If anything exists, then its source of existence can be logically tracked down. If its source can be tracked down, it can be mathematically explained. Only problem is to find out how.
Contentment. Love. Beauty. I look forward to your description of the source and mathematical explanation
- Contentment can be measured in the units known as holla dollaz. Beauty can be measured with the Golden Ratio (see below).
I sit here with one eyebrow raised - this doesn't make a lot of sense to me. For one thing, you clearly have a different definition of mathematics than I, a math PhD, have.
I agree, although only a lowly Ph.D candidate. :)
I think that this is a very strong affirmation. You may need to answer WhyMathWorks? or even WhyMathExists? first, before considering that EveryThingIsMath.
- Unless math is part of your answer for WhyAnythingExists?, something that is necessarily related to why the universe is described by mathematics, although many people don't seem to concern themselves with it.
- Good point. But I don't see such theory here. It would be cool.
A statistical description of everything just doesn't cut it, due to simplicity, and the
DistributionOfAllStatistics. --
JuanPabloNunnezRojas.
I like this one: mathematics is the study of all the possible kinds of structure.
Mathematics is a notational representation of Logic. If anything is to exist, there should be logic behind its existence. If there is logic behind its existence, then it should be possible to denote it through some representation. That representation can be a mathematical notation. I do not say that I have mathematical notations for Love, beauty etc. That has to be found out. But ItIsThere?.
Beauty can have logic. What we essentially think of cognitive and emotional phenomenon is basically because we do not understand it (at least completely). Once we understand the logic behind it, we can find out a notation for it.
Think of it this way: Nothing is magic. Everything has a cause behind its existence. If there is cause and effect, then there is a way to find out the relation between them. That way is mathematics.
There is no a priori reason to assert a logical basis for beauty.
Beauty depends on the observer. It depends on that person's mood (when I am in good mood, I find more beauty in things), cultural background (A Chinese can appreciate the beauty in calligraphy more than me), knowledge (I tend to find less beauty in things that I do not understand), etc. So it does depend on some conditions. If we can successfully denote those conditions, we can denote beauty. Yes I agree that conditions such as mood, cultural background etc is difficult to denote mathematically. But I believe that it is still possible. We just have to find a way out.
Let's have a look at this:
- Mathematics is a notational representation of Logic.
- If anything is to exist, there should be logic behind its existence.
- If there is logic behind its existence, then it should be possible to denote it through some representation.
- That representation can be a mathematical notation.
- Probably, but not certainly.
- Not even probably. Mathematics can't handle discontinuity or quanta - but algorithms can.
- Mathematics can handle discontinuity and quanta quite well in my experience, perhaps you could be more specific. Another page might be indicated.
- Not without infinite series; Math can approximate but, in finite time, it can't model something as simple as a square wave or find prime numbers. That takes an algorithm.
- You should by now be getting the point, from all these responses (from people who are really leaning over backward to be polite), that your statements are simply wrong; it's merely that you are not familiar with the areas of mathematics that model square waves (see for instance non-analytic functions, fourier analysis, compact support, Slepian/Landau/Pollak, Generalized Uncertainty Principle, operational calculus, generalized functions, etc).
- And finding prime numbers is the domain of number theory, including even introductory number theory -- and in fact the definition of prime numbers lies in number theory, so that is a particularly ironic mis-example. To even be aware of what a prime number is, but to not be aware of the existence of number theory (and that a big chunk of it concerns finding prime numbers) is truly mind boggling. Indeed, see "The Fundamental Theorem of Arithmetic". You mean there's an expression that generates all the prime numbers?! Boy, am I out of date!
- Yes, there is, and there was before your grandfather was born, so this is again a matter of being out of touch, not of being out of date with recent discoveries. (That's not to say that such formulae are necessarily pragmatically useful, but that's a vastly, vastly different issue.)
- The notion that "algorithms" are not part of mathematics is most mind boggling of all. Even skipping modern fields that address algorithms, like lambda calculus, just look at the history and origin of the word "algorithm".
