“ஒரு எழுத்தாளனை எதற்காக ஆவணப்படம் எடுக்க வேண்டும்? அவனுக்காக அவனது
எழுத்துக்கள் பேசும். அவன் போனபின்னும் அவை பேசிக் கொண்டிருக்கும்.
கலைஞனின் சொற்கள் அழியாது. தன் ஆக்கங்களில் பேசியவற்றுக்கு அப்பால், அவன்
ஒரு பேட்டியிலோ அல்லது ஆவணப்படத்திலோ ஒன்றும் சொல்லிவிடப்போவதில்லை. இலக்கியம் சார்ந்த நோக்கில் இத்தகைய ஆவணப்படுத்தல்களுக்கு எந்த இடமும் இல்லை.
ஆனால் நமக்கு இலக்கியவாதி என்ற ஆளுமை தேவைப்படுகிறது. வள்ளுவரும் கம்பனும்
எப்படி இருந்தார்கள் என நாம் அறிவதில்லை. ஆனால் அவர்களைப்பற்றிய கதைகள்
நமக்குக் கிடைக்கின்றன. அவர்களை நாம் மனக்கண்ணில் வரைந்துகொள்கிறோம். இன்று
அவர்களுக்கு முகங்களை உருவாக்கியிருக்கிறோம். தாடிமீசையுடன் வள்ளுவரும்,
அடர்ந்த பெரிய மீசையுடன் கம்பரும்.
ஏன்? காரணம் நாம் படைப்பை படிக்கையில் படைப்பாளியுடன் உரையாடுகிறோம்
என்பதே. அருவமான எழுத்தாளனுடன் நம்மால் பேச முடிவதில்லை. நமக்கு உருவம்
தேவையாகிறது. எந்தக் காரணத்தால் கடவுள்களுக்கு உருவம் அமைந்ததோ அதே
காரணத்தால்தான் நாம் கலைஞர்களுக்கும் உருவம் அளிக்கிறோம்.
பெரும் கலைஞர்களின் உருவத்தைப் போற்றுவது உலக மரபு. ஹோமரின் சிலை நமக்குக்
கிடைக்கிறது. நம்மாழ்வார் ஆழ்வார் திருநகரியில் கோயில் கொண்டிருக்கிறார்.
புகைப்படக்கலை வந்தபின்னர் இது இன்னும் முக்கியமானதாக ஆகியது. பாரதியின்
பாடல்களுக்கு நிகராகவே அவரது தீவிரமான கண்கள் கொண்ட புகைப்படங்களும் ஆர்யா
வரைந்த ஓவியமும் தமிழ் மக்களின் மனதில் பதிந்திருக்கின்றன. அந்த
சித்திரங்களே கூட மக்களிடம் உக்கிரமாக உரையாடக்கூடியவையே. அவரது பாடல்களில்
இருந்து அந்த முகத்தை பிரிக்க முடியாது
கலைஞனின் உடல் அவனுடைய கருத்துக்களின் பிம்பமாக மாறிவிடுகிறது. ஒரு
கட்டத்தில் அது அவன் சொன்ன அனைத்துக்கும் உரிய குறியீடாக ஆகிறது. ஆகவேதான்
நாம் கலைஞனின் உடலை ஆவணப்படுத்துகிறோம். நம் நாட்டில் முறையான
ஆவணப்பதிவுகள் அனேகமாக இல்லை. இப்போதுதான் தொடங்கியிருக்கின்றது.
ரவிசுப்ரமணியன் இயக்கிய ‘ எல்லைகளை விஸ்தரித்த எழுத்துக்கலைஞன் -
ஜெயகாந்தன் ‘ என்ற ஆவணப்படம் அதில் ஒரு முக்கிய சாதனை.”
மா. அரங்கநாதனும் கொஞ்சம் கவிதைகளும் ஆளுமைகள் குறித்த ஆவணப்படங்களோ, ஆளற்ற பொட்டலில் மேடைப் பேச்சு போல் பரிதாபத்துக்குரியவை. இந்த அவலங்களின் மிகச் சில விதிவிலக்குகளில் ரவிசுப்ரமணியனின் 'மா.அரங்கநாதனும் கொஞ்சம் கவிதைகளும்' ஒன்று.
