Mathematics is less precise than Programming

[jayjacobus]

Aside from the fact that "precision" is not precisely definable...

“Mathematics is much less formally complete and precise than computer programs.” — William Thurston, 1994
"Math is less precise than Programming." --Cody Roux (echoed by Andrej Bauer), 2021

Are you sure?

Are you sure about that?

How can you be sure?

[Skepdick]

Are you sure?

Are you sure about that?

How can you be sure?

Trivial empirical observation.

Take your favourite theorem from contemporary Mathematics and prove it using a proof assistant.

Observe the level of detail missing from informal proofs.
Observe the leaps of thought, assumptions and axioms left implicit in informal proofs.
Observe the incompleteness of informal mathematics as you have to express/communicate your thought process to a computer.

[attofishpi]

Aside from the fact that "precision" is not precisely definable...

“Mathematics is much less formally complete and precise than computer programs.” — William Thurston, 1994

It's always important to understand, ironically perhaps ..the "con_text" ..context of what Bill was suggesting:-

If he is stating "computer programs" as in, past tense - then absolutely - the program is now working specifically to the how the programmer left it, compiled for machine processing, bugs and all. So the computer program is precise, since the code language used was compiled...it is constrained to that compiler spec, it is precise.

Maths on the other hand, is in a continual progression until the point in time when a phycisist can use it and finally bangs heads with 'God'..

"Math is less precise than Programming." --Cody Roux (echoed by Andrej Bauer), 2021

Maths is clearly open to a far wider scope than the preciseness of what has been programmed into a binary machine.

[Skepdick]

It's always important to understand, ironically perhaps ..the "con_text" ..context of what Bill was suggesting:-

If he is stating "computer programs" as in, past tense - then absolutely - the program is now working specifically to the how the programmer left it, compiled for machine processing, bugs and all. So the computer program is precise, since the code language used was compiled...it is constrained to that compiler spec, it is precise.

Maths on the other hand, is in a continual progression until the point in time when a phycisist can use it and finally bangs heads with 'God'..

Maths is clearly open to a far wider scope than the preciseness of what has been programmed into a binary machine.

You are doing all of your reasoning in the "con_text" of a binary machine. You have a target platform in mind. An "assembly" language for which you are compiling (reducing) a set of logical operators which you are pre-supposing. But all of that stuff reduces to some silicon implementing a function.

But what is a Boolean function? What is the minimum set of functions you need in order to be able to derrive Boolean logic?
One possible answer is Sheffer stroke; or its dual: NOR.

The "continual progression" of Mathematics you are speaking about is called Continuation Passing Style. You can express ANY mathematical truth as a (very very very) long Continuation.

And obviously, when you are expressing Continuations you are talking about control and control-flow. It's one stupid mistake from projecting your desire to exercise control onto the universe.

[attofishpi]

It's always important to understand, ironically perhaps ..the "con_text" ..context of what Bill was suggesting:-

If he is stating "computer programs" as in, past tense - then absolutely - the program is now working specifically to the how the programmer left it, compiled for machine processing, bugs and all. So the computer program is precise, since the code language used was compiled...it is constrained to that compiler spec, it is precise.

Maths on the other hand, is in a continual progression until the point in time when a phycisist can use it and finally bangs heads with 'God'..

Maths is clearly open to a far wider scope than the preciseness of what has been programmed into a binary machine.

You are doing all of your reasoning in the "con_text" of a binary machine. You have a target platform in mind. An "assembly" language for which you are compiling (reducing) a set of logical operators which you are pre-supposing. But all of that stuff reduces to some silicon implementing a function.

But what is a Boolean function? What is the minimum set of functions you need in order to be able to derrive Boolean logic?
One possible answer is Sheffer stroke; or its dual: NOR.

..sorry, but explain within the thread - i'm not going to traverse the internet to comprehend any point attempting to be made here.

A boolean function returns a binary result. What is your point? - as I alluded to, it is precise.

The "continual progression" of Mathematics you are speaking about is called Continuation Passing Style. You can express ANY mathematical truth as a (very very very) long Continuation.

And obviously, when you are expressing Continuations you are talking about control and control-flow. It's one stupid mistake from projecting your desire to exercise control onto the universe.

Skeppy, skeppy...what have you been smoking tonight---a BIT of this dude perhaps:-

..in other words, me no comprende!

[Skepdick]

A boolean function returns a binary result. What is your point? - as I alluded to, it is precise.

