1. DJM Mar 2003 Lawrence Technologies, LLC The Math Over Mind and Matter Doug Matzke matzke@ieee.org and Nick Lawrence nick@lt.com Presented at Quantum Mind II, Tucson, AZ

2. DJM Mar 2003 Lawrence Technologies, LLC Math over Mind and Matter Results from math field of probabilistic geometry Describes classical neuron behavior – Patented result from 30 years of work – Corob tokens, computation and language Describes quantum ensemble state behavior – Results of Air Force contract #F30602-02-C-0077 – Quantum corob tokens, computation and language Corob perspective describes both!!

3. DJM Mar 2003 Lawrence Technologies, LLC Data Tokens Survive Classical Neurons Quantum Spins   Classical firing Classical  Quantum  Classical 0 = min or not firing 1 = max firing rate

4. DJM Mar 2003 Lawrence Technologies, LLC The Math: Correlithm Objects Neural Corob Models Humans are smart Mimic brain statistics Quantum Universe Massive parallelism Mimic quantum statistics Quantum Corobs corob tokens mapped onto quantum states Corob: A point in a high dimensional space N>20

5. DJM Mar 2003 Lawrence Technologies, LLC Tokens from Randomness Soft data tokens emerge out of pure randomness (uniformly distributed) All tokens are the same standard distance apart (with standard deviation) 3 random points in bounded space for 3 tokens Capture Zones

6. DJM Mar 2003 Lawrence Technologies, LLC High Dimensional Tetrahedron Soft data tokens emerge out of pure randomness All tokens are the same standard distance apart Works for any number of corob soft tokens (N>20) 4 random points in bounded space for 4 tokens

7. DJM Mar 2003 Lawrence Technologies, LLC Corob Computing Soft data tokens emerge out of pure randomness All tokens are the same standard distance apart Works for any number of corob soft tokens Tokens can uniquely represent concepts and the states of computation Forms an N-dim tetrahedron for 5 tokens

8. DJM Mar 2003 Lawrence Technologies, LLC Expected Standard Distance Every token is equidistant from all other tokens so forms an N-shell or an N-equihedron for 2000 tokens

9. DJM Mar 2003 Lawrence Technologies, LLC Constant-like expected values For N=96, Standard distance = 4For N=2400, Standard distance = 20

10. DJM Mar 2003 Lawrence Technologies, LLC Constant Standard Deviation Best if N>35 because standard distance is 10 times standard deviation Standard DeviationConfidence Interval ±10.6826895 ±20.9544997 ±30.9973002 ±40.9999366 ±50.9999994 for N=3,12,100,1000

11. DJM Mar 2003 Lawrence Technologies, LLC Standard Distance & Standard Radius 0 1 0 1 S = 1 Space Center is [.5.5 …] Exact Measures Probabilistic Measures for unit N R -cube

12. DJM Mar 2003 Lawrence Technologies, LLC Distance from Corner to Random Point Distance from random corner to a random point is D=2R so call it the diameter D. Notice equalities: Z 2 + R 2 = D 2 and Z 2 + Z 2 = K 2 where is the Kanerva distance of random corners 0 1 0 1 S = 1 for unit N R -cube

13. DJM Mar 2003 Lawrence Technologies, LLC Normalized Distances Summary 0 1 0 1 for unit N R -cube

14. DJM Mar 2003 Lawrence Technologies, LLC Normalized Random Phase Qubits 1 1 1 1 0 0 for array of qubits N q

15. DJM Mar 2003 Lawrence Technologies, LLC Quantum Corob Encoding Q 0 Q 1 Q 2 Q 3 Q 4 Q 5 Q 94 Q 95 Q 96 Q 97 Q 98 Q 99 Start Qubit array Q i Answer Binary States A i Measurement of Qubits Q i End Qubit States E i Start real array S i Encode as random phase Qubits Q i ensemble Quantum Corob Measurement Process!! S 0 S 1 S 2 S 3 S 4 S 5 S 94 S 95 S 96 S 97 S 98 S 99 0 1 1 0 1 0 0 1 0 0 1 1

16. DJM Mar 2003 Lawrence Technologies, LLC Qubit Projection Probability plotted for qubit phase versus measurement phase qubit phase phase of measurement

17. DJM Mar 2003 Lawrence Technologies, LLC Corobs Survive Measurement Starting Qubit arrays Q i Answer Binary states A i Probabilistic Measurement of Qubits Q i Ending Qubit states E i Start real array S i Encode as random phase Qubits Q i Q 0 Q 1 Q 98 Q 99 S 0 S 1 S 98 S 99 Q 0 Q 1 Q 98 Q 99 0 1 0 1 Q 0 Q 1 Q 98 Q 99 0 1 1 1 Answers are 75% same from multiple trials of same S i !! Trial 1Trial 2

18. DJM Mar 2003 Lawrence Technologies, LLC Quantum Corobs Survive Projection Standard Distance << Standard Distance X Cluster Y Cluster Two random phase corobs X,Y Encode as arrays of qubit phases Measure qubits to form class. corob Repeat process or run concurrently All Xs will look like noisy versions of each other. All Ys will look like noisy versions of each other.

19. DJM Mar 2003 Lawrence Technologies, LLC Token Distance Histograms random similar

20. DJM Mar 2003 Lawrence Technologies, LLC Math over Mind and Matter Corobs exist for both neural & quantum states Corob tokens merrily survive re-encoding – From neural to quantum state – From quantum to neural state (measurement) Same math works for both mind and matter – Gray Matter and – Quantum Mind Applicable to any Quantum Mind proposal!! – Thinking about high dimensional spaces is hard!

21. DJM Mar 2003 Lawrence Technologies, LLC Think High Dimensional 1 1 1 1 0 0 0 1 0 1 Neural Topology Quantum Topology