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Topic: all of math is just addition and multiplication
Replies: 36   Last Post: Jun 17, 2013 6:04 PM

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GS Chandy

Posts: 7,218
From: Hyderabad, Mumbai/Bangalore, India
Registered: 9/29/05
Re: all of math is just addition and multiplication
Posted: Jun 12, 2013 2:43 PM
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Responding to Robert Hansen's (RH's) post of Jun 12, 2013 5:11 PM (pasted below my signature for ready reference:

1. Joe Niederberger's thought experiment:
QUOTE
Here's a thought experiment, maybe it will work for you, maybe not. Suppose an extra-terrestrial intelligence examines one of our computers, and suppose it is a completely different technology from anything they've seen. Furthermore, let's grant them supreme knowledge and competence in measuring and analyzing electro-magnetic and quantum phenomenon. So they could see all the voltages flying around, the whole fantastic dance at quite a closeup and complete viewpoint.

Now uppose they don't have a vocabulary and mental concepts that includes the likes of, RAM, CPU, register, ALU, program, etc. etc. etc. Well then, this intricate mechanism may be a complete mystery to them, even though in principle they have complete physical knowledge of it. Those higher level concepts serve as a key to unlocking the meaning of the device, much like a Rosetta stone. Without those concepts further understanding may be completely blocked. Its not as if complete physical knowledge serves as any kind of automatic gateway to obtaining these higher level concepts.

So too with nervous systems.
UNQUOTE

In response to the above, RH had claimed that Joe Niederberger's thought experiment above "described the development of mathematics" (call this 'Claim A'). which claim I had questioned.

2. I believe your explanation below does not actually provide justification for your 'Claim A' (to the effect that the 'thought experiment' suggested describes the development of math: in my opinion it does not do this at all).

If justification there is, it is, I believe, extremely tenuous. I'm sorry I don't see it at all.

3. I do, however, agree with some of the individual statements in the 'justification': one such is "Primarily, we do not have in our mental possession, the paradigm on which natural intelligence is based."

4. It all appears to me somewhat similar to the fundamentalist Christian 'proof' of the existence of God, or the fundamentalist atheist's 'proof' of the non-existence of such a being.

GSC
RH's post of Jun 12, 2013 5:11 PM:
>
> On Jun 12, 2013, at 1:21 AM, GS Chandy
> <gs_chandy@yahoo.com> wrote:
>

