Is 9.9 exponentially greater than 9?

[Admiral2]

Okay, I'm new here, and I'm new to the whole forum thing in general, so I probably wasn't sufficiently prepared for what I was letting myself in for. If this is something that has already been addressed a million times I apologize.

On a Trek board a thread asked what kind of ship the Enterprise-F should be. I posted some specs relating to the type of ship I'd want to see, and one of the things I said I wanted was a propulsion system other than Warp. One of the other posters rose to defend Warp Propulsion, and part of his argument was the assertion that Warp Speeds between Warp 9 and 10, speeds like 9.9, 9.997, etc., were exponentially greater than Warp 9. He even linked to a page full of mathematical formulas that supposedly prove this to be true.

Now, last time I checked, a decimal number wasn't "exponentially" greater than anything. Have I missed some revolution in Mathematics that makes such a thing possible? I just want to know. I'll be more than happy to admit my mistake if somebody can point to the rule - in a pure math context - that allows 9 and 9/10 to be exponentially greater than 9.

[Ghost Rider]

Off to PST.

[Lord Revan]

Okay, I'm new here, and I'm new to the whole forum thing in general, so I probably wasn't sufficiently prepared for what I was letting myself in for. If this is something that has already been addressed a million times I apologize.

On a Trek board a thread asked what kind of ship the Enterprise-F should be. I posted some specs relating to the type of ship I'd want to see, and one of the things I said I wanted was a propulsion system other than Warp. One of the other posters rose to defend Warp Propulsion, and part of his argument was the assertion that Warp Speeds between Warp 9 and 10, speeds like 9.9, 9.997, etc., were exponentially greater than Warp 9. He even linked to a page full of mathematical formulas that supposedly prove this to be true.

Now, last time I checked, a decimal number wasn't "exponentially" greater than anything. Have I missed some revolution in Mathematics that makes such a thing possible? I just want to know. I'll be more than happy to admit my mistake if somebody can point to the rule - in a pure math context - that allows 9 and 9/10 to be exponentially greater than 9.

the Warp scale is non-linear so an increace in warp factor after warp 9 will cause an exponental increace relative speeed (in m/s) and warp 10 is infitive speed.

[dragon]

Its not so much as that the number is exponentially greater but that the speed it represent is.

[Morilore]

The curve that gives you speed in m/s when you input warp factor is asymptotic at x=10.

Just a more geeky way of saying what everyone else has.

[Praxis]

The curve that gives you speed in m/s when you input warp factor is asymptotic at x=10.

Just a more geeky way of saying what everyone else has.

Miles per second? Must be a very, very long number.

[Lancer]

The curve that gives you speed in m/s when you input warp factor is asymptotic at x=10.

Just a more geeky way of saying what everyone else has.

Miles per second? Must be a very, very long number.

miles is abreviated mi. it's in meters/second, an even bigger number.

[Morilore]

Ah yes, but that's where scientific notation comes in.

[Praxis]

Ah yes, but that's where scientific notation comes in.

Can't we just measure it in lightseconds per second? (sounds weird, eh?)

[Lord Revan]

since the SI unit for Speed/velocity is m/s. Better unit would be multiple of c.

[Kuroneko]

Pardon me for being pedantic, but the abuse of mathematical concepts is not acceptable. With respect to x (say, speed ration), geometric growth varies as x^a, for some exponent a. Exponential growth varies as a^x, for some constant a. Star Trek's warp rating is definitely not exponential, since no exponential function has an asymptote, whereas the ST warp ratings do.

It's not difficult to say that warp speeds have a vertical asymptote, certainly no more difficult than saying they grow exponentially. There is no need to bastardize mathematical language by not saying what is meant.

[Pcm979]

AFAIK, the warp-speed notation the Federation uses post-TOS assumes that there is no such thing as Warp 10 (kinda like non-scifi lightspeed it is impossible to get to or surpass); Hence stupid terms like warp 9.999999999999 instead of say, warp 15.