What We Cannot Know: Explorations at the Edge of Knowledge

by Marcus du Sautoy

‘If you pursue that to its end you just end up with solipsism.’

solipsism

If consciousness is about integration of information across a network, then that applies from things as small as an amoeba to the consciousness of the whole universe.

Hmm how big des it get

Since we are finding it difficult to access each other’s consciousnesses while we are alive, to investigate consciousness after someone’s death appears an impossible challenge.

Life after death logic

Consciousness does emerge from a developing brain when some critical threshold is hit – like the moment when water begins to bubble and boil and turn into a gas.

Threshold

Some argue that nothing physical is ever going to answer the problem of what it feels like to be me, that the very existence of consciousness implies something that transcends our physical realm. But if mind can move matter, then surely there must be a physics which connects these two realms and allows science back into the game.

Interesting

Wittgenstein challenges whether the same principle can apply to naming ‘pain’. Pain does not involve an object that is external to us, or that we can point at and call pain. We may be able to find a correlation between an output on an fMRI scanner that always corresponds to my feeling of pain. But when we point at the screen and say that is pain, is that what we really mean by ‘pain’?

Wittgenstein

We can get at the problem of identifying what is going on inside our heads by imagining that we each have a box with something inside. We all name the thing inside ‘a beetle’, but we aren’t allowed to look in anyone else’s box, only our own. So it is quite possible that everyone has something different in the box, or that the thing inside is constantly changing, or even that there is nothing in the box. And yet we all call it ‘a beetle’.

Good take

If there is no way to distinguish the unconscious zombie from the conscious human, what point is there having a word to describe this difference? Only when you can know there is difference is there any point having a word to describe it.

Wittgenstein

Dennett cites vitalism to support his stance. Vitalism suffered such a fate: we’ve given up on the idea that there is some extra special ingredient, an élan vital, that breathes life into this collection of cells. If you show me a collection of cells that have the ability to replicate themselves, that miaows and purrs like a cat, and then declare that it isn’t actually alive, it would be very difficult to convince me. Some believe that arguments over consciousness will go the same way as those over vitalism.

Vitalism

Natural language is prone to throw up paradoxical statements. Just putting words together doesn’t mean they make sense or have a truth value.

so true

The distinguished physiologist Emil du Bois-Reymond had addressed the Berlin Academy in 1880, outlining what he regarded as seven riddles about nature that he believed were beyond knowledge, declaring them ‘ignoramus et ignorabimus’. Things we do not know and will never know. In the light of my attempt to understand what questions may be beyond knowledge, it is interesting to compare my list with the seven riddles presented by du Bois-Reymond:

ignoramus et ignorabimus 1. The ultimate nature of matter and force 2. The origin of motion 3. The origin of life 4. The apparent teleological arrangements of nature 5. The origins of simple sensations 6. The origins of intelligent thought and language 7. The question of free will.

For the mathematician there is no Ignorabimus, and, in my opinion, not at all for natural science either … The true reason why no one has succeeded in finding an unsolvable problem is, in my opinion, that there is no unsolvable problem. In contrast to the foolish Ignorabimus, our credo avers: Wir müssen wissen. Wir werden wissen. [We must know. We shall know.]

Hilbert

Cantor wanted to know whether there are sets of numbers which are bigger in size than whole numbers but small enough that they can’t be paired with all infinite decimal expansions. In other words, can there be a tribe whose members are numbered with a set of numbers that beats the whole-number tribe but is outdone by the tribe with all infinite decimal numbers? The name given to the infinity of all infinite decimal numbers is the continuum. The continuum hypothesis posited that there was no infinity smaller than the continuum but larger than the infinity of all whole numbers.

cantor. continuum

Suppose a scientist cooks up a perfectly consistent logical theory of how the universe might work, but then discovers that it doesn’t match the experimental evidence of our own universe. The hypothetical theory is booted out and is no longer of interest to the world of science. If a biologist starts writing papers about a hypothetical beast that potentially could exist, like a unicorn, but doesn’t actually walk this Earth, no one is going to be interested unless it casts some light on the animals that do exist. By contrast, in mathematics such new worlds and beasts are celebrated and embraced. They become part of a richer tapestry of mathematical possibilities. Science does the actual, mathematics does the possible. Science charts a single pathway through a tree of possible universes, mathematics maps every possible journey.

possibility

quantum physics currently posits a limit to how far we will be able to penetrate in our investigation of what’s inside my dice: that beyond the Planck length, it’s simply no-go. There is an edge beyond which we cannot know.

planck length. no-go.

