Surprising numbers seem okay with it. A teenager’s question at Tik Tok ended up triggering an academic debate:
“I believe that the only way to make sense of mathematics is to believe that there are objective mathematical facts, and that they are discovered by mathematicians,” says James Robert Brown, a philosopher of science recently retired from the University of Toronto. “Working mathematicians overwhelmingly are Platonists. They don’t always call themselves Platonists, but if you ask them relevant questions, it’s always the Platonistic answer that they give you.”
Other scholars—especially those working in other branches of science—view Platonism with skepticism. Scientists tend to be empiricists; they imagine the universe to be made up of things we can touch and taste and so on; things we can learn about through observation and experiment. The idea of something existing “outside of space and time” makes empiricists nervous: It sounds embarrassingly like the way religious believers talk about God, and God was banished from respectable scientific discourse a long time ago …
Rovelli goes further, calling into question the universality of the natural numbers: 1, 2, 3, 4… To most of us, and certainly to a Platonist, the natural numbers seem, well, natural. Were we to meet those intelligent aliens, they would know exactly what we meant when we said that 2 + 2 = 4 (once the statement was translated into their language). Not so fast, says Rovelli. Counting “only exists where you have stones, trees, people—individual, countable things,” he says. “Why should that be any more fundamental than, say, the mathematics of fluids?” If intelligent creatures were found living within, say, the clouds of Jupiter’s atmosphere, they might have no intuition at all for counting, or for the natural numbers, Rovelli says.Dan Falk, “What is math?” at Smithsonian Magazine
That’s pretty deceptive, isn’t it? The natural numbers are what they are whether the intelligent aliens have a use for them or not. Carlo Rovelli stops short of saying that 2+2=5 but the article gives every sense that many would love to go there if only they could get some kind of a nudge.
Indeed, if that’s the best he can come up with, it is far to say that the war on Platonism is just the war on math, PhD version.
See also: One of Boghossian’s hoaxers started the Woke on the 2 + 2 + 5 drive.
10 Replies to “Mathematicians debate the war on math”
It is the same old question of whether we “develop” or “discover” math.
I am firmly in the camp that we discover it (as the Designer was kind enough to give us the ability. He did not give the same ability to animals). This then allows us to start understanding the grand design of our world, as it is all based on math. Obviously the Designer knows math. The aliens from Jupiter would know the exact same math.
The statements like “Rovelli believes that math “works” because we crafted it for its usefulness.” are from the people in that other camp, who believe that we “develop” math, and it just so happens to also describe everything in our world. What a convenient coincidence!
As to establishing the objective existence of math,,,
George Ellis takes the ‘pragmatic view’ of causation and existence, in which “If Y is a physical entity made up of ordinary matter, and X is some kind of entity that has a demonstrable causal effect on Y as per Definition 1, then we must acknowledge that X also exists (even if it is not made up of such matter).”
And if we adopt Ellis’s more than reasonable criteria for assessing whether a immaterial entity, such as logic and/or mathematics, exists, then we are forced to conclude that mathematics certainly exists.
We are forced to this conclusion that mathematics must certainly exist simply by the ‘real’ causal effects that mathematics brings about in the world.
As Peter Tyson pointed out, “Mathematics underlies virtually all of our technology today.”
Such technology simply would not be possible if mathematics were merely a ‘invention’ of man.
Moreover, given that Godel’s incompleteness theorem proves that mathematics cannot be a cause unto itself, then we are further forced to conclude that the Mind of God must be behind the causal efficacy that we witness in immaterial mathematics.
Verse and quote:
I’m wondering about the motivation behind this kind of chatter.
Is someone just enjoying a flight of fancy?
Is someone banking on “discovering” a new field of mathematics and being famous for it?
Is someone trying to soothe the hurt feelings of innumerates?
Is someone laying the groundwork for dismissing sound arguments when there’s math involved?
I think the last of these is the most dangerous. When disputes cannot be settled by reason, they will be settled by force.
I don’t think many are eager to go there, actually. Certainly not Rovelli.
But the question of whether the natural numbers exist independently of our minds is very interesting. Perhaps they are simply an artifact of the way our minds function? I can barely conceive of that, tbh. However, there are challenges to Platonism which I don’t have a good response to as well.
Ever since modern science was born in medieval Christian Europe, science has had a history of looking for ‘platonic perfection’, and assuming the Mind of God to be behind that ‘platonic perfection’. That is to say, that science has a history of reaching for perfect agreement between the immaterial mathematics that might describe a certain facet of this universe and the experimental results that measure those mathematical predictions of that facet, and assuming the Mind of God to be behind any perfect mathematical description of the universe that might be found.
Copernicus, (who was heavily influenced by Platonic thinking), imagined (incorrectly) that the planets move in perfect circles (rather than ellipses). Later, Newton, for allowing God could adjust the orbits of the planets, was chastised by Leibniz, (and even Laplace) for having a “very narrow ideas about the wisdom and the power of God.”.. i.e. For having a narrow view of the perfection of God.
