We all learned pi in school in the context of circles. Pi is the ratio of a circleâs circumference to its diameter. It is an irrational number approximated by 3.14.
It turns out that pi shows up all over the place, not just in circles. Here is just one instance. Take a piece of paper and a stick. Draw several lines along the paper so that the lines are the length of the stick from each other. Then randomly drop the stick on the paper. The probability that the stick will land so that it cuts a line is exactly 2/pi, or about 64%. If one were to perform millions of trials, one could use the results to perform a very precise calculation of the value of pi without ever considering its relation to circles.
This is just one of many places pi pops up in reality, and pi is just one of several mathematical constants that appear to be woven into the fabric of the universe. One mathematician likened it to looking out over a mountain range, where the bases of the mountains are shrouded in fog, and the symbol for pi is etched into the top of each mountain â one intuitively knows that it is all connected at some basic level even if one has no idea why.
What are we to make of what physicist Eugene Wigner called the âunreasonable effectiveness of mathematicsâ in describing reality? The word âunreasonableâ makes sense only in the context of expectations. If one expects the mathematical structure of the universe to be elegant and beautiful, the fact that it turns out to be elegant and beautiful is not unreasonable at all. It is only unreasonable if one approaches it from the perspective of the metaphysical materialist. In his universe reality consists of nothing but particles in motion randomly bumping into each other.  In that universe there is no reason to expect any underlying mathematical order, no reason to expect mountain tops etched with pi to pop up all over the place, and no reason to suspect that those mountain tops are connected by a unifying order at the base.
Given materialist premises, none of this makes the slightest bit of sense. It is just a brute fact. It cannot be denied or explained. Yet there it is.
MIT cosmologist Max Tegmark has a theory. He says consider a character in a computer game (letâs call him Mario) that is so complex and sophisticated that he is able to achieve consciousness. If Mario were to begin exploring his environment, he would find a lot of mathematical connections.  And if continued to explore, Mario would ultimately find that his entire world is mathematical at its roots. Tegmark believes we live in a universe that is not just described by mathematics; he believes that mathematics defines all of reality, just as the reality of Marioâs computer game world is defined by mathematics.
Here is the interesting part. Tegmark makes no design inference. (He is a multiverse fanatic). This is astounding. All he needs to do is take his own analogy one step further. Why is Marioâs computer game world connected mathematically? Obviously, it is because that mathematical structure was imposed on the game by the game designer.
Why is the universe we live in connected by an unreasonably beautiful, elegant and effective mathematical structure? Come on Max. You are a smart guy. I know you can figure it out.
Kronecker famously said “God made the integers, all else is the work of man.”
Personally, I think Kronecker gave God too much credit. Mathematics is entirely man made.
Wigner was mistaken (and many others are similarly mistaken).
Beauty is in the eye of the beholder.
It isn’t. The universe is a disorderly mess. We have assigned it a conceptual order for our own purposes. But that order is only to be found in our conceptualization of the universe.
I’d like to think most people that spent much time thinking about this would stumble on the relation to circles. Hint: the calculation presumes a uniform distribution of angles.
Beauty is in the eye of the beholder.
Everything is beautiful, in its own way.
Beauty is in the eye of the beholder.
Do you likewise believe that truth and goodness “is in the eye of the beholder”?
Neil R. Personally, I think Kronecker gave God too much credit. Mathematics is entirely man made.
Are you trained to any degree in higher mathematics? If so then you can tell us why two of the dimensionless constants, pi and e, will appear in the study of electromagnetism and even in the behavior of a single photon.
I could ask the identical question in regards to a whole other slew of studies in the natural sciences, but we could start with those two if you don’t mind.
But that order is only to be found in our conceptualization of the universe.
And entities which lack the ability to conceptualize are just SoL.
Neil Rickart # 1:
——————–
“It isnât. The universe is a disorderly mess. We have assigned it a conceptual order for our own purposes. But that order is only to be found in our conceptualization of the universe.”
——————–
Our body therefore is a disordered mess, with pi woven all over the place in the fabric of blood vessels, blood cells, long bones, and a host of other structures in the body, and every life form?
Clearly convergent evolution.
Clearly ordered by the imagination, and imaginary numbers.
Or better still, we are fearfully and wonderfully made by intelligence: the Alpha and the Omega, the perfect infinate wheel of eternity.
“Mathematics is entirely man made.”
Preposterous assertion.
Mathematics is a symbolism of truth. Numbers don’t lie. 2+2 does not equal 5. We are not free to force our own desires of meaning upon the numbers, precisely because the truth they represent is not our own.
Neil Rickert @ 1 engages in this style of argumentation:
https://www.youtube.com/watch?v=X90qKQAMh8A
Skip to 2:05
These are interesting questions, but I can’t conceive of a universe in which pi, for example, does not turn up in a variety of contexts. How could it be otherwise? Can someone describe such a universe in some detail (and not simply as “chaos”)?
DaveS, a universe with a slightly slightly larger or smaller cosmological constant would have no pi.
What? How would a different cosmological constant affect the ratio of the circumference to the diameter of a circle?
I don’t think Neil really understood the question.
Mathematics is abstract. “…all sensible aspects are left behind except the quantitative, and hence the beings studied are resolved not in the senses but in the imagination…Mathematics is therefore the study of things that can be imagined and conceived without matter…”
daveS @ 9:
“I canât conceive of a universe in which pi, for example, does not turn up”
Are you then suggesting that a universe infused with pi is logically necessary? If so, make your case.
Barry:
You’re thinking of Buffon’s Needle Problem .
2/pi is part of the probability: that of the angle it would make relative to the drawn lines. The total probability of the stick (needle) falling between the lines is 4/L*pi, where L equals the length of the stick (needle).
It is not surprising that the atheists would claim that mathematics is a man-made construct and that the universe is a ‘disorderly mess’ since Darwinism itself has no rigid mathematical basis, i.e. falsification criteria, and as well, Darwinian argumentation also relies heavily on the ‘argument from ugly’, i.e. the ‘God would not have done it that way’ argument.
Thus it is only natural for atheists who cut their teeth on Darwinian argumentation to try extend their pseudo-scientific level of argumentation that they use to the universe at large.
Aleta, a universe with a very very slightly larger or smaller cosmological constant would either collapse or fling apart. No conscious beings let alone mathematicians. If pi is “man made” then no pi there.
Of related interest. This video was just released today:
I guess there could be a universe where nothing was spherical, circular or periodic. But, as Dave says, it’s hard to imagine it would be anything other than chaos.
BTW, have you now seen the circles in your original example of an unexpected appearance of pi?
Barry,
I can’t make a positive case for that, but I’m struggling to see how the number pi could be avoided by a sufficiently advanced being in any universe.