My point is you are ignoring the input of the function and only focusing on the output.

The NOT function takes one Boolean and produces one Boolean.
The OR function takes a pair of Booleans and produces one Boolean.
The function that is your head takes as input an English squestions and produces Booleans.

The difference between an OR function and your head is.... huuuuge.

[attofishpi]

A boolean function returns a binary result. What is your point? - as I alluded to, it is precise.

My point is you are ignoring the input of the function and only focusing on the output.

The NOT function takes one Boolean and produces one Boolean.
The OR function takes a pair of Booleans and produces one Boolean.
The function that is your head takes as input an English squestions and produces Booleans.

The difference between an OR function and your head is.... huuuuge.

lol

You need to understand your thread title is "Mathematics is less precise than Programming"

..the statement is wide open to refutation, and rather simply. Eg. A shit programmer is going to be 'non' precise.

[Skepdick]

lol

You need to understand your thread title is "Mathematics is less precise than Programming"

..the statement is wide open to refutation, and rather simply. Eg. A shit programmer is going to be 'non' precise.

I won't accept any statement/argument as refutation - words mean nothing against living proof.

Have you ever used a languge so strict the compiler is akin to Gandalf fighting the Balrog screaming "You shall not pass!".

Pick up a proof assistant and try be a shit programmer - it mandates a level of verbosity, explicitness and strictness even the most disciplined programers aren't used to! If you are a shit programmer you won't succeed in making the proof assistant cooperate with you.

[attofishpi]

lol

You need to understand your thread title is "Mathematics is less precise than Programming"

..the statement is wide open to refutation, and rather simply. Eg. A shit programmer is going to be 'non' precise.

I won't accept any statement/argument as refutation - words mean nothing against living proof.

Have you ever used a languge so strict the compiler is akin to Gandalf fighting the Balrog screaming "You shall not pass!".

lol, maybe.

Pick up a proof assistant and try be a shit programmer - it mandates a level of verbosity, explicitness and strictness even the most disciplined programers aren't used to! If you are a shit programmer you won't succeed in making the proof assistant cooperate with you.

Not sure what you mean by a "proof assistant" - but once that code is compiled - at runtime, data goes in and eventually inaccuracies come into effect - so, shit programmer, shit testers = unprecise result.

[Skepdick]

Not sure what you mean by a "proof assistant" - but once that code is compiled - at runtime, data goes in and eventually inaccuracies come into effect - so, shit programmer, shit testers = unprecise result.

For the purpose of the discussion think of a "proof assistant" as an asshole-compiler.

Yes, once the code is compiled.... IF you can compile it. Proof assistant says "your code is shit! Try again."

[Eodnhoj7]

"Aside from the fact that "precision" is not precisely definable..." renders the arguments invalid given the core term from which the arguments expand from is undefined thus equivocal to anything. One cannot say mathematics is less precise than programming if "precision" can equivocate to anything.

[Skepdick]

"Aside from the fact that "precision" is not precisely definable..." renders the arguments invalid given the core term from which the arguments expand from is undefined thus equivocal to anything. One cannot say mathematics is less precise than programming if "precision" can equivocate to anything.

Idiot. The absence of a definition doesn't render precision is unrecognizable.

Which of these two requests is more precise?

Please bring me a teacup from the kitchen.
Please bring me the yellow ceramic teacup with the cat pattern and red handle from the kitchen.

But lets not stop there, while you are being stupid, The word "definition" is undefined thus equivocal to anything.

[Eodnhoj7]

"Aside from the fact that "precision" is not precisely definable..." renders the arguments invalid given the core term from which the arguments expand from is undefined thus equivocal to anything. One cannot say mathematics is less precise than programming if "precision" can equivocate to anything.

Idiot. The absence of a definition doesn't render precision is unrecognizable.

Which of these two requests is more precise?

Please bring me a teacup from the kitchen.
Please bring me the yellow ceramic teacup with the cat pattern and red handle from the kitchen.

But lets not stop there, while you are being stupid, The word "definition" is undefined thus equivocal to anything.

Your use of the word "idiot" is a projection of your own inadequacies in argumentation.

Your words not mine: "Aside from the fact that "precision" is not precisely definable..."

I never said precision is not definable....you did and then built an argument around precision.

You contradict yourself in one respect while dually twisting what I wrote....