இந்திரா பார்த்தசாரதி எனும் நவீன நாடகக் கலைஞன்
நூற்றுக்கணக்கான விவரணப்படங்களையும் குறும்படங்களையும் ஆவணப்படங்களையும் தொலைக்காட்சிகளுக்காக தயாரித்திருக்கிற ரவிசுப்ரமணியன், அவ்வகை தொலைக்காட்சிப் பார்வையாளர்களைத் தவிர்த்து விட்டு, அதன் பாதிப்புகளிலிருந்தும், அதன் எளிமையிலிருந்தும் விலகி, இந்திராபார்த்தசாரதி என்ற நாடகாசிரியரைப் பற்றிய ஒரு ஆவணப்படம் எடுத்திருப்பதில் தனது அடுத்த கட்டப் பாய்ச்சலை நிரூபித்திருக்கிறார்.
சைவத்தமிழ் வளர்க்கும் சேக்கிழார் அடிப்பொடி
திருலோகம் என்றொரு கவி ஆளுமை
திருலோக சீதாராம் மறைந்து பல ஆண்டுகளாகின்றன. இன்னும் ஒன்றிரண்டு ஆண்டுகளில் அவருடைய நூற்றாண்டே வரப்போகிறது. ஆனால் இந்த ஆவணப்படத்தைப் பார்த்துமுடித்த தருணத்தில் நம்மிடையே அவர் இன்னும் வாழ்ந்துகொண்டிருப்பவர் என்னும் எண்ணம் சட்டென எழுந்ததை உணர்ந்தேன். ஏன் அப்படி நினைத்தேன் என ஒருகணம் யோசித்த பிறகுதான் புரிந்தது. - பாவண்ணன்
Proper chemical management is necessary to protect the health and safety of the University and surrounding communities and the environment. There are federal and state regulations that require all generators of chemical waste receive training and follow proper waste management and disposal procedures. These regulations have severe monetary and civil penalties associated with them. Between 1990 and 2004, over twelve million dollars in fines have been levied against University and Colleges for hazardous waste and other environmental violations, leading the EPA to question waste management at educational institutions.
DEFINITION OF CHEMICAL WASTE, Step 1
Chemical waste is defined by the United States Environmental Protection Agency and by the Delaware Department of Natural Resources and Environmental Control. Definitions, management practices and compliance are outlined in 40 Code of Federal Regulations and the Delaware Rules Governing Hazardous Waste. All policies and practices developed by the University of Delaware are designed to meet or exceed these regulations and assure compliance.
University Policy 7-18 states that all University of Delaware personnel must manage all chemical and hazardous waste in compliance with these federal and state regulations and in accordance with procedures set up by the Department of Environmental Health & Safety.
Chemical waste is a broad term and encompasses many types of materials. Consult your Material Safety Data Sheet (MSDS), Product Data Sheet or Label for a list of constituents. These sources will tell you if you have a chemical waste that needs special disposal. To reduce its long-term liability, the University is proactive in managing all of its chemical waste in an environmentally sound manner. If there are any questions on whether a material must be managed through the chemical waste management program,
Unused and surplus reagent grade chemicals
Intermediates and by-products generated from research & educational experiments
Batteries
Anything contaminated by chemicals
Used oil of all types
Spent solvents - including water based
Mercury containing items
Photographic film processing solutions and chemicals
Equipment and apparatus containing hazardous waste
Computer/electronic equipment
Toner cartridges
Ethylene glycol
Paints - both oil and latex
Fluorescent light bulbs
Light ballasts
Preserved specimens
Custodial and industrial cleaners
Uncured Resins(Phenolic, Epoxy, Styrene, etc....)
Dye and glazes
Degreasing solvents
Brake/Transmission/Power Steering Fluids
SELECTING A CONTAINER, Step 2
Liquid Chemical Waste
Once it is determined that chemical waste will be generated, a container must be selected prior to waste generation. Forbulk solvent and aqueous liquid waste streamsuse a Low Density PolyethyleneNalgenecontainer. These containers will be returned within a week to the lab and are available from most laboratory supply companies and the campus storerooms.Nalgenecontainers are compatible with most chemical wastes, but there are a few waste streams that should not be accumulated in these containers.