For example, Leibniz’ formula states:
pi/4 = 1/1 – 1/3 + 1/5 – 1/7 + 1/9 – …
and there are countless other such simple representations of pi.
In what kind of universe would this not be the case? I don’t know.
Edit: As in the needle experiment, there is a geometric connection to Leibniz’ formula, but you can also look at it purely as a statement about the real numbers.
If pi is âman madeâ then no pi there.
Nor cake.
If you deal with rotations, then you deal with pi. Neither electromagnetism, nor the weak force, nor the strong force will function without rotations. So, to postulate a world without pi, is to postulate a world that is completely outside of our experiences.
Sort of like postulating a world where they have ’round’ squares.
DaveS states:
Perhaps DaveS would like to add his expertise on the necessity of pi for the universe to the busted theory of inflation in which they unsuccessfully tried to explain the roundness and flatness of the universe?
It is interesting to note just how precise, and mysterious, the ’roundness’ of the Cosmic Microwave Background Radiation is:
Here is a still shot of the image at the 3:36 minute mark of the preceding video
Moreover, the Bible ‘predicted’ this roundness for the universe thousands of years before it was discovered by modern science:
The same with the ‘flatness’ of the universe
Besides the Cosmic Background Radiation, there are two other places in the universe where ‘unexplained roundness’ is found:
and also this ‘exceptional roundness’:
The delicate balance at which carbon is synthesized in stars is truly a work of art. Fred Hoyle (1915-2001), a famed astrophysicist, is the scientist who established the nucleo-synthesis of heavier elements within stars as mathematically valid in 1946. Hoyle is said to have converted from staunch atheism into being a Theist/Deist after discovering the precise balance at which carbon is synthesized in stars. Years after Sir Fred discovered the stunning precision with which carbon is synthesized in stars he stated this:
Neil Rickert: I think Kronecker gave God too much credit. Mathematics is entirely man made.
Why does it describe the universe so well?
Are we inventing mathematics or discovering it?
Did “blind evolution” bequeth such riches to the human brain?
Are you a denier?
Ignore that last question.
as to the fallacy of ‘mathematical necessity’:
Even Stephen Hawking himself admitted that Godel’s incompleteness theorem proves there cannot ever be a ‘complete’ mathematical theory of everything,
Steven Weinberg, an atheist, is exceptionally honest about the ‘fix’ atheists are in
Did âblind evolutionâ bequeth such riches to the human brain?
Obviously needed for survival.
Or just pure dumb luck.
Mathematics is entirely man made.
Do you know of any mathematical theorem that is falsifiable by empirical data?
The Fibonacci sequence. Game. Set. Match.
bornagain77 @ 25,
Interesting that you should mention the flatness of the universe. A flat universe is the only one with a maximum value for Pi. In a curved universe, there are circles whose value for Pi is exactly 3.0000. Unfortunately in those universes, Pi is variable, depending on the size of the circle. A corollary is that you can tell whether you’re in a curved part of space if you could detect a deviation from a flat value of Pi. đ
-Q
Nevermind, misread the post.
To AnimatedDust at 31: ?
Please explain. I agree with Mung (imagine that) that you can’t falsify a mathematical theorem theorem empirically. You can demonstrate a theorem, and you can model and theorem and then test the model, but the truthfulness of math resides within the system of math itself, not in reference to anything outside the math.
P.S. The Fibonacci sequence isn’t even a theorem, so there is nothing to falsify. It’s just a definition based on a rule for creating a sequence of numbers.
We live in 3 dimensions, which is why Tau (not the less elegant Pi) describes our world elegantly. In a higher dimension, we would require a completely different set of reference constants. Pi or Tau would no longer work elegantly.
Aleta @ 35
“Nothing to see here folks. Move along. Just a sequence that shows up everywhere in the universe for no apparent reason.”
Yet another instance where materialism has required one of its adherents to say something screamingly stupid. One would think they would grow tired of it. Yet, instead they seem to relish it.
Do you have an example of this? So far we’ve had a lot of hand waving and zero actual examples.
wd400 @ 39: Are you suggesting that that the Fibonacci sequence does not show up everywhere in the universe we’ve looked from spiral galaxies to heads of cabbage?
If the answer is yes, we have yet another screamingly stupid comment from a materialist.
If the answer is no, we have a materialist throwing up dust to distract from the truth.
Not looking good for you either way WD.
Pinecones fit pretty close to Fibonacci sequences, and there a few other examples of so-called golden spirals. The rest, spiral galaxies included, is mostly mysticism.
This whole thread seems to be based on your what you think is true, absent any evidence. Unless you have some examples?
Mung and Aleta,
Depends on your definitions.
1. Ever hear of non-euclidean geometries?
2. Try testing the Pythagorean Theorem on the surface of a sphere.
3. One mole of hydrogen plus two moles of oxygen reacts to form one mode of water, not three.
That the Fibonacci sequence is common in nature is indeed surprising. That the ratio of two successive Fibonacci numbers approaches Phi as the pairs get bigger is even more so.
Euler’s equation, e^(pi*i) = -1, is also haunting.
-Q
I am amazed at how much the materialist is willing to deny to defend his position. The irony of course is his banking on reason that there is no reason.
Stupefying!!!
What’s looking bad for materialism is quantum theory.
Quantum theory is now widely accepted by physicists. For example, Vlatko Vedral is a professor of Physics at the University of Oxford who specializes in quantum theory and whose research papers are widely cited expresses the concept this way:
Compare Dr. Vedralâs description to the beginning of the Gospel of John in the New Testament, where we encounter the following statement:
The word âWordâ here is translated from the Greek word logos, which encompasses meanings in English that include a word, a thought, a concept, a plan, reasoning, and logicâall of which represents information.
Please note that I’m not claiming that quantum theory “proves” the Bible. I would warn you away from connecting science with the Bible, since science is always in flux. I do find this conjunction, though perhaps temporary, fascinating.
-Q
Q
Logos….. everything is logos through Him and for Him……
Love John 1:1 can never ever stop marveling at how it explains the entire universe. It is a beautiful description of our reality.
Folks,
Mathematics as a discipline is sometimes quite reasonably and in my view aptly defined in terms of being the study of the logic of structure and quantity, including of course spatial structures.
The underlying logic of distinct identity and connected structures and quantities would seem to be innate, and something we can discover, model and analyse. For instance, the very name geometry suggests how surveying and similar exercises led to the steps that built up classical Euclidean Geometry. This can be ext6ended through co-ordinates and linked to abstract representations of variables, parameters and constants, i.e. algebra. Complex numbers represent vectors, which are connected to co-ordinates. The complex plane can be used to define a euclidean space in strict terms.
