being generalized to the general masses. What do you think?

I feel like this is the problematic crux of this discussion. The OP's question can be viewed in two lights. Which is the more practical constant for most common uses? Pi, obviously (as I would assume the majority to vote). Now, which is the more fundamentally natural? I'm not sure, and I believe this is still quite debatable. The usefulness in application deal is wholly irrelevant in regards to the abstract naturalness of the circle constant. What would a pure mathematician consider to be the more natural, the more beautiful? For the latter question, I'd have to favor [math]2\pi[/math]. A circle is defined as the set of all points of distance [math]r[/math] from a certain point. That variable is the radius, and I simply prefer a constant that forms a united conversion factor between that variable and the circle's circumference. Anyway, I don't really trust the famous Eulerian identity [math]e^{i\pi}+1=0[/math]. It's really not anything special if one thinks about it. The identities [math]e^{i\tau}=1[/math] and [math]e^{i\pi}=-1[/math] are much more representative of the complex exponential. The argument-output relationship for the complex exponential is after all just angular measures and their respective revolutions in the complex unit circle. All in all, pi's good for physical measurements, but when it comes down to the abstract and beautiful mechanism of pure mathematics, [math]\tau[/math] seems to take the cake. And I reference Michael Hartl's wonderful Tau Manifesto, from beginning to end, as unchallenged corroboration. Still, for conventional reasons, I will most likely keep using [math]\pi[/math] in my everyday math, for school, whatever. I don't care if plumbers or engineers keep using it; it's convenient and totally practical.

I see what you mean. It probably depends on whether one is more facile with "stream typing" or point-and-click. I can type fast, but I'm not very familiar with the TeX codes. It's like learning a language; one just has to practice to become more fluent. You're right. And don't think I didn't report you for derailing a perfectly good thread. (just kidding, the original poster does not mind, so discuss away!)

Well our new presidential family member here in the US has bad breath and is incapable of speech (but then again, she's a dog).

LaTeX is great and pretty comprehensive if you ask me. It is a bit tedious though for larger and/or more complex expressions. If mathematical notation is going to become standard on an electronic medium, I think it should go the route of Microsoft Word's equation editor. The interface is intuitive and everything's quick and easy. However, the version I'm familiar with isn't as complete as TeX.

As ajb noted, that's simply using a different base system, base-5 in your case. Notation is a different matter, though I don't doubt the benefits of using certain bases. That's true. I guess a comprehensive standardization would either be impossible or impractical. In a way, I think notation (and nomenclature) in elementary mathematics is already rather standardized.

I was somewhat aware of the discrepancy, which is why I said it was one of the odd plurals (derived as a plural, but treated as singular in construction). Though all in all, I never knew that. Thanks.

Yes, and so the matter returns to convention. I read that some fields use [math]v^j[/math] for vector notation, and I would have terrible frustration having to constantly remind myself that [math]x^2[/math] is not x squared! I suspect that the field-endemic conventions of today are direct results of the personal preferences of very authors that contributed to the development of those areas. Then maybe this universal guidebook will have to be very comprehensive in its notational "alphabet". I'm thinking analogously to the International Phonetic Alphabet, which assigns a unique symbol or symbol pair to every practical sound the human mouth produces in speech. Of course, the 20 - 30 letters of modern Greco-Latin alphabets aren't enough to accomplish this, so many symbols exist beyond any individual one. Likewise, for universal notation to be comprehensive, many more forms will likely have to be introduced to avoid that non-uniqueness you brought up. We may also reserve multi-use notation for more "exotic" objects, which are less likely to be mixed up and confused. I'm just asking for us to weigh the pros and cons. Yes, though these cases may not be so bad for certain reasons. Geometry helps one to visualize the scenario and the objects therein, whether by textual description or an actual diagram (where they are explicitly shown or stated). "Line segment AB intersects ray Q> at its point of tangency to circle P". One cannot do so this easily with symbolic analysis or similar approaches.

