Wikipedia:Reference desk/Archives/Mathematics/2008 April 20

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April 20

What do you think of the expression "...mathematicians answer only to God."?

Actually the full expression is; "Biologists answer only to Chemists. Chemists answer only to Physicists. Physicists answer only to Mathematicians. Mathematicians answer only to God". I find the notion of math being the closest thing we have to expressing reality an interesting concept. When I think about this I'm reminded of my favorite Foghorn Leghorn cartoon where Foghorn is trying to befriend the little boy (who happens to be a genius) of a widow he's trying to get with. Anyways, during a game of hide and seek, the kid, using a complex mathematical formula, finds Foghorn's hiding spot,- in a place he didnt hide! Since figures dont lie, he really was hiding there.

Exaggerated as that cartoon may be (or is it?), it got me thinking. Could math be the tool to express ultimate truth? One apple plus one apple equals two apples. One hubcap plus one hubcap equals,-you guessed it, two hubcaps. How did you guess it? Because you understand the concept of "oneness". This may be oversimplified here, but basically, you know that one plus one of anything will equal two whether it be apples, hubcaps, atoms, or ex-wives. It's a symbol, a shortcut, or just an all encompassing way of expressing anything. Correct? And this is just the simple math. I can't even imagine what calculus could express.--Sam Science (talk) 04:22, 20 April 2008 (UTC)

You might be interested in the (currently in need of a little work) article Philosophy of mathematics. A lot of thought has gone into just why it all works like it does, and how it can be that 1+1=2 works whether you're talking about apples or hubcaps, and there are about as many answers as there are mathematicians. Some of the schools suggest that these things work because our mathematical rules were based initially on observations in the real world, so it's natural that they will work on real world things, whereas others believe that there is a fundamental mathematics, and it's a happy coincidence that it models the real world so nicely. Confusing Manifestation(Say hi!) 07:33, 20 April 2008 (UTC)

I have to say, mathematicians do not answer to god. They answer to the only two real forces in the universe - the grim reaper and the taxman. -mattbuck (Talk) 08:10, 20 April 2008 (UTC)

But doesn't the taxman also answer to the mathematicians? — Omegatron (talk) 00:21, 27 April 2008 (UTC)

There's something nice about mathematics where if a theorem is proven, it remains so. Even vicious nazis like Bieberbach get to keep their results. A person who has proven a theorem does not have to answer to anyone (but God?) as far as mathematics is concerned. 134.173.93.127 (talk) 09:33, 20 April 2008 (UTC)

Well, you could say that mathematicians answer to logicians - depends on whether you count logic as part of maths, or something that maths is based on. --Tango (talk) 13:29, 20 April 2008 (UTC)

I read an article once that argued that numbers were not created by God because you cannot not have numbers, and must therefore have existed before creation. After all, you cannot count the days of creation unless the tool for counting first exists. I wish I could remember where I saw it. SpinningSpark 14:39, 20 April 2008 (UTC)

I don't know how clear it is that the world uses numbers - or even identity - in reality. It's one thing I've never managed to get an answer to from my friends who've studied physics. 90.209.36.146 (talk) 19:12, 20 April 2008 (UTC)

And sadly you are probably never going to get one. The problem is in some sense independent of physics and maths and stems from the difficult of finding a good definition of reality. Taemyr (talk) 12:40, 22 April 2008 (UTC)

Compare Leopold Kronecker's famous quote: God made the integers; all else is the work of man. Regards, High on a tree (talk) 19:27, 20 April 2008 (UTC)

Knuth's Surreal numbers suggests that God created not only the integers but more numbers too. – b_jonas 20:10, 20 April 2008 (UTC)

Which brings us the question: can god change the value of e or π? — Kieff | Talk 11:00, 21 April 2008 (UTC)

No. Algebraist 11:27, 21 April 2008 (UTC)

Awesome! I've made the right bet. In your face, god! — Kieff | Talk 12:03, 21 April 2008 (UTC)

Is it just me, or does Algebraist's link betray a misunderstanding of non-Euclidean geometry? "Note that the later invention of non-Euclidean geometry does not resolve this question; for one might as well ask, 'If given the axioms of Riemannian geometry, can an omnipotent being create a triangle whose angles do not add up to more than 180 degrees?'" 75.3.84.77 (talk) 22:31, 22 April 2008 (UTC)

Sounds right to me. What do you think is wrong with that statement? --Tango (talk) 22:39, 22 April 2008 (UTC)

Math probably is the ultimate truth because, when you think about it, one plus one equals two - no matter what universe you're in! Even God Himself couldn't change it. I imagine the conversation going something like this:

God: I hereby declare that one plus one now equal three. Observe, my son- one apple, another apple. Three apples! (Lightning, wind, indiscribable feeling comes over your spirit/body)

Me: Uh...G,...there's still only two apples here.

God: Doh!

By the way, here's a [| link] to the Foghorn Leghorn cartoon of the little boy math genius I was referring to, if anyone's interested.Sam Science (talk) 18:01, 21 April 2008 (UTC)

"One apple" only exists in our minds, because apples are composed of more than one thing. Where do you draw the line, and does it apply to every case? Mathematics is just a system with a set of rules that are, on a universal scale, completely arbitrary because they have emerged from the human perspective. Damien Karras (talk) 09:43, 22 April 2008 (UTC)

Well, I'm pretty sure we can all agree on what an apple is. I dont think I'd want to know someone who'll sit there and argue with me that an apple isn't really an apple, that it's really all relative. There's a guy who's gone way overboard on philosophy, and probably walks around asking himself whether he exists or not.