Various extensions can be used to define other spatial geometries that may be relevant to other circumstances, but that does not remove the validity of the framework just noted. For example, using Wiki for convenience:
So once we have distinct identity, structures and quantities, there is a built in logic that would then shape a possible world — and note the definition in the Collins English Dictionary:
Mathematics allows us to explore this domain, and actualisation is what happens to hold for this actualised world.
I think also it is important to put on the table an astonishing result that draws together whole domains of mathematics into a unified whole, that arises as a seemingly simple consequence of the use of complex numbers and sinusoids in analysis of the plane:
0 = 1 + e^ (i* pi)
This Euler expression should give sobering pause to those who would glibly dismiss mathematics as a man-made artifice of no great significance.
It also brings to bear the issue that to think logically and creatively based on understanding and insight, we must be responsibly, rationally free. Otherwise, we would be stuck in the grinding out of the equivalent of Leibniz’ wheels in a mill that neither understand nor care what they do, they only play out the cause-effect bonds of the forces of chance and necessity at work and the contingency of how they are arranged.
Schemes of thought that lead to us being mechanisms shaped by blind chance and mechanical necessity acting blindly on matter and energy, run into serious (but usually unacknowledged) problems in the face of mathematics.
KF
PS, Q, that Oxygen and hydrogen interact to form water which has a structural composition such that two moles of the former react with one mole of the latter to yield one mole of the third is not a violation of 2 + 1 = 3, which requires that he same sort of thing be on LHS and RHS. The conservation of mass involved in solving the equation shows us that we have composition of a compound entity that depends on interaction of the underlying substances at atomic-molecular level, transforming the type of substance involved. Likewise, in quantum theory, superpositions and the like are not contrary to ordinary logic, indeed to do q-mech one has to base oneself on the foundation of logic, cf the UD correctives no 38 on this.
Excellent OP and good comments along the way.
Andre, I couldn’t agree more!
Exactly right! So if you read down through the comments you see the other side trying to downplay the significance of this clue to the nature of reality.
For them, it just exists and they pretend not to be moved by it. They try and say that it doesn’t need explaining – a wise move since they are unable to explain it. Someone says that “Beauty is in the eye of the beholder” and tries to simply dismiss it all.
Well, give ’em an A for trying, but an F for logic. I guess though, seen through their worldview, it must seem logical to them.
At least Eugene Wigner realized, and was honest enough to say, that the observations do not fit with his beliefs.
Now, he could adjust his beliefs to fit the evidence or he could simply ramp up his faith in spite of the anomalous evidence.
Someone else didn’t like Wigner’s statement so they simply claimed that Wigner was wrong. Only an atheist sees it that way.
Try telling him he is wrong!
Anyway, this data IS what we would expect in an Intelligently Designed world. It fits best within that paradigm in my opinion. It makes perfect sense to my evolved monkey mind.
Wow – you guys didn’t understand my statement about the Fibonacci sequence at all.
Barry wrote,
Ignoring the entirely unnecessary name-calling, all I said is that you can’t prove a theorem empirically. I didn’t even begin to say that the theorem (or in this case the mathematical object, since the Fibonacci sequence itself is not a theorem) doesn’t show up in the world. It does, in all sorts of wonderful places. The same is true about all sorts of math. The fact that math can describe the world so elegantly is wonderful – I spent 35 years teaching that to students, both showing them how math worked and how we can apply it to the real world.
So I have no idea why Barry jumped to the hostile conclusions that he did.
I’ll note that I also said you can demonstrate math empirically, and use math in empirical models of the world, but Barry seemed to ignore that part of my comments.
Querius writes,
I have written whole posts here about non-Euclidean geometries, so yes, I have heard of them. Again, I think my remark was badly misinterpreted.
There are three possible 2-d geometries, each using a different version of the parallel postulate. (We touched on this when we discussed circle on curved surfaces last night.)
Each of these geometries leads to different theorems about triangles, including both the angle sum and the Pythagorean analogs. Those theorems are all true within their own system.
However, if you then go and apply those theorems to a particular surface, only one of them will be true. Therefore, you can theoretically test the nature of the curvature of a surface by seeing which of the theorems most closely applies. Gauss actually tried to do this by measuring the angles of a triangle formed from three mountaintops in Germany.
However, in this case you are not testing the theorems themselves — those are proven true within their respective geometries — you are testing to see if the math correctly applies to the world.
That’s why I said that you can’t empirically prove that the theorem is true: what you do is logically prove the theorem is true and then empirically show that it applies to the real world.
Do you guys see the distinction?
And P.S. I used to spend a whole day at the end of calculus using what we had learned about infinite series for sine, cosine, and e, as well as reviewing what we knew about complex numbers, to show that e^(pi*i) = -1.
Aleta,
I misunderstood you and apologize. You should talk to your fellow materialist WD400. He’s in denial.
Thank you, Barry.
I am very glad you brought this topic up, and am working on a long reply to the OP, so I hope to address some of these issues later toady.
KF,
Regarding your post #46, do you believe that Euler’s identity, e^(iπ) + 1 = 0, is true in every possible world? (Anyone else interested in the question is invited to respond).
Querius: A flat universe is the only one with a maximum value for Pi. In a curved universe, there are circles whose value for Pi is exactly 3.0000. Unfortunately in those universes, Pi is variable, depending on the size of the circle. A corollary is that you can tell whether youâre in a curved part of space if you could detect a deviation from a flat value of Pi.
Interesting comment. However, any universe with a non-zero mass Querius in it is curved.
DS, yes. Given the logic, structure and quantities involved. That is not about physical spaces in the first instance. Remember numbers and extensions are inherently abstract. Start from {} –> 0. KF
dave, this question relates to the post I just wrote at 48.
Let’s call e^(i?) + 1 = 0 EI for Euler’s identity, for short. EI is true within a certain mathematical system – one which starts with the natural numbers and then defines certain mathematical objects along the way. The truth of EI is not connected to the existence of any physical world, although it can’t be expressed in any physical way (that is, written down) without someone to do so.
EI itself doesn’t have a direct application to the real world that I know of, but the whole subject of which it is a part, vectors written as complex numbers in exponential form, has tremendously useful applications. Is there a possible world where these theorems wouldn’t apply?
Here’s a question: is there a developed theory of waves on a curved surface? How about a theory of complex numbers based on number lines on a curved surface?
When I taught this, I proved EI using infinite series for sine, cosine, and e, which is all independent from any geometrical interpretation.
So I think your question perhaps continues a confusion that I am trying to clarify: the difference between the logical proof of a mathematical fact and the application of that fact.
So when you ask, “do you believe that Eulerâs identity, e^(i?) + 1 = 0, is true in every possible world?,” I think my answer is this:
In any conceivable world where someone developed a mathematical system with the same axiomatic beginning as our, EI is true.
That doesn’t necessarily mean that EI and the larger topic of which it is a part might apply to that world in identical ways.
