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Mar 19, 2015, 10:01:04 PM3/19/15

to

Hi,

What is the currently most Pythonic way for doing deep comparisons between dicts?

For example, say you have the following two dictionaries

a = {

'bob': { 'full_name': 'bob jones', 'age': 4, 'hobbies': ['hockey', 'tennis'], 'parents': { 'mother': 'mary', 'father', 'mike'}},

'james': { 'full_name': 'james joyce', 'age': 6, 'hobbies': [],}

}

b = {

'bob': { 'full_name': 'bob jones', 'age': 4, 'hobbies': ['hockey', 'tennis']},

'james': { 'full_name': 'james joyce', 'age': 5, 'hobbies': []}

}

Previously, I though you could do a cmp():

cmp(a, b)

However, this page seems to imply that cmp() is deprecated?

https://docs.python.org/3/whatsnew/3.0.html#ordering-comparisons

Should we just be using the equality operator ("==") instead then? E.g.:

a == b

What is the reason for this?

Or is there a better way to do this?

Regards,

Victor

What is the currently most Pythonic way for doing deep comparisons between dicts?

For example, say you have the following two dictionaries

a = {

'bob': { 'full_name': 'bob jones', 'age': 4, 'hobbies': ['hockey', 'tennis'], 'parents': { 'mother': 'mary', 'father', 'mike'}},

'james': { 'full_name': 'james joyce', 'age': 6, 'hobbies': [],}

}

b = {

'bob': { 'full_name': 'bob jones', 'age': 4, 'hobbies': ['hockey', 'tennis']},

'james': { 'full_name': 'james joyce', 'age': 5, 'hobbies': []}

}

Previously, I though you could do a cmp():

cmp(a, b)

However, this page seems to imply that cmp() is deprecated?

https://docs.python.org/3/whatsnew/3.0.html#ordering-comparisons

Should we just be using the equality operator ("==") instead then? E.g.:

a == b

What is the reason for this?

Or is there a better way to do this?

Regards,

Victor

Mar 19, 2015, 10:33:52 PM3/19/15

to pytho...@python.org

Victor Hooi <victo...@gmail.com> writes:

> What is the currently most Pythonic way for doing deep comparisons

> between dicts?

What distinction do you intend by saying “deep comparison”? As
> What is the currently most Pythonic way for doing deep comparisons

> between dicts?

contrasted with what?

> For example, say you have the following two dictionaries

>

> a = {

> 'bob': { 'full_name': 'bob jones', 'age': 4, 'hobbies': ['hockey', 'tennis'], 'parents': { 'mother': 'mary', 'father', 'mike'}},

> 'james': { 'full_name': 'james joyce', 'age': 6, 'hobbies': [],}

> }

>

> b = {

> 'bob': { 'full_name': 'bob jones', 'age': 4, 'hobbies': ['hockey', 'tennis']},

> 'james': { 'full_name': 'james joyce', 'age': 5, 'hobbies': []}

> }

behave for those two values?

> However, this page seems to imply that cmp() is deprecated?

> https://docs.python.org/3/whatsnew/3.0.html#ordering-comparisons

> Should we just be using the equality operator ("==") instead then? E.g.:

>

> a == b

above two values. Would you expect different behaviour?

> What is the reason for this?

dicts with the built-in operators. That's the reason; are you expecting

some other reason?

> Or is there a better way to do this?

from the built-in comparison operators do you want?

--

\ “I went over to the neighbor's and asked to borrow a cup of |

`\ salt. ‘What are you making?’ ‘A salt lick.’” —Steven Wright |

_o__) |

Ben Finney

Mar 19, 2015, 10:57:26 PM3/19/15

to

Hi Ben,

When I said "deep", I meant, as in, to an arbitrary level of nesting (i.e. dicts, containing dicts, containing dicts etc) - sorry if I got the terminology wrong.

The two dicts weren't equal by intention - the idea was that a comparison operator would return "False" for those two.

I was just curious why cmp() was phased out (as in, were there cases where "==" was better) - but if functionality they're the same, and it's just a nomenclature thing, that's also fine =).

