Slashdot Mirror

Fractional integrals/differentiation is way more fun and hard to get your head around. Not that it is actually that useful outside niche engineering applications, but hey, it's maths and at least it's not Measure theory -- this was the killer for me in math classes.

Fractional integrals/differentiation is way more fun and hard to get your head around. Not that it is actually that useful outside niche engineering applications, but hey, it's maths and at least it's not Measure theory -- this was the killer for me in math classes.

In other news, 640k ought to be enough for everybody.

Also, factoring large prime numbers will break all encryption!

---

From http://mathworld.wolfram.com/PrimeNumber.html:

Because a prime number p has only the trivial factors 1 and p, in his The Road Ahead, Bill Gates accidentally referred to a trivial operation when he stated "Because both the system's privacy and the security of digital money depend on encryption, a breakthrough in mathematics or computer science that defeats the cryptographic system could be a disaster. The obvious mathematical breakthrough would be the development of an easy way to factor large prime numbers [emphasis added]" (Gates 1995, p. 265).

I have little idea what works for supercomputers and highly parallized data analysis (I've never used one).

Oh ok. So when you said Sage is okay for "small-midsize projects" and recommended Mathematica for large projects? You've only used Mathematica for small projects, and have no idea what a large-scale project is. And your pricing info is woefully outdated if you're recommending this to a new user.

Well, here's an algorithm that generates music

You could download a 30 day free demo of Wolfram Mathematica and play with its GPU support. They have done a good job of automating a big part of the complex GPU programming process. http://www.wolfram.com/products/cuda-opencl-programming-mathematica.html

and has been proven that it is entirely possible with today's technology to walk down near every path of a chess game

No, no it hasn't. The number of moves playable in a game keeping the game under 40 moves is ~10^43. It is estimated that the total amount of moves past that is 10^10^50. This is more than atoms in the universe (~10^80)

http://mathworld.wolfram.com/Chess.html

"No and I mean No" are strong words. I could think of at least one example: Rotatable polyhedra on Mathworld pages, such as dodecahedra seen here, use a Java applet to let the user rotate the three-dimensional figures. Look immediately above the text "The regular dodecahedron is the Platonic solid".

MIT OCW certainly is a start. The lectures will certainly help a lot in ways the textbook could not.

Then for reading material you could use some or all of these (if you like it chewed up for you):

http://www.jirka.org/ra/

http://www.webskate101.com/webnotes/home.htmld/home.html

http://www.trillia.com/zakon-analysisI.html

If you can deal with non linear information even Wikipedia has very extensive articles on Analysis. You can start from here:

http://en.wikipedia.org/wiki/Mathematical_analysis

Or MathWorld:

http://mathworld.wolfram.com/classroom/Analysis.html

In this case, however, it's not religious: free software should be the only option in education and science.

You have just perfectly described religion when it comes to software. Perhaps you have English as a second language? Religion is when your chosen option is the only thing you will consider.

Onto your example of mathematics, I'm going to introduce you to a program called Mathematica. I believe a five second Google search will quickly show it's use in academia one of the world's leading academic programs for mathematics. An additional five second Google search will quickly show it's use in industry all over the world. You know places that pay good money in terms of careers, exactly the types of things that /schools/ are supposed to be concerned about.

Here is their website, as you can see their software is not free.
http://www.wolfram.com/mathematica/how-to-buy/education/higher-education.html

As someone that works in one of the worlds largest Universities (Top 5 in the US) I think I can safely say that I'm fairly familiar with the subject of making sure students have what they need. I can also assure you that I will use and promote open source and Mac software on a fairly routine basis as well. A computer, it's operating system and it's software are simply tools, select the best for a given situation and always maintain an open mind.

For those not comprehending "pi/2"...Wolfram demonstrates it.