The always instructive analog is the geometries: in any world the three geometries are potentially formalizable just as they are for us, but they might be applicable in different ways in different worlds.
KF,
I agree. And thanks for the reminder. đ
Aleta,
Interesting points.
Definitely so for the first question; I don’t know about the second.
I think we are in agreement on this:
Aleta, the Euler result will be valid in any abstract plane structure where a unit circle on the origin is definable and an i (or j, as some use . . .) operator. How it is expressed may vary but the matter of substance will obtain. The quantities 1, 0, e, i and pi as well as addition, equality, multiplication and exponentiation as well as sine and cosine are all definable in an abstract plane and the result follows. KF
Yes, kf, I agree entirely. That’s what I was referring to when I wrote “EI is true within a certain mathematical system â one which starts with the natural numbers and then defines certain mathematical objects along the way.” I just didn’t list some of the necessary precursors ideas that must first be in place.
Aleta, While we agree on that, my point is that such structures and relationships do not require us to posit axiom systems as models etc. The logic of structure and quantity is antecedent to our study of it. KF
FWIW, I’m glad Barry started this thread because it is one of my favorite subjects.
I’d like to divide the topic into two issues:
1. Why is there a universe which is amenable to mathematical descriptions, and
2. What is the nature of the mathematics we use to formalize those descriptions.
Barry’s topic question is mainly about the first question above. However, I think there are some misconceptions in his exposition of the topic that I’d like to reply to, as well as add some thoughts of my own.
Topic 1: The universe is amenable to mathematical description.
Barry writes,
Elegant and beautiful are human value judgments, but are somewhat separate afrom the question of why the universe is amenable to mathematical description. Most of us who like math consider it elegant and beautiful, both in it’s pure abstract form and in its ability to model the world. The Mandelbrot set is elegant and beautiful, even though it has no direction application to the physical world, as far as I know. On the other hand, Feynman’s procedures for calculating the path of a particle over all possible paths in the universe is messy and beyond the comprehension of all but a few, and yet it is extremely powerful and describes the world in very accurate terms.
The relevant issue, therefore, is that we are able to describe the world, at many levels including the most fundamental, in mathematical terms.
Whys is this so? That is the question.
As a strong agnostic, my fundamental answer is that we don’t know. I start with the universe as we find it, preferring not to think I know more than I can actually justify about metaphysical speculations about things beyond the reach of human knoweldege.
With that disclaimer, I don’t mind metaphysically speculating.
One possibility is that there is some omniscient, omnipotent cosmic intelligence through whose creative powers arises physical universes which are saturated throughout with mathematical regularities. Notice that I phrase this carefully. Such a cosmic intelligence need not have particular intentions or purposes in created a universe, and such an intelligence might create many universes – each universe might be a single act which is repeated many times. We don’t know. In positing such an intelligence I am in no way making the huge leap to the kind of Christian deity who has conscious, willful engagement with the world and a particular interest in human beings: that is a much larger subject.
But I am acknowledging that a cosmic non-material intelligence could be the craetive source of a universe like ours that is not only pervaded by mathematical regularities and is such that particles have the properties to make interesting things possible, such as chemical elements and more complicated substances.
My metaphysical preference for the notion of the Tao fits into this possibility.
Another possibility is the more Western idea of an engaged deity specifically creating this world and ultimately human beings, with whom he has a special relationship. I don’t believe this is very likely at all, but it is possible.
Another possibility is that there is a Platonic world of mathematical and logical ideals that impress themselves upon any physical world even though those ideals are not themselves the source of those worlds. That is, it might be that an underlying structure of quantum fluctuations is really the fundamental physical nature of reality, and the cause of universes, but that the world of Platonic ideals necessarily manifest within those worlds: that is, the creation of the world and the mathematical regularities of the world come from different sources, not the same source.
I will note that the Western idea assumes that if there is a design, there must be a designer: that math must pervade the world because some being made it that way. I don’t think that assumption that there must be a designer is true. In several of the options mentioned above, the mathematics is primary, not the creation of a creator. In both the Platonic and Taoist speculations, no one specifically makes the world mathematical: mathematics is something that must be there.
Here is a way to think about this issue.
Consider a traditional omniscient, omnipotent Western version of God.
Could God create a square circle? The answer is no: that is a logical impossibility and God can’t do the logically impossible. I believe kf made this point back in one of the infinity threads.
But here’s a slightly different question. Could God make a 2 dimensional circle on a flat surface in which pi was not 3.14….?
I say the answer is no? pi is a logical consequence of the definition of a circle. What this says to me is that the formal mathematical theorems are independent of God. He can build a world that is curved one way or another, but he can’t change the geometrical facts about a flat 2-dimensional surface.
Mathematical facts have a validity of their own in respect to the axioms upon which they are based: they aren’t created by God even if God creates the world in which people discover and use the math.
Here’s another metaphysical speculation I’d like to offer. Barry says,
I don’t think that conclusion is at all true. It seems to me that a non-material cosmic intelligence could create a completely material universe which was saturated with mathematical regularities. To a materialist, the world is definitely not ” nothing but particles in motion randomly bumping into each other.” It’s particles interacting with each other in very particular ways based on the nature of those particles and upon forces which exist between particles. If the universe were just particles bumping into each other without any interaction between them, nothing would happen. This is definitely not what the materialist believes.
The materialist believes that the world is pervaded by mathematical regularities, even though the materialist doesn’t ascribe any non-materialistic cause to the existence of the universe that contains those regularities. I know you don’t think such is possible, but please don’t confuse beliefs about what caused the material universe with beliefs about the nature of the material universe. The materialist accepts those regularities as a given: you misconstrue that position when you say something like the universe is “nothing but particles in motion randomly bumping into each other.”
Well, that’s a lot of rambling. I had thought to write a more structured essay, but this has taken enough time, so I’ll leave it as a first draft of ideas and move on. Food for thought for those interested.
I’ll note that I didn’t even get to point 2 above: “2. What is the nature of the mathematics we use to formalize those descriptions.” Maybe later…
kf writes, “Aleta, While we agree on that, my point is that such structures and relationships do not require us to posit axiom systems as models etc. The logic of structure and quantity is antecedent to our study of it. KF”
I don’t understand this comment. The pure mathematics that leads to Euler’s Identity is independent of any model that might apply it to the real world. Is that what you are meaning when you use the world “model” above. If so, we are in agreement.
However, the pure mathematics also requires some axioms of logic and quantity. Axioms are necessary someplace to get the math started.
So when you say “The logic of structure and quantity is antecedent to our study of it,” what is “it” referring to? Do you mean antecedent to the model, and if not, what does “it” refer to?
Good points all, and actually not very far apart.
Mathematics is a structured method of logic that can be judiciously applied to describe physical phenomena. But there’s more to it than that.