Finally, so cmp()/== return true/false for comparison - just noticed this which actually prints out diff-style comparisons:

https://pypi.python.org/pypi/datadiff

Cheers,

Victor

> `\ salt. 'What are you making?' 'A salt lick.'" --Steven Wright |

> _o__) |

> Ben Finney

When I said "deep", I meant, as in, to an arbitrary level of nesting (i.e. dicts, containing dicts, containing dicts etc) - sorry if I got the terminology wrong.

The two dicts weren't equal by intention - the idea was that a comparison operator would return "False" for those two.

I was just curious why cmp() was phased out (as in, were there cases where "==" was better) - but if functionality they're the same, and it's just a nomenclature thing, that's also fine =).

Finally, so cmp()/== return true/false for comparison - just noticed this which actually prints out diff-style comparisons:

https://pypi.python.org/pypi/datadiff

Cheers,

Victor

> _o__) |

> Ben Finney

Mar 19, 2015, 11:28:09 PM3/19/15

to

On Friday, March 20, 2015 at 8:27:26 AM UTC+5:30, Victor Hooi wrote:

> Hi Ben,

>

> When I said "deep", I meant, as in, to an arbitrary level of nesting (i.e. dicts, containing dicts, containing dicts etc) - sorry if I got the terminology wrong.

>

> The two dicts weren't equal by intention - the idea was that a comparison operator would return "False" for those two.

>

> I was just curious why cmp() was phased out (as in, were there cases where "==" was better) - but if functionality they're the same, and it's just a nomenclature thing, that's also fine =).

>

> Finally, so cmp()/== return true/false for comparison...
> Hi Ben,

>

> When I said "deep", I meant, as in, to an arbitrary level of nesting (i.e. dicts, containing dicts, containing dicts etc) - sorry if I got the terminology wrong.

>

> The two dicts weren't equal by intention - the idea was that a comparison operator would return "False" for those two.

>

> I was just curious why cmp() was phased out (as in, were there cases where "==" was better) - but if functionality they're the same, and it's just a nomenclature thing, that's also fine =).

>

I guess you are confusing two orthogonal questions:

1. deep vs shallow comparison

2. binary vs trivalent comparison

Numbers (not complex) satisfy the trichotomy law: ie for any 2 numbers x,y:

x < y or x > y o x = y

Unfortunately most logic in programming languages is binary -- true or false

(well Fortran had an arithmetic if -- very unfashionable even in Fortran --

but thats because of the need to goto)

Likewise C's strcmp is trivalent. But a trivalent value is clumsy in a binary logic. Unfortunately no switch statement for <, =, > -- so we are stuck with

if-else-if-else.

All this is unrelated to deep-vs=shallow: cmp is deep, == is deep

In fact what would/could a shallow comparison mean??

Shallow/deep only make sense for copy not comparison

[If at all: Languages like Haskell are explicitly constructed so that the

programmers is disallowed from making that distinction at all]

Mar 19, 2015, 11:35:19 PM3/19/15

to pytho...@python.org

On Fri, Mar 20, 2015 at 2:27 PM, Rustom Mody <rusto...@gmail.com> wrote:

> Numbers (not complex) satisfy the trichotomy law: ie for any 2 numbers x,y:

> x < y or x > y o x = y

Real numbers, yes, and integers in most computer representations, but
> Numbers (not complex) satisfy the trichotomy law: ie for any 2 numbers x,y:

> x < y or x > y o x = y

not IEEE floating point. Be careful of that distinction; we're talking

about computers here, not mythical numbers.

ChrisA

Mar 19, 2015, 11:47:53 PM3/19/15

to

On Friday, March 20, 2015 at 9:05:19 AM UTC+5:30, Chris Angelico wrote:

that is Not-A-Number looks more mythical/mystical/Zen-ish than classical

math numbers.

IOW: float is a poor approximation to ℝ.

Most of us laymen use it because its an approximation that works (kinda).

Numerical analysts earn their keep because of the 'poor'

Not too many people are interested in float independent of ℝ except perhaps

hardware designers who need to design respecting the IEEE standard.

