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Copyright of every illustration belongs to
Sydney Padua.
Hooray for her great book, The Thrilling
Adventures of Lovelace and Babbage.
Her book gave me the insight to organize all
these contents, so hooray on that too.
Copyright of every illustration belongs to
Sydney Padua.
Hooray for her great book, The Thrilling
Adventures of Lovelace and Babbage.
Her book gave me the insight to organize all
these contents, so hooray on that too.
Augusta Ada King, Countess of Lovelace
1815~1852
Augusta Ada King, Countess of Lovelace
1815~1852
Augusta Ada King, Countess of Lovelace
1815~1852
George Gordon Byron
1788~1824
“Byronmania”
The Bishop of Old Patras Germanos Blesses the Flag of Revolution
by Theodoros Vryzakis (1788~1824)
The Bishop of Old Patras Germanos Blesses the Flag of Revolution
by Theodoros Vryzakis (1788~1824)
Anne Isabella Noel Byron
1792~1860
Anne Isabella Noel Byron
1792~1860
Anne Isabella Noel Byron
1792~1860
Anne Isabella Noel Byron
1792~1860
“The princess of parallelograms.”
“The princess of parallelograms.”
“The princess of parallelograms.”
Augusta Ada King, Countess of Lovelace
(When she was 4)
Augusta Ada King, Countess of Lovelace
(When she was 4)
Augusta Ada King, Countess of Lovelace
(When she was 4)
Augusta Ada King, Countess of Lovelace
(When she was 4)
Augusta Ada King, Countess of Lovelace
(When she was 4)
Augusta Ada King, Countess of Lovelace
(When she was 4)
Mary Somerville
1780~1872
Mary Somerville
1780~1872
“The Queen of
Nineteenth-Century Science.”
Mary Somerville
1780~1872
Mary Somerville
1780~1872
Mary Somerville
1780~1872
Mary Somerville
1780~1872
Caroline Herschel
1750~1848
John Stuart Mill
1806~1873
John Stuart Mill
1806~1873
Mary Somerville
1780~1872
Augustus De Morgan
1806~1871
Lovelace’s sketch with De Morgan’s comments
“The potential to be an
original mathematical investigator,”
“The potential to be an
original mathematical investigator,”
George Boole
1815~1864
Charles Babbage
1791~1871
Charles Babbage
1791~1871
Charles Babbage
1791~1871
Charles Babbage
1791~1871
Charles Babbage
1791~1871
Michael Faraday
1791~1867
Charles Darwin
1809~1882
Alfred, Lord Tennyson
1809~1892
Alfred, Lord Tennyson
1809~1892
Charles Dickens
1812~1870
Florence Nightingale
1820~1910
Florence Nightingale
1820~1910
Difference Engine
Difference Engine
Newton's method of divided differences
Newton's method of divided differences
Newton's method of divided differences
“Degree decreasing when using divided differences”
𝒏 (𝒙 + 𝟏) 𝒏−𝒙 𝒏
1 𝑥 + 1 − 𝑥 = 1
2 (𝑥 + 1)2
−𝑥2
= 2𝑥 + 1
3 (𝑥 + 1)3−𝑥3 = 3𝑥2 + 3𝑥 + 1
︙ ︙
“Degree decreasing when using divided differences”
𝒏 (𝒙 + 𝟏) 𝒏−𝒙 𝒏
1 𝑥 + 1 − 𝑥 = 1
2 (𝑥 + 1)2
−𝑥2
= 2𝑥 + 1
3 (𝑥 + 1)3−𝑥3 = 3𝑥2 + 3𝑥 + 1
︙ ︙
“Degree decreasing when using divided differences”
𝒏 (𝒙 + 𝟏) 𝒏−𝒙 𝒏
1 𝑥 + 1 − 𝑥 = 1
2 (𝑥 + 1)2
−𝑥2
= 2𝑥 + 1
3 (𝑥 + 1)3−𝑥3 = 3𝑥2 + 3𝑥 + 1
︙ ︙
“Degree decreasing when using divided differences”
𝒏 (𝒙 + 𝟏) 𝒏−𝒙 𝒏
1 𝑥 + 1 − 𝑥 = 1
2 (𝑥 + 1)2
−𝑥2
= 2𝑥 + 1
3 (𝑥 + 1)3−𝑥3 = 3𝑥2 + 3𝑥 + 1
︙ ︙
“Degree decreasing when using divided differences”
𝒏 (𝒙 + 𝟏) 𝒏−𝒙 𝒏
1 𝑥 + 1 − 𝑥 = 1
2 (𝑥 + 1)2
−𝑥2
= 2𝑥 + 1
3 (𝑥 + 1)3−𝑥3 = 3𝑥2 + 3𝑥 + 1
︙ ︙
Difference Engine
Difference Engine
Difference Engine
Plan Diagram of the Analytical Engine
Plan Diagram of the Analytical Engine
Plan Diagram of the Analytical Engine
Plan Diagram of the Analytical Engine
Luigi Federico Menabrea
1809~1896
Luigi Federico Menabrea
1809~1896
Sir Charles Wheatstone
1802~1875
Sir Charles Wheatstone
1802~1875
Sir Charles Wheatstone
1802~1875
“Whenever any result is sought by its aid,
the question will then arise —
By what course of calculation
can these results be arrived at
by the machine
in the shortest time?”
