ONE BOOK / 25 CONNECTED PARTS

From neurons to intelligent machines.

An illustrated journey through neuroscience, connectomics, spiking networks and embodied AI

Edition 0.2 · Evolving illustrated edition · Updated 2026-10-16

25illustrated introductions
102chapter outlines
28reading sources
16project briefs

Inside this edition

All 25 parts include an illustrated introductory lesson, a worked mathematical example and executable teaching code. The 102-chapter depth map is retained for expansion; it is not yet 102 fully developed chapters. Examples are synthetic unless explicitly stated otherwise. No new biological experiment, flight test or benchmark result is claimed.

The explanations, examples and schematic illustrations connect established ideas for learning. Original research remains credited to its authors in the reading sources. Work through the opening lessons before selecting a deeper chapter to expand.

THE CONTENTS

From the first ion to the next question.

Every part opens with a lesson, an illustrated model, an equation, a worked example and a Python experiment. The chapter outlines map the depth still to come.

25 parts

STUDY COMPANION

Learn in layers. Keep the evidence.

Start with foundations. Read each part's prerequisites; the research and project parts can be companions throughout your study.

Prerequisite map for all 25 parts
6 study roadmaps
30 days

Build the foundation

Parts I–II, with the first exercises from Part XXIV.

  1. Week 1: units, charge, voltage, current and a neuron sketch.
  2. Week 2: resistance, capacitance, functions and exponential relaxation.
  3. Week 3: derivatives, RC equations and a hand-calculated Euler step.
  4. Week 4: a tested subthreshold simulation, a short explanation and a prerequisite review.

Evidence: Explain every unit in the RC equation and show that timestep refinement approaches the analytic solution.

3 months

From cells to executable models

Parts III–IV and VI; begin VII after the prerequisite checks.

  1. Develop probability, vectors and graph representations alongside circuits.
  2. Build the single-neuron and 100-neuron projects.
  3. Compare rate and timing measurements on synthetic stimuli.
  4. Read one paper using a problem/method/evidence/limitations worksheet.

Evidence: A reproducible simulator with reset/refractory tests, plots and a model-limitations note.

6 months

Vision and connectome literacy

Parts V, VII–IX and XI; treat X as a source audit.

  1. Trace a documented visual pathway without inventing missing edges.
  2. Build motion, looming and event-stream experiments.
  3. Query a versioned small subgraph and retain provenance.
  4. Compare each model against a simple conventional baseline.

Evidence: A graph-to-model notebook and a negative-control experiment that the detector correctly rejects.

1 year

Close the loop in simulation

Parts XII–XVII; revisit Part I whenever mathematics becomes a gap.

  1. Build a simulated rover before a drone interface.
  2. Measure full-loop latency and sensor-dropout behavior.
  3. Add a learned policy only after a stable control baseline.
  4. Evaluate whether spiking computation improves the chosen task.

Evidence: A multi-seed benchmark with bounded controls, failures, ablations and compute accounting.

2 years

Develop an independent research question

Parts XVIII–XXV, returning to earlier implementation details.

  1. Reproduce a published result at feasible scale.
  2. Identify a concrete limitation and competing explanations.
  3. Design and preregister a controlled hypothesis test.
  4. Write a research report with code, data provenance and negative findings.

Evidence: An independently rerunnable experiment and a defensible contribution; publication is not guaranteed.

5 years

Build a durable research direction

Choose a specialization, maintain mathematical and experimental foundations.

  1. Select a recurring problem such as efficient sensorimotor learning.
  2. Build collaborations across neuroscience, learning and control.
  3. Re-evaluate tools and hardware against evidence rather than novelty.
  4. Maintain a portfolio of replicated results, tested ideas and documented failures.

Evidence: A coherent research program with external feedback; no promise about which technology will dominate.

Your mastery notebook

Record separate evidence for theory, mathematics, implementation and paper reading. Reading a page is not proof of mastery. The worksheet begins unassessed; keep and update your own copy.

