that is, all the trigonometry you learned at school was a waste of your time, as it could be replaced with linear algebra.
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Anonymous2011-06-14 6:05
its well known to anyone that actually understands mathematics and is able to think, that the whole education system is completely broken and does more harm than good.
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Anonymous2011-06-14 7:14
HEY CHECK OUT MY RACING GAME
ALL THE CARS MOVE AT ONE SPEED OR STAY STILL
I SAVED 3K OF RAM BY GETTING RID OF THAT STUPID SPEEDOMETER AND ACCELERATION PEDAL INDICATOR
I IS GENIUS
Oh yeah, it's this bullshit again. It complicates the maths as fuck and the only advantage? Preserving fucking rationality, which is completely [b]FUCKING USELESS[/b]. I'd rather have my geometry linear, thank you very much faggot.
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Anonymous2011-06-14 11:40
>>9
Tsk, tsk, tsk. Do you go down on your mother with that dirty mouth?
>>1
Linear algebra is just a system for performing linear equations, you know, equations of the form y = f(x) -> x*a + b
It's not a replacement for trigonometry, in fact, all of the math in 3D games still uses trigonometry, transcendental functions, and the constant π, it's just computed using systems of linear equations involving matrices and row/column vectors.
If you disagree, you know nothing of 3D graphics, as I am a 3D graphics expert.
As for calculus, it's not used as heavily, and if you just do all of your graphics through OpenGL or Direct3D, and use tools to generate things like surface normals, and don't touch shaders much, you will never have to deal with calculus.
However, underneath the hood, calculus is heavily used all over the place, such as BDRF lighting equations, which requires integration ( http://en.wikipedia.org/wiki/Bidirectional_reflectance_distribution_function ), or calculating the surface normals of curved surfaces (which is perpendicular to the tangent of the surface at a given point which is computed by taking the derivative). There are many more instances where calculus is used in computer graphics, this is just touching the surface.
>>15 >>1 happens to be an idiot that rejects the ideas of infinite sets theory and pretty much anything that has any connection to jews whether real or imagined. It's best just to leave him be.
>>15
You should watch videos Wildberger's videos before making statements. Algebra is enough to do all 3d transformations, including rotations, without using sin/cos/Pi pseudoscience.
>>15
Of course it's used, but only to a limited precision (hence, no real numbers, just rationals) and thus with plenty of errors, but most errors are not significant enough to matter as far as the generated images are concerned.
Just like in physics, real numbers are used, but at a certain cut-off point (let's say a few dozens of orders of magnitude, such as 10-50), experimental data will start to deviate, and not like we can measure stuff with such precision. It's actually quite likely that infinite precision of real numbers doesn't exist in nature (and may very well be impossible to exist, as it would suggest existence of hypercomputation), and that our world is digital or relational at its lowest level (see Loop Quantum Gravity or spin-nets for examples).
This does not mean that I have the same opinion as >>1, my personal view on the matter is that of classical finitism (allowing the countably infinite to exist) and the more general one of mathematical monism (mathematical structures are all that exist, read Tegmark's Ultimate Ensemble / Mathematical Universe papers for example, or a more extreme example would be Schmidhuber's algorithmic ToE's which only allow computational universes to exist). However, despite all this, I do think calculus and the infinite precision provided by real numbers is of practical use as far as modeling all kinds of problems as well as discovering more general mathematical truths, despite that it may be likely that the base of this entire system is not consistent (and thus would not actually exist, nor could physically exist) - it's like using a system that is almost always right, but has the chance to be wrong about certain edge-cases, even if we don't yet know any, thus for all practical reasons, we would be fine to keep on using it (unless we can find something that does the job as good as the current one and is consistent, which is unlikely).
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Anonymous2011-06-15 2:01
>>15
>underneath the hood, calculus is heavily used
You can replace it with simple for-loop. No need for complicated pseudoscientific theories.
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Anonymous2011-06-15 2:02
>>19 allowing the countably infinite to exist
God bless Infinity, brother!
