## It’s been a while

Wow … almost 4 years … Well I am back … at least for the moment. Diderot on my mind.

## 23 years ago

I started an experiment called the Journal of Ideas. This week I scanned the contents into PDFs and added it. I will also be using the omega23 website to archive various speculative pieces on knowledge exploration and more.

## New blog to watch

SK Gupta just launched a fascinating new blog, Pursuit of Unorthodox Ideas.

Check it out … first entries include:

- Eight Innovations that are changing the manufacturing industry
- Can open source hardware movement be used to realize low cost educational robots?
- Are you ready to receive emails from your refrigerator?
- Instant Gratification Culture Demands a New Manufacturing Paradigm
- 3D Printing: Hype or New Manufacturing Revolution?
- The Role of Engineering Educators in the Age of MOOCs (Massively open online courses)
- Increasing the Pool of Innovators.

## Unprovability, nonvalidity, infallability

Am reading Zermelo’s 1908 paper “*A new proof of the possibility of a well ordering*“. You know the one I mean … and so there, in black on white (or similar shades) he writes:

Now even in mathematics unprovability, as is well known, is in no way equivalent to nonvalidity, since, after all not everything can be proved.

he also writes:

there are no infallible authorities in mathematics

Ok, if that’s not enough, what is?

Politicians, take note …

Cheers … The best is yet to come …

## Mathematical fictionalism, weaselism, and castles in the air …

what are we to make of Mathematical fictionalism?

the post linked above states:

Platonism is the view that (a) there exist abstract mathematical objects (i.e., nonspatiotemporal mathematical objects), and (b) our mathematical sentences and theories provide true descriptions of such objects. … snip snip … And abstract objects, platonists tell us, are wholly nonphysical, nonmental, nonspatial, nontemporal, and noncausal. Thus, on this view, the number 3 exists independently of us and our thinking, but it does not exist in space or time, it is not a physical or mental object, and it does not enter into causal relations with other objects.

Fictionalism, on the other hand, is the view that (a) our mathematical sentences and theories do purport to be about abstract mathematical objects, as platonism suggests, but (b) there are no such things as abstract objects, and so (c) our mathematical theories are not true.

and essentially that things like the number three or 2+2=4 don’t even exist …

and that my friends, is what some philosophers debate … so for sure, one case question the existence of trillion dollar deficits and debts 🙂

SEP entry also mentions* easy-road fictionalism*, or *weasel fictionalism*.

but on a more serious note the article discusses the serious issue of the continuum hypothesis and undecidability,

The most famous example here is probably the continuum hypothesis (CH), which is undecidable in currently accepted set theories, e.g., Zermelo-Frankel set theory (ZF). (In other words, ZF is consistent with both CH and ~CH; i.e., ZF+CH and ZF+~CH are both consistent set theories.) Given this, it follows from Field’s view that neither CH nor ~CH is part of the story of mathematics and, hence, that there is no objectively correct answer to the CH question.

and that is a topic actually worth thinking about … what is it that we CAN prove, and what is it that we CANNOT prove, and CAN there be machines we create that could prove [really hard] things that we couldn’t [unaided?]

## NTS: Coherence

Today’s watch word is coherence, closely related to alignment.

Motivation for thinking about coherence is biology and coordination of cells in common action.

Issue is the success of coherence over randomness. Why should there be coherence and coherent activity / coordinated activity of cells [of all kinds]. Absent some level of coherence … randomness and perhaps chaos ensues. Question arise about chaos. Where does chaos fall? Is chaos ‘better’ or ‘worse’ than randomness?

Natural randomness appears easy, yet man-made randomness appears hard to generate.

## Automated Discovery

on the todo list: Review progress in Automated Discovery and MetaTools.