Download the 102-chapter worksheet (.csv)
The teaching sequence for deeper chapters
  1. Beginner explanation
  2. Intuitive analogy and its limits
  3. Scientific terminology
  4. Architecture or circuit diagram
  5. Biological interpretation
  6. Mathematical intuition and equation
  7. Every symbol and unit
  8. Worked numerical example
  9. Executable Python example
  10. Code walkthrough
  11. Visualization where useful
  12. AI/ML connection
  13. Robotics connection
  14. Real-world applications
  15. Limitations
  16. Current research questions
  17. Exercises
  18. Mini-project
  19. Conceptual assessment
  20. Research extension questions

THE CONCEPT TOOLKIT

Build your vocabulary.

20 mathematical concepts
  1. Units and dimensional analysis

    Check that both sides of an equation describe the same kind of quantity.

  2. Functions and graphs

    Relate an input to an output before introducing more complex models.

  3. Derivatives

    Describe an instantaneous rate of change, such as voltage change per second.

  4. Integrals

    Accumulate a changing signal over time, such as current contributing charge.

  5. Differential equations

    Specify how a state evolves and which initial conditions it needs.

  6. Exponentials and time constants

    Describe relaxation and compare fast and slow processes.

  7. Numerical integration

    Approximate continuous dynamics and test error as the timestep changes.

  8. Vectors and norms

    Represent multi-dimensional state and define distances with explicit meaning.

  9. Matrices and linear transformations

    Describe connectivity and coordinate changes while tracking dimensions.

  10. Eigenvalues and eigenvectors

    Identify modes of linear dynamics; interpret stability within model assumptions.

  11. Probability distributions

    Represent variable outcomes rather than treating noise as an exception.

  12. Conditional probability and Bayes rule

    Update uncertainty when evidence is observed.

  13. Expectation, variance and covariance

    Summarize average behavior, spread and co-variation.

  14. Estimation and confidence intervals

    Distinguish a sample estimate from the population quantity of interest.

  15. Hypothesis tests and effect sizes

    Assess evidence while reporting how large a measured difference is.

  16. Gradients and optimization

    Adjust parameters according to a stated objective and constraints.

  17. Graph theory and sparse algebra

    Represent interactions and avoid storing absent connections unnecessarily.

  18. Dynamical systems and stability

    Reason about equilibria, trajectories, perturbations and feedback.

  19. Sampling and signal processing

    Understand what temporal measurements preserve and what they alias.

  20. Entropy and mutual information

    Quantify uncertainty and statistical dependence under a chosen probability model.

20 neuroscience concepts
  1. Neuronal compartments

    Dendrites, soma and axon organize communication; one scalar state is an abstraction.

  2. Membranes and ions

    Membranes separate ionic environments and support electrical gradients.

  3. Electrochemical gradients

    Electrical and concentration differences jointly influence ion movement.

  4. Membrane potential

    Voltage is a difference across a membrane, measured relative to a reference.

  5. Ion channels and conductance

    Selective channels change which currents can flow and when.

  6. Action potentials

    A regenerative voltage event; its timing and context matter to interpretation.

  7. Refractory periods

    Recent activity can limit or alter responsiveness to the next input.

  8. Synaptic transmission

    Cells interact through chemical or electrical mechanisms.

  9. Excitation and inhibition

    Effects depend on receptor, reversal potential, current state and circuit context.

  10. Neuromodulation

    Signals can alter responsiveness and plasticity over different timescales.

  11. Synaptic plasticity

    Synaptic properties can change through activity and other mechanisms.

  12. Hebbian learning and STDP

    Families of activity-dependent learning ideas, not one universal learning law.

  13. Homeostasis

    Regulatory processes can help keep neural activity within workable ranges.

  14. Rate coding

    Analyze information represented in spike counts over a defined window.

  15. Temporal and population coding

    Analyze information across spike times and groups of cells.

  16. Recurrent circuits

    Feedback connections allow history and state to shape future responses.

  17. Sensory transduction

    Physical signals become changes in cellular activity.

  18. Sensorimotor loops

    Actions change the sensory evidence available to the organism.

  19. Connectome and cell type

    Wiring and annotations constrain hypotheses without specifying all function.

  20. Measurement and causal intervention

    Recording correlations and perturbing a circuit answer different questions.

