Fundamental MetaNumber (MN) Rules:

Version 2015 May 12 V 2.0 ©MN & Joseph E. Johnson PhD

The MetaNumbers Format is

number *units*metadata where:

Number: is in scientific notation 3.56e4

or in a standard form like 135.6

Accuracy: is given by the number of significant digits for values that contain a decimal point and are automatically converted to a class ufloat which carries the uncertainty as 3.749+/-0.003e5. Numbers that are to be treated as exact with no error must have any decimal point removed and absorbed into the exponential value. If this value were to be exact, it would be written as 3749e2.

Units: are always: singular, lower case, alphanumeric ASCII plus “_”, without symbols, Greek, or special fonts,

& without superscripts & subscripts.

- Use units like math variables with operations:

4.1*meter+7*yard-11.2*inch

The result will be in default meters

Meaningful combinations are always valid

- Metric units and a few others have these abbreviations for powers:

ft2 = ft*ft m_3 = 1/(m*m*m)

-Prefixes can be compounded and multiplied in any order:

mega*thousand*gross*nano*micro

-Output units are automatically metric unless:

one writes (expression) ! (units desired)

-Constants may be used also as “units”:

c !mach gives the speed of light in

units of the speed of sound.

MetaData: attached to an individual value is in the form:

{var1=val1 | var2=val2 |…} such as

{lon=30.2 |lat=81.3 | alt= 443* m |time= 20140818}

This construction {…..} always evaluates to “1”

-If the ‘var’ is missing then the value describes the

value itself as with 43.22*kg*m_3*{=alloy J18 density}

MetaNumber Operations:

The MetaNumber Program evaluates expressions among

MetaNumbers which come from three sources:

Sources of MetaNumbers:

  • Keyed in directly by the user into an expression
  • Retrieved from the history file of past expressions

Format: [my_seq#] (see discussion below)

  • From Archived MetaNumberFormatted Tables

which have been standardized and stored in tables

- MN Archives can be tables of any size or dimension:

- Format: [ServerPath_Directory_File_Row_Column]

With the default server and directory the

elements properties table, ‘e’ would be accessed:

[e_gold_thermal conductivity] which can be used

just like a variable, retuning that metanumber.

- MetaNumber options will soon allow the

display of tables being sought and showing the

row and column unique reference names

  • Row and Column names match between requested and stored values by first removing all whitespace and then lowering all case in both strings.

Objectives & Properties of the MN Archive:

  • The objective is to standardize ALL measured numerical values in MN Archived Tables – i.e. all tables in government, industry, commerce, & science.
  • Archived tables contain data in any number of dimensions: 0 (single value), 1 (a list of values), 2 (a standard table of entities verses properties) etc.
  • Archived tables are to be Excel compatible and stored in Comma Separated Values (CSV) format which is viewable by a person in Excel and by the Python software.
  • The path given by [Table Name _ Row Name_ Column Name…] provides a unique name to every possible stored numerical value – along with its units, uncertainty, and metadata descriptors.
  • This MN framework allows data to be stored one time in any convenient units. Then the retrieval of the data item never again requires any preprocessing to alter the units or understand its meaning. This saves time and prevents errors for all data exchange.
  • The MN framework can now support transformative new artificial intelligence and smart agents that can read the dimensional units, the level of accuracy to determine risk and reliability, and the exact meaning.
  • Furthermore the historical tracing of all computations provides the evolutionary history of every number.

Objectives & Properties of the MN History File:

  • When a user is performing calculations, they may be done with a designated “Subject” defined by {subject= J48 Oil viscosity study 2964} .
  • If several users indicate the same subject, then a file is written that consists of “subject, user, seq#} which provides an exact link to the input and result of each user using that subject. This archive file can be shared among and only among those users for collaboration. If {Subject= } deletes the subject.
  • A user can also document their work with remarks which are entered as

#...Any text here is stored as a result”

  • Thus when an individual user or a group collaboration under a subject which to insert and share documentation or comments, this means can be used.
  • The result of any calculation can be retrieved and inserted into future calculations with the expression: [my_seq#] thus using the same general format of retrieving data from an archived table.
  • The term “my” points to a table that is maintained for each user with the following variables: UserPIN; Seq#; DateTIme;Subject; InputString; OutputString; UnitsID, Optional Subject.
  • In retrieving either the MN Archive table data, or the MN Historical table data, the RowName, ColumnName, and the Subject, and Item are compared for a match by removing all white spaces, and lowering all case. Thus [my_Viscos ity_Oil SAE 43] will match [my_viscosity_oilsae43].
  • A user can download any of their past archived work from their [my_seq#] using criteria described on the web page such as between two dates or on a subject.

