Getting Information: revelation
When knowledge is faithful.
The information we have about the world does not come to us by one single mechanism. We saw in Essay #23a that we can learn about the world by reason, and we can learn about the world by observation. These are irreducibly independent modes of finding things out: one cannot be explained in terms of the other. We also saw that both reason and observation are internally diverse: numerical and geometrical reasoning are distinct; visual and olfactory observation are distinct. Finally, we saw that new discoveries and developments in our understanding of how we know things can be readily rolled in to science.
Given we already accept a plurality of ways of knowing — many of which we had, until recently, never even thought of — are we certain that we have now considered all possible ways of knowing? Might there be other ways of obtaining information about the universe? There seems little reason to insist a priori that there cannot be. This Essay considers possibilities for ways of knowing beyond reason and observation.
Knowing by faith
Fortunately, we are by no means the first people to consider this. There are many well-established traditions that have well developed ideas regarding other ways of knowing. We take our first example from Christianity.
Christianity has historically held that, just as light interacts with the eye to provide information distinct from reason, so the divine interacts with the heart (or mind, or soul) to provide information distinct from both reason and observation. The position might be summarized as follows:
If there exists a God, and if that God should choose to make something known to us, then we should arguably not be surprised that such an activity would provide a basis for knowledge. We should also arguably not be surprised that such an activity might not proceed by the same mechanism as our interactions with the mundane world around us. Given the qualitatively different nature of the mechanism by which information is obtained, a new category seems warranted.
Other traditions may not adopt the terms “revelation” and “faith”, but very similar concepts are widespread: things like oracles, visions, awakenings, or divinations. In each case, the person is accessing knowledge, but the mechanism for obtaining that knowledge is rooted neither in their own rationality nor in their mundane senses.
Why, though, would Christianity call such a source of knowledge “faith”? Faith, surely has nothing to do with obtaining genuine information about the world. Just look at a dictionary:
A firm belief in something for which there is no proof.
This definition seems open and shut: if you have faith, you do not have proof. You cannot start calling that a source of information, much less the basis of knowledge. If the dictionary is talking about the same thing as Christian theologians, then the theologians are simply wrong that faith can be a basis for knowledge. That said, we have seen in previous Essays that, sometimes, we must chew carefully around simple dictionary definitions and see what else there is. Given that we are considering a Christian notion of faith, let us get it from the horse’s mouth. Here is what the bible says about faith:
“Faith is… the evidence of things not seen.” (Hebrews 11:1.)
Some might attempt to fudge this into agreement with the dictionary by interpreting the bible to mean that you have proof for things that you see, and that faith — relating to things unseen — is belief in the absence of proof: faith is what you rely on when you have no evidence. But that is not what the bible says! Faith is not what you rely on when you have no evidence; faith is the evidence!
Why should we reject a priori a source of information simply because it relates to things unseen? Considering sensory information, when we hear a door slam behind us, we have knowledge of what is happening behind us, even though it is unseen. Considering reasoned information, when we rationalise that a bachelor is unmarried, we do so even if we have never seen a bachelor. Let us draw out the similarities between the unseen evidence of reason and the unseen evidence of faith.
Reason as evidence
Consider, first, a situation in which there are nine people in a room and then one more person enters. I can — without looking — say that there are ten people in the room. (For simplicity, we will not revisit the existential concerns of Essay #17. Let us assume that people and rooms exist.)
Still, a skeptic may object, “But you did not look in the room. You did not see these ten people. What evidence do you have for your belief?”
The reply is simple: “9+1=10. Rationality says it is so. Reason is the evidence of things unseen.”
It would be very strange for anyone to reply, “So you have no evidence! You have not seen it! You have reason instead of evidence!”
That would be a ridiculous claim. You do not have reason instead of evidence. Reason is the evidence!
The mathematics going on in your mind is quite separate from anything impinging on your eyes. There is no shame in that. You do not need to reduce your reason to some special — possibly weakened — form of observation. It stands on its own.
Faith as evidence
Now, consider a situation in which God forgave me of my sin, and then revealed to me that He had done it. I can — without looking — say that my sins are forgiven. (For simplicity, we will not revisit the existential concerns of Essay #17. Let us assume that God and sins exist.)
Still, a skeptic may object, “But you have not seen — cannot see — the forgiveness of your sins. What evidence do you have for your belief?”
The reply is simple: “God told me. Revelation says it is so. Faith is the evidence of things unseen.”
It should, on this view, be very strange for anyone to reply, “So you have no evidence! You have not seen it! You have faith instead of evidence!”
That would, on this view, be a ridiculous claim. You do not have faith instead of evidence. Faith is the evidence!
