The Math Over Mind and Matter

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The Math Over Mind and Matter
Presented at Quantum Mind II, Tucson, AZ

• Doug Matzke matzke_at_ieee.org
• and
• Nick Lawrence
• nick_at_lt.com

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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!!

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Data Tokens Survive
0 min or not firing 1 max firing rate
Classical Neurons
Classical firing
Quantum Spins
0 or 1
?
?
Classical ? Quantum ? Classical
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The Math Correlithm Objects
Corob A point in a high dimensional space Ngt20

• Neural Corob Models
• Humans are smart
• Mimic brain statistics

• Quantum Universe
• Massive parallelism
• Mimic quantum statistics

Quantum Corobs corob tokens mapped onto quantum
states
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Tokens from Randomness
for 3 tokens
3 random points in bounded space

• Soft data tokens emerge out of pure randomness
  (uniformly distributed)
• All tokens are the same standard distance apart
  (with standard deviation)

Capture Zones
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High Dimensional Tetrahedron
for 4 tokens
4 random points in bounded space

• Soft data tokens emerge out of pure randomness
• All tokens are the same standard distance apart
• Works for any number of corob soft tokens (Ngt20)

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Corob Computing
for 5 tokens
Forms an N-dim 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
• Tokens can uniquely represent concepts and the
  states of computation

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Expected Standard Distance
for 2000 tokens
Every token is equidistant from all other
tokens so forms an N-shell or an
N-equihedron
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Constant-like expected values
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Constant Standard Deviation
for N3,12,100,1000
Standard Deviation Confidence Interval
1 0.6826895
2 0.9544997
3 0.9973002
4 0.9999366
5 0.9999994
Best if Ngt35 because standard distance is 10
times standard deviation
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Standard Distance Standard Radius
for unit NR-cube
Exact Measures
Probabilistic Measures
Space Center is .5 .5
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Distance from Corner to Random Point
for unit NR-cube
Distance from random corner to a random point is
D2R so call it the diameter D. Notice
equalities Z2 R2 D2 and Z2 Z2 K2
where is the Kanerva distance of
random corners
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Normalized Distances Summary
for unit NR-cube
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Normalized Random Phase Qubits
for array of qubits Nq
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Quantum Corob Encoding
Start real array Si
S0 S1 S2 S3 S4 S5
S94 S95 S96 S97 S98 S99
Encode as random phase Qubits Qi ensemble
Start Qubit array Qi
Q0 Q1 Q2 Q3 Q4 Q5
Q94 Q95 Q96 Q97 Q98 Q99
Measurement of Qubits Qi
End Qubit States Ei
Answer Binary States Ai
0 1 1 0 1
0
0 1 0 0 1
1
Quantum Corob Measurement Process!!
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Qubit Projection
phase of measurement
qubit phase
Probability plotted for qubit phase versus
measurement phase
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Corobs Survive Measurement
Start real array Si
Encode as random phase Qubits Qi
Trial 1
Trial 2
Starting Qubit arrays Qi
Probabilistic Measurement of Qubits Qi
Ending Qubit states Ei
Answer Binary states Ai
Answers are 75 same from multiple trials of same
Si!!
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Quantum Corobs Survive Projection

• 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.

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Token Distance Histograms
random
similar
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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!

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Think High Dimensional
Quantum Topology
Neural Topology