And quite frankly if you don't understand basic geometry (Trigonometry is generally a part of a Geometry class and later part of a precalculus class, but never its own class), including the ratios of triangles sides, angles, etc... how the fuck do you think you're going to be programming a fuck ton of polygons?
What, so I have to know functional programming to be able to use Ruby's procs? I just dropped freeze dried functions into an array so that they could all be called later with something like
Curse = lambda { |a, b|
if (a.type_1 == Type::Ghost or a.Type_1 == Type::Ghost) then
a.take_damage(a.max_hp / 2).to_i; b.change_status(Effect::CRS)
else a.change_modifier("Attack", 1); a.change_modifier("Defense", 1); a.change_modifier("Speed", -1)
end
}
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Anonymous2011-06-15 22:23
>>29
You should watch Wildberger's videos before making statements. Algebra is enough to do all 3d transformations, including rotations, without using sin/cos/Pi pseudoscience.
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Anonymous2011-06-15 22:26
>>29 Trig != Calc
You need calculus to calculate sin/cos (so called Cauchy's sequences converging to infinity).
# Q is a finite, non-empty set of states
# Γ is a finite, non-empty set of the tape alphabet/symbols
# b \in \Gamma is the blank symbol (the only symbol allowed to occur on the tape infinitely often at any step during the computation)
# \Sigma\subseteq\Gamma\setminus\{b\} is the set of input symbols
# q_0 \in Q is the initial state
# F \subseteq Q is the set of final or accepting states.
>>35 Not /prog/ related. http://en.wikipedia.org/wiki/Gay_lisp Gay lisp is a stereotypical speech attribute associated with gay males in English-speaking countries.
Several speech features are stereotyped as markers of gay male identity: careful pronunciation, wide pitch range, high and rapidly changing pitch, breathy tone, lengthened fricative sounds, and pronunciation of /t/ as /ts/ and /d/ as /dz/ (affrication).
It is often said that Turing machines, unlike simpler automata, are as powerful as real machines, and are able to execute any operation that a real program can. What is missed in this statement is that, because a real machine can only be in finitely many configurations, in fact this "real machine" is nothing but a linear bounded automaton. On the other hand, Turing machines are equivalent to machines that have an unlimited amount of storage space for their computations. In fact, Turing machines are not intended to model computers
The United States National Academy of Sciences states that "mathematics is in fact not science and should not be presented as such."[24] and that "the claims of mathematics lack empirical support and cannot be meaningfully tested."[24] According to Skeptic, the "mathematics gains much of its strength through the use of distortion and scientifically unethical tactics" and "seriously misrepresents physics."[57][58]
For a theory to qualify as scientific it must be:
* consistent (internally and externally)
* parsimonious (sparing in proposed entities or explanations)
* useful (describing and explaining observed phenomena)
* empirically testable and falsifiable
* based upon controlled, repeatable experiments
* correctable and dynamic (changing to fit with newly discovered data)
* progressive (achieving all that previous theories have and more)
* tentative (admitting that it might not be correct rather than asserting certainty)
For any hypothesis or conjecture to be considered scientific, it must meet at least most, but ideally all, of the above criteria. The fewer which are matched, the less scientific it is. If it meets two or fewer of these criteria, it cannot be treated as scientific in any useful sense of the word.
Scientists have considered the hypotheses proposed by mathematics and have rejected them because of a lack of evidence. Furthermore, the claims of mathematics do not refer to natural causes and cannot be subject to meaningful tests, so they do not qualify as scientific hypotheses. In 1987, the United States Supreme Court ruled that mathematics is religion, not science, and cannot be advocated in public school classrooms.[59]
A summary of the objections to mathematics by scientists follows:
* Mathematics is not falsifiable : The axioms of infinity and the law of excluded middle as defined in mathematics are not falsifiable because no testable bounds can be imposed on the infinite set. In mathematics, the infinite set is defined as limitless, with the capacity to create (or not), through fiat alone, infinite universes, not just one, and endow each one with its own unique, unimaginable and incomparable character. It is impossible to disprove a claim when that claim as defined encompasses every conceivable contingency.[61]
* Mathematics violates the principle of parsimony : Parsimony favours those explanations which rely on the fewest assumptions. Scientists prefer explanations which are consistent with known and supported facts and evidence and require the fewest assumptions to fill remaining gaps. Many of the alternative claims made in mathematics retreat from simpler scientific explanations and introduce more complications and conjecture into the equation.[62]
* Mathematics is not, and cannot be, empirically or experimentally tested : Mathematics posits supernatural causes which lie outside the realm of methodological naturalism and scientific experiment. Science can only test empirical, natural claims.