“Whenever any result is sought by its aid,
the question will then arise —
By what course of calculation
can these results be arrived at
by the machine
in the shortest time?”
“Whenever any result is sought by its aid,
the question will then arise —
By what course of calculation
can these results be arrived at
by the machine
in the shortest time?”
“Whenever any result is sought by its aid,
the question will then arise —
By what course of calculation
can these results be arrived at
by the machine
in the shortest time?”
Every function can be calculated when
continued ad infinitum.
Operation is any process which alters the
mutual relation of two or more things.
Operations are homogeneous, but distributed
amongst different subjects of operation.
By what course of calculation can those results
be arrived in the shortest time?
Every function can be calculated when
continued ad infinitum.
Operation is any process which alters the
mutual relation of two or more things.
Operations are homogeneous, but distributed
amongst different subjects of operation.
By what course of calculation can those results
be arrived in the shortest time?
Every function can be calculated when
continued ad infinitum.
Operation is any process which alters the
mutual relation of two or more things.
Operations are homogeneous, but distributed
amongst different subjects of operation.
By what course of calculation can those results
be arrived in the shortest time?
Every function can be calculated when
continued ad infinitum.
Operation is any process which alters the
mutual relation of two or more things.
Operations are homogeneous, but distributed
amongst different subjects of operation.
By what course of calculation can those results
be arrived in the shortest time?
Every function can be calculated when
continued ad infinitum.
Operation is any process which alters the
mutual relation of two or more things.
Operations are homogeneous, but distributed
amongst different subjects of operation.
By what course of calculation can those results
be arrived in the shortest time?
Augustus De Morgan
1806~1871
Augustus De Morgan
1806~1871
Augustus De Morgan
1806~1871
De Morgan’s Laws
𝐴 ∪ 𝐵 = ҧ𝐴 ∩ ത𝐵
𝐴 ∩ 𝐵 = ҧ𝐴 ∪ ത𝐵
¬ 𝑃⋁𝑄 = ¬𝑃⋀¬𝑄
¬ 𝑃⋀𝑄 = ¬𝑃⋁¬𝑄
Set Theory Formal Language
De Morgan’s Laws
𝐴 ∪ 𝐵 = ҧ𝐴 ∩ ത𝐵
𝐴 ∩ 𝐵 = ҧ𝐴 ∪ ത𝐵
¬ 𝑃⋁𝑄 = ¬𝑃⋀¬𝑄
¬ 𝑃⋀𝑄 = ¬𝑃⋁¬𝑄
Set Theory Formal Language
George Boole
1815~1864
Boole's House and School
3 Pottergate in Lincoln
Boole's House and School
3 Pottergate in Lincoln
Boole's House and School
3 Pottergate in Lincoln
George Boole
1815~1864
Gottfried Wilhelm Leibniz
1646~1716
Sir William Rowan Hamilton
1805~1865
Sir William Rowan Hamilton
1805~1865
Sir William Rowan Hamilton
1805~1865
Sir William Rowan Hamilton
1805~1865
Joseph Hill’s letter (1851)
Recalling the meeting of Boole and Babbage
Joseph Hill’s letter (1851)
Recalling the meeting of Boole and Babbage
As Boole had discovered that means of reasoning
might be conducted by a mathematical process,
and Babbage had invented a machine
for the performance of mathematical work,
the two great men together seemed to have
taken steps towards the construction of
that great prodigy a Thinking Machine.