DO Not Useglass, plastic-coated glass or other re-used reagent chemical bottles to store or accumulate bulk liquid chemical waste.
Examples of chemical that should not be stored inNalgenecontainers:
Amyl Chloride
Bromine
Butyric Acid
Carbon disulfide
Nitrobenzene
Sulfur Dioxide
Thionyl Chloride
Vinylidene Chloride
Certain types ofNalgenecontainers work best for DEHS' operations. Please try to purchase containers that meet the following requirements:
Low density polyethylene
Either a 53B or 83B screw cap
Containers with a large handle
Capacity no larger than 5 gallons
For bulk corrosive liquid waste streams, use theJustrite Safety Containers for Waste Disposal. These containers are specially designed for corrosive chemical waste and vent under emergency conditions.DO NOTstore or accumulate bulk liquid corrosive chemical waste in any other container. Go to Liquid Corrosive Chemical Waste Management for more information on managing corrosive waste streams.
Do Notuse containers that are old, dented, damaged, leaking or cracked. The container must be able to be capped, sealed or closed. The container must be compatible with the waste streams that will be placed in it. For example, do not use a metal container to store acids, do not use a glass container to store hydrofluoric acid, do not use glass or metal containers to store organic peroxides and do not use metal containers to store picric acid and solutions of picric acid. Do not use containers that can be confused with consumer commodities like soda bottles or milk jugs. Do not use metal containers for flammable liquid waste, unless proper bonding and grounding precautions are taken.
Laboratory Clean Out of Regent Chemicals
All laboratories should, based on the hazards they pose, inspect all of their reagent chemicals. Look for chemicals that are no longer needed, old and out of date or unusable. Try to redistribute unneeded chemicals around the department or building. If no one else needs the chemical or if they are out of date or unusable, then package them as follows for disposal through DEHS:
Package by hazard class in sturdy cardboard boxes. Go toChemical Storagefor guidance on packaging by hazard class.
Use sufficient packing material to prevent container damage en route.
Place a completedchemical waste labeland packing slip on the outside of the box.
Sample Vials - Sealed 15 ml or less
Some laboratories generate a number of sealed sample vials. If the laboratory does not want to reuse the glassware or plasticware and does not want to empty the contents into a liquid chemical waste container, the following procedures must be used:
Obtain a clean 5-gallon polyethylene pail with lid.
Line the pail with a heavy-duty plastic bag.
Place achemical waste labelon the outside of the pail.
Place only compatible material in pail. Go toChemical Storagefor guidance on compatibility.
Place the lid on the pail.
When full, tightly seal bag with tape or bag closure tie.
Solid Waste Streams
Solid waste includes any laboratory material that has come in contact with a chemical or is potentially contaminated with a chemical. Examples include gloves, bench-top paper, weighing boats and papers, paper towels, clean up material and permanently contaminated glassware and plasticware. Go toLaboratory Solid Waste Disposal Proceduresfor a flow chart that helps decide if a material requires management as chemical waste or if it can be placed in the normal trash. Use the following procedures to manage solid chemical waste:
Use five-gallon poly pails, cardboard boxes, or other sturdy containers.
All containers must have lids.
Apply a completedchemical waste labelon the outside of the container or in vinyl tags attached to the containers.
Line the container with a 7-mil polyethylene bag or three standard trash bags.
All bags must be sealed unless laboratory personnel are actively adding waste. Seal the bag with a bag closure tie or a large binder clip.
When the container is full, seal the bag with tape. If the container is in a cardboard box, secure the box with tape as well.
It is important not to overload containers. Full boxes should not weigh more than 40 pounds. Do not use overly large boxes. Only fill boxes two-thirds full if they contain broken glass.
Chemically Contaminated Sharps
Anything that is capable of cutting or puncturing must be managed in a sharps container. Examples of sharps include needles, syringes, razor blades, slides, scalpels, pipettes, broken plastic or glassware, micropipettes and pipette tips. Sharps containers are available free of charge from DEHS. Go toSharp and Piercing Object Disposalfor more information about sharps management. If a sharp is chemically contaminated, simply place it in a sharps container that is labeled with a properly filled outOrange Chemical Waste Label.