> On Fri, Mar 20, 2015 at 2:27 PM, Rustom Mody wrote:

> > Numbers (not complex) satisfy the trichotomy law: ie for any 2 numbers x,y:

> > x < y or x > y o x = y

>

> Real numbers, yes, and integers in most computer representations, but

> not IEEE floating point. Be careful of that distinction; we're talking

> about computers here, not mythical numbers.

A putative set that claims to be some-kind-of-numbers and has an element
> > Numbers (not complex) satisfy the trichotomy law: ie for any 2 numbers x,y:

> > x < y or x > y o x = y

>

> Real numbers, yes, and integers in most computer representations, but

> not IEEE floating point. Be careful of that distinction; we're talking

> about computers here, not mythical numbers.

that is Not-A-Number looks more mythical/mystical/Zen-ish than classical

math numbers.

IOW: float is a poor approximation to ℝ.

Most of us laymen use it because its an approximation that works (kinda).

Numerical analysts earn their keep because of the 'poor'

Not too many people are interested in float independent of ℝ except perhaps

hardware designers who need to design respecting the IEEE standard.

Mar 20, 2015, 12:36:06 AM3/20/15

to pytho...@python.org

On Fri, Mar 20, 2015 at 2:47 PM, Rustom Mody <rusto...@gmail.com> wrote:

> IOW: float is a poor approximation to ℝ.

Of course it's a poor approximation. That's because real numbers are
> IOW: float is a poor approximation to ℝ.

uncountably infinite, so it's rather tricky to represent and

manipulate them efficiently. IEEE 754 gives us practicality rather

than purity.

ChrisA

Mar 20, 2015, 1:09:48 AM3/20/15

to pytho...@python.org

Chris Angelico <ros...@gmail.com> writes:

> Real numbers, yes […] but not IEEE floating point. Be careful of that

than real numbers? Just what are you saying, man?

--

\ “Pinky, are you pondering what I'm pondering?” “Wuh, I think |

`\ so, Brain, but how will we get three pink flamingos into one |

_o__) pair of Capri pants?” —_Pinky and The Brain_ |

Ben Finney

> Real numbers, yes […] but not IEEE floating point. Be careful of that

> distinction; we're talking about computers here, not mythical numbers.

So real numbers are mythical? IEEE floating point values are more real
than real numbers? Just what are you saying, man?

--

\ “Pinky, are you pondering what I'm pondering?” “Wuh, I think |

`\ so, Brain, but how will we get three pink flamingos into one |

_o__) pair of Capri pants?” —_Pinky and The Brain_ |

Ben Finney

Mar 20, 2015, 1:28:14 AM3/20/15

to pytho...@python.org

On Fri, Mar 20, 2015 at 4:09 PM, Ben Finney <ben+p...@benfinney.id.au> wrote:

> Chris Angelico <ros...@gmail.com> writes:

>

>> Real numbers, yes […] but not IEEE floating point. Be careful of that

>> distinction; we're talking about computers here, not mythical numbers.

>

> So real numbers are mythical? IEEE floating point values are more real

> than real numbers? Just what are you saying, man?

Poor choice of words. Not "mythical", but "theoretical". Comparisons
> Chris Angelico <ros...@gmail.com> writes:

>

>> Real numbers, yes […] but not IEEE floating point. Be careful of that

>> distinction; we're talking about computers here, not mythical numbers.

>

> So real numbers are mythical? IEEE floating point values are more real

> than real numbers? Just what are you saying, man?

in Python are between actual representable numbers, not some

theoretical entire range of reals. Python operators and operations are

not defined in terms of real numbers, but objects.

ChrisA

Mar 20, 2015, 2:36:00 AM3/20/15

to

On Friday 20 March 2015 14:47, Rustom Mody wrote:

> On Friday, March 20, 2015 at 9:05:19 AM UTC+5:30, Chris Angelico wrote:

>> On Fri, Mar 20, 2015 at 2:27 PM, Rustom Mody wrote:

>> > Numbers (not complex) satisfy the trichotomy law: ie for any 2 numbers

>> > x,y: x < y or x > y o x = y

>>

>> Real numbers, yes, and integers in most computer representations, but

>> not IEEE floating point. Be careful of that distinction; we're talking

>> about computers here, not mythical numbers.