Even the mathematics created to understand my dice is something of a fantasy. What is probability? If I throw my dice 600 times, I expect to get 100 6s. But I just want to throw it once and know something about how it will fall. The equations of chaos theory tell us that so much of the future is dependent on extremely fine-tuning of the decimal places that control the input of the equations. So I can never know the present completely enough to have any chance of knowing the future or the past.

main. dice. next roll?

The limitations of language are at the heart of many of the limits of knowledge, and these could possibly evolve and change. Certainly, many philosophers identify language as a problem when it comes to the question of consciousness. Understanding quantum physics is such a problem because the only language that helps us navigate the ideas is mathematics. Try to translate the mathematics into the language of everyday experience and we create the absurdities that make quantum physics so challenging. So the unknowability of position and momentum isn’t really a genuine unknowable. Rather, it is a failure of translation from mathematics to natural language.

language

I wonder, though, whether, as I come to the end of my exploration at the limits of knowledge, I have changed my mind about declaring myself an atheist. With my definition of a God as the existence of things we cannot know, to declare myself an atheist would mean that I believe there is nothing we cannot know. I don’t believe that anymore. In some sense I think I have proved that this God does exist. It’s now about exploring what quality this God has.

God

Two thousand years ago Socrates declared: ‘True knowledge exists in knowing you know nothing.’ An acknowledgement of your ignorance is the only true statement of knowledge.

Knowledge

Gödel’s incompleteness theorem.

Let p be the true statement among the two options: ‘there are an even number of dice in my house’ and ‘there are an odd number of dice in my house’. I don’t know which one is true, but one of them must be. The existence of an unknowable truth is squeezed out of the existence of this unknown truth. The following statement is an unknowable truth: ‘p is true but unknown’. It is certainly true. Why is this unknowable? Because to know this means I know that p is true and unknown, but that’s a contradiction because p can’t be unknown and known simultaneously.

So true

The only way out of this is if I already know it all. The only way that all truths are knowable is if all truths are known.

Wittgenstein summed this up colourfully: ‘You cannot shit higher than your arse.’

Lol

in addition to sight, hearing, taste, touch and smell, we also have a sense called proprioception that gives us an awareness of how our body is located in space. There are also senses that give us information about the inner state of our body. The fluid in the inner ear tells us how our body’s position is changing in relation to gravity. But are there physical phenomena that we miss because we don’t have the sensory tools to interact with them?

Senses

Kant believed that the ways things really are will always remain hidden from our view. All we can ever know is the appearance of things.

Interesting

I think most scientists spend some time reading about this debate concerning ontology and epistemology, and listening to philosophers who question whether science is really telling us how it is. And then they get back to the science, telling themselves that if we can never know what reality is really like, then let us at least try to say what the reality that we apprehend through our senses is like. After all, that is the one that impacts on us.

Main. Very true

perhaps the best we can hope is that science gives us verisimilitudinous knowledge of the universe; that is, it gives us a narrative that appears to describe reality. We believe that a theory that makes our experience of the world intelligible is one that is close to the true nature of the world,

Closest

As Niels Bohr said: ‘It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.’

Although we are physical systems, no amount of data will help us to completely predict human behaviour. The humanities are the best language we have for understanding as much as we can about what it is to be human.

What we cannot know creates the space for myth, for stories, for imagination, as much as for science. We may not know, but that doesn’t stop us creating stories to fill the unknown, and these stories are crucial in providing the material for what one day might be known. Without stories, we wouldn’t have any science at all.

Story. Main

Wittgenstein concluded his Tractatus Logico-Philosophicus with the famous line: ‘Whereof one cannot speak, thereof one must be silent.’ I think that is defeatist, as did Wittgenstein in later life. A better denouement would be: ‘Whereof we cannot know, there our imaginations can play.’ After all, it’s by telling stories that we began our journey to know what we know.