If you want a great spreadsheet: http://www.quantrix.com/
If you want to beef up the programming language but are fine with Excel: http://www.wolfram.com/products/applications/excel_link/

If you are talking non commercial: Siag (suggested above) is cool: http://siag.nu/index.shtml
This hasn't seen much activity in a decade but Haxcel: http://www.johanmalmstrom.se/haxcel/ is Haskell in a spreadsheet.

The small business that I work for (that just finally, after years, saw decent growth in 2012) just switched to Quantrix, and let me tell you, that's an amazing piece of sotware. Not sure if it was OP's answer, but the what if scenarios are actually decent, not fluff, and another good feature was the fact that it wasnt =AVERAGE() or some other excel BS. (It almost replaced my job -- seriously, i'm not that important)

If you want a great spreadsheet: http://www.quantrix.com/
If you want to beef up the programming language but are fine with Excel: http://www.wolfram.com/products/applications/excel_link/

If you are talking non commercial: Siag (suggested above) is cool: http://siag.nu/index.shtml
This hasn't seen much activity in a decade but Haxcel: http://www.johanmalmstrom.se/haxcel/ is Haskell in a spreadsheet.

I also give my backing to R. There are other packages which look more like integrated though like Octave or Euler. You can even get Mathematica for Linux but it is somewhat expensive.

In a few months, Mathematica on a Surface Pro will be more powerful and still be portable.

Maybe they are using 2.5" HDDs each of which has 8x less volume than a 3.5" HDD. That would be an easier exercise.

In either case, the drives are probably not hot-swap (unless you do it like a puzzle)

Gee, lawyers & judges would *never* have a vested interested in MORE laws to provide work for themselves. /*cough* bullshit

Sadly Shakespeare's wisdom "The first thing we need to do is kill all the lawyers." won't solve the problem of greed.

Imaginary Property is neither real, nor property. Stop pretending it is, because I have a patent on two *numbers* to sell you ...
http://mathworld.wolfram.com/PrimeNumber.html

Because of their importance in encryption algorithms such as RSA encryption, prime numbers can be important commercial commodities. In fact, R. Schlafly (1994) has obtained U.S. Patent on the following two primes (expressed in hexadecimal notation):
98A3DF52AEAE9799325CB258D767EBD1F4630E9B ... and
93E896DAFD9DFECFD00B466B68F0EA68AF5DC9.

The fact that the fashion industry operates without copyright, and the for the last, you know, a few *hundred* *thousand *years* WITHOUT copyright, patents, and trademarks is proof that it is *ONLY* because of greed that we have these legal fictions in the first place.

When are you going to grow up and stop drinking the imaginary Kool-Aid (TM).

I find these titbits about number theory absolutely fascinating... I followed a few courses at undergraduate level that touched on this material - without giving me a solid grounding. What I'd like to know is this: Is there a good textbook that would bring me up to speed with this material? I like Wikipedia articles - but I find them disjointed.. what I'd like from a textbook is something that leads me through the subject from undergraduate level onwards. Can anyone make any recommendations?

I've had pretty good success with Wolfram MathWorld.

"They all still afford college and everything else because they only buy what they need. They don't buy two cars per person, they make large meals and reuse leftovers, the first two kids get new clothing and everyone else has hand-me-downs, they go to cheaper schools, etc... Their cable and internet bills are the same as yours, they go to more community activities and have enough people to play board and card games with themselves so less expensive electronic gaming, they've got multiple people to split up the chores so everything gets done faster despite there being a little more work. It really isn't that harder to wash 6 dishes than wash and dry 2 dishes (another kid will do the drying of the 6 dishes). It's just as easy to read to four kids the same story as it is to read to two kids. Eventually the older kids will start helping out the younger kids, providing you with more time and the older kid better experience compared to an only child. Assuming all the kids don't hate each other, they've got their brothers and sisters who will back them up when needed thus less prone to depression and feeling like an outcast. There are many, many more examples. I'm not sure which large families you've seen, but the one's I've seen get by by having a more sustainable life style. Tax breaks don't out weight the cost of a kid. If they did, kids wouldn't be expensive and everyone would have many. Each kid after 2 or 3 becomes cheaper than the last."