Empty Chemical Containers
Empty chemical containers are still hazardous to the University personnel and the environment until they are properly managed. Go toGlass Only Disposal/Empty Chemical Container Disposal Proceduresfor complete information on empty container management. Below is a summary of the steps required to make empty chemical containers safe for disposal:
Triple rinse with copious amounts of water. Collect the first rinse as chemical waste. Rinse two and three can go down the sanitary sewer.
Place a label over the original container label or deface the label.
Do not replace the cap on the container.
Place empty/triple rinsed containers in a glass only box, recycling container or directly into the dumpster.
Clean, Uncontaminated Broken Glassware
In an effort to minimize the amount of chemical waste generated on campus, clean, uncontaminated glassware and plasticware should not be managed as waste. Unwanted clean non-broken glassware and plasticware can be packaged up by the laboratory personnel and taken to the dumpster or recycling area. Broken glassware and plasticware creates a potential hazard so special procedures are needed:
Purchase a glass only box from a campus storeroom or a laboratory supply company, or reuse a heavy corrugated cardboard box lined with a plastic liner.
Construct the box as per directions.
Tape the bottom.
When the container is 3/4's full, seal and take to the dumpster yourself. Remember that you must wear personal protective equipment (PPE) while handling these boxes. Minimum PPE includes leather work gloves and safety glasses. Custodial Services will not handle broken laboratory glassware and plasticware.
Gas Cylinders
The disposal of gas cylinders is extremely expensive. Unknown gas cylinders may cost in excess of $1,000 to identify and properly manage. Always check to make sure that all labels on gas cylinders are in good condition and legible. Contact the cylinder supplier and arrange a return if possible. It is best to use cylinders that will be returned. If lecture cylinders are required for research, use cylinders supplied by Aldrich, Matheson Tri Gas or Messer Gas. Disposal of Aldrich cylinders are inexpensive and Matheson and Messer Gas have a lecture bottle return program.
Recycling and Laboratory Wastes
Certain laboratory materials can be recycled while others cannot. Go toCampus Computer, Electronic Equipment and Office Supplies Recyclingfor complete information on recycling. Below is information specific for laboratories:
Laboratory materials that can be recycled:
Brown glass
Clear glass
Metal cans
Computer and electronic equipment
Laboratory materials that cannot be recycled:
Any glass bottles that are plastic coated
Pyrex
Glass only boxes
LABELING CHEMICAL WASTE, Step 3
After you have determined what waste you are going to generate and have obtained the appropriate containers, you must properly fill out achemical waste labeland attach it to the containers. Chemical waste labels are available from DEHS, free of charge. There are directions on theback sideof the label and labels must be applied on all chemical waste containers as soon as waste is added. These labels are designed to meet the regulatory requirements, therefore, every piece of information on the label is critical and must be completed.
How to Label:
The generator is the person who is filling out the waste label, not the lab group or Principal Investigator (PI) unless the PI is filling out the waste label.
Date the label with the date that the waste is first added.
Fill in building, room number and telephone number where the person who is filling out the waste label can be reached.
Circle the appropriate waste steam(s) or write it in.
List each waste constituent down to 1%; heavy metals must be listed down to the parts per million range. Label contents must add up to 100%. Volumes are acceptable.
Use only common chemical names or IUPAC nomenclature when listing the chemical constituents on the label.
Do not use:
Abbreviations
Chemical symbols
Trade names
Check the appropriate boxes for the waste stream.
If this waste is being moved to a Central Accumulation Area such as the Brown Solvent Shed, Colburn Solvent Shed or the McKinly Waste Storage Area, fill in the date that it is moved on the line at the bottom of the waste label.
ADDING WASTE TO A CONTAINER, Step 4
Waste can be added only after you choose the proper container and it is labeled. The minimum personal protective equipment (PPE) may be dictated in the Chemical Hygiene Plan. If not, all personal working with chemical waste must wear the following:
Safety glasses
Splash goggles if working with liquid waste
Lab coat
Gloves specific for the compounds in use
Procedure for liquid chemical waste management:
Perform liquid chemical waste management in a fume hood. Mixing of liquid waste may generate toxic or corrosive aerosols.