20 AI and computational concepts
  1. Algorithms and complexity

    State the computational work and memory required as a problem grows.

  2. State and representation

    Choose what information the system retains and what it discards.

  3. Supervised learning

    Fit an input-output mapping using labeled examples and held-out evaluation.

  4. Losses and regularization

    Specify the learning objective and constraints rather than relying on a model name.

  5. Gradient descent and autodiff

    Compute and use parameter sensitivities while checking numerical behavior.

  6. CNNs

    Use spatially shared operations for structured inputs such as images.

  7. RNNs and temporal state

    Carry information between time steps and reason about credit assignment.

  8. Transformers and attention

    Learn interactions among sequence elements with explicit context and compute costs.

  9. Spiking neural networks

    Combine event outputs with evolving internal state and chosen neuron dynamics.

  10. Encoding and decoding

    Define the interfaces between physical measurements, neural states and actions.

  11. BPTT and surrogate gradients

    Train time-dependent models while recognizing approximations at discontinuities.

  12. Sparse and event-driven computation

    Exploit inactivity when indexing and communication overhead permit.

  13. MDPs and reinforcement learning

    Learn sequential behavior under a specified state, action and reward model.

  14. Policies and value functions

    Separate action selection from prediction of future return.

  15. State estimation and control

    Infer uncertain state and use feedback to regulate behavior.

  16. World models

    Predict environment dynamics and test whether predictions support better decisions.

  17. Retrieval and memory

    Manage stored information, provenance, updating and recall.

  18. Agent architectures

    Organize tools, plans and feedback with explicit authority and failure handling.

  19. Generalization and distribution shift

    Test behavior when inputs or environments differ from training.

  20. Ablations and reproducibility

    Identify which component matters using controlled, repeatable comparisons.

PUT IDEAS TO WORK

The project ladder.

Project briefs for your own experiments. Begin with synthetic data and simulation; these are not claims of completed research.

1. Single LIF neuron

Implement the membrane update, threshold, reset and refractory interval.

Prerequisites: Foundations: matter, mathematics & computation; Computational neuroscience

Data: Constant-current synthetic input

Evidence and tests: Analytic subthreshold voltage and timestep-convergence tests.

2. 100-neuron SNN

Add recurrent sparse connections and inspect raster activity.

Prerequisites: Spiking neural networks

Data: Seeded synthetic spike trains

Evidence and tests: Reproducible spikes, delay tests and a dense reference implementation.

3. Motion detector

Distinguish leftward and rightward synthetic motion.

Prerequisites: Biological vision

Data: Moving bars with known speed

Evidence and tests: Reverse direction; sweep contrast and speed; compare a frame-difference baseline.

4. Looming detector

Separate expansion from translation and brightness changes.

Prerequisites: Biological vision

Data: Synthetic disks with controlled approach

Evidence and tests: Report true/false alarms across held-out motion regimes.

5. Camera to SNN

Encode a prerecorded frame sequence and decode a task signal.

Prerequisites: Spiking neural networks; Biological vision

Data: Consented or synthetic recorded frames

Evidence and tests: Compare end-to-end latency and accuracy with a simple non-spiking detector.

6. Event camera to SNN

Process synthetic events first; evaluate real data only with known provenance.

Prerequisites: Event-based vision

Data: Synthetic event tuples, then a licensed event dataset

Evidence and tests: Timestamp ordering, polarity tests, event loss and frame-baseline comparison.

7. Fly-inspired collision avoidance

Couple a looming detector to a bounded controller in simulation.

Prerequisites: Biological vision; Robotics: estimation, planning & control

Data: Simulated approach scenarios

Evidence and tests: Measure collision rate, false braking and recovery over randomized scenes.

8. Connectome graph explorer

Query and visualize a versioned small subgraph.

Prerequisites: Connectome programming

Data: Approved public connectome subset

Evidence and tests: Check edge direction, ID mapping, counts and reconstruction provenance.

9. Drosophila subcircuit simulation

Assign explicit dynamics to a documented biological subgraph.

Prerequisites: Connectome programming; Drosophila: anatomy, circuits & datasets

Data: Versioned subset plus cited physiological assumptions

Evidence and tests: Sweep missing parameters; compare rewired controls; do not claim full biological fidelity.