- I disagree. You seem to think mathematics can and does only deal with continuous functions. This turns out not to be the case. Perhaps your experience is so, but not mine. My math courses, and my research, had discontinuous and non-differentiable functions all over them.
- And who kicked algorithms out of Mathematics? Kick the algorithms out and there goes graph theory, and probably the whole discrete and combinatorics math as well. Not nice. Put the algorithms back, please.
- Well, who did kick algorithms out? And when? They were certainly part of my math courses. Perhaps your school(s) were a bit blinkered.
- When I was in school (around the time of the dinosaurs) my math profs drew a distinction between algorithms and mathematics; algorithms were impure, not elegant. If these have now merged, I stand corrected. Does this mean that for every halting computer program, there's a mathematical formula that produces the same result? Or, is the program the formula?
- They were never separate, and you're not really asking the right questions. Your math profs (assuming they were saying reasonable things rather than stupid things) would have been distinguishing between, roughly, construction of solutions/enumerating solutions versus proving the existence of solutions. There has been a minority interest (bordering on the fringe) in purely constructive mathematics, where non-constructible entities are (with the extreme practitioners) denied to exist. That approach was demonstrated, practically from the beginning, to exclude the majority of mathematics, for no particularly compelling reason.
- In fact, it is in general more useful and powerful and compelling to prove the existence of solutions without necessarily constructing them. Construction is important in real world applications of math, of course, but in general not so much so in pure math. Algorithms are frequently viewed by mathematicians in non-algorithmic areas of math as ways of constructing particular solutions, although that is certainly not the most insightful view of the subject, and hence are often considered by such people to be essentially nothing but constructive applied math rather than pure.
- This is sort of correct in terms of what they have in mind, but it is dead wrong as an absolute. Algorithms in a more general sense have always been part of mathematics -- but a different area of math than the specialty of the math profs you're talking about. Differential calculus, for instance, is not an area of math that directly has much to do with algorithms, although algorithms can be used to find approximate solutions to differential equations.
- Basically you took opinions that you heard from people you thought were experts (they obviously were not experts on the topic of mathematical algorithms Don't you mean algorithmic math?) [Let's not worry about minor terminology. Look up, say, Lambda Calculus, to see an example of something over in that kind of area of math]
- ...and took them to heart as perhaps a matter of definition, and that is a highly error prone way to approach anything.
- The phrase "non-algorithmic areas of math" says a great deal. I've been labouring under the misconception that this was the whole of math. It still leaves my question unanswered: Does this mean that for every halting computer program, there's a mathematical formula that produces the same result? Or, is the program the formula?
- The first important point is that the stress on "formula" vs "algorithm" was part of the confusion to start with, so to continue to have a keen interest in formula vs algorithm is suspicious, if you see what I mean. The literal answer to your question becomes a mere matter of curiosity once you get past the misconception -- in this context, that is. It can in fact be an important mathematical topic in itself, e.g. in Goedel's proof. The short answer, anyway, is yes, in general one can construct formulae that are formally equivalent to algorithms (qualifications, exceptions, and other discussion would be extremely premature, here). It is quite common for the results to be less pragmatically useful than the algorithm, but then that's a matter of application, not of pure math.
- Curiosity is never "mere". Fortunately, I know a few mathematicians I can annoy. I can't wait to see how conditionals, and goto and things like feistel networks are translated (assuming that's the right term). Thanks Doug.
- I do not say that I have mathematical notations for Love, beauty etc.
- Bother - I was looking forward to it.
- But ItIsThere?.
- Beauty can have logic.
- Convince me.
- For starters, there is evidence to suggest human beauty is rooted in the GoldenRatio. The proportion of the body and a number of facial features -- even the width of the teeth with respect to eachother, apparently revolve around this figure. Of course there is logic in beauty; evolutionary theorists have supposed that appreciation of beauty supported the morale of what was once a ruthlessly hunted species (us) and, in some cases, serves as a kind of compass for various behaviors: what is more beautiful to you, a factory dumping effluents into a lake, a cracked, barren asphalt plain, or a rainforest? The question that remains is: why the hell are we here? Nobody has given me a satisfactory answer for this one and I don't think I can find one myself, unfortunately. -- TheerasakPhotha
- What we essentially think of cognitive and emotional phenomenon is basically because we do not understand it (at least completely).