> > I disagree with you. I'd be grateful if you could
> explain as to just how that 'thought-experiment'
> suggested by Joe Niederberger describes, in your
> view, "the development of mathematics".
>
> Joe described the process of reverse engineering an
> alien technology by studying its construction and
> behavior. That is how mathematics is and was
> developed, often simultaneously by separate cultures.
> That is how all knowing is developed. You study and
> note recurring themes and when you have enough of
> those themes you form a theory and as you form a
> theory you develop an ontology to label the elements
> of that theory.
>
> Back to Joe's example...
>
> A computer is an electronic device and I assume from
> his description that the beings examining the
> "computer" at least understood electricity and
> magnetism. So rather than complicate this with
> aliens, let's just suppose that we take a computer
> back in time and show it to "radio" engineers of the
> early 1900's. Let's also assume that this is a vacuum
> tube computer so as not to complicate the experiment
> with not only a technology gap but a physics gap as
> well. If you know anything about the technology of
> computers and their development, vacuum tube
> computers were every "bit" a computer as is the PC
> right in front of you. The same principles, the same
> components, but different physics.
>
> So, how long would it take the radio engineers to
> become computer engineers? What is it that
> differentiates a vacuum tube computer from a vacuum
> tube radio? The answer is discrete logic versus
> analog logic. In other words, once they recognize
> that these tubes and components have been arranged
> around scenarios involving "on and off" they will be
> in. That is not a remarkable paradigm shift for radio
> engineers of the early 1900's because the telegraph
> engineers of the mid 1800's had already been there
> and done that. In fact, those same telegraph
> engineers had already established bit encoding
> patterns with the same purpose as the encoding
> patterns used by your hard drive. I guess necessity
> is the mother of invention. Recognizing that this
> computer device is "digital" is the key but it isn't
> the whole story. Now that they understood the
> paradigm (digital) they would have to reverse
> engineer this particular application of that paradigm
> (a computer). I am not saying that this would be a no
> brainer but it would progress fast enough. The math
> for binary arithmetic was already established, since
> the 1600's and boolean logic in the 1800's. However,
> actually combining that with circuits didn't come
> till Claude Shannon published the following paper in
> 1937...
>
> http://dspace.mit.edu/bitstream/handle/1721.1/11173/34
> 541425.pdf?sequence=1
>
> And then, as Joe mentioned, there is the system
> (block) organization to contend with. Ram here and
> cpu over there and so on. But I don't think any of
> this would stump the radio engineers because they had
> already established complexity and blocks in their
> own work with RF equipment. For Joe's experiment to
> work I would say that we would have to send this
> vacuum tube computer back as far as the 1500's. That
> would I think be far enough back such that the
> technology would be truly out of the reach of the
> engineers of the day. They would have to put this
> vacuum tube curiosity on the shelf for probably 200
> years. However, we would probably have computers in
> the 1800's rather than the 1900's. Actually, the
> thing would probably have been lost in a fire long
> before that. (Things getting lost in fires appears to
> be popular back then).
>
> And that is where we are with reverse engineering
> people. Primarily, we do not have in our mental
> possession, the paradigm on which natural
> intelligence is based. It isn't analog and it isn't
> digital. Even if we understand how a neuron works we
> certainly don't understand this application of them.
> Not only do we lack a pivotal paper like Shannon's,
> we don't even have the arithmetic for such a paper to
> be based on. My focus has been on the arithmetic and
> the paradigm on which natural intelligence is based,
> not the science. I also don't call it "information
> processing" because I think that term applies to a
> different paradigm.
>
> Back to math...
>
> An example of a paradigm in mathematics is the
> concept of limits. That isn't the only paradigm that
> can lead to calculus and "digital" wasn't the only
> paradigm that could lead to computers, but when the
> dust settled those were the paradigms. If I handed
> you the paradigm of limits I have essentially handed
> you calculus. That doesn't mean I gave you a book of
> calculus, but over time, starting there, you will
> create a book of calculus. But it would be quick, if
> the time was right. Just like, once we caught on to
> "digital" we rewrote electronics in just one decade.
> But no one was handed the paradigm of limits. What we
> had were problems of calculus in nature and
> mathematicians had to illicit a paradigm from them.
> And yes, it took 1000's of years and other problems
> are still beyond our current reach. Joe's process
> continues.
>
> Bob Hansen
>



Message was edited by: GS Chandy


Date Subject Author
6/3/13
Read all of math is just addition and multiplication
Donald Sauter
6/4/13
Read Re: all of math is just addition and multiplication
Dave L. Renfro
6/5/13
Read Re: all of math is just addition and multiplication
Robert Hansen
6/4/13
Read Re: all of math is just addition and multiplication
kirby urner
6/5/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/5/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/6/13
Read Re: all of math is just addition and multiplication
Michael de Villiers
6/6/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/6/13
Read Re: all of math is just addition and multiplication
kirby urner
6/7/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/7/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/7/13
Read Re: all of math is just addition and multiplication
Louis Talman
6/8/13
Read Re: all of math is just addition and multiplication
Robert Hansen
6/7/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/8/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/8/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/8/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/8/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/8/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/8/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/9/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/14/13
Read Re: all of math is just addition and multiplication
kirby urner
6/9/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/10/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/10/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/11/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/11/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/11/13
Read Re: all of math is just addition and multiplication
Robert Hansen
6/12/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/12/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/12/13
Read Re: all of math is just addition and multiplication
Robert Hansen
6/12/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/13/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/13/13
Read Re: all of math is just addition and multiplication
Joe Niederberger
6/13/13
Read Re: all of math is just addition and multiplication
GS Chandy
6/17/13
Read Re: all of math is just addition and multiplication
Donald Sauter
6/17/13
Read Re: all of math is just addition and multiplication
Donald Sauter

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