Four scientists weigh in, on behalf of the Japanese Kavli Foundation:
Max Tegmark (pro real): It’s actually an old idea. Even Galileo exclaimed that the universe is a grand book written in the language of mathematics because he was wowed by all the astronomic regularities discovered in his time, for instance the precise circular or elliptical orbits of planets. Long afterwards, a whole set of subatomic particles were predicted by mathematical principles and then discovered, the Higgs boson being the most recent example. Even the possibility of curved shape of outer space was predicted centuries earlier by non-Euclidian geometry. So nature is clearly giving us hints that the universe is mathematical. I’ve taken it to the extreme by proposing that our entire physical reality isn’t just described by math, but that it is a mathematical structure, having no properties besides mathematical properties.
Brian Butterworth (anti-real): We’ve pinpointed an area of the human brain where there’s a specialist neural network that responds to counting the number of objects in a set. This area of the brain can recognize numbers across modalities. In other words, it can recognize three cats, three tones or three wishes. A similar area in the brain of the monkey does the same job. We even discovered the guppy — a small fish with a tiny brain — has one system for detecting small sets of up to four objects and one for larger sets. My argument is that we evolved a brain-based system for detecting and comparing the number of items in groups. Humans have developed symbolism for these numbers and elaborated on them to create the kinds of mathematics that Max and Simeon need to describe the universe. Numbers are not necessarily a property of the universe, but rather a very powerful way of describing some aspects of the universe.
TKF: (moderator)So you disagree with Dr. Tegmark’s notion that electrons are merely numbers?
Brian Butterworth (anti-real):Yes, because in order to have a physical explanation for phenomena, you have to have a cause for it. But how can a number be a cause? It’s true that you can use numbers to describe electron properties, but that doesn’t mean those numbers are actually a property of that physical object. Twoness is a property of a set of objects, such as two cups, or two electrons. But it is independent of the kinds of objects that are in the set for which it is a property. A set of two cups is different from a set of two electrons so twoness can’t have the same causal property for cups and electrons.
Why not? Thoughts? More.
0 = 1 + e^ i*pi
. . . Euler.
KF
As I read Metaphysics, “numbers cannot be a cause” is actually central to Aristotle’s objection to Plato’s account of the Forms. (Better put: we cannot comprehend how numbers could be a cause.) These problems have been with us for a long, long time!
I think the anti-realist argument as put here is pretty vulnerable to realist objections. The realist isn’t necessarily committed to saying “twoness is a cause”, but to saying that reality has the right sort of structure to be describable by mathematics.
And she can say that just as we have perceptual capacities that reliably detect the presence of visible things, and touchable things, and so, we also have the conceptual capacities that reliably detect abstract structures and patterns.
I think that the whole history of nominalism-cum-skepticism shows that it’s exceedingly difficult — the Platonic realist would say “impossible!” but who knows? — to develop a fully coherent, consistent view that says that our perceptual capacities reliably put us in cognitive contact with concrete objects, but that our conceptual capacities do not reliably puts us in cognitive contact with abstract objects.
Any view that undermines the latter will, sooner or later, undermine the former (Hume); any view that affirms the latter will, sooner or later, affirm the latter (Plato, Aristotle).
My main objection to Platonic realism is that it requires mind-body dualism, and that falls afoul of the interaction problem. But I’ll readily admit that a nominalistic treatment of mathematics, while nicely consistent with materialism, is unsatisfying as an account of mathematics.
Kairos,
I was going to comment on your Euler post but comments were turned off.
In particular, I was going to address the idea of “freethinking.” The freethinkers are not atheist materialists, who are slavethinkers, still mired in decaying 19th-century pseudoscience. The real freethinkers are ID proponents, who are following the evidence where it leads.
Here’s one of my UD posts on this topic from 2011, which inspired 686 comments:
http://www.uncommondescent.com.....ethinking/
Well, where to start?, Let’s see, leading quantum physicist Anton Zeilinger has followed in John Archibald Wheeler’s footsteps (1911-2008) by insisting reality, at its most foundational level, is ‘information’.