10. SNN-controlled simulated rover

Decode activity into bounded rover commands.

Prerequisites: Robotics: estimation, planning & control; Spiking neural networks

Data: Synthetic navigation environments

Evidence and tests: Compare PID/reactive baselines, delay tolerance and held-out layouts.

11. SNN-controlled simulated drone

Keep flight stabilization in the autopilot and test high-level reflex commands.

Prerequisites: Drones: simulation before flight

Data: SITL scenarios with scripted disturbances

Evidence and tests: Test timeouts, command limits and fallback; no hardware-flight claim.

12. Hybrid YOLO + SNN robot

Combine a conventional detector with a separate fast reflex in simulation.

Prerequisites: Hybrid Physical AI

Data: Licensed/synthetic labeled scenes

Evidence and tests: Ablate each layer and compare benefit against integration cost.

13. SNN + reinforcement learning

Train a spiking policy on a bounded simulated task.

Prerequisites: Reinforcement learning + SNNs

Data: Versioned environment and independent evaluation seeds

Evidence and tests: Compare parameter-matched non-spiking policies and equal training budgets.

14. Neuromorphic deployment study

Map a validated small model to an accessible platform or its documented emulator.

Prerequisites: Neuromorphic computing

Data: Same input traces as the software baseline

Evidence and tests: Measure quantization drift and full-system cost; hardware results pending access.

15. Connectome-derived Physical AI architecture

Test whether a biological topology improves a clearly defined capability.

Prerequisites: Hybrid Physical AI; World models & prediction; Connectome programming

Data: Versioned connectivity and a bounded task suite

Evidence and tests: Use degree-matched rewiring, learned topology and equal-budget baselines.

16. Original research project

Form a falsifiable question and produce a reproducible research submission.

Prerequisites: Research training & scientific practice; Frontier questions & experiment design

Data: Documented public or synthetic data with appropriate permissions

Evidence and tests: Predefine outcomes, report uncertainty and failures; publication remains an external decision.

READ, QUESTION, REPRODUCE

The reading ladder.

  1. AFTER Parts I–II / Author-hosted textbook

    Neuronal Dynamics — Gerstner, Kistler, Naud & Paninski (2014) ↗

    Start with a passive membrane model. List the units, assumptions and variables before reproducing one trace.

  2. AFTER Part VI / Primary paper

    Hodgkin & Huxley (1952): membrane-current model ↗

    Explain what a conductance model adds beyond LIF. Identify which quantities came from measurement and which were fitted.

  3. AFTER Parts V and VIII / Primary paper

    Maisak et al. (2013): a directional tuning map ↗

    Draw the experimental question and contrast ON versus OFF motion responses. Do not infer a complete control circuit from tuning alone.

  4. AFTER Part VIII / Primary paper

    Klapoetke et al. (2017): radial motion opponency ↗

    Sketch the stimulus controls. Explain why an expansion-selective response needs more than generic motion sensitivity.

  5. AFTER Part IV / Primary paper

    Dorkenwald et al. (2024): neuronal wiring diagram of an adult brain ↗

    Inspect reconstruction scope, proofreading and data availability. Write a list of information a connectome still lacks.

  6. AFTER Part IV and graph mathematics / Primary paper

    Lin et al. (2024): network statistics of the fly connectome ↗

    Choose one network statistic. Explain its null model and how filtering may change its interpretation.

  7. AFTER Parts VI and XI / Primary paper

    Shiu et al. (2024): a Drosophila computational brain model ↗

    Draw a boundary between measured connectivity, modeled dynamics and validated predictions. Propose a sensitivity analysis.

  8. AFTER Part VII and gradients / Research tutorial / author manuscript

    Neftci, Mostafa & Zenke (2019): surrogate gradient learning ↗

    Write the forward spike function and the backward approximation separately. Identify a failure mode for gradient-based learning.

  9. AFTER Part IX / Author manuscript / survey

    Gallego et al.: Event-based Vision, A Survey ↗

    Use this survey as a map to primary experiments. Compare one event representation with a frame-based baseline.