Check the container label to assure that waste is being added to the correct container.
The container must be in secondary containment, i.e. large plastic bin or bucket.
Uncap the container.
Use a funnel sufficient for the size of the container and volume of waste being added.
Slowly add the waste, watching for any unintended reactions. If you observe a reaction, immediately stop adding the waste, close the fume hood sash and contact DEHS.
After the waste has been added, remove the funnel and seal the container with the cap.
Another option for liquid waste management is to use a specially designed waste funnel called ECO-Funnel. Go toSafety Ecological Funnelsfor more information.
Procedures for solid waste management:
Go toLaboratory Solid Waste Disposal Set-UpandLaboratory Solid Waste Disposal Proceduresfor information and guidance on how to set up your solid chemical waste management program in your lab.
Obtain and label a proper container as described above.
Open the lid to the container and unseal the bag.
Add the waste.
Seal the bag with a bag closure tie or large binder clip.
Reseal the lid.
STORING YOUR WASTE, Step 5
Proper storage of chemical waste is extremely important. Explosions have occurred on campus that are attributed to improper storage of chemical waste. If you improperly label a container, other laboratory personnel unknowingly may add incompatible material to the container. For example, if an organic solvent solution is added to a container that is not labeled or labeled as an aqueous inorganic acid, and a fellow researcher may generate an inorganic nitric acid solution and add it to the container. Nitric acid and organic solvents are extremely incompatible and the container over a short period of time generates pressure and explodes. Go toChemical Storagefor guidance. Adhere to the following procedures on chemical waste storage to protect the health and safety of others, protect the University's facilities and to keep the University in compliance with all federal, state and local regulations:
Waste containers must remain closed or sealed at all times, except when waste is being added or removed from the container.
Liquid waste containers must be stored in secondary containment systems according to hazard class.
Store all bulk liquid waste containers in appropriate cabinets. DO NOT store bulk liquid chemical waste containers in fume hoods that have active experiments or reactions occurring.
Flammable Cabinets
Corrosive Cabinets
Under Fume Hood Cabinets
Do not allow excess accumulation of chemical waste to build up in your lab. Go toHazardous Waste Definitionsfor more information on the limitations of waste storage.
Containers can only be filled to a maximum 90% full. Head space is needed for expansion and/or ease of dispensing.
INSPECTING YOUR WASTE ACCUMULATION AREAS, Step 6
All satellite chemical waste accumulation areas must be inspected on a weekly basis. This inspection does not have to be a formal inspection with documentation but laboratory personnel must inspect all chemical waste stored in their laboratories to assure the following:
There are no leaking containers of chemical waste.
All containers holding chemical waste are labeled with a completed orange chemical waste label.
All containers are sealed and closed. This includes waste containers holding solid chemical waste.
All liquid chemical wastes are stored in secondary containment bins.
Incompatible wastes are stored away from each other and in separate containment bins.
There is not an excessive accumulation of waste stored in the laboratory.Immediately correct any of the above if they are encountered during the course of the weekly inspection.
HOW TO HAVE CHEMICAL WASTE REMOVED, Step 7
Certain departments and buildings have a Central Accumulation Area (CAA) set up in close proximity to their building. Laboratories in McKinly, Wolf, Brown, Lammot DuPont, Drake Hall, Colburn and Spencer should take their waste to the CAA. Go toChemical Waste Removal Processfor complete information on the CAA's.
Once a chemical waste container is full, DEHS should be contacted to remove the container or it should be moved to the CAA. In addition, if a chemical waste container has been in a laboratory for more than a year, it should be removed.
Common Violations Found in Laboratories
DEHS routinely encounter a group of common problems and issues with chemical waste. These common problems are listed below with suggestions to prevent them from occurring. The EPA has fined Universities and Colleges for the problems listed below. Your support in eliminating these problems will greatly reduce the University's liability.