Materialism had postulated for centuries that everything reduced to, or emerged from material atoms, yet the correct structure of reality is now found by science to be as follows:
Here are my references for the claim that mass “normally” reduces to energy:
The reduction of matter to energy is comparatively easy to accomplish as is demonstrated by nuclear/atomic bombs:
Whereas, on the other hand, to convert energy to matter is a far more difficult proposition:
Moreover, it is important to note that a simple atom is certainly not ‘simple’:
Yet somehow, serendipitously, shortly after the big bang, and in the nucleosynthesis of stars, all the pieces of the puzzle ‘spontaneously’ fell together to get these complex atoms to form ‘spontaneously’ from energy (at least according to atheists it had to be ‘spontaneous’):
Here are my references for the claim that “energy and mass both reduce to information”:
It is also very interesting to note that the quantum state of a photon is actually defined as ‘infinite information’ in its uncollapsed quantum wave state:
Of related note:
I don’t know about Feynman, but as for myself, being a Christian Theist, I find it rather comforting to know that it takes an ‘infinite amount of logic to figure out what one stinky tiny bit of space-time is going to do’:
Here are my references for the claim that “information reduces to consciousness”:
Of related note: The following site is of related interest to establishing the claim of “consciousness preceding ‘material’ reality” through geometric considerations:
The preceding interactive graph points out that the smallest scale visible to the human eye (as well as a human egg) is at 10^-4 meters, which ‘just so happens’ to be directly in the exponential center of all possible sizes of our physical reality (not just ‘nearly’ in the exponential center!). i.e. 10^-4 is, exponentially, right in the middle of 10^-35 meters, which is the smallest possible unit of length, which is Planck length, and 10^27 meters, which is the largest possible unit of ‘observable’ length since space-time was created in the Big Bang, which is the diameter of the universe. This is very interesting for, as far as I can tell, the limits to human vision (as well as the size of the human egg) could have, theoretically, been at very different positions than directly in the exponential middle;
Of course there is a lot more that has and can be said by people much more qualified than I to speak on the subject, but in my limited capacity I find the universe to be far more friendly to Theistic presupposition, particularly Christian Theistic presuppositions, than many physicists realize or are willing to admit.
Music and Verse:
1. I always have to laugh when someone says we have, “…pinpointed an area of the human brain…”. What they mean is that when someone actualizes data this area of the brain has more activity. They use this proxy of activity in a certain area as evidence against dualism. But they really have no idea what the nerves are doing, or how the meaning of a number is comprehended.
2. A number can be a cause if I mentally assign it to be a cause.
For example, when I play a game of monopoly whether I go forward 5 or 6 spaces may make the difference between paying $75 to the bank or $2000 to the owner of boardwalk.
Or for another example, when someone asks me to to a task in 10 minutes, what is the cause of me eventually doing it in 10 minutes. It is the number 10. The reason I believe the number ( or maybe – my perception of the number ) to be the cause is that the number 10 can be communicated to me in many different ways — orally ( in many different languages ), by writing it down, by tapping that many times ( making me both count, and then respond ). It is the number 10, not the specific material of media through which the number is communicated, that causes the response.
Materialists really have no answer for how human beings can perform delayed future actions after an arbitrary time. We know this happens, but they can not come up with a reasonable description of how it happens without introducing the concept of libertarian free will.
It is hard to find a less important question than whether numbers (or other mathematical objects) are real.
Personally, I’m a fictionalist. I’ve had people tell me that mathematics can’t work with fictionalism, or can’t be used in science. What nonsense. It works the same for me as for anybody else. The question of whether numbers are real does not arise.
Neil Rickert, I have a cartoon for you:
Calvin and Hobbes – cartoon – The Mathematical Atheist
http://s3.hubimg.com/u/270622_f520.jpg
as to your overall belief, all I can say is that One man’s trash is another man’s treasure:
The Unreasonable Effectiveness of Mathematics in the Natural Sciences – Eugene Wigner – 1960
Excerpt: ,,certainly it is hard to believe that our reasoning power was brought, by Darwin’s process of natural selection, to the perfection which it seems to possess.,,,
It is difficult to avoid the impression that a miracle confronts us here, quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions, or to the two miracles of the existence of laws of nature and of the human mind’s capacity to divine them.,,,
The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.
http://www.dartmouth.edu/~matc.....igner.html
Mathematics and Physics – A Happy Coincidence? – William Lane Craig – video
http://www.metacafe.com/w/9826382
Kurt Gödel – Incompleteness Theorem – video
http://www.metacafe.com/w/8462821
BRUCE GORDON: Hawking’s irrational arguments – October 2010
Excerpt: Rather, the transcendent reality on which our universe depends must be something that can exhibit agency – a mind that can choose among the infinite variety of mathematical descriptions and bring into existence a reality that corresponds to a consistent subset of them. This is what “breathes fire into the equations and makes a universe for them to describe.” Anything else invokes random miracles as an explanatory principle and spells the end of scientific rationality.,,,
Universes do not “spontaneously create” on the basis of abstract mathematical descriptions, nor does the fantasy of a limitless multiverse trump the explanatory power of transcendent intelligent design. What Mr. Hawking’s contrary assertions show is that mathematical savants can sometimes be metaphysical simpletons. Caveat emptor.
http://www.washingtontimes.com.....arguments/
Nature by Numbers – The Fingerprint of God – video
https://vimeo.com/9953368
What pi sounds like when put to music – cool video
http://www.youtube.com/watch?v=YOQb_mtkEEE
“It appears that the Creator shares the mathematicians’ sense of beauty.”
