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Re: Definition of an Algorithm

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Rick C <gnuarm.deletethisbit@gmail.com> writes:
> Much of the engineering and computer science I learned in college was
> taught like math.  Terms were defined, in order to know what is being
> said.  Look at math.  It's as much about the definitions as the
> various rules.  

I believe electrical engineers frequently use the Dirac delta function,
whose value is infinite at x=0 and zero everywhere else.  When you
convolve it with another function, you get back the function that you
convolved with.  But by standard mathematical formalism, there is no
such function as the Dirac delta.  That didn't stop physicists and
engineers from using it anyway, starting around the 1920s(?).

A rigorous mathematical formalism for such "functions" was not developed
until the 1950s, called "generalized functions" or "Schwartz
distributions".  I'd be very surprised if any engineers ever study that.
They just use the Dirac delta without worrying too much about
mathematical rigor, and as long as they don't go too crazy, it acts the
way they expect it to.

> If a term like algorithm is not well defined, then I won't use it in
> engineering unless I define it first.

Engineering practice by others has not been so careful.  You might find
a "definition" of the Dirac delta in an engineering book, but if you
look closely at the mathematical details, it will be hand-wavy or have
gaps.  They want mostly to agree on the features that they rely on, and
to not worry about the corner cases that they don't use.

Here's a definitional problem for you.  Let's say you flip a coin and
then cover it with your hand, so you don't see how it came up.  What is
the probability that it came up heads?  One notion is that the
probability is obviously 50%, assuming it was a fair coin.  A
conflicting notion is that it is obviously not 50%: the coin has already
been flipped and has landed, so it is either definitely heads or else it
is definitely tails.  That is, the probability is either 100% or 0%, and
you simply don't know which.

Those two notions of probability are claled Bayesianism and frequentism.
Philosophers have been arguing about them for 100s of years and they
still haven't stopped.  Mathematicians deal with this by treating
probability as a topic in analysis involving measure spaces of yada
yada.  But a philosopher might say instead that probability is a
sub-topic in the part of philosophy that deals with the nature of
knowledge, and then the Bayesian view is simply a scheme for saying how
strongly you believe a given proposition.

What I'm saying here is that probability, like algorithm, is another one
of those terms that doesn't have a single, universally accepted,
rigorous definition, but that doesn't stop it from being important
anyway.  

Re probability, this article is pretty good:

https://ncatlab.org/nlab/show/Is+probability+theory+a+branch+of+mathematics%3F

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Definition of an Algorithm Rick C <gnuarm.deletethisbit@gmail.com> - 2022-11-01 20:04 -0700
  Re: Definition of an Algorithm Paul Rubin <no.email@nospam.invalid> - 2022-11-01 22:18 -0700
    Re: Definition of an Algorithm Rick C <gnuarm.deletethisbit@gmail.com> - 2022-11-01 22:42 -0700
      Re: Definition of an Algorithm David Brown <david.brown@hesbynett.no> - 2022-11-02 09:17 +0100
        Re: Definition of an Algorithm Rick C <gnuarm.deletethisbit@gmail.com> - 2022-11-02 11:37 -0700
          Re: Definition of an Algorithm Paul Rubin <no.email@nospam.invalid> - 2022-11-02 15:56 -0700
          Re: Definition of an Algorithm David Brown <david.brown@hesbynett.no> - 2022-11-03 09:56 +0100
          Re: Definition of an Algorithm George Neuner <gneuner2@comcast.net> - 2022-11-03 08:41 -0400
      Re: Definition of an Algorithm Paul Rubin <no.email@nospam.invalid> - 2022-11-02 14:12 -0700
  Re: Definition of an Algorithm David Brown <david.brown@hesbynett.no> - 2022-11-02 09:49 +0100
    Re: Definition of an Algorithm Rick C <gnuarm.deletethisbit@gmail.com> - 2022-11-02 11:45 -0700
      Re: Definition of an Algorithm Dimiter_Popoff <dp@tgi-sci.com> - 2022-11-02 21:29 +0200
        Re: Definition of an Algorithm Rick C <gnuarm.deletethisbit@gmail.com> - 2022-11-02 15:26 -0700
          Re: Definition of an Algorithm David Brown <david.brown@hesbynett.no> - 2022-11-03 10:25 +0100
      Re: Definition of an Algorithm Niklas Holsti <niklas.holsti@tidorum.invalid> - 2022-11-02 21:53 +0200
        Re: Definition of an Algorithm David Brown <david.brown@hesbynett.no> - 2022-11-02 21:53 +0100
        Re: Definition of an Algorithm Rick C <gnuarm.deletethisbit@gmail.com> - 2022-11-02 15:30 -0700
      Re: Definition of an Algorithm David Brown <david.brown@hesbynett.no> - 2022-11-02 22:12 +0100
      Re: Definition of an Algorithm Paul Rubin <no.email@nospam.invalid> - 2022-11-02 14:45 -0700

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