Mod parent up. With a solar system that is almost entirely empty, I'm just shocked to see all the people on Slashdot celebrating low fertility. Sure, a small cafe (the Earth) in a big city (the Solar system) may have an occupancy limit, but we don't go around telling people not to have kids because some cafe is too crowded. People generally just open another cafe...

Here is a step towards how:
http://www.kurtz-fernhout.com/oscomak/SSI_Fernhout2001_web.html
http://pcast.ideascale.com/a/dtd/A-global-effort-to-develop-self-replicating-space-habitats/76206-8319

And here is why:
http://scienceworld.wolfram.com/biography/Tsiolkovsky.html
"Russian physicist and theoretical father of rocketry. Tsiolkovsky was the son of a Polish deportee to Siberia. Tsiolkovsky was an inventor and aviation engineer who was also an insightful visionary. As early as 1894, he designed a monoplane which subsequently flew in 1915. He also built the first Russian wind tunnel in 1897. In 1903, as part of a series of articles in a Russian aviation magazine, Tsiolkovsky published the rocket equation, Eric Weisstein's World of Physics and in 1929, a theory of multistage rockets. Tsiolkovsky was also the author of Investigations of Outer Space by Rocket Devices (1911) and Aims of Astronauts (1914). One of Tsiolkovsky's many memorable and inspiring quotes is "Mankind will not forever remain on Earth, but in the pursuit of light and space will first timidly emerge from the bounds of the atmosphere, and then advance until he has conquered the whole of circumsolar space" (1911). Tsiolkovsky's most famous quote is, "Earth is the cradle of humanity, but one cannot remain in the cradle forever." "

The more people, the more vision and imagination...
http://www.juliansimon.com/writings/Ultimate_Resource/

This "overpopulation" meme is so short sighted and despairing. Someday maybe we will see potential parents getting obsessed with "pleasure traps" of modern technology as perhaps a bad thing, rather than something that is now celebrated. Industrialized populations (especially places like Japan and Italy, and even the USA just about without immigration) are no longer even replacing themselves and their populations demographically will fall. Where does tha

We usually regard two particles to be in a bound state if they remain "close" to each other, but that's only because we're used to forces that decay to zero at infinite range. Particles that are infinitely far from each other don't experience gravitational or electromagnetic attraction, so they're regarded as free particles. The strong force is completely different, because it gets weaker as quarks are brought together. Thus quarks are "more free" the closer they are to each other; this is called asymptotic freedom.

The force between nucleons is more intuitive because the gluons that mediate the strong force between the (not literal) red, blue or green color charges of quarks are confined inside each nucleon. Our intuition is based on electromagnetism which is mediated by electrically neutral photons, but gluons aren't color neutral, so they interact with each other in strange ways. The residual strong force is mediated by composite particles that leak from each nucleon called pions which are color neutral. As a result, the binding energies of atomic nuclei are easy to explain, but those of individual nucleons are counter-intuitive in many ways.

Please note that I'm not a particle physicist or an expert in quantum chromodynamics, so my interpretation and explanation should be taken with a huge grain of salt.

Also, I noticed your conversation with dudpixel, and tried to explain that scientists aren't just assuming that nuclear decay rates are constant.

I'm going to disagree. Try Tesla âEdison. By the way, how do I type that? I had to find a site to copy â and supposedly the UTF-8 or whatever is 8811. I've tried alt+8811; no luck.

And previewing my post makes it look like a-hat. Oh well, I'm still going to post. I'm not going to potentially spend hours trying to get it to post correctly. Maybe someone can get it to work for me.

http://mathworld.wolfram.com/GoldbachNumber.html

Wolfram says the same thing. So Nyah! Pttttthhhhhpt!

http://mathworld.wolfram.com/GoldbachConjecture.html

Goldbach's original conjecture (sometimes called the "ternary" Goldbach conjecture), written in a June 7, 1742 letter to Euler, states "at least it seems that every number that is greater than 2 is the sum of three primes" (Goldbach 1742; Dickson 2005, p. 421). Note that here Goldbach considered the number 1 to be a prime, a convention that is no longer followed. As re-expressed by Euler, an equivalent form of this conjecture (called the "strong" or "binary" Goldbach conjecture) asserts that all positive even integers >=4 can be expressed as the sum of two primes.