  10. AFTER Matrices and optimization in Part I / Primary paper / author manuscript

    Vaswani et al. (2017): Attention Is All You Need ↗

    Track tensor shapes through one attention operation. Explain why this alone does not supply an embodied agent.

  11. AFTER Part XVI / Primary paper / preprint

    Schulman et al. (2017): Proximal Policy Optimization Algorithms ↗

    Explain the objective, clipping and evaluation budget. Design a baseline that receives the same environment interactions.

  12. AFTER Part XVIII / Primary research / versioned manuscript

    Hafner et al.: Mastering Diverse Domains through World Models ↗

    Track observations, latent dynamics, imagined trajectories and action learning. Name a way model error could mislead planning.

Separate results from possibilities.

Established knowledge

Electrical quantities and experimentally supported cellular mechanisms within their stated scope.

Engineering practice

Explicit sensor encoders, numerical simulators, bounded decoders and feedback controllers.

Active research

Methods for learning and scaling temporal spiking systems; results remain task- and setup-dependent.

Promising hypothesis

A biological wiring prior might improve sample efficiency on a specified task. Test it against matched controls.

Speculation

Combining multiple brain-inspired modules might contribute to broad future intelligence. This is not an established route to AGI.

Unsupported claim

Copying a connectome automatically creates intelligence or consciousness. A wiring diagram alone does not establish this.

Durable foundations

  • Dimensional reasoning and mathematical derivation
  • Algorithms, data structures and computational complexity
  • Probability, statistics and uncertainty
  • Neuroscience mechanisms and careful measurement
  • Learning theory and generalization
  • Dynamical systems and numerical methods
  • Information theory and signal processing
  • Feedback control and state estimation
  • Computer architecture and resource accounting
  • Robotics and sensorimotor reasoning
  • Experimental design, baselines and replication
  • Clear scientific writing and honest limitations

Recheck as the field changes

  • Dataset versions, annotation schemas and API access
  • SNN libraries and accelerator toolchains
  • Camera models and neuromorphic hardware availability
  • Model families, robotics middleware and simulation interfaces
  • Commercial services, benchmark conventions and deployment costs

SOURCE REGISTER

Go back to the original work.

These sources support further study. The book's explanations and synthetic examples are original educational synthesis, not reproduced papers. Research findings belong to their cited authors.

Neuronal Dynamics — Gerstner, Kistler, Naud & Paninski (2014)

Author-hosted textbook

Use for neuron-model prerequisites and notation; this site provides an original curriculum, not a reproduction of the textbook.

Read the original source ↗
Hodgkin & Huxley (1952): membrane-current model

Primary paper

A mechanistic modeling milestone. Read after RC circuits and differential equations; distinguish squid-axon measurements from universal neuron parameters.

Read the original source ↗
Maisak et al. (2013): a directional tuning map

Primary paper

Experimental work on direction-selective T4/T5 populations and ON/OFF motion. Ask how tuning was measured and what the measurements do not establish.

Read the original source ↗
Klapoetke et al. (2017): radial motion opponency

Primary paper

A study of LPLC2 looming selectivity. Compare outward expansion with translation, contraction, and brightness controls.

Read the original source ↗
FlyWire — official project and dataset resources

Official dataset resource

An adult female fly brain resource. Record the exact release and annotation version; a brain dataset should not be described as a complete brain-and-body model.

Read the original source ↗
Dorkenwald et al. (2024): neuronal wiring diagram of an adult brain

Primary paper

Start with reconstruction, proofreading, scope, and data availability. Structural completeness does not supply every physiological parameter.

Read the original source ↗
Lin et al. (2024): network statistics of the fly connectome

Primary paper

Study motif and network analysis with attention to filtering and null-model choices. Graph centrality is not automatically causal importance.

Read the original source ↗
Shiu et al. (2024): a Drosophila computational brain model

Primary paper

A connectome-based computational model of sensorimotor processing. Separate experimentally tested predictions from the model assumptions and untested behaviors.

Read the original source ↗
MaleCNS — official release and downloads

Official dataset resource

The official download page exposes versioned data, including v1.0 resources. Keep specimen, release, filtering and annotation provenance with every derived graph.

