some of you on the comments on the previous video of
Mentioned computer systems some experimental ones that were [once] built
Working on a base three basics Roman base two
sometimes a base three number either 0 1 or 2
Following on from bits is called tricks because the base 3 system some textbooks call it trinary some
Textbooks call it Ternary, but it's the same thing. It's a base 3 system
Now here's the magic thing
With these things being exact negative powers of 3 I can confidently
predict that if only we could calculate entropy in traits and
[codings]
Traits we could probably get a more efficient coding. Let's have a look we can do this probably quite quickly now
But if you're doing it base 3 the rule now is you combine the three?
Rightmost probabilities all in one go and the 3 right most things are 1/9
19.9 so I'm getting here a trinary or Ternary tree, not a binary one
190 190 1/9 combine them all into one third
Till to those and then if you're combining in threes well, you put a third a third a third easy good good
Good
Probably see one point no good
Now here's a clever thing
What you now do in labeling your branches of course is if you go left
Label at 0 we go down the middle label it 1 if you go to the right label it, too
and then as you recursively descend down this you're on a 2 now if you then go to the left you append to 0
If you then go down, the middle [you]
[append] a 1 and if you then go to the right again you end up with 2 those are codes that
[have] been worked out in tricks. I can then tell you this 0 is for Cod
They code one is for they
Catch a bass
Tuna Shark and Barracuda
Effectively in sequence become 2 0 [2] 1 and 2 2 [in] [trick] codings [I] have now
Calculated my entropy as being the sum over these five states
Minus p. I
log to the Base 3
of p I I worked out he lost the base 3 so the answer comes out in tricks and
It's one point three three
trips
my average length is the sum from 1 to 5 of
The length of code associated with the given catch or state times the probability of that catch
So you're getting things like?
You know a one trick code times the third plus a one trick code tons another third add them all together
Amazing it comes to one point three three trips
Because [of] the nature of these probabilities they map into being whole numbers of tricks needed
The probably doing of this bits
was that
They don't map exactly
[onto] logs the base 2 is clean whole numbers so you end up [having] to waste a bit and round up as it were
Whereas [tritt] hits it right on the nail look at this efficiency
Is [1.33] over one point three three hits?
100%
however
the word of warning, I think I ought to say is someone says hey look that's
fantastic you've
Got one point three three traits of entropy. You've got two point 1 1 3 bits of entropy over the same thing
Why not use traits all the time you've lowered the entropy
No, I haven't. It's just using different units and the way to think of this is something like the following
The amount of information is constant that you can measure it in different units
It's a bit like having a 1 kilogram bag of sugar the one kilogram bag of sugar is an amount of sugar
If I choose to I could revert back to imperial units and say it's actually
2.2 pounds, and of course those of you in North America still use the imperial system. We'll say hey
I'd like that in pounds and ounces so yes, it's
[2/10] of
16 ounces which is 3.2 and
yeah, so it's 2 pounds and 3.2 ounces so if you want it totally in ounces to 16 to 32
it's
[35] point two ounces
Worth of sugar, but it's still the same amount of sugar that
[doesn't] [change] at all same thing here
1.3 three tricks of information is the same amount as
[2.11] three bits, so you're not winning out in bt
Entropy, but where you are winning out here is being able to get your average code length down
That might matter to you quite a lot saying oh if only I'm allowed to use digits like zero one and two
I can send fewer of them than if I have to be limited to zeros and ones