Actually... every even integer GREATER THAN TWO. See http://mathworld.wolfram.com/GoldbachConjecture.html

None of your examples are in fact true. ... I know of no one who said air vehicles were impossible

I beg your pardon? What, have you never heard of Kelvin? Yes, that Kelvin. The one who did all the stuff with thermodynamics and heat transfer and has a temperature scale named after him - you might recognize that, at least?

Then you do know of someone who said that heavier-than-air vehicles were impossible:

"heavier-than-air flying machines are impossible" (Australian Institute of Physics, 1985) ... "I have not the smallest molecule of faith in aerial navigation other than ballooning...I would not care to be a member of the Aeronautical Society." (1986)

http://scienceworld.wolfram.com/biography/Kelvin.html

But hey, I suppose now you'll read that link, discover that his interpretation of the two laws of thermodynamics led him to be a young-earther, and you'll dismiss him from the annals of history...

I'd have liked to hear what he had to say about global warming, though.

The correct formulation of "every possible pattern" is that given an infinite sequence of letters (or digits) from an alphabet A, where every letter is chosen uniformly, the probability that a given pattern of finite length will appear somewhere is 1.

Probably worth adding that the distribution of digits in pi appears not to be significantly different from the uniform distribution.

At least now that teenager has Google, and perhaps she'll be able to find the correct answers out there.

If you want a correct answer from Google you need to formulate a correct question. This is not possible without at least knowing the terms in which the problem is described. If that young worker is sent on a sales trip she will not even know that the Traveler's problem exists, is well known, and has solutions. If that young worker is tasked with coloring a map of the USA she will not know how many paint colors to order. I agree that she doesn't need to remember proofs of any of that (and I never knew them to begin with) but at very least she needs to know that the problem exists and may have ways to solve it.

research in a library, bleh

Perhaps. But books are written by humans for humans. They don't just dump a solution, loaded with jargon, onto you. Books teach you, step by step. Following through mathworld.com hyperlinks is just like being in RPM Hell where each new item requires ten more new items. The most important link leads here, and good luck figuring out how it relates to salesmen unless you understand most of the words there.

At least now that teenager has Google, and perhaps she'll be able to find the correct answers out there.

If you want a correct answer from Google you need to formulate a correct question. This is not possible without at least knowing the terms in which the problem is described. If that young worker is sent on a sales trip she will not even know that the Traveler's problem exists, is well known, and has solutions. If that young worker is tasked with coloring a map of the USA she will not know how many paint colors to order. I agree that she doesn't need to remember proofs of any of that (and I never knew them to begin with) but at very least she needs to know that the problem exists and may have ways to solve it.

research in a library, bleh

Perhaps. But books are written by humans for humans. They don't just dump a solution, loaded with jargon, onto you. Books teach you, step by step. Following through mathworld.com hyperlinks is just like being in RPM Hell where each new item requires ten more new items. The most important link leads here, and good luck figuring out how it relates to salesmen unless you understand most of the words there.

You'd better tell these folks
      http://mathworld.wolfram.com/DynamicalSystem.html
they're wrong.

In case you think authors should hire a contract lawyer, let me tell you the vast bulk do make less than they would have made by working the same hours flipping burgers.

While it's certainly true that the vast bulk of authors do make less than they would have made by working the same hours flipping burgers, there's still significant money involved. It's the hours it takes to write a book that brings down the hourly rate.

My first visit to a contract attorney turned a profit for me. He reviewed the draft contract sent by the publisher and (because he knew what was usual and customary in the industry and I, a first-time author, did not) doubled the royalty percentages it offered. The modified contract was accepted without comment by the publisher, and the increase in first year's royalties alone, due to the attorney's work, more than paid his fee.

