# Dapthar

Senior Members

169

1. ## hey there any free engineering reference site?

What kind of engineering reference are you looking for? Chemical, Electrical, Mechanical, Nuclear, or something else? If you could be a tad bit more specific, it would help.
2. ## Is Noise Cancelling Done Biologically?

I've been wondering about the benefits of noise cancelling headphones. For those who aren't familiar with these devices, they essentially generate a sound wave that is $180^o$ out of phase with the low-frequency noise that is picked up by the microphones that are present in the headset. For example, see the attached picture. If the noise waveform was the red sine wave, the waveform generated by the headphones would be the blue sine wave, and when added together, these waveforms cancel out, resulting in no sound. (Note this is an idealized view, in reality the headphones can't generate the "anti-noise" waveform immediately, resulting in an incomplete cancellation, which is perceived as a quiet hissing sound.) However, my question is, is this addition of waveforms done in the air, or by one's ear? The reason I ask is if the cancellation is done in the air, then no sound actually reaches one's ear, and thus the ear does no work. But, if and the summation is done inside one's ear, i.e. biologically, then the ear is working twice as hard as it has to, leading to the twice the damage that constant exposure to the noise would inflict.
3. ## In what order should I go through Math subjects?

The number of Calculus classes usually varies by institution. A typical division is: Calculus I: Covers limits, continuity, symbolic and numerical derivatives, and applications of these topics. (Restricted to one dimension) Calculus II: Covers symbolic and numerical integration, advanced integration techniques, Taylor series, and applications of these topics. (Again, restricted to one dimension) Calculus III: Extension of differentiation and integration to n dimensions (with most of the time being spent on functions of two independent variables), vector calculus, and applications of these topics. The above topics are sometimes shifted between classes, but usually maintain the same relative order, e.g., basic symbolic and numerical integration may be shifted to Calculus I, but differentiation is in all but the rarest cases, taught before integration. Also note that the above structure is closely follows that of the text I learned Calculus from, authored by Edwards and Penney.
4. ## Finding Square Roots Manually

It depends on what you mean by "best". If you want a simple' date=' and quick way to get a reasonably accurate estimate of a square root, try the first method on this page: http://mathforum.org/dr.math/faq/faq.sqrt.by.hand.html If you want a more accurate approach, you could use the Binomial Theorem, and the details of how to use such a method are also on the aforementioned page, under the heading [b']Square Roots Using Infinite Series[/b].
5. ## Ender's Game

I suggest reading the "2001" series by Arthur C. Clarke. Namely: 2001: A Space Odyssey 2010: Odyssey Two 2061: Odyssey Three 3001: The Final Odyssey In general, anything Clarke has written by himself is worth reading, while books he co-authors tend to be lackluster.

7. ## Apple to Announce Intel Conversion Monday

I wonder how this will play with Intel's decision to begin embedding Digital Rights Management hardware into their dual core processors. But then again, Apple seems to have dealt with the DRM/iPod issue in a manner that hasn't alienated their user base.

9. ## New Server

Could you please make the SFN logo at the top left of the page link to the SFN homepage once again? Apparently the link was broken/forgotten when the style was updated. Thanks.
10. ## Higher-level language

There's Java. Not much else immediately springs to my mind besides C#, but that's a variant of C++.

12. ## A Geometric progression problem.

It looks right to me. I would have worked out this problem in the same manner, since it seems to call for an algebraic approach.
13. ## Real number axioms

I don't really have a personal version per say, I'm just quoting from memory. If you'd like, I can dig up my old Abstract Algebra book and post those field axioms here. Alternatively, I can just tell you the page number if you already have access to his book; Algebra by Michael Artin.
14. ## Real number axioms

I believe associativity and commutativity are all that's left.
15. ## Real number axioms

Yup. My mistake. I've fixed the original post.
16. ## Real number axioms

A set that is closed under addition and multiplication (both operations are commutative and associative), where multiplication distributes over addition, has multiplicative and additive inverses, and multiplicative and additive identity elements. The axioms are not 'absolute truths' as it were, for they cannot be proven to be true, you just have to 'believe' that they are. I suppose it injects a bit of faith into Mathematics. You know that the '0' and '1' I referred to are not integers, or reals, correct? They're just names given to members of the field. If you like, you can call them 'x' and 'y', or whatever you want. It doesn't, because I'm only saying that this is true for elements of the field with one element. As what I've said earlier indicates, I'm doing no such thing. What I mentioned does not apply to the real numbers, since the reals are not a field with one element.
17. ## Real number axioms

Because it doesn't have to hold in a field. In a field with one element, the additive identity equals the multiplicative identity.
18. ## Rose petals

I think that's there just to make people feel better about taking a while. RedAlert: Consider the following questions: What is the rose? What are the petals? Also, examine the situation where there are 0 petals around the rose very carefully. Finally, the pattern is not very complicated, so don't overthink it. If a mod thinks this post gives too much away, feel free to edit it.
19. ## The coming neurotechnological revolution

A small note, the New Scientist link that you reference is dead. You might want to replace it with Google's cached page. Link: http://64.233.161.104/search?q=cache:YxzXUxtnee8J:www.newscientist.com/article.ns%3Fid%3Ddn3488+&hl=en
20. ## Fermat Goes Back on the "Unsolved" Pile

I'm sorry if this sounds a bit pro-establishment, but I think the guy is a little shady. First, note Wiles's reply: Sounds a bit sarcastic, don't you think? (Italics and bold are my own.) Also, what tipped me off is that the man found fault with the trichotomy axiom of the real numbers. For those who are a bit rusty, the trichotomy axiom of the real numbers states that all real numbers are either negative, positive, or zero. It's a bit difficult to fault with that. Finally, the whole "The result is a new real number system that is free from defects and contradictions," reeks of pseudoscience, since as Godel proved: Thus, you can't make the real numbers, "free of defects", as it were. Source: http://www.math.hawaii.edu/~dale/godel/godel.html#FirstIncompleteness According to the Mathematics Geneology Project, the Mr. Escultura does have a legit Ph.D., but apparently, something went horribly wrong between 1970 and the present day. I'll reevaluate when some other news sources collaborate the story, but for now, I'm betting on a hoax.
21. ## Government deports citizen as illegal immigrant.

That my friend, is 7 shades of messed up. It's a shame that people can just fall through the cracks just like that. On a lighter note, regarding the first article: Doesn't this seem like a bit of an odd thing to report in an article? One can almost hear the voices now... Austrailian Govt. Official: "Now we can abide people smoking marijuana, but doing so while sewing?! This kind of reckless behavior can not be tolerated in civilized society!" At least, that's the mental image I got when I read that passage.
22. ## Sciforums

I used the same alias at Sciforums as I do here. Yup.
23. ## Respect

[Tootsie pop narrator voice] The world may never know. [/Tootsie pop narrator voice]
24. ## Spino Vs Tyranno

[geek] Count Dooku hovers in one of the Clone Wars animated shorts. [/geek]
25. ## Twist on the BT paradox

You have to be able to create a non-Lebesgue measurable subset of the object of interest, and for physical objects, this is not possible, since they are composed of atoms. From a Banach-Tarski perspective, it doesn't matter if the space shares all the properties of Euclidean space, if the objects that inhabit that space cannot be divided into non-Lebsegue measurable subsets.
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