Not really. You have stored something which has a representation of more than 15 bytes, but you will struggle to find a way to store most things longer than 15 bytes in this way. (everything can be transformed into a representation which is infinite in size anyway, for example by using an irrational base). Information really comes down to the number of possible values you can distinguish.
If you do the ratio thing you have described you will find that alpha and beta are many, many times the size of the observable universe for something like a book. If you allow the length of the rod itself to also contribute to the information, you have added another symbol so you can store more than 15 bytes, but this doesn't even double the amount of bytes you can store.
Assuming all of it can be described as ascii characters, (ratio of.12152205 could be read as 12-15-22-05, or “l-o-v-e.”) then let's assume 4 numbers will be required to encode one letter. That gives us, in our limited system, 4 decimal bits to a byte (we really can't limit ourselves to just ratios that are sufficiently large and only made of 1s & 0s).
So, all human knowledge is, in our system,
250*(1024^6)=288230376151711740000 bytes.
As we assumed that all of it can be described as ascii characters, and in the standard system 1 byte holds one character, there are now 288230376151711740000 characters. Expressing these many characters in our 4-byte decimal numbers will require a ratio with
(288230376151711740000*4)=1152921504606846976000
numbers in it. All the ratios with 1.15 * 10^21 numbers will be the candidates which can be used to store all of humanity's contemporary knowledge.
Now, as I said earlier, the ratios may have an impressive number of numbers in them, expressed in a decimal system, and there are an infinite number of them on the number line itself, that does not mean all of those are available for use. We are limited to ratios derived from lengths which are multiples of the plank length. Assuming, for a particular rod and it's notch, there is a set 'h' that contains all the possible ratios. We will be limited to such ratios only to find our matching ratio, the ratio through chance of cosmic infinity, or not. If not, then we have to increase/decrease the design length of the rod and the notch to change the set 'h', and hope there is a number we are looking for.
How many such ratios, of the required length of 1.15 * 10^21 numbers, would exist if derived solely through the ratios, is unknown and wholly dependent on the information that has to be encoded. The longer the data, the higher the probability of not finding the right number. As you put it, there will be 15 bytes of choice, or in a one meter rod there will be 10^32 number of choices of ratios to play with. If you doubled the length of the rod, you would have twice the amount of choice, as so on. Again,
Are you just saying the length of the rod can be variable along with the position of the notch? If so, it seems like that means you approximately square the number of possibilities, so if there was a maximum of 25 bytes, then there is an maximum of 50 bytes available in something the width of the universe. Still not large.
Your comment is a non-sequitor; reread what he said.
He's saying that there exists a certain ratio in the set of ratios whose decimal representation represents a corpus of knowledge, in this case the entirety of human knowledge.
How did you not get that the term '25 bytes' is merely the size necessary to store the number of possible ratios instead of any actual information?
Did no one read the discussion below about encoding information into pi? This is the same concept. Yes, there are only 25 bytes worth of ratios to chose from, but those ratios themselves can, possibly, POSSIBLY, store all the information.
If you do the ratio thing you have described you will find that alpha and beta are many, many times the size of the observable universe for something like a book. If you allow the length of the rod itself to also contribute to the information, you have added another symbol so you can store more than 15 bytes, but this doesn't even double the amount of bytes you can store.