Since quantum theory demonstrates that everything tangible in the universe is determined by probability waves (wavefunctions), consciousness, and logic, materialism is no longer a viable scientific position.
If my observing something can determine whether and how it exists, my consciousness can’t be the result of what I observe.
If you doubt this, go down the rabbit hole and learn about the quantum zeno effect, quantum erasure, and quantum entanglement.
-Q
Aleta, my point is that structures and quantities are antecedent to our putting up frameworks to address and study them, these things — not all mathematical things — are discovered not invented, nor are they confined to this particular world. The logic of such necessary being structures and quantities, esp where necessary links exist from one to the other, will mean some things will apply to any possible world. In short there is a hard core quantitative and structural reality that is foundational to any world existing. I used twoness as a case in point which obtains once distinct identity obtains. The Euler relationship is another thing like that and it ties together domains of Mathematics that we were for good reason surprised to see connected in that way, KF
PS: For context, sitting over for the moment, the tax and UK grant funded radio station pointedly playing a song on corruption immediately thereafter. Maybe that is about the CLICO scandal which came up, maybe not.
Querius @ 61
That’s a common misconception. It is the instrument that measures the state. Alice, Bob or Charlie’s consciousness has nothing to do with Zeno effect.
For me to be “in denial” there would have to be some kind o substantive claim being made. You still haven’t given an example of the Fibonacci sequence appearing in nature “for no apparent reason”. Others have pointed out where you only example for pi fails.
So. Do you have some examples or not?
âIt has been experimentally confirmed,, that unstable particles will not decay, or will decay less rapidly, if they are observed. Somehow, observation changes the quantum system. Weâre talking pure observation, not interacting with the system in any way.â
Douglas Ell â Counting to God â pg. 189 â 2014 â Douglas Ell graduated early from MIT, where he double majored in math and physics. He then obtained a masters in theoretical mathematics from the University of Maryland. After graduating from law school, magna cum laude, he became a prominent attorney.
Interaction-free measurements by quantum Zeno stabilization of ultracold atoms â 14 April 2015
Excerpt: In our experiments, we employ an ultracold gas in an unstable spin configuration, which can undergo a rapid decay. The objectârealized by a laser beamâprevents this decay because of the indirect quantum Zeno effect and thus, its presence can be detected without interacting with a single atom.
http://www.nature.com/ncomms/2.....S-20150415
‘Zeno effect’ verified: Atoms won’t move while you watch – Oct. 22, 2015
Excerpt: One of the oddest predictions of quantum theory â that a system canât change while youâre watching it,,,
Graduate students Yogesh Patil and Srivatsan Chakram created and cooled a gas of about a billion Rubidium atoms inside a vacuum chamber and suspended the mass between laser beams. In that state the atoms arrange in an orderly lattice just as they would in a crystalline solid. But at such low temperatures the atoms can âtunnelâ from place to place in the lattice. ,,,
The researchers demonstrated that they were able to suppress quantum tunneling merely by observing the atoms.
http://www.news.cornell.edu/st.....-you-watch
The Mental Universe â Richard Conn Henry â Professor of Physics John Hopkins University
Excerpt: The only reality is mind and observations, but observations are not of things. To see the Universe as it really is, we must abandon our tendency to conceptualize observations as things.,,, Physicists shy away from the truth because the truth is so alien to everyday physics. A common way to evade the mental universe is to invoke âdecoherenceâ â the notion that âthe physical environmentâ is sufficient to create reality, independent of the human mind. Yet the idea that any irreversible act of amplification is necessary to collapse the wave function is known to be wrong: in âRenninger-typeâ experiments, the wave function is collapsed simply by your human mind seeing nothing. The universe is entirely mental,,,, The Universe is immaterial â mental and spiritual. Live, and enjoy.
http://henry.pha.jhu.edu/The.mental.universe.pdf
The Renninger Negative Result Experiment â video
http://www.youtube.com/watch?v=C3uzSlh_CV0
ElitzurâVaidman bomb tester
Excerpt: In 1994, Anton Zeilinger, Paul Kwiat, Harald Weinfurter, and Thomas Herzog actually performed an equivalent of the above experiment, proving interaction-free measurements are indeed possible.[2] In 1996, Kwiat et al. devised a method, using a sequence of polarising devices, that efficiently increases the yield rate to a level arbitrarily close to one.
http://en.wikipedia.org/wiki/E.....xperiments
Experimental Realization of Interaction-Free Measurement â Paul G. Kwiat; H. Weinfurter, T. Herzog, A. Zeilinger, and M. Kasevich â 1994
http://www.univie.ac.at/qfp/pu.....994-08.pdf
Interaction-Free Measurement â Zeilinger – 1995
We show that one can ascertain the presence of an object in some sense without interacting with it.
http://archive.is/AjexE
Realization of an interaction-free measurement â 1996
http://bg.bilkent.edu.tr/jc/to.....rement.pdf
The following video also clearly demonstrates that âdecoherenceâ does not solve the measurement problem:
The Measurement Problem in quantum mechanics â (Inspiring Philosophy) â 2014 video https://www.youtube.com/watch?v=qB7d5V71vUE
Does Quantum Physics Make it Easier to Believe in God? Stephen M. Barr – July 10, 2012
Excerpt: Couldnât an inanimate physical device (say, a Geiger counter) carry out a âmeasurementâ (minus the ‘observer’ in quantum mechanics)? That would run into the very problem pointed out by von Neumann: If the âobserverâ were just a purely physical entity, such as a Geiger counter, one could in principle write down a bigger wavefunction that described not only the thing being measured but also the observer. And, when calculated with the Schrödinger equation, that bigger wave function would not jump! Again: as long as only purely physical entities are involved, they are governed by an equation that says that the probabilities donât jump.
Thatâs why, when Peierls was asked whether a machine could be an âobserver,â he said no, explaining that âthe quantum mechanical description is in terms of knowledge, and knowledge requires somebody who knows.â Not a purely physical thing, but a mind.
https://www.bigquestionsonline.com/content/does-quantum-physics-make-it-easier-believe-god
The following video also clearly demonstrates that the oft cited âdecoherenceâ does not solve the measurement problem:
Dean Radin, who spent years at Princeton testing different aspects of consciousness, recently performed experiments testing the possible role of consciousness in the double slit. His results were, not so surprisingly, very supportive of the contention that consciousness has an integral role in the experiment:
Then of course, there is the epistemological failure that is inherent in the atheist’s claim that consciousness is not primary but merely illusory
BA77
I think we have already discussed Dean Radin, the parapsychologist at the Institute of Noetic Sciences. I don’t wish to comment on his ‘experiments’ as no physicist was able to reproduce his research.
So you have reservations about Radin but concede that you were wrong on the quantum zeno effect?
