Seventy years on from AI appearing on the public scene and all the optimistic projections have been largely overtaken with systems outgunning humans at all board, card and computer games including Chess, Poker and GO. Of course; general knowledge, medical diagnosis, genetics and proteomics, image and pattern recognition are now all firmly in the grasp of AI. Interestingly, AI is treading a similar path to computing in that it began with single purpose/task machines that could only deal with a company payroll calculations or banking transactions and nothing more! General purpose computing emerged over further decades to give us the PCs and devices we now enjoy. So, AI currently runs as task specific applications on these general purpose platforms, and no doubt, general purpose AI will also become tractable in a few decades too! Recent progress has promoted a deal of debate and discussion along with hundreds of published papers and definitions that attempt to characterise biological and artificial intelligence. But they all suffer the same futility and fail! Without reference to any formal characterisation, all discussion and debate remains relatively meaningless. Somewhat ironically, it was the defence industry that triggered the analysis work here. Two of key steps to success were: the abandonment of all performance comparisons between biological and machine entities; and the avoidance of using the human brain as some ‘golden’ intelligence reference. This presentation is suitable for professionals and public alike, and comes fully illustrated by high quality graphics, animations and movies. Inevitably, it contains (engineering) mathematics that non-practitioners will have to take on trust, whilst professionals may wish challenge on the basis that the focus on getting a solution rather than the purity of the process!

1. Quantifying
Machine Intelligence
Mathematically
Professor Peter Cochrane OBE, DSc
Sentient Systems Research
London Institute for Mathematical Sciences
28 March 2022

2. S H O R T D e f i n i t i o n
O F E N G I N E E R I N G
“The appliance of Science”
“Achieving more with £1 than a lay person might with £100”

3. D I F F E R E N C E
W R I T L A R G E ( 1 )
“Whilst Scientists are free to declare that there is
no solution to a problem…Engineers enjoy no
such luxury - we always have to find a solution
even if it is wrong”
Guess
Iterate
Analogies
Approximate
Experiment
Compute
Consult
Model
Trial &
Error

4. D I F F E R E N C E
WRIT LARGE (2)
“Problems are alway urgent
with limited time
and funding”
“Problems come thick and
fast - there is seldom
time to ponder”

5. D I F F E R E N C E
WRIT LARGE (3)
“Engineers enjoy a supreme arrogance that says;
we know that time travel and free energy
are impossible, but everything else
we can do given the time and
resources”

6. AND SO IT STARTS
WITH A CALL OUT
O F T H E B L U E
“We have 3 machines that
cannot be exhaustively tested
- can you come up with a means of
quantifying their relative intelligences?”

7. STATE OF THE ART
PUBLISHED Studies
Incredibly broad
(spanning machines and many biological lifeforms)
Worryingly simple
(at a macro level of memory and processing power) M .P
Unbelievably complex
(at a micro level of neurons, connectivity at scale) Modelling dendrites,
neurons, synapse,
axons +++

8. 26 Jun 2020 — Moravek and Kurzweil’s human brain
estimates ~ 1016 Tlops = 10 PFlops
UNCERTAINTY
and CRUDITY
Human Brain
Equivalence
Estimate

9. Human brains are clearly more complex than many
realise - both analogue and digital, combining
computing & memory within each neuron
THE DAWN
OF REALITY
Human brain ~200 billion neurons linked by
trillions of synapses containing ~1000
switches routing electrical impulse
The ‘switching’ of neurons in influenced
by > 50 different chemicals
Some evidence of Quantum effects have also
been reported recently

10. Way beyond anything conceived and built by man
and in no way resembles an electronic computer
- moreover, it is distributed across the entire body!
HUMAN
B R A I N
Human brain ~1011 neurons linked by ~102 - 105
Human body ~ has yet to be charted!

11. ERROR BARS REPORTED
on ABSOLUTE ESTIMATES
Span Factor ~ 102 to 105
From an engineering perspective this renders all such results as useless unless
significant improvements can be realised…which appears to be highly unlikely!

12. Problem
AT Scale
This
may never
fully
understand
This
Dissection, Modelling,
Experimentation
So far we have a wiring map,
+ some models of individual
functions, but full life cycle
understanding remains a
, mystery!
~10^11 Neurons
~300 Neurons

13. AXIOM
This
will never
understand
This
Vis Thermodynamics
This is increasingly becoming apparent, and we most likely
need the help of Quantum Computers - but that is not going
to happen for decades!