>

> A putative set that claims to be some-kind-of-numbers and has an element

> that is Not-A-Number looks more mythical/mystical/Zen-ish than classical

> math numbers.

Forget NANs. The trichotomy of floating point values was violated before the
> On Friday, March 20, 2015 at 9:05:19 AM UTC+5:30, Chris Angelico wrote:

>> On Fri, Mar 20, 2015 at 2:27 PM, Rustom Mody wrote:

>> > Numbers (not complex) satisfy the trichotomy law: ie for any 2 numbers

>> > x,y: x < y or x > y o x = y

>>

>> Real numbers, yes, and integers in most computer representations, but

>> not IEEE floating point. Be careful of that distinction; we're talking

>> about computers here, not mythical numbers.

>

> A putative set that claims to be some-kind-of-numbers and has an element

> that is Not-A-Number looks more mythical/mystical/Zen-ish than classical

> math numbers.

IEEE-754 standard was invented. In fact, IEEE-754 was invented in order to

bring some semblance of order to the unspeakable mess of floating point

arithmetic prior to that. With IEEE-754 floats, at least you can guarantee

that the trichotomy applies to all values apart from NANs.

I cannot remember the details, and I don't have my copy of the Apple

Standard Numerics manual here to look it up, but in the 1970s there was

hardware where the following could fail with Divide By Zero error for

certain values of x:

if x > 0.0:

print 1/x # Divide By Zero here

If you find that hard to believe, it's because you're spoiled by the

astonishing success of IEEE-754 floating point arithmetic.

> IOW: float is a poor approximation to ℝ.

Even *finite* floats violate some of the usual properties of Real numbers:

# Associativity

py> 0.1 + (0.2 + 0.3) == (0.1 + 0.2) + 0.3

False

# Distributivity

py> 1.3*(0.3+0.4) == 1.3*0.3 + 1.3*0.4

False

[Aside: why is my spell checker flagging plus signs as misspelled words?]

And then there's the whole thing where there is an uncountable infinity[1]

of Real numbers, and only a finite number of floats.

> Not too many people are interested in float independent of ℝ except

> perhaps hardware designers who need to design respecting the IEEE

> standard.

[1] Uncountable infinity doesn't just mean that you cannot count them all

because there's an infinite number of them. It means that you cannot

enumerate them all, even in an infinite amount of time.

http://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument

--

Steve

Mar 20, 2015, 8:49:38 AM3/20/15

to

In article <550bbfc1$0$13010$c3e8da3$5496...@news.astraweb.com>,

Standard Apple Numerics Environment (SANE). I think I still have my

copy of the manual somewhere.

> If you find that hard to believe, it's because you're spoiled by the

> astonishing success of IEEE-754 floating point arithmetic.

There's two things we're spoiled by. IEEE-754 is, of course, one of

them. But, more than that, are good math libraries built on top of it.

One of the truly unappreciated things to come out of the early BSD Unix

releases was a C math library written by people who understood (and

worried about) things like accurate FP calculations, rounding, corner

cases, and all that gunk. Sure, I could sit down with a C compiler and

the Wikipedia Gamma function article and code up gamma(). It would work

well enough to get a decent grade as a homework assignment for

Introduction To Programming 101. But, fundamentally, it would be a

piece of crap because I know just enough about numerical programming to

know that I should leave it to the experts.

Steven D'Aprano <steve+comp....@pearwood.info> wrote:

> I cannot remember the details, and I don't have my copy of the Apple

> Standard Numerics manual here to look it up

Amongst the details you don't remember is the correct name :-) It was
> I cannot remember the details, and I don't have my copy of the Apple

> Standard Numerics manual here to look it up

Standard Apple Numerics Environment (SANE). I think I still have my

copy of the manual somewhere.

> If you find that hard to believe, it's because you're spoiled by the

> astonishing success of IEEE-754 floating point arithmetic.

them. But, more than that, are good math libraries built on top of it.

