Transcript Numbers serve to discipline rhetoric. Without them it is too easy to

Numbers serve to discipline rhetoric. Without them it is
too easy to follow flights of fancy, to ignore the world as it
is and to remold it nearer the heart's desire
Ralph Waldo Emerson
Imagine:
• If every number came with its units, uncertainty, and
exact meaning all attached in a “metanumber” object:
– a universal standard for all numerical data • Instantly readable by both humans and computers,
• And there was a simple unique name for every number,
– Which could be used as a name in expressions where
• Dimensional & error analysis is automatically done &
• Where all metadata is tracked allowing reuse of results
• Supporting automated data exchange, Big Data & AI.
And Also Imagine :
• An algorithm continuously scraping all numerical data from the web and
converting it to standardized MetaNumber tables and then
• With a novel process each table is converted to two networks
– One among entities (rows) and one among properties (columns)
• From which the dominant clusters are extracted and ordered
– Using a novel agnostic cluster identification algorithm
• Then with still another algorithm these clusters are linked
– into a single supernet spanning all numeric information.
• A single network spanning our entire numerical universe !
MetaNumber
A Standardization of
Numerical Information
AAPT - Charleston SC
Joseph E. Johnson, PhD
[email protected]
October 30, 2015
MetaNumber - Powerful yet Easy
> 6.3*ft + 4.83*m -37*inch
• >>5.810+/-0.032*m
Mix as needed
Result is metric by default
> 6.3*ft + 4.83*m -37*inch ! ft
Gives result in ft
• >> 19.06+/-0.11*(ft) Uncertainty from sig. dig.
> 43*yard*72e6*inch !acre No decimal implies exact
•
>> 17768.523967*(acre)
> 5.3*[e_gold_density]
An ‘exact’ result
Use [table_row_column]
• >> (1.022+/-0.019)e+05*m_3*kg Input standard data
> 18*[my_482] Inputs the result of users line 482
Some Harder Problems
Compute the gravitational attraction between a 188 lb
man and a 632.3 kg golf cart that is 7.93 yards away:
> g*188*lb*632.3*kg/(7.93*yard)**2 g = G
>> (6.844+/-0.017)e-08*m*kg*s_2 note the uncertainty
If a BMW can accelerate from 0 to 70 mi/hr in 1.3 sec.
then how much acceleration is this in “ g’s ” :
> (70*mile/hour)/(1.3*s) ! ag where ag is the acc. of gravity
>> 2.45+/-0.19*(ag)
Unit and Constant Names
• Unit and constant names are:
• Lower case, alphanumeric (with internal ‘_’).
• NO Fonts, symbols, upper/lower cases, & plurals.
• This makes names consistent with variable names
in modern computer languages.
• MetaNumber has about 600 internal units and
constants.
• www.metanumber.com/resources see unit names
MN has Six Basic SI Units
1.
2.
3.
4.
5.
6.
m = meter
s = sec = second
kg = kilogram
a = amp = ampere
k = kelvin
cd = candela
length
time
mass
electrical current
temperature
luminosity
With Six Additional Base Units
1. b = bit
2. op = flop
information (Shannon, 1/0, T/F)
operation rate
(a double precision floating point operation)
3.
4.
5.
6.
p = person
d = usd = dollar
bn
ln
living human (as in per capita)
value
baryon number (protons, ……)
lepton number (electrons … )
Note: byte = 8*b for the information in an ASCII character.
Note: ops = op/s and flops = ops = floating point operations per second.
Note: both bn and ln are exactly conserved quantities like electrical charge.
These units are optional but strongly encouraged
Numerical Accuracy (uncertainty)
• If a value contains a decimal point then it is
converted to an ‘uncertain number’ (ufloat):
> 2.34 * 7.632e2
>> 1785.9+/-7.6
• If there is no decimal (or is removed using
scientific notation) then it is treated as exact:
> 234e-2 * 7632e-1 >> 1785.888
Metadata & Meaning-1
Information is accessed by an internet path:
• [ip path to server_dir__table_row_column…]
• Use just [table_row_column…] for the MN default server.
Examples:
• [e_gold_density] retrieves the value of the density of gold
from the elements table (abbreviated ‘e’)
• [mass_higgs] retrieves the mass of the Higgs particle
• Each row and column name must be unique in that table
• For comparison case is lowered and white space removed.
Metadata & Meaning-2
• MetaNumber tables have table variables in row 1 and values
of these in row 2. These apply to all values in the table.
• Metadata for row/column data is indicated by indices (row
and column names) that begin with ‘%’
• If the metadata is a unique index it begins as ‘%%’.
• This allows table entries for a row or column of descriptive
data associated with that row or column.
• This could include web links, and other reference material
that qualifies the data in that row or column
Metadata & Meaning - 3
• Metadata of any form can be attached in { .. anything..}
– 2.451*kg*m_3*{=density of kl47 plastic} or
– 3.72*milli*(gram/cc)*{=organic matter|lon=30.45*deg|lat=80.2*deg}
– Thus {…} is a carrier of information that can be attached to any
metanumber and becomes = 1 on evaluation and thus disappears.
• This structure allows metadata descriptions, meaning,
conditions, and defining data or tags to link to all data in that
table, row, column, or individual values.
The Numerical Universe
MN Tables -> Networks
• A MN table Tij representing things (rows) with properties
(columns) suggests that some ‘things’ are more alike.
– Rewrite Tij as ratios to remove dimensionality.
– Construct a network C’jk = exp-(Si Tij - Tik )2
– Define the diagonal Cjj = - Si≠j C’ij
• We have proved that Cij is in the Lie algebra that generates all
continuous Markov transformations:
– M(a) = exp(a C) is a Markov transformation.
•
The eigenvectors of M identify the clusters in the network C
– And can be labeled with the eigenvalue corresponding to each cluster
SuperNet
• Clusters abstract the essential information in
each table.
• These clusters can be linked to other clusters
using the eigenvalue weights of table indices
(nodes).
• This results in a single network that joins all
numerical information in …
•
The Numerical Universe
Thank You
• Joseph E. Johnson, PhD
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Distinguished Professor Emeritus
Department of Physics and Astronomy
University of South Carolina, Columbia SC, 29208
Room 405 Physical Sciences Center
Email: [email protected]
www.asg.sc.edu and
www.metanumber.com
Web application powered by the University of South Carolina’s RCI group directed by Dr. Phil
Moore