In addition to this, the attorney added clauses that stipulated what would happen in cases I had not considered -- for example, what would happen if the book were published in non-traditional media (only a theoretical possibility at the time, but most of my sales now) and how I would be compensated if the publisher bought the rights to the book, but never published it. Things like that.

In my opinion, people who sign business contracts without the advice of an attorney are taking a huge risk. Ask Eric Weisstein, author of Mathworld, about the dangers involved when an author signs a contract without consulting an attorney first.

Corporations always do what's necessary to bolster their bottom line and it is always at the expense of people.

By all means, post an example - just one would be more than sufficient since I stated an absolute - of a corporation lobbying on the behalf of the public good AND that is detrimental to their profits.

Actually, as a matter of logic, a counter-example would consist of a corporation lobbying on the behalf of the public good OR in a manner that is detrimental to their profits. The negation of (A AND B) is (NOT (A AND B)), equivalent to (NOT A OR NOT B) [ref: de Morgan's laws], whereas you've phrased the counter example as (NOT A AND NOT B). It's probably pretty easy to find something that consists of "lobbying on behalf of the public good", because there are companies lobbying against SOPA/PIPA. They're probably motivated by profit to a large degree, but that's irrelevant, logically speaking.

I seriously doubt these drones have anything more than a camera onboard.

As to how far such a camera can see. Well if it's large ships you're looking for, the limiting factor (in good weather) is going to be the curvature of the earth. Since the ship itself will register on camera from huge distances.

http://demonstrations.wolfram.com/ShipSailingOverTheHorizon/
(btw you should add the ceiling of the drone to the height of the ship)

Right, but you should be sure to use the proper units.

1GB equals exactly 1,000,000,000 bytes by definition.

1GiB (notice the 'i') is the one that equals 1,073,741,824 bytes.

I think you were looking for this.

They are demanding for no logical reason except how it was taught to them. Most STEM students just need a one year survey of math course that teaches them how to use the tools that you will use in industry to complete the math related problems you will face and to understand how they work. If you want to be able to do it with a pen a paper from memory you should consider a math minor. If it can be done in Wolfram Alpha, one of its excellent mobile tools or one of its competitors then there is no point in grinding on it. We don't make kids lean arithmetic for the same reasons, calculators are cheep, plentiful and they work.

Teach how the various math disciplines work, where they came from and how to use proper tools to solve them. Freshman Chem/Phys are just math classes with some memorization of simple concepts and high school level lab assignments. Those concepts are diluted by all the math teaching that is not necessary (to make it last four years). It is important to understand that you will use computerized tools to solve almost every one of these "math" issues in your industrial career, if you don't, you are inefficient at your job (academia). If an employee brings me a page+ long handwritten math problem he should expect me to send him back to do it in Mathematica, I don't have time and neither does anyone else to check his work for errors and half the time I cant read his writing, its 2012, everything is on the computer, deal with it.

I am not suggesting just handing them a calculator, they of course need an understanding of how it works and the underlining concepts. Most students get the calculator treatment and no understanding of the underlying math or how to use the the calculator properly. I don't think most math professors understand how to use calculators and computer math tools properly. I can pass the College Algebra CLEP exam with an approved calculator using very limited mental math and no scratch paper. The difference is understanding the concepts of algebra and how to use the calculator (tool) properly. Ten pages of long algebra problems does not give the student time to master the actual subject and they will never do it that way again once they leave academia. Every thing that people had trouble with in Freshman Chem can be determined using the wolfram general Chem assistant mobile app. This form of teaching is great at educating academics who can teach in this manner and pushes out the creative minds and risk takers that will lead to future major discoveries.

I agree. It kinda reminds me of Feynman's Wobbling Plate.

No, it's an N-dimensional configuration space. This is a variation on the Piano Mover's Problem.

