title: One Neuron Can Make A Difference

The brain is unlike any other organ in the body. It is unimaginably complex,
and very nonlinear in its behaviour, and in many ways is inherently unpredictabe.
If we know roughly how many Newtons of force an individual muscle fibre exerts
when it contracts, and we know how many fibres are contracting, given that they
are reasonably randomly distributed amongst the collection of fibres in a muscle,
we can reasonably infer the behaviour of that muscle in terms of how much force
it exerts. In the case of the brain there is no such luck. 

In this [blog article by Astra Bryant at neuwritewest.org](https://www.neuwritewest.org/blog/4541) we read
```quotes1
To ruthlessly simplify, treating all 86 billion neurons in the human brain as copies of that a single "typical" neuron, ignoring all of the glorious cellular specificity that characterizes the brain, we're left with a range of 86 billion to 17.2 trillion action potentials per second.
```
And that is ruthlessly simplifying. In reality *which particular action potentials* makes all the difference
in the brain's overall behaviour. Now there are likely many structures in the brain where many neurons
are summed in many ways to get the equivalent of an analogue signal which can take a range of values,
rather than the all-or-nothing situation with whether an neuron fires or not. The quantity of action
potentials, on its own, tells you nothing meaningful about what behaviours will result from those
action potentials. At its extreme, if we start with two identical brains, A and B, in identical universes,
and perturb one slightly so that a single neuron in A fires whereas in B it doesn't, and all else
is identical, that one less action potential in B may mean that other neurons fail to fire whereas
in A they did, and then that causes others to fail, and so on, that single missing action potential
can be amplified until brain B's behaviour deviates drastialy from that of brain A.

A much simpler example of how a tiny difference can be amplified is found in computer science, 
in particular cryptography, and what is know as a [crytographic hash](/csci/crypto/CryptographicHash).
In the case of a hashing algorithm like SHA256 (one standard hashing algorithm in 2025 as I write this),
if we take a 1GB file, and change a single bit, then the SHA256 hash of the modified file will be
essentially completely different than the hash of the original file. Essentially that single changed
bit sets in motion a cascade of other changed bits until eventually, after a few rounds, the entire
state of the hash computation diverges completely from what it would have done with the original file.
The brain, in a similar way, can amplify a single extra action potential, or the absence of
an action potential, into a qualitatively different overall behaviour.

This has important consequences for psychiatry, mental health, and psychology: many of the
reasonable simplifying assumptions underling an approach like 'evidence based medicine', and
determining things by testing them in 'randomised controlled trials', no longer hold when
the complexity of the brain can no longer be ignored. Many statistical methods require what
is known as a 'representative sample'. The trouble with the brain is that, even if we simplify
things drastically so that *only the configuration of the connections between the neurons matters*,
then the space of possible brain configurations is *beyond astronomical*, and so
*a representative sample of possible brain configurations will itself be astronomical, and
far greater than the number of human beings living on Earth in 2025*. Thus when brain complexity
can't be ignored, it is practically impossible to obtain a representative sample. If we
do take a sample of people, we must understand that as a 'representative sample', it is
*only representative of a small minority of people* (call this minority M) and, furthermore, it is an
*essentially intractable problem* to determine *who is in M and who is not*.

The trouble with psychological and psychiatric research is that these problems are quietly,
possibly even silently assumed away. This is akin to the desperate-student-in-an-exam
situation where they don't know how to solve a problem, get 0 marks for a wrong answer,
get 0 marks for writing nothing, and so just have a wild guess, blindly assume that
the method they're applying works, and hashing out something to put on the exam paper.
For that 'desperate student', whatever they put down is 'the best they can do',
and they 'cannot see how they could have done it differently'. What they put down
is essentially completely wrong, and the defence that 'it is the best they can do'
and 'they cannot see how to do it differently' is an empty defence. I have known
people defend the 'evidence based paradigm' in mental health using just such language:
"I don't see how we could do it any differently". *Just because it's the best you
can do doesn't mean it works.*