14. K i l l e r
ProbleM
We cannot describe, accurately
quantify or measure intelligence
in any form !

15. ABSOLUTE ESTIMATES
OF ’N' INTELLIGENCES
An incredibly broad span of machines and biological lifeforms
From worryingly simple minded assumptions
(at a macro level of memory and processing power alone)
To unbelievably complex modelling
(at a micro level of neurons, and large scale connectivity)

16. “An ability to learn from experience and to adapt/shape, selected environments”
So, What about
p h i l o s o p h Y ?
All are of a general (descriptive) form:
“A capacity for abstraction, logic, understanding, self-awareness, learning, emotional
knowledge, reasoning, planning, creativity critical thinking, and problem solving”
+
+
+
+
From an engineering perspective all such descriptors are useless!
“The faculty of rational behaviour”
“The capacity to experience feelings and sensation”
>1000 years of thinking & debating
sees >150 intelligence definitions

17. Alfred Binet IQ Test 1909 ??
"Philosophers have given their moral approval to the deplorable
verdict that affirms human intelligence is fixed, and cannot be
augmented. We must protest against this brutal pessimism; we will
try to demonstrate that it is founded on nothing"
A test of a machine's ability to exhibit intelligent behaviour,
equivalent to, or indistinguishable from, that of an actual human
based on a natural language conversation. All participants are
separated. If the judge cannot reliably tell the machine from the
human, the machine is said to have passed.
Alan Touring IQ Test 1950 ??
Z E R O W O R T H
I R R E L E V A N T ?

18. M e a n i n g l e s s - I Q

19. T u r i n g T E S T
“The good news Dave, is that the
computer’s passed the Turing
Test, but you have failed”
GO
Poker
Chess
Complexity
Mamagrams
Comp Games
Protein Folding
Medical Diagnosis
Composing Music
Drawing/Painting
Circuit Design
Data Analysis
Transcription
Chip Design
++++
Machine learning and rule creation have
overtaken human programming for AI

20. H U M A N I S I N G
I N T E R F A C E S
Human-AI voice interactions now the
norm and getting better by the day!

21. P H I L O S O P H E R S
WERE VERY WRONG
Their opinions did/do not stand
up to scientific scrutiny big time!

22. C O M M O N
E R R O R
The attributes of physical dexterity, flexibility,
mobility, communication, intelligence and
evolved to meet the specific demands of
given environments - many of which we
(humans) cannot survive in!
Our specific human capabilities and attributes
were tuned by evolution to meet the physical
opportunities and limitations of surface living
on planet earth - not in water, air or space!
“Speciated superiority is a nonsense”

23. F r o m N a r r o w
T O G e n e r a l A I
O NTO S E NT I E N CE
C o m p u t i n g / I T p r o g r e s s i o n : t a s k
s p e c i f i c t o g e n e r a l p u r p o s e - P C !
“ T h e s i n g l e b i g g e s t m i s t a k e t h e
A I c o m m u n i t y h a v e m a d e i s t o
a s s u m e h u m a n s a s s o m e g o l d
s t a n d a r d r e f e r e n c e o f a b i l i t y
a n d / o r p e r f o r m a n c e f u n c t i o n ”
“ B u i l d i n g a n a r t i f i c i a l h u m a n
b r a i n i s a n i n t e r e s t i n g t a r g e t ,
b u t c r e a t i n g n e w i n t e l l i g e n c e s
i s a f a r m o r e i m p o r t a n t / u r g e n t o n e ”

24. All biological brains evolve slowly are now more
or less in stasis - in comparison our technology
is advancing exponentially - so equivalence is
not a question of IF, but WHEN ?
W H A T W E
D o K N O W
-100M -1M 1940 1990 2040
-103
-106
-109
-1012
-1015
-1018
FLOPS
Biological intelligence
has now ‘flat-lined’
Tech induced intelligence has only
recently reached a critical growth
stage and is exponential

25. “As a species our dependence on AI is
now total - and societies can no longer
function without this core technology”
W H A T W E
D o K N O W

26. Transformation OF THE
C o m p l e x to S i m p l e ( R )
“Estimating the comparative
intelligences of similar
‘animals’ might just be a lot
easier, far more accurate,
and far more useful given the
stated problem set !”
Note: For the same starting conditions (biology or technology) the error bars are generally negated,
or greatly reduced for dissimilar entities for a given ratio calculation!
Concatenation
to Division of
Error Bars!

27. A R R O G A N C E I S N O T
UNIQUE TO ENGINEERS
Samuel Johnson 1709 -1784
English critic, biographer, essayist, poet,
and lexicographer, compiled/published
the first English Dictionary
SO, I started by ‘doing a Dr Johnson’
and defined intelligence!
“Intelligence is the way I define it
and not what others consider it to be”
My misquote!