Visualize getting a point-sized object through a maze. The maze can be treated as a graph, with junctions as graph nodes. All dead end links and closed subgraphs not containing the endpoints can be discarded. What remains contains a usable path. Then you use a path finding graph algorithm. If links have costs, there are ways to find an optimal or (with much less work) a near-optimal solution.

Now consider getting a round object through a 2D maze. You can just expand all the walls by the radius of the object. This may close some paths. Then proceed as above.

The next step up is moving a rectangular object through a 2D maze. Turns may be needed to get through tight corners. This is the piano mover's problem. For this, consider a 3D stack of 2D mazes, representing all the possible orientations of the rectangle. Expand the walls as before to make the problem into a graph, then find the path through the graph.

It's possible to extend this concept to handle arms with joints. The dimensionality of the space increases with the number of joints, but in the end, it's a graph problem. This is where advanced motion planning was in the mid-1980s.

That approach leads to solutions which work, but are sort of clunky, since velocity and acceleration aren't considered. The graph gets very large as the workspace gets cluttered, and you need full information about the workspace before you can start. It's a reasonable approach for CNC machine tools, but not robots that have to work in a less structured environment.

So robotics has moved on to techniques which use more randomized search and produce more efficient motion. See the paper from the article.

Anyway, that's a very brief introduction to motion planning in configuration space.

While I am well aware that infinite sets can be congruent with at least one of their own subsets (actually it is the definition), they are not necessarily (or perhaps even commonly) congruent with ALL of their own subsets.

Two sets under some operations are congruent according to Wikipedia if there is a homomorphism between them, or a mapping that preserves the operations. For example, as I understand it, the interval [-pi/4, pi/4) of the reals under modular addition is a group, and the reals under tangent addition are also nearly a group (except for infinity, which I don't feel like resolving in the space of this comment). A homomorphism maps this interval to the entire real line using the tangent function. So the reals are not only of the same cardinality as an open interval but also congruent.

So if a set A under one operation is congruent to a subset B under another operation, with a bijection between A and B, is there a rigorous way to determine which has a greater magnitude? You could solve this by linking to an existing accepted definition (e.g. on Mathworld or Wikipedia or some mathematics professor's web site) of the "magnitude" of a set that is not cardinality.

As it's a plain-text format, you should be able to write it in a text editor or write your own tools. But the syntax looks arcane, and their example document is full of CompressedData blobs. These could just be images, but it's hard to tell. How open is the format really? Where's the spec?

The distribution certainly looks like it follows Benford's law (probability of initial digit being n is logarithmic).

In fact, to within noise, the graph of Benford's law http://mathworld.wolfram.com/BenfordsLaw.html
is nearly indistinguishable from the graph in the article (original source: http://amitay.us/blog/files/most_common_iphone_passcodes.php )

Such sequences are called hailstone sequences because the values typically rise and fall, somewhat analogously to a hailstone inside a cloud. While a hailstone eventually becomes so heavy that it falls to ground, every starting positive integer ever tested has produced a hailstone sequence that eventually drops down to the number 1 and then "bounces" into the small loop 4, 2, 1, ....

It lists as one of its sources this book on the etymology of math terms in English. It looks interesting. Maybe I'll get a copy myself....

No. Context is important, here. It is defined in some contexts, but that is the exception rather than the rule. It is undefined in most common contexts.

Learn more: http://mathworld.wolfram.com/DivisionbyZero.html

For those with a bent toward Mathematica, GPU computing is baked into Version 8.
There's more information at http://reference.wolfram.com/mathematica/guide/GPUComputing.html

In the spirit of full disclosure, I'm solely a long-time user, not a Wolfram employee.

That isn't what MathWorld says about the summation of matrices.

I was, as you pointed out, trying to apply the commutative property to RPN. I've rarely used RPN and want to make check to see if I remembered the basics. So, thanks.

You could (in theory at least) write a program that took a set of axioms and a hypothesis, and it could tell you reasonably quickly whether the hypothesis was something that could be proven using those set of axioms.