Joseph Hill’s letter (1851)
Recalling the meeting of Boole and Babbage
As Boole had discovered that means of reasoning
might be conducted by a mathematical process,
and Babbage had invented a machine
for the performance of mathematical work,
the two great men together seemed to have
taken steps towards the construction of
that great prodigy a Thinking Machine.
Joseph Hill’s letter (1851)
Recalling the meeting of Boole and Babbage
As Boole had discovered that means of reasoning
might be conducted by a mathematical process,
and Babbage had invented a machine
for the performance of mathematical work,
the two great men together seemed to have
taken steps towards the construction of
that great prodigy a Thinking Machine.
Joseph Hill’s letter (1851)
Recalling the meeting of Boole and Babbage
As Boole had discovered that means of reasoning
might be conducted by a mathematical process,
and Babbage had invented a machine
for the performance of mathematical work,
the two great men together seemed to have
taken steps towards the construction of
that great prodigy a Thinking Machine.
Claude Shannon
1916~2001
Claude Shannon
1916~2001
“… it just happened that
no one else was familiar
with both fields at the same time.”
“… it just happened that
no one else was familiar
with both fields at the same time.”
Switch representation
of AND, OR and NOT function
Switch representation
of AND, OR and NOT function
Switch representation
of AND, OR and NOT function
Howard Hathaway Aiken
1900~1973
Harvard Mark I
Harvard Mark I
Harvard Mark I
“… felt like Babbage was addressing
me personally from the past.”
“… felt like Babbage was addressing
me personally from the past.”
Harvard Architecture
Harvard Architecture
Grace Hopper
1906~1992
Grace Hopper
1906~1992
First computer bug while working on Mark II (1947)
First computer bug while working on Mark II (1947)
First computer bug while working on Mark II (1947)
John von Neumann
1903~1957
John von Neumann
1903~1957
John von Neumann
1903~1957
Von Neumann Architecture Harvard Architecture
One memory simplifies design. But
one bus acts as a bottleneck.
Two buses are expensive. Control
unit is tricky to develop.
One unified cache. Two separate cache.
Freedom to organize memory.
But could be error prone.
Free data memory not utilized.
H/W accelerated parallel execution
impossible. Only simulated by S/W.
Parallel access to data and
instruction.
Von Neumann Architecture Harvard Architecture
One memory simplifies design. But
one bus acts as a bottleneck.
Two buses are expensive. Control
unit is tricky to develop.
One unified cache. Two separate cache.
Freedom to organize memory.
But could be error prone.
Free data memory not utilized.
H/W accelerated parallel execution
impossible. Only simulated by S/W.
Parallel access to data and
instruction.
Boolean algebra gives operations of reasoning in
the symbolical language of calculus.
Prepositions are variables.
Yes/No in Boolean logic is now 1/0 in circuitry.
Variables are just signals before we chose to
look at it as variables.
Boolean algebra gives operations of reasoning in
the symbolical language of calculus.
Prepositions are variables.
Yes/No in Boolean logic is now 1/0 in circuitry.
Variables are just signals before we chose to
look at it as variables.
Boolean algebra gives operations of reasoning in
the symbolical language of calculus.
Prepositions are variables.
Yes/No in Boolean logic is now 1/0 in circuitry.
Variables are just signals before we chose to
look at it as variables.
Boolean algebra gives operations of reasoning in
the symbolical language of calculus.
Prepositions are variables.
Yes/No in Boolean logic is now 1/0 in circuitry.
Variables are just signals before we chose to
look at it as variables.
Boolean algebra gives operations of reasoning in
the symbolical language of calculus.
Prepositions are variables.
Yes/No in Boolean logic is now 1/0 in circuitry.
Variables are just signals before we chose to
look at it as variables.