28. A L L P h y s i c a l
& M e ta p h y s i c a l
E X P E R I E N C E S
Life introduces physical order into a system
Intelligence transforms information in systems
Both introduce Positive Entropy into systems
Ergo; Life and Intelligence are strongly related

29. H Y P O T H E S I S
C O N C AT E N AT E D
Life => an emergent property of Complexity
Intelligence => an emergent property of Life
Sentience => an emergent property of Intelligence
Complexity => an emergent property of Clustering in Chaos
Complexity & Chaos => the ground state of our non-linear universe

30. H Y P O T H E S I S
C O N C AT E N AT E D
This is suggested, and increasingly,
supported by a growing body of evidence
Life => an emergent property of Complexity
Intelligence => an emergent property of Life
Sentience => an emergent property of Intelligence
Complexity => an emergent property of Clustering in Chaos
Complexity & Chaos => the ground state of our non-linear universe

31. Nature v Man/Machine
Mother Nature: Chance action
- no intelligence required!
Mankind: Purposeful
intelligence applied!
Machine: Mankind /AI application
of intelligence and mechanisms!

32. C o n c i s e
d e f i n i t i o n
Intelligence = Directed (or Forced) System Entropy
I later realised Efficacy to be related to some IQ
measure, whilst at the same time recognising
that IQ is actually worthless as a measure :-(

33. A P O I N T O F
C L A R I T Y
Intelligence = I = IEi - EoI
As intelligences can both increase or decrease the system Entropy;
we redefine in terms of the Modular value…
At this point we had something
that might just work!
NOTE: Entropy E = The information required
to exactly define the
state of the system

34. A P r o c e s s i o n o f o r g a n i c
a n a l o g u e s n o w f o l l o w e d
i n o r d e r o f i n c r e a s i n g
c o m p l e x i t y …

35. Actuator
A
System
Environs
Sensor
S
T h e s i m p l e s T
S ta r t i n g P o i n t
A single and simple biological
cell or slime mould
A thermostat or light sensitive
switch
No signal/state processing
or memory

36. C O U N T E r
C A N D I T I O N
No signal/state processing life form with
hunting and complex problem solving
capabilities - simple elements combining
to create complex/intelligent organisms

37. Actuator
A
System
Environs
Sensor
S
A D D I T I O N
O F M E M O R Y
Memory
M
Venus Fly Trap + many
other carnivorous plants
A programmable thermostat
It is not exactly clear if any signal
processing is necessary as a discreet
function but this ‘hic-up’ conveniently
turns out to be unimportant !

38. Processor
P1
Memory
M
Processor
P2
System
Environs
Sensor
S
Actuator
A
Many species of very
simple insects
Artificial Ant - a colony
of which is capable of
solving the Travelling
Salesman Problem
PROCESSING
& M E M O R Y
In Nature processing and memory are
combined in the synapses - only We
make them discrete in our Silicon world

39. I M P O R T A N T
R E VE L AT I O N
Long term comatosed hospital patients
appear brain dead due to a lack of I/O
- ie Sensors and Actuators
Clinically Dead
- No eye movement
- No reflex action
- No bodily responses

40. I M P O R T A N T
C O N D I T I O N A L S
These are really helpful/vital in setting
the bounds on the form of our final
solution and our analysis direction
Intelligence = 0 Iff
P + M
S + A = 0
Intelligence ≠ 0 If = 0
Without any I/O - Sensory/Actuator
faculty no intelligence is evident
Without any Processing or Memory
intelligence is still possible

41. System
Environs
Memory
ShortTerm
Processor
1
Actuators
Sensors
Memory
LongTerm
Processor
2
scope for ever
more complexity

42. Actuator
A1
Actuator
System
Environs
Memory
Mlocal
Actuator
Memory
Mshort
Memory
Mlong
Processor
P21
Processor
P11
Sensors
Easy to conjure
unviable configs
w r t a n a l y s i s

43. Actuator
Processor
P1
System
Environs
Memory
M
Processor
P2
Sensors
S
cHoice of Viable
S ta r t i n g P o i n t

44. Where: s, p ,m, a are complex temporal operators
that cannot in general be fully defined or detailed
Actuator
A
Processor
P1
System
Environs
Processor
P2
si
i
o
p1 si
(1 + m) p1 si
Sensors
S
.
Memory
M
A s s u m i n g A
Nomenclature
a(1 + m + p1 p2 + p2 m p1 ) si

45. Ic = I Ei - Eo I = I Ei ( si ) - Eo ( a[1 + m + p1 p2 + p2 m p1 ] si ) I
Where: s, p ,m, a are complex operators that cannot,
in general, be fully defined or detailed
E N G I N E E R I N G
LICENCE APPLIED
We simply neglect/ignore/hide the
time variability of all the functions
and mask it with a new formulation
Comparative
Intelligence