Regardless of whatever you think about Radin, here are a few more irreconcilable things with your naturalistic philosophy for you to think about:
Of related interest to the philosophical battle going on behind the scene:
BA77 @ 68,
No. I am still saying Zeno effect (or for that matter all Quantum experiments) has nothing to do with consciousness. The ‘observers’ are instruments. It is the instrument that measures the Quantum state. Unless you concede that machines have consciousness, there is no proof that consciousness affects the Quantum state (except of course in Parapsychologist Radin’s non-reproducible experiment)
That is just plain denial on your part. (if there were a ‘you’ to deny anything in your illusory worldview anyway), You were shown the papers for interaction free zeno effects. Do you deny those experiments? Oh well, denial is part and parcel for atheists. I’ve seen it a thousand times at least.
Of related interest:
Dean Radin defends the mathematical and empirical integrity of some his previous work at Princeton here. As well, the less than forthright ad hominem attacks of atheists against him are discussed and exposed for the baseless attacks they were and are:
Quote of note:
of note: That is my last response to you on this thread. I have given up hope of ever convincing any atheist of the plain common sense fact that they are not a machine and that they really do have a conscious mind. It is really something so plain and obvious that you should not have to convince anybody of the fact they are not a machine:
Aleta:
I agree that pi is a logical consequence of the definition of a circle, but I’m not sure that this means mathematical theorems are independent of God. I still tend to think the circle is His idea even though its definition has logical consequences. I think math is in God rather than being independent of Him. Math is immutable because God is immutable. Similarly logic. Logic doesn’t exist outside God, but inside Him. God cannot be illogical because to do so would be against His immutable nature.
Just a question: Do people who think mathematics is manmade mind if it is reorganized so as to consistently give someone else more money for the same job?
People typically base their case for fairness on the theory that the mathematics is not manmade, but is an external standard to which one can appeal.
Barry Arrington: How Did Mathematics Come to be Woven Into the Fabric of Reality?
It’s all about symmetry.
WD400 @ 64. If I had to resort to evasion, dissembling, and bad faith to defend my position, I hope I would rethink my position. It does not seem to bother you. It should.
lol. Stop evading and just give some examples.
News,
I’m not sure that all of mathematics is human-made, but I believe at least some (probably most) is.
But how would this reorganization work in the real world? Can you give us more specifics? I really don’t see any way it could be accomplished.
Aleta @ 59 writes:
“Another possibility is the more Western idea of an engaged deity specifically creating this world and ultimately human beings, with whom he has a special relationship. I donât believe this is very likely at all, but it is possible”
Aleta, the second sentence is not logical or sensical. The use of the word “(un)likely” assumes you have a “matrix of possibilities” (cf Dembski) from which to choose or refer to. The lingo and thought is part of your mathematical training.
The subject of God can’t be talked about in mathematical or statistical terms. This is a heart issue. Belief, faith, whatever. You are basically saying you don’t “feel” there is a personal God. I “feel”, to the point of knowing, there is a personal God.
Conway’s Game of Life is man-made mathematics. There are an infinite number of initial patterns, and the only way to know the resulting end pattern is to step though the generations. I can’t imagine that every result of the Game of Life has some metaphysical counterpart.
See https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life
Neil Rickert, “Personally, I think … Mathematics is entirely man made.”
Hmmm, is this the opinion that popped into your head one day, or is it something you determined with reason? If so, please share your reasoning.
Well, yes, at least from one point of view, all of mathematics is man-made: there is a fascinating history of it from the first numbers system and geometry up to calculus and beyond. Any math we know about must have been formalized by humans someplace in history. (I wrote a couple of posts about some of this over in one of the infinity threads.)
On the other hand, because new results in math seem inevitable, in some sense, being logically connected consequences, especially after we have worked them out, there is a sense that there we already there and we just discovered them.
As one of my students once said as we discussed this in class, she thought that perhaps math was discovered (that is, existed somehow separate from us), but we invented the means of talking and writing about it.
And as my Game of Life example was meant to illustrate, there is some math that clearly was just invented, and then the logical consequences of it was explored.
So I don’t think it’s unreasonable to say that math is man-made in the sense that we have chosen the starting points (the axioms, definitions, and logical rules) and then continued the process as we worked out more and more results. That has been the result of the work of human beings, and thus, in that sense, made by man.
Aleta, everything man-made is woven into the fabric of reality. That includes mathematics. So back to the original question by Mr A – how did it happen. Just atoms & void & oops?
Aleta at 81: Sorry, that won’t work. Either man is observing something that underlies the universe and working within those given results or mathematics is an adaptation for survival (it could be completely irrational and is only tangentially related to how the universe works).
The second position saves naturalism (and its creation story, Darwinism) at the price of science. But naturalists are increasingly eager to dump falsifiability and evidence-based thinking. Many are cool with criminalizing dissent.
See also: Tyson bombshell: Universe likely just computer sim
Science will pick up where it left off, with a hiatus of naturalism in between.
Aleta, I note again, the definition that mathematics as practised is the study of the logic of structure and quantity (including of course space). Structure and quantity in material part are necessary facets of any possible world and as such are necessary beings. I pointed to twoness and its involvement in distinct identity, pivotal to a world being possible. I would suggest that this lies at the heart of possibility and being, manifesting a world of mathematical realities as necessary to reality. A very obvious longstanding view is that such realities are eternally contemplated by the inherently good necessary and maximally great being at the root of an actual world existing, i.e. God. KF
I’ll go with the second of those, except for the “completely irrational” part.
Science is highly systematic. Mathematics is the study of systematicity and systematic methodology. The mathematics does not come from the universe itself, but from the highly systematic nature of the methods used by the scientists. And please note that many scientists were/are mathematicians.
Using a systematic methodology is a highly rational approach to exploring our world.
News liked my comment at 81 đ , so I’ve replied on the thread she started at http://www.uncommondescent.com.....-will-win/
I propose a thought experiment. We start with two identical sand beaches, and set up two scenarios. In the first scenario, we bury gold bars a the same relative location on each beach.
In scenario 1, we ask two participants to locate the gold bars. In scenario 2, we ask the two participants to build sand castles.
What do we expect?
In scenario 1 we expect each participant to have no clue where the gold is until an eureka moment happens, he declares that he is done, and he reports the known location of the gold bar.
In the second scenario, we expect to find two very different looking sand castles. We will not be surprised at all if someone declares that they are done, then goes back and makes a few changes.
What is the fundamental difference between these two scenarios?
wd400 @41:
Google “Fibonacci sequence in nature” and select ‘images’. You’ll have plenty of examples. Oh, wait, you’re an atheist, so if I gave you 100, you’d require 101.
I can google. I just also happen to know what the Fibonacci series and golden spirals are.
