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3. Everything / Maths, Science & Technology / Mathematics

Conceptual Tables

If furniture tables are impressive for their ability to hold things up, conceptual tables are arguably even more impressive in their ability to contain all sorts of information.

Purely conceptual tables are used in so many practical and educational ways that it nearly boggles the imagination. What keeps people from recognising the ever-presence of conceptual tables is our tendency to discover them individually at different ages and in different venues.

Organisational Tables

The most basic form of the conceptual table is a grid used to lay out content in tabular format. The word 'table' was most likely coined in reference to the common dinner table - the top of which is a square or rectangle that seats related1 yet distinct individuals in an efficient grid-like configuration. For practical purposes, the organisational table is a formatting trick applied mostly to huge quantities of data, which is why most tables of this variety exist in a digital format.

To demonstrate the concept of an organisational table, a teacher might sit down a child with a ruler. They might then ask the child to draw a grid and put a word in each square. The teacher could then point out the parts of the table as follows.

An organisational table is divided by a series of lines running horizontally and vertically. In between two vertical lines, the table forms a column. In between two horizontal lines, the table forms a row. The smallest unit in a table, created by the intersection of a row and a column, is a cell.

Each cell holds a bit of content, the sum of which can now be neatly organised. The usual trick is to ensure that all items in each row and all items in each column share a similarity. The teacher might ask their pupil to think of a small blue thing, a medium blue thing, and a large blue thing. This would be followed with a small yellow thing, a medium yellow thing, and a large yellow thing, and so on and so forth. Each row and column could then be labelled - for example, columns could be 'small things', 'medium things' and 'large things', while rows could be 'blue things' and 'yellow things').

In cases where tables are used to hold huge quantities of information in logical categories, they are called databases. When the contents in the cells are expressed in numbers that maintain mathematical relationships to one another, said tables are called spreadsheets. The former is great for organising huge quantities of data, while the latter is proficient at expressing interactions between bits of information. When numeric values in spreadsheets are further manipulated into pleasing graphical displays, they are called charts and graphs.

Spreadsheets and databases are anything but mutually exclusive. In fact, they combine to form what is called a mathematical database. Such things have greatly expanded humanity's ability to keep track of pretty much everything, allowing us to do more with less people all the time. For example, a mathematical database makes it easier for a retailer to record the cost of wholesale purchases, keep track of inventory, estimate future profitability, and change the prices of items as needed.

Tables of Contents

The table of contents near the front of many books represents the most elementary form of the organisational table. One column gives the chapter number and/or title. Another column provides the first page number of each successive chapter. By locating a chapter of interest and following the table row to the right, the reader can quickly find the right page to turn to.

Realistically speaking, many tables of contents are rarely, if ever, used in this fashion. This is particularly true with works of fiction, for which chapter titles are more likely given to provide the reader with early thematic foreshadowing.

In a few rare cases, page numbers have been omitted altogether. This, technically, makes it a list of contents rather than a table. However, the possibly elitist tradition of including a table of contents is so strong that publishers always refer to the page as such.

On a brief side-note, the index page at the back of many textbooks and reference books is also an organisational table. The alphabetical list of subjects covered in the book, corresponding with page numbers, is actually a later offspring of (and likely improvement on) the table of contents.

Timetables

Another great example of an organisational table, the timetable, lists the arrival and departure times for trains, buses, or aeroplanes. Timetables are often available in the form of a hand-out brochure obtainable at the ticket desk or inside the bus or train. They are sometimes accessible online as well. Lucky travellers will even find them prominently posted at the station, terminal, or bus stop.

To use a timetable, you would first find your location (usually on the left hand side of the table). Then you would follow the associated row for your location across a series of times until you found a suitable departure time from your station/terminal/stop. By subtracting the current time from the time listed, you would know how long you'll be waiting for your mode of transportation to arrive.

Advanced users will then take it a step further. They'll find the location they're travelling to on the timetable and look for the appropriate intersection between its row and the column detailing the journey of their particular conveyance. This will tell the clever commuter when they'll arrive at their destination. Plus they can determine how long they'll be in transit by subtracting the departure time from the arrival time.