Special Values:

  • Missing values are denoted as {.} or {.|…} .Thus one could also indicated a reason such as {.|Reason=Sensor failed|
  • Any expression containing a missing value has the result set to missing itself.
  • Questionable data is indicated with {?} where again a ‘reason’ is allowed. Such values are computed and returned but the {?} tag is attached to the result.
  • Other features and product updates are described in the web notes.

Background:

“Numbers serve to discipline rhetoric. Without them, it is too easy to follow the flights of fancy, to ignore the world and to remold it nearer the heart’s desire.” Ralph Waldo Emerson

When we say “Number” one might write “18.4251” yet one has much more information that is not present in that value alone: (1) First there is the meaning of what the value refers to such as “The interior N to S length of the Richland High School gym at Lon 81.23, Lat 30.56” which is often referred to as the “Metadata” or designation or meaning of the value. Without meaning, the value is useless. Furthermore it is critical to know: (2) How accurate is this value? Are all these digits truly significant or did they result from arithmetic operations among numbers, some of which that only had perhaps three significant digits? This information is critical because in engineering, science and certainly financial investments we need to know how much uncertainty or risk is involved when relying on a particular value. The catastrophic financial recession that began in 2007/2008 was a direct result of a lack of proper risk analysis in the uncertainty of diverse financial instruments. A similar necessity for accuracy obtains in the medical profession. So it is essential that we also track the accuracy of numeric information from its sources through all operations to its current value. Finally (3) the units or dimensionality of the value are also as important as the number: Is the value in meters, feet, yards, or what. So the units must likewise be maintained attached to the value. So it is essential that these units, accuracy, and metadata stay linked with the value and are processed mathematically correctly.

Currently these attachments are generally unattached to numerical values in both print and electronic digital sources. One only has to look at almost any government, corporate, or public table to realize that the units, accuracy, and meaning are scattered in footnotes, titles, row, and column headings and sometimes are not even explicitly stated! The value is then itself in question when this information cannot be read by both humans and by computers. In this digital age this can be costly to clarify and can have disastrous consequences that our computers cannot easily integrate these four scattered items: Value, Accuracy, Units, and Metadata. This is especially true with Big Data.

Our Vision and Solution:

We will use the name “MetaNumber” to designate a complete information entity that is of the form: Value*Units*Metadata. We have developed very simple, fast algorithms for the management of each component. (1) For Units, we use variable names and abbreviations that express those units and act as variables that are combined exactly as one would form them mathematically: ft/sec; kg/m3; etc. These are to multiply the value in the MetaNumber expression as described in this document. The management of all dimensional analysis is automatic with our software and can provide answers in any convenient units without any problem.

(2) For Accuracy, the one generally universal denotation is the “number of significant digits, which is automatically captured when a decimal point is detected in a value and then the value is converted to a new class of object, a “ufloat” like 3.749+/-0.003e6. Such objects correctly track the uncertainty under all mathematical operations. An exact value is represented with no decimal which can be accomplished by changing the power of the scientific notation. If the number above were exact, it would be written as 3749e3. No other explicit symbol structure is needed to track the numerical accuracy.

(3) The attachment of specific Metadata to a single value is done as {variable1=value1|var2=val2|…}. This expression also becomes unity when evaluated and multiplied by the value, and thus it can carry unlimited data with highly flexible encoding without issue. This form can also carry any othercritical information.

An important component of our design are the MetaNumber Tables which are Comma Separated Value (CSV) tables containing potentially any and all numeric data formatted as MetaNumbers. Reference to a value in a MN Table is with the expression [table name_rowname_columnname ] for a two dimensional table of say entities versus properties. The ability of this format to implicitly link volumes of metadata for an entire table, or row, or column, without transferring the data, is essential to our design. These links: [….] can be used as variables to retrieve any value and insert it into an expression. Likewise any past values can be retrieved by [my_seq#]. These are covered in more detail in the web site.

