I should preface this post by saying that there aren’t any pictures and that it has nothing to do with Emerson, except that maybe he and I will talk about things like this in the future. Like when he’s 3 and asking “Why?”

**Base (n-1) numbering systems**

Todd an I talked about this already, but I’ve been thinking about it more since then. It seems incorrect to me that we call our counting system ‘Base 10’. On face value, it makes sense – we have ten fingers, and it’s at values of ten that we change order of magnitude. But as this comic shows, every base is base 10. Consider what we call base 8. For us it’s easy to call it base 8, as we have a unique digit to refer to the number 7 + 1. But for those who are native to that base, there is no digit for 8. Their system goes 1, 2, 3, 4, 5, 6, 7, 10, 11.. etc. Their order of magnitude changes where we would count 8. The binary system has no ‘2’, just famously ‘0’ and ‘1’.

I suggest that there’s a lesson to be learned from the binary system and the natural inclusion of ‘0’. Our decimal system should not count 1 though 10, but 0 through 9. It may be proper to refer to the system as decimal, but I think it should actually be called base-9, and the binary system called base-1. That avoids the base-10 confusion and provides for a naming convention that allows everyone to know what they’re talking about, once the lower-based natives are clued into the new digits above what they’re familiar with.

If we don’t do that, we’re all going to have to start memorizing whatever digits those crazy base-billion folk use above ‘9’.

**The expansion and contraction of the universe is compression and decompression**

I’m no expert on Astro-physics – I know just enough to speculate while being lazy enough not to look up all of the details online that could confirm or deny what I think; at least until Todd and I start talking about it and we’re on a race to figure it out.

It seems to me, though (even if I do find it likely that someone will handily explain why this is wrong), that the unexplained accelerating expansion of the universe – the one that is accounted for by some with “Dark Energy” – could actually be explained if spacetime is compressing or decompressing in the presence and absence of gravity-causing matter. Matter is frequently described as “warping” space-time, and drawings of black holes usually show them poking deep pits into a planar space-time surface. It seems better to me to think about the space-time there not as stretching, but as compressing, so your units of space and time each become “smaller” when seen from an outside viewpoint. (I don’t even think that makes sense.) Gravity is, in effect, matter taking the path of least resistance and moving in the direction where units of space-time are “smaller”. Since objects moving closer together combine their gravitatoinal compression, the feedback is positive.

The reverse is true for areas with low or no matter, but the feedback is still positive. With no mass to pull it together, space and time continually decompress (infinitely?), expanding the units of space and time. As the distance between mass grows, the decompression continues faster, causing the expansion to accelerate.

Does that seem feasible?

## 7 comments

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June 10, 2009 at 6:33 pm

MomOk… way above my head. I am so glad you and Todd can talk about these things. Followed the first one and it makes sense to me. Kind of sort of followed the second one, but I don’t know anything at all about compression and decompression of space stuff. BUT I do know that you would love to be in a classroom speaking with lots of other folks about stuff like this and letting it ruminate and cogitate in your mind until you do understand

June 10, 2009 at 7:14 pm

ToddThe comic is funny I admit, but I think the issue with the current “base-#” format is that the “#” is the base-10 value of the digits “10” in base-#. It is a translation. It has to be.

In your system what is base-16? base-15 or base-F?

If base-15, then “15” is still a base-10 translation of the base-16 value of “F”. And now it doesn’t represent the number of digits in the base (there are 10 digits in base-10 as there are 16 digits in base-16) instead it excludes the value 0? That doesn’t seem any better to me.

If base-F, then what would base-60 be?

June 10, 2009 at 8:22 pm

BryanThe problem is that Base-10 doesn’t work in either direction, up or down. Base-10 is meaningful in a binary system, a decimal system, and a hexadecimal system, but it means something different in each. Base-9 is at least meaningful in one direction (to people with a higher base than us), and since it’s unrecognizable until translated to people with a base lower than us, at least it has meaning as a higher-level base instead of an ambiguous and false meaning.

Base-16 is base-F, since you and I and a lot of people know that A-F are the characters that associate to our 10-15. To ask how to refer to base-60/59 properly is something of a non-starter, I think, because either we know the character set for that base and the question is null, or we don’t and can’t discuss that base in terms of that base until we do, right? Is that sensible?

June 10, 2009 at 10:07 pm

ToddMy point is that Base-X is a meaningful nomenclature for us (being Base-10 speakers). The digits 0-9 are Base-10 digits. Anyone unknowledgeable of that nomenclature is likely to use different symbols for digits anyway needing a translation from their symbology to ours. It is meaningful for us to say that there are 10 digits in a base 10 number system and 2 digits in a base 2 number system. Using 9 to represent a decimal system seems wrong (as does 7 to represent and octal system or worse 1 for a binary system). What does 9 mean then, there are 9 digits + a digit for zero? or 9 non zero digits? That seems way more cumbersome. A decimal number system is a system of ten digits, it just makes sense to say it has a base of 10. And if it is wrong to say base 10 then it seems wrong to say it is a decimal system. I know I will not be able to convince you, but I’d rather stick with the current system.

June 10, 2009 at 10:16 pm

BryanActually, no, that’s fairly convincing. It is cumbersome to say that we have a base-9 system because 9 is the highest single digit in the system, rather than because there are 9 different digits in the system. I guess if we were trying to develop a systematic communication, it might be only slightly more cumbersome but more accurate to call it a base (9+1) system.

June 10, 2009 at 10:08 pm

Toddand all your base are belong to us

June 10, 2009 at 10:20 pm

BryanNot base(§+1).

😀