Even further advanced users may also attempt to use timetables to estimate when they should leave home to avoid a long wait before embarking. This is unfortunately a gamble, since timetables are not always accurate. All too often, the times given must be viewed as general guidelines. This is especially true when inclement weather occurs, at which point the system may have reverted to chaos or stopped running altogether2.

It is more practical with some forms of transportation to note, for instance, that the local bus comes about every half-hour on weekdays and hourly on weekends. Due to the peculiarities of public transportation, you might have to wait up to twice the usual amount. In most cases, a much longer wait indicates that something may be wrong.

A special note should also be made for airline timetables, since they are notoriously inaccurate. There are often monitors inside the terminals for this reason, that list whether individual planes are expected to arrive and/or depart on time. It's also important to recognise that aeroplanes often begin boarding half an hour before the listed take-off time. Arriving one minute before your indicated departure time might result in your being grudgingly allowed on board while your poor luggage is held aside for later transport.

The optimists among us will want to practise Bus Stop Logic.

Maths Tables

As might be expected from the earlier description of spreadsheets and their relation to charts and graphs, tables have a special place in the heart of mathematicians. The earliest example of this comes from the unavoidable memorisation of multiplication tables.

Anyone who can recall chanting their multiplication tables3 or sitting cross-eyed with a headache trying to figure out the answer to a multiplication table not yet memorised will know what the author is talking about. No matter how unskilled at maths we may be, we are all familiar with the use of maths tables.

Mathematical tables are used to work out unit conversions, as look-up tables for trigonometric values like sin and tan, to express the common logarithms, and much more. One particularly devilish example is the table method of factorising quadratic expressions.

Some mathematical uses of the table are simply not for the weak of heart. They carry over into many areas of science that utilise maths, including physics, geology, and astronomy. In fact, whole books have been written that contain nothing but mathematical tables. Buy one if you're very brave, but proceed with caution.

Other uses of mathematical tables can be tremendously entertaining when viewed in the proper light. Statistical tables can be used to express probability for all sorts of games, for instance. Or they may act as windows through which we view the population as a whole, most notably through polls and census reports. Sports statistics tables are especially popular among the younger set. For the older set, stock market reports can be viewed as large, ever changing mathematical tables.

HTML Tables

HTML4 is a tool that's continually updated to help designers create web pages. As websites have grown in complexity, the need naturally arose for designers to present data in the form of organisational tables. Therefore, the table tag was added to the growing profusion of HTML Tags. Other related markup languages also include tables, including XHTML and SGML. Even h2g2 has its own table tags in GuideML.

Over time, the usage of HTML tables has largely shifted from one of data-sorting to one of design-formatting. To accomplish this, the lines between cells are made invisible by turning the border value to zero. Then the table is used to help the designer place content visually in a certain place on the screen. The designer can either choose to format tables by specifying an absolute pixel size, or by using a percentage of the total screen area.

For instance, a table with three columns might be used to help the designer put his text on the far-left side of the screen and his graphic on the far-right side with a large valley of space between the two. This was originally decried by HTML purists. They argued that tables were never meant to be used for design purposes. Furthermore, they complained that ignorant web designers were creating visual messes by using table designs that looked nice on their own monitors and horrible on everyone else's.

Former print publishers entering the realm of web design countered that the practice should be fair game, since no other method of formatting was included in HTML. They also predicted that errors would decrease once visually-based programs that automatically generated HTML code became commonplace. The ultimate solution will no doubt be the new elements for formatting that are currently being devised and standardised, most notably including CSS5.

Water Tables

A couple of environmental concepts are called tables due to their similarities to flat table-tops. These might have alternatively been called shelves or counters, but an analogy to furniture tables may have seemed more natural due to their sheer ubiquitousness.

