Non anthropic decimal sequence origins?

[Rhoops]

I am having difficulty trying to find any history in mathematics of the concept that the decimal number system is not just a product of human ingenuity. This anthropic assumption (and assumption is all that is) seems to have entirely precluded the contrary hypothesis that decimal sequence formation is as independent of human involvement as say any of the laws of physics.
Whether one believes in the anthropic/non anthropic origin of regular numerical sequence is not the question here, the question is: can anyone provide me with reference to any proponents of the significantly more obscure non anthropic hypothesis? I can't find a single example!

And since the Pythagoreans and Tegmark are embarrasingly quiet on the logical necessity of a regular unit combination (numeric) sequence causality premise in any 'Mathematical Universe' hypotheses, I don't think they really count.

 

[micromass]

We work with the decimal number system today because we have 10 fingers. So I think it's rather obvious that we invented it.

 

[HallsofIvy]

Mathematics is NOT physics. Mathematics is entirely a human construct. NO part of mathematics is independent of human involvement.

 

[Rhoops]

Thanks, but the obvious is obvious. It's the non obvious I'm rather more interested in. The ten finger idea is the essence of the anthropic argument. But science generally tries to avoid anthropic solutions: 'the universe revolves around us'... because they have all been wrong so far. Human ego and empiricism make poor bedfellows.

'Has any mathematician previously considered an independent origin of decimal formation?' - is my question? Unsuprisingly I am asking it because I am fully aware of the orthodox uniformity of the ten digit assumption. The uniformity of that opinion, based on nothing but a mere assumption: "it's obvious" is something that should ring alarm bells. I would have thought any hint of uncertainty in the most basic premise of mathematics (origin of unit combination) would be something worth investigating.

This thread is NOT about the orthodox ten digit concept, we all already know that idea, it's about identifying any history in mathematics of an alternative possibility. I'm not a mathematical historian, but I'm willing to bet that there is no history. Why? Because it's an axiomatic assumption that by definition nobody questions. And the idea that nobody questioning something makes it correct is a social convention, not a scientific one. So are we all happy with just a socially acceptable vagary at the beginning of mathematics...?

 

[micromass]

Is there any evidence that we use the decimal system for some other reason than that we have 10 fingers? I really don't see any other possible reason.

And again, you are conflating science with mathematics. Science doesn't like anthropic solutions. But mathematics is entirely man-made, so anything there is invented by humans one way or another.

 

[D H]

Rhoops, you appear to be under the misconception that base 10 is special. It isn't. The only thing special about base 10 is that we have 10 digits on our two hands. The computer on which you typed those messages -- it uses base 2. The ancient Mayans used base 20. The ancient Egyptians, a mix of base 10 and base 12. (We have twelve hours in a half day thanks to the Egyptians). The ancient Sumerians and Babylonians used base 60.

 

[Erland]

Of course, the specifically decimal number system is a human invention, probably based upon our ten fingers. An intelligent species with, say, eight fingers, may instead develop octal numbers.

It is, however, not entirely clear to me what you think is mysterious in this. Is it the representation of real numbers as infinite decimal sequences (or in other bases) that you consider as specifically human? That this is possible to do follows from our definition of real numbers (by e.g. Dedekind cuts). Such definitions are of course also human artifacts, and it is possible that another intelligent species can use other concepts than our real numbers to describe the universe.
But since there is an underlying common reality, our and their concepts should be somehow related, just as there are several equivalent ways to formalize e.g. quantum mechanics (by Heisenberg and Schrödinger), calculus (by Newton and Leibniz), real numbers (by Dedekind, Cantor, et. al.), etc.

 

[Rhoops]

"Mathematics is entirely a human construct..."

Are you aware of the scientific protocols against making statements concerning negative evidence?

The Pythagoreans before and Max Tegmark currently are beating the Mathematical Universe drum which contradicts a human only origin to mathematics. That viewpoint EXISTS.

I would be most interested to hear the positive evidence you can give that contradicts their hypotheses. As far as I know they are still viable hypotheses because to contradict them you need proof that they don't exist. Thats how science works... They teach you that in in your first week at any legitimate university. They also teach you that: mere assertion is not a legitimate scientific methodology.

Again, I'll repeat my request:
'History of decimal origins in mathematics... alternative possibilities' please.
Assertions of orthodoxy are assumed here, we all already know them thank you.

 

[micromass]

Rhoops, you appear to be under the misconception that base 10 is special. It isn't. The only thing special about base 10 is that we have 10 digits on our two hands. The computer on which you typed those messages -- it uses base 2. The ancient Mayans used base 20. The ancient Egyptians, a mix of base 10 and base 12. (We have twelve hours in a half day thanks to the Egyptians). The ancient Sumerians and Babylonians used base 60.

Let me go ever further and say that 99.99% of mathematics don't care about the base we are considering. Whether we write our numbers in base 10 or base 8 or whatever, the mathematics would remain exactly the same. Entire calculus, analysis, geometry, etc. wouldn't change at all. The mathematics needed for physics wouldn't change at all. The reason is that numbers can be and are defined independently of the decimal representation

The only thing which would change are mathematics which somehow depend on the specific representation of numbers. This is usually recreational mathematics and not really important. Some of the more important ones are however checking divisibility of a number. For example, whether a number is even or odd. However, we see that other bases have other divisibility properties. And it actually turns out that other bases have more convenient divisibility properties. So again, nothing special with base 10 other than the fingers on our hand.