Unknown / Unlabeled chemical wasteis very difficult and expensive to dispose of and poses an unnecessary risk to laboratory personnel as well as University personnel handling the waste. Unlabeled containers are a direct violation of the Federal and State hazardous waste regulations. Typically, DEHS covers the cost of all wastes generated by academic departments and programs. Departments generating unknown wastes may be charged for its disposal because of the extreme costs.
Prevention- Label all chemical waste with an orange chemical waste label. Update the constituents on the label every time waste is added. Inspect waste on a weekly basis to assure that containers are labeled and that the labels are in good condition. Inspect your chemical reagents to assure that the labels are still attached. Tape or replace as necessary.
Mixing or storage of incompatible chemicalsmay result in an explosion, fire or generation of toxic aerosols, vapor or fumes.
Prevention- Having an accurate, up-to-date waste label on each container will greatly reduce the possibility of mixing incompatible materials. Store incompatibles away from each other and in separate secondary containment bins.
Chemical containers that are left uncapped / open- This is a direct violation of Federal and State chemical waste and air permitting regulations and must not occur
Prevention- Seal all containers immediately after waste is added. Inspect accumulation areas to assure all containers are sealed. Purchase and useECO-Funnels.
Laboratory personnel that are inadequately trained in the proper management of chemical waste- This is a direct violation of Federal and State chemical waste regulations. Additionally a lack of training places University Personnel, facilities and the environment at risk.
Prevention- Complete DEHS' onlineChemical Wastetraining class. Go toEnvironmental Health & Safety Training Scheduleto sign up for a live training session in the EHS Office .
Liquid containers stored outside of secondary containers- If container(s) fail, the contents may migrate and commingle with incompatible chemicals or migrate to floor or sink drains. This is a direct violation of the Federal and State chemical waste regulations.
Prevention- Store all liquid chemical waste in secondary containment.
Waste Containers Stored In and/or Near Sink Areas and Floor Drains- If containers leak the contents could discharge down the drain. If this occurs, it is a direct violation of the Federal and State chemical waste and safe drinking water regulations.
Prevention- Store all liquid chemical waste in secondary containment and away from all floor and sink drains.
Conclusion
Proper chemical waste management protects the health and safety of everyone and prevents or minimizes pollution. All generators of chemical waste should do their best to minimize the amounts or chemical waste they generate and recycle whenever possible.
Georg Cantor died in 1918 in a sanatorium in Halle, Germany. A pre-eminent mathematician, he had laid the foundation for the theory of infinite numbers in the 1870s. At the time, his ideas received hostile opposition from prominent mathematicians in Europe, chief among them Leopold Kronecker, once Cantor’s teacher. In his first known bout of depression, Cantor wrote 52 letters to the Swedish mathematician Gösta Mittag-Leffler, each of which mentioned Kronecker.
But it was not just rejection by Kronecker that pushed Cantor to depression; it was his inability to prove a particular mathematical conjecture he formulated in 1878, and was convinced was true, called the Continuum Hypothesis. But if he blamed himself, he did so needlessly. The debate over the conjecture is profoundly uncertain: in 1940 Kurt Gödel proved that the Continuum Hypothesis cannot be disproven (technically speaking, that the negation of the Hypothesis cannot be proven), and in 1963 Paul Cohen proved that it cannot be proven. Poor Cantor had chosen quite the mast to lash himself to.
How is it possible, though, for something to be provably neither provable nor disprovable? An exact answer would take many pages of definitions, lemmas, and proofs. But we can get a feeling for what this peculiar truth condition involves rather more quickly.
Cantor’s Continuum Hypothesis is a statement regarding sizes of infinity. To see how infinity can have more than one size, let’s first ask ourselves how the sizes of ordinary numbers are compared. Consider a collection of goats in a small forest. If there are six goats and six trees, and each goat is tethered to a different tree, then each goat and tree are uniquely paired. This pairing is called a “correspondence” between the goats and the trees. If, however, there are six goats and eight trees, we will not be able to set up such a correspondence: no matter how hard we try, there will be two trees that are goat-free.