When I google your search term so I find a lot of photos of nautlius shells, which are not golden spirals. And lots of spiral galaxies, which vary greatly in how tightly they turn. There are good examples (pinecones, sunflower seeds) but don’t appear “for no reason” as Barry claims, but just as a result of very simply growth processes.
God can count, to suggest otherwise is silly.
By definition there can only be one true absolute God, and in whatever essence God exists; and as the Alpha and Omega of eternal space and eternal time.
Mathematics, while dealing with infinity, cannot prove or disprove eternal infinity exists, or God. It seems God wills to be found primarily by means of faith. Jesus said, His miracles were the sign of who He is.
Philosophically or theologically speaking, such an all powerful uncreated, uncaused Creator may select a point in eternal time to create the cosmos. Therefore, He would choose the exact time to create, otherwise, God would not be in control.
It follows, once a predetermined, fixed point occurred intelligently, no matter what that point consisted of, then there is a case for every point that follows to be ordered. Speed would be ordered, design would be ordered. Material would be delivered to order, all to a higher law initially, that is by an unknown process; a super science known only as a miracle.
Darwin dismissed miracles, the biggest mistake he would ever make. The biggest blindfold consensus science will ever use.
That God can make something instantly perfect, must be the case; therefore, the first matter would be delivered perfectly, complete in its first state; the action of a perfect being.
It follows, therefore, that any first material substance could be created mature, or immature. We have it on record, that God calculated, six days would do the job to complete a perfect creation, that is, to suit humans.
You may disagree with that figure. However, a vexing question then remains, if you were all powerful and all intelligent, how then would you create, for loveâs sake, and with every atom to be able to be created and numbered to do your will.
God wrote intelligently, plain and simple, and in stone, He created in six days. An important point is, He in no way gave an explanation to how miracles affect certain data. We have his word, recorded as divine law, which should be enough!
He created a cosmos fit for gods, a home to move in straight away. The fittest is God, who would, you think, have created all in a fit and proper manner.
That is, Good enough to generate perfectly fit children of the Most High.
According to Darwin, who ignored such priceless data; that is, a true recorded miraculously embedded history of a developing nation, from whom the creator God would be born.
An unbroken chain of worship every seven days back to the miracle of Sinai. A test of pure faith. God counted Ten Commandments, He therefore knew how to count up to six.
Mathematically, the God-Man said even the hairs on our heads are numbered. Every hair circumference honed with pi. In evolutionary terms, how did pi get to the attention of the illusive phantom natural selector!
Creation in six days is equal to Jesus saying he would generate himself from dead matter, as six days divided by two days equals three yom(s).
Of course, historic miracles have all gone pie in the sky in this day and age.
Today, such is dismissed and thoroughly done over, as calculated by the number of âdarwins.’
I darwin, is mathematically greater than any intelligent designed miracle, as there are none: the equation mathematically proves it – http://blackwellpublishing.com.....ution2.asp
Wow, Me_Think.
You just got owned by bornagain77! And all you can come up with is further unsupported assertions?
I hate to break it to you, but your naked assertions do not constitute irrefutable proof.
As I said, you might want to read up on quantum theory, including some of the latest experimental evidence, before you post something contrary.
Considering your continued evasion of my simple questions in the Do You Believe in Evolution post, your confusion between squaring velocity with doubling it in the equation for kinetic energy, and your being owned in that thread by RexTugwell has pretty much established your low credibility, not to mention that your style reminds me a lot of someone else here with a lot of sock puppets who once posted some fundamental errors in computing statistics.
Goodbye.
-Q
Bornagain77,
Thanks for your posts and links. It will take me a while to go through them.
As you probably know, quantum theory has been the most intensively challenged and validated area in all of science to a precision of up to 10 parts per billion. The wild controversy is in the interpretations—what does it all mean to existence and consciousness. Is the interpretation of quantum effects exclusively the domain of faith and philosophy, or can the scientific method extend to these interpretive areas, and to what extent?
-Q
Querius, for me personally, the fact that consciousness is integral to quantum mechanics is not really even a matter of philosophical debate anymore but is now simply an established empirical fact despite how much atheists bitch and moan to the contrary:
Querius @ 91
Instruments don’t have consciousness. Quantum effects are observed by instruments. Unless you believe instruments are conscious, your assertions don’t work. The interaction free measurement which is being used to claim effect of consciousness by using Zehnder interferometer is not really ‘interaction free’. Like many terms in QM (Nothing is not Nothing), ‘interaction free’ is not interaction free! Avshalom C. Elitzur and Lev Vaidman clearly state that in their paper. In fact many QM researchers have avoided using the term as it gives the wrong connotation.
Here’s direct quote from Avshalom C. Elitzur and Lev Vaidman
I really don’t have a problem with – of all people- you thinking I have low credibility ! I gave you a homework.Please do it. If you can’t even do multiplication and see 20,000 years x 6 days is not anywhere near 13.8 billion years or can’t understand that to equate bya to biblical days in the first three days of calculations by Schroder (7.1 bya, 3.6bya, 1.8bya), God’s speed would have to be above light speed, you can’t really be taken seriously, and no, I certainly don’t go by any other handle here at UD.
Of related note to homodyne measurements
Also of note, since the atheistic Many Worlds Interpretation (MWI) denies quantum wave collapse, the preceding experiment also effectively falsifies the atheistic MWI:
also of note: Like practically everything else of significance in the atheistic worldview, their many worlds interpretation of quantum mechanics is built out of pure imagination
bornagain77,
It’s simple.
Since it’s now been conclusively demonstrated in experiments that do not directly interact with what’s being observed . . . that conscious observation collapses the wave function, psi, into matter and energy waves, therefore the absence of observation leaves no possibility of an emergent consciousness. Therefore, a pre-human, conscious Mind was necessary for the existence of all mass-energy that could eventually be formed into, among everything else, conscious humans.
The only way to avoid this conclusion is to scientifically demonstrate the spontaneous collapse of unobserved wave functions.
What would this look like? There are two parts:
1. One has to be certain that a wave function collapse had occurred, and
2. One has to be certain that this collapse was not part of a von Neumann chain, nor an observation by any human or non-human mind.
Since 2 is not possible to prove, then emergent consciousness is not logically possible, but had to have been the result of a pre-existing conscious Mind.
-Q
bornagain77,
Thanks for posting this. And then there’s the issue of what caused the wave function collapse at the initiation of the big bang. Perhaps a Mind?