 

[micromass]

"Mathematics is entirely a human construct..."

Are you aware of the scientific protocols against making statements concerning negative evidence?

The Pythagoreans before and Max Tegmark currently are beating the Mathematical Universe drum which contradicts a human only origin to mathematics. That viewpoint EXISTS.

I would be most interested to hear the positive evidence you can give that contradicts their hypotheses. As far as I know they are still viable hypotheses because to contradict them you need proof that they don't exist. Thats how science works... They teach you that in in your first week at any legitimate university. They also teach you that: mere assertion is not a legitimate scientific methodology.

Again, I'll repeat my request:
'History of decimal origins in mathematics... alternative possibilities' please.
Assertions of orthodoxy are assumed here, we all already know them thank you.

OK, so is there any evidence that there is more to base 10 than the fingers on our hand? If not, I don't know why you are asking this questions. It's like you hope for something deep and independent of human construct, while it just isn't there.

My cat is named Smeagol. Now, one could say that I saw the lord of the rings and got the name from there. Or you could say that there is something deep about the name Smeagol that we haven't figured out yet. Which is more likely.

 

[Erland]

I never read Max Tegmark, but I am quite sure that he doesn't say that there is anything particularly deep with the number ten.

 

[D H]

I would be most interested to hear the positive evidence you can give that contradicts their hypotheses. As far as I know they are still viable hypotheses because to contradict them you need proof that they don't exist. Thats how science works... They teach you that in in your first week at any legitimate university. They also teach you that: mere assertion is not a legitimate scientific methodology.

You have things exactly backwards. The burden is on you as the proponent of this hypothesis to show evidence for your hypothesis rather than on us to disprove it.

I wrote this earlier, but you appear to have ignored it: There is *nothing* magical about base 10. Not one thing. Our accounting and mathematics would work just fine if we used base 2, base 8, base 12, or base 42 for that matter. That we use base 10 is purely an invention, and a rather arbitrary one at that. The Indians who developed the place-value notation happened to have counted in base 10.

The Indian place-value notation supplanted every other numbering system in existence because of the vast superiority of a place-value notation compared to (say) Roman numerals. The Indian system doesn't get its power from the number of digits on our fingers. It gets its power from zero, and how the Indian mathematicians used zero both as a placeholder and as a number in and of itself. It's the place-value notation that makes the Indian notation so superior to every system that came before it. If the Indians had counted using joints rather than digits we would probably have a base 12 place-value notation, and everything would still work just fine. There is nothing special about base 10.

 

[Rhoops]

"You have things exactly backwards. The burden is on you as the proponent of this hypothesis to show evidence for your hypothesis rather than on us to disprove it."

Does anybody else not know the basic difference between a hypothesis, a Theory and an enquiry?

I am under no obligation to prove anything, because I am simply asking a question.

"Does anybody know of any historical mathematical precedent for the idea that the formation of unit combination uses the regular repetition of decimal sequence with a non anthropic origin."

If you don't like the idea, fair enough, but please don't assert that YOUR idea is the only one available, indeed the only possible concept- on the sole premise that YOU believe it. The unfortunate reality is that there is no evidence either way. I am not interested in debating the orthodox arguments you have all presented,they are utterly familiar, and rather than try and patronise me futher with those unedifying simplicities we all had drilled into us as children, perhaps some kind heart could possibly consider ANSWERING THE QUESTION?

[Oh, and somebody above did actually ask the connection between Max Tegmark and decimality? YAAAY We have our first winner in the 'Think & Consider' category! 'None whatsoever', but its nice to see a spark of intelligence in the darkness. Maybe though you should ask him, he just might not have considered the idea! Look at the responses above, not exactly a showcase for healthy wide ranging intellectual debate of conceptual possibilities- is it?]

 

[micromass]

"You have things exactly backwards. The burden is on you as the proponent of this hypothesis to show evidence for your hypothesis rather than on us to disprove it."

Does anybody else not know the basic difference between a hypothesis, a Theory and an enquiry?

I am under no obligation to prove anything, because I am simply asking a question.

"Does anybody know of any historical mathematical precedent for the idea that the formation of unit combination uses the regular repetition of decimal sequence with a non anthropic origin."

If you don't like the idea, fair enough, but please don't assert that YOUR idea is the only one available, indeed the only possible concept- on the sole premise that YOU believe it. The unfortunate reality is that there is no evidence either way. I am not interested in debating the orthodox arguments you have all presented,they are utterly familiar, and rather than try and patronise me futher with those unedifying simplicities we all had drilled into us as children, perhaps some kind heart could possibly consider ANSWERING THE QUESTION?

[Oh, and somebody above did actually ask the connection between Max Tegmark and decimality? YAAAY We have our first winner in the 'Think & Consider' category! 'None whatsoever', but its nice to see a spark of intelligence in the darkness. Maybe though you should ask him, he just might not have considered the idea! Look at the responses above, not exactly a showcase for healthy wide ranging intellectual debate of conceptual possibilities- is it?]

Ok, so this thread is truly going nowhere. There is no shred of evidence that base 10 is somehow a fundemantal property of the universe. So the rest is just speculation.

I am locking this thread. If anybody has any evidence that he wishes to discuss, then please send me a PM and I can reopen this.