Boolean algebra gives operations of reasoning in
the symbolical language of calculus.
Prepositions are variables.
Yes/No in Boolean logic is now 1/0 in circuitry.
Variables are just signals before we chose to
look at it as variables.
Boolean algebra gives operations of reasoning in
the symbolical language of calculus.
Prepositions are variables.
Yes/No in Boolean logic is now 1/0 in circuitry.
Variables are just signals before we chose to
look at it as variables.
Claude Shannon
1916~2001
“The fundamental problem of
communication is that of
reproducing at one point from a
message selected at another point.”
𝑁 bits can
represent 2 𝑁
numbers.
=
𝐶 number of data can be
represented by log2 𝐶 bits.
𝑁 bits can
represent 2 𝑁
numbers.
=
𝐶 number of data can be
represented by log2 𝐶 bits.
Shannon entropy for a biased coin
Shannon entropy for a biased coin
Shannon entropy for a biased coin
Shannon entropy for a biased coin
Shannon entropy for a biased coin
Shannon entropy for a biased coin
Shannon entropy for a biased coin
Shannon entropy for a biased coin
Shannon entropy for a biased coin
Shannon entropy for a biased coin
“Entropy is the average rate
at which information is produced
by a stochastic source of data.”
“Entropy is the average rate
at which information is produced
by a stochastic source of data.”
“Lower uniform probability means
more bits needed,
so more information.”
“Lower uniform probability means
more bits needed,
so more information.”
“Lower uniform probability means
more bits needed,
so more information.”
“Lower uniform probability means
more bits needed,
so more information.”
John von Neumann
1903~1957
“You should call it entropy, for two reasons.
In the first place your uncertainty function
has been used in statistical mechanics under that name,
so it already has a name.
In the second place, and more important,
nobody knows what entropy really is,
so in a debate you will always have the advantage.”
“You should call it entropy, for two reasons.
In the first place your uncertainty function
has been used in statistical mechanics under that name,
so it already has a name.
In the second place, and more important,
nobody knows what entropy really is,
so in a debate you will always have the advantage.”
“You should call it entropy, for two reasons.
In the first place your uncertainty function
has been used in statistical mechanics under that name,
so it already has a name.
In the second place, and more important,
nobody knows what entropy really is,
so in a debate you will always have the advantage.”
“You should call it entropy, for two reasons.
In the first place your uncertainty function
has been used in statistical mechanics under that name,
so it already has a name.
In the second place, and more important,
nobody knows what entropy really is,
so in a debate you will always have the advantage.”
The 2nd Law of Thermodynamics
Total entropy of an isolated system
can never decrease over time.
The 2nd Law of Thermodynamics
Total entropy of an isolated system
can never decrease over time.
The 2nd Law of Thermodynamics
Total entropy of an isolated system
can never decrease over time.
The 2nd Law of Thermodynamics
Total entropy of an isolated system
can never decrease over time.
Ludwig Boltzmann
1844~1906
Ludwig Boltzmann
1844~1906
Entropy of Gases
Entropy of Gases
Entropy of Gases
Entropy of Gases
Entropy of Gases
Entropy of Gases
Entropy of Gases
Entropy of Gases
Entropy of Gases
Entropy of Gases
Entropy of Gases
Entropy of Gases
Entropy of Gases
Entropy of Gases
𝐻 𝑦, ො𝑦 = ෍
𝑖
𝑦𝑖 log
1
ෝ𝑦𝑖
= − ෍
𝑖
𝑦𝑖 log ෝ𝑦𝑖
Cross Entropy
Encoding the i-th symbol wrongly with log ෝ𝑦𝑖 bits.
Therefore always larger than entropy.
𝐻 𝑦, ො𝑦 = ෍
𝑖
𝑦𝑖 log
1
ෝ𝑦𝑖
= − ෍
𝑖
𝑦𝑖 log ෝ𝑦𝑖
Cross Entropy
Encoding the i-th symbol wrongly with log ෝ𝑦𝑖 bits.
Therefore always larger than entropy.
𝐻 𝑦, ො𝑦 = ෍
𝑖
𝑦𝑖 log
1
ෝ𝑦𝑖
= − ෍
𝑖
𝑦𝑖 log ෝ𝑦𝑖
Cross Entropy
Encoding the i-th symbol wrongly with log ෝ𝑦𝑖 bits.