The divine assurance going on in your soul is quite separate from anything impinging on your eyes. There is no shame in that. You do not need to reduce your faith to some special — possibly weakened — form of observation. It stands on its own.
This notion of faith is, admittedly, different from the view put forward in many dictionaries. It is not our concern here to consider how the modern usage came to be so far removed from earlier understandings of faith, or argue that either usage is better or worse than the other. Rather our intention here is to demonstrate that any claim that there are only two ways to obtain knowledge — reason and observation — is, at best, a radical simplification of how we apprehend the world around us. At worst, it blinkers us to a vast array of other possible ways of knowing.
Scientific and religious knowledge
For so long we have resisted the pressure to make neat demarcations between the scientific realm and the religious realm. One may imagine that here we might finally buckle. Here we finally have a clear distinction: scientific knowledge involves reason and observation; religious knowledge involves revelation.
[Do not, please, for the love of all that is good, highlight that last sentence! If you highlighted it, please go back and un-highlight it. If you are unsure why the sentence it is utterly false, please keep reading.]
Two-list-ism fails. It has failed before, and it fails again here. Firstly, it fails because obtaining religious knowledge can involve reason and observation. Secondly, it fails because obtaining scientific knowledge can involve revelation.
Reason in religion
Whatever else you think about it, biblical prophesy is, by any measure, religious talk. When God speaks through the prophet Isaiah to warn and encourage the tribe of Judah, he takes on the tone of a parent to a child:
“Come, let us reason together.” (Isaiah 1:18.)
The entire passage surrounding this verse can be roughly paraphrased as follows: “I love you, and I know what I am doing. So if you follow My lead, things will work out better for you than if you follow your own ideas. That makes sense, right? It stands to reason.” Thus, even God Himself, when speaking through His prophets (which is clearly in the realm of religion, and also clearly in the realm of revelation) invokes reason. Religion has a place for reason.
Some Christian theologians might appear to object to the claim that reason has a place in religion. Martin Luther himself (whose schema we are using) wrote that “reason in no way contributes to faith.”  In saying this, however, he is not claiming that reason does not contribute to religion. He is claiming that reason and faith are irreducibly independent ways of knowing. His claim should therefore be read in much the same ways as if he had said “reason in no way contributes to observation.” I observe that putting my finger in a flame hurts, and reason is a mute bystander in the process. Reason in no way contributes to observation. By faith it is revealed to me that God loves me, and reason is a mute bystander in the process. Reason in no way contributes to faith.
Despite such a separation, we saw in Essay #23a that reason and observation do interact with each other. A claim to have “empirically” demonstrated superconductivity is a claim that necessarily draws on reason as well as observation. In a similar vein, Luther held that reason and revelation interact with each other: “The understanding [i.e. reason], through faith, receives life from faith… so it is with human reason, which strives not against faith, when enlightened, but rather furthers and advances it.” 
Observation in religion
However much we might want God to send prophets to explain everything to us, sometimes God finds alternative ways of getting through to us. If He made it already, He sometimes sticks to the old adage, “show, don’t tell.”
“God,” we implore, “tell us your wisdom regarding farming, industry, the importance of preparation, and the turning of the seasons.”
“Go to the ant you sluggard. Observe her ways and be wise.” (Proverbs 6:6.)
We don’t have to wait for God to tell us what an ant is like. God Gave us ants. And God gave us eyeballs. And He said, “You go do the footwork.” That provides a role for observation in religion.
Reason in science
Having argued that reason and observation have a place in religion, we should now turn to consider whether revelation has a place in science. But before we do that, let us ask whether mathematics has a place in science. And if so, on what grounds? This simple case study will help us to form a framework for thinking about revelation in science.
In “The unreasonable effectiveness of mathematics” , Eugene Wigner pointed out that the fact that maths works is surprising. Mathematicians go and have all sorts of crazy ideas, and a lot of them seem to apply to the universe. It does not have to apply to the universe, and when it does apply it does not have to apply broadly. (If irrational numbers apply to anything, they do not apply to how many apples I have.) But while maths doesn’t have to work in in the universe, it seems that, a lot of the time it does.
So why do we accept it?
— Because it works.
Do we know why it works?
Do we care that we don’t know why it works?
— No. (At least, scientists don’t care. Philosophers might worry about it. But scientists don’t.)
Do theoreticians always get it right?
Do they get it right sufficiently often that it is worth keeping them around?
Experimentalists could just measure everything. They could spend vast sums of money measuring blindly. Or a theoretician could say, “I suggest you try measuring this bit here”: Try building a particle collider with a collision energy that gets up to 14 TeV. (Why 14 TeV? Why not more? or less?) Try to measure the absorption of 250 nm light in this part of the sky. (Why not 300 nm? Why not some other piece of sky? Or the ground?)