Correspondences can be used to compare the sizes of much larger collections than six goats—including infinite collections. The rule is that, if a correspondence exists between two collections, then they have the same size. If not, then one must be bigger. For example, the collection of all natural numbers {1,2,3,4,…} contains the collection of all multiples of five {5,10,15,20,…}. At first glance, this seems to indicate that the collection of natural numbers is larger than the collection of multiples of five. But in fact they are equal in size: every natural number can be paired uniquely with a multiple of five such that no number in either collection remains unpaired. One such correspondence would involve the number 1 pairing with 5, 2 with 10, and so on.
If we repeat this exercise to compare “real” numbers (these include whole numbers, fractions, decimals, and irrational numbers) with natural numbers, we find that the collection of real numbers is larger. In other words, it can be proven that a correspondence cannot exist between the two collections.
The Continuum Hypothesis states that there is no infinite collection of real numbers larger than the collection of natural numbers, but smaller than the collection of all real numbers. Cantor was convinced, but could never quite prove it.
To see why, let’s begin by considering what a math proof consists of. Mathematical results are proven using axioms and logic. Axioms are statements about primitive mathematical concepts that are so intuitively evident that one does not question their validity. An example of an axiom is that, given any natural number (which is a primitive concept), there exists a larger natural number. This is self-evident, and not in serious doubt. Logic is then used to derive sophisticated results from axioms. Eventually, we are able to construct models, which are mathematical structures that satisfy a collection of axioms.
Crucially, any statement proven from axioms, through the use of logic, will be true when interpreted in any model that makes those axioms true.
It is a remarkable fact that all of mathematics can be derived using axioms related to the primitive concept of a collection (usually called a “set” in mathematics). The branch of mathematics that does this work is known as set theory. One can prove mathematical statements by first appropriately interpreting the statement in the language of sets (which can always be done), and then applying logic to the axioms of sets. Some set axioms include that we can gather together particular elements of one set to make a new set; and that there exists an infinite set.
Kurt Gödel described a model that satisfies the axioms of set theory, which does not allow for an infinite set to exist whose size is between the natural numbers and the real numbers. This prevented the Continuum Hypothesis from being disproven. Remarkably, some years later, Paul Cohen succeeded in finding another model of set theory that also satisfies set theory axioms, that does allow for such a set to exist. This prevented the Continuum Hypothesis from being proven.
Put another way: for there to be a proof of the Continuum Hypothesis, it would have to be true in all models of set theory, which it isn’t. Similarly, for the Hypothesis to be disproven, it would have to remain invalid in all models of set theory, which it also isn’t.
It remains possible that new, as yet unknown, axioms will show the Hypothesis to be true or false. For example, an axiom offering a new way to form sets from existing ones might give us the ability to create hitherto unknown sets that disprove the Hypothesis. There are many such axioms, generally known as “large cardinal axioms.” These axioms form an active branch of research in modern set theory, but no hard conclusions have been reached.
The uncertainty surrounding the Continuum Hypothesis is unique and important because it is nested deep within the structure of mathematics itself. This raises profound issues concerning the philosophy of science and the axiomatic method. Mathematics has been shown to be “unreasonably effective” in describing the universe. So it is natural to wonder whether the uncertainties inherent to mathematics translate into inherent uncertainties about the way the universe functions. Is there a fundamental capriciousness to the basic laws of the universe? Is it possible that there are different universes where mathematical facts are rendered differently? Until the Continuum Hypothesis is resolved, one might be tempted to conclude that there are.
குறிப்பிட்ட சில ஆங்கில எழுத்துக்கள், ஒருவரின் வாழ்வில் தாக்கத்தை ஏற்படுத்தும். அதில் பெரும்பாலானோரது பெயர் குறிப்பிட்ட எழுத்துக்களில் ஆரம்பமாகும். அதிலும் "A, S, J" போன்றவை மிகவும் சக்தி வாய்ந்த எழுத்துக்களாக கருதப்படுகிறது. உங்களது பெயர், இவற்றில் 'S'-இல் ஆரம்பமானால், இக்கட்டுரை உங்களுக்கானது. எண் கணிதத்தின் படி, 'S' என்ற எழுத்து எண் ஒன்றிற்கு இணையானது. இத்தகையவர்கள் தலைவர்களாக மற்றும் அனைத்து செயல்களிலும் மிகச்சிறப்பாக செயல்படுபவராகவும் இருப்பர். இதுப்போன்று 'S' என்ற எழுத்தில் ஆரம்பமாகும் பெயரைக் கொண்டவர்களைப் பற்றிய ஏராளமான சுவாரஸ்யமான தகவல்கள் தான் கீழே கொடுக்கப்பட்டுள்ளது.