One of the truly unappreciated things to come out of the early BSD Unix

releases was a C math library written by people who understood (and

worried about) things like accurate FP calculations, rounding, corner

cases, and all that gunk. Sure, I could sit down with a C compiler and

the Wikipedia Gamma function article and code up gamma(). It would work

well enough to get a decent grade as a homework assignment for

Introduction To Programming 101. But, fundamentally, it would be a

piece of crap because I know just enough about numerical programming to

know that I should leave it to the experts.

Mar 20, 2015, 9:36:16 AM3/20/15

to

On Friday, March 20, 2015 at 10:39:48 AM UTC+5:30, Ben Finney wrote:

years who have said more or less exactly what Chris is saying: "The set ℝ is

nonsense." In fact these fights are the very reason that CS came

into existence.

1880s: Kronecker and his student Cantor were working together when Cantor

started off on 'set-theory'

For a while Cantor was bemused with the direction of his (favorite!) student.

But he soon found it unacceptable and started disagreeing with Cantor, first

privately then publicly.

His famous statement dates from this disagreement:

"The Good Lord made the Natural numbers. All the rest is the work of man"

He was specifically implying that things like ℝ are just nonsense.

At that time almost all mathematicians were Kroneckerians.

Cantor ended up in an 'institution.'

Other famous statements of that time were from Gordon who said:

"This sir, is not mathematics, its theology"

[referring to a standard construction of set theory called

Axiom of choice]

A couple of generations later things had turned.

Mainstream mathematicians all accepted set theory, except a few trouble-makers

called constructivists.

The constructivists said that the other mathematicians who they called

'Platonist' which derisively signified mystic after the cave allegory of Plato

http://dwildepress.net/critica/mystic4.html were being ridiculously loose and

sloppy in talking about infinity as though it exists.

Hilbert -- the head of the classicists/platonists -- was angry with this charge,

made the famous statement: "Nobody will drive us out of the paradise created by Cantor."

And (in what he thought was super-cleverness) formulated the Entscheidung problem:

If the questions about mathematics could be finitistically (ie mechanically)

solved, then the constructivists' charge (of mysticism) could be kicked out

But then Gödel showed that the dream of a complete and consistent math was a pipe-dream.

A job that Turing completed by showing the unsolvability of the Entscheidung problem.

http://www.philocomp.net/home/hilbert.htm

From a math/logic pov these were all disastrous results.

But a side-effect of this disaster was that something called a 'universal-

machine' got invented…

viz a computer

An entertaining and longer account:

http://research.microsoft.com/en-us/um/people/gurevich/opera/123.pdf

Particularly note the Polya-Weyl bet

==================================

tl;dr "Real numbers are not real" is an argument at the creation of CS.

To find and work with a set that

- Does not have the nonsensical behaviors of floats

- Is not nonsensical in the sense of the constructivists' objections

is really a bit of an open problem:

http://www.encyclopediaofmath.org/index.php/Constructive_real_number

> Chris Angelico writes:

>

> > Real numbers, yes […] but not IEEE floating point. Be careful of that

> > distinction; we're talking about computers here, not mythical numbers.

>

> So real numbers are mythical? IEEE floating point values are more real

> than real numbers? Just what are you saying, man?

In all fairness to Chris, there have been notable mathematicians in the last 100
>

> > Real numbers, yes […] but not IEEE floating point. Be careful of that

> > distinction; we're talking about computers here, not mythical numbers.

>

> So real numbers are mythical? IEEE floating point values are more real

> than real numbers? Just what are you saying, man?

years who have said more or less exactly what Chris is saying: "The set ℝ is

nonsense." In fact these fights are the very reason that CS came

into existence.

1880s: Kronecker and his student Cantor were working together when Cantor

started off on 'set-theory'

For a while Cantor was bemused with the direction of his (favorite!) student.

But he soon found it unacceptable and started disagreeing with Cantor, first

privately then publicly.

His famous statement dates from this disagreement:

"The Good Lord made the Natural numbers. All the rest is the work of man"

He was specifically implying that things like ℝ are just nonsense.

At that time almost all mathematicians were Kroneckerians.