Let's take a fundamental particle,- an atom. There is absolutely no arguing that its two parts hydrogen and one part oxygen to make one molecule of water....Nope, can't think of a way around it. Sam Science (talk) 04:27, 23 April 2008 (UTC)

Except that atoms are composed of different constituent parts? Does the universe assign the number one to an atom, or does the human mind? We draw arbitrary lines based on our perspective around collections of unique objects to define "oneness" and "twoness", and so forth. Just because we agree in general that an apple is roughly a distinct object does in no way mean that the concept of number is inherent in it. Damien Karras (talk) 07:03, 23 April 2008 (UTC)

Well, it certainly looks like the Universe assigns one-ness to things. — Kieff | Talk 07:24, 23 April 2008 (UTC)

I strongly disagree with the notion that having a finer structure suggests that the whole only exists in our minds. And, as implied by Kieff, objects such as photons apparently have no internal structure and thus their quantity surely has independent existence. -- Meni Rosenfeld (talk) 14:35, 23 April 2008 (UTC)

Unfortunately I haven't enough knowledge about quantum physics to counterpoint this argument, but I still will say that I think it's rash to accept that nature stops at the photon. It is my understanding that Kelvin said before the dawn of the 20th Century: "There is nothing new to be discovered in physics now, All that remains is more and more precise measurement." And few were to know that the quantum enigma was about to impact on physics and change our perspective forever. It's like the ancient Greek concept of the "atom" - literally, "indivisible"- yet that turned out to not be the case. The point is, although I have no solid argument with which to say that even a photon has constitutent parts, you will agree that our perspective of what is "one" thing is always changing (string theory posits, for instance, an even finer structure). If there is no fundamental unit in reality, then the definition of unity simply is arbitrary. Damien Karras (talk) 06:59, 24 April 2008 (UTC)

Wow, photons have no internal structure, yet they have a "oneness" quality to them. Now that's a question for later!.... You guys are blowin my mind.Sam Science (talk) 16:32, 23 April 2008 (UTC)

May I suggest some Vaxasneeze, proven to stop people blowing on your mind. _{Side effects may include loss of memory, blurred vision and brain rot. Do not take while pregnant, operating light machinery or breathing.} -mattbuck (Talk) 16:39, 23 April 2008 (UTC)

I have a problem with the OP's original example. Arithmetic works for several reasons. Maybe it's logically sensible, maybe it's drawn from experience, maybe it's divinely inspired, whatever. The thing most people leave out of the list is that it works because we ignore all situations where it doesn't. And I mean "works" in terms of the original example, where it gives the right answer to a natural question about the real world. Take a hubcap, and sit it next to another hubcap. You now have exactly a pair of hubcaps, in close proximity to each other. Great. Take a bowl, partially filled with water. Sit it next to another bowl of water. You now have two bowls of water. Fantastic. Now pour one bowl into the other. How many bowls of water are left? You have one bowl of water, filled higher than before, and something that's not a bowl of water since it's empty. In what way did one plus one become two in this case? And it doesn't help to say the new bowl is twice as full as before. There's no reason to think the two bowls were filled equally, and regardless, the water's depth isn't part of the definition of "bowl of water". A similar problem with piles of sand. A single grain is not a pile of sand, so there are zero piles. Combine zero piles with zero piles a few thousand times, and you have one pile. Combine one pile with another, you still have one. See the problem? Mathematics applies best to a world where shades of gray and irritating exceptions either don't exist, or can be exhaustively categorized. In such a world, maybe math reigns supreme, but in the real world we get by by quietly ignoring anything that doesn't fit the rules. Black Carrot (talk) 22:25, 23 April 2008 (UTC)

I think it's safer to say that simple math like "1+1=2" only applies in the cases you mention. The more complicated the real-life phenomenon, the more complicated the math involved. -- Meni Rosenfeld (talk) 08:59, 24 April 2008 (UTC)

Basic Probablity that's annoying me, immensely

In a certain sample space, the events A and B are independent and P(A U B) = 5/8 and P (A n B') = 7/24. Calculate a) P(B), b) P(A n B), c) P(A), d) P(A' U B')

P(B) = 1/3, as far as I've calculated, but I've hit a brick wall after that. AlmostCrimes (talk) 04:43, 20 April 2008 (UTC)

set a=P(A) and b=P(B). Express P(A'), P(B'), P(A U B), P(A n B), etc. in terms of a and b. Solve the two equations in the two unknowns a and b. Substitute the solutions into the other expressions. Have fun! Bo Jacoby (talk) 06:49, 20 April 2008 (UTC).

I'm not quite sure how that dovetails in with the problem. AlmostCrimes (talk) 08:12, 20 April 2008 (UTC)

See Probability. -- SGBailey (talk) 08:52, 20 April 2008 (UTC)

a=P(A). b=P(B). P(A')=1−a, P(A U B)=a+b−ab, P(A n B)=ab. The equations are a+b−ab=5/8 and a(1−b)= 7/24. Can you solve these equations? Bo Jacoby (talk) 12:39, 20 April 2008 (UTC).

How to use artificial neural nets for time series forecasting?

I'm interested in using a neural net for forecasting multivariate time series (only one dependant time series, several independant series). Probably a feedforward neural network unless anyone has a better suggestion. I understand this is somewhat like doing multiple regression. Two questions please@ a) how do I actually present the data to the neural net. If the data is in a table with the time axis vertical, do I just present it a row at a time? b) More importantly, when using multiple regression there is a problem if the time series correlate with each other. Is this a problem with neural nets, and if so how do I overcome it please? Thanks 80.0.109.128 (talk) 23:57, 20 April 2008 (UTC)

Temporal_Difference_Learning looks like a good place to start. JohnAspinall (talk) 14:20, 21 April 2008 (UTC)