I think the abbreviation explanation is more likely. "Mathematics" is an odd plural form, and we keep the "-s" when we abbreviate it. Though we ever rarely say "maths" here in the US, many college students do say "stats" for statistics (though "stat" may be a bit more common) All in all, it ties back to the plurality of the subject name. "-matics" has a sense of mechanical observation: blueprints, movement, mechanism, etc. With mathematics, we are studying the "blueprints and mechanisms" of quantitative entities and their logical relations, loosely speaking -- and at a progressed level, constructing our own abstract devices. One can look to chemistry. Besides the reference to the generic subject itself, we can speak of the chemistry of a certain substance, i.e. its states, its bonding, reactive tendencies, role in larger structures, etc. Hypothetically speaking, we could have ended up with "chemistries", which bears similar sense to mathematics as described above.

1) Why are there so many notations for vectors and related operations? v, [math]\vec{v}[/math], [math]v^j[/math], [math]v_j[/math], [math]|v\rangle[/math], etc. I understand that there are conventions endemic to certain fields of math/physics, but is there any practicality to get out if it? 2) As for mathematical notation in general, do you think it would be practical to establish a universal set of notation that could be used across all fields of mathematics and science?

Before this thread, I never gave much thought to the fact that my classmates and I tend to refer to statistics as "stats" (more so to the class than the actual subject though). I was just a bit surprised since "maths" always sounded odd to my ear, but now I have something to relate.

It's a colloquial form of frequenter (with no official denotation). Edit: By the way, though I did not mean it in this manner, the usage can be interpreted as usage of adjectives as nouns. Can you fetch me my deliverable? I read that it's actually characteristic of language in scientific circles (literature or casual discussion, I'm not sure), despite being frowned upon grammatically.

It's pretty funny how someone uses the niches of vernacular language as a justification of their silly prejudice. I would say this thread deserves some sort of moderating action, if it weren't for the sincere language discussion that arose among frequents here.

This excerpt follows directly from your statement, "Many things are not explainable by the conventional scientific logic which does not accept many truths like miracles, omens, etc and tries to answer every question with not a very open view." Are the points following that statement supposed to be supporting examples? String theory is still a tentative work-in-progress that is in continuuing development. You expect a fully functioning device from an incomplete blueprint. Also, it would be odd for a physicist to study the composition of an electron since it is a point-particle in the Standard Model (as we are discussing current scientific theory). And a good layman's book on quantum mechanics will give you the proper context of that "infinite barrier". You are using your own misconceptions as a basis for miracles beyond the natural world, and you use this as a rationale to build up your own personal theory (none of which, from what I read, has any verifyable observational evidence).

I think the orignal "people who...are broken" thread was rather misled, and this one is no better. You feel like you're not broken. Your individual case implicates nothing for theists abroad. You feel like you're not broken. One's psychology goes beyond what is apparent to themself. Anyway, you failed to properly present your matter, which is whether people who believe in God are broken. You did not address your position, elaborate on your reasoning, or give any evidence relevant to the title. Instead, you provided personal reasoning for why you may believe in God, but it had very little to do with "brokeness", for either you or theists in general.

If I'm understanding your process correctly, you're basically doing: [math]p_{n+1}=2^{p_{n}}-1[/math] for [math]p_1=2[/math]? The statement is that "For [math]M_n=2^n-1[/math], if [math]M_n[/math] is prime, then [math]n[/math] itself is also prime." However, the converse is not generally true, and so the primality of the resulting numbers in your sequence will be uncertain. Your sequence will get very large very quickly, so you'll be testing extremely large numbers (though I may be misinterpreting your idea).

Yeah, I got to that as well, but it doesn't seem like it could do anything. Because one requires that "+1" for both primes, the relation becomes pretty trivial. We're simply looking at powers of 2 separated arithmetically by a relatively large number, so I don't see how it could shed light on your candidate's primality. However, I may be thinking too superficially, and one could use more indirect logic and make use of it in a proof.