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How inevitable is the concept of numbers?

writings.stephenwolfram.com

201–210 of 211 posts

Re: How inevitable is the concept of numbers?

#201
post #142

I guess one of the most fundamental difference between Wolfram’s model for fundamental physics and traditional physics is that Wolfram’s doesn’t have the concept of measure or of continuum at the fundamental level. Space and time, according to Wolfram’s model of the universe, are emerging properties of ‘the network’. Without such things as space and measures, there is no numbers in the fundamental “equations” that dr…

>I think it’s a bit backwards that he took something that he knows very well and somehow finds that it’s how the universe works That's in a sense how every model works. All theoretical models of the world are human inventions that aid in making sense of the world in terms familiar to us and nothing more. If you get good results from thinking the world is made of atoms, then the world is made out of atoms. When someon…

Well yes in a way. But it somehow makes the claim more dubious.

It’s like when you go see an osteopath and they tell you that your stomach problem is due to your bad posture...

Re: How inevitable is the concept of numbers?

#203

Earlier quoted context omitted.

It's so sad to see that he is taking an interesting question and turns it into a sales pitch of his computational universe theory. It's as if Stephen Wolframs mental horizon starts getting more and more restricted over the years since he tries to frame everything he sees in terms of his physical theory.

Or maybe he has an interesting theory he understands deeply, and think its valuable to show how this theory can give insight to the problem in question. Why be so cynical?

I had that view initially. And then I followed his writings for quite a few years and it started getting old.

And long. Loooong. His sales pitches seem to always go in circles. Computational irreducability here, causal graph there, namedrop Wolfram Language a few times with pretty pictures, make sure that "in our models" Einsteins theory and quantum mechanics are mentioned as special cases and "surprisingly everything works out beautifully". Yeah no right.

Time to move on. I've read enough of his 20-mile-long self-praising sales pich novels. He is just going in circles.

Re: How inevitable is the concept of numbers?

#204

Earlier quoted context omitted.

> Did we really know what “5” was then? What is five-ness really? Ah, but we do, and it’s very simple: it is what five cows an five fingers have in common in the most obvious sense. There’s no mystery there. Or, stated in another way, “fiveness is something you’ll be very sad not to see when you look at your hand.”

I lost one of my fingers when i was a child, so after getting used to it i don't experience sadness when i look at it. That statement also checks out for four, in this case.

Ok

Re: How inevitable is the concept of numbers?

#206

Earlier quoted context omitted.

Or if any of the students are from New Zealand

NZ = Sux Aus = Sex

Most Kiwi accents I've heard noticeably pronounced other vowels as "i". e.g. "dick" instead of "deck", "tinnis" instead of "tennis"

Re: How inevitable is the concept of numbers?

#208
post #198
post #189

Earlier quoted context omitted.

> I feel the inconsistency in your (circular) argument is not getting through. I guess it's not, since I'm not convinced that mine is a circular argument. My argument - to put is simply - is that we are all part of the same system and that there are no divisions. Without divisions, no numbers. I don't need any distinction between 'real' and 'arbitrary' for this to hold, that's a dichotomy you assume on your part.

Yes, we may be all part of the same whole. But there definitely are divisions – you are manifesting them with your own words. QED. Let me try differently. Your premise seems to be that "base reality" (your words) is a single teeming interconnectedness, indivisibly unique, from which it follows "there are no discrete systems", no categories, from which it follows that counting discrete things is an "artifact of human…

> Let me try differently. Your premise seems to be that "base reality" (your words) is a single teeming interconnectedness, indivisibly unique, from which it follows "there are no discrete systems", no categories, from which it follows that counting discrete things is an "artifact of human cognition".

Yes, I think you summarized it pretty good! Thanks for that.

> Yes, we may be all part of the same whole. But there definitely are divisions – you are manifesting them with your own words. QED.

Woah, not so fast, there! Where exactly do my words manifest divisions? The words you read on the screen, that manifest in your mind as meaning are not discrete things themselves. No word stands for itself, else we would not need dictionaries. They are fuzzy things that often change their meaning, depending on context, place and time, on the reader and what she ate in the morning. To claim that words are discrete things that exists

> The world being interconnected doesn't mean it's undifferentiated.

I agree. Just as there are patterns in stellar nebulae that swirl and dance but never quite separate, all the world manifests its decay in wonderful shapes and patterns.

But none of these patterns can be isolated from the others, for non of the patterns can there a definite line be drawn to say "your existence starts here and ends here". The boundary of every definition, of every category can be shifted and shifted and shifted some more. They are - as already mentioned - artifacts of cognition that allow us to form a mental model of the world that surrounds us. Replacing the unfathomable interconnectedness with a simple game of blocks and strings and forces that fit into the limited capabilities of the simulation we run in our heads.

> All work is still ahead of you in showing that categories and words are somehow "not intrinsic" (again, your words).

Categories and words, numbers and letters and the human mind are fleeting. How can they be intrinsic if they exist for only an eye blink?

Re: How inevitable is the concept of numbers?

#209
post #194
post #189

Earlier quoted context omitted.

> I feel the inconsistency in your (circular) argument is not getting through. I guess it's not, since I'm not convinced that mine is a circular argument. My argument - to put is simply - is that we are all part of the same system and that there are no divisions. Without divisions, no numbers. I don't need any distinction between 'real' and 'arbitrary' for this to hold, that's a dichotomy you assume on your part.

In your world without numbers, do letters exist? Does the letter "n" exist? Is there any relation between "n" and "nn" and "nnn"? If so, how would you describe that relation?

Do letters have an existence outside of our heads? I doubt it.

With regards to the relationship between repeating sequences; we (humans) invented funny games to describe these patterns as we perceive them. Some of these games have very strict and elaborate rules, although most of them are either inconsistent, incomplete or undecidable or trivial.

Even constructive mathematics offers no help here.

Re: How inevitable is the concept of numbers?

#210
post #13
post #11

Earlier quoted context omitted.

IIRC (edit: and as alluded in the article) there are languages which count as "one, two, three, many". But one two and three are also innate (immediately recognizable) quantities are they not? So does a person using such a number system actually count, or recognize and categorize only?

This Lexicon Valley podcast goes into the “having a vocabulary for large numbers is actually weird” thing. https://slate.com/podcasts/lexicon-valley/2021/03/english-la...

Great addition (no pun intended), thanks.
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