– Alexander Vilenkin (stated in reference to Euler’s Identity in particular)
http://rfforum.websitetoolbox.com/post?id=3754268
Think of a Number
What nonsense, indeed!
We perceive duality (and a lot of other concepts attributed to what we call mathematics) because our senses evolved or were created to perceive practical information for our survival as an integral part of the universe.
“Oh,” some people might argue, “but you can see double when it’s not true, therefore our senses are *unreliable*, and everything could be an illusion. Thus, no one (especially me) can be held responsible for anything they do by anyone else (especially God).”
“Oh,” God might observe, “you lived in all other ways as if you could and did trust your senses as reality, so I’ll simply judge you by your own standards.”
Oops.
However, I’m not so keen on the significance of the middle of things (including dynamic range). I think Sagan was extremely impressed that sun wasn’t the center of the universe (as well as our earth being a pale blue dot from some arbitrary vantage point in space, and with numbers with a lot of zeros in them). As everyone with a belly button knows, the middle of anything is of *prime* importance! Not.
On the other hand, we do seem to be on a “privileged planet” with respect to observational astronomy–including our place in Time, considering the current apparent sizes of the sun and moon.
Math is NOT real. The divisions we call math are just a language of the reality. our language is just sounds organized to expressed thoughts. Yet our thoughts are not sounds.
Math has nothing to do with the universe. Its in fact just that the universe is so well ordered that divisions can produce a representation of this order and finely ordered indeed.
Numbers only represent things. They are not the essence of things.
It could only be a natural ordered universe would be measurable.
Math is a measuring of order. It does not exist without the order.
Math is not real. The order of the universe is real. Mans invention of math is a primitive language of this sell done order.
Biology probably has a greater order then physics. however putting it into math is still too complicated.
Wild ideas like evolution proving this.
Groan. Is this the future of ID ? Discussing how many angels on the head of a pin ?
At least its a break from the usual theology, I guess.
Gil Dodgen;
Really? What is this evidence? Is there now a working theory of “Intelligent Design” that makes some testable prediction?
This would be rather more interesting than whether numbers are real or not.
On topic:
Numbers are complex and thus can be real, imaginary or both!
Shoot, apparently some atheists are not even sure if they are real, much less if math is:
Why Intellectuals Laugh at Atheists (Part 3) – video
http://www.youtube.com/watch?v=eaBMtiXaoWI
semi-related notes:
Why No One (Can) Believe Atheism/Naturalism to be True – video
Excerpt: “Since we are creatures of natural selection, we cannot totally trust our senses. Evolution only passes on traits that help a species survive, and not concerned with preserving traits that tell a species what is actually true about life.”
Richard Dawkins – quoted from “The God Delusion”
http://www.youtube.com/watch?v=N4QFsKevTXs
Scientific Peer Review is in Trouble: From Medical Science to Darwinism – Mike Keas – October 10, 2012
Excerpt: Survival is all that matters on evolutionary naturalism. Our evolving brains are more likely to give us useful fictions that promote survival rather than the truth about reality. Thus evolutionary naturalism undermines all rationality (including confidence in science itself). Renown philosopher Alvin Plantinga has argued against naturalism in this way (summary of that argument is linked on the site:).
Or, if your short on time and patience to grasp Plantinga’s nuanced argument, see if you can digest this thought from evolutionary cognitive psychologist Steve Pinker, who baldly states:
“Our brains are shaped for fitness, not for truth; sometimes the truth is adaptive, sometimes it is not.”
Steven Pinker, evolutionary cognitive psychologist, How the Mind Works (W.W. Norton, 1997), p. 305.
http://blogs.christianpost.com.....ism-12421/
Around the 12:00 minute mark of the following video Pastor Joe Boot reflects on the self-defeating nature of the atheistic worldview:
Defending the Christian Faith – Pastor Joe Boot – video
http://www.youtube.com/watch?v=wqE5_ZOAnKo
Alan Fox:
It has been presented and you choked on it, as usual.
Yes, however it is obvious that your position doesn’t have anything like that.
Really? What is this evidence?
Computer programs are designed. Living systems include computer programs, far more sophisticated than anything designed by the most intelligent humans.
This is why I no longer waste my time arguing with flat-earthers and other science-deniers who ask for evidence of design in living systems.
A more interesting question is whether mathematicians are real or not.