Read the original source ↗
neuPrint — official connectome explorer

Official dataset tool

Inspect dataset availability and access requirements before writing queries. Do not silently combine IDs from different datasets.

Read the original source ↗
Neftci, Mostafa & Zenke (2019): surrogate gradient learning

Research tutorial / author manuscript

Read after gradients, temporal state and LIF. Identify which derivative is replaced and why the resulting learning rule is an approximation.

Read the original source ↗
Gallego et al.: Event-based Vision, A Survey

Author manuscript / survey

A field map for sensing, representations and algorithms. Follow its cited primary experiments before asserting an application advantage.

Read the original source ↗
Vaswani et al. (2017): Attention Is All You Need

Primary paper / author manuscript

Read after matrix multiplication and optimization. Reconstruct query-key-value shapes and distinguish sequence modeling from embodied control.

Read the original source ↗
Schulman et al. (2017): Proximal Policy Optimization Algorithms

Primary paper / preprint

Read after policy gradients. Explain the clipped objective and assess results under matched environment and training budgets.

Read the original source ↗
Hafner et al.: Mastering Diverse Domains through World Models

Primary research / versioned manuscript

Read after latent dynamics and actor-critic learning. Evaluate imagined rollouts, model errors, and the scope of reported task results.

Read the original source ↗
FlyDrones — upstream repository and limitations

Engineering repository; not independent validation

The README describes the browser MiniFly as synthetic and hand-wired. It identifies engineered sensory/readout mappings and says hardware adapters have not been flight-tested by its authors. No reproduction is claimed here.

Read the original source ↗
Brian 2 — official documentation

Optional simulation tool

Evaluate equation-oriented modeling after a small independent simulator. Availability of documentation does not establish compatibility with this website environment.

Read the original source ↗
NEST — official simulator documentation

Optional simulation tool

Evaluate for network simulation requirements. Pin the version and model semantics in a separate experiment environment.

Read the original source ↗
Norse — official documentation

Optional PyTorch-oriented tool

An option to examine for differentiable spiking models. Benchmark the required model and workload before selecting it.

Read the original source ↗
snnTorch — official documentation

Optional PyTorch-oriented tool

An option for spiking learning tutorials and experiments. Dependencies belong in an approved experiment environment, not the website runtime.

Read the original source ↗
Intel — neuromorphic computing research

Official hardware research resource

Study event processing, memory and mapping constraints. Do not assume public hardware access or transfer platform-specific energy claims to a new task.

Read the original source ↗
PX4 — official simulation guide

Official engineering documentation

Begin with simulation and versioned interfaces. Simulation success alone does not establish hardware flight readiness.

Read the original source ↗
Gerstner et al. — passive membrane and integrate-and-fire equations

Author-hosted textbook

Reference for the passive-membrane approximation and integrate-and-fire conventions.

Read the original source ↗
Hopfield (1982) — neural networks and collective computation

Primary paper

A source for attractor-network memory; the simplified pattern example here is original and does not reproduce its experiments.

Read the original source ↗
Friston (2010) — The free-energy principle: a unified brain theory?

Theory / review by its proponent

Read as a proposed theoretical framework, not a settled description of every brain computation.

Read the original source ↗
Lynch & Park — Modern Robotics, feedback control

Author-hosted engineering textbook

Reference for control concepts. Our scalar examples are teaching models, not robot-ready control implementations.

Read the original source ↗
FlyDrones — upstream architecture documentation

Primary engineering documentation

Describes the engineered processing pipeline; repository claims have not been independently reproduced here.

Read the original source ↗
FlyDrones — upstream science and assumptions

Primary engineering documentation

Consult alongside the biological papers; labels and interfaces in a model do not establish biological equivalence.

Read the original source ↗

A BOOK THAT GROWS

Edition notes.

EDITION 0.2 / 2026-10-16

Unified as one authored book. Added 25 illustrated part introductions, worked mathematical examples, executable Python, interactive explorations and an extensible book catalog.

EDITION 0.1 / 2026-10-16

Initial curriculum, prerequisite map, chapter outlines and reading register.

Use the edition and part title when citing this book. New material will retain the same book address.

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