Cantor ended up in an 'institution.'

Other famous statements of that time were from Gordon who said:

"This sir, is not mathematics, its theology"

[referring to a standard construction of set theory called

Axiom of choice]

A couple of generations later things had turned.

Mainstream mathematicians all accepted set theory, except a few trouble-makers

called constructivists.

The constructivists said that the other mathematicians who they called

'Platonist' which derisively signified mystic after the cave allegory of Plato

http://dwildepress.net/critica/mystic4.html were being ridiculously loose and

sloppy in talking about infinity as though it exists.

Hilbert -- the head of the classicists/platonists -- was angry with this charge,

made the famous statement: "Nobody will drive us out of the paradise created by Cantor."

And (in what he thought was super-cleverness) formulated the Entscheidung problem:

If the questions about mathematics could be finitistically (ie mechanically)

solved, then the constructivists' charge (of mysticism) could be kicked out

But then Gödel showed that the dream of a complete and consistent math was a pipe-dream.

A job that Turing completed by showing the unsolvability of the Entscheidung problem.

http://www.philocomp.net/home/hilbert.htm

From a math/logic pov these were all disastrous results.

But a side-effect of this disaster was that something called a 'universal-

machine' got invented…

viz a computer

An entertaining and longer account:

http://research.microsoft.com/en-us/um/people/gurevich/opera/123.pdf

Particularly note the Polya-Weyl bet

==================================

tl;dr "Real numbers are not real" is an argument at the creation of CS.

To find and work with a set that

- Does not have the nonsensical behaviors of floats

- Is not nonsensical in the sense of the constructivists' objections

is really a bit of an open problem:

http://www.encyclopediaofmath.org/index.php/Constructive_real_number

Mar 20, 2015, 9:46:24 AM3/20/15

to

On Friday, March 20, 2015 at 12:06:00 PM UTC+5:30, Steven D'Aprano wrote:

> On Friday 20 March 2015 14:47, Rustom Mody wrote:

> > Not too many people are interested in float independent of ℝ except

> > perhaps hardware designers who need to design respecting the IEEE

> > standard.

>

> I don't understand what you are trying to say here.

The reason for creating float (IEEE or previous hacks) is that people want to do
> On Friday 20 March 2015 14:47, Rustom Mody wrote:

> > Not too many people are interested in float independent of ℝ except

> > perhaps hardware designers who need to design respecting the IEEE

> > standard.

>

> I don't understand what you are trying to say here.

ℝ-ish stuff.

The only justification for float is that it is consistent with ℝ

[Is it? Aint it? Depends on how you squint]¹

Nobody wants to do float for the sake of float.

The only parties that (presumably) want to do "pure" float (ie ignore ℝ completely)

are the h/w-guys who need to get an "IEEE-compliant" stamp.

=============

¹ Even the IEEE standard writers need to do a tight-rope walk between

- respecting ℝ

- making a spec that is 'hardware-able"

- And will not have us software-guys screaming

Ie There is no one (I can think of) except hw engineers who would care to think

float without minding ℝ.

Mar 20, 2015, 10:10:31 AM3/20/15

to

Rustom Mody <rusto...@gmail.com>:

> In all fairness to Chris, there have been notable mathematicians in

> the last 100 years who have said more or less exactly what Chris is

> saying: "The set ℝ is nonsense."

Intuitionism is nonsense.

> In fact these fights are the very reason that CS came into existence.

I trace it to Hilbert's program.

Marko

> In all fairness to Chris, there have been notable mathematicians in

> the last 100 years who have said more or less exactly what Chris is

> saying: "The set ℝ is nonsense."

> In fact these fights are the very reason that CS came into existence.

Marko

Mar 21, 2015, 2:02:12 AM3/21/15

to

On Friday, March 20, 2015 at 7:40:31 PM UTC+5:30, Marko Rauhamaa wrote:

> Rustom Mody:

On second thoughts Ive misplaced my boxing gloves.

[And my legs are more reliable than my arms..........

............

]

>

> > In fact these fights are the very reason that CS came into existence.

>

> I trace it to Hilbert's program.