Sometimes theorists are wrong, and there is nothing interesting there at all. But sometimes they are right. And they are right often enough that we say they should be given money to keep taking part in science.
Sometimes theorists disagree with each other. They may disagree regarding specific predictions. (For example, one theory may predict a particle’s mass to be 100 GeV, while another theory predicts it to be 125 GeV). They may disagree regarding the fundamental nature of the model. (One theory assumes that space is continuous, while another requires space to be discrete). They may even disagree about the fundamental nature of mathematics itself. (If I give you an infinite number of pairs of socks, can you select one sock from each pair? It seems a silly question, but disagreements over the answer set up a problem at the heart of mathematics.) This utter lack of universal agreement among theorists is unproblematic for most practical purposes, because the important question for inclusion in scientific practice is a pragmatic one: is this branch of mathematics sufficiently helpful, sufficiently often, to keep talking to people who work on it?
Some may argue that the requirement of universality in science should see mathematics excluded from science: not everyone can do maths. Some people cannot do maths for fundamental reasons—like those with acalculia. Some people cannot do maths for practical reasons — like those who have never sat down to work at it. But, on reflection, it would be odd to exclude higher calculus from scientific research simply because only some can master it, and even then only after years of training.
Consider a theorist saying to an experimentalist, “This integral tells me that you need to tune your laser to 422 nm.” Does the experimentalist say, “Science can only be universal and tracable if all people can understand all steps. I do not understand how you got that answer. So I must ignore you”? Not at all. They say, “Thank you very much.” And then they tune their laser to 422 nm. And doing so does not make them a bad scientist.
Revelation in science (Example I)
George Washington Carver, each morning, would go into the woods and pray. And he would ask God what He wanted him to do that day. And he would listen, and (so he claimed) God would speak. God would tell him to crush a peanut. Or to plant a particular type of plant in a particular place, with a particular type of soil and a particular shading. And Carver would go and do it.
Not all of his experiments worked. But they worked sufficiently often that he became famous for doing all sorts of interesting things with peanuts, and plants, and botany.
Carver explained his method like this:
“A person is at liberty to experiment with anything that he can… Our eyes and ears are always open. We must be patient and wait…” 
Thus far, he sounds like a scientist: experiment, observation; looking, listening. But he continues,
“… as were the old prophets. Isaiah and the old prophets always had their eyes and ears open. You know, Isaiah, listening, heard a voice.
“God speaks to you through the things He has created. That’s what He was doing while I was developing all these things from the peanut. He was telling me I could do what I have done. I was interpreting for the Lord.” 
Carver may have been a botanist, but understood himself as standing in the position of a prophet. He obtained information from God, and interpreted it for the world. And this inspired the science experiments he was doing.
One can consider the part involving empirical verification of particular ideas, and say that this is science. This is traceable. This is demonstrable. Anyone with eyes can see that the peanuts grow better in this soil than that soil.
And then one could consider the part by which Carver came to those ideas, and insist that this part should not be called science. We do not know where the ideas came from. We do not understand the mechanism by which they were created, or why they relate to the empirical world. The process is not transparent or tracable. This cannot (so the argument goes) be considered part of science.
But if we did that, we would have to ask what to do with mathematics. From where do mathematicians get their ideas? And why should their ideas have any relation to the empirical world? Their process is — for reasons variously practical and fundamental — neither universally transparent nor tracable. Can maths be considered part of science?
We desperately want to salvage from such criticism the tremendously useful insights provided by mathematics. We salvage mathematics by not immediately accepting what the theorist says. (We cannot bang the table and insist, “The theorist says it, I believe it, that settles it.”) Rather, we take what the theorist says, look at ways to test it empirically, and see if it works. Admittedly, as noted in Essay #6, we can never entirely disentangle such tests from an a priori acceptance of the theoretical conclusion. And we accept that limitation. Moreover, if it is not empirically supported, we cannot a priori say that the fault is with the theory, rather than with the experimental test. Still, when what the theorist says and what the experimentalist observes kind of line up, we say we have an answer, and it looks like we are doing science. And if the collaboration works often enough to be useful, we keep the theorist around, and even call them a scientist.
If, on such grounds, we can salvage the tremendously useful insights of mathematics as being part of science, there is an argument for doing the same with revelation. We do not bang on the table and insist “The prophet says it, I believe it, that settles it.” But we can take what the prophet says seriously, and take it as a provocation to experimental and / or theoretical activity. And if revelation, theory, and experiment do not all give the same answers, we can argue about it until we feel like we have a handle on things. And that looks a lot like science. And if the collaboration works often enough to be useful, can we not keep the prophet around, and even call them a scientist?