Therefore always larger than entropy.
𝐻 𝑦, ො𝑦 = ෍
𝑖
𝑦𝑖 log
1
ෝ𝑦𝑖
= − ෍
𝑖
𝑦𝑖 log ෝ𝑦𝑖
Cross Entropy
Encoding the i-th symbol wrongly with log ෝ𝑦𝑖 bits.
Therefore always larger than entropy.
𝐻 𝑦, ො𝑦 = ෍
𝑖
𝑦𝑖 log
1
ෝ𝑦𝑖
= − ෍
𝑖
𝑦𝑖 log ෝ𝑦𝑖
Cross Entropy
Encoding the i-th symbol wrongly with log ෝ𝑦𝑖 bits.
Therefore always larger than entropy.
𝐻 𝑦, ො𝑦 = ෍
𝑖
𝑦𝑖 log
1
ෝ𝑦𝑖
= − ෍
𝑖
𝑦𝑖 log ෝ𝑦𝑖
Cross Entropy
Encoding the i-th symbol wrongly with log ෝ𝑦𝑖 bits.
Therefore always larger than entropy.
𝐻 𝑦, ො𝑦 = ෍
𝑖
𝑦𝑖 log
1
ෝ𝑦𝑖
= − ෍
𝑖
𝑦𝑖 log ෝ𝑦𝑖
Cross Entropy
Encoding the i-th symbol wrongly with log ෝ𝑦𝑖 bits.
Therefore always larger than entropy.
𝐻 𝑦, ො𝑦 = ෍
𝑖
𝑦𝑖 log
1
ෝ𝑦𝑖
= − ෍
𝑖
𝑦𝑖 log ෝ𝑦𝑖
Cross Entropy
Encoding the i-th symbol wrongly with log ෝ𝑦𝑖 bits.
Therefore always larger than entropy.
𝐻 𝑦, ො𝑦 = ෍
𝑖
𝑦𝑖 log
1
ෝ𝑦𝑖
= − ෍
𝑖
𝑦𝑖 log ෝ𝑦𝑖
Cross Entropy
Encoding the i-th symbol wrongly with log ෝ𝑦𝑖 bits.
Therefore always larger than entropy.
𝐻 𝑦, ො𝑦 = ෍
𝑖
𝑦𝑖 log
1
ෝ𝑦𝑖
= − ෍
𝑖
𝑦𝑖 log ෝ𝑦𝑖
Cross Entropy
Encoding the i-th symbol wrongly with log ෝ𝑦𝑖 bits.
Therefore always larger than entropy.
𝐻 𝑦, ො𝑦 = ෍
𝑖
𝑦𝑖 log
1
ෝ𝑦𝑖
= − ෍
𝑖
𝑦𝑖 log ෝ𝑦𝑖
Cross Entropy
Encoding the i-th symbol wrongly with log ෝ𝑦𝑖 bits.
Therefore always larger than entropy.
𝐻 𝑦, ො𝑦 = ෍
𝑖
𝑦𝑖 log
1
ෝ𝑦𝑖
= − ෍
𝑖
𝑦𝑖 log ෝ𝑦𝑖
Cross Entropy
Encoding the i-th symbol wrongly with log ෝ𝑦𝑖 bits.
Therefore always larger than entropy.
KL Divergence
Number of extra bits needed if wrongly encoded.
Minimizing KL divergence is same with minimizing cross entropy.
𝐾𝐿(𝑦| ො𝑦 = 𝐻 𝑦, ො𝑦 − 𝐻(𝑦, 𝑦) = ෍
𝑖
𝑦𝑖 log
𝑦𝑖
ෝ𝑦𝑖
KL Divergence
Number of extra bits needed if wrongly encoded.
Minimizing KL divergence is same with minimizing cross entropy.
𝐾𝐿(𝑦| ො𝑦 = 𝐻 𝑦, ො𝑦 − 𝐻(𝑦, 𝑦) = ෍
𝑖
𝑦𝑖 log
𝑦𝑖
ෝ𝑦𝑖
KL Divergence
Number of extra bits needed if wrongly encoded.