And on third thoughts:

What was Hilbert's program in defence against?

Seriously:

I dont take a side on these matters [Or which side do you see me on?]

However I am talking some historical facts, viz:

Because some nuts did the 20th century equivalent of:

"Break each others' heads about how many angels can dance on the head of a pin"

therefore much of the world around us exists as it does (for better or worse)

including my (and I guess your) degree and job.

> Rustom Mody:

>

> > In all fairness to Chris, there have been notable mathematicians in

> > the last 100 years who have said more or less exactly what Chris is

> > saying: "The set ℝ is nonsense."

>

> Intuitionism is nonsense.

You are challenging me?!?! Come on lets have it out!!
> > In all fairness to Chris, there have been notable mathematicians in

> > the last 100 years who have said more or less exactly what Chris is

> > saying: "The set ℝ is nonsense."

>

> Intuitionism is nonsense.

On second thoughts Ive misplaced my boxing gloves.

[And my legs are more reliable than my arms..........

............

]

>

> > In fact these fights are the very reason that CS came into existence.

>

> I trace it to Hilbert's program.

What was Hilbert's program in defence against?

Seriously:

I dont take a side on these matters [Or which side do you see me on?]

However I am talking some historical facts, viz:

Because some nuts did the 20th century equivalent of:

"Break each others' heads about how many angels can dance on the head of a pin"

therefore much of the world around us exists as it does (for better or worse)

including my (and I guess your) degree and job.

Mar 21, 2015, 2:28:43 AM3/21/15

to

Rustom Mody <rusto...@gmail.com>:

> However I am talking some historical facts, viz: Because some nuts did

> the 20th century equivalent of: "Break each others' heads about how

> many angels can dance on the head of a pin" therefore much of the

> world around us exists as it does (for better or worse) including my

> (and I guess your) degree and job.

The deep philosophical questions around the year 1900 in both

mathematics and physics were left embarrassingly open. The way out was

to stop caring.

Mathematics gave up on defining numbers and settled with a standard

chain of beads:

0 = {}

1 = { 0 }

2 = { 0, 1 }

3 = { 0, 1, 2 }

<URL: http://en.wikipedia.org/wiki/Set-theoretic_definition_o

f_natural_numbers#Contemporary_standard>

Marko

> However I am talking some historical facts, viz: Because some nuts did

> the 20th century equivalent of: "Break each others' heads about how

> many angels can dance on the head of a pin" therefore much of the

> world around us exists as it does (for better or worse) including my

> (and I guess your) degree and job.

mathematics and physics were left embarrassingly open. The way out was

to stop caring.

Mathematics gave up on defining numbers and settled with a standard

chain of beads:

0 = {}

1 = { 0 }

2 = { 0, 1 }

3 = { 0, 1, 2 }

<URL: http://en.wikipedia.org/wiki/Set-theoretic_definition_o

f_natural_numbers#Contemporary_standard>

Marko

Mar 31, 2015, 11:54:10 PM3/31/15

to

On Saturday, March 21, 2015 at 11:58:43 AM UTC+5:30, Marko Rauhamaa wrote:

> Rustom Mody :

>

> Rustom Mody :

>

> > However I am talking some historical facts, viz: Because some nuts did

> > the 20th century equivalent of: "Break each others' heads about how

> > many angels can dance on the head of a pin" therefore much of the

> > world around us exists as it does (for better or worse) including my

> > (and I guess your) degree and job.

>

> The deep philosophical questions around the year 1900 in both

> mathematics and physics were left embarrassingly open. The way out was

> to stop caring.

Ive collected some of the above points and some from earlier threads here:
> > the 20th century equivalent of: "Break each others' heads about how

> > many angels can dance on the head of a pin" therefore much of the

> > world around us exists as it does (for better or worse) including my

> > (and I guess your) degree and job.

>

> The deep philosophical questions around the year 1900 in both

> mathematics and physics were left embarrassingly open. The way out was

> to stop caring.

http://blog.languager.org/2015/03/cs-history-0.html

Anyone un-mentioned there that wants to figure -- or conversely :-) --

just give me the say-so.

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