-Q
As to, “then thereâs the issue of what caused the wave function collapse at the initiation of the big bang. Perhaps a Mind?”, this might interest you Querius:
At the 8:30 minute mark of the following video, Schrodingerâs cat and Wigner’s Friend are highlighted:
Divinely Planted Quantum States – video
https://youtu.be/qCTBygadaM4?t=512
also of note:
Stephen Hawking: “Philosophy Is Dead” – Michael Egnor – August 3, 2015
Excerpt: The metaphysics of Aristotle and Aquinas is far and away the most successful framework on which to understand modern science, especially quantum mechanics. Heisenberg knew this (Link on site). Aristotle 2,300 years ago described the basics of collapse of the quantum waveform (reduction of potency to act),,,
Real scientists have a meaningful understanding of natural philosophy as it relates to their work. No atheist scientist in the public spotlight today would pass a freshman philosophy class. Think Dawkins. Think Krauss. Think Myers. Think Moran. Think Novella. Think Coyne. Think Hawking.
Our 21st-century scientific priesthood — mostly atheists and materialists to the extent that their metaphysics is coherent enough to be described — is dominated by half-educated technicians with publicists.,,,
http://www.evolutionnews.org/2.....98261.html
âI think that modern physics has definitely decided in favor of Plato. In fact the smallest units of matter are not physical objects in the ordinary sense; they are forms, ideas which can be expressed unambiguously only in mathematical language.â
Werner Heisenberg – As quoted in The New York Times Book Review (March 8, 1992). – “Uncertainty,” David C. Cassidy’s biography of my father, Werner Heisenberg
Aquinasâ First Way â (The First Mover â Unmoved Mover) – video
http://www.youtube.com/watch?v=Qmpw0_w27As
Aquinasâ First Way
1) Change in nature is elevation of potency to act.
2) Potency cannot actualize itself, because it does not exist actually.
3) Potency must be actualized by another, which is itself in act.
4) Essentially ordered series of causes (elevations of potency to act) exist in nature.
5) An essentially ordered series of elevations from potency to act cannot be in infinite regress, because the series must be actualized by something that is itself in act without the need for elevation from potency.
6) The ground of an essentially ordered series of elevations from potency to act must be pure act with respect to the casual series.
7) This Pure Actâ Prime Moverâ is what we call God.
http://egnorance.blogspot.com/.....t-way.html
Or to put it much more simply:
“The âFirst Moverâ is necessary for change occurring at each moment.”
Michael Egnor â Aquinasâ First Way
http://www.evolutionnews.org/2.....first.html
Double Slit, Quantum-Electrodynamics, and Christian Theism â video
https://www.facebook.com/philip.cunningham.73/videos/vb.100000088262100/1127450170601248/?type=2&theater
Verse:
Acts 17:28
For in him we live and move and have our being.’ As some of your own poets have said, ‘We are his offspring.’
Thank you, bornagain77.
Just thinking about it, even the double-slit experiment, just as quantum tunneling, requires the wave function. As one website notes:
And another website notes:
What starts out as an observed electron, becomes a mathematical function as it passes through the slits of the physical barrier, and then collapses to a wave or particle depending on whether the slits are observed!
As you well know, quantum erasure simply determines the wave function collapse independent of time such that it appears to be erasing and redoing the past based on belated observation.
All this is a convincing demonstration that the nature of the universe is fundamentally mathematical, and that conscious observation is also fundamental to the universe.
The big bang was not observed by humans, so a non-human Mind outside of our universe must have initiated the big bang by creating and observing a wave function along with space-time, some of which God left to us to observe.
Paraphrasing what others have said, the good news is that we’ve discovered that God created the universe, the bad news is that God turned out to be a mathematician, not a physicist.
But . . .
Is it possible that the universe as we observe it simply a gigantic von Neumann chain, which as it collapses forms our history? I think that the answer is perhaps, but it still requires at least an initial wave function so as not to violate cause-and-effect.
-Q
Slightly OT
Thanks everyone for the enlightening discussion.
While math is not my strong suit, I appreciate that the universe is quantifiable precisely because it is finite, and as such, it had a beginning.
I will have to increase my math skills this coming fall, as (at the age of 54),I continue my studies at California State University, San Bernardino. I am a music major, and have been studying music all my life, pretty much, but at the university level for the last 3 years. I decided 4 years ago that I needed to earn a degree in music, so that I could improve my composition skills, and perhaps become a music educator.
What does music have to do with math?
The average person would be surprised to learn that all music has a mathematical structure; particularly Western music, beginning with JS Bach and the study of “equal temperament”: the realization that tonal music requires precise tuning.
“a system of tuning, in which every pair of adjacent pitches is separated by the same interval. In other words, the pitches of an equal temperament can be produced by repeating a generating interval. Equal intervals also means equal ratios between the frequencies of any adjacent pair, and, since pitch is perceived roughly as the logarithm of frequency, equal perceived “distance” from every note to its nearest neighbor.”
https://en.wikipedia.org/wiki/Equal_temperament
In addition to precise tuning, the structure of Western tonal music is based on a 12 tone chromatic scale, and the “Circle of 5ths.”
http://www.flupe.com/lessons/f....._notes.htm
http://randscullard.com/CircleOfFifths/
These aren’t structures that were necessarily invented by humans, although their “evolution” certainly progressed out of human ingenuity, as humans increasingly experimented with tone, rhythm, harmony and counterpoint.
So I think the particular insight we can gain from this is that the structures were there to discover, but what we do with those structures is left to the imagination; to our free will in creating: the endless possibilities that we arrive at when we work with the raw material is woven into the mathematical structure of the universe.
At one time (in ancient times, actually), humans understood that the basic structure of music was a part of the makeup of the universe. They called it the “Music of the Spheres.,” which isn’t strictly speaking, audible; but in similarity to musical structures, they are: “mathematical relationships (which) express qualities or ‘tones’ of energy, which manifest in numbers, visual angles, shapes and sounds.”
https://en.wikipedia.org/wiki/Musica_universalis
So Rock and Roll, or Rhythm and Blues were never inevitable, because they are human inventions; but the rhythm and tonal structures that made them possible, were inevitable as humans continued to develop their understanding of what was musically possible. Bach, Mozart, Beethoven and so many others, merely took full advantage of their understanding of those possibilities, and they made them work in ways that are both beautiful and inspiring.
My spouse is a musician, and we were just talking about the overtone series, which is one of the things that makes notes based on ratios (as Pythagorus first explained) harmonious. She is reading a book called “This Is your brain on music”, by Daniel Levitin, and she read me a part about how if you listen to the overtones of a note with the actual note damped, your mind fills in, so to speak, the missing note based on the overtones it’s hearing. Your might like this book.
Aleta,
Very interesting.
I was walking through my neighborhood the other day, and I heard the sound of a freight train “horn” or “whistle” (don’t know which it is), but based on that sound, which lasted several minutes, I was able to fill in notes to make up a major triad, plus I believe a major minor 3rd above the 5th, which would have made a 7th chord. I heard it in the sound, while I don’t really know if all of those notes were actually audible. They seemed to be. But having studied harmony for so many years, I begin to hear those structures even in nature.