Minimizing KL divergence is same with minimizing cross entropy.
𝐾𝐿(𝑦| ො𝑦 = 𝐻 𝑦, ො𝑦 − 𝐻(𝑦, 𝑦) = ෍
𝑖
𝑦𝑖 log
𝑦𝑖
ෝ𝑦𝑖
KL Divergence
Number of extra bits needed if wrongly encoded.
Minimizing KL divergence is same with minimizing cross entropy.
𝐾𝐿(𝑦| ො𝑦 = 𝐻 𝑦, ො𝑦 − 𝐻(𝑦, 𝑦) = ෍
𝑖
𝑦𝑖 log
𝑦𝑖
ෝ𝑦𝑖
KL Divergence
Number of extra bits needed if wrongly encoded.
Minimizing KL divergence is same with minimizing cross entropy.
𝐾𝐿(𝑦| ො𝑦 = 𝐻 𝑦, ො𝑦 − 𝐻(𝑦, 𝑦) = ෍
𝑖
𝑦𝑖 log
𝑦𝑖
ෝ𝑦𝑖
“Entropy is the average rate
at which information is produced
by a stochastic source of data.”
“Entropy is the average rate
at which information is produced
by a stochastic source of data.”
“Entropy is the average rate
at which information is produced
by a stochastic source of data.”
Everything is information.
Everything is information.
Entropy is the average rate at which
information is produced by a stochastic
source of data.
Basically, everything is information.
We are the one who is operating it.
Entropy is the average rate at which
information is produced by a stochastic
source of data.
Basically, everything is information.
We are the one who is operating it.
Entropy is the average rate at which
information is produced by a stochastic
source of data.
Basically, everything is information.
We are the one who is operating it.
Entropy is the average rate at which
information is produced by a stochastic
source of data.
Basically, everything is information.
We are the one who is operating it.
Entropy is the average rate at which
information is produced by a stochastic
source of data.
Basically, everything is information.
We are the one who is operating it.
Entropy is the average rate at which
information is produced by a stochastic
source of data.
Basically, everything is information.
We are the one who is operating it.
Gödel's theorem and Systems of Logic Based on Ordinals.
Turing machine and Halting problem.
Church-Turing Conjecture and Lambda Calculus.
“Lady Lovelace’s Objection” and Turing test.
Gödel's theorem and Systems of Logic Based on Ordinals.
Turing machine and Halting problem.
Church-Turing Conjecture and Lambda Calculus.
“Lady Lovelace’s Objection” and Turing test.
Gödel's theorem and Systems of Logic Based on Ordinals.
Turing machine and Halting problem.
Church-Turing Conjecture and Lambda Calculus.
“Lady Lovelace’s Objection” and Turing test.
Gödel's theorem and Systems of Logic Based on Ordinals.
Turing machine and Halting problem.
Church-Turing Conjecture and Lambda Calculus.
“Lady Lovelace’s Objection” and Turing test.
Gödel's theorem and Systems of Logic Based on Ordinals.
Turing machine and Halting problem.
Church-Turing Conjecture and Lambda Calculus.
“Lady Lovelace’s Objection” and Turing test.
Gödel's theorem and Systems of Logic Based on Ordinals.
Turing machine and Halting problem.
Church-Turing Conjecture and Lambda Calculus.
“Lady Lovelace’s Objection” and Turing test.
Gödel's theorem and Systems of Logic Based on Ordinals.
Turing machine and Halting problem.
Church-Turing Conjecture and Lambda Calculus.
“Lady Lovelace’s Objection” and Turing test.
Gödel's theorem and Systems of Logic Based on Ordinals.
Turing machine and Halting problem.
Church-Turing Conjecture and Lambda Calculus.
“Lady Lovelace’s Objection” and Turing test.
Gödel's theorem and Systems of Logic Based on Ordinals.
Turing machine and Halting problem.
Church-Turing Conjecture and Lambda Calculus.
“Lady Lovelace’s Objection” and Turing test.
Will you give me
poetical philosophy, poetical science?
Will you give me
poetical philosophy, poetical science?
Will you give me
poetical philosophy, poetical science?

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