Dually your grounding for what constitutes precision lies in intuition, not logic, about which phrase is more precise. You have no definition of precision other than a subjective hunch about what "feels" more appropriate. One can feel just about anything and this does not render a point valid or even moot...it is just a feeling. In observing the differences between sentence 1 and 2 of your examples one may equally feel 1 is more precise as it is simpler and more general because it is covering a multitude of phenomenon. Sentence 2 may be felt as less precise because the pedantry (ie too much detail) lends itself to obscurity. Precision is thus subject not only to the angle of observation but it dependent upon the simplest and most unified way of expressing a phenomenon.

I know what precision is, it is definition (and definition is the observation of relations (the observation of relations is the manifestation of parts (the manifestation of parts is division (the manifestation of division is opposition))) etc.....the definitions go on until eventually they loop back.

[Skepdick]

Your use of the word "idiot" is a projection of your own inadequacies in argumentation.

No, it isn't. It's an objective assertion about your argumentation strategy based on evidence.

Your words not mine: "Aside from the fact that "precision" is not precisely definable..."

I never said precision is not definable....you did and then built an argument around precision.

Q.E.D You struggle with basic reading comprehension. I didn't say precision is not definable.

I said precision is not precisely definable.

You misrepresented my words so they are easier to attack (which is a strawman argument).

That is why you are an idiot.

y̶o̶u̶ I contradict y̶o̶u̶r̶s̶e̶l̶f̶ myself in one respect while dually twisting what I̶ you wrote....

Fixed if for you.

Dually your grounding for what constitutes precision lies in intuition, not logic, about which phrase is more precise.

It lies in empiricism. Given two phrases (A and B) you have three possible relations between them.

1. Phrase A is more precise than B: Precision(A) > Precision(B)
2. Phrase B is more precise than A: Precision(B) > Precision(A)
3. Phrase A and B are equally precise: Precision(A) = Precision(B)

You have no definition of precision other than a subjective hunch about what "feels" more appropriate.

I have a subjective judgment/assertion based on the objective properties of the two expressions on which one is more precise.

One can feel just about anything and this does not render a point valid or even moot...it is just a feeling.

What's the difference between a "feeling" and "just a feeling". What does "just" feel like?

In observing the differences between sentence 1 and 2 of your examples one may equally feel 1 is more precise as it is simpler and more general because it is covering a multitude of phenomenon.

Which is precisely why it's not precise - it's ambiguous.

Sentence 2 may be felt as less precise because the pedantry (ie too much detail) lends itself to obscurity.

And yet you know precisely which cup of tea I am talking about.

Precision is thus subject not only to the angle of observation but it dependent upon the simplest and most unified way of expressing a phenomenon.

See! You agree with me. Expressing A phenomenon - singular. Not phenomena - plural!

I know what precision is, it is definition (and definition is the observation of relations (the observation of relations is the manifestation of parts (the manifestation of parts is division (the manifestation of division is opposition))) etc.....the definitions go on until eventually they loop back.

That's an imprecise definition of "definition".

Definitions never loop back. Definitions are recursive. It's definitions all the way down.

[RCSaunders]

Aside from the fact that "precision" is not precisely definable...

“Mathematics is much less formally complete and precise than computer programs.” — William Thurston, 1994
"Math is less precise than Programming." --Cody Roux (echoed by Andrej Bauer), 2021

Computer programs are only more precise if one is only referring to the limits of a particular programming language. No digital processor is capable of either the precision or accuracy of mathematics itself.

There is, first of all, the built in problem of not being able to represent all real numbers. "Squeezing infinitely many real numbers into a finite number of bits requires an approximate representation. Although there are infinitely many integers, in most programs the result of integer computations can be stored in 32 bits, (or these days, 64 bits).

Since most scientific mathematical operations use floating point math, there is the ubiquitous, "rounding problem."

One distinguishing feature that separates traditional computer science from scientific computing is its use of discrete mathematics (0s and 1s) instead of continuous mathematics and calculus.

Arithmetic with integers is exact, unless the answer is outside the range of integers that can be represented (overflow). In contrast, floating point arithmetic is not exact since some real numbers require an infinite number of digits to be represented, e.g., the mathematical constants e and π and 1/3.

I think you are confusing precision and accuracy:

Precision vs. accuracy. Precision = tightness of specification. Accuracy = correctness. Do not confuse precision with accuracy. 3.133333333 is an estimate of the mathematical constant π which is specified with 10 decimal digits of precision, but it only has two decimal digits of accuracy.