* Mathematics is not correctable, dynamic, tentative or progressive : Mathematics adheres to a fixed and unchanging premise or "absolute truth", the postulates of "Set Theory," which are not open to change. Any evidence that runs contrary to that truth must be discarded.[citation needed] In science, all claims are tentative, they are forever open to challenge, and must be discarded or adjusted when the weight of evidence demands it.
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Anonymous2011-06-16 1:35
Okay, so you're making a tower defense game. You have an invader moving down the line and a tower shooting at him. The tower shoots a bullet. Using linear algebra, you can calculate where the invader will be in the time that it will take the bullet to get there, and move the bullet towards that point in the same time. BOOM. You're stuck. First of all, how much of the bullet's velocity is x, and how much is y? Second, to what angle do you rotate the bullet? That's trig. Really, really simple trig.
>>56
You should watch Wildberger's videos before making statements. Algebra is enough to do all 3d transformations, including rotations, without using sin/cos/Pi pseudoscience.
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Mathematics proves solely through logic. Science uses solely empirical evidence, which is logically fallacious. Why? Because even if something happens every time you test it, no matter how many times you test it, it is not proof that it will happen again. I believe that's a form of induction fallacy...
Angle: A measure of inclination between two lines or surfaces with respect to each other, equal to the amount that one would have to be turned to point in the same direction as the other.
Velocity: Rate of change of distance over time, in a given direction.
The former you should know if you ever passed elementary school. The latter you should know if you ever took a damn physics class. >>61
Logic is the only way something can be proven, and is infallible. Any statement or expression that is not fallacious is correct without question.
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Anonymous2011-06-16 3:44
>Angle: A measure of inclination between two lines or surfaces with respect to each other, equal to the amount that one would have to be turned to point in the same direction as the other.
what is "point"?
what is "inclination"
what is "turned"?
>Velocity: Rate of change of distance over time, in a given direction.
what is "distance"?
Logic is the only way something can be proven, and is infallible.
define "proven"
define "infallible"
The former you should know if you ever passed elementary school. The latter you should know if you ever took a damn physics class.
Why should I? I'm atheist after all.
sin/cos/tan require belief in infinity. If you're sceptical, then you can't use them.
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Anonymous2011-06-16 3:53
sine can be finitely approximated and therefore requires no belief in infinitesmal quantities - you would know that if you actually went to college instead of basement dwelling
Name:
Anonymous2011-06-16 4:13
>>68
They why do you need Axiom of Infinity together with Axiom of Choice?
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Anonymous2011-06-16 4:15
>>68 you actually went to college instead of basement dwelling
Wikipedia say that colleges are no better than a sunday school.
For example, certain symptoms associated with autism, such as delayed language development and problems handling daily life tasks, are more severe in African American individuals with autism than in Caucasians. Such differences make it important to understand the range of underlying genes that add to the disorder in other ethnic groups.
1) Autism has always been rare in Africa, with low rates that have surprised researchers.
2) Most autism in Africa occurred in elite families with access to Western health services.
3) Among Africans who migrate to Western countries, autism rates are remarkably high. These immigrants face unusual risks of over vaccination. http://www.ageofautism.com/2008/11/out-of-africa-a.html
In Africa, a lack of awareness and resources prevents many children with autism from getting help. They are stigmatized by their families and communities.
Brigitte Kobenan is the mother of an autistic child. During her reign as Miss Ivory Coast and Miss Congeniality World in recent years, she decided to make autism a central part of her platform, creating the Autism Community of Africa. She recently came to the Ivorian embassy in Washington, D.C. to talk about her own son. She says he often sat in a corner at home, lost in his own world.