- Once we understand the logic behind it, we can find out a notation for it.
- Think of it this way: Nothing is magic. Everything has a cause behind its existence. If there is cause and effect, then there is a way to find out the relation between them. That way is mathematics.
- Maybe, but not certainly.
You seem to have an odd idea of mathematics.
Hmmm, statements of faith from mathematicians?
Indeed. See the remarks of RamanujanSrinivasa? on the nature of 2^n-1, for instance. -- TheerasakPhotha
Not long ago, (some) mathematicians were dead set to find algebraic formulae for solving all polynomial equations, the circle's quadrature, trisection of an angle were very much alive and subject of active research. Then Galois came along. Later on, there were G�del, Turing and many others who put an end to similar enthusiastic endeavours. So much for having faith in a particular result of mathematics. It would be ironic for mathematicians to actually prove that you can't comprehend beauty and love.
In order to do that you'd need a mathematical characterization of them, and that counts as understanding them mathematically, even if we show certain aspects of them can't be worked out.
Ok, let's admit that theorizing the human brains and emotions and other such great subjects, could hypothetically be done. But what if the computational complexity needed to have a grasp of some "cause-effect relations" and their mathematics is way beyond the poor little human brain?
In the meantime we have serious problems mastering these damn computers which have no emotions whatsoever, and are so utterly predictable, at least until a human writes some programs.
Yes, It could have potentially incomprehensible complexity. But also this complexity could also probably be automatized (a personal dream of mine ;-)). If we look at complexity of the computer, and try to mathematically denote an execution of a program completely, it might be immensely difficult. But we have automatized (with hardware, software, compilers etc...) most of the complexity. The program is still math at heart. But for us humans, it has taken up some form other than clear math.
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- I must report that back when the [ArtificialIntelligence] arguments were still white hot, it was the oddest feeling to debate someone like Cybernetic Totalist philosopher Daniel Dennett. He would state that humans were simply specialized computers, and that imposing some fundamental ontological distinction between humans and computers was a sentimental waste of time.
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- "But don't you experience your life? Isn't experience something apart from what you could measure in a computer?", I would say. My debating opponent would typically say something like "Experience is just an illusion created because there is one part of a machine (you) that needs to create a model of the function of the rest of the machine- that part is your experiential center."
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- I would retort that experience is the only thing that isn't reduced by illusion. That even illusion is itself experience. A correlate, alas, is that experience is the very thing that can only be experienced. This lead me into the odd position of publicly wondering if some of my opponents simply lacked internal experience. (I once suggested that among all humanity, one could only definitively prove a lack of internal experience in certain professional philosophers.)
--
JaronLanier, OneHalfaManifesto
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... It still leaves my question unanswered: Does this mean that for every halting computer program, there's a mathematical formula that produces the same result? Or, is the program the formula?
surely by definition a program in a pure functional language is a mathematical formula? in other words it is equivalent to an expression in lambda calculus, you could trivially say the same thing about a program written with combinators, and given that any program in any existing language could be rewritten in terms of any of these (church-turing thesis) then all programs are expressions.
Nothing can be represented by a zero.
Zero is a concept of Math.
Therefore: Nothing is Math.
That relies on some semantic acrobatics. When we say: nothing can be represented by a zero (or sunya, soon, ling, cifr, whatever), we mean that the concept of nothing can be represented by zero. Contrast this to what you seem to imply: { x : set of everything | x can't be represented by 0 }, that is, the set of things that can be represented by zero is empty. If you have no rupees, for instance, the concept of rupeelessness itself can be represented by zero. And observe that the Thai/Lao word for promise is sunya. LOL.
And yes, in all seriousness, I think you were just cracking an AxiomaticJoke?. -- TheerasakPhotha
NovemberZeroFive
See Also: EverythingIsa
CategoryMath or rather CategoryPhilosophy
Every Thing Is Math