46. Ic = I Ei - E[a.s ( 1 + m + p + mp ) ] I
E N G I N E E R I N G
LICENCE APPLIED
C o m b i n i n g s i m i l a r c o m p l e x
o p e r a t o r s f o r t h e e a s e o f
manipulation and explanation

47. A P O I N T O F
C L A R I T Y
Intelligence = I = IEi - EoI
As intelligences can both increase or decrease the system Entropy;
we redefine in terms of the Modular value…
At this point we had something
that might just work!
NOTE: Entropy E = The information required
to exactly define the
state of the system

48. Finally, we have something meeting
all our practical bounds and limiters
that we can work with in practice
Ic = k log2 [1 + K.S.A (1 + P + M + P.M ) ]
System Constants
Ic ~ k log2 [1 + K.S.A (1 + P.M ) ]
For P.M >> (P + M)
C o n c e p t u a l
ENTROPIC LEAP
This resemble the Shannon-Hartley
theorem in Information Theory

49. A P R I M A R Y
IMPLICATION
We are not racing toward a singularity as
fast as people have previously projected
Increasing S. P. M. A by a factor of 1000
would only see intelligence grow 10 fold due
to the logarithmic nature of intelligence !

50. EXPONENTIAL
V logarithmic
Estimated Entropic Growth
of AI capabilities

51. Computing
Power
1960 70 80 90 2000 10
MIP/s
A Wider Set
of AI Estimates
EXPONENTIAL
V logarithmic
20
Intelligence
Level

52. i n < 4 0 Y e a r s
~ 1,000,000,000 x chip capacity
Processing
Memory
Sensors
MacBook Pro >50Bn transistors
iPhone = ~15Bn transistors
IBM > 30Bn transistors/chip
Feature size now ~ 5nm

53. i n < 4 0 Y e a r s
~ 1,000,000,000 x chip capacity
Processing
Memory
Sensors
Adapta
bility
Softwa
re
Compl
exity
Auton
omy
AI
Processing
Memory
Sensors
Manipulators
Communication
Networking
MacBook Pro >50Bn transistors
iPhone = ~15Bn transistors
IBM > 30Bn transistors/chip
Feature size now ~ 5nm

54. i n < 4 0 Y e a r s
~ 1,000,000,000 x chip capacity
~Dog Brain
~Mouse Brain
~Human
Brain
There is far more to intelligence
than a very crude analogy to transistor
- neuron equivalence and count, but this serves to
indicate one reason why AI has been along time coming !
Processing
Memory
Sensors
Adapta
bility
Softwa
re
Compl
exity
Auton
omy
AI
Processing
Memory
Sensors
Manipulators
Communication
Networking
MacBook Pro >50Bn transistors
iPhone = ~15Bn transistors
IBM > 30Bn transistors/chip
Feature size now ~ 5nm

55. G A M E C H A N G E R 2 0 1 2
Considered to be impossible by philosophers
Medicine today
I B M W a t s o n

56. G A M E C H A N G E R 2 0 1 4
Considered to be impossible by philosophers

57. HYPER-LEARNING
Human ex perience 5 - 20k
opera tion s in a lifetime
Ne two rked AI - Robot >20k
opera tion s per day

58. T hinkin g the right way
People fear, & complain, overlook the big gains
V i v e
L a
d i f f e r e n c e

59. Exemplar
N e w C r e a t i v i t y

60. Exemplar
N e w C r e a t i v i t y Criticism
It is just copying and
aping what human
composers have done !
Retort 1
You mean exactly
like human
composers do ?
Retort 2
AI has only just got
into this game that
humans have be at
for well over 3M years

61. SPOT THE
A I S y t e m

62. Ic ~ k log2[1 + K.A.S {𝜇 + P (Ms + Ml }]
The I/O elements A.S
shape our perception
of experiences at the
most fundamental and
Processing
and reflexes further
refine all perceived
activity & experience
(P + 𝜇)
Ml
Long Term Memory
provides context &
central awareness in
t i m e & s p a c e o n
relational axes of who,
what, when, where why
The Seat of Sentience ?
S O W H E R E I S
S E N T I E N C E ?
Ms
Short Term Memory
provides almost ‘unthinking’
functionality, largely free of
context, could be likened to an
auto-pilot!
For the human brain/body it appears to
be dominated by long term memory that
is distributed throughout the structure &
most influenced by sensory activity

63. S O W H E R E I S
S E N T I E N C E ?
F U R T H E R
A N A L Y S I S
The mathematical framework sufficient to
tackle the stochastic complexity in the round
may not yet exist/may be impossible…

64. T h a n k Y o u
www.petercochrane.com