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Examples to Compute:

  1. Compute (3.5 + 18.3 + 81.1 – 16.334):

> 3.5 + 18.3 + 81.1 – 16.334

  1. Compute the area of a circle of radius 5.7 inches in units of square centimeters:

math.pi * (5.7*inch*5.7*inch) ! cm2

  1. Compute the cos of 35.4 radians:

math.cos(35.4)

  1. Compute the volume of water in m3 needed to irrigate a 35.2 acre field to a depth of 1.8 inches:

> 35.2*acre*1.8*inch

  1. How long in hours must 46.9 gallon per minute irrigation pump run in order to irrigate that field:

> (35.2*acre*1.8*inch / (46.9*gallon/minute))! hr

  1. A Corvette can accelerate from zero to 60 mph in 1.8 seconds. What equivalent acceleration is this in units of acceleration due to gravity:

>(60* mph/(1.8*s)) ! ag

  1. What is the caliber of a 9mm gun:

>(9*mm) ! caliber

  1. What is the gravitational attraction in newtons between a mass of 345 lbs and a mass of 452 lbs that are 2.1 ft apart:

> (g*345*lb*452*lb)/(2.1*ft*2.1*ft)

  1. An Olympic runner can run at 100.24 meters in 10 seconds and has a mass of 240 pounds. What is his kinetic energy in joules:

> (1/2) * (240*lb) * (100.24*m/(10*s))**2 = ½ mv^2

  1. What is the ratio of the thermal conductivity of gold to that of silver:

> [e_gold_thermal conductivity] / [e_silver_thermal conductivity] note this result is dimensionless

  1. What is the mass of the newly discovered Higgs boson in terms of the proton mass:

> [mass_higgs]/[mass_proton]

  1. What is 4.5 times the result of my calculation of the viscosity of Oil SAE 45 a in seq# 953:

4.5*[my_953] which will match and bring that result into the current calculation.

MetaNumber Archived Tables:

There are three ways to enter data in to the MetaNumber program for processing. The first of these is to key in various values, with their units, accuracy and any metadata that we wish to track and record with the number. One is familiar with this process from the simpler exercises above. But would it not be better when one retrieves data from electronic sources, if that data had the values, accuracy, units, and metadata already linked? This is absolutely critical if one is processing even medium size data sets and a necessity with large data and Big Data. In other words, we would really like to have all existing numeric data stored in the form of MetaNumbers and published that way from its inception. Then scientists, economists, engineers, business analysts, even students could use data without concerns of unit conversion and worries about tracing the accuracy through statistical analysis. It would also provide a metanumber trail. We have devised a methodology that not only enables this process, but it also allows unlimited metadata to be linked to each value.

We will explain this with an example that uses a two dimensional table of rows and columns (although our system will allow tables of zero, one ( a column of values), two dimensions such as a table or matrix of value. or higher dimensions). We will use row one to list metadata variables for the table as a whole (author name, author email, table name,…) and in row two, just below these variables we place the actual values (Bob Smith, , etc. This is a standard with digital information that one has a title row or two that describes the information in that file with metadata that is applicable to the entire structure. Imagine this data is in a spreadsheetfile named “e” such the 110 chemical elements (Hydrogen, Helium, …) listed in column one beginning in row four (4) and perhaps 40 or 50 properties of these elements with the property names in row three (3) for the columns below them. These properties might be atomic weight, density, melting point, etc. Thus to find the density of gold, our MetaNumber (MN) software will recognize the name [e_gold_density]. MN will look in the default directory for a file named “e”, then look in the first column for the entry “gold”, and then across row three for the name “density” and retrieve the value from that row and column in the table. When the number is retrieved, it will already have the units, accuracy, and metadata attached.

MetaNumber Names are Unique:

This methodology is more powerful than it appears: It provides a unique name for every possible numerical value(metanumber). That is achieved because the directory has a unique name and the file, row name, and column name are also unique in the expression [e_gold_density]. If the data is stored on another computer, then we use the internet path name to that computer and the directory to precede the default above as: [ComputerPath_Directory_FileName_RowName

_ColumnName]. Thus every value has a unique name in the same way that we have unique email addresses for every person. This name can be used to insert the value into any mathematical expression for evaluation.

MetaNumber Archived Tables Provide Unlimited Attached Metadata:

This structure also allows for additional rows below the third row, and additional columns after the first one, to be used to contain other descriptive metadata, web links to videos, images, maps, footnotes, and other data that applies to all the entries in that exact row or that exact column. Then the use of the path [e_gold_density] name alone links one with all the metadata that is contained in the row with “gold” (such as the symbol “Au” in column 2) or the column with “density” (with the equation for density in row 4). Thus the construction of a table supports the listing of any and all metadata that goes with all the values in the table as a whole, the row as a whole or the column as a whole without transferring that data. It is maintained by reference using the path name alone leaving the system unencumbered.

MetaNumber Archived Historical Values Can Also Be Referenced:

Each time a user enters an expression to be evaluated, the system records the following fields: UserPIN,Seq#, DateTime, Input Expression, Output Expression, Unit ID,Subject. The expression [my_seq#] will allow a user to retrieve any line result named with item under the active subject name. Other parts of that record can also be retrieved. Means are underdevelopment to allow fully generalized data retrieval for large scale processing.