விசுவாசமானவர்கள் இந்த எழுத்தில் ஆரம்பமாகும் பெயரைக் கொண்டவர்கள் மிகவும் விசுவாசமானவர்களாக கருதப்படுவர். இத்தகையவர்களுக்கு மிகவும் ரொமான்டிக்காக பேசத் தெரியாது. வார்த்தைகளால் அன்பை வெளிக்காட்டுவதை விட, செயலில் காட்டவே விரும்புவர்.
இரக்கமுடையவர் 'S' என்ற எழுத்தில் ஆரம்பமாகும் பெயரைக் கொண்டவர்கள் அன்பானவர்களாகவும், அதிக இரக்க குணமுடையவர்களாகவும் இருப்பர். இவர்கள் முன்பு யாரேனும் பிரச்சனையில் இருந்தால், அவர்களுக்கு உதவி செய்து விடுவிக்க பெரிதும் முயற்சி செய்வர்.
நம்பத் தகுந்தவர் இவர்கள் நேர்மையானவர்கள் மற்றும் நம்பத் தகுந்தவர்கள். இவர்களுக்கு கோபம் வந்தாலோ அல்லது மன வருத்தம் அடைந்தாலோ, மிகுதியாக உணர்ச்சிவசப்படுவார்கள். சில நேரங்களில் இவர்களைப் புரிந்து கொள்வது என்பது கடினமாக இருக்கும்.
உணர்வுகளை மறைப்பார்கள் இந்த எழுத்தில் பெயரைக் கொண்டவர்கள், தங்களது உணர்வுகளை மற்றவர்களுடன் பகிர்ந்து கொள்ள விரும்பமாட்டார்கள். இதனாலேயே இவர்களைப் புரிந்து கொள்வது கஷ்டமாக இருக்கும். இந்த குணத்தாலேயே, இவர்கள் அதிக மன இறுக்கத்திற்கு உள்ளாவார்கள்.
மிகவும் கவர்ச்சிகரமானவர்கள் இந்த எழுத்தில் ஆரம்பமாகும் பெயரைக் கொண்டவர்களது அகம் மற்றும் புறம் அழகாக இருக்கும். இவர்கள் மற்றவர்களுக்காக அதிகம் சந்தோஷமும் கொள்வார்கள், துன்பமும் கொள்வார்கள். இவர்களது கவர்ச்சிகரமான பேச்சு மற்றும் தோற்றத்தாலேயே, பலருக்கும் இவர்களுடன் பழகப் பிடிக்கும்.
வெற்றிகரமான தொழில் இத்தகையவர்கள் பணத்திற்கு அதிக முக்கியத்துவம் கொடுப்பார்கள். இதனால் இவர்கள் வெற்றிகரமான தொழிலதிபராகவோ, அரசியல்வாதியாகவோ இருப்பர்.
இருப்பர் ஒரு லட்சியத்துடன் வாழ்க்கையை வாழ்பவர்களாக இருந்தாலும், உறவுகளுக்கு அதிக முக்கியத்துவம் கொடுப்பர். தனிப்பட்ட அல்லது தொழில்முறை உறவுகளாகட்டும், அனைவரிடமும் உண்மையாக இருப்பர்.
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அல்லது ஆவணப்படத்திலோ ஒன்றும் சொல்லிவிடப்போவதில்லை. இலக்கியம் சார்ந்த நோக்கில் இத்தகைய ஆவணப்படுத்தல்களுக்கு எந்த இடமும் இல்லை.
அல்லது ஆவணப்படத்திலோ ஒன்றும் சொல்லிவிடப்போவதில்லை. இலக்கியம் சார்ந்த நோக்கில் இத்தகைய ஆவணப்படுத்தல்களுக்கு எந்த இடமும் இல்லை.