And indeed for most of the history of modern science in the Christian west, finding ‘platonic perfection’ for the mathematical descriptions of the universe has been a very elusive goal.
For instance Newton’s mathematical description of gravity could not take into account the precession of Mercury’s orbit. That is to say that Newton’s theory of Gravity was not a perfect mathematical description of the universe.
This all changed with the discoveries of Special Relativity, General Relativity and Quantum Mechanics.
That is to say, as far as experimental testing will allow, there is no discrepancy to be found between what the mathematical descriptions of Relativity and Quantum Mechanics predict for the universe and what our most advanced scientific testing of those predictions are able to measure.
As well, quantum electrodynamics (QED), which is a combination of special relativity and quantum mechanics, also now joins the list of perfect mathematical descriptions of the universe in which we can find no deviation from what the mathematics predict and what our best experimental testing can discern. In other words, as far as we can tell, ‘platonic perfection’ is reached for QED:
As Nima Arkani-Hamed, the discoverer of the amplituhedron, stated “It seems inconceivable that this intricate web of perfect mathematical descriptions is random or happenstance. This mystery must have an explanation.”,,,
Another very important place where ‘platonic perfection’ has now been found in the universe, (as far as our most precise testing will allow), is for the ‘flatness’ of the universe.
Moreover, as was alluded to in the preceding articles, the ‘plantonic perfection’ of a flat universe just so happens to be necessary for us to even be able to practice math and science, (and apply technology in our world), in the first place: i.e. it is necessary for the universe to ‘make sense’.
In fact, all of the constants also play into the universe ‘making sense’
Another interesting thing about the ‘platonically perfect’ flatness of the universe is that it allows us to see that the “tiny temperature variations (in the Cosmic Microwave Background Radiation(CMBR)) correspond to the largest scale structures of the observable universe.”
Moreover, in regards to the largest scale structures of the universe, Radio Astronomy now reveals a surprising rotational coincidence for Earth in relation to the quasar and radio galaxy distributions in the universe:
Moreover, there are also anomalies in the CMBR itself that ‘strangely’ line up with the earth,
Here is an excellent clip from the documentary “The Principle” that explains, in an easy to understand manner, how these ‘anomalies’ that line up with the earth and solar system were found, via ‘averaging out’, in the tiny temperature variations in the CMBR data.
In other words, the “tiny temperature variations” in the CMBR, and the large scale structures in the universe, both reveal teleology, (i.e. a goal directed purpose, a plan, a reason), that specifically included the earth and solar system from the start. ,,, The earth, from what our best science can now tell us, is not some random cosmic fluke as atheists had presupposed.
Of supplemental note:
To give us a glimpse at just how delicately balanced this solar system actually is, (so as to allow the earth to host life over long periods of time), the following article states that “As an example, shifting your pencil from one side of your desk to the other today could change the gravitational forces on Jupiter enough to shift its position from one side of the Sun to the other a billion years from now.”,,,
Might I be so bold as to suggest that Liebniz, Newton, and even LaPlace would all be very impressed by the ‘wisdom and power of God’ that has been revealed by modern cosmology?
Rovelli is correct.
No need to imagine Jovian aliens. We wouldn’t treat objects as discrete and countable if our perception was somewhat different. If we sensed electrostatic fields or acoustic signatures instead of visible light, the world would be far more continuous and less digital. To a mud-dwelling fish or a blind person, the electrostatic and acoustic auras of objects are gradual and often merged, not precise and separable.
I think Rovelli is right, and I see that polistra agrees with me: I like his examples. The counting numbers are natural, and seem inevitable, because we are the kind of being that experiences discrete objects with clear distinctions from other objects. It may very well be that the universe is fundamentally fluid, and that discrete objects are an emergent property related to the kind of being we are. In such a case, the mathematics that is truly embedded in the universe is something that is not fundamentally related to the counting numbers. As the article says about Rovelli’s views, math “works” because we crafted it for its usefulness. (Wigner said some similar things.) We are macroscopic beings, so a math based on our macroscopic experience of discrete objects is what seems “natural” to us.
I also agree with DaveS. Rovelli doesn’t “stop short of saying that 2+2=5”: what he has to say has nothing to do with the silly 2 + 2 = 5 meme, or whatever “war on math” might be being waged (which makes no sense to me). I thought the article by Falk was a pretty good description of the age-old controversy about the nature of math, and I’m glad this site pointed it out to me.
It took some time for my first post here to be allowed through moderation, although I’m assuming that now my posts will show up promptly. This is probably not an important topic here (as it seems all the main topics of discussion are political), but I’ll post this one more time to see if anyone else is interested in the post on Rovelli.
Hmmm. I see that the recent comments section of this site doesn’t work. I think I’ll write this off as a lost cause.