A water table is an approximated plane beneath the earth's surface, under which water has saturated the soil and is available to be collected. Water tables contain groundwater, which collects as a result of run-off from precipitation and melting snow and due to changing conditions in local streams, rivers, and lakes.

When water tables are too low, wells and other below-ground sources of drinkable water are depleted. When they are too high, flooding becomes increasingly likely. A polluted water table is likely to spread its unhealthy contaminants throughout the local area. Much environmental consideration goes towards maintaining healthy water tables, though other factors6 have the power to counter even the greatest of efforts.

Land Tables

Another commonly-referenced geographical table is the land table or tableland. Sometimes called a plateau, the most commonly-known land table is a large, relatively level tract of land raised above its surrounding area. Tables are often featureless and geologically stable.

A land table may be known as a piedmont when it occurs near the base of a mountain. In this case, an otherwise gentle slope towards the basin below may suddenly hit a cliff. Another variation of a land table, a caprock, occurs when a flat layer of hard rock survives erosive forces, protecting layers of more erosive materials directly underneath it in stark contrast to the surrounding area.

The term land table may also be used to denote an extended area full of numerous flat mesas. These are typically created by horst and graben structures, where tectonic processes either cause an area bounded by fault-lines to raise above its surrounding area or alternatively cause the surrounding area to sink down.

There is no set rule for a plateau's appearance or location. Lava plateaux, for instance, are created directly by the geological instability of volcanic eruption. Some 'land tables' are even located under the sea. In fact, anything flat and risen may be called a table by the populace at large - as indicated by the separately named Table Mountains found in California, Colorado, Washington, and Wyoming, USA.

The most famous geological table is undoubtedly the Table Mountain in Cape Town, South Africa. The top of this popular tourist attraction is accessible via hiking paths, rock-climbing, or cable car. Weather and season permitting, visitors can look out over Table Bay, witness the surprising spectacle of the mountain being floodlit at night, or view the white mist that descends from time to time that the locals affectionately call a tablecloth.

The Most Clever Table Yet Devised

Each cell in the periodic table of the elements contains a symbol for a basic element of matter, the element's atomic weight, and its atomic number. By grouping these cells in a cleverly-calculated fashion, one can see that certain elemental traits show up at regular intervals - or, one might say, periodically. Hence the name.

While the rest of the periodic table's history is too complex to cover here, its genius lies in what it didn't originally contain. You see, in order to format the table to maintain its periodic glory, a number of cells had to be left blank. It was immediately apparent that these cells must represent elements that had not yet been discovered. Most amazing of all, many undiscovered elements could be searched for based on the traits they must logically possess according to the table. Eureka!

The periodic table, as the height of intellectual tabular conceptualisation, seems wildly removed from the common dinner table after which organisational tables were originally named. However, Theodore Gray has brought the whole thing full circle with his design of the periodic table table. The periodic table table is a fully-functional modern art piece that mimics the periodic table's design, complete with carefully-labelled inlaid boxes containing most of the basic elements. This just goes to prove that the best-laid conceptual tables can usually be traced back to their classical furniture roots.

A more clever conceptual table will no doubt be devised eventually. Until then, the periodic table gets a big gold7 star.


1 Literally, in the case of a family's kitchen table.
2 Due to leaves on the line, or some such excuse.
3 Two times two is four. Two times three is six. Two times four is eight, and so on.
4 Hyper Text Markup Language.
5 Cascading Style Sheets.
6 From competing economic forces, to rapid weather changes.
7 Au, atomic weight 197.0, atomic number 79.

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Entry Data
Entry ID: A1304768 (Edited)

Written and Researched by:
Fragilis - h2g2 Cured My Tabular Obsession

Edited by:
Joe C (goodness me!)


Date: 11   December   2003


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Referenced Guide Entries
Numbers
Climbing Table Mountain, Cape Town, South Africa
The Periodic Table of the Elements
The History of the Periodic Table of the Elements
Rulers
The Table Method of Factorising Quadratic Expressions
HTML Tags
Furniture Tables
Bus-Stop Logic


Referenced Sites
table tag

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