No actually, no program can do that.

How is this a cloud?

Well there's a couple of BBP-type formulas for pi^2 that MathWorld lists here that might even convert to spigot algorithms (I'm not in the mood to check whether or not the usual BBP-type pi formula's spigot algorithm applies to these cases, where there's a fraction out front). Hmm, that's very jargon filled. What I meant is that it may be possible to compute arbitrary digits of pi^2 without computing the previous digits. This is indeed possible with pi. The thing here, though, is that all of the first 40 trillion digits were computed. TFA is just written by someone not steeped in math enough to know to be careful about equating such computations. The natural log of 2, for instance, admits a very simple spigot algorithm through manipulation of its basic Maclaurin series, as Wikipedia will tell you.

Take a look at this data http://en.wikipedia.org/wiki/File:Albedo-e_hg.svg. Notice that the albedo of dry earth ranges from 22 to 35. Snow is up to 85. The number 10% is very low.

The main issue with this article is that it does not articulate what is causing the problem. It just tries to measure it an inaccurately at that.

10% is perhaps a bit low on average, but not very low. It is in the normal range for asphalt, damp soil, water surfaces, grass, forest, and even entire urban areas.

Science is already well past that point. String theory: Is it science's ultimate dead end? Some respond to Japan earthquake by pointing to global warming (Global warming - is there anything it can't do?)

Some random people on twitter makes outrageous claims, and that means that science is broken?

As for string theory, I don't get why it is considered science, but a lot of people more knowledgeable in the field than me thinks it is, so I would prefer to wait and see where it ends up.

Occam's razor is a guide, not an iron law. If it was an iron law, we would probably be using the TeVeS theory of gravity and leave the search for "dark matter & dark energy" (supposedly the matter and energy that makes up all but a tiny fraction of the Universe despite never really being seen) to compete for funding with the search for eluminiferous Ether.

TeVeS? The theory that doesn't explain all of the data, and where even it's proponents agree that dark matter is still needed?

Moreover, there are limits to what can be known, and what is provable. Godel's incompleteness theorems

So, since Gödel's theorem is relevant, science must somehow be an axiomatic system that is capable of expressing elementary arithmetic. Weird, I thought it was all about observations, hypotheses and testing.

Every creationist regardless of religious orientation depends on a logical fallacy to advance their beliefs. Which is essentially a form of lunacy as the OP advanced.

So, committing a logical fallacy renders you insane? I would say that you've just condemned pretty much the entire human race as insane, no doubt including yourself.

As soon as you reject occum's razor and introduce non-empirical shenanigans every theory is subject to the Spaghetti Monster/Last Tuesday fallacies.

Science is already well past that point. String theory: Is it science's ultimate dead end?
Some respond to Japan earthquake by pointing to global warming (Global warming - is there anything it can't do?)

The experiments to try and generate the chemicals of life in what is thought to be conditions on the young earth are interesting, but they are at best a form of speculation. I don't believe there is any way to prove that any given method truly resembles what actually occurred. The fact that some scientists are attributing life or the presence of the chemicals of life on earth to meteors doesn't really change things either. If anything, it just confuses the picture even more - "life didn't begin on earth, but in space, and it came here on meteors!" And how did it start in space? Isn't that just a bit more of a hostile environment?

Occam's razor is a guide, not an iron law. If it was an iron law, we would probably be using the TeVeS theory of gravity and leave the search for "dark matter & dark energy" (supposedly the matter and energy that makes up all but a tiny fraction of the Universe despite never really being seen) to compete for funding with the search for eluminiferous Ether.

Moreover, there are limits to what can be known, and what is provable.
Godel's incompleteness theorems

Godel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems for mathematics. The theorems, proven by Kurt Godel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The two results are widely interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all of mathematics is impossible, thus giving a negative answer to Hilbert's second problem.

I think the ground you're on is shakier than you recognize, or care to admit.

Read anything by Donald Knuth lately?