Revelation in science (Example II)
Christianity does not have a monopoly on this way of doing science.
Srinivasa Ramanujan was a self-taught mathematician that worked with G.H. Hardy in Cambridge. He came up with fantastical mathematical conjectures; conjectures that he himself could not prove. Some of them turned out to be wrong. Some turned out to be right. Some turned out to be wrong, but prompted really interesting research in the course of either showing them to be wrong, or modifying them to make them right.
When asked where his ideas came, he stated that he was told them in his sleep by his family goddess, Namagiri (a form of the Hindu goddess Lakshmi):
“While asleep I had an unusual experience. There was a red screen formed by flowing blood as it were. I was observing it. Suddenly a hand began to write on the screen. I became all attention. That hand wrote a number of results in elliptic integrals. They stuck to my mind. As soon as I woke up, I committed them to writing.” 
“An equation has no meaning for me unless it expresses a thought of God.” 
Hardy was not convinced that Ramanujan was genuinely receiving divine revelation from Namagiri, though he was also unable to offer any other account of where Ramanujan’s ideas came from. Still, neither the untracability of the inspiration, nor its putatively divine origin, were considered reasons to exclude Ramanujan’s conjectures from academic mathematical discourse. Rather, they were included in academic mathematical discourse because they were interesting.
Parallels, parallels everywhere
In considering the role of mathematics in science, we do not have a clear handle on why it works to provide information about the physical world. So, too, with revelation. It may not be absurd to accept it as part of science, even if we do not agree about or understand the mechanism by which it works.
In considering the role of mathematics in science, theorists save exprimentalists time by suggesting key parameter ranges to focus on, or to ignore. Try tuning your laser to this wavelength. So, to, with revelation. Try planting your peanut here.
In considering the role of mathematics in science, the theory does not need to be always right in order to be useful to science. So, too, could revelation, even if fallible, be useful to science provided it is right (or interestingly wrong) sufficiently often?
In considering the role of mathematics in science, we freely admit that different branches of mathematics can be wildly divergent, to the point of being contradictory. So, too, we must freely admit that different branches of religion can be wildly divergent, to the point of being contradictory. Evaluated against the pragmatic measure used by science, as long as the oracles from any particular religion are sufficiently helpful, sufficiently often, we may well be justified in keeping on talking to them.
In considering the role of mathematics in science, we accept that not everyone is able to do maths. And we accept that those who can do maths may need training to raise their abilities to level which offers any significant or reliable insight. This is a key task of the university. So, too, with revelation. It may be that not everyone can hear God’s voice. And those who can may need to practice or be taught to hone their sensitivity to it, before they can offer significant or reliable insights. Could universities, perhaps, be provided funding for such?
This list of parallels is no-where near exhaustive. Still, we hope that it provides an indication of why revelation can, and arguably should, have an appropriate place in scientific practice.
To be sure, this is not how science is generally practiced. We do not train people as oracles, or have lectures in visionary physics. But it is not without precedent. In any event, following the considerations of this essay, we seem to be faced with three options:
1) Be consistent and accept both theorists and oracles within scientific practice;
2) Be consistent and exclude both theorists and oracles from scientific practice;
3) Embrace special pleading and accept theorists while excluding oracles.
Being inclined to avoid arbitrary inconsistency in scientific practice, we are loathe to endorse Option #3.
Being timid souls, averse to making overly radical suggestions, we do not wish to exclude mathematics from scientific practice, so Option #2 is off the table.
After that, we must follow where the logic of science leads us.
 Luther, Martin (1566, 1955). Table Talk. Translated by William Hazlitt. Philadelphia: The Lutheran Publication Society. §CCCLIII.
 Luther, Martin (1566, 1955). Table Talk. Translated by William Hazlitt. Philadelphia: The Lutheran Publication Society. §CCXCIV
 Wigner, Eugene (1960). “The Unreasonable Effectiveness of Mathematics.” Communications on Pure and Applied Mathematics. 13, pp. 1–14.
 Carver, George Washington (1942). “Address to Martha-Mary Chapel” Austin Curtis Papers. Michigan Historical Collections, Bentley Historical Library, University of Michigan. Cited in Burchard, Peter Duncan (2005). George Washington Carver: For His Time and Ours. National Park Service: United States Department of the Interior.
 Kanigel, Robert (2016). The Man Who Knew Infinity: A Life of the Genius Ramanujan. Washington Square Press.
 Ramanujan, Srinivasa, quoted by Shiyali Ramamrita Ranganathan (1967) in Ramanujan, the Man and the Mathematician.